DEVELOPMENT OF IRON-RICH NANOCRYSTALLINE MAGNETIC MATERIALS TO MINIMIZE MAGNETOSTRICTION FOR HIGH CURRENT INDUCTOR CORES

Transcription

1 DEVELOPMENT OF IRON-RICH (FE1-X-YNIXCOY)88ZR7B4CU1 NANOCRYSTALLINE MAGNETIC MATERIALS TO MINIMIZE MAGNETOSTRICTION FOR HIGH CURRENT INDUCTOR CORES By ANTHONY MARTONE Submitted in partial fulfillment of the requirements For the degree of Master of Science Thesis Advisor: Dr. Matthew Willard Department of Materials Science and Engineering CASE WESTERN RESERVE UNIVERSITY August 2017

2 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis of Anthony M Martone candidate for the degree of Master of Science*. Committee Chair Professor Matthew Willard Committee Member Professor David Matthiesen Committee Member Professor Alp Sehirlioglu 30 June 2017 *We also certify that written approval has been obtained for any proprietary material contained therein.

3 Table of Contents 1. Acknowledgements Abstract Introduction Technological Demand for New Magnetic Core Material Magnetic Material and Properties : Inductor Magnetic Core Properties : Coercivity and Grain Size : Microstructure of Nanocrystalline Magnetic Alloys : Magnetostriction in Nanocrystalline Magnetic Alloys Alloy Design : Alloy Design Overview : Alloy Design Paths Experimental Procedure Experimental Overview Alloy Processing Characterization of Ribbons : As-Spun Ribbon X-Ray Diffraction : Differential Scanning Calorimetry : Heat-Treated Ribbon X-Ray Diffraction

4 3.4: Room Temperature Magnetic Hysteresis : Magnetostriction Characterization : Thermomagnetic Characterization Results and Discussion Structural and Thermal Analysis : X-Ray Diffraction Overview : Structural Analysis: As-Spun Ribbon : Thermal Analysis: As-Spun Ribbons : Structural Analysis: Heat-Treated Ribbons Magnetic Property Analysis : Magnetic Analysis Overview : Magnetic Hysteresis : Magnetostriction : Thermomagnetic Characterization : Discussion of Magnetic Property Relations Future Work Multivariate Regression of Magnetostriction : Multivariate Regression Overview : (Fe,Ni,Co) 88Zr 7B 4Cu 1 Analysis : (Fe,Ni,Co) 86Zr 7B 6Cu 1 Analysis

5 2. Nanocrystalline Magnetic Powder Conclusion Appendix Experimental Procedure Magnetic Analysis Future Work Nanocrystalline Magnetic Powders References

6 List of Tables Table 1: Alloy compositions (atomic %) created and analyzed Table 2: Onset and peak crystallization temperatures of primary (Tx1) and secondary (Tx2) crystallization for (Fe,Ni,Co)88Zr7B4Cu1 as-spun samples at 10 K/min DSC scan Table 3: Lattice parameter (ao) and crystallite sizes (D) of ribbons annealed at 550 C for 3600 s Table 4: RT hysteresis properties (saturation specific magnetization, Ms, and coercivity, Hc) of (Fe,Ni,Co)88Zr7B4Cu1 as-spun ribbons Table 5: RT hysteresis properties (saturation specific magnetization, Ms, and coercivity, Hc) of (Fe,Ni,Co)88Zr7B4Cu1 ribbons annealed at 550 C for 3600 s Table 6: Magnetostrictive coefficients, λ, for (Fe,Ni,Co)88Zr7B4Cu1 as-spun and 550 C annealed for 3600 s ribbons Table 7: Summary of structural (crystallite size, D) and magnetic properties (saturation specific magnetization, Ms, coercivity, Hc, and magnetostriction coefficient, λ) of nanocrystalline (Fe,Ni,Co)88Zr7B4Cu1 alloys annealed at 550 C for 3600 s Table 8: Various alloys compositions with predicted zero magnetostriction in (Fe,Ni,Co)88Zr7B4Cu1 nanocrystalline alloy systems based on multivariate regression.. 67 Table 9: Various alloys compositions with predicted zero magnetostriction in (Fe,Ni,Co)86Zr7B6Cu1 nanocrystalline alloy systems based on multivariate regression Table 10: Sensitivity, accuracy, and model information for equipment and instruments used for alloy production and analysis

7 Table 11: Pictures of all equipment and instruments used for alloy production and analysis Table 12: Crystallite size determined from each peak for (Fe,Ni,Co)88Zr7B4Cu1 alloys annealed at 550 C for 3600 s Table 13: Magnetostriction, λ, data of FexNiyCo88-x-yZr7B4Cu1 nanocrystalline alloy systems used for multivariate analysis 1,10, Table 14: Magnetostriction data, λ, of FexNiyCo86-x-yZr7B6Cu1 nanocrystalline alloy systems used for multivariate analysis from Muller Table 15: Processing conditions for Fe77Ni5.5Co5.5Zr7B4Cu1 magnetic powders Table 16: Saturation specific magnetization (Ms), coercivity (Hc), lattice parameter (ao) and crystallite size (D) of Fe77Ni5.5Co5.5Zr7B4Cu1 magnetic powders and ribbons Table 17: Stress annealed (SA) and milling conditions for Fe77Ni5.5Co5.5Zr7B4Cu1 magnetic powder Table 18: Saturation specific magnetization (Ms) and coercivity (Hc) of Fe77Ni5.5Co5.5Zr7B4Cu1 stress annealed (SA) magnetic powders Table 19: Processing conditions including heat treat (HT) for NASA spun Fe77Ni5.5Co5.5Zr7B4Cu1 magnetic powders Table 20: Saturation specific magnetization, Ms, and coercivity, Hc, of Fe77Ni5.5Co5.5Zr7B4Cu1 NASA spun magnetic powders Table 21: Atomic fraction of elements in NASA spun Powder 2_

8 List of Figures Figure 1: Hysteresis loop of example "hard" and "soft" magnet, showing various magnetic properties Figure 2: Coercivity dependence on grain size for various soft magnetic alloys Figure 3: Pseudo-ternary compositional diagram showing alloy compositional paths, P1 and P2, in the (Fe1-x-yNixCoy)88Zr7B4Cu1 alloy system Figure 4: Research process cycle used for developing nanocrystalline magnetic ribbons 25 Figure 5 (left) and 6 (right): Ribbon mounted on VSM holder with Teflon tape (left), tape partially removed to show alignment of ribbon (right) with applied magnetic field, H Figure 7: Ribbons mounted strain gauge for magnetostriction measurement, each image is a different side of gauge Figure 8: Raw magnetostriction data collected for Fe77Ni6.875Co4.125Zr7B4Cu1 ribbon annealed at 550 C for 3600 s under positive bias (blue) and negative bias (orange) Figure 9: Sinusoidal Fit (green) of magnetostriction component of strain gauge data for 550 C for 3600 s annealed Fe77Ni6.875Co4.125Zr7B4Cu1 ribbon Figures 10: Induction components of strain gauge data for Fe77Ni6.875Co4.125Zr7B4Cu1 ribbon annealed at 550 C for 3600 s Figure 11: XRD diffractogram of (Fe,Ni,Co)88Zr7B4Cu1 as-spun ribbons using Cu-Kα x- ray source from 20 to Figure 12: Differential Scanning Calorimetry (DSC) scan of (Fe,Ni,Co)88Zr7B4Cu1 asspun ribbons at 10 K/min from 50 to 750 C. Primary crystallization, Tx1, secondary crystallization, Tx2, and annealing temperature of 550 C indicated

9 Figure 13: Onset crystallization temperatures determined from a K/s (10 K/min) DSC scan vs average number of valence electrons from magnetic elements per atom for all (Fe,Ni,Co)88Zr7B4Cu1 alloys Figure 14: Determination of lattice parameter from XRD data using the Nelson-Riley function of theta for alpha-fe phase in Fe77Ni6.875Co4.125Zr7B4Cu1 annealed at 550 C for 3600 s Figure 15: FWHM determination of the (110) peak in Fe77Ni6.875Co4.125Zr7B4Cu1 annealed at 550 C for 3600 s. XRD scan with Cu-Kα source Figure 16: XRD diffractograms of (Fe,Ni,Co)88Zr7B4Cu1 alloys annealed at 550 C for 3600 s. XRD scan with Cu-Kα source Figure 17: Room temperature magnetic hysteresis loop up to 1.2 MA/m of Fe77Ni6.875Co4.125Zr7B4Cu1 as-spun ribbon and ribbon annealed at 550 C for 3600 s. Saturation specific magnetization, Ms, indicated by red arrows Figure 18: Width of hysteresis loop (indicated by red arrows) of as-spun and annealed at 550 C for 3600 s Fe77Ni6.875Co4.125Zr7B4Cu1 ribbons. Coercivity, Hc, indicated Figure 19: RT magnetic hysteresis up to 1.2 MA/m magnetic field for all (Fe,Ni,Co)88Zr7B4Cu1 as-spun ribbons Figures 20: RT magnetic hysteresis up to 1.2 MA/m magnetic field for all (Fe,Ni,Co)88Zr7B4Cu1 ribbons annealed at 550 C for 3600 s Figure 21: Determination of the Curie temperature of the amorphous phase, Tc am, in asspun Fe77Ni6.875Co4.125Zr7B4Cu1 at 3.18x10 5 A/m saturating field

10 Figure 22: Thermomagnetic data for all (Fe,Ni,Co)88Zr7B4Cu1 as-spun alloys at 3.18x10 5 A/m saturating field (Happlied) Figure 23: Coercivity dependence on grain size of (Fe,Ni,Co)88Zr7B4Cu1 nanocrystalline alloys heat treated at 550 C for 3600s with additional data from literature values for similar nanocrystalline magnetic alloys Figure 24: Slater-Pauling curve (dashed curve) for nanocrystalline (Fe,Ni,Co)88Zr7B4Cu1 alloys with literature values of similar nanocrystalline alloys 10, Figure 25: Magnetostriction vs number of magnetic valence electrons/atom for (Fe,Ni,Co)88Zr7B4Cu1 alloys heat treated at 550 C for 3600 s. Compositional paths, P1 and P2, indicated with inaccessible alloy compositions shown as red dashed line Figure 26: Curie temperature of the amorphous phase variation dependence on cobalt fraction (with annotated magnetostriction values for nanocrystalline material) in (Fe,Ni,Co)88Zr7B4Cu1 as-spun alloys with literature data from (Fe1-2xCoxNix)88Zr7B4Cu1 system Figure 27: Magnetostrictive coefficient vs the square of saturation magnetization for (Fe,Ni,Co)88Zr7B4Cu1 as-spun ribbons and ribbons annealed at 550 C for 3600 s with literature values of Fe-based amorphous alloys Figure 28: Coercivity vs magnetostrictive coefficient for (Fe,Ni,Co)88Zr7B4Cu1 ribbons annealed 550 C for 3600 s with literature data from Fe88-2xNixCoxZr7B4Cu1 nanocrystalline ribbons 1, Figure 29: Multivariate regression of magnetostriction as a function of fraction of iron and nickel in (Fe,Ni,Co)88Zr7B4Cu1 nanocrystalline alloy systems

