MICRO- AND NANO-SCALE CORROSION IN IRON-BASED BULK METALLIC GLASS SAM 1651 AND SILVER-CORED MP35N LT COMPOSITE

Transcription

1 MICRO- AND NANO-SCALE CORROSION IN IRON-BASED BULK METALLIC GLASS SAM 1651 AND SILVER-CORED MP35N LT COMPOSITE by HUNG MANH HA Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Dissertation Advisor: Joe H. Payer, Ph.D Department of Materials Science and Engineering CASE WESTERN RESERVE UNIVERSITY January, 2010

2 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of HUNG M. HA candidate for the Doctor of Philosophy degree *. (signed) JOE PAYER (chair of the committee) FRANK ERNST JAMES MCGUFFIN-CAWLEY UZIEL LANDAU (date) Aug 3 rd, 2009 *We also certify that written approval has been obtained for any proprietary material contained therein.

3 Table of Contents Table of Contents... i List of Tables...viii List of Figures... x List of Symbols... xvii Acknowledgements... xxi Abstract... xxii Chapter 1 INTRODUCTION Objectives Structure of the dissertation... 3 Chapter 2 CORROSION OF AN IRON-BASED BULK METALLIC GLASS SAM 1651 AND THE EFFECT OF HEAT TREATMENT Background The development of Fe-based metallic glasses Fe-based BMG SAM 1651 with exceptionally high corrosion resistance Devitrification of amorphous metals Mechanical property of partially devitrified amorphous metals Corrosion behavior of partially devitrified amorphous metals Devitrification of Fe-based BMG SAM Passivity and pseudo-passivity Materials and experiments Materials Solution and electrochemical cell setup i

4 2.2.3 Specimen preparation Heat treatment Specimen for X-ray diffraction (XRD) Specimen for transmission electron microscopy (TEM) Specimen for electrochemical experiments Specimen for bulk immersion experiments Experiments X-ray diffraction (XRD) Transmission electron microscopy (TEM) Cyclic potentiodynamic polarization (CPP) Constant potential exposure Electrochemical impedance spectroscopy (EIS) Bulk sample immersion TEM foil immersion Structural and compositional study Scope Results XRD results TEM micrographs EDS and EF-TEM Discussion Characterization of the structure and the composition of the fully amorphous BMG SAM The effect of heat treatment on the structure of BMG SAM The effect of heat treatment on the composition of BMG SAM Summary ii

5 2.4 Corrosion behavior of partially devitrified SAM Scope Results Electrochemical experiments TEM foil immersion Discussion Effect of acid concentration and heat treatment on corrosion behavior Material characteristics and corrosion behavior Summary Formation of pseudo-passive film on partially devitrified SAM Scope Results Growth rate of the film Structure of the film Chemical composition of the film Electrochemical impedance of the film Discussion Characterization of the pseudo-passive film Formation of the pseudo-passive film Summary Conclusion References Chapter 3 CORROSION OF SILVER-CORED MP35N LT COMPOSITE Background Networked Neuroprosthetic System (NNPS) iii

6 3.1.2 Silver-cored MP35N LT composite for the networked segment cables Human body as a corrosive environment Toxicology of silver and silver compounds Corrosion of silver and formation of AgCl in chloride environments The mixed potential theory Materials and experiments Materials Solution and electrochemical cell setup Specimen preparation Flat-exposed surface specimens U-bended specimens Artificial pit specimens Experiments Potentiodynamic polarization Constant potential exposure Cyclic voltammetry Galvanostatic polarization Electrochemical impedance spectroscopy (EIS) Immersion tests Precipitation and growth of AgCl SEM and EDS XRD FIB and SEM Corrosion of silver-cored MP35N LT composite for NNPS Scope iv

7 3.3.2 Results Potentiodynamic polarization and corrosion potential Constant potential exposure Corrosion product characterization Immersion test Discussion Corrosion behavior of the silver-cored MP35N LT composite in 9 g/l NaCl solution at room temperature The effect of temperature and minor ions Summary Precipitation and growth of AgCl on silver substrate in physiological solution and the effect on the dissolution kinetics of silver Scope Results Precipitation and growth of AgCl Structure of AgCl layer The ohmic response behavior of silver dissolution underneath AgCl layers Resistance of AgCl layer Discussion Precipitation and growth of AgCl Ionic conductivity of the electrolyte inside the micro-channels The apparent conductivity of the AgCl layer The effect of the continuous AgCl layer on the silver dissolution mechanism Summary v

8 3.5 Corrosion model of silver-cored MP35N LT composite in physiological solution Scope Corrosion cell in the silver-cored MP35N LT composite in vitro Description of the corrosion process Determination of the corrosion current in Stage The accumulation of the Ag + cations in Stage The dissolution of the silver core and the growth of the AgCl layer in Stage Theoretical model The effect of the potential difference The effect of the AgCl apparent conductivity The effect of the polarization time The effect of the potential scan rate Validation of the model Constant potential experiment Cyclic voltammetry The dissolution of the silver core and the growth of the AgCl layer in Stage Theoretical model Discussion The effect of the potential difference The effect of the AgCl apparent conductivity Comparison between the kinetics of the silver dissolution and the AgCl growth in Stage 3 and Stage Summary vi

9 3.6. Application of the theoretical models on the corrosion of a freshly broken silvercored MP35N LT networked cable in vivo and the release of silver ions to the ambient Scope The dissolution of the silver core of a freshly broken wire and the formation of a AgCl layer Release of silver to the ambient Summary Conclusion References Chapter 4 MAIN CONCLUSIONS Appendix A. Characterization of the Micro-Channels in the AgCl layer Appendix B. Solving for the Transport Equations and the Electroneutrality Equation in Stage Appendix C. Solving for the Kinetics of the Silver Core Dissolution and the Growth of the AgCl Layer in Stage Appendix D. Calculating the Concentration Profile and the Amount of Ag + Cations Released to the Ambient due to Diffusion vii

10 List of Tables Table 2-1. Summary of the heat treatment regimes Table 2-2. Summary of the quantitative EDS analysis in atomic percentage Table 2-3. Summary of average (Cr, Fe) 23 C 6 crystal sizes at different heat treatment conditions Table 2-4. Summary of the characteristic parameters from cyclic polarization curves of the fully amorphous and the partially devitrified SAM 1651 (700 o C, 3 hours) in 1 and 6M HCl Table 2-5. Summary of the current densities from CPP and constant potential exposure experiments in 6M HCl and the corrosion rates calculated from the CPP, constant potential exposure and weight loss experiments Table 2-6. Composition of the films in atomic percentage after polarization at V vs. SCE in 6M HCl for different periods of time Table 3-1. Summary of the characteristic parameters in polarization curves and open circuit potential vs. time curves of the MP35N LT alloy, silver and the composite Table 3-2. Summary of weight loss and depth of penetration at the silver core and the weight gain and thickness of the AgCl corrosion product layer calculated from constant potential exposure experiments Table 3-3. Parameters used for calculation of the conductivity of the electrolyte inside the micro-channels in the AgCl layers during galvanostatic experiments Table 3-4. Summary of the calculated exchange current density Table 3-5. Values of the parameters used in evaluating the condition for AgCl formation Table 3-6. The values of the parameters used in evaluating the effect of constant potential difference on the kinetics of the silver dissolution and the AgCl formation Table 3-7. The values of the parameters used in evaluating the effect of the AgCl layer conductivity on the kinetics of the silver dissolution and the AgCl formation Table 3-8. The values of the parameters used in evaluating the effect of the polarization time on the kinetics of the silver dissolution and the AgCl formation viii

11 Table 3-9. The values of the parameters used in evaluating the effect of the potential scan rate on the kinetics of the silver dissolution and the AgCl formation Table Summary of the slopes of the 1/i vs. t 1/2 curves obtained from theoretical calculations and from constant potential exposure experiments Table The values of the parameters used in evaluating the effect of constant potential difference on the kinetics of the silver dissolution and the AgCl formation in Stage Table The values of the parameters used in evaluating the effect of the AgCl layer apparent conductivity on the kinetics of the silver dissolution and the AgCl formation in Stage Table The values of the parameters used in evaluating the effect of the geometry of the AgCl layer on the kinetics of the silver dissolution Table Values of parameters used to calculate the pit depth and the time at which AgCl starts precipitating Table The values of the parameters used to calculate the silver dissolution rate, the AgCl thickness and the depth of the silver core dissolved Table Summary of the dissolution current density and the geometrical characteristic parameters of the AgCl layer during the corrosion of a freshly broken silver-cored MP35N LT wire in vivo Table The values of the parameters used to calculate the concentration profile of Ag Table A-1. Summary the number of micro-channels in each size group ix

12 List of Figures Figure 2-1. Hypothetical free energy diagram to illustrate the crystallization of a metallic glass. G, α, θ, M are the free energy curves of the glass, a terminal solid solution, a stable intermetallic phase and a metastable phase, respectively [32]. The numbered arrows refer to the crystallization processes described in the text Figure 2-2. Atom distributions in (a) crystalline; (b) amorphous; and (c) nanocrystalline materials Figure 2-3. DSC traces of BMG SAM 1651 for (a) glass transition event determined at a heating rate of 0.33K/s [53]; (b) crystallization; and (c) melting events determined at a heating rate of 0.17K/s [54] Figure 2-4. Schematic of Cr concentration profile around a Cr-rich carbide as the result of diffusion controlled growth. C Cr c -concentration of Cr in the carbide; C Cr b -concentration of Cr in the bulk amorphous matrix; C Cr i -concentration of Cr in the amorphous phase at the carbide/amorphous matrix interface Figure 2-5. A schematic of log i vs. E curve for pseudo-passive behavior in comparison with typical passive and active behavior in potentiodynamic polarization Figure 2-6. Time-temperature path for the heat treatment process Figure 2-7. Schematic of the specimen preparation procedure Figure 2-8. XRD results of the as-received and heat treated SAM 1651 at 600, 700 and 800 o C for 3, 3 and 1 hour, respectively Figure 2-9. XRD pattern of SAM 1651 heat treated at 700 o C for 3, 24 and 72 hours Figure BF-TEM micrographs of SAM 1651; (a) as-received; (b) annealed at 600 o C for 3 hours; (c) annealed at 700 o C for 3 hours; and (d) annealed at 800 o C for 1 hour 35 Figure BF-TEM micrographs of partially devitrified SAM 1651 heat treated at 700 o C for (a) 3 hours; (b) 24 hours; and (c) 72 hours Figure Structure of the partially devitrified SAM 1651 annealed at 700 o C for 3 hours; (a) BF-TEM micrograph; (b) SAED pattern from a devitrified region; and (c) SAED pattern from a PFZ Figure TEM micrographs at high magnification of the partially devitrified SAM 1651 annealed at 700 o C for 72 hours; (a) at 220,000x; and (b) at 660,000x Figure EDS line-scan of the fully amorphous and partially devitrified SAM 1651; (a) as-received; and (b) at 700 o C for 3 hours x

13 Figure STEM micrographs showing the locations of EDS analysis (a) Location 1 in the dark phase and Location 2 in the bright phase of the fully amorphous SAM 1651; and (b) Location 3 in the PFZ and Location 4 in the matrix of the partially devitrified SAM Figure EDS analysis conducted at the locations shown in Figure Figure EELS mapping of the elements in the fully amorphous SAM 1651 using Energy-filtered TEM Figure EELS mapping of the elements in SAM 1651 annealed at 700 o C for 3 hours using Energy-filtered TEM Figure Schematic of the devitrification of SAM 1651 and the formation of nanometer Cr-depleted zones Figure Cyclic potentiodynamic polarization curves of the fully amorphous and the partially devitrified SAM 1651 (700 o C, 3 hours) in open air, 1M HCl at room temperature Figure Cyclic potentiodynamic polarization curves of the fully amorphous and the partially devitrified SAM 1651 (700 o C, 3 hours) in open air, 6M HCl at room temperature Figure Open circuit potential vs. time curves of the fully amorphous and the partially devitrified SAM 1651 (700 o C, 3 hours) during 1 hour in 6M HCl at room temperature Figure Current vs. time curves of the fully amorphous and the partially devitrified SAM 1651 (700 o C, 3 hours) at the applied potential E = V vs. SCE Figure Current vs. time curves of the fully amorphous and the partially devitrified SAM 1651 (700 o C, 3 hours) at the applied potential E = V vs. SCE Figure Current vs. time curves of the fully amorphous and the partially devitrified SAM 1651 after heat treatment at 600, 700 and 800 o C at an applied potential E = V vs. SCE in 6M HCl Figure BF-TEM micrographs of the as-received SAM 1651 after immersion in 6M HCl for different periods of time Figure BF-TEM micrographs of the partially devitrified SAM 1651 (700 o C, 3 hours) after immersion in 6M HCl for different periods of time Figure STEM images of TEM specimens after 60 hours immersion in 6M HCl showing the locations of EDS analysis; (a) Location 1 at the edge of a hole and Location 2 in the matrix of the fully amorphous SAM 1651; and (b) Location 3 and Location 4 at xi

14 the edge of a hole and Location 5 in the matrix of the partially devitrified SAM 1651 (700 o C, 3 hours) Figure EDS analysis conducted at the locations shown in Figure Figure Current density vs. time curve during constant potential exposure experiments at E = V vs. SCE in 6M HCl Figure Film thickness vs. polarization time curves during constant potential exposure experiments at E = V vs. SCE in 6M HCl Figure TEM micrographs of the pseudo-passive film after 5-hour polarization in 6M HCl at the constant potential of V vs. SCE; a) BF-TEM; and b) STEM Figure TEM micrographs of the pseudo-passive film after 15-hour polarization in 6M HCl at the constant potential of V vs. SCE; a) BF-TEM; and b) STEM Figure TEM micrographs of the pseudo-passive film after 30-hour polarization in 6M HCl at the constant potential of V vs. SCE; a) BF-TEM; and b) STEM Figure BF-TEM micrographs of the pseudo-passive film after 30-hour polarization in 6M HCl at the constant potential of V vs. SCE; a) the inner porous layer; and b) the outer dense layer Figure Selected area electron diffraction patterns taken from a specimen after 30- hour polarization in 6M HCl at the constant potential of V vs. SCE; a) substrate; b) inner layer; and c) outer layer Figure Quantitative EDS analysis showing composition of the film after 5 hour polarization in 6M HCl at E = +0.4V vs. SCE Figure Quantitative EDS analysis showing composition of the film after 15-hour polarization in 6M HCl at E = +0.4V vs. SCE Figure Quantitative EDS analysis showing composition of the film after 30-hour polarization in 6M HCl at E = +0.4V vs. SCE Figure Bode plot obtained from EIS experiments of the films during polarization at V vs. SCE in 6M HCl for different period of times; a) dependence of impedance with frequency; and b) dependence of phase angle with frequency Figure Hypothesis for the formation and growth of the pseudo-passive films Figure 3-1. Schematics of the Networked Neuroprosthetic System Figure 3-2. SEM micrograph showing a cross section of a composite single wire Figure 3-3. Schematic of a cross section showing the configuration of the network cable. The conductors are helically coiled xii

15 Figure 3-4. Conductivity of AgCl layers formed at different applied current densities in different solutions. The values are taken from different sources [20, 29, 39] Figure 3-5. Two metals Fe and Cu immersed in an electrolyte; (a) No electrical contact between Fe and Cu; (b) Fe and Cu are electrically connected to each other Figure 3-6. Evans diagram showing anodic and cathodic polarization curves for determination of the corrosion current and corrosion potential in a galvanic couple Figure 3-7. Evans diagram showing the effect of the cathode-to-anode area ratio Figure 3-8. Schematic of the flat-exposed surface specimens for electrochemical experiments Figure 3-9. Schematic of the U-bended specimens for electrochemical experiments Figure Schematic of the procedure to prepare artificial pit specimens filled with the test solution Figure Open circuit potential vs. time curves of the MP35N LT alloy, silver and the composite in 9 g/l NaCl solution at room temperature Figure Potentiodynamic polarization curves of the MP35N LT alloy, silver and the composite in 9 g/l NaCl solution at room temperature Figure Open circuit potential vs. time curves of the MP35N LT alloy, silver and the composite in Ringer s solution at 37 o C Figure Potentiodynamic polarization curves of the MP35N LT alloy, silver and the composite in Ringer s solution at 37 o C Figure Current vs. time curves of 7 composite wires in 9 g/l NaCl solution at room temperature with the applied potentials of +0.03, and V vs. SCE Figure SEM micrographs of specimens after constant potential exposure experiments in 9 g/l NaCl solution at room temperature; (a) at V vs. SCE for 4 hours; (b) at V vs. SCE for 4 hours and (c) at V vs. SCE for 1 hour Figure EDS spectrum of the corrosion products on the specimen after constant potential exposure experiment in 9 g/l NaCl solution at room temperature; (a) spectrum at point 1; and (b) spectrum at point 2 in Figure 3-16b Figure SEM micrograph of the corrosion product layer after constant potential exposure experiment in 9 g/l NaCl solution, room temperature at V vs. SCE Figure SEM micrographs of the 2mm long silver-cored MP35N LT composite specimens after immersion in 9 g/l NaCl solution at 37 o C for different periods of time; (a) 1, (b) 5 and (c) 25 weeks xiii

16 Figure The depth of penetration at the silver core of the 2 mm long silver-cored MP35N LT composite specimens after different immersion time in 9 g/l NaCl solution at 37 o C Figure Calculated and experimental potentiodynamic polarization curves of the silver-cored composite in 9 g/l NaCl solution at room temperature Figure Evans diagram showing the cathodic polarization curve of the MP35N LT outer tube and the anodic polarization curve of the silver core in Ringer s solution at 37 o C. The areas of the MP35N LT outer tube and of the silver core are 1.8x10-3 and 1.1x10-5 cm 2, respectively Figure Current vs. potential curve of the silver wire specimens during potentiodynamic polarization with different terminated potentials Figure SEM micrographs of specimen surfaces at different terminated anodic potentials of Figure EDS spectrum of the non-continuous film on the specimen after polarization to V vs. SCE in the potentiodynamic polarization experiment Figure XRD pattern of the continuous film formed on the specimen after polarization to V vs. SCE in the potentiodynamic polarization experiment Figure SEM micrographs of the surface morphology of specimens after potentiodynamic polarization with final anodic potentials of (a) +0.08, (b) and (c) V vs. SCE Figure SEM micrographs of the cross sections of the AgCl layers grown by galvanostatic polarization at 0.5 ma/cm 2 to pass a coulomb amount of 5 C/cm 2 ; (a) FIB cross sectioning, before AgCl decomposition; (b) FIB cross sectioning, AgCl under decomposition; and (c) ultrasonic cleaning to break the top layer Figure Silver dissolution current density vs. overpotential in potentiostatic step experiment Figure Potential vs. time curve during galvanostatic preparation of AgCl layer with i = 0.5 ma/cm Figure Dependence of AgCl layer resistances on the amounts of coulomb passed per unit area during galvanostatic experiments at different applied current densities of 0.1, 0.2, 0.5, 1 and 2 ma/cm Figure The apparent conductivity of the AgCl layers during galvanostatic experiments in 9 g/l NaCl solution at different current densities of 0.1, 0.2, 0.5, 1 and 2 ma/cm xiv

17 Figure Calculated and measure overpotential vs. time during galvanostatic polarization experiment with the applied current density of (a) 0.1; (b) 0.2; (c) 0.5; (d) 1 and (e) 2 ma/cm Figure Dependence of the offsets between the calculated and the measured overpotentials on the applied current densities during galvanostatic experiments Figure Schematic of the corrosion cell of a broken silver-cored MP35N LT composite wire in vitro Figure Schematic of the stages for the dissolution of silver and the formation of AgCl in vitro Figure Evans diagram of the silver core and the MP35N LT alloy outer tube in Ringer s solution at 37 o C. The electrode areas of the silver core and the MP35N LT alloy outer tube are 11x10-6 and 16x10-6 cm 2, respectively Figure Schematic of a broken silver-cored MP35N LT wire for modeling of the transport process inside the pit at the silver core Figure The dependence of the concentration of Na +, Cl -, Ag + and the potential drop on i.y: (a) i.y varies in the range of 0 to 3x10-3 A/cm; and (b) i.y varies in the range of 0 to 1x10-9 A/cm Figure Conditions for AgCl precipitation as a function of the dissolution current density and the distance from the pit mouth Figure The effect of the potential difference on the silver dissolution rate and the AgCl thickness after 1 hour of constant potential polarization Figure The effect of AgCl layer apparent conductivity on the silver dissolution rate and the AgCl thickness after 1 hour of constant potential polarization Figure The effect of polarization time on the dissolution current density of silver Figure The effect of polarization time on the thickness of AgCl layer Figure The effect of the scan rate on the silver dissolution rate Figure The effect of the scan rate on the thickness of the AgCl layer Figure The 1/i vs. t 1/2 curves obtained from constant potential exposure experiments at different applied potentials of 0.1, 0.2, 0.6 and 1.0 V vs. SCE in physiological solution of 9 g/l NaCl solution Figure The i vs. E curves obtained from the cyclic voltammetry experiments at different scan rates in physiological solution of 9 g/l NaCl solution xv

18 Figure The i vs. s 1/2 curves obtained from the cyclic voltammetry experiments and from the theoretical model Figure Schematic of the silver core dissolution and the growth of the AgCl layer in Stage Figure Schematic of the resistance components in the AgCl layer in Stage Figure The effect of the potential difference on the silver dissolution rate and the geometry of the AgCl layer after 1 hour of constant potential polarization Figure The effect of the AgCl apparent conductivity on the silver dissolution rate and the geometry of the AgCl layer after 1 hour of constant potential polarization Figure Schematic of the two different scenarios of the corrosion of the silver core; (a) a pit with an infinite depth; and (b) a pit with a finite depth Figure The 1/i vs. t 1/2 curves calculated in the infinite pit depth scenario and in the finite pit depth scenario Figure The dependence with time of the characteristic geometrical parameters of the AgCl layer in the infinite pit depth scenario and in the finite pit depth scenario Figure The dependence with time of the total volume of AgCl formed during corrosion of the silver core in the infinite pit depth scenario and in the finite pit depth scenario Figure Schematic of the dissolution of the silver core and the formation of the AgCl layer on a freshly broken silver-cored MP35N LT wire Figure Evans diagram of the silver core and the MP35N LT alloy outer tube in Ringer s solution at 37 o C. The anodic polarization curve is for a silver electrode with an area of 11x10-6 cm 2. The cathodic polarization curves are for a MP35N LT alloy outer tube with the electrode area of 16x10-6 cm 2 (dash line) and 0.11 cm 2 (solid line), and a hypothetical situation (dash-dot line) Figure Evolution of the pit depth, the growth of the AgCl hemispherical cap and the silver dissolution current density with time Figure Schematic of the diffusion model for Ag + cations; (a) the AgCl layer and the proximity region of constant radius a; and (b) concentration profile at time t Figure Concentration profiles of Ag + cations at different time Figure The dependence of the total amount of the Ag + cations released to the ambient with time Figure A-1. SEM photo of the AgCl layer for statistical analysis xvi

19 List of Symbols a size of the proximity region surrounding the silver core in which the concentration of Ag + cations is constant, cm A surface area, cm 2 A mc average cross sectional area of the micro-channels, cm 2 B broadening factor in XRD pattern C capacitance of passive films, F/cm 2 C 1, C 2, C 3 concentration of Ag +, Na +, Cl -, mol/cm 3 C b concentration of Na + and Cl - in bulk solution, mol/cm 3 C o saturated concentration of Ag + ion in chloride solution, mol/cm 3 d size of crystals, nm D diffusivity, cm 2 /s D 1, D 2, D 3 diffusivity of Ag +, Na +, Cl -, cm 2 /s E F electrode potential, V vs. SCE Faraday s constant, C/equiv i corrosion current density, A/cm 2 i L limiting current density, A/cm 2 I corrosion current, A j unit imaginary number, the square root of -1 K K mc apparent conductivity of AgCl layers, S/cm conductivity of the electrolyte inside the micro-channels, S/cm K sp solubility product of AgCl, mol 2 /cm 6 xvii

20 l L m Ag m AgCl M M AgCl n n 1 size of the Cr depleted zones, m corrosion depth at the silver core, cm mass of silver dissolved, g mass of AgCl layers, g molar weight, g/mol molecular weight of AgCl, g/mol number of electron transferred in reaction, eq./mol power factors in the constant phase element of the inner porous layer, CPE = Y -1.(jω) -n n 2 power factors in the constant phase element of the outer porous layer, CPE = Y -1.(jω) -n N N r number of the micro-channels running through the AgCl layer total amount of Ag + released, mol q number of coulomb passed per unit area, C/cm 2 r r o distance from a point in the ambient to the silver core, cm the radius of the silver core, cm R s resistance of solution, Ω cm 2 R 1 resistance of the inner porous layer of the pseudo-passive film, Ω cm 2 R 2 resistance of the outer porous layer of the pseudo-passive film, Ω cm 2 R R s S gas constant, J/mol.K resistance of AgCl layers, Ω potential scan rate, V/s correction factor for X-ray diffractometer xviii

21 t t 1 t 2 t 3 t 4 t r T V x x o time, s time when AgCl starts forming, s time when AgCl fills the pit at the silver core, s time when AgCl forms a hemispherical cap of radius r o, s time when the radius of the AgCl hemispherical cap is larger than r o, s transport number temperature, K potential at an external cathode, V vs. SCE thickness of AgCl layers, cm thickness of AgCl layers when the AgCl forms a hemispherical cap of radius r o, cm y y o y 1 Y 1 pit depth at the silver core, cm pit depth at the silver core when AgCl starts forming, cm pit depth at the silver core when AgCl fills the pit at the silver core, cm admittance of the inner porous layer of the pseudo-passive film, Ω -1 s n 1 cm -2 Y 2 admittance of the outer porous layer of the pseudo-passive film, Ω -1 s n 2 cm -2 z thickness of the Ag core dissolved, cm z* charge of ions z 1, z 2, z 3 z s3 z s4 charges of Na +, Cl -, Ag + ions thickness of the Ag core dissolved in Stage 3, cm thickness of the Ag core dissolved in Stage 4, cm xix

22 Greek β structural factor of AgCl layer representing the increase in the ionic transport distance due to the tortuousness of the micro-channels δ Φ η η a η c η Ω λ θ diffusion layer thickness, cm potential drop, V overpotential, V activation overpotential, V concentration overpotentials, V ohmic overpotential, V wavelength of X-ray source, nm Bragg angle, o ρ Ag density of silver, g/cm 3 ρ AgCl density of AgCl, g/cm 3 τ transient time to reach steady-state, s xx

23 Acknowledgements I would like to take this opportunity to express my gratitude to people who make my journey joyful and without whom this dissertation will never be finished. I am grateful to my advisor, Prof. Joe Payer, for his guidance throughout my research. His insight and support during my study at Case provided invaluable experiences for me. He set an excellent example as a person who actively and tirelessly contributes to the development of the field he pursuits. I thank the committee members who spent their time to read the manuscript and gave their comments throughout the thesis and during my defense. The quality of the thesis was improved after useful discussion with them. I thank my lab mates, both former and current members, for their help and useful discussion. Especial thanks to Dr. Xi Shan who took a very good care for the lab and for every single pieces of equipments. I also thank my lab mate Jason Miller who was with me in one of the projects and actively contributed to the success of the project. I am grateful to the technical staffs who trained me since the first days I came to the Department. I also want to thank engineers at the FES center at CWRU for their help and technical supports during this work. Their skills, knowledge and friendship will remind me about them. I am indebted with my parent and my family in Vietnam, people who always take care of me and give me their relentless support. This dissertation is dedicated to them. Finally, I thank my wife for being with me during this long journey. She brings joys to my life and makes it more vibrant. xxi

24 MICRO- AND NANO-SCALE CORROSION IN IRON-BASED BULK METALLIC GLASS SAM 1651 AND SILVER-CORED MP35N LT COMPOSITE Abstract by HUNG MANH HA The corrosion of two engineering materials, an Fe 48 Cr 15 Mo 14 C 15 B 6 Y 2 (at.%) bulk metallic glass (SAM 1651) and a silver-cored 35%Co-35%Ni-20%Cr-10%Mo (wt.%) composite (silver-cored MP35N LT), was studied. The structural and compositional heterogeneities in the Fe-based metallic glass of nanometer scales and the dimension of the silver-cored composite of micrometer sizes enabled the formation of corrosion cells on the micro- and nano-scales. Selective dissolutions occurred at the Y-Mo-rich constituents (ca. 10 to 100 nm) in both fully amorphous and partially devitrified SAM 1651, at the nanometer Cr-depleted zones (ca. 10 nm) in the partially devitrified SAM 1651 and at the silver core (ca. 30 μm) of the composite. Heat treatment of SAM 1651 at 600, 700 and 800 o C caused devitrification of the amorphous structure with the precipitation of nanocrystalline (Cr, Fe) 23 C 6 and (Cr, Fe) 7 C 3 carbides following primary transformation. The formation of nanometer Cr-depleted zones surrounding the carbides is proposed to be the reason for the degradation in the corrosion resistance of SAM 1651 after heat treatment observed at both macroscopic and nano-scale. Under diffusion controlled growth, the sizes of the carbide particles and of the Cr-depleted zones increased with the increase of the heat treatment temperature. The xxii

25 increase in the size of the Cr-depleted zones resulted in the decrease of the corrosion resistance of SAM 1651 as observed when temperature increased from 600 to 800 o C. However, the heat treated material still exhibited good corrosion resistance in 6M HCl with the corrosion rate of less than 5 μm/year as measured in weight loss test. The corrosion of 30 μm diameter silver cores of the composite in vitro was studied. The exchange current density of the Ag/Ag + redox reaction in NaCl solution was found to be on the order of 10-4 A/cm 2. The deposition of AgCl corrosion product layer at the silver microelectrode slowed the kinetics of the anodic dissolution. Ionic transport via micro-channels running through AgCl layer was the rate controlling process. As the layer was thin, i.e. on the order of micrometers, the silver dissolution process was under mixed activation-ohmic controlled regime. As the layer was thick, i.e. on the order of tens micrometers or thicker, the silver dissolution process was under ohmic controlled regime. The geometry and the apparent conductivity of the AgCl layer played an important role in determining the corrosion kinetics. The anodic dissolution current decreased with increase of the size and the decrease of the apparent conductivity of the AgCl layer. When the AgCl layer was in cylindrical or hemispherical shape, the corrosion kinetics was found to increase linearly with the square root of the AgCl layer apparent conductivity, to increase linearly with the square root of the potential difference between the cathode and the anode, and to decay linearly with the square root of time. xxiii

26 Chapter 1 INTRODUCTION Most corrosion in aqueous environment is of electrochemical nature which involves at least two reactions namely the oxidation of metal at the anode and the reduction at the cathode. Usually corrosion is the process occurred at the anode, however both oxidation and reduction are required for the proceeding of corrosion. At the atomic scale, the corrosion process may involve several elementary reactions however the overall reactions can be described as following: - At the anode, metal atoms are oxidized to cations and generate electrons: M = M n+ + ne - (1.1) - At the cathode, electrons are consumed in reduction reactions such as oxygen reduction or hydrogen evolution: H 2 O + 1/2O 2 + 2e - = 2OH - (1.2) 2H + + 2e - = H 2 (1.3) The electrons generated at the anode must travel to the cathode where they are consumed therefore create a current in the metallic phase. Meanwhile in the electrolyte, there are fluxes of cations and anions moving from the anode to the cathode or vise versa under concentration gradient or electric field between the electrodes forming a current in the aqueous phase. The magnitude of the current in the metallic phase and in the aqueous phase must equal and represents for the kinetics of the corrosion process. In this work, the corrosion of two engineering materials, an iron-based bulk metallic glass (BMG) structurally amorphous metals (SAM) 1651 and a silver-cored MP35N LT composite, was studied. The structural and compositional heterogeneities in the Fe-based amorphous metal of nanometer sizes and the dimension of the silver-cored composite of 1

27 micrometer sizes enabled the formation of corrosion cells at the micro- and nano-scales. The dissolution kinetics at the anodes is discussed in terms of the composition, the size and the distribution of the electrodes at micro- and nano-scales. The effect of the anodic films formed during corrosion on the kinetics of the dissolution process is also discussed. 1.1 Objectives In the first part of this work, the effect of heat treatment on the corrosion behavior of an Fe-based BMG SAM 1651 with the nominal composition of Fe 48 Cr 15 Mo 14 C 15 B 6 Y 2 (at. %) was studied. This Fe-based material has extremely high corrosion resistance which is superior to Ni-based alloy 22 in some highly aggressive environments, including concentrated calcium chloride brines at elevated temperatures. Exposure of SAM 1651 to high temperatures causes crystallization of the amorphous structure. The change in the corrosion behavior of the BMG after the heat treatment is discussed in term of structural and compositional change at the nano-scales. The objectives of the first part are as follows: - to investigate the effect of heat treatment on the structure and the composition of SAM to examine the effect of heat treatment on the corrosion behavior of SAM 1651 in macroscopic and nanometer scales. - to study the formation of pseudo-passive films on the heat treated SAM 1651 in a concentrated hydrochloric acid solution. In the second part of this work, the corrosion of a silver-cored MP35N LT composite in vitro was studied. The composite is the material of choice for lead wire cables, with the 2

28 diameter on the order of tens of micrometers, in Networked Neuroprosthetic System (NNPS). Mathematical models for the corrosion of the micro-sized electrodes are developed with experimental validation. Based on the established models, the release amount and the release rate of metals from a broken lead wire can be predicted. The objectives of the second part are as follows: - to examine the corrosion behavior of the silver-cored composite in vitro. - to characterize the corrosion products formed at the anode and their effect on the kinetics of the corrosion. - to develop mathematical models for the corrosion of the silver-cored MP35N LT composite in vitro. - to describe the corrosion of the silver-cored composite quantitatively in a time step process and predict the amount of metal released after the event of mechanical failure. 1.2 Structure of the dissertation The dissertation includes four chapters. Chapter 1 introduces some general aspects of corrosion and the objectives of the studies. Chapter 2 presents the study on the corrosion of the Fe-based amorphous metal SAM 1651 and the effect of heat treatment. Chapter 3 presents the study on the corrosion of the silver-cored MP35N LT composite. Chapter 4 summarizes the studies with some concluding remarks. The contents in the two main chapters of the dissertation, Chapter 2 and Chapter 3, are as follows: 3

29 Section 2.1 of Chapter 2 provides backgrounds for the corrosion behavior of the Febased amorphous metals SAM 1651, the devitrification in amorphous metals and particularly the devitrification in SAM Section 2.2 of Chapter 2 introduces the materials, the specimen preparation procedures, and the experimental methods used in the study. In Section 2.3 of Chapter 2, the effect of heat treatment on the structure and composition of SAM 1651 is examined experimentally. Two aspects of the heat treatment conditions are considered including the treatment temperature and the holding time. Section 2.4 of Chapter 2 reports the effect of heat treatment on the corrosion behavior of SAM 1651 at macroscopic and nanometer scales. The corrosion resistance of both fully amorphous and heat treated materials is explained in terms of the chemical and structural characteristics of the alloys. A hypothesis of nano-sensitization which accounts for the degradation in the corrosion resistance of SAM 1651 after heat treatment is proposed. In Section 2.5 of Chapter 2, the formation of a pseudo-passive film on the heat treated SAM 1651 in concentrated hydrochloric acid is studied. The composition, structure and electronic properties of the film are characterized. The similarity and disparity between the pseudo-passive film and a typical passive film is also discussed. Section 2.6 of Chapter 2 summarizes the main findings in the corrosion of SAM 1651 and the effect of heat treatment. Section 3.1 of Chapter 3 provides backgrounds on the structure of NNPS, the corrosion issues in vivo, and the corrosion of silver in chloride environments. 4

30 Section 3.2 of Chapter 3 introduces the materials, the specimen preparation procedures, and the experimental methods used in the study of the silver-cored composite corrosion. Section 3.3 of Chapter 3 presents the corrosion behavior of the silver-cored composite in vitro. The electrochemical effect of the component materials on the overall behavior of the composite is elucidated. The formation of AgCl corrosion product layers and their effects on the dissolution kinetics of the corroding electrode is discussed. In Section 3.4 of Chapter 3, a detail characterization on the precipitation and growth of the AgCl layer on silver in a physiological solution of 9 g/l NaCl is presented. The ionic transport mechanism through the AgCl layer is revealed. The role of the AgCl layer on the dissolution kinetics of the underneath silver substrate is elucidated. In Section 3.5 of Chapter 3, the overall corrosion process of a broken silver-cored composite cable is described. Mathematical models for each stage of the corrosion process are developed. Experimental results validating the models are also presented. The effect of physical parameters on the silver dissolution kinetics is discussed. In Section 3.6 of Chapter 3, the corrosion of a freshly broken silver-cored MP35N LT cable is studied based on the models developed in Section 3.5. The dissolution at the anode, the precipitation and growth of the corrosion product layers is analyzed quantitatively. The amount of metal released to the ambient is also calculated. Section 3.7 of Chapter 3 summarizes the main findings in the corrosion of the silvercored MP35N LT composite for NNPS. 5

