Field Assisted Sintering Technique Courtesy of Prof. Ricardo Castro (rhrcastro@ucdavis.edu) and Dr. D. V. Quach (dvquach@ucdavis.edu) Early Sintering Stage
Sintering Driving Forces Why Sintering Happens? 1) Surface Energy Blow Here STOP dw R da When you blow a film of soap, an arc will form while you re blowing. When you stop, the surface becomes flat. This is because there is an extra energy to create a surface. In this case, it is a reversible work (provided by blowing) needed increase the surface of a unit area.
Surface tension is different however from surface enery. Surface energy is the energy needed to create a new surface and not only tension it to expand. In liquids, there is no difference between them, but in solids, they are usually different. This is because to create a surface in a solid means to create a surface free of tension and in equilibrium. If this surface is ever tensioned, this tension will remain, since the atomic mobility is very limited. S de da T, P, n i
The surface energy will always drive the small particles to be unstable. The system tends to decrease its energy even if locally, for instance by defining new shapes proportional to the interface energies. Wulff s figure Example: Determine the equilibrium shape of the grain below using Wulff s principle and knowing that: (110) = 2 erg/cm 2 ; (121) = 1.5 erg/cm 2 ; (111) = 0.5 erg/cm 2 ; (101) = 4 erg/cm 2 :
The driving force related to the interface energy is: G d da A A Two phenomena that occur during sintering: Densification + Coarsening
The system is eliminating one surface but creating another.
But surface energy is not the only driving force acting during sintering, and LOCAL driving forces apply. 2) Pressure due to curvature If you blow a straw inside oil, you re providing work needed to expand the spherical surface. This work (pressure. volume) must be equal to the area variation times the surface tension (.da). PdV da
If the area is spherical, the volume variation is dv=4 r 2 dr, and the variation of area is da=8 rdr, where r is the radius, then: P da dv 4 8 r rdr 2 dr 2 r The smaller the radius, the higher the pressure needed to create it, and vice-versa. infinite
3) Vapor Pressure Difference Chemical potential is related to vapor pressure (or solubility) by: RT ln The difference of the chemical potential for an atom in the curved surface (p) and in a flat surface (p 0 ) will be given by the curvature only. p RT ln p RT ln p 0 If dv=4 r 2 dr, p RT ln da 8 p 0 rdr dr V M 4 r 2 p p 0 exp V M 2 RT r
G r G G G X X r X B X r 1 r 2 Concentration
dw R da Since the solubility (or vapor pressure) is dependent on the particle size (because of curvature), we expect the small particles to dissolve/evaporate and re-precipitate (condense) on the larger ones. dw R da
In Sintering: Moving material from the convex surface to the concave surface of the pore. Evaporation- at flat or convex surfaces, condensation at concave surfaces. Other Driving forces: Vacancy Conc. can be considered a dispersed phase in vacuum
Stages of Sintering http://www.esrf.eu/usersandscience/publications/highlights/2002/materials/mat3 1 2 3 4
Driving Forces during Initial Stage of Sintering G d da A A Two particles model The pressure difference is given by If: P da dv The vapor pressure difference is given by: The vacancy concentration difference is:
Material transport mechanism during sintering Material transport paths during sintering x neck size a- particle radius
Summary of kinetic equations for various mechanisms of initial stage sintering
Current/Field Role in Sintering Field/current in conductive and non-conductive materials Same sintering stages? Mechanisms? Materials dependence? Evaporation Plasma - difficult to capture experimentally (setups precluding plasma generation) Dielectric induced plasma generation in flash sintering Local fields Field contribution to early sintering (e. g., polarization effects) Stage 1 enhanced kinetics
Early Sintering Stage (FAST) Initial sintering stage-usually when x= 2/3 a. Olevsky: transition point based upon the kinetics of the various mass transfer mechanisms Undoped Y 2 O 3 30 nm onset at 873 vs 1473 in CS (Yoshida et al, 2008) SnO 2-92% TD in 10 min at 1163 K vs CS: 61% TD in 3 h at 1273 K (Scarlat et al, 2003) Enhanced densification in Al 2 O 3 (Stanciu et al, J.Am.Ceram.Soc. 2007) Arrhenius plot of (αρ) for nano α- Al 2 O 3 sintered by different techniques: α thermal diffusivity ρ density The product (αρ) is proportional to the relative neck radius.
Maximum shrinkage rates 1-2 order of magnitude higher than CS (973 K for ZnO, 1373 K for ZrO 2 and 1423 K for Al 2 O 3 ) (Nygren and Shen, 2003). FAST sintering curves for ZnO, 3YSZ and Al 2 O 3 with a heating rate of 100 o C.min -1
Cleaning Effects TEM of FAST sintered AlN Clean grain boundaries in metals and ceramics
Enhanced Neck Growth Cu sphere-plate experiments under current application (900 o C) Multilayer graphite / copper plungers to control current density at constant power (P=I 2 R) Frei J M, Anselmi-Tamburini U and Munir Z A (2007), Current effects on neck growth in the sintering of copper spheres to copper plates by the pulsed electric current method, J. Appl. Phys., 101, 114914/1-8.