11 Figure 30: Compositional curve of zero magnetostriction based on multivariate regression in (Fe,Ni,Co)88Zr7B4Cu1 nanocrystalline alloy systems Figure 31: Multivariate regression of magnetostriction as a function of fraction of iron and nickel in (Fe,Ni,Co)86Zr7B6Cu1 nanocrystalline alloy systems Figure 32: Compositional curves of zero magnetostriction based on multivariate regression in (Fe,Ni,Co)86Zr7B6Cu1 nanocrystalline alloy systems Figure 33: Alumina standard diffractogram from Bruker XRD with Cu-Kα source Figure 34: Alumina standard diffractogram from Rigaku XRD with Cu-Kα source Figure 35: Diffractogram of fused silica glass slide used for ribbon sample mounting Figure 36: LaB6 standard diffractogram from Bruker XRD with Cu-Kα source Figure 37: Coercivity vs number of magnetic valence electrons/atom for (Fe,Ni,Co)88Zr7B4Cu1 alloys annealed at 550 C for 3600 s, showing compositional paths, P1 and P Figure 38: Diffractogram of for Fe77Ni5.5Co5.5Zr7B4Cu1 magnetic powders using Cr-Kα source Figure 39: Room temperature magnetic hysteresis of Fe77Ni5.5Co5.5Zr7B4Cu1 magnetic powders and ribbons Figure 40: Room temperature magnetic hysteresis of Fe77Ni5.5Co5.5Zr7B4Cu1 stress annealed magnetic powders and ribbons Figure 41: Magnetization vs stress anneal time for Fe77Ni5.5Co5.5Zr7B4Cu1 SA magnetic powders

12 Figure 42: Coercivity vs stress anneal time for Fe77Ni5.5Co5.5Zr7B4Cu1 SA magnetic powders Figure 43: Room temperature magnetic hysteresis of NASA spun Fe77Ni5.5Co5.5Zr7B4Cu1 magnetic powders Figure 44: Scanning Electron Microscope image of NASA spun powder showing areas used for energy dispersive x-ray spectroscopy analysis

13 1. Acknowledgements I would like to thank my thesis advisor, Professor Matthew Willard for his support, knowledge, and leadership throughout my graduate career. I would also like to thank my committee members, Professor Alp Sehirlioglu and Professor David Matthiesen, for their roles as teachers and for serving on my defense committee. I would also like to acknowledge the other members of Willard s research group, Song Lan, Bowen Dong, Jonathan Healy, and Ethan Field, who have helped me through various stages of my Master s research. This study would not be possible without the financial support from the Ohio Federal Research Network (OFRN). I would also like to express my gratitude for the support in large-scale melt spinning provided by NASA Glenn Research Center. In particular, I would like to thank Dr. Randy Bowman and Dr. Ron Noebe for their continued support in this project. Furthermore, I would like to thank all the faculty, staff, and students of the Materials Science and Engineering Department at Case Western Reserve University, with which I have been so lucky to have completed my undergraduate and graduate careers. Finally, I would like to thank my parents and family for their continuous support and encouragement. 11

14 2. Abstract Development of Iron-Rich (Fe 1-x-y Ni x Co y ) 88 Zr 7 B 4 Cu 1 Nanocrystalline Magnetic Materials to Minimize Magnetostriction for High Current Inductor Cores ANTHONY MARTONE Advanced power electronic systems, with increased switching frequencies, demand greater efficiency and higher operating temperature inductors. This demand can be met by developing a new magnetic core material. Nanocrystalline magnetic materials, in particular, Fe77Co5.5Ni5.5Zr7B4Cu1, have been developed for use at elevated temperatures 1. While this nanocrystalline alloy having iron substituted with equal atomic percentages of cobalt and nickel has resulted in small coercivity, 10 A/m, and high Curie temperature, 220 C, magnetostriction persists as the main source of losses 1. Coercivity in this alloy system has proven to have a strong dependence on the magnetostriction. Through alloy development, low coercivities and high Curie temperatures can be achieved while minimizing magnetostrictive losses. This thesis focuses on varying the magnetic element content in the iron-rich (Fe1-x-yNixCoy)88Zr7B4Cu1 alloy system to minimize magnetostriction. Fe77Ni8.25Co2.75Zr7B4Cu1 has shown the best results with a coercivity of 10 A/m, magnetostrictive coefficient of 4.8 ppm, and Curie temperature of 218 C. 12

15 3. Introduction 1. Technological Demand for New Magnetic Core Material As technology advances, inductors in electric systems must improve to keep up with performance demands. In particular, there is a need for improved inductors in motors for propulsion, power convertors, and other applications 2. Many electrical systems would benefit from increased energy output afforded by increasing switching frequencies. An increased frequency from 60 Hz (typical electrical grid current frequency) to 400 Hz (typical aeronautic current frequency) will have an increased inductor power output of greater than 15 times 2. An increase from 60 Hz to 20 khz (upper range of planned aeronautic switching frequency) will have an increased inductor power output of greater than 2 million times 3. To maintain an equivalent power output while increasing the switching frequency, the magnetic flux of the inductor can be decreased. The magnetic flux can be decreased by miniaturizing the magnetic core and therefore the entire volume of the inductor. Miniaturization of inductor components will allow for decreased weight of the electrical system, extremely important for aeronautic applications. However, at higher switching frequencies, core losses will be greater. Greater losses may also lead to higher operating temperatures. These high current inductors would require an improved magnetic core material to operate at higher temperatures with less lossses 4,5. An improved magnetic core will allow for (not only increased efficiency in the inductor but also) a reduction in component size and weight and increased operation temperature 5. 13

16 2. Magnetic Material and Properties 2.1: Inductor Magnetic Core Properties Inductor magnets in any application require low coercivities (less than ~400 A/m), low core losses (less than ~100 kw/kg from a sinusoidal waveform and an applied induction amplitude of ~0.2 Tesla), and high saturation magnetization (greater than 5 MA/m) to operate effectively. Magnets with these properties are known as soft magnets. Soft magnetic materials are able to easily switch their magnetic polarity, making them especially useful in AC current applications. Coercivity, core loss, and saturation magnetization are all defined by the magnetic response of a material under the influence of an applied magnetic field (aka hysteresis loop). In the Case Western Reserve University magnetics laboratory, vibrating sample magnetometer (VSM) is used to make quasi-static hysteresis loops, which allows for the evaluation of magnetic properties of new alloys. How these properties relate to the hysteresis loop can be seen in Figure 1. Saturation Magnetization 2 Coercivity Core Loss Figure 1: Hysteresis loop of example "hard" and "soft" magnet, showing various magnetic properties 14

17 The coercivity is a property that describes the difficulty of demagnetizing a ferromagnetic material. Coercivity is equivalent to the applied field required to demagnetize (reduce to zero magnetization) the material. This value is equivalent to half the width of the hysteresis loop. When the applied field is strong enough to align all the magnetic moments of a material, the material has reached magnetic saturation. The saturation magnetization is equivalent to the maximum height of the hysteresis loop at a large (saturation) field. The hysteresis of the magnetism upon cycling the applied field is the result of losses in the material. These losses are partially due to domain wall pinning on sites such as grain boundaries 6. The hysteresis results in an energy loss per switching cycle, which equals the area of the magnetic induction applied field (B-H) hysteresis loop and is known as the core loss of a magnet. A soft magnet is meant to have an easily switched magnetization, meaning a small coercivity with small core losses. The coercivity is proportional to the magnetic anisotropy of a material. In ribbonshaped magnetic material (as the material in this study), magnetocrystalline anisotropy and magnetoelastic anisotropy will be the primary contributors to the total magnetic anisotropy. Because the magnetization vector will have a minimum energy when aligned in a certain crystallographic directions (a.k.a. easy axis ), energy is required to orient the magnetization in a higher energy direction. This energy density is known as the magnetocrystalline anisotropy energy, E. This energy is expressed as a series expansion of direction cosines (represented by α) of the magnetization direction relative to the crystal axes ([100], [010], [001] for a cubic crystal), see Equation 1 6. E K K ( ) K ( )... (1) o

18 Ko, K1, K2, and so on are constants for a material at constant temperature. The first direction dependent constant, K1, having units of J/m 3 [SI] or erg/cm 2 [cgs] in this expansion is known as the magnetocrystalline anisotropy 6. The magnetoelastic anisotropy couples magnetization to strain direction 6. In turn, magnetizing a ferromagnetic material can cause a strain response known as magnetostriction. Magnetostriction will cause a dimensional change of the material from domain reorientation from an applied field. This means that as a sample is magnetized, it will either expand or contract. Domains that comprise the material will not in fact be cubic but in actuality be tetragonal (for a cubic system). When magnetized, domains in the magnetization direction will grow, and, when saturated, the material will become single domain in the magnetization direction. When demagnetized, a single crystal will be cubic because the elongations of the domains cancel each other out, as they are randomly oriented. When a magnetic field is applied, the single crystal will deviate from cubic as the domain in the magnetization direction dominates. This shape change will also occur in polycrystalline and nanocomposite magnetic materials. In high current applications where losses increase operating temperatures, magnetic materials must also have high Curie temperatures in order to stay magnetized. The Curie temperature is the temperature at which a magnetic material loses magnetic order and becomes paramagnetic. This means that above the Curie temperature, the residual magnetization will reduce to a zero value without the presence of an applied magnetic field. Iron-cobalt magnetic alloys are known for their soft magnetic properties and high Curie temperatures. Hiperco 50 (Fe49Co49V2), for example, has a Curie temperature of 940 C 7. Unfortunately, magnetic core materials have increased losses with increased switching 16