31 Chapter 2 CORROSION OF AN IRON-BASED BULK METALLIC GLASS SAM 1651 AND THE EFFECT OF HEAT TREATMENT 2.1 Background The development of Fe-based metallic glasses Metallic glasses, or amorphous alloys, are an emerging class of alloys which have high interest due to their ability to be designed for special properties. While all metallic glasses do not necessarily have high corrosion resistance, recent reviews document substantial progress in the development of corrosion resistant alloys [1-3]. However, one of the challenges for fabricating amorphous alloys is that they typically require extremely high cooling rates to avoid crystallization on cooling. Advances to overcome this challenge have been made in both alloy composition design and innovation in fabrication technology. The first amorphous alloy formed from a liquid phase, a Au-Si binary alloy, was successfully created by Duwez and his colleagues at the California Institute of Technology in 1960 [4]. In 1967, the success in fabrication of the first Fe-based amorphous metals was reported by Duwez s group with a ternary system of Fe-P-C [5]. However, the range of composition to form amorphous phase was relatively narrow (several at.%) and the critical cooling rate was high (10 6 K/s) [6]. With the introduction of the concept of multi-component alloy systems, Fe-based bulk metallic glasses (BMG) were made in 1995 by Inoue and his colleagues [7]. The addition of metalloid elements and transition metals is effective for the extension of the supercooled liquid region and 6

32 the reduction of the critical cooling rate for the formation of the amorphous phase. Recently ingots of 5mm in diameter of (Fe 80 B 20 )-X amorphous alloys where X are refractory elements such as Zr, Nb, Ta, W or Mo, could be made without difficulty using a copper mold [8]. In addition to developments in alloy design, many advanced technologies have been developed to meet the requirement of rapid cooling rates including melt spinning, arc melting with drop casting, thermal spraying, chemical and physical vapor deposition, electrodeposition, ion beam mixing, laser pulsing, etc [1-3]. Thermal spray coating is of interest for application on substrates to obtain beneficial properties of amorphous alloys and to minimize the challenge to fabricate low toughness materials. The thermal spray process is enhanced via careful selection of powder sizes and process temperatures to enable the production of coatings with glassy structure, virtually pore free and good bond strength [9]. Thickness of the coatings may vary in the range of several hundred of microns Fe-based BMG SAM 1651 with exceptionally high corrosion resistance Two compositions of structurally amorphous metals, SAM 1651 and SAM 2X5, having corrosion resistance superior to nickel-based alloy 22, which is one of the best corrosion resistant materials commercially available, in some highly aggressive environments, including concentrated calcium chloride brines at elevated temperatures have been reported [9, 10]. Iron-based BMG SAM 1651 with nominal composition of Fe 48 Cr 15 Mo 14 C 16 B 6 Y 2 (at.%) has been found to have more positive corrosion potential, breakdown potential and repassivation potential than those of alloy 22 in brine of different concentrations at both room temperature and elevated temperature [11-13]. 7

33 Shan et al. investigated the corrosion behavior of SAM 1651 and crystalline Ni-based alloy 22 in hot concentrated brine and showed that SAM 1651 was more corrosion resistant than alloy 22 at high oxidizing potentials. In concentrated brine, crevice corrosion was more difficult to initiate on SAM 1651, and once it initiated the corrosion current was sustained at lower value than that of alloy 22 [13]. Pang et al. developed a Y- free modified version of SAM 1651 with the composition of Fe 50-x Cr 16 Mo 16 C 18 B x (x = 4, 6, 8 at.%) and measured the corrosion rate of these alloys in the range of mm/ year in 1, 6 and 12N HCl solution at room temperature. The alloys did not suffer pitting corrosion even when polarized anodically in 12N HCl solution up to 1.0 V (Ag/AgCl) [14]. Addition of P in the Fe-Cr-Mo-C-B system had beneficial effect on the corrosion resistance [15, 16]. Asami et al. investigated a BMG system of Fe 43 Cr 16 Mo 16 (C, B, P) 25 (at.%) and observed an improvement in corrosion resistance of P-containing alloys in comparison with the P-free alloys. However, they also concluded that alloying with P had detrimental effect on the glass-forming ability of the BMG [16]. A study by Jayaraj et al. in which they compared the corrosion behavior between a N-containing Fe 49 Cr 15.3 Mo 15 Y 2 C 15 B 3.4 N 0.3 (at.%) alloy and SAM 1651 in concentrated HCl solution, showed that minor addition of N significantly improved the corrosion resistance of the Fe-Cr-Mo-C-B-Y alloy [17]. Corrosion resistant coatings can not be achieved with thermally sprayed crystalline materials such as 316L stainless steels or Ni-based alloy 22 due to the segregation of undesirable phases which leads to the loss of their corrosion resistance during the thermal sprayed process. However, thermal spray coatings of SAM 1651 retained their excellent corrosion resistant performance as long as the amorphous structure is maintained [9]. 8

34 Iron-based, high-performance amorphous-metal thermal-spray coatings are under development for potential use for ships and potentially for use to coat containers for the transportation and long-term disposal of spent nuclear fuel [9, 18-29] Devitrification of amorphous metals The effect of heat treatment on the structure and corrosion behavior of crystalline materials has been extensively investigated. Sensitization of stainless steels and Ni-based alloys is well known and is a classic case study for intergranular corrosion in many textbooks [30, 31]. However, the characteristics of the devitrification processes of glassy materials with the formation of carbides and other phases are not well known, and little has been done to determine devitrification effects on the corrosion behavior. Upon exposure to elevated temperatures, amorphous alloys can undergo the crystallization process via several routes including phase separation, polymorphous crystallization, eutectoid crystallization and primary crystallization depending on the alloy composition, the heat treatment path and the thermal history of the alloys. A schematic of these phase transformation processes is illustrated in Figure 2-1 which demonstrates an energy diagram of a metallic glass phase with high free energy and tendencies to crystallize by a nucleation and growth process [32]. Stable equilibrium is indicated by the solid line and metastable equilibrium is indicated by the broken lines. The two stable crystalline phases are a terminal solid solution α and an intermetallic θ. A metastable phase M is more stable than the metallic glass, but it is metastable with respect to the mixture of α and θ. The three crystallization routes of the metallic glass can be briefly described as follows. Polymorphous crystallization is the transformation process in which the crystalline product phase and the precursor metallic glass phase 9

35 have the same composition. This transformation is demonstrated in Figure 2-1 by arrows (1), (2) and (3). The metastable products, i.e. supersaturated solid solution α and metastable phase M may undergo further phase transformation indicated by arrows (2 ) and (3 ). Eutectoid crystallization is the transformation process in which eutectic reaction of the glass phase results in mixtures of either α and M or α and θ phases. This transformation is demonstrated in Figure 2-1 by arrows (4) and (5). Primary crystallization is the transformation process in which a primary α phase is formed in a matrix of remaining amorphous phase. This transformation is demonstrated in Figure 2-1 by arrow (6). M θ G G (J/mol) α (3) (3 ) (6) (4) (5) (2) (2 ) (1) 0 C α C α C α C g C m C θ 1 X (%) Figure 2-1. Hypothetical free energy diagram to illustrate the crystallization of a metallic glass. G, α, θ, M are the free energy curves of the glass, a terminal solid solution, a stable intermetallic phase and a metastable phase, respectively [32]. The numbered arrows refer to the crystallization processes described in the text. The devitrification of metallic glasses is complex and depends not only on the alloy composition but also on the heat treatment condition. The thermal history and the heat 10

36 treatment path have strong effect on the chemistry, structure and distribution of the crystalline phases. For instance, heat treatment of an amorphous (Fe 0.8 Cr 0.2 ) 81 B 17 W 2 (at.%) alloy following different heat treatment path developed different devitrified structures [33]. Heat treatment at 500 o C for 100 hours triggered the primary crystallization reaction resulting in α-fe particles of 20 nm size embedded in a remaining amorphous matrix. Heat treating the alloy at 300 o C for 100 hours and then at 700 o C for 10 minutes resulted in α-fe particles, which were originally formed in the amorphous matrix at 300 o C, contained in a crystalline phase after completion of crystallization. In another heat treatment regime for the same alloy using a one step heat treatment at 700 o C for 10 minutes, a three-phase crystalline structure with no precipitate was formed [33]. Similar to the crystallization from liquids, amorphous metals crystallize through nucleation and growth process. However, there are some differences in the kinetics. In conventional crystallization, the embryos have to cluster to a critical size so that it becomes stable nuclei, then the growth can start [34]. However in amorphous metals, because of the metastable nature of the structure, the materials are virtually undergo phase transformation at any temperature. In addition, it is common to find that there are a large number of quench-in nuclei which act as the nucleation sites for phase transformation during reheating. Therefore, these materials often yield a high density of crystalline particles after heat treatment. If the heating temperature is low, diffusion is inhibited and the size of the crystalline phases is limited to nanometer scale. For instance, a density as high as 4x10 21 cm -3 of nearly spherical, 22 nm diameter Al nanocrystals was reported to form after heating a Al-7Y-5Fe amorphous alloy at 245 o C for 10 minutes. This unique microstructure of nanocrystalline in a matrix of remaining amorphous 11

37 material brings many interesting characteristics for the partially devitrified amorphous materials Mechanical property of partially devitrified amorphous metals Figure 2-2 illustrates the atomic distributions in the three different structures, namely crystalline, amorphous and nanocrystalline. Due to their periodically atomic arrangement, conventional crystalline materials deform by movement of dislocations (Figure 2-2a). Defects inside the structure such as grain boundaries, phase boundaries, micro cracks, etc. reduce their strength to levels of far from the theoretical strength. In contrast, amorphous metals with no long range order structure, in terms of both chemically and geometrically (Figure 2-2b), exhibit outstanding mechanical properties which approach the theoretical strength, elastic strain, and elastic energy storage [35]. They exhibit either homogeneous or inhomogeneous deformation depending on the ambient temperature and the strain rate. Homogeneous deformation occurs at high temperatures (T > T g the glass transition temperature) in which the materials deform under a homogeneous flow regime and a global plasticity can be achieved [35]. However, at low temperatures (T < T g ) and/or under high strain rate (dε/dt > 10-2 s -1 ), amorphous metals flow inhomogeneously via the formation and propagation of shear bands [36, 37]. Shear bands which are typically nm in width form locally and with a small amount, therefore the strain is concentrated at these locations and the consequence is catastrophic. Nanocrystalline materials, inheriting the mechanical properties of their precursor amorphous metals, usually demonstrate different and frequently superior mechanical properties to those of conventional materials. The structure of nanocrystalline materials contains high density of defects, most of which are grain boundaries and interphase 12

38 boundaries with the spacing between neighboring defects approaching the interatomic distances (Figure 2-2c) [38]. The introduction of the nanocrystalline phases in the amorphous matrix can alter the flow mechanism and in some cases may effectively enhance the ductility and toughness of the nanocrystalline materials. The ideal has been realized the first time by He and his colleagues to produce a Ti-based nanostructuredendrite composite [39]. The deformation in the novel Ti-based composite was reported to occur partially through dislocations in dendrites and partially through a shear-banding mechanism in the amorphous matrix. The dendrites acted as obstacles restricting the excessive deformation by isolating the highly localized shear bands in small, discrete interdendritic regions, and contributed to the plasticity [39]. (a) (b) (c) Figure 2-2. Atom distributions in (a) crystalline; (b) amorphous; and (c) nanocrystalline materials. 13

39 Corrosion behavior of partially devitrified amorphous metals Similar to the mechanical properties, corrosion resistance is also dependent on the structure of materials. Heterogeneities in the microstructure such as grain boundaries, phase boundaries, inclusions, chemical segregations, etc. make the materials prone to corrosion. Therefore, the amorphous structure is an advantage for the metallic glasses in comparison with their conventional crystalline counterparts. Another advantage of amorphous alloys is the ability to accommodate a large amount of beneficial alloying elements for corrosion resistance such as Cr and Mo that could not be done in conventional materials due to the barrier of thermodynamics stability. However, after devitrification, the amorphous structure is changed and it is likely to alter the corrosion behavior of the devitrified alloys. In some alloy systems such as Al-Fe-Gd, Al-Ni-Y or Cr-Zr, formation of the nanocrystalline phases did not compromise the corrosion resistance of the precursor amorphous materials as long as the size of the crystalline phase does not exceed a critical value [40-42]. One plausible explanation is based on the oxide bridge theory originally proposed by Mehmood et al. [42] which is described as follows. During devitrification, nanocrystals formed and rejected the corrosion resistant alloying elements into the surrounding amorphous matrix. The built-up of the beneficial elements in the remaining amorphous matrix facilitated the formation of a passive film. If the size of the crystalline phase was small enough, the passive film would be able to cover the less corrosionresistant crystalline phases and protect them from pitting corrosion. However, in other systems such as Cr-Ni-P or Cr-Ti, formation of nanocrystalline particles had detrimental effect on the corrosion performance of the heat treated materials 14

40 [43, 44]. In Cr-Ni-P alloys, the precipitation of a Cr 3 P phase with more positive corrosion potential than the matrix was attributed to the decrease of the corrosion resistance. This crystalline phase acted as the cathodic sites in the corrosion cell at the nanoscale and accelerated the corrosion process [44]. In Cr-Ti alloys, the precipitation of a less corrosion-resistant hcp Ti phase was attributed to the decrease in the corrosion resistance of the amorphous alloys after heat treatment. However, when the heat treatment temperature was increased so that the hcp phase was replaced by a more corrosionresistant bcc Ti phase with 14% Cr in the solid solution, the corrosion behavior of the partially devitrified alloy was similar to that of the fully amorphous material. Notably, in some alloys such as Fe-Cr-P-C-Si and Fe-Cu-Nb-Si-B, the partially devitrified materials after certain heat treatment regimes were reported to have enhanced corrosion resistance compared to the amorphous alloy counterparts [38, 45]. The authors of these works drew their conclusions basing on the characteristic parameters in potentiodynamic polarization curves such as critical passivation potentials, break down potentials, critical passivation current densities and maximum passive current densities. However, no more detail characterization or complementary test was performed to investigate the mechanism of this improvement in the corrosion resistance. The difference in the corrosion behavior of partially devitrified amorphous materials is due to the variety in the chemical, size and distribution of the nanocrystalline phases and due to the heterogeneity in the composition of the remaining amorphous matrix [40-45]. 15

41 2.1.4 Devitrification of Fe-based BMG SAM 1651 Primary crystallization has been found to be the predominant route for the devitrification of many Fe-based amorphous metals [46-52]. The crystallization temperature for Fe-based amorphous metals, T x, was typically in the range of o C, and the melting temperature, T m, was often reduced to ca o C as reported in several review papers [33, 46]. Therefore, the crystallization occurs at a temperature of T m where the diffusion is limited and the driving force for nucleation is tremendous [33]. This results in a very high frequency for nucleation and a short time for growth due to the impingement of diffusion field. Ultrafine α-fe particles with mean sizes on the order of ten nanometers were usually found embedded in a remaining amorphous matrix in many Fe-based amorphous metals with high content of Fe, i.e. more than 60 at.%, after heat treatment [46-52]. The structure of these partially devitrified Fe-based amorphous alloys was considered stable at room temperature due to an extremely slow kinetics of further crystallization at this temperature. This class of material showed good soft magnetic properties and was used in electric transformers [46]. The glass transition temperature and the crystallization reactions during continuous heating SAM 1651 was studied with differential scanning calorimetry (DSC). Figure 2-3 shows DSC traces of BMG SAM 1651 for (a) glass transition event determined at a heating rate of 0.33K/s [53]; (b) crystallization; and (c) melting events determined at a heating rate of 0.17K/s [54]. The glass transition temperature of SAM 1651 reported in reference [53] was ca. 575 o C, the crystallization and melting temperatures of SAM 1651 reported in reference [54] were ca. 630 o C and ca o C. These values are consistent 16

42 with the ones reported in other studies [9, 20]. Two maxima in the DSC trace at the temperatures of ca. 630 o C indicated two crystallization events at this temperature range. A maximum at the temperature of ca. 970 o C represented another crystallization reaction. (a) (b) (c) Figure 2-3. DSC traces of BMG SAM 1651 for (a) glass transition event determined at a heating rate of 0.33K/s [53]; (b) crystallization; and (c) melting events determined at a heating rate of 0.17K/s [54]. The concentration of Fe in SAM 1651 is accounted for 48 at.% which is lower than that in the soft magnetic Fe-based amorphous alloys. A considerable amount of Cr in SAM 1651, i.e. 15 at.%, on one hand facilitates the formation of protective passive films for corrosion resistance of the alloy, on the other hand it also promotes the formation of carbide during heat treatment of the material due to the high affinity of Cr to C. Several 17

43 studies on the effect of heat treatment on the properties of SAM 1651 or modified-sam 1651 have been done [21-23, 35, 53]. It was shown that with the test temperatures below or at 400 o C, the microstructure and the hardness of the alloy experienced essentially no change during the testing period of up to 300 minutes. The hardness dropped significantly at higher test temperatures [23, 35]. Evolution in the microstructure was examined at the temperatures around the glass transition temperature with in-situ transmission electron microscopy which revealed the existence of nanocrystalline M 23 C 6 (M = Cr, Fe) carbide embedded in a remaining amorphous matrix [23, 35]. In these studies, most of the experimental work was performed at temperatures around the glass transition temperature and up to 620 o C, knowledge on the behavior of the material heat treated above 620 o C is limited. Especially the effect of heat treatment on the corrosion resistance of SAM 1651, which is an importance issue for the practical application of SAM 1651, has not been investigated thoroughly. The formation of Cr-rich carbides such as M 23 C 6 at the temperature near the glass transition temperature or other possible carbides at higher temperature ranges may be detrimental to the corrosion resistance of SAM Under diffusion controlled growth, consumption of Cr, which is the dominant element of the carbides and has relatively slower diffusivity than C, to form the crystalline phases results in a concentration gradient of Cr at the crystalline/amorphous matrix interface. If the rate of transfer of atoms across the advancing interface is much faster than the rate of diffusion of atoms toward the growing phases, Cr-depleted zones, which are prone to corrosion, form in the amorphous matrix near the interphase boundaries. Illustration for this process is presented 18

44 in Figure 2-4. Therefore exposure of SAM 1651 to heat treatment may have detrimental effect on the corrosion resistance of the alloy. Cr-depleted zone Cr-depleted zone C Cr c C Cr b C Cr i Amorphous Cr-rich Carbide Amorphous Distance Figure 2-4. Schematic of Cr concentration profile around a Cr-rich carbide as the result of diffusion controlled growth. C Cr c -concentration of Cr in the carbide; C Cr b -concentration of Cr in the bulk amorphous matrix; C Cr i -concentration of Cr in the amorphous phase at the carbide/amorphous matrix interface Passivity and pseudo-passivity Except some noble metals, the corrosion resistance of most engineering materials depends on the formation of passive films on the material surfaces [55-58]. Passive films are only several nanometers thick but are highly diverse in chemistry and structure. The chemistry of passive films is dependent on the electrode potential, the characteristics of the base material, i.e. composition, microstructure, surface condition, etc., and on the 19

45 nature of the environment in which the material is exposed, i.e. chemistry, temperature, ph, etc. [59-63]. The structure of passive films is complicated with at least an inner protective barrier layer and an outer hydrated layer [59]. Passive films can be amorphous or crystalline in nature [64-69] or may experience both structures in the multi-layer film [61, 66, 70, 71]. The transition from an amorphous to a crystalline structure of passive films has also been observed [67]. The growth of passive films was extensively studied which showed that the growth rates follow either a logarithmic or an inverse logarithmic law. The mechanism underneath these growth rates is the high field conduction of ions through the oxide film firstly suggested by Cabrera and Mott for the growth of oxide layers on metals [72] and then was modified by Macdonald and others to apply for the growth of passive films [73-75]. These models based on the assumption that there is a potential drop across the films, either at the interfaces or inside the films, resulting in the generation of an electric field with the strength on the order of 10 6 V/cm which enables the transport of ions through the films. The formation of a passive film results in the typical E-log i relationship obtained in potentiodynamic polarization experiments as shown in Figure 2-5. At low potentials, when the passive film has not formed yet, the metal dissolves actively with a proportional increase of current density with increasing potential. At higher potentials, the passive film forms resulting in a drop in the potential of the electrode, therefore the dissolution current density decreases. As the applied potential increases, the passive film growth so that the potential drop across the passive film compensate with the increase of the applied potential; the consequence is a constant dissolution current density in the potential range 20

46 that the passive film is still stable and growing. However, there are still disputes on the exact mechanism of the potential drops at the passive film interfaces and inside the film at the atomic scale [73, 75]. At potentials where the passive film dissolves globally, i.e. transpassive dissolution, or locally, i.e. pitting or crevice corrosion, the dissolution current density increases with increasing potential. passive E / V pseudopassive active log (i / A cm -2 ) Figure 2-5. A schematic of log i vs. E curve for pseudo-passive behavior in comparison with typical passive and active behavior in potentiodynamic polarization. The pseudo-passive behavior of a partially devitrified BMG SAM 1651 in 6M HCl at room temperature was reported [76]. In contrast to the typical passive behavior aforementioned, the current density of the partially devitrified BMG in the pseudopassive range increased proportionally with increasing potential. However, the current density still stayed at low value (ca A cm -2 ) and did not show active dissolution (Figure 2-5). Examination of the surface after experiment revealed the formation of a thin black film with strong adherence to the substrate [76, 77]. Compared to the fully 21

47 amorphous BMG, the partially devitrified BMG experienced degradation in corrosion resistance; however, it still possessed good corrosion resistance in 6M HCl [76]. The corrosion resistance of the partially devitrified BMG was attributed to the formation of a pseudo-passive film. 22

48 2.2 Materials and experiments Materials A Fe-based amorphous alloy SAM 1651 with a nominal composition of Fe 48 Cr 15 Mo 14 C 15 B 6 Y 2 (at.%) was used in this study. The material was prepared at the Oak Ridge National Laboratory by drop casting into water-cooled copper molds to form cylindrical rods with a diameter of approximately 4.2 mm. The riser at one end of the rods which was partially crystallized due to undergoing lower cooling rate was removed by a low speed saw. The length of each rod after riser removal was approximately 7 cm. The reported glass transition temperature, the crystallization temperature, the melting temperature and the critical cooling rate of SAM 1651 were 584 o C, 653 o C, 1121 o C and 80 o C/s, respectively [9, 11]. The as-received materials were stored at room temperature Solution and electrochemical cell setup All electrochemical tests were performed in either 1 or 6M HCl prepared by dilution of reagent grade 12N HCl solution (Fisher Scientific, USA) with deionized water. The test cell was a standard three-electrode configuration cell which was open to air and kept at room temperature. A saturated calomel electrode (SCE) was used and all reported potentials were referred to this reference electrode. The counter electrode was a platinum wire with diameter of 0.5mm and was coiled to provide a total surface area of approximately 2 cm 2. 23

49 2.2.3 Specimen preparation Heat treatment As-received SAM 1651 rods were cut into 1 and 5 mm thick discs. The specimens were heat treated at 600 o C, 700 o C and 800 o C for either 1, 3, 24 or 72 hours in a Lindberg Hevi-Duty furnace. The time-temperature path for the heat treatment process is as follows: First, the temperature of the furnace was ramped from the ambient temperature (ca. 25 o C) up to the desired holding temperature (T 2 ) with the heating rate of 10 o C/min. After the furnace temperature was stabilized, the specimens were introduced and the temperature was held constantly for the desired time period (T 3 ). The specimens were furnace cooled to 25 o C in approximately 5 hours. Figure 2-6 shows the heat treatment procedure and Table 2-1 shows the heat treatment regimes used in this study. Temp. t 1 t 2 t 3 t 4 T 2 Introduce specimen at this time T 1 Time Figure 2-6. Time-temperature path for the heat treatment process T 1 room temperature (25 o C); T 2 holding temperature t 1 ramping time; t 2 temperature stabilization time; t 3 holding time; t 4 cooling time. 24

50 Table 2-1. Summary of the heat treatment regimes. T 2 ( o C) t 1 (min) t 2 (min) t 3 (hours) t 4 (hours) Specimen for X-ray diffraction (XRD) Specimens for XRD were 1 mm thick discs. Before XRD analysis, specimens were ground with 600-grit silicon carbide to remove the cast-formed oxide film (on as-received specimens) or oxide scale (on heat treated specimens) and then cleaned with acetone to remove oils and greases Specimen for transmission electron microscopy (TEM) TEM foils were prepared by either conventional preparation method or with a focused-ion-beam (FIB) system. In conventional preparation method, the specimens were prepared from 1 mm thick discs. The specimens were ground to approximately 80 μm with 1200-grit silicon carbide. Then the specimens were dimpled with a Gatan Dimple Grinder (Gatan Inc., USA) to approximately 20 μm using 3 μm diamond paste and then 1 μm diamond paste for 5 minutes. Final thinning was conducted in a Gatan Precision Ion Polishing System (Gatan Inc., USA) at a potential of 5 kv and the milling angle of 5 o. The final thinning was stopped when a small hole was formed at the center of the specimen. 25

51 To prepare TEM specimens by FIB method, a dual beam FIB system FEI xt Nova Nanolab 200 (FEI Company, USA) was used. The specimens were coated with a thin palladium layer of ca. 50 nm thick before putting into the specimen chamber to minimize the electrostatic charging on the specimens. A thin layer of platinum was deposited at the location of interest on the specimens for protection from damage during ion milling. TEM foils with the dimension of approximately 10 μm x 10 μm x 100 nm were prepared with an ion beam bias voltage of 30 V Specimen for electrochemical experiments Specimens for electrochemical experiments were cylinders of 4.2 mm diameter x 5 mm length. The surfaces of both as-received and heat treated specimens were ground with 600-grit silicon carbide to remove the oxide films and then were cleaned with acetone to remove oils and greases. The electrical contact was made by coiling an alloy 22 wire of 1 mm diameter around the peripheral of the cylinder specimens. The electrical contact was tested with a Fluke 87III True RMS multimeter (Fluke Corporation, USA). Then the specimens were coated with Duralco 4525 epoxy (Cotronics Corp., USA) except one circular cross section to form an exposed area of approximately 0.14 cm 2. The specimen preparation procedure is illustrated in Figure 2-7. Working electrodes were prepared by mechanically polishing the exposed surface with 600-grit silicon carbide paper before each experiment. The specimens were then cleaned ultrasonically with deionized water, followed by rinsing in methanol. 26

52 Alloy 22 wire Alloy 22 wire SAM 1651 cylinder SAM 1651 cylinder SAM 1651 cylinder Epoxy Figure 2-7. Schematic of the specimen preparation procedure Specimen for bulk immersion experiments Specimens for bulk immersion experiments were cylinders of 4.2 mm diameter x 10 mm long. The cylinders were polished to a 600-grit finish using silicon carbide. Then, the specimens were ultrasonically cleaned in acetone for 5 minutes and rinsed in deionized water. Specimens were placed into an oven which was set at 100 C to evaporate the water. Finally the specimens were taken out and cooled to room temperature Experiments X-ray diffraction (XRD) Specimen preparation procedure for XRD analysis was described in Section The structure of the specimens was examined with a Scintag X-1 X-ray Diffractometer using Cu (Kα) radiation. The experiments were set up with 2 theta angles in the range of 30 o and 80 o, a scan step of 0.02 o and a data acquisition time of 10 s/step. 27

53 The peak positions were manually determined from XRD patterns. The chemical analysis was performed with the PCPDFWIN software version 2.1 (International Centre for Diffraction Data, USA). The crystal sizes were calculated from the 5 strongest peaks of the XRD patterns by Scherrer s formula [78]: 0.9 λ d = (nm) (2.1) B cosθ where d is the crystal size (nm); λ is the wavelength of the X-ray source (λ = nm); θ is the Bragg angle ( o ); B is the line broadening factor obtained from the full width at half the maxima (FWHM) intensity with a correction for the broadening effect caused by the instrumentation: B 2 2 = FWHM S (2.2) Using a standard Al 2 O 3 sample, the correction factor, S, was Transmission electron microscopy (TEM) TEM specimen preparation procedures were described in Section TEM imaging and gathering of the electron diffraction (ED) was performed with a 200 kv Conventional TEM Philips CM-20 (FEI Company, USA). Energy dispersive spectroscopy (EDS), scanning transmission electron microscopy (STEM), electron energy loss spectroscopy (EELS) and high resolution transmission electron microscopy (HR-TEM) imaging were performed with a 300 kv FEG TEM Tecnai F-30 (FEI Company, USA). 28

54 Cyclic potentiodynamic polarization (CPP) Cyclic potentiodynamic polarization was performed in a 3-electrode configuration cell set up. The electrolyte preparation procedure was described in Section and specimen preparation procedure was described in Section A Solartron 1280B Electrochemical System (Solartron, UK) controlled by a Corrware software version 2.0 (Scribner Associates Incorporated, USA) was used. The open-circuit potentials (OCP) of the specimens were monitored for 1 hour after immersion in the test cell. CPP curves were obtained by sweeping the potential from V more negative than the OCP up to the potential at which the current density was approximately 0.1 A/cm 2 and then reversing the scan direction from that potential down to the potential at which the current density was approximately 10-5 A/cm 2. A scan rate of 1 mv/s was used Constant potential exposure Constant potential exposure was performed in a 3-electrode configuration cell set up. The electrolyte preparation procedure was described in Section and the specimen preparation procedure was described in Section A Solartron 1280B Electrochemical System (Solartron, UK) controlled by a Corrware software version 2.0 (Scribner Associates Incorporated, USA) was used. The OCP of the specimens were monitored for 1 hour after immersion in the test cell. Constant potentials of either +0.40, or V vs. SCE were applied to the working electrode for different time periods up to 30 hours, and the polarization currents 29

55 were measured during the polarization time. The specimens after polarization were cleaned in deionized water and stored in a box at room temperature for further analysis Electrochemical impedance spectroscopy (EIS) The electrochemical impedance spectroscopy was performed in a 3-electrode configuration cell set up. The electrolyte preparation procedure was described in Section and the specimen preparation procedure was described in Section A Solartron 1280B Electrochemical System (Solartron, UK) controlled by a Corrware software version 2.0 integrated with a Zplot software version 3.1 (Scribner Associates Incorporated, USA) was used. EIS experiments were performed at OCP. The AC signal amplitude was 10 mv and the frequency was swept from 20,000 Hz to 0.02 Hz Bulk sample immersion Bulk sample immersion experiments were performed in glass bottles containing 100 ml of the 6M HCl test solution. The electrolyte preparation procedure was described in Section and the specimen preparation procedure was described in Section A Mettler Toledo XS204 Analytical Balance with an accuracy of 0.1 mg (Mettler-Toledo International Inc., USA) was used for weight measurement. The weights of each specimen before experiments were measured. The specimens were placed on the balance, and the reading was allowed one minute to stabilize. The specimens were then suspended from a polytetrafluoroethylene (PTFE) thread in 100 ml of the 6M HCl test solution. After 168 hours, the specimens were removed from the test solution, rinsed in deionized water and again oven dried as described in Section

56 The weights of each specimens after immersion were measured. Immersion tests were repeated 3 times for each specimen TEM foil immersion The corrosion behavior at the nano-scale of the tested materials was examined by observation of the change in the morphology of TEM foils after immersion in 6M HCl solution for different periods of time. TEM specimens were prepared following conventional method as described in Section TEM foils of both as-received and heat treated SAM 1651 were immersed in 6M HCl solution for 5, 30 and 60 hours. After each immersion period, the foils were taken out, rinsed with deionized water and then were imaged with a 200 kv TEM Philip CM-20. After imaging, the specimens were put back into the test solution for longer immersion period. TEM micrographs at different immersion times were taken from the same locations of each specimen. 31

57 2.3 Structural and compositional study Scope Devitrification of metallic glasses may occur via different routes such as primary crystallization, eutectoid crystallization or polymorphous crystallization depending on the composition of the glasses, the heat treatment path and the thermal history of the material. Structural and compositional changes during thermal exposure may have beneficial or detrimental effects on the performance of the material. Toughness of some metallic glasses was improved due to the formation of nanocrystalline particles dispersed in the amorphous matrix. However precipitation of Cr-rich carbides could result in depletion of this element in the remaining amorphous matrix, and has detrimental effect on the corrosion resistance of the alloys. In this section, the effect of heat treatment on the chemistry and structure of SAM 1651 is examined experimentally. Fe-based BMG SAM 1651 was heat treated at temperatures below and above its crystallization temperature, i.e. at 600, 700 and 800 o C, for either 1, 3, 24 or 72 hours to enhance the devitrification process. The effect of heat treatment on the chemistry and structure of devitrified material was investigated by XRD, EDS, EELS and TEM imaging. More details on the specimen preparation and experiment procedures are presented in Sections and 2.2.4, respectively. The effects of the heat treatment on the corrosion behavior of SAM 1651 are presented in Section Results XRD results 32

58 XRD patterns of the as-received and the heat treated SAM 1651 exposed to temperatures of 600, 700 and 800 o C are shown in Figure 2-8. The XRD pattern of the asreceived SAM 1651 shows a broad diffuse peak at approximately 44 o, typical of the lack of long range order exhibited by metallic glasses. The XRD pattern of the specimen annealed at 600 o C for 3 hours also shows a diffuse peak at ca. 44 o, however it was not as broad as that of the as-received material. Specimens annealed at 700 o C for 3 hours and at 800 o C for 1 hour exhibited significant crystallization. The diffuse peak at ca. 44 o was not discernable, and sharp crystalline peaks were present in the XRD patterns. The crystalline peaks were identified as (Cr, Fe) 23 C 6 and (Cr, Fe) 7 C 3 according to the PCPDFWIN software version 2.1 (International Centre for Diffraction Data, USA). (Cr, Fe) 23 C 6 (Cr, Fe) 7 C o C-1 hour 700 o C-3 hours 600 o C-3 hours As-received Figure 2-8. XRD results of the as-received and heat treated SAM 1651 at 600, 700 and 800 o C for 3, 3 and 1 hour, respectively. 33

59 XRD patterns of SAM 1651 heat treated at 700 o C for 3, 24 and 72 hours are shown in Figure 2-9. The patterns for all specimens were similar with the same positions and intensities of the peaks, which indicate no significant additional structural change during extended holding time at 700 o C. Again, the crystalline peaks were identified as (Cr, Fe) 23 C 6 and (Cr, Fe) 7 C 3 according to the PCPDFWIN software version 2.1. (Cr, Fe) 23 C 6 (Cr, Fe) 7 C o C-72 hours 700 o C-24 hours 700 o C-3 hours Figure 2-9. XRD pattern of SAM 1651 heat treated at 700 o C for 3, 24 and 72 hours TEM micrographs The structure of the as-received and the heat treated SAM 1651 was examined further by TEM, and the results are shown in Figure Diffuse rings in the ED pattern (inset in Figure 2-10a) confirmed the fully amorphous structure of the as-received SAM Bright field-tem (BF-TEM) micrographs of the fully amorphous structure 34

60 depicted no grain boundary in the primary phase or segregation of second phases. However, the different contrast in the BF-TEM micrograph between regions in the specimen indicated chemical heterogeneity in the as-received material. As-rec d 600 o C a 100nm b 100nm 700 o C 800 o C c 100nm d Figure BF-TEM micrographs of SAM 1651; (a) as-received; (b) annealed at 600 o C for 3 hours; (c) annealed at 700 o C for 3 hours; and (d) annealed at 800 o C for 1 hour. The BF-TEM micrograph of a specimen annealed at 600 o C for 3 hours (Figure 2-10b) showed the existence of nanocrystalline particles dispersed in a remaining amorphous matrix. The size of the nanocrystalline particles was less than 10 nm, and these particles were undetectable by X-ray diffractometer (Figure 2-8). 35