P I 2 [2 R cp 2( x 1) R cu 4 xr co 2 xr gf R sa ] I x 1 1 / 2 P 4 R co 2 R gf 1 / 2
Effect of current on neck formation between copper spheres and copper plates at 900 o C for 60 min: (a) no current, (b) 700 A, (c) 850 A, and (d) 1040 A
Enhanced Neck Growth cont d Conventional (no current) sintering: n = 4.13 (volume diffusion with E-C contribution) Different sintering mechanisms under current application: n = 8.76 20.64 (different sintering mechanisms than in CS) Evaporation-condensation (E-C), surface diffusion (SD) contributions to re-start neck growth (by faster coarsening step) E-C, SD visualized as new ledge patterns around the necks and voids, depending on current magnitude (no ledges in CS). Cu vapor pressure at 900 C: 10-4 Pa (insufficient for significant mass transport) Enhanced evaporation by adatom detachment form ledges or desorption from terraces due to electromigration force (F = Z*eE) Voids at the neck edge:
Evaporation-Condensation vs Surface Diffusion Demonstrated enhanced evaporation Enhanced grain boundary and volume diffusion Surface diffusion no effect due to external current in YSZ (70 nm) Neck formation (n, Q values by ionic conductivity measurements) in early stages with negligible shrinkage. t i ( 2 d σ t (σ i )= sample (intrinsic) conductivity (with Q=Q i +Q/n), X t = diameter of contact area M. Cologna, R. Raj, Surface Diffusion-Controlled Neck Growth Kinetics in Early Sintering of Zirconia with or without Applied DC Electrical Field, JACS, 2010, 1-5 X t )
MOLECULAR DYNAMIC SIMULATIONS Results with no field applied and pulses of 109V/m applied of 1, 5, 10, and 50 ps duration (on /off). displacement of surface and bulk atoms in an AlN nanosphere of 4 nm radius (25,384 atoms).
Plasma, Sparks, Breakdown No plasma under specific FAST conditions (>100 C, no local effects) Arc discharges electron emissions Dielectric breakdown: intrinsic or soft Electric field enhancement local field effects (e. g., about 200x in HA) Dielectric induced plasma generation in flash sintering Enthalpy (bonding) (ΔH 0 ) changes in dielectrics: 2 k H H p ( ) E o 0 3 po- dipole moment, k- dielectric constant, E- electrical field (McPherson, J et al, APL, 82, 2121, 2003)
Spark Arc) (Electric Visual observation -effect of pulsed current on neck formation during the sintering of 550 um Cu powder in a customdesigned FAST equipment (optical microscope). Yanagisawa O, Kuramoto H, Matsugi K, Komatsu M (2003), Observation of particle behavior in copper powder compact during pulsed electric discharge, Mat Sci Eng A, 350, 184-189.
Spark (Electric Arc) Contd. Visual observation -Local melting was also observed at locations where strong sparks occurred - A minimum macroscopic current density for spark to occur (e. g., 10 ka cm -2 at 6.9 MPa pressure) -Current density - two orders of magnitude greater than in a typical FAST - Local current density at particle contact can be higher. - Spark formation at lower pressure and higher current density - Spark probability at particle contacts is low (less than 2% in the above work).
Pulsing Current Effects PAS sintering of ~3 μm Cu powders. Initial Pulsed Current : 30 s 80 ms on/80 ms off Temp measurements thermocouple inside the powder bed Pulsed current promoted an earlier onset of sintering (compared to direct current). Time of maximum shrinkage displacement (t msd ) was 180 s under pulsed current vs 240 s with no pulses (at 420 A). No pulsing effect at > 700 A Xie et al (2003) found no effect of pulsing on final density, electrical resistivity and mechanical properties of fully sintered Al. It is possible that the magnitude of the pulsed current overshadows any influence of the pulse pattern. Wang S W, Chen L D, Kang Y S, Niino M, Hirai T, (2000), Effect of plasma activated sintering (PAS) parameters on densification of copper powder, Mater. Res. Bull., 35, 619-628. Xie G, Ohashi O, Chiba K, Yamaguchi N, Song M, Furuya K and Noda T (2003), Frequency effect on pulse electric current sintering process of pure aluminum powder, Mat Sci Eng A, 359, 384-390
Pore Stability The surface curvature of the grains around an isolated pore is affected by their number and the dihedral angle. Three possible mechanisms for pore motion: surface diffusion, volume diffusion through the vapor phase, and volume diffusion through the matrix. Does evaporation control pore elimination in late sintering stages? Raichenko argument
Final Sintering Stages (Raichenko) Higher electric current density at the root of large pores (R-pore radius) creates temperature gradients which in turn produce a vacancy gradient and mass transport in opposite sense ( o - electrical conductivity, C M - specific heat, To- initial temperature, E o - intensity of electric field, - time of electric field effect): T 1 R 0 2C M T 0 E 0 n 2 Conclusion: large pores shrink under applied electric current.
Pore Elimination The velocity of the migration of a pore is defined by both mobility and force:
Bibliography S-J. L. Kang; Sintering: Densification, Grain Growth & Microstructure, Elsevier 2005 Others: R. W. Baluffi et al.; Kinetics of Materials, Wiley 2005 R. M. German; Sintering Theory and Practice, Wiley 1966 M. N., Rahaman; Ceramic Processing and Sintering, 2nd Ed., CRC Press, 2003 D. A. Porter et al.; Phase Transformations in Metals and Alloys, CRC Press, 2008 Y.-M. Chiang et al.; Physical Ceramics - Principles for Ceramic Science and Engineering, John Wiley & Sibs Inc. 1997