19 frequency, which increase with a power-law of the switching frequency and result in energy dissipation as heat. As an example, the coercivity of Hiperco 50 increases from 1420 A/m (18.0 Oe) at 100 Hz to 1700 A/m (21.3 Oe) at 3000 Hz, increasing the core loss from 100 W/kg at 100 Hz to 3000 W/kg at 3000 Hz 8. Currently, aerospace applications operate at 400 Hz 2. At this frequency, the core losses in Hiperco 50 would be three times as large (around 300 W/kg) compared to 100 Hz. These large core losses with increased switching frequencies make Hiperco 50 inefficient at high frequency applications 8. The large mangetostrictions of Fe-Co alloys contribute to the core losses. Polycrystalline Hiperco 50, for example, has a saturation magnetostriction of 60 parts per million (ppm) 7. By minimizing the magnetostriction to a near zero value (< 1 ppm), the core losses of FeCo magnetic material can be decreased. By creating nanocrystalline FeCo magnetic alloys, the magnetostriction has been observed to have lower values (described in Section 2.4) 9. However, it was only recently that Fe-Co-Ni nanocrystalline alloys have shown good high temperature performance (up to 550 C) with small magnetostriction (down to 2.5 ppm) (described in section 2.4) 1,9, : Coercivity and Grain Size In a magnetic material, grain size can greatly affect the coercivity. The grain size dependence of coercivity is shown in Figure

20 Figure 2: Coercivity dependence on grain size for various soft magnetic alloys 11 Two trends exist between grain size (D) and coercivity (Hc). An inverse relation exists, (Hc D -1 ), at grain sizes above 1x10-7 m (100 nm) due to domain wall-grain boundary pinning mechanism. However, at nano-sized grains the coercivity decreases drastically (H c D 6 ) with smaller grain size (i.e. when the grain size is less than the domain wall width). This means that nanocrystalline materials possess extremely small coercivities, due to smaller interactions between the domain walls and the grains. In the large grain size region (D > 100 nm), the coercivity decreases as the grain size increases 7. With larger grain sizes, the magnetic material will have less grain boundaries on a volumetric basis. This means that there will be less sites for domain wall pinning. This domain wall pinning will increase the coercivity as it creates a barrier for domain wall motion during magnetization. In the small grain size region (D < 100 nm), the coercivity decreases with smaller grain size, which can be explained by the random anisotropy model. The crystal anisotropy 18

21 energy (mentioned in Section 2.1), quantifies the energy associated with saturating a magnetic material in a non-easy direction. The magnetocrystalline anisotropy will be opposed by the magnetic exchange stiffness. The magnetic exchange stiffness, A, having units of J/m [SI] or erg/cm [cgs] describes the energy associated with how strongly the magnetic moments want to align together in a common direction independent of anisotropy direction. If a material has a 180 domain wall, the magnetic anisotropy will favor an infinitesimally small domain wall with a direct change in magnetic moment while the magnetic exchange stiffness would favor an infinitely wide domain wall with the magnetic moments aligning. In the case of a 180 domain wall, the width of the wall is proportional to A/ K 1 (i.e. a quantity known as the exchange correlation length) 9. In nanocrystalline magnetic materials, the grain size is much smaller than this exchange correlation length. This means that the exchange correlation length will contain many grains and average the magnetic anisotropy of these grains (due to the influence of the exchange stiffness). This creates a smaller effective magnetic anisotropy, and because the coercivity is dependent on the magnetic anisotropy; ultimately, lowers the coercivity. 2.3: Microstructure of Nanocrystalline Magnetic Alloys Nanocrystalline magnetic alloys are typically composed of at least two of the following four classes of elements: magnetic transition metals (MTM), early transition metals (ETM), metalloids/post-transition metals (PTM), and a late transition metals (LTM) 9. MTMs such as iron, cobalt, and nickel, contribute significantly to the magnetic properties of the alloy. ETMs such as zirconium, niobium, hafnium, and titanium as well as metalloids/post-transition metals such as boron, silicon, and aluminum act as glass 19

22 formers by creating a deep eutectic with the MTM that stabilizes the melt 9. Early transition metals will also act as grain growth inhibitors to prevent grains from growing to large sizes by decreasing the diffusivity of the MTM 9. A late transition metal such as copper or gold acts as a grain initiator for heterogeneous nucleation due to its lack of solubility in the MTM-rich matrix 9. Nanocrystalline magnetic alloys can be produced by rapid solidification of the molten alloy and subsequent annealing. Rapid solidification through techniques such as singleroller melt spinning (quenching at up to 10 6 C/s) will produce an amorphous ribbon 9. This ribbon can then be annealed above the primary crystallization temperature (but below any further crystallization temperatures) to produce nanocrystalline grains amongst a matrix of residual amorphous phase. Upon annealing, copper will cluster. Grains will then nucleate at the copper clusters 9. In Fe-Ni-Co-Zr-B-Cu alloys, iron, cobalt, and nickel will crystallize into an α-(fe,ni,co) phase while the boron and zirconium will stabilize the amorphous phase 1,9, : Magnetostriction in Nanocrystalline Magnetic Alloys Nanocrystalline magnetic materials can achieve very low coercivities (0.5 A/m) by means of lowering their magnetocrystalline anisotropy according to the random anisotropy model as well as reducing the magnetoelastic anisotropy with near zero magnetostrictions. Nanocrystalline magnetic materials will have differing magnetostrictions in their crystalline phase compared to their amorphous phase. The overall magnetostriction of the nanocrystalline composite will simply be a weighted average of these two 20

23 magnetostrictions. In similar nanocrystalline alloys to this study, the amorphous phase will have a positive magnetostriction while the crystalline phase has a negative value 9. Finemet TM alloys (nanocrystalline Fe,Si,B,Cu,Nb alloy) have excellent coercivities of around 0.5 A/m 12. This low coercivity can be achieved because Finemet TM has a low magnetocrystalline anisotropy and near zero magnetostriction from the positive value of the amorphous phase balanced with the negative Si-rich crystallite value. However, this magnetic material does not perform well at high temperatures 12. Finemet TM alloys cannot operate effectively above ~150 C 13. Nanocrystalline iron-cobalt alloys as do other Fe-Co alloys have high Curie temperatures (greater than 200 C) that allow them to perform well for high temperature applications 9,14,15. In order to minimize the magnetostriction in iron-cobalt magnetic materials, nickel alloying is believed to be effective 1.9,10. Because nanocrystalline magnetic materials are comprised of mostly iron, the effects of cobalt and nickel alloying on the magnetostriction of pure iron is of interest. The magnetostriction of iron is -8 ppm 6. When alloyed with cobalt or nickel in a polycrystalline structure the magnetostriction increases with increased solute concentration. The magnetostriction will become zero at 2.5 at% Ni and 3.5 at% Co (possessing positive values for both alloys with greater substitution), respectively 6. The estimated linear rate at which the magnetostriction increases for Ni is 3.3 ppm/at% and 2.5 ppm/at% for Co 6. Iron-based amorphous alloys will have a positive magnetostriction of around 32 ppm 6. In the compositional range of interest for alloying nanocrystalline magnets (0-11 at% Co, Ni) the magnetostriction increases for Co alloying and decreases for Ni alloying in amorphous alloys 6,9,14. The magnetostriction will decrease at a rate of -0.3 ppm/at% for 21

24 Ni and increase at a rate of 0.5 ppm/at% for Co 6. The decrease of magnetostriction from Ni substitution gives evidence that increasing the nickel content in (Fe,Co,Ni)-based nanocrystalline alloys can minimize the magnetostriction. Nickel has proven to decrease the magnetostriction in (Fe,Co,Ni)-based alloys, but not entirely eliminate it 1,9,10. Previous work performed on Fe88-2xCoxNixZr7B4Cu1 nanocrystalline alloys have shown that Curie temperatures as high as 570 C and coercivities of less than 5 A/m can be achieved 1,9,10. The equal substitution of iron with cobalt and nickel proved to reduce the magnetostriction to ~2.5 ppm at x= This thesis focuses on modifications in the (Fe,Co,Ni)Zr7B4Cu1 alloy system in order to minimize the magnetostrictive losses to a less than 1 ppm value while maintaining high operation temperatures greater than 200 C. 3. Alloy Design 3.1: Alloy Design Overview Five (Fe, Ni, Co)88Zr7Cu1 alloys were created and analyzed based on two compositional paths, intersecting at a known alloy, Fe77Ni5.5Co5.5Zr7B4Cu1 1,10. The compositions were chosen with the objective of achieving a magnetostriction of less than 1.0 ppm, a Curie temperature of greater than 200 C, and saturation magnetization of greater than 150 (A m 2 )/kg. 3.2: Alloy Design Paths In order to minimize magnetostriction, two alloy design paths have been chosen. These paths can be seen in the (Fe, Ni, Co) pseudo-ternary diagram for the 22

25 (Fe1-x-yNixCoy)88Zr7B4Cu1 alloy system, shown in Figure 3. The alloy compositions are listed also in Table 1. Figure 3: Pseudo-ternary compositional diagram showing alloy compositional paths, P 1 and P 2, in the (Fe 1-x-yNi xco y) 88Zr 7B 4Cu 1 alloy system The two alloy design paths intersect at known high temperature alloy (Curie temperature of 220 C) with very low magnetostriction (~2.5 ppm) Fe77Ni5.5Co5.5Zr7B4Cu1-1,10. Path P1 holds the atomic percent of iron constant while simply increasing the nickel to cobalt ratio. The alloys were chosen to have greater nickel to cobalt content, which is believed to decrease the magnetostriction. The first alloy along this path was chosen to have 50% more nickel and 50% less cobalt than the known composition above. An alloy with any lower amount of cobalt risks lowering the Curie temperature below 200 C. Therefore, the final alloy along this path was chosen to have 25% more nickel and 25% less cobalt. 23

26 The second compositional path, P2, was chosen to explore a region in the ternary compositional diagram with less iron. These alloys were chosen to have a nickel to cobalt ratio that consistently increased. Starting with the known alloy, Fe77Co5.5Ni5.5Zr7B4Cu1, the Ni/Co ratio increased from 1 to 2 in steps of 0.5. This increasing Ni/Co ratio is compensated by decreasing iron content in order to explore a higher nickel content region along a linear path. 24

27 4. Experimental Procedure 1. Experimental Overview The following sections will describe the creation and analysis of our (Fe, Ni, Co)-based nanocrystalline ribbons in detail. In this section, the general process and types of testing are outlined to give an overall perspective of the work (Fig. 4). Alloy compositions were first chosen based on prior research 1,10, in particular, trends in magnetic properties of similar high temperature soft magnetic alloys. Chosen alloys were synthesized from pure elements by arc melting the components into 25 gram ingots. Ingots were then melt spun into amorphous ribbons. Differential Scanning Calorimetry (DSC) was performed in order to determine crystallization temperatures of the alloys. Ribbons were then isothermally heat-treated to develop a nanocrystalline microstructure. Annealed ribbons were then analyzed using X-Ray Diffraction (XRD), Vibrating Sample Magnetometry (VSM), and a home-built magnetostriction system for microstructural and magnetic properties. Figure 4: Research process cycle used for developing nanocrystalline magnetic ribbons 25