61 Dot patterns in ED patterns of SAM 1651 annealed at 700 o C for 3 hours and 800 o C for 1 hour indicated the existence of crystalline phases (Figure 2-10c and Figure 2-10d). BF-TEM micrographs of the specimens depicted nanocrystalline particles dispersed throughout the remaining amorphous matrix corresponding to the dark contrast regions in the as-received material. This is consistent with the finding by Nouri et al. [23, 35]. Particle-free-zones (PFZ) of 10 to 200 nm were observed in the specimen heat treated at 700 o C for 3 hours. The number of PFZ in the specimen heat treated at 800 o C for 1 hour decreased with respect to the one heat treated at 700 o C for 3 hours, and the maximum size of the PFZ decreased to several tens of nanometers. From XRD and TEM results, the fully amorphous structure of the as-received SAM 1651 was confirmed. Upon exposure to 600, 700 and 800 o C for 3, 3 and 1 hour, respectively, the amorphous structure partially devitrified with the formation of nanocrystalline particles dispersed in a matrix of remaining amorphous phase. Hereafter, the as-received and the heat treated SAM 1651 will be referred to as the fully amorphous and the partially devitrified SAM 1651, respectively. Figure 2-11 shows the microstructure of the partially devitrified SAM 1651 during heat treatment at 700 o C for 3, 24 and 72 hours. No significant change in the microstructure was observed which is consistent with XRD results. In all of these specimens, nanocrystalline particles with sizes of approximately 10 nm were dispersed throughout the remaining amorphous matrix, in areas corresponding to the dark contrast regions in the as-received material. PFZ of 10 to 200 nm diameter, corresponding to the light regions in the as-received material, were also observed for all heat treatment times. 36

62 3 hours 24 hours 72 hours 100nm 100nm a b c 100nm Figure BF-TEM micrographs of partially devitrified SAM 1651 heat treated at 700 o C for (a) 3 hours; (b) 24 hours; and (c) 72 hours. The structure of the partially devitrified SAM 1651 was examined further with selected-area ED (SAED), and the results are shown in Figure SAED pattern from the PFZ with diffuse rings revealed that these regions had amorphous structure. SAEP pattern from devitrified regions shows a mixture of diffuse ring pattern and dotted pattern. TEM micrographs in Figure 2-13 show the morphology of devitrified regions at higher magnification. Nanocrystalline particles with lattice ordered structure dispersed in a matrix of remaining amorphous structure were observed. A diffraction pattern obtained by fast Fourier transformation of the crystalline region is shown in the inset of Figure 2-13b. 37

63 700 0 C b a 100nm c Figure Structure of the partially devitrified SAM 1651 annealed at 700 o C for 3 hours; (a) BF- TEM micrograph; (b) SAED pattern from a devitrified region; and (c) SAED pattern from a PFZ nm 60nm Crystalline particle Remaining amorphous matrix a b Figure TEM micrographs at high magnification of the partially devitrified SAM 1651 annealed at 700 o C for 72 hours; (a) at 220,000x; and (b) at 660,000x EDS and EF-TEM EDS analysis of the fully amorphous and the partially devitrified SAM 1651 are shown in Figure An EDS line-scan through a dark contrast region in STEM 38

64 micrograph of the fully amorphous SAM 1651 (Figure 2-14a), which corresponds to the bright contrast region in the BF-TEM micrograph (Figure 2-10a), indicated that this phase was richer in Y and Mo and depleted in Fe and Cr with respect to the matrix. From hereafter, this phase will be referred to as Y-Mo-rich islands. An EDS line-scan through a PFZ in the partially devitrified SAM 1651 (Figure 2-14b) indicated that the zone was richer in Y and Mo and depleted in Fe and Cr in comparison with the surrounding matrix. STEM image 100nm a STEM image 100nm b Figure EDS line-scan of the fully amorphous and partially devitrified SAM 1651; (a) asreceived; and (b) at 700 o C for 3 hours. 39

65 EDS analysis at different locations inside each phase of the fully amorphous and partially devitrified SAM 1651 was also performed. Figure 2-15 shows the locations in each specimen where EDS analysis was conducted. Figure 2-16 shows the EDS spectra of different phases in the specimens used in the compositional quantitative analysis. Due to the limitation of the EDS sensitivity for light elements such as B and C, the quantitative analysis for these elements was excluded. The atomic percentages of Fe, Cr, Mo and Y were calculated from five measurements, and the results were summarized in Table 2-2. In the fully amorphous SAM 1651, Fe and Cr contents of the matrix were higher than those of the Y-Mo rich islands while Mo and Y contents of the matrix were lower than those of the island. Similarly, in the partially devitrified SAM 1651, Fe and Cr contents of the matrix were higher than those of the PFZ while Mo and Y contents of the matrix were lower than those of the PFZ. These quantitative EDS analyses were consistent with the EDS line-scan shown in Figure Location 1 Location 2 Location 4 Location 3 a b Figure STEM micrographs showing the locations of EDS analysis (a) Location 1 in the dark phase and Location 2 in the bright phase of the fully amorphous SAM 1651; and (b) Location 3 in the PFZ and Location 4 in the matrix of the partially devitrified SAM

66 Spectrum at Location 1 Spectrum at Location 2 Spectrum at Location 3 Spectrum at Location 4 Figure EDS analysis conducted at the locations shown in Figure

67 Table 2-2. Summary of the quantitative EDS analysis in atomic percentage. Material Phases Fe S Fe Cr S Cr Mo S Mo Y S Y Fully amorphous Devitrified Y-Mo rich island Matrix PFZ Matrix S i standard deviation of the calculation for element i. Figure 2-17 and Figure 2-18 show the EELS element mapping of the fully amorphous and the partially devitrified SAM 1651 using EF-TEM. The figures demonstrate the distribution of individual elements of Fe, Cr, Mo, C, B and Y in the materials. Brighter contrast depicts higher concentration of the element at the location. In agreement with the EDS line-scan results (Figure 2-14), composition of the Y-Mo-rich islands in the fully amorphous material (Figure 2-17) and of the PFZ in the partially devitrified SAM 1651 (Figure 2-18) were confirmed to be enriched in Y and Mo and depleted in Fe and Cr with respect to the surrounding matrix. The similarity in size, chemistry and structure between the Y-Mo-rich islands and the Y-Mo-rich PFZ indicated that the PFZ in the partially devitrified SAM 1651 correspond to the Y-Mo-rich islands in the fully amorphous material. 42

68 Fe Cr Mo C B Y 200nm Figure EELS mapping of the elements in the fully amorphous SAM 1651 using Energy-filtered TEM. Fe Cr C B Mo Y Figure EELS mapping of the elements in SAM 1651 annealed at 700 oc for 3 hours using Energy-filtered TEM. 43

69 In addition to the mapping of Fe, Cr, Mo and Y distribution, EF-TEM was able to determine the distribution of light elements such as C and B which was difficult to detect by EDS. Results in Figure 2-17 and Figure 2-18 indicated that C was enriched in the Y- Mo-rich islands and in the PFZ in both fully amorphous and partially devitrified materials; while B was slightly depleted in the Y-Mo-rich islands of the fully amorphous SAM 1651 and became slightly enriched in the PFZ of the partially devitrified material. The redistribution of B during heat treatment may be due to the small size of this element so that it easily diffused from the devitrified regions and segregated in the PFZ during the crystallization. However, no further analysis has been done to confirm this hypothesis Discussion Characterization of the structure and the composition of the fully amorphous BMG SAM 1651 The amorphous nature of the as-received BMG SAM 1651 was confirmed by XRD (Figure 2-8), ED pattern and BF-TEM micrograph (Figure 2-10). However, chemical heterogeneity in the fully amorphous structure was revealed by EDS line-scan (Figure 2-14a), STEM micrograph (Figure 2-15a) and EELS mapping (Figure 2-17). The difference in the contrast between the dark contrast islands and the bright surrounding matrix in the STEM micrographs (Figure 2-15a) indicated heterogeneity in the composition between these regions. The EDS line-scan through the dark contrast island showed that the island was enriched in Y and Mo and depleted in Fe and Cr with respect to the surrounding matrix. The EELS mapping (Figure 2-17) confirmed the results of the EDS line-scan. The quantitative EDS analysis shown in Table 2-2 indicated that the ratios of Fe:Cr:Mo:Y were approximately 41:16:29:14 and 58:21:19:2 for the Y-Mo-rich 44

70 islands and for the surrounding matrix, respectively. Similar results have been recently reported on the as-received material of similar pedigree [23, 35] The effect of heat treatment on the structure of BMG SAM 1651 Structural changes of the fully amorphous SAM 1651 upon heat treatment at temperatures below and above the reported crystallization temperature were investigated with XRD and TEM, and the results are shown in Figure 2-8 and Figure In the specimen heat treated at 600 o C for 3 hours which was below the reported crystallization temperature (ca. 653 o C) [9], XRD (Figure 2-8) and ED results (inset in Figure 2-10b) results did not show evidence of crystallization but BF-TEM micrograph (Figure 2-10b) revealed the existence of particles with diameter less than 10 nm in the annealed specimen. This observation at 600 o C is in agreement with the results by Nouri et al. in which they performed an in-situ TEM study on the structural change of SAM 1651 at different annealing temperatures up to 620 o C. In specimens annealed at 700 and 800 o C which were above the reported crystallization temperature, for 3 hours and 1 hour respectively, XRD results (Figure 2-8), ED pattern and BF-TEM micrographs (Figure 2-10c and Figure 2-10d) indicated the existence of nanocrystalline particles. From XRD results (Figure 2-8), the nanoparticles were identified as mainly (Cr, Fe) 23 C 6 carbide and a small amount of (Cr, Fe) 7 C 3 carbide. The nanocrystalline particles were distributed fairly uniformly in a matrix of remaining amorphous phase (Figure 2-13a). The diffraction pattern of a particle obtained from the HR-TEM image by fast Fourier transformation (inset in Figure 2-13b) represented a pattern from fcc <111> planes. Lattice spacing was measured after magnification calibration with a Si standard sample. The measured (111) spacing of the particle was ca. 45

71 0.60 nm which is close to the reported value for (Cr, Fe) 23 C 6 of 0.61 nm [23, 80]. This analysis confirms the existence of the nanocrystalline (Cr, Fe) 23 C 6 in the partially devitrified SAM The size of the (Cr, Fe) 23 C 6 carbides was calculated using the Scherrer s formula [78] as described in Section Average crystalline sizes of 16 ± 2 and 21 ± 2 (nm) were calculated from the 5 strongest peaks in the XRD patterns for specimens heat treated at 700 o C for 3 hours and at 800 o C for 1 hour, respectively. The intensity of the (Cr, Fe) 7 C 3 peaks was not strong enough to give a reasonable accuracy for the calculation, however from the BF-TEM micrographs (Figure 2-10c and Figure 2-10d) the size of these particles was no larger than the size of the (Cr, Fe) 23 C 6 carbide in the same specimens. The size of the (Cr, Fe) 23 C 6 carbide particles formed at different heat treatment conditions are summarized in Table 2-3 which shows a trend of increased particle size with increasing annealing temperature. Table 2-3. Summary of average (Cr, Fe) 23 C 6 crystal sizes at different heat treatment conditions. T 2 ( o C) t 3 (hour) D (nm) S Remarks < 10 N/A Estimated from TEM micrograph ± 2 Calculated from XRD pattern ± 2 Calculated from XRD pattern ± 2 Calculated from XRD pattern ± 2 Calculated from XRD pattern T 2 holding temperature; t 3 - holding time; D particle size; S standard deviation. 46

72 In contrast with the carbide size vs. annealing temperature relationship, the size and the number of the PFZ decreased with increase of the annealing temperatures. The PFZ in the specimen annealed at 600 o C had a maximum diameter ca. 200 nm while the PFZs in the specimen annealed at 800 o C had a maximum diameter ca. 50 nm (Figure 2-10). This observation indicated that higher heat treatment temperature caused a higher extent of devitrification in the BMG SAM 1651 with an increase in the size of the nanocrystalline particles and the shrinking of the amorphous PFZ. Increased annealing time to 72 hours at 700 o C did not change either structure or chemical composition of the crystalline phases (Figure 2-9 and Figure 2-11). This observation indicated that both (Cr, Fe) 23 C 6 and (Cr, Fe) 7 C 3 carbides were relatively stable at this temperature. No devitrification was found in the PFZ, and the size of this zone was unchanged during 72 hours of exposure. This confirmed the relatively high thermal stability of this remaining amorphous phase. The volume fraction of the nanocrystalline phases in the specimen heat treated at 700 o C for 72 hours were estimated with knowledge of the specimen thickness and the size and number of the nanocrystalline particles [81]. The thickness of the specimen was estimated ca. 20 nm which is a reasonable value for the center of specimens prepared by ion milling technique. The size and number of the nanocrystalline particles were calculated from the HR-TEM micrograph (Figure 2-13a). The volume fraction of the nanocrystalline particles in specimens heat treated at 700 o C for 72 hours was approximately 20%. At annealing temperatures of 600, 700 and 800 o C, partially devitrification of the fully amorphous SAM 1651 caused formation of nanocrystalline carbide phases dispersed 47

73 in a matrix of the remaining amorphous phase. This devitrification process followed primary crystallization as described earlier in Section A key finding is that chromium rich carbides formed in the remaining amorphous phase, and these result in chromium depleted zones surrounding the carbides. This nano-sensitization in the BMG is analogous to the more classic sensitization observed in crystalline stainless steel alloys The effect of heat treatment on the composition of BMG SAM 1651 The composition of different phases in SAM 1651 after heat treatment was investigated with EDS and EELS. An EDS line-scan through a PFZ in the partially devitrified material (Figure 2-14b) showed that this zone was rich in Y and Mo and depleted in Fe and Cr in comparison with the surrounding matrix. The EELS mappings (Figure 2-18) confirmed the observation of the EDS line-scan. Quantitative EDS analysis of the PFZ showed a ratio of Fe:Cr:Mo:Y was 35:11:37:17 in comparison with the ratio of 41:16:29:14 for Y-Mo-rich islands in the fully amorphous SAM The similarity in size, chemistry and structure between the Y-Mo-rich islands and the Y-Mo-rich PFZ indicated that the PFZ in the partially devitrified SAM 1651 were the Y-Mo-rich islands in the fully amorphous material. The high thermal stability of the Y-Mo-rich islands in the fully amorphous SAM 1651 may be explained partially by the enrichment in Y and C in this phase as observed by EELS mappings (Figure 2-18). The Y atoms with a medium atomic size and the C atoms with a small atomic size increase the packing density of the glassy phase, thereby hindering the diffusion process required for nucleation and growth of the crystalline phase [25, 82]. Another possible mechanism is that the addition of Y destabilizes the 48

74 meta-stable carbide phases formed upon devitrification of the Fe-Cr-Mo-C-B system and hence suppresses the competing crystallization process [20]. Quantitative EDS analysis of the remaining amorphous matrix was also performed, and the results were summarized in Table 2-2. Compared with the matrix of the fully amorphous material, the remaining amorphous matrix in the devitrified SAM 1651 had lower content of Fe and Cr and higher content of Mo and Y. The small size of the carbide particles in the devitrified SAM 1651 made it difficult to conduct EDS quantitative analysis on these particles due to the interference with the surrounding matrix. However, the particles were identified as (Cr, Fe) 23 C 6 and (Cr, Fe) 7 C 3 from XRD results (Figure 2-8 and Figure 2-9). The redistribution of Fe, Cr, Mo and Y observed in specimens after annealing can be explained as the result of the formation of the (Cr, Fe) 23 C 6 carbide. The nucleation of the carbides which were rich in Cr and Fe consumed these atoms in the amorphous phase and rejected Mo and Y to the surrounding matrix. As the particles grow, Cr and Fe must diffuse toward the growing particles and Mo and Y must diffuse away from the advancing carbide/amorphous matrix interfaces. Eventually the matrix becomes depleted in Cr and Fe and enriched in Mo and Y as indicated by EDS results. The depletion of Cr in the amorphous material is detrimental to the corrosion performance of the alloy after heat treatment. Sensitization of stainless steels and Ni-based alloys due to the formation of (Cr, Fe) 23 C 6 which results in depletion of Cr in the surrounding matrix has been widely studied both theoretically and experimentally [83-87]. It was shown that the extent of Cr depletion in the surrounding matrix depends on the size, distribution, volume fraction of the carbide and the post-heat treatment practice. 49

75 Figure 2-19 demonstrates the devitrification of SAM 1651 and the formation of nanometer Cr-depleted zones associated with carbide precipitation. The size of the Crrich carbide increases with increasing annealing temperature. For conservation of matter, the amount of Cr enriched in the carbides must equal the amount of Cr depleted in the Crdepleted zones. Therefore, as the size of the carbide increases, the extent of Cr depletion in the depleted zones also increase which results in lowering of the Cr content in the depleted zones and/or increasing in the size of the zones. If the Cr content in the depleted zones is lower than a critical value, e.g. 12 at. % Cr in stainless steels, the zone will lose its corrosion resistance and to be prone to localized corrosion. Fully amorphous HT at 600 o C HT at 700 o C HT at 800 o C Y-Mo rich islands (10-200nm) Amorphous matrix Y rich amorphous constituent Nano crystalline phase Nano Cr-depleted zone (Fe, Cr) 23 C 6 (~5nm) Nanometer Cr-depleted zone (Fe, Cr) 23 C 6 (~20nm) Figure Schematic of the devitrification of SAM 1651 and the formation of nanometer Crdepleted zones. The maximum size of the Cr depleted zones, l, can be estimated by the follow equation obtained from the random-walk theory [84]: l= 2 Dt. (m) (2.3) 50

76 where D is the diffusivity of Cr (m 2 /s); and t is the growth time of the carbide (s). The value of the diffusivity for Cr in the amorphous matrix at 700 o C is not available. Therefore the diffusivity of Fe in fcc Fe at 700 o C was taken instead which is approximately m 2 /s [23, 32, 35]. According to in-situ TEM results from Nouri et al., at the heat treatment temperature of 620 o C, the carbide nucleation and growth process occurred within 30 minutes of exposure, therefore the maximum growth time was 30 minutes. Substitute the values of diffusivity and growth time into the above equation yields the maximum size of the Cr-depleted zone is l = 27nm Summary Structural and compositional change in a Fe 48 Cr 15 Mo 14 C 15 B 6 Y 2 bulk metallic glass during annealing at different temperatures near the reported crystallization temperature for different periods of time was determined. The findings are summarized as follows: 1. As-cast, 4 mm rods of SAM 1651 have a fully amorphous structure. Chemical segregation was found in the material with islands of 10 to 200 nm diameter enriched in Y, Mo and C and depleted in Fe and Cr with respect to the surrounding matrix. 2. Heat treatment in the range of 600 to 800 o C caused partial devitrification of the BMG with the formation of nanocrystalline (Cr, Fe) 23 C 6 and (Cr, Fe) 7 C 3 carbides in a matrix of remaining amorphous phase. These carbides were stable during exposure at 700 o C up to 72 hours. The devitrification process followed a primary crystallization route. The amorphous particle-free-zones (PFZ) in the partially devitrified material were found corresponding to the Y-Mo rich islands in the 51

77 fully amorphous SAM The latter indicates that the islands had higher thermal stability than the surrounding amorphous matrix. 3. In the range of 600 to 800 o C, higher annealing temperatures caused a greater extent of devitrification of SAM The size of the crystalline particles increased from less than 10 nm to ca. 21 nm. The maximum diameter of the amorphous PFZ decreased from ca. 200 nm to tens of nanometer when the annealing temperature increased from 600 to 800 o C, respectively. The volume fraction of nanocrystalline phases in specimens annealed at 700 o C for 72 hours was determined to be approximately 20 %. 4. The formation of Cr-rich carbide during devitrification caused the formation of nanometer Cr-depleted zones surrounding the carbide particles. Cr-depleted zones are more prone to corrosion and are detrimental to the corrosion performance of the alloy after heat treatment. 52

78 2.4 Corrosion behavior of partially devitrified SAM Scope Exposure of the amorphous metals to elevated temperatures either deliberately, such as during structural modification for mechanical performance improvement, or as part of processing and application, such as during thermal spray coating or plasma spray coating, can lead to devitrification of the amorphous structure. In Section 2.3 the structural and compositional changes in SAM 1651 during annealing at different temperatures near the reported crystallization temperature for different periods of time was determined. The formation of (Cr, Fe) 23 C 6 and (Cr, Fe) 7 C 3 carbides embedded in a remaining amorphous matrix was observed. A speculation of degradation in the corrosion resistance of SAM 1651 due to nano-sensitization was put forward. In this section, the effect of heat treatment on the corrosion behavior of SAM 1651 is examined. The specimens were heat treated at 600, 700 and 800 o C for 3, 3 and 1 hour, respectively, following the procedure described in Section The global corrosion behavior of both fully amorphous and partially devitrified SAM 1651 was investigated by cyclic potentiodynamic polarization and constant potential exposure experiments. The corrosion rate was measured by bulk sample immersion experiments. The corrosion of both fully amorphous and partially devitrified SAM 1651 at nano-scale was studied by TEM foils immersion experiments. More details on the specimen preparation and experiment procedures are described in Sections and The corrosion resistance of both fully amorphous and partially devitrified materials is explained in terms of chemical and structural characteristics of the alloys. 53

79 2.4.2 Results Electrochemical experiments The electrochemical behavior of the fully amorphous and partially devitrified SAM 1651 (700 o C, 3 hours) was examined by cyclic potentiodynamic polarization (CPP) and constant potential exposure experiments. All electrochemical experiments were repeated at least 3 times and the curves traced each others. Figure 2-20 shows the CPP curves of the tested materials in 1M HCl solution at room temperature. The fully amorphous SAM 1651 showed typical response for highly corrosion resistant metal, i.e. a large range of passivation up to the transpassive potential and little or no hysteresis. The partially devitrified specimen showed passive behavior on the forward scan with the passive current density, i pass, ca A/cm 2 ; however, an atypical, small hysteresis loop was observed on the reverse scan with a current density on the order of 10-3 to 10-4 A/cm 2 extending from approximately +0.9 V vs. SCE to +0.4 V vs. SCE. Typically, large hysteresis loops are observed for many stainless steels and nickel alloys. The behavior referred to here as pseudo-passivity is indicative of neither fully passive nor fully active corrosion. Corrosion potentials of the fully amorphous and the partially devitrified SAM 1651 were ca and V vs. SCE, respectively. 54

80 1M HCl, open air, RT 1mV/s Figure Cyclic potentiodynamic polarization curves of the fully amorphous and the partially devitrified SAM 1651 (700 o C, 3 hours) in open air, 1M HCl at room temperature. Figure 2-21 shows the CPP curves of the tested materials in 6M HCl solution at room temperature. The fully amorphous SAM 1651 still exhibited passivation in the forward scan with i pass approximately 4x10-5 A/cm 2, however the passive range decreased in comparison with that in 1M HCl. This material also showed a small hysteresis loop at lower potentials in the reverse scan. In contrast, the partially devitrified materials (700 o C, 3 hours) did not show typical passive behavior, rather a pseudo-passive polarization curve was observed on both forward and reverse scans. Corrosion potentials of the fully amorphous and the partially devitrified SAM 1651 were ca and V vs. SCE, respectively. Table 2-4 summarizes the characteristic parameters from the cyclic polarization curves of the tested materials in 1 and 6M HCl. 55

81 6M HCl, open air, RT 1mV/s Figure Cyclic potentiodynamic polarization curves of the fully amorphous and the partially devitrified SAM 1651 (700 o C, 3 hours) in open air, 6M HCl at room temperature. Table 2-4. Summary of the characteristic parameters from cyclic polarization curves of the fully amorphous and the partially devitrified SAM 1651 (700 o C, 3 hours) in 1 and 6M HCl. 1M HCl 6M HCl Materials OCP (V vs. SCE) i passive (A/cm 2 ) E transpassive OCP (V vs. SCE) (V vs. SCE) i passive (A/cm 2 ) E transpassive (V vs. SCE) Fully amorphous x x HT at 700 o C for 3 hrs x N/A N/A Figure 2-22 shows the typical open circuit potential (OCP) vs. time curves of the fully amorphous and the partially devitrified materials (700 o C, 3 hours) in 6M HCl at room temperature during 1 hour. The OCP of the fully amorphous material monotonically increased with time indicating the formation and thickening of passive 56

82 films. The OCP of the partially devitrified material decreased slightly at first but then increased gradually and was ca V vs. SCE after 1 hour which was comparable with the OCP of the fully amorphous material. The high OCP value without a sudden drop indicated the formation of passive films on both materials and no depassivation occurred before subsequent electrochemical tests. 6M HCl, open air, RT Figure Open circuit potential vs. time curves of the fully amorphous and the partially devitrified SAM 1651 (700 o C, 3 hours) during 1 hour in 6M HCl at room temperature. Current vs. time curves at constant potential of the fully amorphous and the partially devitrified SAM 1651 (700 o C, 3 hours) in 6M HCl at the applied potentials of and V vs. SCE are shown in Figure 2-23 and Figure 2-24, respectively. At E = V vs. SCE, the current density of the fully amorphous SAM 1651 decreased with time to approximately 6 μa/cm 2 after 3 hours of exposure (Figure 2-23). In contrast, the current 57

83 density of the partially devitrified SAM 1651 decreased during the first half hour of exposure but then increased relatively slowly with time, and the current was still rising at a fairly steady rate of 0.25 μa/cm 2 /min when the test ended at 3 hours. The current was approximately 80 μa/cm 2 after 3 hours and was one order of magnitude higher than that of the fully amorphous material at the same test condition. At E = V vs. SCE, the current density of the fully amorphous SAM 1651 stayed at a steady state value of approximately 2 ma/cm 2 after 600 s exposure (Figure 2-24). The current density of the partially devitrified SAM 1651 was decreased at first and then after approximately 30 s the current density increased relatively slowly with time to a value of 38 ma/cm 2 after 500 s exposure. E = 0.4V vs. SCE 6M HCl, open air, RT Figure Current vs. time curves of the fully amorphous and the partially devitrified SAM 1651 (700 o C, 3 hours) at the applied potential E = V vs. SCE. 58

84 E = 0.9V vs. SCE 6M HCl, open air, RT Figure Current vs. time curves of the fully amorphous and the partially devitrified SAM 1651 (700 o C, 3 hours) at the applied potential E = V vs. SCE. Current vs. time curves at constant potential of the fully amorphous and the partially devitrified SAM 1651 (600, 700 and 800 o C for 3, 3 and 1 hour, respectively) in 6M HCl at the applied potential of V vs. SCE are shown in Figure The current density of the fully amorphous SAM 1651 decreased with time to ca ma/cm 2 after 60 minutes of exposure. In contrast, the current densities of the devitrified SAM 1651 specimens decreased during the first few minutes of exposure but then increased with time. The current increasing rates were higher for specimens heat treated at higher temperature. The current densities after 60 minutes exposure for specimens heat treated at 600, 700 and 800 o C were approximately 0.12, 0.83 and 5.29 ma/cm 2, respectively, and 59

85 were ca. 2 to 80 times higher than that of the fully amorphous material at the same test condition. 6 4 As-received 600 o C/180 min 700 o C/180 min 800 o C/60 min 6M HCl, RT E=+0.60 V vs. SCE i (ma/cm 2 ) time (min) Figure Current vs. time curves of the fully amorphous and the partially devitrified SAM 1651 after heat treatment at 600, 700 and 800 o C at an applied potential E = V vs. SCE in 6M HCl TEM foil immersion Results of TEM foil immersion experiments are shown in Figure 2-26 and Figure After 5 hours of exposure, no significant dissolution was observed for either the fully amorphous or the partially devitrified SAM 1651 (700 o C, 3 hours). After 30 hours of exposure, holes in TEM foils were observed in both specimens indicating significant selective dissolution. After 60 hours of exposure, the extent of dissolution in the fully amorphous TEM foil, represented by the number and the size of the holes, did not 60

86 increase; whereas the extent of the dissolution in the partially devitrified specimen was intensified. 5hrs 30hrs 60hrs Y-Mo rich island 0.5μm Hole at Y-Mo rich island Figure BF-TEM micrographs of the as-received SAM 1651 after immersion in 6M HCl for different periods of time. 5hrs 30hrs 60hrs Y-Mo rich PFZs 0.5μm Hole at Y-Mo PFZs Figure BF-TEM micrographs of the partially devitrified SAM 1651 (700 o C, 3 hours) after immersion in 6M HCl for different periods of time. The composition of the material around the edges of the holes in the TEM foils after immersion was examined with EDS. Figure 2-28 shows the STEM images of the fully amorphous and the partially devitrified SAM 1651 specimens after 60 hours immersion in 6M HCl with the representative locations where the EDS analysis was conducted. Figure 2-29 shows the EDS spectra at the edges of the holes and in the matrix in both fully amorphous and partially devitrified TEM specimens. The EDS spectra at Location 1 and Location 3 show higher intensities for Y and Mo and lower intensities for Fe and Cr with respect to those at Location 2 and Location 5. However, the EDS spectrum at Location 4 was similar to that at Location 5. It has been shown in Section 2.3 that there were islands of Y-Mo rich in the fully amorphous material and Y-Mo rich PFZ in the 61

87 partially devitrified SAM Therefore, the existence of the holes in these Y-Mo rich constituents indicates that these constituents were partially dissolved during the immersion tests. In addition to the holes at the Y-Mo rich PFZ in the partially devitrified SAM 1651, the small hole at Location 4 with similar composition with the matrix indicates that holes were formed in the matrix of the partially devitrified SAM Holes with similar size as the one at Location 4 were observed scattering in the partially devitrified specimen while none of them was observed in the fully amorphous SAM These holes can also be seen in the BF-TEM micrographs of the partially devitrified SAM 1651 as shown in Figure 2-27 forming the lacy morphology in the specimen after 60 hour immersion in 6M HCl. Location 1 Location 2 Location 4 Location 3 a b Location 5 Figure STEM images of TEM specimens after 60 hours immersion in 6M HCl showing the locations of EDS analysis; (a) Location 1 at the edge of a hole and Location 2 in the matrix of the fully amorphous SAM 1651; and (b) Location 3 and Location 4 at the edge of a hole and Location 5 in the matrix of the partially devitrified SAM 1651 (700 o C, 3 hours). 62

88 Spectrum at Location 1 Spectrum at Location 2 Spectrum at Location 3 Spectrum at Location 4 Spectrum at Location 5 Figure EDS analysis conducted at the locations shown in Figure

89 2.4.3 Discussion Effect of acid concentration and heat treatment on corrosion behavior Cyclic polarization curves in Figure 2-20 and Figure 2-21 showed a detrimental effect of heat treatment on the corrosion resistance of SAM The anodic polarization curves of the partially devitrified SAM 1651 (700 o C, 3 hours) shifted to higher current density indicating an increase in corrosion rate. For comparison, at a potential of V vs. SCE, current densities of the fully amorphous SAM 1651 in 1 and 6M HCl solutions were on the order of 10-5 A/cm 2, while current densities of the partially devitrified SAM 1651 (700 o C, 3 hours) in 1 and 6M HCl solutions were on the order of 10-4 A/cm 2. In 1M HCl where both materials exhibited spontaneous passivation behavior, a larger hysteresis loop in the CPP curves of the partially devitrified SAM 1651 in comparison with the fully amorphous alloy indicated that the partially devitrified SAM 1651 (700 o C, 3 hours) was more susceptible to localized corrosion than the fully amorphous material. In 6M HCl, while fully amorphous SAM 1651 still showed passive behavior, the partially devitrified material exhibited pseudo-passive behavior. In 6M HCl solution, at an applied potential of E = V vs. SCE, which is in the passive range of the fully amorphous SAM 1651, the anodic current density of the fully amorphous SAM 1651 decreased gradually to a steady state current density of approximately 6 μa/cm 2 after 3 hours. In contrast, in the same 6M HCl solution and at the same applied potential of E = V vs. SCE, the anodic current density of the partially devitrified SAM 1651 (700 o C, 3 hours) decreased during the first half hour of exposure but then increased with time to approximately 80 μa/cm 2 after 3 hours, i.e. one order of magnitude higher than that of the fully amorphous material. In 6M HCl solution, 64

90 at an applied potential of E = V vs. SCE, corrosion current densities of the fully amorphous and devitrified materials after 10 minutes were approximately 2 and 38 ma/cm 2 respectively, and again the current density of the partially devitrified SAM 1651 (700 o C, 3 hours) was one order higher than that of the fully amorphous material. Table 2-5 summarizes the current densities at the potentials of E = and V vs. SCE taken from CPP and constant potential exposure experiments and the corrosion rate calculated from the weight loss experiments in 6M HCl. The equivalent corrosion rates of the tested materials in the electrochemical tests were calculated from Faraday s law with the assumption that general corrosion occurred. This assumption is valid because no localized corrosion was observed on the specimen surfaces after electrochemical tests. The difference in the mass of specimens before and after immersion in 6M HCl was beyond the resolution of the balance which was 0.1 mg. Table 2-5 shows that despite the fact that heat treatment had adverse effect on the corrosion resistance of SAM 1651, the partially devitrified material (700 o C, 3 hours) still possessed good corrosion resistance even in highly aggressive environment of concentrated hydrochloric acid. Table 2-5. Summary of the current densities from CPP and constant potential exposure experiments in 6M HCl and the corrosion rates calculated from the CPP, constant potential exposure and weight loss experiments. Material Fully amorphous Devitrified (700 o C, 3 hrs) Experiment CPP Const. Pot. Immersion CPP Const. Pot. Immersion E (V vs. SCE) i (A/cm 2 ) 3x10-5 9x10-4 6x10-6 2x10-3 8x x10-3 8x x10-3 Corrosion rate (mm/year) < <

91 The dependence of the corrosion behavior on the heat treatment temperature can be seen from Figure After 1 hour in 6 M HCl at the applied potential of V vs. SCE, the corrosion current densities of the partially devitrified SAM 1651 increased from 0.12 to 0.83 and to 5.29 ma/cm 2 with the increase in the heat treatment temperature from 600 to 700 and to 800 o C, respectively. It appears that increasing the heat treatment temperature increased the corrosion rate of the partially devitrified SAM More details analysis on the effect of heat treatment temperature on the corrosion behavior of SAM 1651 is reported in a master thesis by a colleague in our group [77]. The thesis also shows that increasing the holding time at 700 o C from 3 hours to 120 hours did not cause significant effect on the corrosion resistance of the partially devitrified material [77] Material characteristics and corrosion behavior The difference in the structure and composition between the as-received, fully amorphous and the partially devitrified SAM 1651 has been discussed in Section 2.3. The macroscopic corrosion behavior of the fully amorphous and partially devitrified SAM 1651 has been investigated and it has been shown that heat treatment had detrimental effect on the corrosion resistance of SAM In this section the corrosion behavior of SAM 1651 is discussed based on the knowledge of the chemistry and structure of the tested materials. The dissolution pattern of the fully amorphous SAM 1651 TEM specimen in 6M HCl (Figure 2-26) demonstrated the exceptionally high corrosion resistance of this material and especially the resistance to localized corrosion. During the first 30 hours of immersion, a preferential dissolution process occurred in the material. The location of the corroded sites was at the Y-Mo-rich islands. An extended immersion period up to 60 66

92 hours did not cause enlargement of the holes in the TEM specimen. From the observation of the dissolution pattern in the fully amorphous SAM 1651, two points are made. Firstly, the observation indicates that chemical heterogeneities in the fully amorphous structure of SAM 1651 facilitated a preferential corrosion process. Heterogeneous structure has an adverse effect on the corrosion resistance in highly concentrated acid. Secondly, the arrest in the growth of the holes observed in TEM micrographs after 30 hours of exposure shows that the dissolution of these corrosion-prone islands does not lead to the corrosion of the surrounding material. The passivation at the edge of the holes in the TEM foil indicates the high corrosion resistance of the matrix material, and this behavior can be mainly attributed to the high content of beneficial elements such as Cr and Mo in the amorphous matrix. The role of Cr in the formation of passive films on Fe-based amorphous metals in HCl solution is discussed in a number of papers by Hashimoto, Pang et al., Tan et al. and Asami et al. [1, 88-93]. These authors concludes that the formation of passive chromium oxyhydroxide (CrO x [OH] 3-2x.nH 2 O) films is responsible for the corrosion resistance of the alloys [1, 88, 89]. It is reported that the addition of Mo facilitates the formation of the passive chromium oxyhydroxide by the formation of a passive tetravalent molybdenum oxide film in the potential regions where Cr actively dissolves, and this suppresses the active dissolution of Cr in these potential ranges [90-93]. Thereby a sufficiently high concentration of Mo in the alloys is necessary for the spontaneous passivation and strong repassivation ability. The dissolution pattern of the partially devitrified SAM 1651 TEM specimen for 60 hours in 6M HCl shows a lacy morphology (Figure 2-27) indicating a degradation in the corrosion resistance of the partially devitrified material in comparison with the fully 67

93 amorphous SAM Similar to the Y-Mo-rich islands in the fully amorphous material, the Y-Mo-rich PFZ in the partially devitrified SAM 1651 was also preferentially corroded. However, the dissolution was not constrained at the PFZ but also occurred in the remaining amorphous matrix. The preferential dissolution of Y-Mo-rich phases is possibly due to the effect of Cr, Mo and Y on the corrosion behavior. The existence of more Mo and less Cr in these phases in comparison with the matrix, as discussed in Section 2.3, results in a less protective passive film which is rich in tetravalent Mo oxide and less in chromium oxyhydroxide [93]. Doping with Y in the passive film effects the thickness and the composition of the film, especially the concentration of high valence Cr and Mo cations, and this effect depends on the Y-doping level [94]. The degradation in the corrosion resistance of the remaining amorphous matrix in the partially devitrified SAM 1651 resulted from the precipitation of nanocrystalline carbide particles. The formation of (Cr, Fe) 23 C 6 and (Cr, Fe) 7 C 3 carbides, probably under diffusion-controlled growth, is likely to cause Cr concentration gradients in the amorphous matrix, i.e. nano-sensitization as mentioned earlier. At the carbide/matrix interfaces, Cr depleted zones on the nanometer scale can be formed, and the depleted zones are prone to corrosion. Note that with increasing temperature, the size of the carbide particles increased and so did the size of the Cr-depleted zone. Therefore a decrease in the corrosion resistance of the partially devitrified materials with increased heat treatment temperature was observed as shown in constant potential exposure experiments (Figure 2-25). Sensitization process is a well known phenomenon on the microscopic scale for conventional stainless steels [30, 31], and similar phenomenon is 68

94 observed here on the nano-scale. Another contribution is that the passive film formed on the remaining amorphous phase is interrupted at the carbide phase and again corrosion can initiate at these weak locations in the passive film. The former theory, i.e. the formation of Cr depleted zones surrounding carbide particles, is deemed to be the primary cause of the preferential attack Summary In this section, the effect of heat treatment on the corrosion behavior of Fe-based bulk metallic glass SAM 1651 was investigated. Corrosion resistance of the fully amorphous and partially devitrified materials was explained in terms of chemical and structural characteristics of the alloys. The following conclusions could be drawn. 1. In 1M HCl, both the fully amorphous and partially devitrified SAM 1651 exhibited spontaneous passivation on the forward scan. The fully amorphous SAM 1651 repassivated rapidly on the reverse scan while the partially devitrified material exhibited pseudo-passivation behavior. 2. In 6M HCl, the fully amorphous SAM 1651 still exhibited spontaneous passivation, however the passive range decreased in comparison with that in 1M HCl. In contrast, the partially devitrified SAM 1651 showed a pseudo-passive polarization curve. 3. Heat treatment at 700 o C for 3 hours followed by furnace cooling caused the devitrification of SAM 1651 and the degradation in the corrosion resistance. However, the devitrified material still exhibited good corrosion resistance even in the highly aggressive environments of 6M HCl. 69

95 4. Heat treatment temperature had strong effect on the corrosion behavior of the partially devitrified SAM Increasing the heat treatment temperature from 600 o C to 800 o C decreased the corrosion resistance of the materials. 5. Compositional heterogeneities in the structure affected the corrosion behavior of the material. Preferential dissolutions occurred in the less corrosion resistant phase, i.e. Y-Mo-rich islands, Y-Mo-rich PFZ and nanometer Cr-depleted zones. Devitrification compromised the corrosion resistance of SAM 1651 via the precipitation of Cr-rich carbide nanoparticles. The carbide precipitation resulted in nanoscale Cr-depleted zones, i.e. nano-sensitization. The formation of more defects at the carbide/metal interphases could also be a contributing factor. 70

96 2.5 Formation of pseudo-passive film on partially devitrified SAM Scope In Section 2.4 it has been shown that the partially devitrified SAM 1651 exhibits pseudo-passive behavior during cyclic potentiodynamic polarization experiments in 6M HCl. In constant potential exposure experiments, the current decreased at first which indicated the formation of a protective passive film, but then the current gradually increased. This atypical behavior was attributed to the formation of a pseudo-passive layer on the specimens. In this section, the growth of the pseudo-passive film on the partially devitrified SAM 1651 is investigated. The partially devitrified SAM 1651 material was prepared by heat treatment of the fully amorphous material at 700 o C for 3 hours following the procedure described in Section The pseudo-passive films were developed by constant potential exposure of the partially devitrified specimen at +0.4 V vs. SCE in 6M HCl for different periods of time. The growth rate of the films was obtained by measuring the thickness of the films with SEM after FIB cross-sectioning. The structure and composition of the films was examined with TEM. The specimens for TEM were prepared by FIB method as described in Section The electronic properties of the pseudo-passive films were studied with EIS. More details on the procedure to conduct the constant potential exposure experiment, FIB, TEM and EIS are described in Section

97 2.5.2 Results Growth rate of the film The growth of the film was conducted in 6M HCl at a constant potential of V vs. SCE. Figure 2-30 shows a representative anodic current monitored during the constant potential polarization. The curve can be divided into 3 regions: (i) in region 1 (the first 10 minutes) the current exhibited a decrease to less than 0.01 ma; (ii) in region 2 (the next 6 hours) the current increased rapidly to ca ma/cm 2 ; and (iii) in region 3 (after 6 hours) the current increased with slower rate and then stayed at a relatively constant value of ca ma. This current response during the anodic polarization is different from that of the typical passive behavior in which the current monotonically decreases with the polarization time due to the growth of the passive film. The thickness of the film was measured with SEM after cross sectioning with FIB. Figure 2-31 shows the dependence of the film thickness on the polarization time. The total thickness increased with the anodic polarization time indicated the growth of the film. The thickness of the film after 5 hour polarization was approximately 250 nm. The film thickness continuously increased during further exposure time to a thickness of approximately 800 nm after 30 hours. On the specimen after 15 hour polarization, a film with a bi-layer structure was observed. Up on longer polarization time, both the newly formed outer layer and the inner layer grew with time. To confirm the formation of this film was not due to the accumulation of contaminant from epoxy, an unmounted specimen was exposed to the same condition. The specimen surface was then sectioned with FIB which revealed a film of similar structures as those on the epoxy mounted specimens. 72

98 Region 1 6M HCl, room temperature E = V vs. SCE Region 2 Region 3 I (ma) Time (min) Figure Current density vs. time curve during constant potential exposure experiments at E = V vs. SCE in 6M HCl Total film thickness Inner layer thickness Outer layer thickness Thickness (nm) Time (hrs) Figure Film thickness vs. polarization time curves during constant potential exposure experiments at E = V vs. SCE in 6M HCl 73

99 Structure of the film The bright field-tem (BF-TEM) micrographs of the cross section of the films after polarization in 6M HCl for 5, 15 and 30 hours are shown in Figure 2-32, Figure 2-33 and Figure 2-34, respectively. Palladium and platinum coating layers were observed in all pictures and were confirmed by EDS analysis indicating these layers were able to protect the pseudo-passive film underneath during ion milling with FIB. The film after 5-hour polarization showed a porous nanostructure (Figure 2-32). The light contrast regions in the BF-TEM micrograph (Figure 2-32a) were the location of pores. The film and the substrate did not have a well defined interface (Figure 2-32b) indicating the strong bonding of the film to the substrate. This is consistent with the observation that the film could not be removed completely by rubbing the surface with a sponge or an eraser. At 15-hour polarization, the film developed a bi-layer structure with an outer dense layer and an inner porous layer (Figure 2-33). Compared to the film after 5-hour polarization, the inner layer of the film after 15-hour polarization was thicker and more porous. After 30- hour polarization, no significant change in the film structure except the thickening of both the outer and the inner layers (Figure 2-34). The inner layer of the 30-hour growth film was more porous than the 15-hour growth one. The BF-TEM micrographs of the inner and the outer layers at higher magnification are shown in Figure The inner layer was porous with channels running through the layer into the substrate (Figure 2-35a). In the outer layer, all channels were filled up with some substances forming a dense layer on top of the porous nano-structure inner layer (Figure 2-35b). Large pores were also observed at the transition region between the inner and the outer layers suggesting a weak bonding between the 2 layers. 74

100 BF-TEM STEM Pd coating Pt Pd coating Pt Porous film Porous film substrate substrate a 100nm b Figure TEM micrographs of the pseudo-passive film after 5-hour polarization in 6M HCl at the constant potential of V vs. SCE; a) BF-TEM; and b) STEM. BF-TEM STEM Pt Pd outer layer Inner layer a substrate b Figure TEM micrographs of the pseudo-passive film after 15-hour polarization in 6M HCl at the constant potential of V vs. SCE; a) BF-TEM; and b) STEM. BF-TEM STEM Pt Pd outer layer Inner layer a substrate b Figure TEM micrographs of the pseudo-passive film after 30-hour polarization in 6M HCl at the constant potential of V vs. SCE; a) BF-TEM; and b) STEM. 75

101 Inner layer Outer layer substrate pores a Pd Pt b Figure BF-TEM micrographs of the pseudo-passive film after 30-hour polarization in 6M HCl at the constant potential of V vs. SCE; a) the inner porous layer; and b) the outer dense layer. Selected area electron diffraction (SAED) patterns of the substrate, inner and outer layers taken from a specimen polarized for 30 hours are shown in Figure The electron diffraction (ED) pattern of the substrate is typical for the partially devitrified structure of SAM 1651 in which the ED spots from nanocrystalline particles form rings rather than ordered spot patterns [23, 95]. The ED from the inner and outer layers with spots indicates some degree of crystallinity of these layers. In addition, all rings of ED patterns from the inner and outer layers overlapped with the rings of the ED pattern from the substrate suggesting the crystalline phases in the film were similar to those in the substrate. a b c Figure Selected area electron diffraction patterns taken from a specimen after 30-hour polarization in 6M HCl at the constant potential of V vs. SCE; a) substrate; b) inner layer; and c) outer layer. 76

102 Chemical composition of the film The composition of the inner layer was examined with EDS. The composition profiles of the film after 5, 15 and 30-hour polarization are shown in Figure 2-37, Figure 2-38 and Figure 2-39, respectively. In all specimens, the ratio of Fe:Cr:Mo:Y measured at the substrate was closed to the composition of SAM The composition across the inner layer was relatively uniform. In comparison with the substrate, the inner layer had a higher content of C and lower content of Fe, Cr and Mo. In addition, a significant amount of O was also detected in this layer. The composition of the outer layer was also examined with EDS. The dark contrast phases in Figure 2-35b had similar composition as the composition of the inner layer. However, the composition of the bright contrast phases in Figure 2-35b was mostly comprised of C and O with only a small amount of metallic elements. Table 2-6 summarizes the EDS analysis of both inner and outer layer of the film after polarization at V vs. SCE in 6M HCl for 5, 15 and 30 hours. 77

103 Table 2-6. Composition of the films in atomic percentage after polarization at V vs. SCE in 6M HCl for different periods of time. Elements (at.%) Fe Cr Mo C O Cl Porous film after 5-hour polarization 21 ± 2 8 ± 1 5 ± 1 53 ± 5 13 ± 4 <<1 Inner layer after 15-hour polarization 30 ± 6 13 ± 1 7 ± 1 27 ± 5 23 ± 4 <<1 Inner layer after 30-hour polarization 23 ± 4 10 ± 2 7 ± 2 35 ± 5 25 ± 4 <<1 Dark phase in the outer layer 15 ± 4 12 ± 2 5 ± 1 49 ± 8 16 ± 2 2 ± 1 Bright phase in the outer layer 4 ± 3 4 ± 2 2 ± 1 70 ± 9 15 ± 4 3 ± Fe Cr Mo Y C O Cl at. % distance from substrate (nm) Figure Quantitative EDS analysis showing composition of the film after 5 hour polarization in 6M HCl at E = +0.4V vs. SCE. 78

104 Fe Cr Mo Y C O Cl at. % distance from substrate (nm) Figure Quantitative EDS analysis showing composition of the film after 15-hour polarization in 6M HCl at E = +0.4V vs. SCE Fe Cr Mo Y C O Cl at. % distance from substrate (nm) Figure Quantitative EDS analysis showing composition of the film after 30-hour polarization in 6M HCl at E = +0.4V vs. SCE Electrochemical impedance of the film The electronic properties of the film during polarization in 6M HCl were examined with EIS. Figure 2-40 shows Bode plot of the EIS data of the film polarized for 0.5, 2, 5, 15, 25 and 30 hours at V vs. SCE in 6M HCl. The spectra of the films polarized for 79

105 0.5, 2 and 5 hours indicate capacitive response in the frequency range of 10-1 to 10 3 Hz which is attributed to the passive behavior of the film. During the first 5-hour polarization, as exposure time increased, the minima of the phase angle shifted to the lower frequency region indicating an increase in the capacitance of the film. The spectra of the film polarized for 15, 25 and 30 hours showing 2 minima in the Bode phase angle plot (Figure 2-40) is coincident with the formation of the outer layer in the film. 80

106 hrs log (/Z/ / Ω cm 2 ) hrs 5 hrs 15 hrs 25 hrs 30 hrs a log (f / Hz) 0 Phase angle (Degree) b log (f / Hz) Figure Bode plot obtained from EIS experiments of the films during polarization at V vs. SCE in 6M HCl for different period of times; a) dependence of impedance with frequency; and b) dependence of phase angle with frequency. 81

107 2.5.3 Discussion Characterization of the pseudo-passive film The EIS spectrum of the film grown in 6M HCl at V vs. SCE showing capacitive behavior in the frequency range from 10-1 to 10 3 Hz (Figure 2-40) confirms the passive characteristic of this film which was discussed in Section 2.4. Thick porous films with passive behavior was reported to be formed on a numbers of alloys such as stainless steels under square wave potential pulse polarization in 5M H 2 SO 4 [96, 97] or Fe-Cr-P microcrystalline alloy immersed in 9M H 2 SO 4 [98]. The structure of the film in this study changed with polarization time from a single layer to a bi-layer with the present of an outer dense layer on top of the inner porous layer. The thickness of both inner layer and outer layer of the bi-layer film increased as the film grew. The film grew to a total thickness of approximately 800 nm with an outer layer of approximately 200 nm after 30-hour anodic polarization (Figure 2-31). This film was much thicker than the typical passive film formed on stainless steels and other passive metals with thickness of few nanometers. The existence of a significant amount of O in the film suggests that it was comprised of oxide or hydroxide. The overlapping between ED rings of the inner layer, the outer layer and the substrate suggests the film contained nanocrystalline (Cr, Fe) 23 C 6 particles. The film was defective with the existence of nano-pores. An enrichment of C in the film was observed during the anodic dissolution of the substrate. The accumulation of C resulted in the formation of the outer dense layer observed in TEM micrographs at 15 and 30-hour polarization (Figure 2-33 and Figure 2-34). 82

108 Formation of the pseudo-passive film Pseudo-passive films formed on the partially devitrified SAM 1651 in 6M HCl followed different mechanism with that of a typical passive film. At an applied potential of V vs. SCE, the pseudo-passive film thickness was on the order of few hundred nanometers and the electric field strength in the film can be estimated on the order of 10 2 V/cm which is much smaller than the electric field strength of 10 6 V/cm established in a typical passive film. The growth rate of the pseudo-passive film was closed to linear relationship which is faster than the logarithmic or inverse logarithmic law observed for a typical passive film. The anodic current density during the pseudo-passive film growth at a constant potential increased (Figure 2-30) rather than decayed exponentially with time as a typical passive film did. A hypothesis for the formation of the pseudo-passive film on the partially devitrified SAM 1651 is present in Figure A similar hypothesis for the formation of a thick corrosion product layer on a Fe-Cr-P microcrystalline alloy in concentrated sulfuric acid has been proposed [98]. The structure of the partially devitrified material was comprised of nanocrystalline carbide particles dispersed in a matrix of remaining amorphous metallic glass. During the anodic polarization, the Y-Mo-rich PFZ and the amorphous matrix was dissolved following preferential paths due to chemical heterogeneities and nano-sensitization as discussed in Section 2.4. These corrosion paths may penetrate deep in to the substrate leaving a porous structure behind. The remaining amorphous matrix in the porous structure that was not dissolved was able to form oxide/hydroxide passive film. Continuous penetration of the preferential dissolution paths in to the substrate caused the thickening of the porous film. Further dissolution of the remaining amorphous 83

109 material in the porous film increased the extent of porosity. The dissolution of the amorphous material also released a large amount of carbon that accumulated in the film. When the solubility of carbon in the electrolyte is reached, the carbon formed a continuous solid phase that filled all the pores and created the outer dense layer. The carbon filled outer layer grew as dissolution proceeded. Carbide Amorphous matrix Preferential dissolution paths Carbon Carbide Metallic glass Figure Hypothesis for the formation and growth of the pseudo-passive films Summary The formation of a thick film with pseudo-passive behavior on a partially devitrified bulk metallic glass SAM 1651 was studied. Characterization of the film was performed and a hypothesis for the film formation was proposed. The conclusions can be summarized as follows: 1. The structure of the pseudo-passive films changed with growth time from a single porous layer to a bi-layer with an outer dense layer on top of the porous inner layer. 2. The pseudo-passive film was formed following approximately linear growth rate during 30 hour polarization and reached a total thickness of approximately 1 μm. 84

110 3. Nanocrystalline carbide particles were found in both inner porous layer and outer dense layer. Carbon formed a continuous solid phase in the dense outer layer. 4. A hypothesis for the formation and growth of the inner nano-porous layer from the preferential dissolution of the partially devitrified material was proposed. Accumulation of dissolved carbon filled the pores of the porous structure and formed the outer dense layer. 85

111 2.6. Conclusion The effect of heat treatment on the properties of a Fe 48 Cr 15 Mo 14 Y 2 C 15 B 6 bulk metallic glass (SAM 1651) was studied. It has been shown that exposure of the material to the temperatures in the range of 600 to 800 o C caused partial devitrification of the amorphous structure. The structural and compositional changes in the partially devitrified material with respect to the fully amorphous material had adverse effect on the corrosion resistance of the alloy. A pseudo-passive film was found to be formed on the partially devitrified material instead of a typical passive film as found on the fully amorphous one. The effect of heat treatment on the properties of SAM 1651 can be summarized as follows: Structural and compositional effects: 1. Heat treatment in the range of 600 to 800 o C caused partial devitrification of the BMG with the formation of nanocrystalline (Cr, Fe) 23 C 6 and (Cr, Fe) 7 C 3 carbides embedded in a matrix of remaining amorphous phase. These carbides were stable during exposure at 700 o C up to 72 hours. The devitrification process followed a primary crystallization route. 2. The heterogeneous Y-Mo-rich islands in the fully amorphous material had higher thermal stability than the surrounding matrix, and the crystallization was more difficult to occur in these islands during heat treatment. After heat treatment, the Y-Mo-rich islands formed the so called amorphous particle-freezones (PFZ) in the partially devitrified material. 3. In the range of 600 to 800 o C, higher annealing temperatures caused a greater extent of devitrification of SAM The size of the crystalline particles 86

112 increased from less than 10 nm to ca. 21 nm. The maximum diameter of the amorphous PFZ decreased from ca. 200 nm to tens of nm when the annealing temperature increased from 600 to 800 o C, respectively. The volume fraction of nanocrystalline phases in specimens annealed at 700 o C for 72 hours was determined to be approximately 20 %. 4. The formation of Cr-rich carbide during devitrification caused formation of nanometer Cr-depleted zones surrounding the carbide particles. Cr-depleted zones are more prone to corrosion and are detrimental to the corrosion performance of the alloy after heat treatment. Electrochemical effects: 1. In 1M HCl, both the fully amorphous and partially devitrified SAM 1651 exhibited spontaneous passivation on the forward scan. The fully amorphous SAM 1651 repassivated rapidly on the reverse scan while the partially devitrified material exhibited pseudo-passivation behavior. 2. In 6M HCl, the fully amorphous SAM 1651 still exhibited spontaneous passivation, however the passive range decreased in comparison with that in 1M HCl. In contrast, the partially devitrified SAM 1651 showed a pseudo-passive polarization curve. 3. Heat treatment at 700 o C for 3 hours caused the devitrification of SAM 1651 and the degradation in the corrosion resistance. However, the devitrified material still exhibited good corrosion resistance even in the highly aggressive environments of 6M HCl. 87

113 4. Heat treatment temperature had strong effect on the corrosion behavior of the partially devitrified SAM Increasing the heat treatment temperature from 600 o C to 800 o C decreased the corrosion resistance of the materials. 5. Compositional heterogeneities in the structure affected the corrosion behavior of the material. Preferential dissolutions occurred in the less corrosion resistant phase, i.e. Y-Mo-rich islands, Y-Mo-rich PFZ and nanometer Cr-depleted zones. 6. The structure of the pseudo-passive films changed with growth time from a single porous layer to a bi-layer with an outer dense layer on top of the porous inner layer. 7. The pseudo-passive film was formed following approximately linear growth rate during 30 hour polarization and reached a total thickness of approximately 1 μm. 8. Nanocrystalline carbide particles were found in both inner porous layer and outer dense layer. Carbon formed a continuous solid phase in the dense outer layer. 9. During constant potential exposure experiments, the resistance of the outer dense layer increased and the capacitance of the outer dense layer decreased. The formation of the outer dense layer helped limiting the dissolution rate. 10. A hypothesis for the formation and growth of the inner nano-porous layer from the preferential dissolution of the partially devitrified material was proposed. Accumulation of dissolved carbon filled the pores of the porous structure and formed the outer dense layer. 88

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121 Chapter 3 CORROSION OF SILVER-CORED MP35N LT COMPOSITE 3.1 Background Networked Neuroprosthetic System (NNPS) Neuroprostheses significantly enhance the independence of people with disabilities by restoring movements and functions. For example, neuroprosthetic devices that electrically stimulate nerves and muscles restore movement ability of extremity for individuals suffering cord injuries or strokes [1-5]. Implantable neuroprosthetic devices can also provide functional enhancements for internal organs such as bladder or bowel [6-8]. Current implanted neuroprosthetic systems utilize considerable external power and signal processing, and each system is tailored to the specific application for which it was intended. The Networked Neuroprosthetic System (NNPS) design is based on a network of small implanted modules, distributed throughout the body [9, 10]. Figure 3-1 shows a schematic of a NNPS. The system is comprised of four basic components including (i) an Access Port that provides power and a transcutaneous link for programming; (ii) Actuator Modules such as muscle-based or nerve-based stimulators; (iii) Sensor Modules such as myoelectric signal sensors; and (iv) one or more Networked Segment Cables for power and communication transmission [10]. The Access Port contains a rechargeable battery that provides the power for the system and can be recharged via a central transcutaneous inductive link. The Actuator and Sensor Modules contain their own processing capability and can be programmed through a bidirectional transcutaneous link. The Access Port and the Modules are connected to the network 96

122 through multi-conductor leads that distribute power and transmits data between modules [10]. The novel design of the NNPS eliminates external components during functional activities and is flexible for a large range of neuroprosthetic applications. Figure 3-1. Schematics of the Networked Neuroprosthetic System Silver-cored MP35N LT composite for the networked segment cables Silver-cored MP35N LT composite with a MP35N LT outer tube and a silver core is the material of choice for the networked cables of the NNPS [11]. The alloy MP35N LT, a Co-based alloy with a nominal composition of 35%Co-35%Ni-20%Cr-10%Mo in weight percent, provides the strength and corrosion resistance for the composite while the silver core provides a high conductivity for the power distribution and data transmission in the NNPS. Figure 3-2 shows a cross section of a composite single wire. Multiple 97

123 composite wires of 58 μm diameter are twisted to form conductors. The conductors are coated with biocompatible materials such as perfluoroalkoxy (PFA) to provide insulation between the individual conductors. The network cables are comprised of multiple conductors which are helically coiled and encapsulated in silicone tubes. A schematic of the cross section showing the configuration of the network cable is presented in Figure 3-3. Epoxy Ag core MP35N LT outer tube Figure 3-2. SEM micrograph showing a cross section of a composite single wire. Silicone tube Perfluoroalkoxy (PFA) coating Silver-cored MP35N LT composite Figure 3-3. Schematic of a cross section showing the configuration of the network cable. The conductors are helically coiled. 98

124 In the nominal condition, the network cables of the NNPS are intact and the silver cores of the composite are isolated from the in vivo environment by the silicone tubes, the polymeric coatings on the conductors and the Co-based alloy outer tube of the individual wires. In the event of mechanical failure of the cables [11, 12], the silver cores of some wires may be exposed to the in vivo environment which is a corrosive environment containing chloride ions and oxygen Human body as a corrosive environment Biological environment is remarkably aggressive, resembling tropical marine conditions [13]. It contains variety of highly active chemicals including chloride and oxygen. Human body blood contains typically 0.14M Cl - anions. The content of oxygen is relatively rich in arteries (ca. 100 mmhg) and veins (ca. 40 mmhg) and is lower in interstitial regions between muscles (from 2 to 40 mmhg). In normal conditions, the ph at the tissue locations varies in a narrow range around neutral condition, from slightly acidic (i.e. ph 6.8) in the intracellular to neutral (i.e. ph 7.0) in interstitial regions to slightly alkaline (i.e. ph 7.35) in blood. However, the ph of fluids may be highly acidic such as in gastric contents (ph 1) or in urine (ph 4.5 to 6.0). The temperature of a normal body varies from 28 o C at skin to 37 o C in the core regions [13]. To simulate in vivo conditions, a numbers of in vitro environments are used which can be categorized in to four classes [13]: (i) Physiological: the environment in which inorganic chemicals compositions and temperature is controlled at normative mammalian values for the intended 99

125 application. For example, Ringer s solution of 9.0 g/l NaCl, 0.43 g/l KCl, 0.24 g/l CaCl 2 and 0.20 g/l NaHCO 3 at 37 ± 1 o C is used to simulate blood. (ii) Biophysiological: modification of the physiological environments in which active cell products such as serum proteins or enzymes are added. (iii) Biological: modification of the biophysiological environments in which appropriate, viable, active cells are added. (iv) Pericellular (circumcellular): the environments in the immediate vicinity of appropriate, viable, active cells. Despite the variety in chemistry, ph and temperature of in vivo conditions, the parameters at a specific location is well controlled. Deviation from the default conditions, e.g. due to the dissolution of metals from implanted devices, will cause response from the host body such as coagulation, inflammation and immune reactions Toxicology of silver and silver compounds The toxicology of silver and silver compounds for humans and animals was reported ranging from minor effect such as skin discoloring to severe dysfunction or fatal [14-19]. Silver cation is a physicochemical mimic of Na + and can enter the ion transporting cell via apical sodium channels [15]. Inside the cell, silver ions disrupt the ionoregulatory enzymes that drive epithelial sodium transport. The inhibition of this pathway by silver can be fatal [18]. In other studies, either silver or silver chloride stimulated the smooth muscle of isolated cannulated hamster cheek pouch arterioles, producing marked vasoconstriction. The vessels then dilated back to control diameter but became refractory to norepinephrine or potassium stimulation [19]. Silver compounds were also reported to cause discoloring of skin and other body tissues, a condition called argyria. 100

126 3.1.5 Corrosion of silver and formation of AgCl in chloride environments The oxidation of silver in chloride containing solutions resulting in the formation of silver chloride films on the silver substrates has been reported [20-30]. The following reaction has been proposed by a numbers of authors [25, 26]: Ag + Cl - = AgCl + e - (3.1) in which the deposition of solid AgCl takes place at a potential near the thermodynamic reversible potential for the Ag/AgCl electrode in Cl - system. The Ag/AgCl reversible potential is dependent on the concentration of Cl - and follows Nernstian behavior [25, 26]: E = log [Cl - ] (V vs. SCE) (3.2) The growth of silver chlorides on silver substrates in chloride environments has been studied for long time due to the wide use of Ag/AgCl electrode in laboratories as secondary reference electrode [31, 32]. Recently Ag/AgCl electrodes find application in sea water activated batteries and dry batteries [22, 29, 33, 34]. The AgCl layers formed on Ag substrates are also utilized for modeling study of porous electrodes [35, 36]. The interesting and useful properties of Ag/AgCl electrodes is partly attributed to the highly reversible of Ag/Ag+ redox reactions in chloride environments [22, 37]. Unfortunately, this behavior makes this noble metal prone to corrosion in chloride environments. The dissolution of silver in chloride environments resulting in the formation of solid AgCl layer on silver substrate can be summarized following several stages including (i) the adsorption of chloride anions on silver surface; (ii) the formation of a monolayer of the AgCl; and (iii) the nucleation and growth of three-dimension AgCl multilayer. A precursor monolayer of AgCl was reported to be formed at potentials below the 101

127 thermodynamic Ag/AgCl reversible potential [25-27]. The formation of the AgCl monolayer was reported following adsorption-desorption mechanism. At a certain overpotential more positive than the Ag/AgCl reversible potential, AgCl multilayer grows laterally via nucleation and growth [29]. Gradually a thick AgCl film was observed on silver electrodes at longer exposure time [28, 30]. Morphology of non-continuous AgCl patches was described as having rounded smooth surfaces without manifestation of any crystal orientation [38]. The thickness of the non-continuous layer was fairly constant, and was less than 0.5 μm. The top surface of the continuous AgCl film was comprised of dense, fine particles [29, 38]. At longer anodic polarization exposure, the morphology of the AgCl top layer changed to mosaic features [29]. Several attempts have been made to characterize the inner structure of the continuous AgCl layer with different cross sectioning techniques including mechanical polishing followed by etching [30], sharp scalpel cross sectioning [29], and breaking by liquid N 2 [30], however a clear description of the inner structure of the AgCl layer has not been documented. The growth of a continuous AgCl film under galvanostatic conditions resulted in a shift of the applied potential to the more positive direction. This behavior was attributed to the ohmic resistance of the AgCl layer [20, 25, 29]. The conductivities of AgCl layers formed at different applied current densities and in different solutions were reported in a number of references [20, 29, 39]. Figure 3-4 summarizes the reported conductivities measured on AgCl layers grown at different applied current densities. Two distinct regions representing different conducting mechanism in the AgCl layer can be seen from this graph. The low field conduction mechanism took place in the lower current density 102

128 (and low overpotential) regions in which the AgCl film was though to be porous and AgCl exhibited extrinsic conductivity, i.e. ohmic conduction via pores. The high field conduction mechanism took place in the high current density (and high overpotential) regions in which AgCl exhibited intrinsic conductivity, i.e. ionic conduction and a exponential relationship between current density and potential [39]. Figure 3-4. Conductivity of AgCl layers formed at different applied current densities in different solutions. The values are taken from different sources [20, 29, 39] The mixed potential theory The mixed potential theory provides useful tools to determine corrosion current and corrosion potential in a galvanic couple when the anodic and cathodic polarization curves of the individual metal are given [40, 41]. Consider two metals Fe and Cu immersed in an electrolyte (Figure 3-5). The anodic and cathodic polarization curves of Fe and Cu in the electrolyte is presented in the Evans diagram as dashed lines (Figure 3-6). The corrosion 103

129 potential and corrosion current of each metal when they are not electrically connected to each other (Figure 3-5a) is determined by the intersection between the anodic and cathodic polarization curves of the corresponding metals (Figure 3-6). When Fe and Cu are brought in to contact by a conducting wire as illustrated in Figure 3-5b, a new rest state is established and the corrosion current and potential of the metals change. e - Fe Cu Fe Galvanic current Cu H 2 O (Active Anode) H 2 O (Noble Cathode) (a) (b) Figure 3-5. Two metals Fe and Cu immersed in an electrolyte; (a) No electrical contact between Fe and Cu; (b) Fe and Cu are electrically connected to each other. 104

130 Cu anodic Fe anodic POTENTIAL E couple (3) E corr(cu) I corr(cu) (2) I couple (Fe) (1) Sum anodic E corr(fe) I couple (Cu) I corr(fe) I total Sum cathodic Cu cathodic Fe cathodic LOG CURRENT Figure 3-6. Evans diagram showing anodic and cathodic polarization curves for determination of the corrosion current and corrosion potential in a galvanic couple. Employing the mixed potential theory, the characteristic parameters of the galvanic couple is determined as follows. First, based on the corrosion potential of the uncoupled metals, the anode and cathode of the galvanic cell are determined. The electrode with the more positive corrosion potential is the cathode (i.e. Cu) and the one with the more negative corrosion potential is the anode (i.e. Fe) in a galvanic couple. Second, the sum of all anodic currents must equal the sum of all cathodic currents. Based on this, the rest state of the galvanic couple is the point where the total anodic polarization curve intersects with the total cathodic polarization curve, i.e. point 1 in the Evans diagram (Figure 3-6). Both Fe and Cu have the same potential of E couple which is more positive than E corr(fe) but is more negative than E corr(cu). At the potential of E couple, the corrosion 105

131 current at the Fe anode is I couple(fe) (point 2) and the corrosion current at the Cu cathode is I couple(cu) (point 3). The mixed potential theory also provides an approach to examine the effect of the cathode-to-anode area ratio. When the area of the cathode increases, the area-corrected polarization curves of the cathode in the Evans diagram will shift accordingly to higher values along the current density axis (Figure 3-7). Therefore the total cathodic polarization curve will shift as well resulting in a displacement of the intersection with the total anodic polarization curve in the Evans diagram. Consequently, new rest state for the galvanic couple is established. The corrosion potential of the couple and the corrosion current at the Fe anode increases with increasing cathode area. Sum cathodic Fe anodic POTENTIAL E couple E couple I couple (Fe) Sum anodic I couple (Fe) Increase cathode-to-anode area ratio LOG CURRENT Figure 3-7. Evans diagram showing the effect of the cathode-to-anode area ratio. 106

132 3.2 Materials and experiments Materials Silver-cored MP35N LT composites, MP35N LT alloys and pure silver were used in this study. The nominal composition of the MP35N LT alloy is 35%Co-35%Ni-20%Cr- 10%Mo in weight percent. The diameters of the composite single wire and of the silver core were 58 μm and 37 μm, respectively (Figure 3-2). The composite was supplied by Fort Wayne Metals (Fort Wayne, IN) in the form of cables (Figure 3-3). Single and strand of 7 composite wires were detached from the cable to use in electrochemical experiments. Silver wires were supplied by Alfa Aesar (Ward Hill, MA) with the purity of 99.99% and the diameter of 0.05, 0.25 and 0.5 mm. Single wires of each material were used in potentiodynamic experiments, and strands of 7 composite wires were used in constant potential exposure experiments Solution and electrochemical cell setup Electrochemical experiments were carried out in a physiological saline solution of 9.0 g/l NaCl at room temperature or at 37 ± 1 o C and in a Ringer s solution of 9.0 g/l NaCl, 0.43 g/l KCl, 0.24 g/l CaCl 2 and 0.20 g/l NaHCO 3 at 37 ± 1 o C. All chemicals were supplied by Fisher Scientific (Thermo Fisher Scientific Inc, USA) in experimental graded crystalline forms. The solution was prepared with deionized water. A saturated calomel electrode (SCE) and pure Pt wires were used for the reference and counter electrodes, respectively. The test cell setup followed a three-electrode configuration. 107

133 3.2.3 Specimen preparation Specimens for electrochemical experiments were either flat-exposed surface, U- bended or receded surface to form 1 mm depth artificial pit. Preparation procedures for each type of specimens are described as follows Flat-exposed surface specimens The specimens of silver-cored composite and pure silver were prepared from 2 cm long wires mounted in glass tubes with Duralco 4525 epoxy (Cotronics Corp., USA). Electrical contacts were made via Cannon Gold Connectors (DF Sale Company, USA). A schematic of the specimens is shown in Figure 3-8. The specimens were mechanically polished to 600-grit silicon carbide papers before each experiment. Deionized water and methanol was used to clean the specimens after polishing. Pure silver or composite wires Epoxy Glass tube Cannon connector Alloy 22 wire Figure 3-8. Schematic of the flat-exposed surface specimens for electrochemical experiments. 108