28 2. Alloy Processing The alloy series explored in this research is the iron-rich (Fe1-x-yNixCoy)88Zr7B4Cu1 nanocrystalline alloys. The created and analyzed alloy compositions are shown in Table 1. Alloy Compositions Fe77Ni5.5Co5.5Zr7B4Cu1 1 Fe77Ni6.875Co4.125Zr7B4Cu1 Fe77Ni8.25Co2.75Zr7B4Cu1 Fe71.5Ni9.9Co6.6Zr7B4Cu1 Fe66Ni14.667Co7.333Zr7B4Cu1 Table 1: Alloy compositions (atomic %) created and analyzed Elemental solids of at least at% purity were weighed using an Ohaus Adventurer Pro (Model: AV264C) mass balance to weigh elements to target masses to create 25 gram ingots. Target masses were determined by converting atomic percent to weight percent and normalizing by 25 grams. Elements were measured to within 0.05% of their target mass. Arc melting was performed using a Thermal Technology LLC Model BJ5 system with a Miller Gold Star 652 power source and diffusion pump. For arc melting, the elemental solids (in their proper wt% proportions) were placed on a water-cooled, hemispherical copper hearth cavity. The arc melting chamber was purged at least 3 times using argon prior to melting the alloy. Vacuum was achieved with a base pressure of at most 2.67x10-4 Pa and subsequently backfilled with around 7.6x10 4 Pa of argon gas. When arc melting, an overpressure of 1.15x10 5 Pa of argon gas was used. The elements were melted into a round ingot, which was flipped and remelted at least 3 times to ensure homogeneity. The button-shaped ingot was then transferred to an elongated oval shaped mold and remelted an additional two times to create a final homogeneous, cigar-shaped ingot. The 26

29 final ingot mass was measured to determine mass loss or gain during arc melting. All final ingots were under 0.5% weight difference from their initial elemental solids. Homogeneous ingots were melt spun into amorphous ribbons using a single-roller melt spinning technique by nozzle ejection (jet casting). Melt spinning was completed using a Yein Tech Rapid Solidification Processing System in an inert atmosphere of 7.6x10 4 Pa of argon gas. The chamber was purged 3 times to less than 0.80 Pa and backfilled with around 7.6x10 4 Pa of argon gas. Ingots were heated in a quartz crucible by using an induction coil. The quartz crucible had dimensions of m length, m OD, 2x10-3 m wall thickness and a x10-4 m orifice. The crucible was separated from the cast wheel by approximately a 6.35x10-3 m. Ejection of the melt was conducted with around 3.4x10 4 Pa of argon ejection gas. The melt was solidified using a 0.25 m diameter copper wheel at between 51.1 to 57.5 rotations per second ( rpm) or a surface velocity of m/s. Solidified ribbons are produced with around a m width and 2.0x10-5 m thickness. All ribbons were collected; however, only high quality ribbons were analyzed. Ribbons were determined to be of high quality based on appearance and flexibility. The appearance of high quality ribbons had smooth edges and surfaces without pinholes or other damage. Higher quality ribbons were flexible enough to be able to be bent in half width-wise without fracturing. Heat-treating of ribbons was performed after encapsulating the ribbons in a fused quartz ampoule with a pressure of 1x10 5 Pa of argon gas. Ribbon sections and zirconium slugs were placed in a 0.10 to 0.15 m long fused quartz tube with a 1.3x10-2 m OD and 1.0x10-2 m ID for encapsulation. Zirconium slugs were used as an oxygen-getter to avoid oxidation of the ribbon sections. An acetylene-oxygen torch was then used to soften and 27

30 close one end of the tubing. The closed tube section was then purged three times to around 1.33 Pa vacuum and backfilled with slightly less than 1.01x10 5 Pa of argon gas. The tube was finally closed off into an ampoule using the torch. The ampoule was submerged underwater to check for air tightness. An air tight ampoule would not cause bubbles to rise from the water and no water would be found inside. After encapsulation, the ribbons were annealed in a Lindberg Model six zone tube furnace at 550 C for 3600 seconds (1 hour). The ampoule was removed and quenched in room temperature water. Finally, ribbons were removed from the ampoule by breaking the glass tubing. 3. Characterization of Ribbons 3.1: As-Spun Ribbon X-Ray Diffraction As-spun ribbons were characterized using a Rigaku D/Max 2200 having a Cu-Kα X- ray source to ensure that they were amorphous. XRD goniometer alignment calibration was performed using an alumina sample. Rigaku scans utilize a horizontal goniometer performing a theta-2 theta scan. Ribbons were mounted on a silica glass slide using doublesided cellophane tape. Ribbons were mounted with the wheel side of the ribbon facing towards the x-ray source. With melt spinning ribbons, the wheel side has a higher cooling rate due to the conduction heat transfer to the copper wheel. This allows the wheel side of the ribbons to have a greater probability of forming an amorphous phase. Scans were performed from 20 to 120 with a step size of 8.33x10-3 /s (0.500 /min). 3.2: Differential Scanning Calorimetry Once the ribbons were confirmed to be amorphous, Differential Scanning Calorimetry (DSC) was conducted on the ribbons using a Netzsch 404 F3 Pegasus. This 28

31 thermoanalytical technique allows for phase transition temperatures to be determined. Ribbon samples were cut into small sections that lay flat at the bottom of an alumina sample holder having a 6.8x10-3 m radius and 8.5x10-5 L volume. Between mg of ribbons were used for each experiment. Data was collected from C at K/s (10 K/min) heating rate having 1.0 ml/s (60 ml/min) flowrate of argon to reduce oxidation. Proteus Analysis software was used to determine onset and peak temperatures. Exothermic peaks indicate crystallization temperatures of the ribbons, which were subsequently used to determine heat-treating temperatures. 3.3: Heat-Treated Ribbon X-Ray Diffraction After heat-treatment, ribbons were characterized for structural properties, room temperature magnetic hysteresis, thermomagnetic properties, and magnetostriction. A Bruker D8 Discover Series II XRD1 was used to identify lattice parameter, crystallite size, and phases1. Heat-treated samples were mounted similarly to as-spun ribbons on a silica slide with double-sided cellophane tape with the wheel-side of the ribbon facing the XRD source. A Cu-Kα X-ray source was used with a 20 to 120 scan at 8.33x10-3 /s (0.500 /min). The resulting diffractograms were analyzed using DIFFRAC.EVA software. Scherrer analysis (Equation 11) was performed on all peaks to determine crystallite size, and the lattice parameter is determination by a Nelson-Riley function of theta (Equation 10) for each peak 16. These techniques are discussed further in Chapter 5, Section The change in XRD instrumentation from as-spun (Rigaku) to heat-treated (Bruker) samples is simply due to a technical issue with the Rigaku instrument. 29

32 3.4: Room Temperature Magnetic Hysteresis A Lakeshore Model 7410 vibrating sample magnetometer was used to measure the room temperature magnetic hysteresis loop for each alloy. This process was performed on both the as-spun and heat-treated ribbons. Ribbon sections were cut to approximately a 2x10-3 m (2 mm) width and 5x10-3 m (5 mm) length. Sections were weighed with a Sartorius MSE3.6P000DM microbalance. Using Teflon tape, ribbon sections were mounted to the bottom of a diamagnetic, quartz sample rod. The ribbons were aligned long-direction parallel to the applied magnetic field as seen in Figure 5 and Figure 6. H 5 mm 5 mm Figure 5 (left) and 6 (right): Ribbon mounted on VSM holder with Teflon tape (left), tape partially removed to show alignment of ribbon (right) with applied magnetic field, H A Ni disk sample is used to calibrate the moment gain of the VSM. All samples are first saddled into the center of the magnetic field before data is collected. Hysteresis curves are then swept out from positive to negative (and back to positive) applied field of 1.19 MA/m. Collected moment data is normalized by mass and analyzed using Microsoft Excel. 30

33 3.5: Magnetostriction Characterization Magnetostriction values are determined using a custom-built system at Case Western Reserve University 17. The magnetostriction system utilizes strain gauges to determine the change in length of ribbon sections upon magnetizing the sample in different directions. Both the as-spun and heat-treated ribbons are tested. Ribbons are cut into sections having approximately a 2x10-3 m (2 mm) width and 3x10-3 m (3 mm) length. Two similarly shaped sections are superglued to either side of a strain gauge. A mounted ribbon strain gauge is shown in Figure 7. 5 mm 5 mm Figure 7: Ribbons mounted strain gauge for magnetostriction measurement, each image is a different side of gauge This strain gauge is then soldered to the magnetostriction rig and aligned on top of a sample stage. The resistance of the strain gauge is measured to determine if all wires are connected properly. Using a LabVIEW program, data is collected as a magnetic field (1.91 ka/m) is rotated about the sample. A Mathematica code is used to interpret the data for magnetostriction (Appendix 1). In order to derive the magnetostriction coefficient from the collected data, the magnetostriction component of the data set must be separated from the raw data and 31

34 interpreted. An example of the raw data is shown in Figure 8; this will be used to explain how the magnetostrictive coefficient is determined for all alloy samples. Raw Data V 0.15 Positive Bias Negative Bias sec Figure 8: Raw magnetostriction data collected for Fe 77Ni 6.875Co 4.125Zr 7B 4Cu 1 ribbon annealed at 550 C for 3600 s under positive bias (blue) and negative bias (orange) The collected data shown in Figure 8 is comprised of a magnetostriction component and an induction component. The magnetostriction component is caused by the expansion or contraction of the sample as the magnetic field changes directions. This change in shape will cause the strain gauge to change shape and therefore its resistance. The change in resistance in turn causes a change in voltage. The induction component is caused by the change in magnetic field inducing a current and therefore change in voltage in the strain gauge wires. These two components can easily be separated by adding and subtracting the data collected under positive and negative bias. 32

35 Subtracting the data sets of the positive and negative bias will isolate the magnetostriction component. Adding the data sets will isolate the induction component. This is because voltage will be of equal magnitude but opposite sign for the magnetostriction component depending on the voltage biases, while the induction voltage will be independent of voltage bias. Therefore, the difference in these data sets will eliminate the constant voltage change (i.e. the induction component). Adding these data sets will eliminate the voltage change with equal magnitude but opposite signs (i.e. the magnetostriction component). Figure 9 and Figure 10 show the separated magnetostriction and induction components. Magnetostriction Component 0.15 V VSin Cos[ t ] sec Figure 9: Sinusoidal Fit (green) of magnetostriction component of strain gauge data for 550 C for 3600 s annealed Fe 77Ni 6.875Co 4.125Zr 7B 4Cu 1 ribbon 33

36 Induction Component V sec Figures 10: Induction components of strain gauge data for Fe 77Ni 6.875Co 4.125Zr 7B 4Cu 1 ribbon annealed at 550 C for 3600 s From the separated magnetostriction component of the strain gauge data, the magnetostrictive coefficient can easily be determined. By taking the difference of the maximum and minimum voltage, the total change in voltage from a negative to positive field (180 change in direction) is found. Halving this value will give the voltage change, ΔV, upon magnetization. This change in voltage can then be converted into a magnetostrictive coefficient value. Through Ohm s law (V=IR) voltage can be related to resistance. In this system, resistance is due in part to the length of wire in the strain gauge. Therefore, with all other factors held constant, the change in voltage is proportional to the change in length of the strain gauge. The mathematics of this are seen in Equations 2 and 3. L R (2) A 34

37 L V I A V A L I (3) In Equation 2 and 3, R is resistance, ρ is the resistivity, L is the length of wire, A is the cross-sectional area of the wire, V is the voltage, and I is the current. Equation 2 is the resistance in a wire. Equation 3 relates the change in length of the wire to the change in voltage, assuming all other values held constant. To simplify matters, strain (ε) can be calculated from the resistance of a strain gauge by a gauge factor (k). Equation 4 shows the relationship of the gauge factor to the strain. R 1 k (4) R If the resistance of the biased circuit is Rb and the resistance of the strain gauge is Rg, this equation can be rewritten as Equation 5. Rg R k Rb b 1 R 1 k R g b 1 (5) Equation 5 incorporates the total resistance, Rg+Rb, in the magnetostriction system from the measured voltage. Finally, by taking into account the average biased voltage, Vb, and the amplifier gain, g, the strain can be determined in the magnetostriction system by Equation 6. V / g Rg 1 k Vb Rb (6) 35

38 In the magnetostriction system, the average bias voltage and amplifier gain are set on the amplifier, bias resistance and strain gauge resistance are measured with a multimeter, and strain gauge factor is specified by the strain gauge manufacturer. To relate the strain to the saturation magnetostrictive coefficient, the strain must be multiplied by (1+υ), where υ is the Poisson s ratio. The Poisson s ratio is estimated as 1/3, simplifying this constant to 4/3 as shown in Equation 7. 4 (7) 3 In the heat-treated Fe77Ni6.875Co4.125Zr7B4Cu1 example (Fig. 9), the magnetostriction coefficient was calculated to be 6.0 ppm. While determining the change in maximum to minimum voltage from the magnetostriction component of the data gives a reasonable magnetostrictive coefficient, by fitting this data to a sinusoidal function, the change in voltage can be more accurately determined. A sinusoidal fit of the heat-treated Fe77Ni6.875Co4.125Zr7B4Cu1 example is shown as the green curve in Figure 9. Using the sinusoidal function to determine the change in voltage and in turn the magnetostrictive coefficient for the heat-treated Fe77Ni6.875Co4.125Zr7B4Cu1 example gives a coefficient of 5.6 ppm. This method for determining the magnetostriction coefficient is done with at least three separate measurements for each sample which are then averaged. The averaged magnetostrictive coefficient for heat-treated Fe77Ni6.875Co4.125Zr7B4Cu1 was determined to be 5.5 ± 0.1 ppm. The sign of the coefficient must be interpreted separately. Because a positive coefficient is due to expansion and negative due to contraction, interpreting the data for sign is relatively simple. This can be done by visual examination of the magnetostriction 36

39 component of the strain gauge data in Figure 8. The sign of the slope of the sinusoidal curve from 0 seconds to around 0.1 seconds (the first positive time linear region) will be equivalent to the sign of the magnetostrictive coefficient. This is because as the time increases in this region, the magnetic field is being rotated to align lengthwise with the sample. If the sample expands in the length direction, the resistance and therefore voltage will increase. If the sample contracts in the length direction, the voltage will correspondingly decrease. 3.6: Thermomagnetic Characterization Finally, ribbons were characterized by thermomagnetic characterization using the LakeShore Model 7410 and Model high temperature oven. As-spun ribbons with a 2x10-3 m width and 3x10-3 m length were mounted with a diamagnetic silver paste (having an acrylic binder) to the bottom of a high temperature, diamagnetic quartz sample rod. These samples are also aligned length-wise parallel to the applied magnetic field. A saturating applied field of 3.18x10 5 A/m was applied while the temperature was ramped from 30 to 550 C. Moment data was collected at every 5 C or 10 C. 5 C steps were used in a 100 C temperature range where the Curie temperatures were predicted to fall. Moment data was normalized by sample mass. The resulting thermomagnetic data was analyzed for the Curie temperature of the amorphous phase, Tc am, described in detail in Chapter 5, Section 2.3. Equipment and instrument brands and models, sensitivity, and accuracies can be found in Table 10 and equipment pictures can be found in Table 11 in Appendix 1. 37

40 5. Results and Discussion 1. Structural and Thermal Analysis 1.1: X-Ray Diffraction Overview X-Ray Diffraction (XRD) has been used to analyze structural and microstructural properties of as-spun and heat-treated magnetic ribbons of all alloy compositions. Theta- 2theta scans were performed on high quality pieces of ribbons. Scans were conducted from 20 to 120 with a 8.33x10-3 /s (0.500 /min) scan rate using Cu-Kα radiation having a wavelength of nm. The resulting diffractograms were analyzed for phases present, lattice parameter, and crystallite size. As-spun ribbons were confirmed to be completely amorphous or in the case of Fe66Ni14.667Co7.333Zr7B4Cu1 mostly amorphous. Alpha-Fe having a BCC structure was identified as the sole crystalline phase present in heat-treated samples, as expected from studies on similar materials 1,9,10,18,19. Lattice parameters of this phase in each alloy were similar but slightly larger than that of alpha-fe, angstroms 20. A larger lattice parameter is partially due to the substitution of cobalt and nickel and perhaps zirconium for iron in the alpha-fe phase. Iron has an atomic radius of 194 pm while cobalt, nickel, and zircounium have atomic radii of 192, 184, and 203, respectively 21. Zirconium in particular will increase the lattice parameter because it has a larger atomic radius than that of iron. Crystallite sizes in each heat-treated sample were between nm, adequate for small coercivities desired in nanocrystalline magnetic materials. A Cu-Kα x-ray source is used for XRD for all samples due to its small wavelength. Compared to other conventional x-ray sources, the small wavelength of copper can capture 38

41 higher angle peaks of the alpha-fe phase of interest in this study. More diffraction peaks allow for a better statistical analysis of lattice parameter and crystallite size. Copper sources are known to show fluorescence with high iron content samples. Fluorescence will create a higher background of counts by exciting secondary x-rays that encounter the detector 16. This higher background, however, will not diminish or obscure the presence of peaks. A standard of alumina, Al2O3, was run on each XRD instrument to determine the alignment of the instrument (see Appendix 2). A scan of the silica glass slide used for sample mounting was also performed (see Appendix 2). This was done to determine if there was any contribution from the glass slide in the ribbon diffractograms. 1.2: Structural Analysis: As-Spun Ribbon Resulting diffractograms of the as-spun ribbons can be seen in Figure 11. Figure 11: XRD diffractogram of (Fe,Ni,Co) 88Zr 7B 4Cu 1 as-spun ribbons using Cu-Kα x-ray source from 20 to

42 The key feature of the diffractograms is a single broad peak at approximately 44. This broad peak is indicative of an amorphous phase 16. Amorphous materials scatter the X-Ray beam due to their lack of long-range order. The materials short-range order will cause a single broad peak. The slight decrease in peak broadening of the Fe66Ni14.667Co7.333Zr7B4Cu1 diffractogram suggest that there may be some crystallinity. However, DSC results suggest that this alloy was indeed amorphous as it exhibited both primary and secondary crystallization peaks. 1.3: Thermal Analysis: As-Spun Ribbons After performing XRD on as-spun ribbons, Differential Scanning Calorimetry (DSC) was performed. In this study, DSC was used to determine the primary and secondary crystallization temperatures of the amorphous ribbons. Annealing of the amorphous ribbons to form a nanocrystalline microstructure is performed above the primary crystallization temperature but below any subsequent crystallization transitions. This allows for the nucleation of a nanocrystalline phase separated amongst a matrix of amorphous phase 1,9,10. Above the secondary crystallization temperature, the residual amorphous phase will crystallize resulting in a higher coercivity material. The crystallization transformations are exothermic for the alloys studied. The transition will produce heat causing the DSC to require less power input in order to raise the sample temperature by the desired heating rate, shown as downward peaks in Figure 12. From the determined crystallization temperatures, an annealing temperature of 550 C was chosen and is indicated on the DSC graph. 40

43 Figure 12: Differential Scanning Calorimetry (DSC) scan of (Fe,Ni,Co) 88Zr 7B 4Cu 1 as-spun ribbons at 10 K/min from 50 to 750 C. Primary crystallization, T x1, secondary crystallization, T x2, and annealing temperature of 550 C indicated In the DSC curves in Figure 12, the primary crystallization peaks are shown as Tx1 and the secondary crystallization peaks are shown as Tx2. The annealing temperature of 550 C is indicated as a red dashed line. From Figure 12, it is clear that the annealing temperature is above the primary crystallization temperature but below the secondary temperature. The onset and peak crystallization temperatures for each alloy are shown in Table 2. The onset crystallization temperature is the point at which crystallization starts to occur and is defined as the position where there is a significant change in slope from the horizontal region to the beginning of a crystallization peak (i.e. beginning of the exothermic phase transformation). The peak crystallization temperature is where there is a local minimum in the DSC curve (i.e. peak of exothermic phase transformation). At this point much of the crystallization has occurred, and the exothermic reaction has begun to slow down. 41

44 Composition Onset Temp ( C) Peak Temp ( C) Tx1 Tx2 Tx1 Tx2 Fe77Ni5.5Co5.5Zr7B4Cu Fe77Ni6.875Co4.125Zr7B4Cu Fe77Ni8.25Co2.75Zr7B4Cu Fe71.5Ni9.9Co6.6Zr7B4Cu Fe66Ni14.667Co7.333Zr7B4Cu Table 2: Onset and peak crystallization temperatures of primary (T x1) and secondary (T x2) crystallization for (Fe,Ni,Co) 88Zr 7B 4Cu 1 as-spun samples at 10 K/min DSC scan The onset and peak temperatures vary based on composition. The alloy compositions can be represented by their average number of valence electrons from the magnetic transition metals per atom. This is because the atomic percent of Zr, B, and Cu are constant amongst alloys. A plot of the crystallization temperature against the composition is shown in Figure 13. In Figure 13, a clear inverse trend in the crystallization temperatures as a function of magnetic valence electrons is exhibited. Increasing the nickel and cobalt content decreases the crystallization temperatures and thus the activation energy for crystallization. 42