134 U-bended specimens The specimens of the MP35N LT alloy were pieces of 3 cm long silver-cored MP35N LT composite single wire bended in to U shape and then mounted in Duralco 4525 epoxy (Cotronics Corp., USA) to expose only the 2 cm long outer tube material. Electrical contacts were made via Cannon Gold Connectors (DF Sale Company, USA). A schematic of the specimens is shown in Figure 3-9. The U-bended specimens were not reused in electrochemical experiments. Before experiments, the specimens were cleaned in deionized water without mechanical polishing. Composite wire Cannon connector Epoxy Glass tube Alloy 22 wire Figure 3-9. Schematic of the U-bended specimens for electrochemical experiments Artificial pit specimens Pure silver wires of 0.5 mm diameter were used to prepare the artificial pit specimens. The adhesive-line PTFE heat-shrink tubes were supplied by McMaster-Carr (McMaster- Carr Supply Company, USA) with the initial inner diameter of 1.6 mm. The tube with an 109

135 inserted silver wire was heated up to approximately 260 o C by a HG-501A heat gun (Master Appliance Corp., USA). Due to the applied heat, the PTFE tube shrank and sealed all the gaps between the tube and the inserted silver wire. The cross section of the specimen was polished with 600 grit silicone carbide papers and cleaned with methanol. An artificial pit of ca. 1 mm depth filled with the test solution was formed by pulling the silver wire while the specimen was immersing in the test solution. The specimen preparation procedure is illustrated in Figure Silver wire Silver wire PTFE heat shrink tube PTFE heat shrink tube Apply heat Grind Test solution Pull Ag wire Test solution 1mm Test solution Figure Schematic of the procedure to prepare artificial pit specimens filled with the test solution Experiments Potentiodynamic polarization Potentiodynamic polarization experiments were performed in a three-electrode configuration cell set up. Electrolytes were either the physiological saline solution of 9 g/l NaCl or the Ringer s solution which were prepared following the procedure described in 110

136 Section Specimens for the potentiodynamic polarization experiments were either the flat-exposed surface or the U-bended specimens. Flat-exposed surface silver and U-bended MP35N LT alloy specimens were cathodically polarized at -1.0 V vs. SCE for 10 minutes, followed by an open circuit potential (OCP) measurement for 24 hours. The anodic polarization experiments were performed with a scan rate of 0.5 mv/s sweeping from an initial potential of V vs. OCP to a final potential of +1.0 V vs. SCE. The cathodic polarization experiments were performed with a scan rate of 0.5 mv/s sweeping from an initial potential of V vs. OCP to a final potential of -1.0 V vs. SCE. Specimens of silver-cored MP35N LT composite were cathodically polarized at -1.0 V vs. SCE for 10 minutes, followed by an OCP measurement for 15 minutes and then the potential was swept from an initial potential of V vs. SCE to a final potential of +1.0 V vs. SCE with a scan rate of 0.5 mv/s Constant potential exposure Constant potential exposure experiments were performed in a three-electrode configuration cell. The electrolyte was the physiological solution of 9 g/l NaCl which was prepared following the procedure described in Section Specimens for constant potential exposure experiments were either the flat-exposed surface or the artificial pit specimens. In constant potential exposure experiments, the specimens were cathodically polarized at -1.0 V vs. SCE for 10 minutes, followed by an OCP measurement for 15 minutes. Then a constant potential was applied for different periods of time. The response currents of the specimens during the constant potential exposure experiments 111

137 were recorded. After the tests, the specimens were rinsed in deionized water and stored in a box for SEM and EDS analysis Cyclic voltammetry Cyclic voltammetry experiments were performed in a three-electrode configuration cell set up. The electrolyte was the physiological solution of 9 g/l NaCl with the preparation procedure described in Section Specimens for cyclic voltammetry were the flat-exposed surface specimens of pure silver. In cyclic voltammetry experiments, the specimens were held at the OCP for 120 s. The potential was cyclically scanned in the range from -0.5 to +1.0 V vs. SCE for 10 cycles. The scan rate in the cyclic voltammetry experiments was chosen as 1, 5, 10, 15, 25, 35, 50, 65, 80 and 100 mv/s. The response currents of the specimens were recorded for every cycle Galvanostatic polarization Galvanostatic polarization experiments were performed in a three-electrode configuration cell set up. The electrolyte was the physiological solution of 9 g/l NaCl with the preparation procedure described in Section Specimens for galvanostatic polarization experiments were the flat-exposed surface or the artificial pit specimens of pure silver. In galvanostatic polarization experiments, the specimens were hold at the OCP for 120 s. Then a constant anodic current was applied to the specimens for different periods of time. Different applied current densities of 0.1, 0.2, 0.5, 1 and 2 ma/cm 2 were used for different polarization times to pass up to 10 C/cm 2. In some galvanostatic experiments, 112

138 the polarization was paused after passing every 2 C/cm 2 for the film resistance measurement by electrochemical impedance spectroscopy. The potentials of the specimens were monitored during the tests. The specimens after the tests were rinsed in deionized water and stored for FIB analysis Electrochemical impedance spectroscopy (EIS) Electrochemical impedance spectroscopy experiments were performed in conjunction with the galvanostatic polarization experiments to measure the resistance of the solid film formed on the specimens during the galvanostatic polarization experiments. EIS was performed by applying a perturbation of 10 mv AC with the frequency sweeping from 1000 Hz to 100 Hz. The high frequencies of the AC perturbation and therefore a short exposure time minimize the interference of the EIS measurements to the galvanostatic polarization experiments. The resistance of the solid film was approximately the impedance obtained from the EIS measurement when the phase angle between the response current and the applied potential approached zero Immersion tests Specimen for immersion tests were the 2 mm long silver-cored MP35N LT composite wires. The corrosion rate of the composite was evaluated by immersing the specimens in lid-covered Costar cell culture plates (Thermo Fisher Scientific Inc, USA) filled with the physiological solution of 9 g/l NaCl. The plates were placed in an Isotemp 120 water bath (Thermo Fisher Scientific Inc, USA) set at a controlled temperature of 37 ± 1 o C. The specimens were taken out at different times during the test period of 1 year. The morphology of the specimen surfaces were examined with SEM before and after the 113

139 immersion tests. The corrosion rate of the composite was evaluated by the depth of dissolution measured with an InfiniteFocus optical 3D microscope (Alicona, Austria) Precipitation and growth of AgCl Specimens for the study of AgCl precipitation and growth were 0.25 mm diameter, 2 cm long silver wires. The Ag wires were ultrasonic cleaned in de-ionized water and methanol prior to experiments. The wires were polarized at a constant potential of -1.0 V vs. SCE for 10 minutes followed by OCP measurement for another 10 minutes. Then the Ag wires were polarized from an initial potential of V vs. SCE to different final potentials varying from V vs. SCE up to +0.60V vs. SCE with a scan rate of 0.5 mv/s. After polarization, the specimens were rinsed in deionized water and stored in a box for SEM, EDS and XRD analysis SEM and EDS The morphology and chemistry of the corrosion products formed on the specimens after electrochemical experiments were analyzed with SEM and EDS. A field-emission gun SEM Hitachi S4500 equipped with a Noran EDS system (Hitachi, Japan) was used. For morphology observation, the SEM was operated at a low bias potential of 5 kv and a working distance of 5 mm using the upper detector. For EDS analysis, the SEM was operated at a high bias potential of 20 kv and a working distance of 15 mm XRD The structure of the corrosion products after potentiodynamic polarization with the terminated potential of +0.6 V vs. SCE was used in XRD analysis. To enhance the 114

140 intensity of the diffraction signal, eight specimens were put side by side on a glass slice and placed in to the specimen stage. A Scintag X-1 X-ray Diffractometer with Cu (Kα) radiation at the wavelength of nm was used. The experiments were set up with 2 theta angles in the range of 25 o and 80 o, a scan step of 0.02 o and a data acquisition time of 5 s/step. The data was recorded by DMNST software FIB and SEM Specimens after galvanostatic polarization experiments were stored for FIB cross sectioning. The inner structure of the corrosion product layer was observed with SEM after cross sectioning the layer with a dual-beam FIB Nova Nanolab 200 equipment (FEI Company, USA). Due to the decomposition of AgCl under energized beams, some prevention measures were taken during cross sectioning with FIB and SEM observation. A thin Pt layer of ca. 1 μm was deposited at the cross section location to protect the AgCl top layer. To compromise between the milling time and the decomposition process, an ion beam of 30 kv and 7 na was used for cross sectioning. An electron beam with low bias potential and intensity of 5 kv and 0.4 na was used for SEM imaging. The illumination times were minimized for both cross sectioning and imaging activities. 115

141 3.3 Corrosion of silver-cored MP35N LT composite for NNPS Scope In this section, the corrosion behavior of a silver-cored composite with a Co-based alloy MP35N LT outer tube and a silver core in vitro conditions is investigated. The electrochemical behavior of the composite is explained in term of the electrochemical behavior of the component metals, i.e. the MP35N LT alloy and silver. The corrosion rate of the composite in vitro is evaluated. The knowledge obtained in this section is the baseline for further analysis and modeling in the preceding sections. Physiological solution of 9 g/l NaCl and Ringer s solution were prepared for the in vitro experiments. The general electrochemical behaviors of the composite, the MP35N LT alloy and pure silver were obtained by potentiodynamic polarization and constant potential exposure experiments. In potentiodynamic polarization experiments, the potentials were swept from either V vs. OCP (in case of the MP35N LT alloy and silver) or -0.5 V vs. SCE (in case of the composite) to +1.0 V vs. SCE to obtain anodic polarization curves, and the potentials were swept from V vs. OCP (in case of the MP35N LT alloy) to -1.0 V vs. SCE to obtain cathodic polarization curves. In constant potential exposure experiments, potentials of +0.03, +0.2 and V vs. SCE were applied on the composite specimens for 4, 4 and 1 hour, respectively. More details on the specimen preparation and experiment procedures are given in Sections and Corrosion rate of the composite in vitro was evaluated by immersion tests. The tests were conducted in vitro for the period of 1 year. Details of the immersion test procedure are provided in Section The corrosion products after electrochemical experiments 116

142 were examined with SEM and EDS. The details of analysis procedures are given in Section Results Potentiodynamic polarization and corrosion potential The representative OCP vs. time curves of the MP35N LT alloy, silver and the composite in 9 g/l NaCl at room temperature are shown in Figure The representative polarization curves of the MP35N LT alloy, silver and the composite in 9 g/l NaCl at room temperature are shown in Figure The corrosion potential of the MP35N LT alloy increased gradually to ca V vs. SCE during the first 4 hours of exposure in 9 g/l NaCl solution at room temperature and then stayed fairly constant. The OCP value of the MP35N LT alloy after 24 hours was calculated approximately ± 0.06 V vs. SCE from 10 experiments. The anodic polarization curve of the MP35N LT alloy exhibited a passive behavior in the potential range near the OCP and showed transpassive behavior at higher potentials. The passive current density of the MP35N LT alloy was on the order of 10-7 A/cm 2 indicating that the metal releasing rate from the Cobased alloy in the passive range was negligible. The cathodic current density of the MP35N LT alloy in the potential range from the OCP to ca V vs. SCE was on the order of 10-7 A/cm 2 indicating the sluggish kinetics of the cathodic reaction on the Cobased alloy in this potential range. 117

143 Composite 9 g/l NaCl, RT Figure Open circuit potential vs. time curves of the MP35N LT alloy, silver and the composite in 9 g/l NaCl solution at room temperature. Composite 9 g/l NaCl, RT Scan rate = 0.5 mv/s Figure Potentiodynamic polarization curves of the MP35N LT alloy, silver and the composite in 9 g/l NaCl solution at room temperature. 118

144 The corrosion potential of silver increased gradually to ca V vs. SCE during the first 4 hours of exposure in 9 g/l NaCl solution at room temperature and then stayed fairly constant. The OCP value of silver after 24 hours exposure was calculated approximately ± 0.02 V vs. SCE from 10 experiments. The anodic current density of silver was on the order of 10-6 A/cm 2 at potentials near the OCP but was abruptly increased to ca A/cm 2 at a potential of approximately V vs. SCE. The transition potential where the abrupt current increase occurred was highly reproducible in the potentiodynamic polarization tests. This potential was approximately the thermodynamic reversible potential for the Ag/AgCl electrode of V vs. SCE calculated from Equation (3.2). At more positive potentials, the anodic current density of silver showed a fairly constant value regardless of increasing applied potentials. Upon exposure in 9 g/l NaCl solution at room temperature, the OCP of the composite rapidly increased to a potential of approximately V vs. SCE. Then the potential increased slowly with a superimposed fluctuation. After 24 hours of exposure, the OCP value of the composite was ca ± 0.02 V vs. SCE. The anodic polarization curve of the composite shows a passive behavior at the potential range near the corrosion potential. Similar to that of silver, the anodic current density of the composite exhibited an abrupt increase at a potential of approximately V vs. SCE. Furthermore, the current density stayed fairly constant with increasing applied potential until ca V vs. SCE. Beyond this potential, the current density increased rapidly with increasing applied potential. The representative polarization curves of the MP35N LT alloy, silver and the composite in Ringer s solution at 37 o C are shown in Figure The representative 119

145 OCP vs. time curves of the MP35N LT alloy, silver and the composite in Ringer s solution at 37 o C are shown in Figure Compared to the data obtained in 9 g/l NaCl solution at room temperature, the polarization curves and the OCP vs. time curves of the materials in Ringer s solution at 37 o C shared similar features except slight differences in some characteristic parameters. The OCP value of the MP35N LT alloy after 24 hours in Ringer solution was approximately ± 0.05 V vs. SCE. The anodic polarization curve of the Co-based alloy exhibited passive behavior at potential range near the OCP and showed transpassive behavior at higher potentials. The passive current density of the MP35N LT alloy was on the order of 10-7 A/cm 2. The cathodic current density of the MP35N LT alloy in the potential range from the OCP to ca V vs. SCE was on the order of 10-7 A/cm 2. The OCP value of silver in Ringer s solution at 37 o C after 24 hours was approximately ± 0.01 V vs. SCE. The anodic current density of silver was abruptly increased three orders of magnitude at a potential of ca V vs. SCE. At more positive potential, the anodic current density of silver showed a fairly constant value regardless of increasing applied potentials. The OCP of the composite in Ringer s solution at 37 o C after 24 hours of exposure was ca ± 0.01 V vs. SCE. Similar to that of silver in this condition, the anodic current density of the composite exhibited an abrupt increase at the potential of approximately V vs. SCE. Furthermore, the current density stayed fairly constant with increasing applied potential until ca V vs. SCE. Beyond this potential, the current density increased rapidly with increasing applied potential. 120

146 Composite Ringer s solution, 37 o C Figure Open circuit potential vs. time curves of the MP35N LT alloy, silver and the composite in Ringer s solution at 37 o C. Composite Ringer s sol., 37 o C Scan rate = 0.5 mv/s Figure Potentiodynamic polarization curves of the MP35N LT alloy, silver and the composite in Ringer s solution at 37 o C. 121

147 Table 3-1 summarizes some characteristic parameters of the polarization curves and the OCP vs. time curves of the MP35N LT alloy, silver and the composite in 9 g/l NaCl at room temperature and in Ringer s solution at 37 o C. Table 3-1. Summary of the characteristic parameters in polarization curves and open circuit potential vs. time curves of the MP35N LT alloy, silver and the composite. In 0.154M NaCl, RT In Ringer s sol., 37 o C Materials OCP i passive E* OCP i passive E* (V vs. SCE) (A/cm 2 ) (V vs. SCE) (V vs. SCE) (A/cm 2 ) (V vs. SCE) MP35N LT +0.24±0.06 ~ ±0.05 ~ Ag -0.02±0.02 ~10-6 ~ ±0.01 ~10-6 ~+0.06 Composite +0.09±0.02 ~10-5 ~ ±0.01 ~10-5 ~+0.06 E* - the potential where current density was abruptly increased three orders of magnitude Constant potential exposure Current vs. time curves of a strand of 7 composite wires in 9 g/l NaCl solution at room temperature at different applied potentials of +0.03, and V vs. SCE for 4, 4 and 1 hours, respectively, are shown in Figure At all applied potentials, the current response showed the same behavior with a rapid decrease during the first 10 minutes following by a slower decreasing rate for the rest of the experiments. However, the magnitude of the response currents at each applied potential which indicated the extent of the corrosion was different. At V vs. SCE the anodic current was on the order of A while at V vs. SCE the anodic current was approximately two orders of magnitude higher. At the applied potential of V vs. SCE the anodic current was on the order of 10-6 A. The extent of the corrosion at each applied potential was examined further with SEM. 122

148 9 g/l NaCl, RT Figure Current vs. time curves of 7 composite wires in 9 g/l NaCl solution at room temperature with the applied potentials of +0.03, and V vs. SCE Corrosion product characterization Figure 3-16 shows the morphology of specimens after constant potential exposure experiments. After 4 hours exposure at the applied potential of V vs. SCE, the cross section of the composite specimen was observed with no significant corrosion at either the MP35N LT outer tube or the silver core. After exposure at the applied potentials of and V vs. SCE, the specimens were covered with a deposition of the corrosion product. In Figure 3-16c, the corrosion product on one of the wire was removed after ultrasonic cleaning revealed a pit at the corroded silver core. EDS analysis of the corrosion product which are shown in Figure 3-17 indicated that it contained Ag and Cl. Silver chloride was widely observed on silver substrates during anodic oxidation of silver in chloride environments [26-30]. SEM micrographs of the top surface of the 123

149 corrosion products (Figure 3-18) revealed that the top layer was comprised of rounded particles of approximately 1 μm. Holes with size of ca. 0.5 μm were also observed. These holes running through the AgCl layer might be the channels for ionic transport during the corrosion of silver. More details on the morphology and structure of the AgCl corrosion product layers will be investigated in Section a b c Figure SEM micrographs of specimens after constant potential exposure experiments in 9 g/l NaCl solution at room temperature; (a) at V vs. SCE for 4 hours; (b) at V vs. SCE for 4 hours and (c) at V vs. SCE for 1 hour. 124

150 Cl Ag EDS spectrum at point 1 EDS spectrum at point 2 Ag Cl Ag Ag a Ag b Ag Figure EDS spectrum of the corrosion products on the specimen after constant potential exposure experiment in 9 g/l NaCl solution at room temperature; (a) spectrum at point 1; and (b) spectrum at point 2 in Figure 3-16b. Figure SEM micrograph of the corrosion product layer after constant potential exposure experiment in 9 g/l NaCl solution, room temperature at V vs. SCE Immersion test The SEM micrographs of the surfaces of the composite specimens after immersion in 9 g/l NaCl solution at 37 o C for different periods of time are shown in Figure After 1 week (Figure 3-19a) the surface of the composite did not show significant corrosion on either the MP35N LT outer tube or the silver core. After 5 weeks (Figure 3-19b), some 125

151 extent of corrosion at the silver core was observed while the MP35N LT outer tube seems intact. After 25 weeks (Figure 3-19c), the corrosion of the silver core was significant leaving a pit depth of ca. 15 μm. The depth of penetration at the silver core was estimated with an infinite focus optical microscope with the assumption that the corrosion of the MP35N LT outer tube was negligible. Figure 3-20 summarizes the depth of penetration at the silver core of the composite during 1 year of immersion. The dissolution depth at the silver core increased steadily during the first 25 weeks but then the penetration rate slowed down at longer immersion time. After one year, the dissolution depth at the silver core was ca. 22 μm. 1 week 5 weeks a b 25 weeks c Figure SEM micrographs of the 2mm long silver-cored MP35N LT composite specimens after immersion in 9 g/l NaCl solution at 37 o C for different periods of time; (a) 1, (b) 5 and (c) 25 weeks. 126

152 9 g/l NaCl, 37 o C Figure The depth of penetration at the silver core of the 2 mm long silver-cored MP35N LT composite specimens after different immersion time in 9 g/l NaCl solution at 37 o C Discussion Corrosion behavior of the silver-cored MP35N LT composite in 9 g/l NaCl solution at room temperature The polarization curves of the MP35N LT alloy, silver and the composite (Figure 3-12) shows that the electrochemical behavior of the composite resembled the characteristic features of its component materials, i.e. the MP35N LT alloy and silver. An abrupt increase in the anodic current density at the potential of ca V vs. SCE following by a fairly constant current density regardless of increasing applied potentials were observed on polarization curves of both composite and silver. In addition, a rapid increase in the anodic current density at higher potential ranges was observed on polarization curves of the composite and the MP35N LT alloy. 127

153 To elucidate the contribution of the component materials to the overall behavior of the composite, a polarization curve of the composite was reconstructed from polarization curves of the MP35N LT alloy and silver. At a specific potential, the current of the composite is the sum of the current of the MP35N LT alloy outer tube and the current of the silver core at the same potential. Note that the ratio of the cross section areas between the MP35N LT outer tube and the silver core in the composite is equal to 59:41. The calculated polarization curve was plotted along with the experimental data as shown in Figure At potentials more positive than ca V vs. SCE the calculated polarization curve predicts exactly the anodic behavior of the composite. An abrupt increase in the current density at the potential of ca V vs. SCE was observed in both calculated and experimental curves. At potentials in between ca and ca V vs. SCE, the current densities were fairly constant regardless of the increasing potential. At potentials more positive than ca V vs. SCE, the current densities of the two curves again increased with increasing potentials. The difference in corrosion potentials between the two polarization curves are due to the difference in the experiment set up. Polarization curves of the MP35N LT alloy and silver were obtained after monitoring the OCPs for 24 hours and the potential was scanned from an initial potential of V vs. OCP while the anodic polarization curve of the composite was obtained after only 15 minutes OCP measurement and the potential was scanned from an initial potential of -0.5 V vs. SCE. These differences in the experimental set up are also attributed to the difference in the current density in the passive range of both materials that causes the shifting of the current density in the potential range between the OCP and the transition potential of ca V vs. SCE. 128

154 9 g/l NaCl, RT Scan rate = 0.5 mv/s Figure Calculated and experimental potentiodynamic polarization curves of the silver-cored composite in 9 g/l NaCl solution at room temperature. Given that the electrochemical behavior of the composite is the contribution of its component materials, the behavior of the silver-cored composite in the constant potential exposure experiments (Figure 3-15) can be explained as following. In 9 g/l NaCl solution at room temperature, at the applied potential of V vs. SCE, the MP35N LT alloy was in its cathodic range and silver was in its passive range as indicated in the polarization curves (Figure 3-12). Therefore, the responded current of the composite in the constant potential exposure experiment (Figure 3-15) was small and the morphology of the specimen after experiment (Figure 3-16a) showed negligible corrosion. At the potential of V vs. SCE which was in the passive range of the MP35N LT alloy and was well above the transition potential of silver corrosion, the MP35N LT alloy was corroded slowly but silver was corroded rapidly. The sum of these two currents resulted in an overall current on the orders of 10-8 A (Figure 3-15). At the potential of V vs. 129

155 SCE, both the MP35N LT alloy and silver corroded rapidly resulted in a higher overall anodic current of the composite (Figure 3-15). The corrosion rates of the silver core of the composite and the amount of the AgCl deposited on the electrode in the constant potential experiments at the two applied potentials of and V vs. SCE were calculated. In this analysis, the passive current on the MP35N LT alloy was disregarded due to the negligible value of this current in comparison with the corrosion current of silver at these applied potentials. It was also assumed that all silver ions were deposited as AgCl and no appreciable amount of Ag + went into the bulk solution due to the low solubility of AgCl in 9 g/l NaCl solution [42]. Table 3-2 presents the weight loss and depth of penetration at the silver core and the weight gain and thickness of the AgCl corrosion product layer. At the potential of V vs. SCE, the amount of dissolved silver was on the order of 10-9 g after 4 hours. This calculation again confirms the observation of low corrosion rate of silver at potentials near the corrosion potential. At V vs. SCE, silver was corroded more rapidly with the depth of corrosion on the order of 10-6 g after 4 hours. At both applied potentials, the initial period accounts for the majority of the silver dissolved and AgCl formed. The coulomb passed during the first 10 minutes exposure at V vs. SCE accounted for half of the total coulomb passed in the 1 st hour of exposure and 2 times higher than that in the 4 th hour. The current also dropped significantly from an initial value of 22 μa to a value of 0.03 μa at the end of the experiment. 130

156 Table 3-2. Summary of weight loss and depth of penetration at the silver core and the weight gain and thickness of the AgCl corrosion product layer calculated from constant potential exposure experiments. Applied Potential Period of time Coulomb passed Coulomb fraction Ag dissolved AgCl deposited (V) (C) (%) μg μm μg μm first 10 min 0.98x x x st hour 2.71x x x th hour 1.02x x x first 10 min 260x st hour 557x th hour 127x It appears that the formation of AgCl corrosion product on the composite inhibited the dissolution process. To sustain a high dissolution rate at the anode, a high ionic transport through the corrosion product layer should be maintained [43]. The ionic transport through the AgCl layer was though to be mainly via the aqueous phase inside the micro-channels in the AgCl layer [29, 30, 39]. As the AgCl layer growth, the microchannels were lengthened and may become narrower which limited the ionic transport. Consequently, the dissolution rate was slow down if the applied potential was constant such as in constant potential exposure experiments (Figure 3-15), or the dissolution rate did not increase if the applied potential kept increasing such as in potentiodynamic polarization (Figure 3-12). The role of the AgCl layer on the corrosion of silver is elucidated in Section 3.5 and a model for the corrosion of silver underneath AgCl layers is developed in Section

157 The effect of temperature and minor ions Compared to those in 9 g/l NaCl solution at room temperature, the electrochemical behavior of the MP35N LT alloy, silver and the composite in Ringer s solution at 37 o C did not show significant difference (Figure 3-12 to Figure 3-13). The behavior of the composite was the combination of its component materials. Similar to those in 9 g/l NaCl solution, the corrosion potentials of the MP35N LT alloy and silver in Ringer solution was approximately and V vs. SCE, respectively. The MP35N LT alloy exhibited passive behavior at low potential range near the OCP and showed transpassive behavior at higher potentials. The cathodic reaction on the MP35N LT alloy exhibited sluggish kinetics in the potential range from the OCP to ca V vs. SCE. The anodic current density of silver was abruptly increased three orders of magnitude at a potential of ca V vs. SCE following by a fairly constant value regardless of increasing applied potentials Galvanic action between the MP35N LT alloy and silver Galvanic corrosion is due to the potential difference between dissimilar metals in contact. The mixed potential theory provides a useful approach to study the galvanic action between two different metals [44]. The more noble metal is the cathode and the more active metal is the anode. In 9 g/l NaCl solution at room temperature, the OCP of the MP35N LT alloy and of silver were ± 0.06 and ± 0.02 V vs. SCE, respectively. In Ringer s solution at 37 o C, the OCP of the MP25N LT alloy and of silver were ± 0.05 and ± 0.02 V vs. SCE, respectively. Therefore, in both test conditions, the MP35N LT alloy is the cathode and silver is the anode of the galvanic couple. 132

158 Based on the mixed potential theory, the corrosion potential and the corrosion current of the galvanic couple can be determined from the intersection between the total anodic and the total cathodic polarization curves. Let s consider the corrosion of the composite during immersion test in 9 g/l NaCl solution at 37 o C. The polarization curves of the MP35N LT alloy and silver in this test condition can be approximated to the polarization curves of these materials in Ringer s solution at 37 o C. The Evans diagram for the anodic polarization curve of silver and the cathodic polarization curve of the MP35N LT alloy in Ringer s solution at 37 o C is shown in Figure The curves were re-plotted with respect to the corresponding exposed areas of the MP35N LT outer tube and the silver core in the composite specimens of 2 mm long. The corrosion potential and the corrosion current of the galvanic couple obtained from the Evans diagram were ca V vs. SCE and 4x10-11 A, respectively. This is in good agreement with the measured OCP value of ca V vs. SCE of composite specimens with the same geometry in Ringer s solution at 37 o C. With the assumption of uniform corrosion at the silver core, the calculated corrosion current at the anode was converted to a depth of penetration of ca. 120 μm/year. This calculated value is 5 times higher than the corrosion rate of 22 μm obtained from immersion tests of the composite in 9 g/l NaCl solution at 37 o C (Figure 3-20). The overestimated corrosion rate from the Evans diagram is due to the assumption that corrosion rate will not change with time. However, due to the formation of corrosion product layer, the ohmic drop inside the pit, etc., the corrosion rate of the silver core will in fact decrease with time. 133

159 Ringer s solution, 37 o C Figure Evans diagram showing the cathodic polarization curve of the MP35N LT outer tube and the anodic polarization curve of the silver core in Ringer s solution at 37 o C. The areas of the MP35N LT outer tube and of the silver core are 1.8x10-3 and 1.1x10-5 cm 2, respectively Summary The corrosion behavior of the silver-cored MP35N LT composite in physiological saline solution of 9 g/l NaCl at room temperature and in Ringer s solution at 37 o C was examined. The corrosion behavior of the composite is the contribution of its component materials, i.e. the MP35N LT alloy and silver. The findings can be summarized as follows: 1. In 9 g/l NaCl solution at room temperature, the corrosion potential of the MP35N LT alloy was approximately ± 0.06 V vs. SCE. The Co-based alloy is passive in the potential range near its corrosion potential. The cathodic reactions on the MP35N LT alloy had slow kinetics with the current density on the order of 10-7 A/cm

160 2. In 9 g/l NaCl solution at room temperature, the corrosion potential of silver was approximately ± 0.02 V vs. SCE. The anodic current density of silver near its corrosion potential was on the order of 10-6 A/cm 2. At potential more positive than ca V vs. SCE, the anodic current density increased abruptly to ca A/cm 2 and stayed fairly constant regardless of increasing applied potentials. 3. Silver chloride corrosion product was formed on the silver substrate at the applied potentials of and V vs. SCE. The formation of AgCl inhibited the dissolution at the silver substrate during the constant potential exposure experiments. 4. The electrochemical behaviors of the MP35N LT alloy, silver and the composite in Ringer s solution at 37 o C were similar to those in 9 g/l NaCl at room temperature. 5. The mixed potential theory is a useful approach to predict the galvanic action between the outer tube MP35N LT and the silver core of the composite. In both 9 g/l NaCl solution at room temperature and in Ringer s solution at 37 o C, the MP35N LT outer tube was the cathode and the silver core was the anode. 6. The depth of penetration at the silver core of 2 mm long silver-cored MP35N LT composite wires during immersion test in 9 g/l NaCl solution at 37 o C increased steadily during the first 25 weeks, but then the penetration rate decreased in longer immersion times. A penetration depth of ca. 22 μm was observed at the silver core after 1 year of immersion. 135

161 3.4 Precipitation and growth of AgCl on silver substrate in physiological solution and the effect on the dissolution kinetics of silver Scope In Section 3.3, the corrosion of the silver core in the composite material has been examined. The formation of AgCl as a corrosion product on the silver core was observed. In this section, the precipitation and growth of AgCl layers on silver electrodes is studied in more detail. The structure of the AgCl layer is characterized and the conductivity of the AgCl layer is measured. The kinetics of silver dissolution underneath AgCl layers is studied. The effect of the AgCl layers on the kinetics of silver dissolution is investigated. Physiological solution of 9 g/l NaCl solution at room temperature was used in this study. Specimens for the study of AgCl precipitation and growth were 0.25 mm diameter, 2 cm long silver wires. The silver wires were polarized from an initial potential of V vs. SCE to different final potentials varying from V vs. SCE up to +0.60V vs. SCE with a scan rate of 0.5 mv/s. The morphology of AgCl was examined with SEM. Structural and compositional analysis was performed with FIB, XRD, and EDS. More details on experiment procedures are given in Sections to For conductivity measurement and kinetics study, artificial pit specimens were used (See Section for specimen preparation). The AgCl layers were grown by galvanostatic polarization as described in Section The resistances of the AgCl layers were measured with EIS as described in Section The dependence of silver dissolution currents on applied potentials with the presence of a continuous AgCl layer was examined with potentiostatic step experiment. A continuous AgCl layer was grown by galvanostatic polarization experiments to pass a charge of 1 C/cm 2. Then, the applied 136

162 potentials were increased from +0.1 V vs. SCE up to +2.0 V vs. SCE with a step of 0.1 V vs. SCE. A short duration of 1 s at each potential step was used to minimize the growth of the AgCl film during the measurement Results Precipitation and growth of AgCl A representative current vs. potential curve during the potentiodynamic polarization to precipitate AgCl is shown in Figure The anodic behavior of silver was characterized by a low anodic current density at the potentials near the corrosion potential followed by an abrupt increase at a potential of ca V vs. SCE. To observe the nucleation and growth of AgCl on the silver surface, the polarization was terminated at different anodic potentials of -0.04, +0.04, +0.06, +0.08, and V vs. SCE. The morphologies of the specimens after polarization are presented in Figure E (V vs. SCE) E=+0.04 E=-0.04 E=+0.06 E=+0.60 E=+0.15 E= E-8 1E-7 1E-6 1E-5 1E-4 1E Current density (A/cm 2 ) Figure Current vs. potential curve of the silver wire specimens during potentiodynamic polarization with different terminated potentials. 137

163 At the terminated anodic potential of V vs. SCE the anodic current density was ca. 8x10-7 A/cm 2. The SEM micrograph of the specimen after polarization (Figure 3-24a) shows a surface free of precipitation. At the anodic potential of V vs. SCE the anodic current density increased to ca. 1.3x10-6 A/cm 2. The morphology of the polarized specimen terminated at V vs. SCE (Figure 3-24b) was featured by particles with size of less than 100 nm scattering on the surface. The anodic current density increased significantly at the potential of V vs. SCE to ca. 1.2x10-5 A/cm 2. Clusters of 100 nm size particles were observed on specimen at this terminated potential (Figure 3-24c). At V vs. SCE, the current density was ca. 1.8x10-3 A/cm 2 and the specimen surface after polarization was covered with patches of non-continuous corrosion product film. The patches kept expanding laterally to cover the silver substrate rather than growing out of the surface. A preferential expanding direction was observed that followed the scratch direction on the surface (Figure 3-24d). At higher anodic overpotentials, the current density did not increase but stayed at high magnitude on the order of 10-3 A/cm 2. The surface of specimen after polarization was covered with a continuous layer as shown in Figure 3-24e and Figure 3-24f. 138

164 i=8.3x10-7 A/cm 2 i=1.3x10-6 A/cm 2 i=1.2x10-5 A/cm 2 a b c i=1.8x10-3 A/cm 2 i=5.2x10-3 A/cm 2 i=2.6x10-3 A/cm 2 d e f Figure SEM micrographs of specimen surfaces at different terminated anodic potentials of (a) -0.04, (b) +0.04, (c) +0.06, (d) +0.08, (e) +0.15, and (f) V vs. SCE Structure of AgCl layer An EDS spectrum taken from a patch on the specimen polarized to V vs. SCE is shown in Figure The spectrum shows that the patch was comprised of silver and chlorine. In addition, a XRD pattern of the corrosion product formed on the specimen after polarization to V vs. SCE is shown in Figure The crystalline peaks in the XRD pattern were identified as AgCl with fcc structure according to PCPDFWIN software version 2.1 (International Centre for Diffraction Data, USA). The two strong peaks of AgCl corresponding to the (111) and (200) crystalline planes were depressed with respect to the standard pattern while the peak corresponding to (220) plane was significantly enhanced in the AgCl samples anodically grown in this study indicating that the (220) planes of grains in the AgCl layer aligned nearly parallel to the silver surface. 139

165 Cl Ag Ag Figure EDS spectrum of the non-continuous film on the specimen after polarization to V vs. SCE in the potentiodynamic polarization experiment. AgCl Ag (111) (200) (220) (311) (222) (220) (311) (222) (331) (420) (422) JCPDF standard for AgCl Figure XRD pattern of the continuous film formed on the specimen after polarization to V vs. SCE in the potentiodynamic polarization experiment. The morphologies of the non-continuous and continuous AgCl layers grown by potentiodynamic polarization are shown in Figure AgCl patches in the noncontinuous layer had rounded edges (Figure 3-27a) and tended to expand laterally rather 140

166 than thickening. In the continuous AgCl film formed after potentiodynamic polarization to V vs. SCE (Figure 3-27b) the top layer was comprised of rounded particles with size of less than 1 μm. Pores between AgCl particles can be seen in the SEM micrograph. The top layer of the continuous AgCl film changed to irregular-shaped grains at the terminated polarization potential of V vs. SCE (Figure 3-27c). The pores between AgCl grains disappeared; instead holes running through the grains can be seen from the top surface. a 1 μm b 1 μm Micro-channels c 5 μm Figure SEM micrographs of the surface morphology of specimens after potentiodynamic polarization with final anodic potentials of (a) +0.08, (b) and (c) V vs. SCE. 141