45 Figure 13: Onset crystallization temperatures determined from a K/s (10 K/min) DSC scan vs average number of valence electrons from magnetic elements per atom for all (Fe,Ni,Co) 88Zr 7B 4Cu 1 alloys 1.4: Structural Analysis: Heat-Treated Ribbons After annealing at 550 C for 3600 seconds in an argon gas atmosphere at around 1.01x10 5 Pa, XRD was performed on heat-treated ribbons to analyze their resulting structure and microstructure. XRD diffractograms were analyzed for phases present, lattice parameter, and crystallite size : Lattice Parameter Determination A Nelson-Riley function of theta was used to determine the lattice parameter for the crystalline phase in the heat-treated ribbons from each corresponding peak 16. Resulting XRD diffractogram patterns of the heat-treated ribbons are comprised solely of an alpha- Fe phase. The alpha-fe phase has a BCC structure with nickel and cobalt substitution. In the resulting diffractograms, (110), (200), (211), (200), and (310) alpha-iron peaks have been identified. From the position of each peak, the interplanar spacing ( d ), can be 43

46 calculated from the x-ray wavelength ( ), the incidence angle ( ), and a positive integer ( n ), using Bragg s law shown in Equation 8. n 2dSin (8) Because alpha-iron has a BCC structure, a cubic variation of Bragg s law can be used to a o calculate the lattice parameter ( ), with the addition of the plane Miller indices (h, k, l) 16. a o 2Sin h k l (9) Equation 9 allows the lattice parameter to be calculated for each peak. The Nelson-Riley function (Eq. 10) can be used to determine a more accurate lattice parameter from those determined for each peak. 2 2 cos cos f ( theta) sin (10) Here, is in radians. The lattice parameter calculated for each peak is plotted against the Nelson-Riley function for the matching incident angle. A linear curve fit is then applied to the plotted data set. The y-intercept of this linear fit gives the overall lattice parameter for the phase of interest. This method minimizes instrumental error occurring at low incidence angles. An example of this fitting is shown in Figure 14, where the lattice parameter is determined to be ± nm. 44

47 Figure 14: Determination of lattice parameter from XRD data using the Nelson-Riley function of theta for alpha-fe phase in Fe 77Ni 6.875Co 4.125Zr 7B 4Cu 1 annealed at 550 C for 3600 s 1.4.2: Crystallite Size Determination The crystallite size has been determined using the Scherrer equation for each peak 16. In diffraction patterns, peaks will be broadened more from smaller particles or crystallites (microstrains as well as instrumental divergence may also cause peak broadening). In smaller crystals, less planes are available to satisfy Bragg s Law. Because less planes satisfy Bragg s law, complete destructive interference of out-of-phase x-ray reflections may not occur. In this case, the out-of-phase reflections will result in peak broadening. As crystal size becomes very small, the Scherrer equation (Eq. 11) relates the full width at half maximum (FWHM) intensity of the peak (B) to the size of the crystallite (D) at the Bragg B peak angle, D (11) B Cos B 45

48 An example of the Scherrer analysis of the FWHM is shown in Figure 15 where B was determined to be 0.7. Figure 15: FWHM determination of the (110) peak in Fe 77Ni 6.875Co 4.125Zr 7B 4Cu 1 annealed at 550 C for 3600 s. XRD scan with Cu-Kα source Before the Scherrer equation can be applied to the FWHM, the value must first be corrected for instrumental broadening. In XRD, the instrumentation used will have a natural instrumental broadening of peaks. This value, which varies with angle, must be determined and subtracted from the observed FWHM in order to provide an accurate measure of the grain size effect on broadening. NIST Standard 660B (lanthanum hexaboride, LaB6) was used to determine the instrument broadening in the Bruker XRD 22. This standard was measured to produce a diffractogram consisting of many narrow peaks from the large particle size and uniformity of the LaB6 sample (Figure 36 in Appendix 2). The broadening of these peaks is assumed to be due solely to instrumental broadening. To determine the instrumental broadening at different angles, LaB6 diffraction peaks located 46

49 at similar angles to those of the alpha-fe peaks were analyzed using Diffrac.Eva for their FWHM. This FWHM is equivalent to the instrumental broadening at these peak angles. This method was performed for peaks located near each of the alpha-fe peaks. After subtracting the instrumental broadening values from the alpha-fe peak FWHM, the Scherrer equation was used to determine the crystallite size. The crystallite sizes determined from the corrected FWHM were typically within 10% of the uncorrected sizes. For Fe77Ni6.875Co4.125Zr7B4Cu1 heat-treated at 550 C for 3600 seconds, the (110) peak gave a crystallite size of 14 nm. From all five alpha-fe peaks, heat-treated Fe77Ni6.875Co4.125Zr7B4Cu1 had an average crystallite size of 16 ± 6 nm : Summary of Heat-Treated Ribbon XRD Analysis The XRD diffractograms of each heat-treated alloy can be seen in Figure 16. Figure 16: XRD diffractograms of (Fe,Ni,Co) 88Zr 7B 4Cu 1 alloys annealed at 550 C for 3600 s. XRD scan with Cu-Kα source 47

50 Using the methodologies explained in Sections 4.1 and 4.2, the lattice parameter and crystallite size of each heat-treated alloy were determined. Table 3 provides the lattice parameters and crystallite sizes for each heat-treated alloy. Composition D (nm) a o (nm) Fe 77 Ni 5.5 Co 5.5 Zr 7 B 4 Cu 1 14 ± ± Fe 77 Ni Co Zr 7 B 4 Cu 1 16 ± ± Fe 77 Ni 8.25 Co 2.75 Zr 7 B 4 Cu 1 12 ± ± Fe 71.5 Ni 9.9 Co 6.6 Zr 7 B 4 Cu 1 14 ± ± Fe 66 Ni Co Zr 7 B 4 Cu 1 12 ± ± Table 3: Lattice parameter (a o) and crystallite sizes (D) of ribbons annealed at 550 C for 3600 s All heat-treated alloys had lattice parameters similar but slightly larger than that of pure alpha-fe and crystallite sizes between nm. Crystallite sizes determined from each individual peak are provided in Table 12 in Appendix 2. 48

51 2. Magnetic Property Analysis 2.1: Magnetic Analysis Overview As-spun and heat-treated ribbons (compositions and processing described in Chapter 4) were analyzed for magnetic properties including room temperature (RT) magnetic hysteresis, thermomagnetic response, and magnetostriction. Saturation specific magnetization and coercivity were determined from room temperature magnetic hysteresis loops (described in Section 2.2). The Curie temperature of the amorphous phase, Tc am, was determined from thermomagnetic measurement (described in Section 2.4). After these properties were determined, the alloys were analyzed for correlations between magnetic properties, structural properties, and alloy compositions. 2.2: Magnetic Hysteresis From the magnetic hysteresis loop, the saturation magnetization and coercivity can be determined as described in Figure 17 and the resulting discussion. 49

52 Ms Figure 17: Room temperature magnetic hysteresis loop up to 1.2 MA/m of Fe 77Ni 6.875Co 4.125Zr 7B 4Cu 1 asspun ribbon and ribbon annealed at 550 C for 3600 s. Saturation specific magnetization, M s, indicated by red arrows. In the hysteresis loop, the saturation magnetization, Ms, is the magnetization value at the saturation field ( 1.2 MA/m). As can be seen from Figure 17, the heat-treated sample has a visibly greater saturation magnetization than the as-spun sample. The coercivity, Hc, is equal to half the width of the hysteresis loop. The width of the hysteresis loop in this case is equal to the difference of positive to negative magnetic field required to demagnetize the sample (result in a zero magnetization). In soft magnets such as the alloys analyzed in this study, the width of the hysteresis loop is extremely narrow. A close up of this section of the hysteresis loop is provided in Figure

53 2 Hc Figure 18: Width of hysteresis loop (indicated by red arrows) of as-spun and annealed at 550 C for 3600 s Fe 77Ni 6.875Co 4.125Zr 7B 4Cu 1 ribbons. Coercivity, Hc, indicated. The coercivity is determined by halving the width of the hysteresis. In Figure 18, it is clear that the coercivity of the as-spun ribbon is smaller than that of the heat-treated ribbon. Hysteresis loops of as-spun and heat-treated ribbons can be seen in the Figure 19 and Figure 20, respectively. 51

54 Figure 19: RT magnetic hysteresis up to 1.2 MA/m magnetic field for all (Fe,Ni,Co) 88Zr 7B 4Cu 1 as-spun ribbons Figures 20: RT magnetic hysteresis up to 1.2 MA/m magnetic field for all (Fe,Ni,Co) 88Zr 7B 4Cu 1 ribbons annealed at 550 C for 3600 s 52

55 Saturation magnetizations and coercivities of as-spun and heat-treated ribbons are shown in Table 4 and Table 5, respectively. As-Spun Ribbon: Magnetic Hysteresis Properties Composition Ms (A m 2 /kg) Hc (Oe) Hc (A/m) Fe77Ni5.5Co5.5Zr7B4Cu Fe77Ni6.875Co4.125Zr7B4Cu Fe77Ni8.25Co2.75Zr7B4Cu Fe71.5Ni9.9Co6.6Zr7B4Cu Fe66Ni14.667Co7.333Zr7B4Cu Table 4: RT hysteresis properties (saturation specific magnetization, Ms, and coercivity, Hc) of (Fe,Ni,Co) 88Zr 7B 4Cu 1 as-spun ribbons Heat-Treated Ribbon: Magnetic Hysteresis Properties Composition Ms (A m 2 /kg) Hc (Oe) Hc (A/m) Fe77Ni5.5Co5.5Zr7B4Cu Fe77Ni6.875Co4.125Zr7B4Cu Fe77Ni8.25Co2.75Zr7B4Cu Fe71.5Ni9.9Co6.6Zr7B4Cu Fe66Ni14.667Co7.333Zr7B4Cu Table 5: RT hysteresis properties (saturation specific magnetization, Ms, and coercivity, Hc) of (Fe,Ni,Co) 88Zr 7B 4Cu 1 ribbons annealed at 550 C for 3600 s 2.3: Magnetostriction Magnetostrictive coefficients for all as-spun and heat-treated samples have been determined at room temperature. These values are shown in Table 6 as all positive magnetostrictive coefficients. 53

56 Composition As-Spun Heat-Treated λ (ppm) λ (ppm) Fe77Ni5.5Co5.5Zr7B4Cu Fe77Ni6.875Co4.125Zr7B4Cu Fe77Ni8.25Co2.75Zr7B4C Fe71.5Ni9.9Co6.6Zr7B4Cu Fe66Ni14.667Co7.333Zr7B4Cu Table 6: Magnetostrictive coefficients, λ, for (Fe,Ni,Co) 88Zr 7B 4Cu 1 as-spun and 550 C annealed for 3600 s ribbons 2.4: Thermomagnetic Characterization Thermomagnetic measurements have been completed for each alloy in order to determine the Curie temperature of their amorphous phase, Tc am. Data is originally collected as moment vs temperature. This moment is normalized by mass to give the specific magnetization. Using a two tangent method, the Curie temperature is determined. Tangents are taken for the varying slopes before and after the apparent Curie temperature. Tangents are determined by optimizing the R 2 values of the linear fits before and after the apparent Curie temperature. Their intersection is determined to be the Curie temperature. This method can be seen in the Figure

57 Tc am Figure 21: Determination of the Curie temperature of the amorphous phase, T c am, in as-spun Fe 77Ni 6.875Co 4.125Zr 7B 4Cu 1 at 3.18x10 5 A/m saturating field In the example shown in Figure 21, the Curie temperature of the amorphous phase was determined to be 229 C. The thermomagnetic data for all alloy samples can be seen in Figure

58 Figure 22: Thermomagnetic data for all (Fe,Ni,Co) 88Zr 7B 4Cu 1 as-spun alloys at 3.18x10 5 A/m saturating field (H applied) The Curie temperature of the amorphous phase along with all other hysteresis properties, magnetostriction, and structural properties of the nanocrystalline ribbons are summarized in Table 7. Composition D (nm) M s (A m 2 /kg) H c (A/m) λ (ppm) T c am ( o C) Fe 77 Ni 5.5 Co 5.5 Zr 7 B 4 Cu 1 14 ± Fe 77 Ni Co Zr 7 B 4 Cu 1 16 ± Fe 77 Ni 8.25 Co 2.75 Zr 7 B 4 Cu 1 12 ± Fe 71.5 Ni 9.9 Co 6.6 Zr 7 B 4 Cu 1 14 ± Fe 66 Ni Co Zr 7 B 4 Cu 1 12 ± Table 7: Summary of structural (crystallite size, D) and magnetic properties (saturation specific magnetization, Ms, coercivity, H c, and magnetostriction coefficient, λ) of nanocrystalline (Fe,Ni,Co) 88Zr 7B 4Cu 1 alloys annealed at 550 C for 3600 s 56

59 2.5: Discussion of Magnetic Property Relations Saturation magnetization, coercivity, and magnetostriction have been analyzed for relationships amongst one another as well as their relationships to structure and composition : Magnetic-Structural Relations Magnetic properties of heat-treated ribbons have been examined for relationships with grain size. At nano-sized grains (D < ~100 nm), the coercivity will decrease at a rate of D 6 according to the random anisotropy model 2. At grain sizes determined for the alloy systems in this study (10-20 nm), the coercivity should be around 10 A/m according to the grain size dependence shown in Figure The coercivities found in the alloys studied, between A/m, align with literature values from similar alloy systems plotted in Figure with a Hc D relationship. Figure 23: Coercivity dependence on grain size of (Fe,Ni,Co) 88Zr 7B 4Cu 1 nanocrystalline alloys heat treated at 550 C for 3600s with additional data from literature values for similar nanocrystalline magnetic alloys 11 57

60 2.5.2: Magnetic-Compositional Relations Magnetic properties have been examined for relationships with composition, in particular, with number of magnetic valence electrons per atom. This parameter of average number of magnetic valence electrons per atom can be used as a compositional variable for this alloy system because zirconium, boron, and copper atomic percentages remain constant. In addition, the valence electrons in the magnetic elements will be dominating contributors in properties such as saturation magnetization. The relationship of saturation magnetization to number of magnetic valence electrons per atom is shown in the Pauling- Slater curve 23,24. Here, a peak in saturation magnetization occurs at around 8.3 valence electrons/atom. At this value, a maximum in unpaired electrons per atom occurs in BCC crystalline material, giving a maximum magnetization achievable 24. A Slater-Pauling curve for the nanocrystalline alloys has been created and populated with literature values for similar nanocrystalline alloys (see Figure 24) 10,15. Figure 24: Slater-Pauling curve (dashed curve) for nanocrystalline (Fe,Ni,Co) 88Zr 7B 4Cu 1 alloys with literature values of similar nanocrystalline alloys 10,15 58

61 The average magnetic moment per atom can simply be calculated from the saturation magnetization by Equation 12. M m s M b / atom N A b (12) In Equation 12, / atom is the magnetic moment per atom in Bohr magnetons/atom, Ms b is the saturation magnetization, mm is the molar mass, NA is Avogadro s number, and is a Bohr magneton equal to 9.274x10-24 J/T [SI] or 9.274x10-21 erg/g [cgs]. From the Slater-Pauling curve, it is clear that the amorphous alloys have a reduced magnetic moment from that of the nanocrystalline alloys. This may be because the nanocrystalline alloys have an alpha-(fe,ni,co) phase with higher magnetic element content, and resultant higher magnetization. The magnetostriction and coercivity can also be compared to the number of magnetic valence electrons per atom. Recalling that the alloy compositions were determined based on two compositional paths; the dependence of the magnetostriction with composition path can be seen in Figure 25. b 59

62 Figure 25: Magnetostriction vs number of magnetic valence electrons/atom for (Fe,Ni,Co) 88Zr 7B 4Cu 1 alloys heat treated at 550 C for 3600 s. Compositional paths, P 1 and P 2, indicated with inaccessible alloy compositions shown as red dashed line. The magnetostriction dependence on compositions is very apparent with R 2 values around Path P1, with constant iron content, has decreased saturation magnetostriction coefficient. Path P2, having varying iron content, has increased saturation magnetostriction coefficient. However, neither path proved to reduce the magnetostriction to a near zero value (i.e. <1 ppm). Following either path s projection to zero magnetostriction is not physical possible. Path P1 will eventually lead to above 8.25 valence electrons/atom, Fe77Ni11Zr7B4Cu1, eliminating all cobalt in the alloy, significantly lowering the Curie temperature 1,9. Path P2 would eventually go below 8.05 electrons/atom, Fe83.6Co4.4Zr7B4Cu1 following the alloy path. This inaccessible path would eventually reach zero magnetostriction at below 8 valence electrons/atom. This might be possible to achieve in another alloy system with elements such as chromium with 6 valence 60

63 electrons/atom. However, this would significantly lower the saturation magnetization and Curie temperature of the alloy 25. Finally, the Curie temperature of the amorphous phase can be analyzed based on composition. In this analysis, composition is represented by the percentage of cobalt in the magnetic elements instead of the average number of magnetic valence electrons per atom. This is because cobalt will have the largest effect of raising the Curie temperature. The plot of Curie temperature of the amorphous phase versus percent of cobalt in the magnetic elements with literature data from the (Fe1-2xCoxNix)88Zr7B4Cu1 system 10 is shown in Figure 26 (with annotated magnetostriction values for nanocrystalline material). Figure 26: Curie temperature of the amorphous phase variation dependence on cobalt fraction (with annotated magnetostriction values for nanocrystalline material) in (Fe,Ni,Co) 88Zr 7B 4Cu 1 as-spun alloys with literature data from (Fe 1-2xCo xni x) 88Zr 7B 4Cu 1 system 10 As seen in Figure 26, in general the greater the cobalt fraction in the alloy, the greater the Tc am. 61

64 2.5.3: Magnetic-Magnetic Property Relationships Along with comparing the magnetic properties with composition and structure, the properties can be related amongst themselves. In amorphous alloys unlike nanocrystalline alloys, the coercivity and magnetostriction have a direct relationship with the square of the saturation magnetization 26. The trend of magnetostriction vs saturation magnetization can be seen for the amorphous ribbons in comparison to the nanocrystalline ribbons studied in the Figure 27. Literature values of Fe-amorphous alloys are also plotted 27. Figure 27: Magnetostrictive coefficient vs the square of saturation magnetization for (Fe,Ni,Co) 88Zr 7B 4Cu 1 as-spun ribbons and ribbons annealed at 550 C for 3600 s with literature values of Fe-based amorphous alloys 27 One final magnetic property relation that was examined was that between magnetostriction and coercivity. Because magnetostriction is the main source of losses for low coercivity nanocrystalline alloys due to the contribution from magnetoelastic anisotropy, there should be a direct correlation between coercivity and magnetostriction. In Figure 28, magnetostriction vs coercivity is plotted for the heat-treated ribbons as well 62

65 as for similar nanocrystalline ribbons from literature 1,10. The literature values are from a similar alloy system having equal part nickel and cobalt substituted for iron, Fe88-2xNixCoxZr7B4Cu1. The magnetic properties shown in Figure 28 were measured in CWRU labs and not taken from the literature source. Figure 28: Coercivity vs magnetostrictive coefficient for (Fe,Ni,Co) 88Zr 7B 4Cu 1 ribbons annealed 550 C for 3600 s with literature data from Fe 88-2xNi xco xzr 7B 4Cu 1 nanocrystalline ribbons 1,10 From the Figure 28, it can be seen that the coercivity is very much correlated to magnetostriction. This relation confirms that with similar alloy systems having low coercivities, magnetostriction dominates as the source of losses. A plot of coercivity vs number of magnetic valence electrons/atom results in a similar trend to that of magnetostriction (see Appendix 3). 63

66 6. Future Work 1. Multivariate Regression of Magnetostriction 1.1: Multivariate Regression Overview The two alloy design paths in this study have not resulted in eliminating magnetostriction in high temperature nanocrystalline magnetic materials. From the data collected in this study as well as from literature values on similar material systems, multivariate regressions of magnetostriction based on alloy composition have been created as predictive models. These models analyzes magnetostriction in (Fe,Ni,Co)88Zr7B4Cu1 and (Fe,Ni,Co)86Zr7B6Cu1 nanocrystalline systems. Mathematica code can be seen in Appendix : (Fe,Ni,Co)88Zr7B4Cu1 Analysis The (Fe,Ni,Co)88Zr7B4Cu1 nanocrystalline alloy system has been analyzed using magnetostriction data from alloys in this study, from literature 1,10,28, and (Co, Ni)88Zr7B4Cu1 alloys created in CWRU labs (not yet published) (values in Appendix 4). This model plots magnetostriction as a function of fractional percent of magnetic elements iron and nickel. The 3D magnetostriction surface predicted from this analysis can be seen in Figure 29 with points representing data used to perform the analysis. 64

67 Figure 29: Multivariate regression of magnetostriction as a function of fraction of iron and nickel in (Fe,Ni,Co) 88Zr 7B 4Cu 1 nanocrystalline alloy systems The multivariate regression resulted in Equation 13. (13) 2 2 reg ffe 6.0 fni 83.1 ffe 2.3 fni 47.9 ffe fni In Equation 13, λreg is the predicted magnetostriction value from the multivariate regression, ffe is the fraction of iron in the alloy, and f Ni is the fraction of nickel in the alloy. This regression resulted with a Pearson chi-squared P-value of >0.99, indicating a high goodness of fit. From the multivariate regression, curves can be determined that intersect the plane of zero magnetostriction. This curve can be seen in the Figure