167 The inner structure of thick, continuous AgCl layers was examined by cross sectioning in the direction vertical to the substrate surface with FIB followed by SEM observation. The SEM micrographs of the cross sections are shown in Figure 3-28a and Figure 3-28b. A cross section of the AgCl layer in the direction parallel to the substrate surface is shown in Figure 3-28c. The cross section was formed after the top layer broke during ultrasonic cleaning. AgCl grains of several micrometers were observed in Figure 3-28a. Some micro-channels running from the top surface through the grains into deeper layers were also observed in Figure 3-28a and in Figure 3-28c. The micro-channel in Figure 3-28a indeed penetrated deep into the AgCl layer, however due to the tortuousness of the channel, only a portion of it was observed in the present cross section. After ca. 20 s exposure under electron beams, the AgCl grains were quickly decomposed creating a porous nanostructure with the pore size of approximately 100nm (Figure 3-28b). The decomposition of AgCl to silver under the illumination of energized beams is well known and is utilized in photography. No significant delamination at the Ag/AgCl interface was observed in Figure 3-28b. To maintain such adherent interface during continuous dissolution of the silver substrate, AgCl must be formed at the bottom of the AgCl layer. 142

168 AgCl Decomposing AgCl Micro-channels Grain boundaries Ag/AgCl interface a 5 μm b Ag 5 μm Micro-channels AgCl c 5 μm Figure SEM micrographs of the cross sections of the AgCl layers grown by galvanostatic polarization at 0.5 ma/cm 2 to pass a coulomb amount of 5 C/cm 2 ; (a) FIB cross sectioning, before AgCl decomposition; (b) FIB cross sectioning, AgCl under decomposition; and (c) ultrasonic cleaning to break the top layer The ohmic response behavior of silver dissolution underneath AgCl layers To examine the dependence of silver dissolution currents on applied potentials with the existence of a continuous AgCl layer, potentiostatic step experiment was performed. Figure 3-29 shows the relationship between the anodic current density and the overpotential during the potentiostatic step experiment. The overpotential was calculated with the assumption that the potential of the silver electrode underneath the AgCl layer was equal to the Ag/AgCl reversible potential calculated by Equation (3.2). In 9 g/l NaCl solution, the Ag/AgCl reversible potential is V vs. SCE. For a large range of 143

169 applied potential from +0.1 to +2.0 V vs. SCE, the response current densities followed linear relationship with overpotentials indicating the dissolution of silver underneath a thick AgCl layer was under ohmic controlled regime. The thickness of the AgCl layer after passing 1 C/cm 2 was approximately 2 μm. 4 3 i (ma/cm 2 ) Overpotential (V) Figure Silver dissolution current density vs. overpotential in potentiostatic step experiment Resistance of AgCl layer The resistances the AgCl layers grown by galvanostatic polarization experiments were measured by EIS at different AgCl thickness during the experiments. Figure 3-30 shows a typical potential vs. time curve during galvanostatic polarization experiments. The potential at the oxidizing electrode increased with time. Potential fluctuation was observed in all experiments however the event occurred at different times and lasted for different durations depending on the applied current density. One notable behavior is that despite the intermittences of the galvanostatic experiments for EIS measurements, the 144

170 overall potential vs. time curves was smooth. The arrows in Figure 3-30 indicate the times of interruption during the galvanostatic experiment. The inset in Figure 3-30 shows a segment of the potential vs. time curve in which two interruption events for EIS measurement took place. The restoration of the potential to the value before the interruption for EIS measurement, even during oscillation periods, indicates the strong dependence of the potential on the physical property of the AgCl layer itself rather than on time dependence processes such as diffusion, at least in the time scale of the experiments. The smoothness of the overall potential vs. time curves also indicates that the alternation between galvanostatic and EIS experiments had negligible effect on the galvanostatic experiments E (V vs. SCE) Time (hours) i = 0.5 ma/cm 2 Figure Potential vs. time curve during galvanostatic preparation of AgCl layer with i = 0.5 ma/cm

171 The resistances of the AgCl layers formed during galvanostatic experiments at different current densities were measured by EIS. Figure 3-31 shows the dependence of the AgCl layer resistance on the amount of coulomb passed per unit area on the silver electrode during the anodic formation of the AgCl layers at different applied anodic current densities of 0.1, 0.2, 0.5, 1 and 2 ma/cm 2. The AgCl resistances increased with the amounts of coulomb passed per unit area or in another word the resistance increased with the thickness of the AgCl layers. However, the resistances of the AgCl layer were not dependent on the magnitude of the applied current density under which it grew. Compared to the resistances of thin AgCl layers, the resistances of thicker AgCl films grown under different current densities were more scattering. Figure Dependence of AgCl layer resistances on the amounts of coulomb passed per unit area during galvanostatic experiments at different applied current densities of 0.1, 0.2, 0.5, 1 and 2 ma/cm

172 3.4.3 Discussion Precipitation and growth of AgCl The nucleation and growth of AgCl on silver substrate in 9 g/l NaCl solution during potentiodynamic polarization was studied. At small anodic overpotentials, the anodic current density was small, i.e. the concentration of dissolved Ag+ in the solution was small, and no AgCl was observed on the silver substrate (Figure 3-24a). As the anodic current density increased due to higher anodic overpotential, the solution near the silver surface became more concentrated with Ag+. Precipitation of AgCl occurred when the solution saturated with Ag+. AgCl particles with size of less than 100 nm were observed at the current density of ca. 1.3x10-6 A/cm 2 (Figure 3-24b). AgCl patches expanded laterally at higher anodic overpotentials and current densities with preferential directions along scratches on the surface. This may be due to a higher extent of Ag + supersaturation at the scratch bottom or due to a decrease in the Gibbs free energy for nucleation at these heterogeneous sites. However, no further study was conducted to elucidate this speculation. When patches impinged and AgCl formed a continuous layer on the silver substrate, the layer started thickening. Pores between AgCl particles were visible in this period (Figure 3-27b). The grain boundaries between AgCl particles might be the primary route for the ionic transport between the corroding silver electrode and the electrolyte and vise versa during this early stage of continuous film growth. As the AgCl layer thickened, the pores between the AgCl particles were closed (Figure 3-28a), and the ionic transport via this route might have been limited. In addition, the field strength through AgCl layer was estimated on the order of 10 3 V/cm, thus intrinsic conduction via solid AgCl layer by 147

173 high field mechanism was ruled out. Therefore micro-channels running through the AgCl particles seem to be the main conduction path at this later stage. The change in the morphology of the AgCl top surface (Figure 3-27) and the adherence of the AgCl layer to the silver substrate (Figure 3-28b) indicate that the formation of AgCl occurred at both the top and bottom of the AgCl layer, respectively. These observations implies that there must be fluxes of Ag + moving from the silver substrate toward the electrolyte and of Cl - moving from the electrolyte toward the silver electrode to support the continuous formation of AgCl at the two aforementioned locations. In the newly formed, continuous AgCl layers, Ag + and Cl - ions may be transported via pores between the AgCl particles. However, in thick AgCl layers, microchannels are probably the main path for ionic transport. In Section 3.3, the effect of the AgCl corrosion product layers on limiting the corrosion of the silver substrate has been mentioned. This effect of the AgCl layer is due to the inhibition of the ionic transport through the layer. It has been known that the movement of ions in an electrolyte can be due to a concentration gradient (i.e. diffusion), an electrostatic field (i.e. migration), or an external force (i.e. convection). During the silver dissolution and AgCl growth, convection inside the micro-channels is negligible and more importantly, this mass transport mechanism does not cause any net current, therefore it does not affect the dissolution current of silver. If diffusion of ions through the AgCl layer determines the dissolution current, the process is under diffusion controlled regime. If migration of ions through this layer determines the dissolution current, the process is under ohmic controlled regime. If none of the two mass transport mechanisms dominate, the process is under mixed diffusion-ohmic controlled regime. It 148

174 is important to elucidate which mechanism is activated in the situation of silver-cored MP35N LT composite corrosion in vitro. The apparent of a constant current density at the high potential ranges during potentiodynamic polarization experiments (Figure 3-23) mimics the behavior of a limiting current density in diffusion controlled regime. However, it should be realized that the thickness of the AgCl layer during potentiodynamic polarization experiments increased during the experiment. The limiting current density, i L, is calculated by: i L = o z* DFC (1 t ) δ r (3.3) where z* is the charge of the ion of interest; D is the diffusivity of the charge carrier; F is the Faraday s constant; C o is the concentration in the bulk in the case of Cl - and Na + ions and is the concentration at the silver electrode in the case of Ag + cations; t r is the transport number of the charge carrier; and δ is the diffusion layer thickness. The limiting current density calculated by (3.3) would decrease as the AgCl layer thickness increased due to the increase of δ with AgCl growth. During potentiostatic polarization experiments, the relationship between the response current and the polarization time in an I vs. t 1/2 plot (which is shown in Section 3.5) follows a linear relationship which is indicative of diffusion controlled regime. Under diffusion controlled regimes, during the growth of the AgCl layer, it is true that the I vs. t 1/2 plot follow a linear relationship. However, this linear relationship will also be observed if the process is under an ohmic controlled regime. A mathematical model for the silver dissolution and the AgCl formation in controlled potential conditions under an ohmic controlled regime is presented in Section

175 The argument that the dissolution of the silver substrate after the formation of a continuous AgCl layer is under ohmic controlled regime should be examined further. This argument implies several points including (i) if the resistance of the AgCl layer is constant, the rate of the silver dissolution will increases proportionally with the overpotential; (ii) if the anodic dissolution current is controlled at a constant value, the overpotential at the electrode will increase proportional to the AgCl resistance; and (iii) if the overpotential is kept constant, the dissolution rate of the silver electrode is determined by the resistance of the AgCl layer. The last point of the implications is discussed in Section 3.5. In this section the first two implications are examined. The results of the galvanostatic step experiment are shown in Figure In this experiment, the pulse duration was chosen as 1 s to minimize the change in the AgCl thickness. Thus, the resistance of the AgCl layer is considered constant during the experiment. Figure 3-29 shows that the dissolution current of silver indeed increased linearly with the overpotential. Extrapolation of this data crosses the origin in the i vs. overpotential plot. This experiment proves point (i) mentioned above. Point (ii) of the implication is proven, at least qualitatively, by the galvanostatic experiments. During these experiments, the thickness of the AgCl layers increased, and so did the resistances of the layers. An increase in the overpotential was observed in Figure 3-30 as the result of an increasing AgCl layer resistance. Furthermore, the restoration of the overpotential to the value before the interruption time for EIS measurement indicates the strong dependence of the overpotential on the resistance of the AgCl layer. Quantitative examination will be performed after the conductivity of the AgCl layer is analyzed. 150

176 Ionic conductivity of the electrolyte inside the micro-channels The resistance vs. coulomb passed per unit area curves in Figure 3-30 shows that the resistance of the AgCl layer increased approximately linearly with the coulomb passed to a certain thickness from which the resistance increased at a faster rate. Assuming that the micro-channels were the main ionic transport path through the AgCl layer, the dependence of the AgCl layer resistance on the coulomb passed can be explained as the result of the lengthening of the micro-channels and/or the clogging of some of the channels. The resistance of the AgCl layer, R, is calculated from the film thickness, x, by: β x 1 R = ( Ω ) (3.4) A K N mc mc where β is a structural factor representing the increase in the ionic transport distance due to the tortuousness of the micro-channels (β > 1); A mc is the average cross sectional area of the micro-channels (cm 2 ); K mc is the conductivity of the electrolyte inside the microchannels (S/cm); and N is the number of the micro-channels running through the AgCl layer. As the film thickened, the ionic transport distance in the micro-channels increased proportionally with the film thickness. If the conductivity of the electrolyte inside the micro-channels does not change, and if the structural factor and the number of the microchannels are constant, the resistance of the AgCl layer will increase linearly with the film thickness. These conditions are easier to be met during a short time of AgCl growth, i.e. when the thickness of the AgCl layer is thin. Therefore a linear relationship was observed in the R vs. q curves at low q regions (Figure 3-31). For longer time, the precipitation of AgCl inside the micro-channels might occur if the saturation condition was met. Precipitation of AgCl was observed at both the top and the bottom of the AgCl layers. Therefore it is likely that AgCl also precipitated inside the 151

177 micro-channels. Thus, the radius of the micro-channels might reduce with time which resulted in a reduction of the micro-channel cross sectional area, A mc. Eventually some of the channels might be blocked which caused a decrease in the number of micro-channels, N. In addition, the formation of AgCl at the Ag/AgCl interface and inside the channels consumed Cl - and Ag + and decreased the concentration of Cl - and/or Ag + ions inside the channels, i.e. a decrease in the conductivity of the electrolyte inside the micro-channels, K mc. Either the decrease in A mc, N or K sm leads to a faster increase in the resistance of the AgCl layer and the deviation of the R vs. q curve from linear relationship. To estimate the concentration of charge carrier inside the micro-channels, the conductivity of the electrolyte inside the micro-channels is calculated from Equation (3.4). The AgCl layer formed after passing 6 C/cm 2 is chosen for this estimation. Assuming that all dissolved Ag + cations precipitated as AgCl, Faraday s law gives: m AgCl A x M Aq F AgCl = ρ AgCl = (3.5) n where m AgCl is the mass of AgCl (g); A is the surface area of the electrode (cm 2 ); x is the thickness of the AgCl layer (cm); ρ AgCl is the density of the AgCl layer (g/cm 3 ); M AgCl is the molecular weight of AgCl (g/mol); n is the number of electron transferred in the silver dissolution reaction (n = 1); q is the number of coulomb passed per unit area (C/cm 2 ); and F is the Faraday s constant (F = C/equiv). Therefore, the thickness of this layer is calculated by: x M q ρ AgCl = (3.6) nf AgCl Substitute (3.6) in to (3.4) and rearrange yields: 152

178 K mc 1 M AgCl q β = (3.7) nf ρ R A N AgCl mc From Figure 3-31, the resistance of the AgCl layer after passing 6 C/cm 2 was ca. 200 kω. The number of the micro-channels and the average cross sectional area of the microchannels is estimated from the SEM micrographs which give approximately 14,410 channels and 0.52x10-8 cm 2 cross sectional area (see appendix A) which is accounted for ca. 4% volume fraction of the AgCl layer. The tortuosity of the micro-channels is assumed to increases the transport distance twice, i.e. β = 2. The density of AgCl was taken as 5.56 g/cm 3 [42]. The values of other parameters are given in Table 3-3. Substituting the numerical values in to Equation (3.7) yields K mc = 2.15x10-4 S/cm. Table 3-3. Parameters used for calculation of the conductivity of the electrolyte inside the microchannels in the AgCl layers during galvanostatic experiments. n F (C/equiv) M AgCl (g) ρ AgCl (g/cm 3 ) q (C/cm 2 ) R (Ω) β A mc (cm 2 ) N 1 96, , x ,410 The concentration of the charge carriers inside the micro-channel is estimated using the relation: K = λ z C (3.8) mc j j j j where j represents the charge carrier species of interest; λ j is the equivalent ionic conductivity of the species (S.cm 2 /mol); z j is the charge of the species; and C j is the concentration of the species (mol/cm 3 ). In micro-channels, it is likely that Na + and Cl - are the dominant charge carriers. The equivalent ionic conductivity of Na + and Cl - ions are 153

179 50 and 76 S.cm 2 /mol, respectively. The conductivity of the solution inside microchannels is K mc = 2.15x10-4 S/cm. Thus, Equation (3.8) can be rewritten as: CNa+ 76CCl = + (3.9) This expression indicates that the concentration of Na + and Cl - inside the micro-channels were on the order of 10-6 mol/cm 3. This concentration is approximately 100 times more diluted than the concentration of these ions in the bulk solution which is ca mol/cm 3. The concentration of Ag + in the micro-channels is limited by the solubility product of AgCl, K sp, which is represented by: C C K (3.10) Ag+ Cl sp At room temperature, the solubility product of AgCl is 1.8x10-16 (mol 2 /cm 6 ) [42]. If the concentration of Cl - was on the order of 10-6 mol/cm 3 as calculated earlier, the concentration of Ag + in the micro-channels was on the order of mol/cm 3 or smaller The apparent conductivity of the AgCl layer Beside the conductivity of the electrolyte inside the micro-channels, another important parameter is the apparent conductivity of the AgCl layer. Based on the resistance of the AgCl layer measured from EIS, the apparent conductivity of the AgCl layer, K, is calculated by: x K = (3.11) R A where x is the thickness of the AgCl layer (cm); R is the resistance of the AgCl layer (Ω); and A is the surface area of the electrode (cm 2 ). The thickness of the AgCl films is calculated from Equation (3.6). The resistance of the AgCl layer at different coulomb 154

180 passed per unit area is taken from EIS measurements. The value of other parameters is given in Table 3-3. The apparent conductivity of the AgCl layer calculated at different charge passed per unit area is shown in Figure A trend of decrease in the apparent conductivity as the film growth was observed. After passing an amount of 10 C/cm 2, the apparent conductivity of the AgCl layer was approximately 3x10-6 S/cm which was 10 times lower than the conductivity of the film after passing 2 C/cm 2. The apparent conductivities obtained in this study are consistent with the values of the AgCl conductivity reported by a numbers authors as summarized in Section 3.1. The decrease in the AgCl apparent conductivity with the film thickness supports the hypothesis of either decrease in the number of micro-channels, the clogging of some of the channels or the decrease of the charge carrier concentration inside micro-channels as the film growth. Figure The apparent conductivity of the AgCl layers during galvanostatic experiments in 9 g/l NaCl solution at different current densities of 0.1, 0.2, 0.5, 1 and 2 ma/cm 2 155

181 The effect of the continuous AgCl layer on the silver dissolution mechanism The transport of ions through the AgCl layer is important for the continuous dissolution process at the silver substrate. As the apparent conductivity of the AgCl layer decrease with the thickness, the transport via this layer becomes more difficult. The continuous increase of the applied potential to pass the same amount of current in the galvanostatic experiment is due to the decrease of the AgCl apparent conductivity. The applied potential in the galvanostatic polarization experiments, V, can be expressed in terms of the electrode potential, E a, the anodic activation overpotential, η a a, the anodic concentration overpotential, η a c, and the ohmic overpotential, η Ω by: V = E a + η a a + η a c + η Ω (3.12) The ohmic overpotential at the silver electrode is mainly due to the ohmic resistance of the AgCl layer. Thus, during galvanostatic experiments, the ohmic overpotential is expressed by Ohm s law: η Ω i x = (3.13) K Combining (3.6) and (3.13) yields: η M q i = AgCl nf Ω ρ AgCl K (3.14) The galvanostatic polarization experiments were performed at different applied current densities of 0.1, 0.2, 0.5, 1 and 2 ma/cm 2. The value of the apparent AgCl conductivity was calculated in Section The value of other parameters is given in Table

182 0.20 i = 0.1 ma/cm 2 η Ω (V) / E (V vs. SCE) Measured data Time (h) Calculated data a i = 0.2 ma/cm 2 η Ω (V) / E (V vs. SCE) Measured data Time (h) Figure (continued) Calculated data b 157

183 1.2 i = 0.5 ma/cm η Ω (V) / E (V vs. SCE) Measured data Calculated data Time (h) 2.0 i = 1 ma/cm 2 c η Ω (V) / E (V vs. SCE) Measured data Calculated data d Time (h) Figure (continued) 158

184 10 i = 2 ma/cm 2 η Ω (V) / E (V vs. SCE) Measured data Calculated data 0 e Time (h) Figure Calculated and measure overpotential vs. time during galvanostatic polarization experiment with the applied current density of (a) 0.1; (b) 0.2; (c) 0.5; (d) 1 and (e) 2 ma/cm 2 Figure 3-33 shows the ohmic overpotential vs. time curves during galvanostatic polarization experiments calculated from Equation (3.14). The calculated curves were plotted in the same graph with the experimental potential vs. time data. In all cases, the calculated curves resembled the experimental data with some offsets. This indicated the dominance of the ohmic overpotential through the AgCl layer during the dissolution of the silver electrode underneath thick AgCl layers. For instance, the ohmic overpotential after 4 hours at the applied current density of 0.5 ma/cm 2 (Figure 3-33.c) was accounted for ca. 80% of the measured potential. At the applied current densities of 1 and 2 ma/cm 2, some deviation in the slopes of the calculated curves from the experimental curves toward the ends of these experiments was observed and may be due to the change 159

185 in the ionic conduction mechanism through the AgCl layer from the extrinsic to an intrinsic one. At these high applied current densities of 1 and 2 ma/cm 2 and therefore high overpotentials, the conduction via micro-channels was competed by the high field conduction in the AgCl solid phase as observed by some authors [39]. Figure 3-33 also shows that there are offsets between the calculated overpotentials and the measured potentials. These offsets are the sum of the electrode potential, the anodic activation overpotential and the anodic concentration overpotential as indicated in Equation (3.12). The offsets between the calculated overpotentials and the measured potentials at different applied current densities were measured when 2 C/cm 2 were passed, i.e. at the first EIS measurements. Figure 3-34 shows the dependence of the offset values on the applied current density in the galvanostatic experiments. This finding indicates that besides the ohmic drop through the AgCl layer which was governed by Ohm s law, another current dependence overpotential term contributed to the overall overpotential at the silver electrode at the beginning of the experiments, i.e. when the AgCl layer was thin. 160

186 Offset (V) i (ma/cm 2 ) Figure Dependence of the offsets between the calculated and the measured overpotentials on the applied current densities during galvanostatic experiments. From Equation (3.12), the offset values can be expressed as: Offset = E a + η a a + η c a (3.15) The dependence of the activation overpotential on the current density is expressed implicitly by the Butler-Volmer equation: αaf a αcf a i = io exp ηa exp ηa RT RT (3.16) The concentration overpotential for an anodic reaction is expressed by: η a c RT i = ln 1+ nf il (3.17) In the above equations, α a, α c are the charge transfer coefficients of the anodic and cathodic reaction, respectively, at the silver electrode (α a + α c n); R is the gas constant (R = J/mol.K); T is temperature (K); i o is the exchange current density of the silver 161

187 dissolution reaction (A/cm 2 ); and i L is the limiting current density of the silver dissolution reaction (A/cm 2 ). Equation (3.17) does not indicate any overpotential limit, unlike the one for the cathodic reaction. At the anode, insufficient diffusion does not cause depletion of the reactant in the solution but may result in precipitation at the electrode when the solution is saturated with cations released from the anodic reaction. If the precipitation forms an insulation layer, the current will be physically limited unless the layer is porous. In the situations considered here, since the AgCl deposit remains porous, the anodic concentration overpotential as indicated in Equation (3.17) is negligible. Thus, Equation (3.15) becomes: a a Offset E η a = + (3.18) The value of the electrode potential, E a, is calculated as V vs. SCE from Equation (3.2) for a Ag/AgCl electrode in 9 g/l NaCl solution. The value of the anodic activation overpotential, η a a, is then calculated by: a a η = (3.19) a Offset E Now, the exchange current density, i o, can be obtained from the Butler-Volmer equation: i o i = αaf a αcf a exp ηa exp ηa RT RT (3.20) Assuming the charge transfer coefficients α a = α a = 0.5, the value of the exchange current density for the silver dissolution reaction at the temperature of 298 K calculated from Equation (3.20) is summarized in Table

188 Table 3-4. Summary of the calculated exchange current density. i (ma/cm 2 ) η a a (V) i o (ma/cm 2 ) i o (average) (ma/cm 2 ) Standard deviation The value of the exchange current density for the Ag/Ag + redox reaction varied in a large range depending on the nature of the electrolyte. An extremely high exchange current density on the order of 10-1 A/cm 2 for Ag/Ag + redox reaction in perchlorate solutions has been used in literature [21, 45]. In other cases, the exchange current density in the range of 10-5 to 10-3 A/cm 2 for the silver electrodeposition in cyanide electrolyte has been reported [46-48]. However no value is available for the reaction in NaCl solution. Since the concentration overpotential in the situation considered here is negligible, the measured potential given in Equation (3.12) can be rewritten as: x a = + + ηa (3.21) K a V E i This expression indicates the contribution of the ohmic overpotential and the activation overpotential on the dissolution kinetics of silver. When the AgCl is a non-continuous layer, the value of the second term in Equation (3.21), which represents the ohmic overpotential, is small in comparison with the third term, which represents the activation overpotential, therefore the activation overpotential is dominant and determines the dissolution current. When the AgCl is a thin, continuous layer, e.g. after 1 hour at i = 0.5 ma/cm 2, the second term and the third term in (3.21) are of the same order, therefore the 163

189 dissolution of silver is under mixed ohmic-activation controlled regime. After a long time when the thickness of the AgCl layer becomes large, e.g. after 4 hours at i = 0.5 ma/cm 2, the second term in (3.21) will dominate the last term. Thus, after a long enough time, the activation overpotential will become negligible and the silver dissolution will be under an ohmic controlled regime Summary The precipitation and growth of AgCl on a silver substrate in 9 g/l NaCl solution were investigated. AgCl particles nucleated at the bottom of the scratches on the surface which may be the less effective sites for diffusion or the favorable sites for heterogeneous nucleation. The particles grew to patches which expanding laterally on the substrate until forming a continuous film. Ionic transport through the newly formed continuous AgCl film was via the pores between the AgCl grains. As the film thickened, the pores between the AgCl grains were sealed and the ionic transport was mainly via micro-channels running through the AgCl grains. The ohmic resistance of the continuous AgCl layer inhibited the dissolution of the silver substrate. At high current densities and when the AgCl layer is thick, the conduction mechanism is transited from extrinsic, i.e. via electrolyte in the micro-channels, to intrinsic, i.e. via AgCl solid phase. The micro-channels were accounted for ca. 4% volume fraction of the AgCl layer. The conductivity of the electrolyte inside the micro-channels was estimated to be on the order of 10-4 S/cm. The concentration of Cl - and Ag + inside the micro-channels was estimated to be on the order of 10-6 mol/cm 3 and mol/cm 3, respectively. The apparent conductivity of the AgCl layer was on the order of 10-6 to 10-5 S/cm and 164

190 decreased with the film thickness. The exchange current density of the Ag/Ag + redox reaction in 9 g/l NaCl was ca. 1.3x10-4 A/cm 2. In the current density range from 0.1 to 2 ma/cm 2, the concentration overpotential at the silver electrode was negligible. When the AgCl is a non-continuous layer, the dissolution of silver is under activation controlled regime. When the AgCl layer is thin, i.e. on the order of several μm, the dissolution of silver is controlled by both the ohmic overpotential through the AgCl layer and by the activation overpotential at the silver electrode. When the AgCl layer is thick, i.e. on the order of tens of μm or thicker, the dissolution of silver is controlled only by the ohmic overpotential through the AgCl layer. 165

191 3.5 Corrosion model of silver-cored MP35N LT composite in physiological solution Scope In Section 3.3, the corrosion behavior of the silver-cored MP35N LT composite in physiological saline solutions has been studied experimentally. It has been shown that in physiological solutions at room temperature and 37 o C, the MP35N LT alloy exhibited passive behavior in a large range of potential up to ca V vs. SCE while silver was subjected to rapid dissolution at potentials above ca V. vs. SCE. In the galvanic couple, the silver core was the anode and the MP35N LT outer tube was the cathode. During immersion tests in 9 g/l NaCl solution at 37 o C, the MP35N LT outer tube appeared to be corroded negligibly, however the silver core of the composite was dissolved leaving a pit at the core. It has also been shown that silver chloride deposited on the silver substrate as the result of the corrosion process. In Section 3.4, the formation of the AgCl layers as the result of the dissolution at a silver electrode has been discussed. During the early growth of the AgCl layer, dissolution of silver was under mixed activation- ohmic controlled regime. As the AgCl layer grew thicker, the ionic transport though the layer becomes more difficult and the ohmic overpotential became dominant over the activation overpotential. Eventually the dissolution of silver was brought into ohmic controlled regime. The AgCl layer acted as an ion transport barrier to limit further dissolution at the silver substrate. In this section, a corrosion model for the silver-cored MP35N LT wire in vitro is developed. The model focuses on the anodic processes occurring at the silver electrode. The Co-based alloy outer tube is considered in passive state and the corrosion on this material is negligible. Experiments to validate the theoretical model were performed. 166

192 Constant potential exposure experiments were conducted in physiological solution of 9 g/l NaCl at different applied potentials of 0.1, 0.2, 0.6 and 1.0 V vs. SCE for 24 hours. Cyclic voltammetry experiments were conducted at various scan rates of 1, 5, 10, 15, 25, 35, 50, 65, 80 and 100 mv/s. More details on the specimen preparation and experiment procedures are presented in Section , Section and Section Corrosion cell in the silver-cored MP35N LT composite in vitro Figure 3-35 presents a schematic of the corrosion cell for a silver-cored MP35N LT wire in vitro. Corrosion occurs at the silver core following the anodic reaction: Ag = Ag + + e - (3.22) Dissolution of the silver core formed a pit with the size on the order of tens of micrometer. Cathodic reactions took place somewhere outside the corroding silver electrode on the outer tube. A common cathodic reaction is the oxygen reduction: 1/2O 2 + H 2 O + 2e - = 2OH - (3.23) Metallic contacts between the silver core and the MP35N LT outer tube formed the electrical path of the cell. The electrolyte containing Na +, Cl -, Ag +, OH -, etc. formed the ionic path of the cell. The electrical field between the cathode and the anode drove the electron current in the electrical path. The concentration gradient and the electrical field between the cathode and the anode drove the movement of the ions in the electrolyte. AgCl layers could form at the silver electrode. The ionic path in the AgCl layers was via the electrolyte inside the micro-channels running though the AgCl grains. 167

193 Cl - Cl - Na + Na + Cl - Na + Cl - Na Na OH O OH - OH - O 2 OH - OH - OH - 2 O 2 O 2 O 2 1/2O 2 + H 2 O + 2e - = 2OH - 1/2O 2 + H 2 O + 2e - = 2OH - OH - Cl - OH - Na + Cl - Cl - Na + Ag + Ag + Ag + Ag + AgCl layer MP35N LT (Cathode) e - Ag = Ag + + e - e - e- e - Silver (anode) MP35N LT (Cathode) Figure Schematic of the corrosion cell of a broken silver-cored MP35N LT composite wire in vitro Description of the corrosion process The corrosion process of the silver core in a broken wire can be described following several stages as illustrated in Figure In stage 1 when the wire has just been broken, the silver core is subjected to corrosion at a rate corresponding to a current density i. Dissolution of silver core forms a pit as shown in stage 2. The Ag + ions are accumulated inside the pit as the corrosion of the silver core proceeds. When the pit is saturated with Ag + ions, AgCl starts precipitating and deposits as the corrosion product on the silver electrode. In stage 3, the AgCl layer grows with the continuous dissolution of the silver core. After a certain time, the kinetics of the silver dissolution and the AgCl formation is controlled by only the ohmic drop through the AgCl layer. In stage 4, the AgCl layer fills the pit and then grows out of the tube to form a hemispherical cap. The kinetics of the 168

194 silver dissolution and the AgCl formation is still under ohmic controlled regime in this stage. MP35N Ag MP35N Ag MP35N Ag AgCl MP35N Ag AgCl i i Stage 1 Stage 2 Stage 3 Stage 4 Figure Schematic of the stages for the dissolution of silver and the formation of AgCl in vitro. With the breakdown of the corrosion process of a broken silver-cored MP35N LT composite wire in vitro in to the four abovementioned stages, theoretical models for the corrosion of the silver core in each stage is developed. Qualitative and quantitative implications from the theoretical models will be discussed and related to the corrosion process in practice Determination of the corrosion current in Stage 1 In stage 1, the wire has just been broken and the silver core is exposed to the ambient. The anodic dissolution occurs at the silver core. The cathodic reactions occur on the MP35N LT alloy outer tube. The corrosion current and potential at the silver core can be determined by the mixed potential theory as introduced earlier in Section The Evans diagram of the anodic polarization curve of the silver core and the cathodic polarization curve of the MP35N LT alloy in Ringer s solution at 37 o C is shown in Figure The electrode areas of the silver core and the MP35N LT alloy are taken 169

195 from the cross section of a composite wire and are equal to 11x10-6 and 16x10-6 cm 2, respectively. From the polarization curves, the corrosion current is determined as 8x10-13 A which is equivalent to an anodic current density of 7x10-6 A/cm 2. The corrosion potential is determined as V vs. SCE MP35N LT Ag Potential (V vs. SCE) E-14 1E-13 1E-12 1E-11 1E-10 1E-9 1E-8 1E-7 1E-6 Current (A) Figure Evans diagram of the silver core and the MP35N LT alloy outer tube in Ringer s solution at 37 o C. The electrode areas of the silver core and the MP35N LT alloy outer tube are 11x10-6 and 16x10-6 cm 2, respectively. In Section 3.1.5, the effect of the cathode-to-anode area ratio on the corrosion current and the corrosion potential has been discussed. It is obvious that as the cathode to anode area ratio increases, the cathodic polarization curve moves relatively with the anodic polarization curve to the higher current direction which results in an increase of both corrosion current and corrosion potential. In practice, the situation occurs when the electrolyte runs into the gaps between the wires and the insulation layer wetting the 170

196 surface of the MP35N LT outer tubes. The rate of the surface wetting process has not been measured in this study however the value is speculated to be small due to the capillary effect of the small scale size The accumulation of the Ag + cations in Stage 2 Consider a broken silver-cored MP35N LT strand as depicted in Figure The silver core is continuously dissolved. A pit is formed at the core and the concentration of the electrolyte inside the pit changes as corrosion proceeds. To set up transport equations for the species inside the pit, several assumptions are made: (i) The main charge carriers inside the pit are Na +, Cl - and Ag + and the diffusivity of these ions are assumed constant as the pit grows. (ii) The oxygen concentration inside the pit is limited therefore all cathodic reactions are considered taking place outside the pit. (iii) (iv) There is no chemical reaction in the pit solution. The rate of the silver dissolution is constant with increasing pit depth and with increasing Ag + concentration. (v) To simplify the model, no convection is included and the transport processes are in one dimension. (vi) The model is developed for steady-state condition. 171

197 Cl - 1/2O Na + Na H 2 O + 2e - = 2OH - 1/2O 2 + H 2 O + 2e - = 2OH - Cathode Cl - Na + Na + Cl - Cathode Cl - Cl - Na + Ag + Ag + Ag + Ag + Ag = Ag + + e - MP35N LT Anode Silver MP35N LT Figure Schematic of a broken silver-cored MP35N LT wire for modeling of the transport process inside the pit at the silver core. The transport of the species inside the pit is governed by the material conservation equations: 2 dc1 d C1 z1f d dφ = D1 + D 2 1 C1 dt dy RT dy dy 2 dc2 d C2 z2f d dφ = D2 + D 2 2 C2 dt dy RT dy dy 2 dc3 d C3 z3f d dφ = D3 + D 2 3 C3 dt dy RT dy dy (3.24) (3.25) (3.26) where the subscripts 1, 2 and 3 represent the charge carriers Na +, Cl - and Ag +, respectively; C is the concentration of the species; D is the diffusivity of the species; z is the charge of the species; t is time; y is the distance from the pit mouth; F is the Faraday s constant; R is the gas constant; T is temperature; and Φ is the electrostatic potential drop 172

198 in the pit. In the right-hand side of Equations (3.24) to (3.26), the first term represents the change in concentration due to diffusion and the second term represents the change in concentration due to migration under an electrostatic field. At steady-state we can assign: dc1 dc2 dc3 = = = 0 (3.27) dt dt dt The justification for the steady-state assumption is that the transient associated with small cavities as observed when the pit intially forms before the precipitation of AgCl are extremely fast. The order of magnitude for such transients in a pit of 1 μm depth is: τ δ D (10 ) = 10 ( s) (3.28) 8 Inside the pit, the electrolyte must satisfy the electroneutrality condition: zc i i = 0 (3.29) With the assumption made earlier that there are only 3 charge carriers in the electrolyte inside the pit, i.e. Na +, Cl - and Ag +, Equation (3.29) becomes: C1 C2 + C3 = 0 (3.30) where C 1, C 2 and C 3 are the concentration of Na +, Cl - and Ag +, respectively. The boundary conditions for Equations (3.24) to (3.26) are: B.C. 1: At the mouth of the pit (y = 0) the potential drop is set to zero: Φ (y = 0) = 0 (3.31) and the concentration of Na + and Cl - is equal to the concentration of those species in the bulk solution, C b : C 1 (y = 0) = C b (3.32) C 2 (y = 0) = C b (3.33) 173

199 The concentration of Ag + at the pit mouth approaches zero due to diffusion and/or convection in the bulk solution: C 3 (y = 0) = 0 (3.34) B.C. 2: At the bottom of the pit (y = L), the flux of the species involving in the anodic reactions are proportional to the current density, the fluxes of the other species are zero. Thus: dc F d 1 φ D1 + DC 1 1 = 0 (3.35) dy RT dy D D dc F D C d φ = (3.36) dy RT dy dc F d φ + DC = i (3.37) dy RT dy F The corrosion current at the silver electrode is related to the overpotential by: a α FV ( E φ) i = io exp RT (3.38) The corrosion current is assumed constant as mentioned earlier. Solving the set of Equations (3.24), (3.25), (3.26) and (3.30) with the boundary conditions of (3.31) to (3.38) (see appendix B) gives the concentration of each species inside the pit and the electrostatic potential distribution: 2 2Cb C = 1 i y 2Cb FD + 3 (3.39) i y C2 = + Cb (3.40) 2FD 3 174

200 C i y 2C 2 = b 3 Cb 2FD + i y 3 + FD 3 2C b (3.41) RT i y φ = ln + 1 F 2C b FD3 (3.42) Figure 3-39 shows the dependence of the concentration of Na +, Cl -, Ag + and the potential drop on the product of i.y as expressed in the Equations (3.39) to (3.42). The diffusivity of silver, D 3, is taken as 1.65x10-5 cm 2 /s. The bulk concentration of Na + and Cl - in physiological solutions, C b, is 0.154x10-3 mol/cm

201 IR drop (V) IRdrop Ag Na Cl 1.4x x x x x x10-4 Conc. (mol/cm3) 0.01 (a) x x x x x x10-3 i.y 2.0x10-4 (b) i.y Figure The dependence of the concentration of Na +, Cl -, Ag + and the potential drop on i.y: (a) i.y varies in the range of 0 to 3x10-3 A/cm; and (b) i.y varies in the range of 0 to 1x10-9 A/cm It appears that the potential drop inside the pit solution is insignificant. With a dissolution current of several ma/cm 2 and a pit depth of few centimeters, the potential drop is only some tens milivolts. Figure 3-39 also shows that at the locations deeper 176

202 inside the pit, i.e. higher y, or at higher dissolution currents, the concentration of Na +, C 1, decreases while the concentrations of Cl -, C 2, and of Ag +, C 3, increase. This result indicates that the product of the silver concentration and the chloride concentration, C 2.C 3 increases when i.y increases. Precipitation of AgCl starts when C 2.C 3 reaches the solubility product K sp for AgCl. The condition is expressed as: C 2. C 3 K sp (3.43) Substituting (3.40) and (3.41) in to (3.43) gives: i y i y 2C 2FD b + Cb + Cb Ksp i y 3 FD 3 2C b FD 3 (3.44) Solving (3.44) with the notice that i.y 0 yields: 2 ( b sp b) i y D F C + K C (3.45) 3 4 The numerical value of the parameters in Equation (3.45) is given in Table 3-5. The plot for (3.45) is presented in Figure 3-40 which shows the condition for the precipitation of AgCl. In the region below the solid line in Figure 3-40, i.e. the dissolution current of silver is small and the pit is shallow, AgCl can not form. In the region above the solid line, i.e. higher dissolution current and/or deeper pit, AgCl starts forming. Table 3-5. Values of the parameters used in evaluating the condition for AgCl formation. D 1 F C b K sp (cm 2 /s) (C/equiv) (mol/cm 3 ) (mol/cm 3 ) x x x

203 Current (A/cm 2 ) No AgCl Form AgCl Distance from pit mouth (μm) Figure Conditions for AgCl precipitation as a function of the dissolution current density and the distance from the pit mouth. If the value of the current density determined in stage 1 is taken, i.e. i = 7x10-6 A/cm 2, the model predicts that AgCl will starts precipitating when the pit depth reaches 4x10-7 cm. In practice, the pit can grow deeper before AgCl precipitation due to several reasons. First, the three dimensional diffusion and the convection inside the pit which is not considered in this model will reduce the concentration of Ag + and Cl - inside the pit solution. Second, the formation of complex compounds such as Ag(Cl) n n-1 which effectively reduces the concentration of Ag + and Cl - can also delay the formation of AgCl. Finally, the model is developed for steady-state condition which is not always satisfied in the real dissolution process of the silver core. 178

204 3.5.6 The dissolution of the silver core and the growth of the AgCl layer in Stage 3 In stage 2, it has been demonstrated that as the pit grows deeper, accumulation of Ag + inside the pit solution will leads to the precipitation of AgCl. Experimental data and theoretical analysis in Section 3.4 shows that the formation of a continuous AgCl layer on the silver electrode causes a potential drop through the layer and when the layer grows thick enough, the kinetics of the silver dissolution is under ohmic controlled regime. A model for the dissolution of the silver core and the growth of the AgCl layer in Stage 3 is developed in this section. Experimental validation for the model is also presented Theoretical model Let s start with some assumptions for the model. First, assume that there is only one reaction at the anode, the dissolution of silver: Ag = Ag + + e - (3.46) This means the anodic current density i is due only to the above reaction. Second, assume that the silver core dissolves uniformly, i.e. the exposed cross section of the core always keeps a circular flat surface during dissolution. Third, assume that all Ag + ions dissolved in Stage 3 precipitates as AgCl and the thickness of the AgCl layer is uniform. This means the reaction (3.46) can be rewritten as: Ag + Cl - = AgCl + e - (3.47) and therefore the dissolution current of silver is equal to the current for AgCl formation. For now, let s skip the transition periods from a non-continuous AgCl layer to a thin AgCl layer and from a thin AgCl layer to a thick continuous AgCl layer. Once the thick, continuous AgCl forms, the dissolution of silver is under ohmic controlled regime, thus the process follows Ohm s law. In addition, the reactions (3.46) and (3.47) have 179

205 electrochemical nature, hence they follow Faraday s law. The dependence of the corrosion current density, i, and the thickness of the AgCl layer, x, on time, t, can be obtained by solving the equations provided by Ohm s law and Faraday s law. With the assumption of uniform silver dissolution and AgCl formation, the AgCl layer will grow in to a cylindrical shape. The mass of AgCl precipitated, m AgCl, is calculated from the anodic current density by Faraday s law: m M iat F = AgCl (3.48) AgCl n where M AgCl is the molecular weight of AgCl; n is the number of electron transferred in reaction (3.47); A is the cross section area of the silver core; and F is the Faraday constant. The mass of AgCl precipitated can also be calculated based on the volume of the AgCl layer and the density of AgCl, ρ AgCl : m AgCl = A x ρ (3.49) AgCl Substituting (3.49) in to (3.48) and differentiate both sides of the equation yields: dx M i AgCl = (3.50) nfρ AgCl dt Equation (3.50) describes the change in the thickness of the AgCl layer after an infinite small time dt. The relationship between the thickness of the AgCl layer, x, with time, t, can be obtained by integrating both side of the Equation (3.50) from time 0 to time t. However, before doing that, the anodic current density, i, must be expressed as a function of x using Ohm s law. The potential at an external cathode, V, is the sum of the anode potential, E a, the activation overpotentials, η a, and concentration overpotentials, η c, at the anode and the cathode, and the ohmic overpotential, η Ω, in the medium between the two electrodes: 180

206 V = E a + η a a + η c a + η a c + η c c + η Ω (3.51) Note that the dissolution process is under ohmic controlled regime, therefore the terms η a a and η c a are negligible. If the activation overpotential and the concentration overpotential at the cathode, η c a and η c c, are also small, the potential at the external cathode is simplified to: V = E a + η Ω (3.52) In another word, the ohmic overpotential can be expressed as: η Ω = V E a (3.53) As shown in Section 3.5.5, the potential drop in the electrolyte inside the pit is insignificant. Hence the ohmic overpotential is mainly due to the resistance of the AgCl layer and can be expressed by Ohm s law as follows: i η Ω = x (3.54) K where K is the apparent conductivity of the AgCl layer. Substituting (3.53) in to (3.54) yields: i = (3.55) K a V E x Rearranging Equation (3.55) obtains the relationship between the anodic current density, i, and the AgCl thickness, x: 1 i= ( V E a ) K (3.56) x Substituting (3.56) in to (3.50) yields: M AgCl a 1 dx = ( V E ) K dt (3.57) nfρ x AgCl 181

207 Rearranging (3.57) gives: M AgCl a xdx = ( V E ) K dt (3.58) nfρ AgCl Now, the relationship between the thickness of the AgCl layer, x, and the anodic polarization time, t, can be obtained by integrating both sides of Equation (3.58) with the initial condition of x(t=0) = 0. The solution of the integration is: 2 x M AgCl a = ( V E ) K t (3.59) 2 nfρ AgCl or it can be written explicitly as: 1/2 2M AgCl a x = ( V E ) K t nfρ AgCl 1/2 (3.60) The corrosion current density, i, is obtained by substituting (3.60) in to (3.56): 1/2 nfρ AgCl a i= ( V E ) K t 2M AgCl 1/2 (3.61) Equations (3.60) and (3.61) represent the dependence of the AgCl thickness and the corrosion current density on time. If the potential difference between the cathode and the anode, V E a, is constant and the conductivity of the AgCl layer, K, are independent of time, the thickness of the AgCl layer, x, will increase with square root of time and the corrosion current, i, will decay with square root of time as the silver dissolution process continues. If the potential difference between the cathode and the anode, V E a, changes with time, the dependence of i and x on t will change. In a special situation, assuming that the potential difference changes linearly with time as: a V E = s t (3.62) 182

208 where s is a positive constant representing the increase rate of the potential difference. The thickness of the AgCl layer and the silver dissolution current density in this condition is obtained by substituting (3.62) in to (3.60) and (3.61), yielding: 1/2 2M AgCl 1/2 x = K s t nfρ AgCl (3.63) and 1/2 nfρ AgCl i= K s 2M AgCl 1/2 (3.64) Equations (3.63) and (3.64) present new kinetics law for the silver dissolution and the AgCl formation under the condition of linear increase of the potential difference between the cathode and the anode. One notable feature is that the silver dissolution rate under this condition is independent of time. The mathematic model for the kinetics of the silver dissolution and the AgCl formation during Stage 3 has been established. Equations (3.60), (3.61), (3.63) and (3.64) shows that the thickness of AgCl layer, x, and the anodic current density, i, are functions of the potential difference between the cathode and the anode, V-E a, the appreance conductivity of the AgCl layer, K, and time, t. The effect of each parameter on the AgCl layer thickness and on the corrosion current density of silver will be discussed in the proceeding sections The effect of the potential difference Silver dissolution current densities and AgCl thicknesses are calculated at different potential difference of 0.1, 0.2, 0.4 and 1.0 V. The time point is chosen at 1 hour. The apparent conductivity of the AgCl layer in 9 g/l NaCl solution is reported to vary in the 183

209 range of 10-6 to 10-5 S/cm. To isolate the effect of the AgCl apparent conductivity, K is assumed to be constant and has the value of 2x10-6 S/cm. The values of other parameters used for the calculation are shown in Table 3-6. Table 3-6. The values of the parameters used in evaluating the effect of constant potential difference on the kinetics of the silver dissolution and the AgCl formation. M AgCl (g) n F (C/equiv) ρ AgCl (g/cm 3 ) K (S/cm) t (s) x The dissolution rates and the AgCl thicknesses after 1 hour polarization calculated at different constant applied potentials are shown in Figure Both the current density and the AgCl thickness increase proportional with the square root of the potential difference, (V E a ) 1/2, (Figure 3-41). In the potential difference range from 0.1 to 1 V, which is commonly observed in corrosion cells, the corrosion current density after 1 hour polarization varies from 0.3 to 1 ma/cm 2 while the thickness of AgCl layer varies in the range of 6 and 20 μm. 184

210 2 i x 30 i (ma/cm 2 ) x (μm) (V - E) 1/2 /(V 1/2 ) Figure The effect of the potential difference on the silver dissolution rate and the AgCl thickness after 1 hour of constant potential polarization The effect of the AgCl apparent conductivity The silver dissolution current densities and the AgCl thicknesses are calculated at different AgCl layer conductivity of 10-6, 2x10-6, 5x10-6 and 10-5 S/cm. These values are selected based on the measured apparent conductivity of the AgCl layer anodically grown in 9 g/l NaCl solution (see Section ). The time point is chosen at 1 hour and the potential difference is 0.2 V which is approximately the difference in the open circuit potential between the MP35N LT alloy and pure silver in 9 g/l NaCl solution (see Section ). The values of the other parameters used for the calculation are shown in Table

211 Table 3-7. The values of the parameters used in evaluating the effect of the AgCl layer conductivity on the kinetics of the silver dissolution and the AgCl formation. M AgCl n F ρ AgCl V E a t (g) (C/equiv) (g/cm 3 ) (V) (s) The dissolution rates and the AgCl thicknesses calculated at different AgCl layer apparent conductivity are shown in Figure Both the dissolution rate and the AgCl thickness increase linearly with square root of the AgCl conductivity. As the conductivity changes in the range of 10-6 to 10-5 S/cm, the dissolution current density varies in the range of 0.3 to 1 ma/cm 2 and the AgCl layer thickness varies in the range of 6 to 20 μm. 2 i x i (ma/cm 2 ) 1 10 x (μm) 0 1.0x x x10-3 K 1/2 (S/cm) 1/2 0 Figure The effect of AgCl layer apparent conductivity on the silver dissolution rate and the AgCl thickness after 1 hour of constant potential polarization. 186

212 The effect of the polarization time The silver dissolution current densities and the AgCl thicknesses are calculated during a polarization period of 1 month. The value of the potential difference is chosen at 0.2 V which is the difference in the open circuit potential between the MP35N LT alloy and pure silver in 9g/l NaCl solution (see Section ). The apparent conductivity of the AgCl layer is varies from 10-6 to 10-5 S/cm to represent the change in the AgCl conductivity during its growth. The values of the other parameters used for the calculation are shown in Table 3-8. Table 3-8. The values of the parameters used in evaluating the effect of the polarization time on the kinetics of the silver dissolution and the AgCl formation M AgCl (g) n F (C/equiv) ρ AgCl (g/cm 3 ) V E a (V) K (S/cm) The change in the kinetics of the silver dissolution with time is shown in Figure For all AgCl apparent conductivities, the inverse of the silver dissolution current density has linear relationship with the square root of time. In another word, the dissolution current density of silver decays proportional with the square root of time. At lower AgCl apparent conductivity, the value of 1/i is higher and the slope of the 1/i vs. t 1/2 curve is higher. This indicates that as the conductivity of the AgCl layer decreases, the dissolution rate of silver decrease and the rate of decreasing is faster. The effect of the AgCl apparent conductivity on the slope of the 1/i vs. t 1/2 curve has important practical implication. During the AgCl growth, the conductivity of this layer indeed decreases as shown in Section Hence the dissolution rate of silver, i, 187

213 decays faster than the square root of time relationship and when plotted in a 1/i vs. t 1/2 coordination, the slope of the curve is predicted to increase with time. The change of the AgCl thickness with time is shown in Figure The thickness of the AgCl layer increases linearly with the square root of time. In another word, the growth of the AgCl layer follows parabolic law. The effect of the AgCl conductivity on the thickness of the AgCl layer is also indicated in the figure. Thinner AgCl layers form on those with lower conductivity. 1/i (ma/cm 2 ) K=10-6 K=2x10-6 K=5x10-6 K= t 1/2 (s 1/2 ) Figure The effect of polarization time on the dissolution current density of silver. 188

214 K=10-6 K=2x10-6 K=5x10-6 K=10-5 x (μm) t 1/2 (s 1/2 ) Figure The effect of polarization time on the thickness of AgCl layer The effect of the potential scan rate If the potential difference between the cathode and the anode is not constant but increases with time, the kinetics of the silver dissolution and the AgCl formation will be expressed by Equations (3.64) and (3.63), respectively. It is not likely that this scenario will occur in the case of the silver-cored MP35N LT composite corrosion because both MP35N LT alloy and silver reached their stable open circuit potentials in quite a short time as shown in Section However, the situation is considered as a special case for the model validation. Moreover, the kinetics law found in this case may be useful for the production of AgCl film on silver substrate in chloride environment. The silver dissolution current density, i, and the AgCl thickness, x, are calculated at different scan 189

215 rates of 1, 10, 50 and 100 mv/s. The values of the other parameters are shown in Table 3-9. Table 3-9. The values of the parameters used in evaluating the effect of the potential scan rate on the kinetics of the silver dissolution and the AgCl formation M AgCl (g) n F (C/equiv) ρ AgCl (g/cm 3 ) K (S/cm) t (s) x The effect of the potential increase rate on the silver dissolution rate is shown in Figure The current density increases linearly with the square root of the scan rate regardless of polarization time. The effect of the scan rate on the AgCl thickness after 1 hour polarization is shown in Figure Similar to the behavior of the current density, the AgCl thickness also increases linearly with the square root of the scan rate. When the scan rate is constant, the thickness of the AgCl layer increases linearly with time as indicated in Equation (3.63). At a scan rate of 100 mv/s, the dissolution current density is approximately 20 ma/cm 2 and the thickness of AgCl layer is approximately 400 μm after 1 hour polarization. However to keep this high dissolution rate, the potential difference between the cathode and the anode, V E a, will have to increase to 360 V after 1 hour and keep increasing with a rate of 100 mv/s. 190

216 25 20 i (ma/cm 2 ) s 1/2 (V/s) 1/2 Figure The effect of the scan rate on the silver dissolution rate x (μm) s 1/2 (V/s) 1/2 Figure The effect of the scan rate on the thickness of the AgCl layer. 191

217 Validation of the model Constant potential experiment Figure 3-47 shows the dependence of the current densities with time during the constant potential experiments at different applied potentials of 0.1, 0.2, 0.6 and 1.0 V vs. SCE. The data are presented in a 1/i vs. t 1/2 plot. The curves at the applied potentials of 0.2, 0.6 and 1.0 V vs. SCE show linear behavior after ca. 1 hour polarization. This linear behavior is predicted from Equation (3.64) and in Figure The 1/i vs. t 1/2 curve at the constant applied potential of 0.1 V vs. SCE showed fluctuation superimposing on an approximately linear behavior. The same fluctuation in the anodic current during the AgCl formation has been reported in literature by a numbers of researchers [29, 30, 49]. The phenomenon was explained by some authors as the result of the coupling between the ion transport and the AgCl precipitation reaction inside the pores of the AgCl layer [29]. Other authors attributed the phenomenon to the breaking and healing of the AgCl film [30]. The fluctuation behavior observed in this study, in both constant potential exposure and galvanostatic experiments, is more likely due to the former reason, i.e. the coupling between the ion transport and the AgCl precipitation reaction inside the pores of the AgCl layer. Another feature should be noticed in Figure 3-47 is that the slope of all 1/i vs. t 1/2 curves increased during the first 1 hour. These segments of the curves represented the relationship between the corrosion current density with time during the transition from a non-continuous AgCl layer to a thick AgCl layer. During this period, the dissolution of silver was under activation controlled regime or mixed activation-ohmic controlled regime, therefore the contribution of the resistance of the AgCl layer on limiting the 192

218 dissolution at the silver electrode was still small. Consequently the rate of decreasing dissolution current in this period, represented by the slopes of the 1/i vs. t 1/2 curves, were smaller than those in the later period which was under the ohmic controlled regime. The slopes of the 1/i vs. t 1/2 curves can be calculated from the theoretical model. From Equation (3.61), the slope of the 1/i vs. t 1/2 curve is given by: nfρ AgCl a Slope = ( V E ) K 2M AgCl 1/2 (3.65) where n is the number of electron transferred in reaction (3.47) (n = 1); F is the Faraday s constant (F = C/equiv); ρ AgCl is the density of the AgCl layer (ρ AgCl = 5.56 g/cm 3 ); M AgCl is the molecular weight of AgCl (M AgCl = g/mol); V - E a is the potential difference between the cathode and the anode; and K is the apparent conductivity of the AgCl layer. The potential of the cathode, V, in the constant potential polarization experiments were the applied potentials of 0.1, 0.2, 0.6 and 1.0 V vs. SCE. The potential of the silver anode covered with a continuous AgCl layer in 9 g/l NaCl solution was ca V vs. SCE (see Section ). The apparent conductivity of the AgCl layer is chosen based on the relationship between K and the coulomb passed per unit area discussed in Section The coulomb passed per unit area during the constant potential polarization for 24 hours was on the order of few tens C/cm 2, thus K was on the order of 10-6 S/cm. The slopes of the 1/i vs. t 1/2 curves calculated by (3.65) are summarized in Table

219 25 20 E = 0.1 V E = 0.2 V E = 0.6 V E = 1.0 V 1/i, (ma/cm 2 ) t 1/2, (s) 1/2 Figure The 1/i vs. t 1/2 curves obtained from constant potential exposure experiments at different applied potentials of 0.1, 0.2, 0.6 and 1.0 V vs. SCE in physiological solution of 9 g/l NaCl solution. Table Summary of the slopes of the 1/i vs. t 1/2 curves obtained from theoretical calculations and from constant potential exposure experiments. V (V vs. SCE) Calc. slope (cm 2.A -1.s -1/2 ) Measured slope (cm 2.A -1.s -1/2 ) ± ± ± 0.01 % difference 37% 97% 68% 194

220 The linear behavior segments in the 1/i vs. t 1/2 curves after 1 hour of constant potential polarization at E = 0.2, 0.6 and 1.0 V vs. SCE were also fitted by Origin 8.0 SR2 software (OriginLab Corporation, USA). The curve obtained at the applied potential of 0.1 V vs. SCE exhibited fluctuation during most of the experiment time and was difficult to performed linear fitting, therefore it was excluded from this analysis. The slopes obtained from the linear fit for others applied potentials are summarized in Table Comparing the calculated and the measured slopes shows that the values obtained from the theoretical model were smaller than those obtained from the experiments with the error varied in the range from 37% to 97%. The reason for this mismatch is partially due to the overestimation of the AgCl density in which the porosity due to the micro-channels was ignored. Another reason is probably due to the overestimation for the value of the AgCl apparent conductivity which might be smaller than 10-6 S/cm for thick AgCl layers Cyclic voltammetry The dependence of the anodic current density with time in the cyclic voltammetry experiments is shown in Figure Below ca V vs. SCE, the anodic dissolution currents were negligible. At ca V vs. SCE, the anodic currents started rising indicating the nucleation and growth of the non-continuous AgCl films. At the early stage when AgCl covered only a small surface fraction of the electrode, the currents increased approximately linear with potentials indicating the dominant of the low-field activation controlled regime. During this time, non-continuous AgCl film expanded laterally rather than grew out of the surface as discussed in Section and Section At higher anodic potentials, the low-field activation controlled regime is transited to the high-field activation controlled regime which is partially attributed to the deviation of the i vs. E 195

221 curves away from the linear behavior. Another reason for the deviation from the linear behavior of the i vs. E curves is that after polarization for a certain time, the AgCl coverage was larger therefore the ohmic resistance of the AgCl layer covering the electrode became significant and so did the ohmic overpotential. Gradually, the increase in the driving force for the dissolution, i.e. the activation overpotential, was compromised by the increase of the ohmic overpotential caused by the AgCl layer and a maximum appeared in the i vs. E curves. With the growth of the AgCl layer, the current started decreasing until a balance between the rate of increasing ohmic overpotential and the rate of increasing applied potential was reached. At this moment, the AgCl layer grew in thickness so that the ohmic overpotential through the AgCl layer increased accordingly with the increasing applied potential, thus the activation overpotential was kept at a constant value. Consequently, the current stayed at an approximately constant value with increasing applied potential as predicted by Equation (3.64). 75 i (ma/cm 2 ) mV/s E (V vs. SCE) 100mV/s 80mV/s 65mV/s 50mV/s 35mV/s 25mV/s 15mV/s 10mV/s 5mV/s Figure The i vs. E curves obtained from the cyclic voltammetry experiments at different scan rates in physiological solution of 9 g/l NaCl solution. 196

222 To examine the effect of the potential scan rate on the current density, the value of the current densities obtained in the cyclic voltammetry experiments at the potential of 1.0 V vs. SCE, where the value of current densities did not change with potential, were used. Figure 3-49 presents the data in an i vs. s 1/2 plot which shows an approximately linear relationship between the current density and the square root of the potential scan rate as predicted by Equation (3.64) and Figure Linear fitting the experiment data in Figure 3-49 was performed with Origin 8.0 SR2 software (OriginLab Corporation, USA) earning a slope of ± A.cm -2.s -1/2. The slope of the i vs. s 1/2 plot predicted by the theoretical model is calculated from Equation (3.64) which gives: nfρ AgCl Slope = K 2M AgCl 1/2 (3.66) where n is the number of electron transferred in reaction (3.47) (n = 1); F is the Faraday s constant (F = C/equiv); ρ AgCl is the density of the AgCl layer (ρ AgCl = 5.56 g/cm 3 ); M AgCl is the molecular weight of AgCl (M AgCl = g/mol); and K is the apparent conductivity of the AgCl layer. The conductivity K is chosen as 2x10-5 S/cm due to the AgCl layer formed during the cyclic voltammetry experiments was thin. Substitute the numerical values of the parameters in to Equation (3.66) earns a slope equal to A.cm -2.s -1/2. The i vs. s 1/2 curve with the calculated slope is plotted together with the experimental data in Figure 3-49 for comparison. The error between the predicted slope and the measured one is ca. 10%. 197

223 70 60 Experiment data Calculated data i (ma/cm 2 ) Slope = Slope = ± s 1/2 (V/s) 1/2 Figure The i vs. s 1/2 curves obtained from the cyclic voltammetry experiments and from the theoretical model The dissolution of the silver core and the growth of the AgCl layer in Stage Theoretical model The assumption that AgCl layer grows in to a cylindrical shape holds until AgCl fills the pit at the silver core as shown in Figure After that, the AgCl layer grows out of the pit and forms mushroom-like cap. New kinetics for the silver dissolution and the AgCl growth will be established depending on the shape of the AgCl layer. Nevertheless the process still obeys Faraday s law and Ohm s law. The dissolution of the silver core and the growth of the AgCl layer after AgCl fills the pit can be described in more detail as shown in Figure The AgCl layer grows out of the pit and is no longer in cylindrical shape (Stage 4a). The AgCl cap grows in perpendicular direction to the wire cross section up to a certain size (Stage 4b). Then the 198

224 cap starts growing in all directions (Stage 4c). To simplify the calculation, the dissolution of the silver core and the growth of the AgCl during Stage 4a will not be included in to the model in Stage 4. In addition, the cap in Stages 4b and 4c is assumed to have hemispherical shape. r o r r o MP35N LT Ag AgCl MP35N LT Ag AgCl MP35N LT Ag AgCl x o MP35N LT Ag AgCl x o z Stage 3 Stage 4a Stage 4b Stage 4c Figure Schematic of the silver core dissolution and the growth of the AgCl layer in Stage 4. The geometry and the dimension of the AgCl layer at Stage 4b is given in Figure It comprises of a cylinder of length x o with cross section area A, and a hemispherical cap of radius r o which is equal to the radius of the silver core. After a dissolution time t, the depth of the silver core dissolved is z and the cap radius increases to r. To obtain the expression for z, r and i in term of t, it needs to establish a set of three equations for these variables. The first equation is established from Faraday s law. The mass of the dissolved silver core, m Ag, is calculated from the anodic current, I, by: m M It F = Ag (3.67) Ag n where M Ag is the atomic weight of silver; n is the number of electron transferred in reaction (3.46); A is the cross section area of the silver core; and F is the Faraday s 199

225 constant. The mass of the dissolved silver can also be calculated based on the volume of the silver core dissolved and the density of silver, ρ Ag : m Ag = A z ρ (3.68) Ag Substitute (3.68) into (3.67) and differentiate both sides of the equation yields: MAg I dz = dt (3.69) nfaρ Ag The second equation is established from the assumption that all the Ag + ions dissolved during Stage 4 precipitated as AgCl on the silver core. Therefore, the volume of the AgCl cap is calculated by subtracting the volume of the AgCl layer precipitated at the bottom of the pit from the total volume of AgCl precipitated. The total volume of AgCl precipitated, V total, is: V total M AgCl It 1 = (3.70) n F ρ The volume of the AgCl layer precipitated at the bottom of the pit, V bottom, is approximately equal to the volume of the silver core dissolved. This is evidenced by the adherence between the AgCl layer and the silver substrate as observed in SEM micrographs in Section Hence: V bottom and the volume of the cap is calculated by: V cap AgCl M Ag It 1 = (3.71) n F ρ Ag = MAgCl It 1 MAg It 1 n F ρ n F ρ (3.72) After t seconds, the AgCl cap grows to a radius r. With the assumption that the cap has a hemispherical shape, the volume of the AgCl cap is: AgCl Ag 200

226 2 ( 3 3 π o ) Combining Equations (3.72) and (3.73) yields: Vcap = r r (3.73) 3 2 M 3 3 AgCl It 1 MAg It 1 π ( r ro ) 3 = n F ρ n F ρ (3.74) AgCl Ag Differentiating both side of Equation (3.74) and rearranging yields: dr MAgCl M Ag 1 I = dt 2 ρagcl ρ Ag 2πr nf (3.75) The third equation is established from Ohm s law: I η = Ω (3.76) R where η Ω is the ohmic drop through the AgCl layer and is expressed by Equation (3.53); I is the anodic current; and R is the resistance of the AgCl layer. The resistance of the AgCl layer is the sum of the four resistance components as shown in Figure 3-51: R = R 1 + R 2 + R 3 + R 4 (3.77) The resistance of the AgCl layer at the bottom of the pit with the thickness z is: z R1 = (3.78) KA The resistance of the AgCl mid-layer with the thickness x o is: R 2 x o = (3.79) KA The resistance of the inner hemispherical AgCl cap with the radius r o is considered to be small and is ignored in this calculation: R 3 = 0 (3.80) The resistance of the outer hemispherical AgCl cap is: 201

227 R = 2π K ro r (3.81) R 4 R 3 r o r R 2 R 1 x o z Ag Figure Schematic of the resistance components in the AgCl layer in Stage 4. Substituting Equations (3.78) to (3.81) in to (3.77) gives: z x 1 o 1 1 R = + + KA KA 2 π K r o r (3.82) Combining (3.53), (3.76) and (3.82) yields: I = a KV ( E ) z xo A A 2π ro r (3.83) Now, the three equations to describe the kinetics of the silver dissolution and the AgCl formation have been established. Substituting Equation (3.83) in to Equations (3.69) and (3.75) yields: a M Ag KV ( E ) dz = dt nfaρ Ag z xo A A 2π ro r (3.84) 202

228 a M AgCl M Ag 1 1 KV ( E ) dr = dt 2 ρagcl ρ Ag 2πr nf z xo A A 2π ro r (3.85) The boundary conditions are set at the beginning of Stage 4b. When t = 0, the pit depth is x o and the cap radius is r o, hence: z (t = 0) = x o (3.86) and r (t = 0) = r o (3.87) The expressions for the changes in the pit depth as the silver core dissolved, z, and the dimension of the AgCl hemispherical cap, r, as functions of time, t, can be obtained by solving the set of differential equations (3.84) and (3.85) with their boundary conditions (3.86) and (3.87). The solution for this problem can be obtained by numerical method using MatLAB software Version (The MathWorks Inc., USA) (see Appendix C) Discussion The effect of the potential difference The silver dissolution current density and the characteristic geometrical parameters of the AgCl layer are calculated at different potential difference of 0.1, 0.2, 0.4 and 1.0 V. The time point is chosen at 1 hour. The dissolution of silver in Stages 1, 2 and 3 is assumed to be negligible, i.e. x o = 0. The apparent conductivity of the AgCl layer is considered to be constant and is equal 2x10-6 S/cm. The values of other parameters used for the calculation are shown in Table

229 Table The values of the parameters used in evaluating the effect of constant potential difference on the kinetics of the silver dissolution and the AgCl formation in Stage 4. M AgCl (g) n F (C/equiv) ρ AgCl (g/cm 3 ) K (S/cm) t (s) r o (cm) x o (cm) x x The dissolution rate and the characteristic geometrical parameters after 1 hour polarization calculated at different constant applied potentials are shown in Figure Similar to the behavior in Stage 3, the current density and the geometrical parameters of the AgCl layer seems proportional to the square root of the potential difference, (V E a ) 1/2. After 1 hour polarization, the dissolution current densities vary in the range of 1.2 and 2.1 ma/cm 2. The depth of the cylindrical part is on the order of several micrometers and the radius of the AgCl hemispherical cap is ca. 22 μm. 3 i z r i (ma/cm 2 ) 2 10 z, r (μm) (V - E a ) 1/2 /(V 1/2 ) Figure The effect of the potential difference on the silver dissolution rate and the geometry of the AgCl layer after 1 hour of constant potential polarization. 204

230 The effect of the AgCl apparent conductivity The silver dissolution current density and the characteristic geometrical parameters of the AgCl layer are calculated at different AgCl layer conductivity of 10-6, 2x10-6, 5x10-6 and 10-5 S/cm. These values are selected based on the measured apparent conductivity of the AgCl layer anodically grown in 9 g/l NaCl solution (see Section ). The time point is chosen at 1 hour and the potential difference is 0.2 V which is approximately the difference in the open circuit potential between the MP35N LT alloy and pure silver in 9 g/l NaCl solution (see Section ). The dissolution of silver in Stages 1, 2 and 3 is assumed to be negligible, i.e. x o = 0. The values of the other parameters used for the calculation are shown in Table Table The values of the parameters used in evaluating the effect of the AgCl layer apparent conductivity on the kinetics of the silver dissolution and the AgCl formation in Stage 4. M AgCl (g) n F (C/equiv) ρ AgCl (g/cm 3 ) V E a (V) t (s) r o (cm) x o (cm) x The dissolution rate and the AgCl thickness calculated at different AgCl layer apparent conductivities are shown in Figure Similar to that in Stage 3, both dissolution rate and geometrical parameters of the AgCl layer increase linearly with the square root of the AgCl apparent conductivity. 205

231 4 3 i z r i (ma/cm 2 ) 2 10 z, r (μm) x x x10-3 K 1/2 (S/cm) 1/2 0 Figure The effect of the AgCl apparent conductivity on the silver dissolution rate and the geometry of the AgCl layer after 1 hour of constant potential polarization Comparison between the kinetics of the silver dissolution and the AgCl growth in Stage 3 and Stage 4 It can be realized intuitionally that the rate of the silver dissolution in Stage 4 decreases slower with time than that in Stage 3 due to the resistance of an AgCl cap is lower than the resistance of a cylindrical AgCl layer of the same volume. To quantify this comparison, let s consider two different scenarios of the silver core dissolution as follows. In the first scenario (Figure 3-54a), the pit at the silver core has an infinite depth so that as the silver core dissolves, the AgCl layer always keeps a cylindrical shape. In the second scenario (Figure 3-54.b), the pit at the silver core has a finite depth so that after the silver core is corroded for a certain time of t o, the AgCl layer fills the cylindrical 206

232 pit at the silver core with a depth of x o and then grows out of the pit in to a hemispherical shape. The dissolution rate of the silver core in the first scenario is obtained from Equation (3.61). The dissolution rate of the silver core in the second scenario is obtained by solving the differential Equations (3.84) and (3.85) with their boundary conditions (3.86) and (3.87). The numerical values of the parameters used in these calculations are given in Table The pit depth x o is chosen at 0.01 cm. AgCl x o AgCl x MP35N Ag MP35N Ag Ag MP35N t = 0 t = t o t > t o (a) r o r AgCl x o AgCl x o MP35N Ag MP35N Ag MP35N Ag z t = 0 t = t o t > t o (b) Figure Schematic of the two different scenarios of the corrosion of the silver core; (a) a pit with an infinite depth; and (b) a pit with a finite depth. 207

233 Table The values of the parameters used in evaluating the effect of the geometry of the AgCl layer on the kinetics of the silver dissolution. M AgCl (g) n F (C/equiv) ρ AgCl (g/cm 3 ) V E a (V) K (S/cm) x o (cm) r o (cm) x x10-4 Figure 3-55 shows the dependence of the silver dissolution rate on time. Before the time t o, the 1/i vs. t 1/2 curves of both scenarios overlap each other. After the time t o, the 1/i vs. t 1/2 curve of the finite pit depth scenario separates from the curve of the infinite pit depth scenario. One interesting feature is that after the time t o, the 1/i vs. t 1/2 curve of the finite pit depth scenario still exhibits a linear behavior, however with a smaller slope. For instance, as x o = 0.01 cm, the slope of the curve in the infinite scenario is cm 2.A -1.s - 1/2 while the slope in finite scenario is cm 2.A -1.s -1/2. The ratio between the slopes indicates that the silver dissolution current underneath a hemispherical AgCl cap decreases 1.7 times slower than that underneath a cylindrical AgCl layer. 208

234 Infinite pit depth scenario Finite pit depth scenario 1/i (ma/cm 2 ) Slope = Slope = t o t 1/2 (s 1/2 ) 1 year Figure The 1/i vs. t 1/2 curves calculated in the infinite pit depth scenario and in the finite pit depth scenario. The characteristic geometrical parameters of the AgCl layer in the two different corrosion scenarios are also calculated. The dependence with time of the AgCl layer thickness in the infinite pit depth scenario, x,, the thickness of the cylindrical AgCl layer, z + x o, and the radius of the hemispherical AgCl cap, r, in the finite pit depth scenario are presented in Figure At the time t o, the z + x o vs. t 1/2 curve starts deviating from the x vs. t 1/2, however it appears still following linear behavior. This is consistent with the linear relationship between i vs. t 1/2 because the dissolved silver core depth is equal to the thickness of the cylindrical AgCl layer. In contrast, the r vs. t 1/2 curve does not show linear relationship and the slope of the curve decreases with time (inset in Figure 3-56). 209

235 x, r, z + x o (cm) x, r, y + x o (cm) t o t 1/2 (s 1/2 ) x r y + x o x r z + x o year t o t 1/2 (s 1/2 ) Figure The dependence with time of the characteristic geometrical parameters of the AgCl layer in the infinite pit depth scenario and in the finite pit depth scenario. The total volumes of the AgCl formed during silver corrosion in the two scenarios are obtained from the characteristic geometrical parameters and are shown in Figure After the time t o, the total volume of the AgCl formed in the infinite pit depth scenario increase faster than that in the first scenario. Note that the volume of the AgCl formed is proportional to the amount of the silver dissolved, therefore this result indicates the silver core in the second scenario dissolves faster than in the first scenario. This conclusion is in agreement with the higher corrosion current for the finite pit depth scenario in comparison with the infinite pit depth scenario observed in Figure

236 1.5x10-6 Infinite pit depth scenario Finite pit depth scenario V AgCl (cm 3 ) 1.0x x t o t 1/2 (s 1/2 ) 1 year Figure The dependence with time of the total volume of AgCl formed during corrosion of the silver core in the infinite pit depth scenario and in the finite pit depth scenario Summary In this section, models for the corrosion process of a broken silver-cored MP35N LT wire in vitro were developed. The corrosion process is described following four stages including (i) the dissolution of the silver core from a freshly broken wire and formation of a pit at the core; (ii) the accumulation of the Ag + cations inside the pit and the precipitation of AgCl on the silver core; (iii) the dissolution of the silver core and the growth of the AgCl layer inside the pit; and (iv) the dissolution of the silver core and the growth of the AgCl layer outside the pit. The mathematical models for each stage describing the kinetics of the silver dissolution, the growth of the AgCl layer and the 211

237 transport of ions in the electrolyte has been established. The findings can be summarized as follows: 1. The corrosion current of the silver core in Stage 1 is determined from Evans diagram of the anodic polarization curve of silver and the cathodic polarization curve of the MP35N LT alloy in vitro. 2. The dissolution of the silver core caused accumulation of the Ag + cations inside the pit. The potential drop in the electrolyte inside the pit was negligible. The precipitation of AgCl starts when the product of corrosion current density and the 2 pit depth satisfies the condition: i y D3F( Cb 4Ksp Cb) The silver dissolution rate and the characteristic geometrical parameters of the AgCl layer in both Stage 3 and Stage 4 are proportional to the square root of the difference potential between the cathode and the anode, (V E a ) 1/2. 4. The silver dissolution rate and the characteristic geometrical parameters of the AgCl layer in both Stage 3 and Stage 4 are proportional to the square root of the AgCl apparent conductivity, K 1/2. 5. The silver dissolution rate in both Stage 3 and Stage 4 decays with square root of time, t 1/2, however the dissolution rate in Stage 3 decreases about 1.7 times faster than the one in Stage The thickness of the cylindrical AgCl layer in both Stage 3 and Stage 4 increases with the square root of time, t 1/2. The radius of the hemispherical AgCl layer in Stage 4 increases with slower rate than the thickness of the cylindrical part. 7. If the overpotential potential at the silver core increases linearly with time, the silver dissolution rate is independent of time and is proportional to the square root 212

238 of the potential increase rate. In contrast, the thickness of the AgCl layer increases linearly with time and is proportional to the square root of the potential increase rate. 213

239 3.6 Application of the theoretical models on the corrosion of a freshly broken silvercored MP35N LT networked cable in vivo and the release of silver ions to the ambient Scope In Section 3.5, the theoretical models for the corrosion of a modeled silver-cored composite in physiological solutions were developed. The effects of the physical parameters such as the potential difference between the cathode and the anode, the conductivity of the AgCl layer and time on the corrosion kinetics were discussed. The mathematical models also provided quantitative predictions for the corrosion kinetics in each stage. In this section, the models developed in Section 3.5 are applied to study the corrosion of a freshly broken silver-cored MP35N LT cable. The evolution of a pit at the silver core, the precipitation and growth of the AgCl layer and the physical parameters in each of the corrosion stages is followed in a real time process. Different scenarios are analyzed and the calculation for corrosion rate is based on the worse case. The release of silver to the ambient in the form of dissolved Ag + cation is also considered The dissolution of the silver core of a freshly broken wire and the formation of a AgCl layer Let s consider a freshly broken cable as illustrated in Figure 3-58 at the time t = 0. The initial dissolution rate of the silver core from this freshly broken wire can be determined from the mixed potential theory discussed in Section and in Section After a dissolution time t 1, AgCl starts precipitating and the pit depth is y o. The pit 214

240 depth y o and the time t 1 are calculated by Equations (3.45) and (3.91), respectively. After AgCl forming, the kinetics of the silver dissolution is under ohmic controlled regime in which the thickness of AgCl layer and the silver dissolution current is described by Equations (3.60) and (3.61), respectively. The AgCl layer fills the pit after the time t 2 and grows to a thickness y 1. Then the AgCl layer grows out from the pit and forms a hemispherical cap. The cap has a radius r o equal to the radius of the silver core and a cylindrical layer thickness x o at the time t 3. The dissolution kinetics of silver and the growth rate of the AgCl layer changes due to the formation of the hemispherical cap. Solving a set of differential Equations (3.84) and (3.85) with the boundary conditions (3.86) and (3.87) gives the new kinetics law and the dependence of the geometrical parameters, z and r, of the AgCl layer with time. y o y 1 MP35N Ag MP35N Ag MP35N Ag AgCl t = 0 r o t = t 1 t = t 2 r r o MP35N Ag AgCl x o MP35N insulator Ag AgCl x o z t = t 3 t = t 4 Figure Schematic of the dissolution of the silver core and the formation of the AgCl layer on a freshly broken silver-cored MP35N LT wire. 215

241 Now, let s consider a freshly broken cable at the time t = 0. If the insulation layers adhere well to the wires, the leakage of the fluids in to the gap between the insulation layer and the wires are negligible, hence only the fracture surface is exposed to in vivo. Assuming that the kinetics of the anodic reaction taking place on the silver core and of the cathodic reaction taking place on the outer tube are described by the anodic polarization curve of silver and the cathodic polarization curve of MP35N LT in Ringer s solution at 37 o C. The anode to cathode area ratio is equal to the cross section ratio of the silver core and the outer tube, i.e. 41 to 59. The dissolution rate of silver can be determined using Evans diagram as shown in Figure The corrosion current at the silver core of a single wire and the corresponding current density is 8x10-13 A and 7x10-6 A/cm 2, respectively. Because the MP35N LT outer tube is in a passive state, the dissolution of the silver core forms a pit at the core. Some Ag + cations released from the silver dissolution reaction forms complexes with chloride and proteins in vivo environment. Some others stay as free Ag + cations and accumulate inside the pit solution. The free Ag + cations move inside the pit under the concentration gradient between the dissolving electrode and the ambient and the electrostatic field between the outer tube cathode and the silver core anode. The transport of the free Ag + cations and other charge carriers has been discussed in Section Solving the transport equations gives the concentration profile of free Ag + and Cl - as described by Equations (3.41) and (3.40), respectively. When the product of [Ag + ].[Cl - ] is equal to the solubility product of AgCl, K sp, AgCl starts precipitating. Based on the condition expressed in equation (3.45) the pit depth at which AgCl forms is given by: 216

242 2 ( b sp b) DF y C K C i (3.88) The time for the silver core to dissolve to the depth y is calculated from Faraday s law: m Ag M i A t F Ag = (3.89) n where M Ag is the atomic weight of silver; n is the number of electron transfer in reaction (3.22); A is the cross section area of the silver core; F is Faraday s constant; and m Ag is the weight of dissolved silver which is expressed as: m Ag = ρ A y (3.90) Ag where ρ Ag is the density of silver. Combine (3.89) and (3.90) gives the time for the pit to grow to the depth y is: nfρ Ag y t = (3.91) M i Ag The dissolution current density of silver, i, is given from the mixed potential theory. If the exposed area of the outer tube cathode is constant, i.e. no leakage of electrolyte in to the gap between the insulation layer and the wire at the broken location, the corrosion current density of silver determined by the mixed potential theory is constant and is 7x10-6 A/cm 2. The solubility of AgCl at 35 o C, which is closed to the human body temperature, is 4.15x10-16 (mol/cm 3 ) 2 [42]. The diffusivity of Ag + ions is 1.65x10-5 cm 2 /s. The values of other parameters are listed in Table Substituting the numerical values in to Equations (3.88) and (3.91) gives y o = 1.2x10-6 cm and t 1 = 1640 seconds. 217

243 Table Values of parameters used to calculate the pit depth and the time at which AgCl starts precipitating. M AgCl (g) n F (C/equiv) ρ AgCl (g/cm 3 ) i (A/cm 2 ) D 3 (cm 2 /s) C b (mol/cm 3 ) K sp (mol/cm 3 ) x x x x10-16 However, if the wetted area of the MP35N LT increased, the cathodic polarization curve in the Evans diagram shown in Figure 3-37 will shift accordingly with the increase of the surface area to higher current density direction. The intersection between the anodic and cathodic polarization curves will displace correspondingly to the higher current and higher potential direction. This displacement indicates that the dissolution current density and the corrosion potential of silver increase. Figure 3-59 shows the shifting of the cathodic polarization curve as a segment of 6 cm long of the MP35N LT outer tube is wetted. The intersection between the anodic and cathodic polarization curves indicates an anodic current of ca. 3x10-9 A which is equivalent to a corrosion current density of 0.3 ma/cm

244 Potential (V vs. SCE) Silver MP35N LT (freshly broken) MP35N LT (longer exposure) Hypothetic cathodic polarization curve E-14 1E-13 1E-12 1E-11 1E-10 1E-9 1E-8 1E-7 1E-6 Current (A) Figure Evans diagram of the silver core and the MP35N LT alloy outer tube in Ringer s solution at 37 o C. The anodic polarization curve is for a silver electrode with an area of 11x10-6 cm 2. The cathodic polarization curves are for a MP35N LT alloy outer tube with the electrode area of 16x10-6 cm 2 (dash line) and 0.11 cm 2 (solid line), and a hypothetical situation (dash-dot line). In fact, the situation is more complicated because the kinetics of the cathodic reaction on the MP35N LT outer tube in the thin electrolyte layer under the insulation is likely to be different from that in the bulk solution. The kinetics of cathodic reaction is speculated to be slower under the insulation layer due to the lack of oxygen and the effect of ohmic drop in this small gap. A hypothetical cathodic polarization curve representing the correction for the effect of thin electrolyte is shown in Figure The intersection between the hypothetical cathodic polarization and the anodic polarization curve moves to lower current and lower potential in comparison with the curve without correction. 219

245 Despite the effect of the thin electrolyte layer on the kinetics of cathodic reaction, the change in the wetted area on the outer tube obviously has strong effect on the corrosion rate of the silver core. The magnitude of the silver dissolution current largely depends on the ratio between the wetted outer tube area and the cross section area of the silver core. The Evans diagram of silver and the MP35N LT alloy shows that the kinetics of silver dissolution before a continuous AgCl film formed (the transition region between low current densities and high current densities) is limited only by the capacity of the cathode. By saying capacity, it means the ability of the cathode to supply the current demanded by the anode. The cathode capacity is proportional to the rate of the cathodic reaction and to the surface area of the cathode. The current demanded by the anode is the dissolution current of silver at the corrosion potential. Figure 3-59 shows that the slope of the anodic polarization curve of silver during non-continuous AgCl growth is nearly zero indicating an extremely high kinetics and strong potential dependence of the anodic reaction. Therefore, only a small anodic activation overpotential can result in high dissolution rate of silver, i.e. a high current demanded for the cathode. If the cathode area keeps increasing with time due to the penetration of the electrolyte in to the gap between the insulation and the wire, the cathode capacity will increase. If the wetted area on the outer tube increases to a value that the cathode to anode area ratio can be considered as infinity, the silver dissolution current is infinity, even with a small anodic overpotential. Fortunately, the abovementioned scenario only occurs if the silver core is partially covered with AgCl. As long as a continuous AgCl film forms, dissolution of silver is 220

246 under ohmic controlled regime in which the anodic current is not only limited by the cathode capacity but also by the resistance of the AgCl layer. For simplification, hereafter we will neglect the effect of cathode capacity and only consider the ohmic resistance limit. The MP35N LT outer tube cathode is assumed to have the ability to supply an infinite current demanded by the anode. The cathode is held at a constant potential of V vs. SCE which is the open circuit potential of the MP35N LT alloy in Ringer s solution at 37 o C. The potential of the anode is the potential of silver underneath a continuous AgCl layer in 9 g/l at 37 o C which is ca V vs. SCE (see Section ). Now, the dissolution kinetics of the silver core underneath a continuous AgCl layer is similar to the kinetics under constant potential polarization that has been discussed in Section Substituting the numerical values of the parameters in Table 3-15 in to Equation (3.60) yields the dependence the AgCl layer thickness, x, with time: 2M AgCl a x = ( V E ) K t = t nfρ AgCl 1/2 1/2 5 1/2 (3.92) The depth of the silver core dissolved in Stage 3, z s3, can be obtained from a simple conversion from the AgCl thickness as: M ρ zs3 x t M ρ Ag AgCl 5 1/2 = = (3.93) AgCl Ag The dissolution current density during this period is expressed by: 1/2 ρ AgCl a 1/2 1/2 nf i= ( V E ) K t = t 2M AgCl (3.94) 221

247 Table The values of the parameters used to calculate the silver dissolution rate, the AgCl thickness and the depth of the silver core dissolved M AgCl (g) M Ag (g) ρ AgCl (g/cm 3 ) ρ Ag (g/cm 3 ) n F (C/equiv) K (S/cm) V (V) E a (V) With a given pit depth y o at the silver core prior to AgCl starts precipitating, the total depth of the silver core dissolved or in another word the pit depth is: y = y o + z s3 (3.95) The pit is filled when: x = y (3.96) Substituting (3.92) and (3.93) in to (3.96) and note that the pit depth prior to AgCl starts precipitating is y o = 1.2x10-6 cm, the time to fill the pit with AgCl is less than 1 second and the pit depth at this time is y 1 = 4x10-6 cm. The current density at this time may be as high as 17 ma/cm 2 as calculated from Equation (3.94). After filling the pit at the silver core, AgCl continues growing and form a hemispherical cap of radius r o as shown in Figure 3-58 at the time t 3. The volume ratio of AgCl to silver is: Ratio = M M AgCl Ag ρ Ag (3.97) ρ AgCl Therefore to form a hemispherical cap of radius r o, the silver core must dissolve a depth of z s4 which satisfies: 2 π r 3 3 o M AgCl ρ Ag = 1 A z M Ag ρ AgCl s4 (3.98) 222

248 The value of r o is 18x10-4 cm which is the radius of the silver core. The cross section area of the silver core is A = 11x10-6 cm 2. Substitute numerical numbers in to (3.98) gives the depth of silver dissolved z s4 is 7.35x10-4 cm. The total thickness of the cylindrical AgCl layer at the moment of hemispherical cap form is x o = y 1 + z s4 = 4x x10-4 = 7.39x10-4 (cm) (3.99). The time to grow the hemispherical of radius r o is calculated from Faraday s law with the assumption of constant current during this period, i.e. i = A/cm 2, yielding Δt = t 3 t 2 = 406 (s) (3.100). At the time t 4 > t 3, as the silver core dissolves, the AgCl layer grows with the increase of the hemispherical AgCl cap radius and the increase of the cylindrical AgCl thickness. The depth of silver dissolved and the radius of the hemispherical AgCl cap can be obtained by solving the differential equations (3.84) and (3.85) using MatLAB software Version (The MathWorks, Inc., USA) (see Appendix C), and the rate of the silver dissolution is obtained by Equation (3.83). The boundary conditions are provided from Equations (3.86) and (3.87). Figure 3-60 shows the evolution of the silver pit depth, the AgCl cap radius and the silver dissolution current density with time. The value of each variable at a specific time point of 60 seconds, 1 hour, 1 day, 1 month, 1 year and 10 years is summarized in Table After 1 day, the pit depth and the cap radius is ca. 30 μm and the silver dissolution current density is ca A/cm 2. As corrosion continues, the pit depth at silver core and the radius of AgCl cap increase while the dissolution rate of the silver core decreases. The pit depth at the silver core increases faster than the radius of the AgCl cap. After one year, the pit depth is approximately 10 times higher than the cap radius. Thus, the resistance of AgCl filled the pit at the silver core becomes 223

249 the dominant component in limiting the rate of the silver core dissolution. Therefore if the AgCl cap is broken off for some reasons, the dissolution current of the silver core will not deviate significantly from this calculation. After 10 year, the pit depth is 1525 μm, the cap radius is 105 μm, and the silver dissolution current density is 2.3 μa/cm 2. Several important assumptions used in the calculations in this section should be pointed out. First, the electrochemical behavior of the materials in vivo was assumed to be the same as that in vitro. Second, reactions in the electrolyte inside the pit such as the formation of silver complexes or hydrolysis of silver cations were not considered. Third, the transport of the charge carriers inside the pit was assumed in one dimension. And last but not the least, all dissolved Ag + ions were considered to precipitate as AgCl. r, z+x o (cm) Cap radius Total pit depth Dissolution current E-3 Current density (ma/cm 2 ) E Time (days) Figure Evolution of the pit depth, the growth of the AgCl hemispherical cap and the silver dissolution current density with time. 224

250 Table Summary of the dissolution current density and the geometrical characteristic parameters of the AgCl layer during the corrosion of a freshly broken silver-cored MP35N LT wire in vivo. t (s) Period y (cm) r (cm) i (A/cm 2 ) Stage t 1 = 1640 ~ 27 min 1.2x x t 2 = 1641 ~ 27 min 4x x t 3 = 2047 ~ 34 min 7.39x x x t 4 = 2107 ~ 35 min 2.0x x x t 5 = 5707 ~ 1.5 hrs 2.1x x t 6 = ~ 1 day 36x x x t 7 = ~ 1 month 154x x x t 8 = ~ 1 year 500x x x t 9 = ~ 10 years 1525x x x Release of silver to the ambient Despite the solubility of AgCl is extremely small, it is not true that all Ag + cations precipitated as AgCl. At 35 o C, the solubility product of AgCl is 4.15x10-10 (mol/l) 2, thus with a nominal chloride ion concentration of mol/l in human fluids, the saturated concentration of Ag + is ca. 2.69x10-9 mol/l. When the silver core dissolves and the AgCl layer forms, the concentration of Ag + cations near the AgCl/electrolyte interface is approximately equal to the saturated concentration of 2.69x10-9 mol/l. Because the concentration of free Ag + cations in human body is approximately zero, there is a concentration gradient between the proximity of the AgCl layer and the ambient that creates a flux of Ag + cations diffusing away from the AgCl product layer. It is possible that other transport mechanisms such as convection and migration also taking place, 225

251 however these processes in vivo are complicated and little has been done to understand. For this reason, only diffusion is considered in the calculation of Ag + release. This approach has been used to develop models for drug release [50, 51]. A model for the diffusion of Ag + is set up with several assumptions as follows. First, assume that during the growth of the AgCl layer, there is a proximity region of radius a surrounding the silver core in which the concentration of Ag + cations is constant. Second, assume further that the size of the proximity regions is large enough so that it is not affected by the growth of the AgCl layer, therefore the radius a is a constant. Third, assume that the ambient is large enough therefore it can be considered as an infinite sink for the diffusion process. These assumptions are conservative in the sense that the flux of the Ag + cations calculated will be higher than in the actual situation. Fourth, ignore all reactions that involve Ag + cations in vivo, thus the distribution of Ag + in the ambient is only affected by the diffusion process. Figure 3-61 shows a schematic of the diffusion model along with the assumptions. C MP35N a C o Ag AgCl Infinite source C(r,t) Infinite sink 0 a r (a) (b) Figure Schematic of the diffusion model for Ag + cations; (a) the AgCl layer and the proximity region of constant radius a; and (b) concentration profile at time t. 226

252 The concentration of the Ag + cations at a point in the ambient depends on the distance from that point to the silver core. In addition, the process is not at steady-state therefore the concentration of Ag + at the same point changes with time. The concentration of Ag + during this diffusion process obeys Fick s second law which is expressed by: 2 Crt (,) C 2 C = D + 2 t r r r (3.101) where C(r, t) is the concentration of Ag + at distance r and time t; and D is the diffusivity of Ag +. The boundary conditions for Equation (3.101) are as follows: B.C. 1: The concentration at all point inside the sphere of radius a is equal C o for all time. Thus, for r a and t 0: C(r, t) = C o. (3.102) B.C. 2: The concentration at a point at infinity is equal zero for all time. Thus, for r = and t 0: C(r, t) = 0. (3.103) Equation (3.101) with the boundary conditions described in (3.102) and (3.103) has been solved as classic example of three-dimensional diffusion. The solution is expressed by [52]: a r a C( r, t) = Co erfc r 2 Dt (3.104) Once the concentration profile of the Ag + cations is known, the total amount of the Ag + cations diffused in to the ambient can be obtained by integrating the concentration of Ag + for the whole volume of the ambient. However, practically this can not be done due to the limitation of computational capability. Therefore an external boundary r = R o in which R o is large enough so that it can be considered as infinity is chosen, i.e. C(R o,t) = 0 for t 0. The total amount of Ag + cations released in to the ambient at a time t is: 227

253 Ro N () t = C( r,) t dr (3.105) r a The size of the proximity region is chosen a = 0.02 cm which is twice the size of the AgCl cap after 10 years. The external boundary is the size of a normal human body, i.e. R o = 50 cm. The diffusivity of Ag + cations in vivo is unavailable therefore the value of the diffusivity in vitro is used instead which is 1.65x10-5 cm 2 /s. In fact, the diffusivity in vivo can vary in a large range depending on the location in the body. A diffusivity as high as that in vitro may be the case for the gastric environment but the value may be several orders of magnitude smaller for the environment inside muscles. The numerical values of other parameters used in the calculation are shown in Table The concentration profile and the amount of silver release is calculated using MatLAB software version (The MathWorks, Inc., USA) (see Appendix D). Table The values of the parameters used to calculate the concentration profile of Ag +. D C o a R o (cm 2 /s) (mol/cm 3 ) (cm) (cm) 1.65x x Figure 3-62 shows the concentration profile of the Ag + cations provided by (3.104). The concentration of the Ag + drops more than 100 times at the location of 2 cm away from the broken wire and is on the order of mol/cm 3 in the ambient. At the external boundary, the concentration of Ag + is ca. 7x10-16 mol/cm 3 after 10 years which is more than 1000 times lower than the concentration at the proximity region. This validates the earlier assumption of an infinite sink for diffusion. 228

254 Figure 3-63 shows the dependence of the total volume of Ag + released in to the ambient calculated by (3.105). The amount released is approximately 2x10-10 mol after the first year. Then the release rate decreases with time. After 10 years, a dose of approximately 7x10-10 mol Ag + is obtained from this calculation. The calculation presented above is applied for a single broken wire. In the case of multiple broken wires, the maximum value of Ag + released is obtained by multiplying the value calculated for a single wire with the number of wires. Note that the impingement of the diffusion field due to the individual wires decreases the amount of Ag + released day 1 week 1 month 1 year 10 years C (mol/cm 3 ) r (cm) Figure Concentration profiles of Ag + cations at different time. 229

255 1.0x10-9 Ag+ released amount (mol) 8.0x x x x Figure The dependence of the total amount of the Ag + cations released to the ambient with time. Day Summary In this section, the corrosion of the silver core of a freshly broken networked cable was examined. The evolution of a pit at the silver core, the precipitation of AgCl, the growth of a cylindrical AgCl layer and then the formation of a hemispherical AgCl cap were calculated based on the models established in the previous sections. The release of Ag + cations to the ambient was also considered. The findings are summarized as follows: 1. Even with a modest corrosion rate, AgCl quickly forms in a shallow pit. 2. In a short time, the pit is filled with AgCl and then grew out of the pit to form a hemispherical cap. 3. The thickness of the cylindrical AgCl layer at the silver core increased faster than the radius of the AgCl cap and became the dominant factor controlling the kinetics of the silver core corrosion. 230

256 4. After 10 years, the depth of the silver core dissolved is calculated on the order of one millimeter and the silver dissolution rate was on the order of few μa/cm Most of dissolved silver stays in the form of AgCl. The concentration of Ag + cations in the ambient is more than 1000 times lower than the saturated concentration of Ag +. After 10 years, a dose of approximately 7x10-10 mol Ag + cations is released from a single broken wire. Table 3-16 summarizes the dissolution current density and the geometrical characteristic parameters of the AgCl layer during the corrosion of a freshly broken silver-cored MP35N LT wire in vivo. 231

257 3.7 Conclusion The corrosion of a silver-cored MP35N LT composite for NNPS lead wire cables was studied. It has been shown that in the event of mechanical failures, the silver core of the composite that exposed to in vivo is corroded while the MP35N LT alloy outer tube is passive. The corrosion process of the silver core of the composite was described following four stages including (i) the dissolution of the silver core from a freshly broken wire and formation of a pit at the core; (ii) the accumulation of the Ag + cations inside the pit and the precipitation of AgCl on the silver core; (iii) the dissolution of the silver core and the growth of the AgCl layer inside the pit; and (iv) the dissolution of the silver core and the growth of the AgCl layer outside the pit. The mathematical models for each stage describing the kinetics of the silver dissolution, the growth of the AgCl layer and the transport of ions in the electrolyte was established. The evolution of a pit at the silver core, the precipitation of AgCl, the growth of a cylindrical AgCl layer and then the formation of a hemispherical AgCl cap on a freshly broken silver-cored MP35N LT wire were calculated based on the models established. The findings are summarized as follows: Electrochemical behavior of the composite: 1. The corrosion behavior of the composite is the contribution of its component materials, i.e. the MP35N LT alloy and silver. In 9 g/l NaCl solution at room temperature, the corrosion potential of the MP35N LT alloy was approximately ± 0.06 V vs. SCE. The Co-based alloy is passive in the potential range near its corrosion potential. In 9 g/l NaCl solution at room temperature, the corrosion potential of silver was approximately ± 0.02 V vs. SCE. The 232

258 anodic current density of silver near its corrosion potential was on the order of 10-6 A/cm 2. At potential more positive than ca V vs. SCE, the anodic current density increased abruptly to ca A/cm 2 and stayed fairly constant regardless of increasing applied potentials. 2. The electrochemical behaviors of the MP35N LT alloy, silver and the composite in Ringer s solution at 37 o C were similar to those in 9 g/l NaCl at room temperature. 3. The depth of penetration at the silver core of 2 mm long silver-core MP35N LT composite wires during immersion test in 9 g/l NaCl solution at 37 o C increased steadily during the first 25 weeks, but then the penetration rate decreased in longer immersion times. A penetration depth of ca. 22 μm was observed at the silver core after 1 year of immersion. Precipitation and growth of AgCl on silver: 1. AgCl particles nucleated at the bottom of the scratches on the silver surface which may be the less effective sites for diffusion or the favorable sites for heterogeneous nucleation. The particles grew to patches which expanding laterally on the substrate until forming a continuous film. 2. In a continuous AgCl layer, AgCl grew at both the interfaces between the layer and the electrolyte and the interfaces between the AgCl layer and the dissolving silver electrode. 3. Ionic transport through the newly formed continuous AgCl film was via the pores between the AgCl grains. As the film thickened, the pores between the AgCl grains were sealed and the ionic transport was mainly via micro-channels 233

259 running through the AgCl grains. The ohmic resistance of the continuous AgCl layer inhibited the dissolution of the silver substrate. The effect of the AgCl layer on the kinetics of the silver dissolution: 1. When the AgCl layer was thin, i.e. on the order of several μm, the dissolution of silver was controlled by the ohmic overpotential through the AgCl layer and by the activation overpotential at the silver electrode. When the AgCl layer was thick, i.e. on the order of tens of μm or thicker, the dissolution of silver was controlled only by the ohmic overpotential through the AgCl layer. 2. The micro-channels were accounted for ca. 4% volume fraction of the AgCl layer. The conductivity of the electrolyte inside the micro-channels was estimated on the order of 10-4 S/cm. The concentration of Cl - and Ag + inside the micro-channels was estimated on the order of 10-6 mol/cm 3 and mol/cm 3, respectively. The apparent conductivity of the AgCl layer was on the order of 10-6 to 10-5 S/cm and decreased with the film thickness. The exchange current density of the Ag/Ag + redox reaction in 9 g/l NaCl was ca. 1.3x10-4 A/cm 2. Mathematical models for the kinetics of the silver dissolution and AgCl formation: 1. The corrosion current of the silver core in Stage 1 is determined from Evans diagram of the anodic polarization curve of silver and the cathodic polarization curve of the MP35N LT alloy in vitro. 2. The dissolution of the silver core caused accumulation of the Ag + cations inside the pit. The potential drop in the electrolyte inside the pit was negligible. The precipitation of AgCl starts when the product of the corrosion current density and the pit depth satisfies the condition: 234

260 2 ( b sp b) i y D F C + K C The silver dissolution rate and the characteristic geometrical parameters of the AgCl layer in both Stage 3 and Stage 4 are proportional to the square root of the difference potential between the cathode and the anode, (V E a ) 1/2. 4. The silver dissolution rate and the characteristic geometrical parameters of the AgCl layer in both Stage 3 and Stage 4 are proportional to the square root of the AgCl apparent conductivity, K 1/2. 5. The silver dissolution rate in both Stage 3 and Stage 4 decays with square root of time, t 1/2, however the dissolution rate in Stage 3 decreases faster than the one in Stage The thickness of the cylindrical AgCl layer in both Stage 3 and Stage 4 increases with the square root of time, t 1/2. The radius of the hemispherical AgCl layer in Stage 4 increases with slower rate than the thickness of the cylindrical part. 7. If the overpotential potential at the silver core increases linearly with time, the silver dissolution rate is independent of time and is proportional to the square root of the potential increase rate. In contrast, the thickness of the AgCl layer increases linearly with time and is proportional to the square root of the potential increase rate. Calculation for the corrosion of a freshly broken silver-cored MP35N LT wire in vivo: 1. Even with a modest corrosion rate, AgCl quickly forms in a shallow pit. 235

261 2. In a short time, the pit is filled with AgCl and then grew out of the pit to form a hemispherical cap. 3. The thickness of the cylindrical AgCl layer at the silver core increased faster than the radius of the AgCl cap and became the dominant factor controlling the kinetics of the silver core corrosion. 4. After 10 years, the depth of the silver core dissolved is calculated on the order of one millimeter and the silver dissolution rate was on the order of few μa/cm Most of dissolved silver stays in the form of AgCl. The concentration of Ag + cations in the ambient is more than 1000 times lower than the saturated concentration of Ag +. After 10 years, a dose of approximately 7x10-10 mol Ag + cations is released from a single broken wire. 236

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266 Chapter 4 MAIN CONCLUSIONS In this work, the micro- and nano-scale corrosion of two engineering materials, an Febased bulk metallic glass SAM 1651 and a silver-cored MP35N LT composite, has been presented. The structural and compositional heterogeneities in the Fe-based amorphous metal of nanometer sizes and the dimension of the silver-cored composite of micrometer sizes enabled the formation of corrosion cells at the micro- and nano-scales. The effect of heat treatment at 600, 700 and 800 o C, which are slightly below and significantly higher than the reported crystallization temperature of SAM 1651 (653 o C), on the structure, composition and corrosion resistance of the material was examined. Devitrification of the amorphous structure occurred via primary transformation with the formation of (Cr, Fe) 23 C 6 and (Cr, Fe) 7 C 3 nanocrystalline particles dispersed in a matrix of remaining amorphous phase. The formation of nanometer Cr-depleted zones surrounding the Cr-rich carbide particles were proposed to be the reason for the degradation in the corrosion resistance of SAM 1651 obaserved at both macroscopic and nano-scale after heat treatment. Under diffusion controlled growth, the sizes of the carbide particles and of the Cr-depleted zones increased with the increase in the heat treatment temperature. The increase in the size of the Cr-depleted zones resulted in the decrease of the corrosion resistance of SAM 1651 as observed when temperature increased from 600 to 800 o C. However, the heat treated material still exhibited good corrosion resistance in 6M HCl with the corrosion rate of less than 5 μm/year as measured in immersion test. 241

267 The corrosion of 58 μm silver-cored MP35N LT composite wires in vitro was studied. The exchange current density of the Ag/Ag + redox reaction in NaCl solution was found to be on the order of 10-4 A/cm 2. Dissolution of the silver core caused the accumulation of Ag + in the electrolyte. AgCl precipitated on the silver electrode as the solubility product was reached and grew to continuous layer to cover the entire silver electrode. The deposition of AgCl corrosion product layer at the silver microelectrode slowed the kinetics of the anodic dissolution. Ionic transport via micro-channels running through AgCl layer was the rate controlling process. When the AgCl layer was thin, i.e. on the order of several μm, the dissolution of silver was controlled by the ohmic overpotential through the AgCl layer and by the activation overpotential at the silver electrode. When the AgCl layer was thick, i.e. on the order of tens of μm or thicker, the dissolution of silver was controlled only by the ohmic overpotential through the AgCl layer. The geometry and the apparent conductivity of the AgCl layer played an important role in determining the corrosion kinetics. The anodic dissolution current decreased with the increase of the size and the decrease of the apparent conductivity of the AgCl layer. When AgCl layer was in cylindrical or hemispherical shape, the corrosion kinetics was found to increase linearly with the square root of the potential difference between the cathode and the anode, to increase linearly with the square root of the AgCl layer s apparent conductivity, and to decay linearly with the square root of time. 242

268 Appendix A. Characterization of the Micro-Channels in the AgCl layer The size and the number of the micro-channels in the AgCl layer were characterized using SEM. A silver wire fresh-exposed surface specimen with a diameter of 0.5 cm was used. A total charge of 6 C/cm 2 was passed to develop the AgCl layer. The SEM photos are shown in Figure A-1. The size of each SEM photo was 22 μm x 26 μm. The size of the micro-channels was categorized in to 5 groups ranging from 0.4 to 1.4 μm. The number of the channel in each group was counted. The statistical results are shown in Table A-1. The average number of the micro-channels in each size group is summarized in column Ave Count. The total cross sectional area of the micro-channels in each size group is summarized in column Channel Area. The total number of the micro-channels in the SEM photos is the sum of all value in the column Ave Count. The total number of the micro-channels in the AgCl layer is calculated by multiplying the number of the micro-channels in the SEM photos with the area ratio between the specimen cross section and the SEM photo. Thus: = 42 4 = N 4 4 The average cross sectional area of the micro-channels is calculated by dividing the total Channel Area to the total Ave Count, thus: Amc = = 42 μm ( ) 243

269 Photo size: 22 μm x26 μm μm μm μm μm μm 5 μm Photo size: 22 μm x26 μm μm μm μm μm μm 5 μm Figure A-1. (Continued) 244

270 Photo size: 22 μm x26 μm μm μm μm μm μm 5 μm Figure A-1. SEM photo of the AgCl layer for statistical analysis. Table A-1. Summary the number of micro-channels in each size group. Size range (μm) Count Count Count Ave Size Ave Count Channel Area (μm 2 ) Total