68 Figure 30: Compositional curve of zero magnetostriction based on multivariate regression in (Fe,Ni,Co) 88Zr 7B 4Cu 1 nanocrystalline alloy systems The multivariate regression will also have another curve of intersection with the plane of zero magnetostriction; however, this curve will have a negative iron fraction. From the above curve, valid alloy compositions can be determined with predicted zero magnetostriction. Because the total atomic fraction of iron and nickel cannot exceed 1, alloy compositions are only valid below ~0.025 Ni. From this small section of the above curve, alloy compositions were determined and can be seen in Table 8. 66

69 Alloy [at%] Valence Electrons Fe87.4Ni0.2Co0.4Zr7B4Cu Fe87.3Ni0.4Co0.3Zr7B4Cu Fe87.1Ni0.7Co0.2Zr7B4Cu Fe86.9Ni0.9Co0.2Zr7B4Cu Fe86.8Ni1.1Co0.1Zr7B4Cu Fe86.6Ni1.3Co0.1Zr7B4Cu Table 8: Various alloys compositions with predicted zero magnetostriction in (Fe,Ni,Co) 88Zr 7B 4Cu 1 nanocrystalline alloy systems based on multivariate regression As seen in Table 8, the alloy compositions predicted to have zero magnetostriction have very small atomic fractions of nickel and cobalt. These alloys would result in poor high temperature magnetic properties and are therefore of little interest in this study. While the predicted zero magnetostriction alloys are not of interest for this study, this regression can help steer future work in this alloy system for other applications. With additional compositional data points, this analysis will become even more accurate and powerful. There exist regions of this regression with few data points, particularly at higher nickel and cobalt regions, that if added will strengthen this analysis. Future work may include analyzing alloys in these regions in order to strengthen the predictive capabilities of this model. 1.3: (Fe,Ni,Co)86Zr7B6Cu1 Analysis Another multivariate regression of magnetostriction has been created for a similar nanocrystalline alloy system of (Fe,Ni,Co)86Zr7B6Cu1 using literature data (values in Appendix 4) 29. This system has larger boron content with decreased magnetic transition 67

70 element content. This analysis has been performed to determine if this change in composition can lead to predicted alloy compositions with zero magnetostriction and good high temperature properties. The regression for this system can be seen in Figure 31. Figure 31: Multivariate regression of magnetostriction as a function of fraction of iron and nickel in (Fe,Ni,Co) 86Zr 7B 6Cu 1 nanocrystalline alloy systems This regression resulted in a Pearson chi-squared P-value of 0.075, indicating a poor fit. The poor goodness of fit of this regression would indicate a large uncertainty in its predicted results. From this regression, compositions predicted to have zero magnetostriction have also been determined in the same fashion as the previous system. The curves of zero magnetostriction are shown in Figure

71 Figure 32: Compositional curves of zero magnetostriction based on multivariate regression in (Fe,Ni,Co) 86Zr 7B 6Cu 1 nanocrystalline alloy systems In this regression there are two curves of zero magnetostriction in valid compositional space. The lower blue curve in the previous image has very low iron content and is not of interest in this study. From the upper orange curve, predicted zero magnetostriction alloys have been determined and are shown in Table 9. Alloy [at%] Valence Electrons Fe74.6Ni4.4Co9Zr7B6Cu Fe71.7Ni8.8Co7.5Zr7B6Cu Fe68.8Ni13.2Co6Zr7B6Cu Fe65.9Ni17.6Co4.5Zr7B6Cu Fe63Ni22Co3Zr7B6Cu Fe60.1Ni26.4Co1.5Zr7B6Cu Table 9: Various alloys compositions with predicted zero magnetostriction in (Fe,Ni,Co) 86Zr 7B 6Cu 1 nanocrystalline alloy systems based on multivariate regression The predicted alloy compositions with zero magnetostriction in this system have compositions more favorable to good high-temperature magnetic properties (i.e. larger 69

72 cobalt fractions) than those in the previous system; however, due to the poorness of fit in this regression, there is much uncertainty in the resulting compositions. Future work may include analyzing these alloys or revisiting previous alloys that appear to be clear outliers to this model. 2. Nanocrystalline Magnetic Powder In collaboration with the University of Cincinnati, nanocrystalline Fe77Ni5.5Co5.5Zr7B4Cu1 ribbons have been processed into nanocrystalline magnetic powders. As-spun ribbons produced at CWRU were then sent to the University of Cincinnati for heat-treating and ball-milling. Powders were then analyzed for magnetic and structural properties at CWRU. Powders will be made into sputtering targets for thin film deposition by the University of Toledo and 3D printed by Youngstown State University. The development of magnetic ribbons, powders, thin films, and 3D printed structures is part of the OFRN project to create a range of applicable magnetic geometries. Magnetic and structural analysis of nanocrystalline magnetic powders is provided in Appendix 5. 70

73 7. Conclusion New nanocrystalline magnetic materials have been created with coercivities ranging between 10.5 to 14.9 A/m, magnetostrictive coefficients ranging from 4.8 to 12.1 ppm, and Curie temperatures between 218 to 348 C. While none of the analyzed alloy compositions resulted in reducing the magnetostriction to a near zero value (< 1.0 ppm), Fe77Ni8.25Co2.75Zr7B4Cu1 resulted in the smallest magnetostrictive coefficient of 4.8 ppm and coercivity of 10.5 A/m with a Curie temperature of the amorphous phase of 218 C. This study has shown a strong correlation in coercivity with magnetostriction in the (Fe, Co, Ni)88Zr7B4Cu1 alloy system. Through multivariate regression of magnetostrictive coefficient, a model for the magnetostriction as a function of composition in this alloy system has been created. This regression can be used to further understand and develop magnetic materials with decreased magnetostrictive losses. 71

74 Appendix 1. Experimental Procedure Instrument Model Sensitivity Accuracy Mass Balance OHAUS Adventurer Pro AV264C 0.1 mg ± 0.3 mg Microbalance Sartorius MSE3.6P000DM mg ± mg DSC * Netzsch 404 F3 Pegasus 1 C ± 3 C XRD * Rigaku D/Max ± 0.1 XRD * Bruker D8 Discover Series II 0.1 ± 0.1 VSM * Lakeshore Model emu ± 0.05 emu Magnetostriction Home-Built 0.01 ppm ± 0.03 ppm 17 *Values estimated based on type of experiment, samples, and analysis completed Table 10: Sensitivity, accuracy, and model information for equipment and instruments used for alloy production and analysis 72

75 Adventurer Mass Balance Sartorius Microbalance Bruker XRD Lakeshore VSM Yein Tech Melt Spinner Lindberg Tube Furnace 73

76 Netzsch DSC Rigaku XRD Magnetostriction System Thermal Technology LLC Arc Melter Table 11: Pictures of all equipment and instruments used for alloy production and analysis 74

77 Mathematic Code for Interpreting Magnetostriction Data Data saved as text (.txt) files after running experiment with LabView program. 75

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84 Magnetostrictive coefficient value displayed in last line (i.e ) in parts per million (ppm) from sinusoidal fit of voltage versus time. This value only accurate to the tenth s digit (i.e ppm). 82

85 2. Structural Analysis Figure 33: Alumina standard diffractogram from Bruker XRD with Cu-Kα source Figure 34: Alumina standard diffractogram from Rigaku XRD with Cu-Kα source 83

86 Figure 35: Diffractogram of fused silica glass slide used for ribbon sample mounting Figure 36: LaB 6 standard diffractogram from Bruker XRD with Cu-Kα source 84

87 Peak Fe77Ni5.5Co5.5 Zr7B4Cu1 Fe77Ni6.875Co4.125 Zr7B4Cu1 Crystallite Size (nm) Fe77Ni8.25Co2.75 Zr7B4Cu1 Fe71.5Ni9.9Co6.6 Zr7B4Cu1 Fe66Ni14.667Co7.333 Zr7B4Cu Avg Std. Dev Table 12: Crystallite size determined from each peak for (Fe,Ni,Co) 88Zr 7B 4Cu 1 alloys annealed at 550 C for 3600 s 85

88 3. Magnetic Analysis Figure 37: Coercivity vs number of magnetic valence electrons/atom for (Fe,Ni,Co) 88Zr 7B 4Cu 1 alloys annealed at 550 C for 3600 s, showing compositional paths, P 1 and P 2 86

89 4. Future Work Willard, 2002, Near-Zero Magnetostriction Fe Ni Co (Fraction) λ (ppm) Jonathan Healy's Sample Fe Ni Co λ (ppm) Knipling, '09, '15 Fe Ni Co (Fraction) λ (ppm) Martone Thesis Work Fe Ni Co (Fraction) λ (ppm) Table 13: Magnetostriction, λ, data of Fe xni yco 88-x-yZr 7B 4Cu 1 nanocrystalline alloy systems used for 1,10, 29 multivariate analysis 87

90 Muller 2002, (Fe, Ni, Co)86, Zr7B6Cu1 Fe Co Ni (Fraction) λ (ppm) Structure BCC+FCC(crystallite) BCC+FCC(crystallite) BCC+FCC(crystallite) BCC+FCC(crystallite) BCC+FCC(crystallite) BCC+FCC(crystallite) BCC+FCC(crystallite) FCC FCC FCC FCC FCC FCC FCC FCC FCC BCC BCC BCC BCC BCC BCC BCC BCC BCC BCC BCC BCC BCC Table 14: Magnetostriction data, λ, of Fe xni yco 86-x-yZr 7B 6Cu 1 nanocrystalline alloy systems used for multivariate analysis from Muller

91 Multivariate Analysis Mathematic Code 89

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99 5. Nanocrystalline Magnetic Powders As-spun, amorphous Fe77Ni5.5Co5.5Zr7B4Cu1 ribbons created at CWRU have been sent to the University of Cincinnati for powder processing. The first set of samples were all ball milled for 12 hours after annealing at different conditions. These processing conditions are seen in Table 15. Powder Conditions Milling Time Powder 1 (BD-013-TF) 600 C (3600 s) dry milled s Powder 2 (BD-005-TF) Powder 3 (BD-003-TF) 510 C (3600 s) wet milled (methanol) 500 C (3600 s) wet milled (methanol) s s Powder 4 (BD-007-TF) 500 C (1800 s) wet milled (methanol) s Table 15: Processing conditions for Fe 77Ni 5.5Co 5.5Zr 7B 4Cu 1 magnetic powders These powders were then analyzed for structural and magnetic properties. The XRD was performed on the Rigaku D/Max 2200 having a Cr-Kα X-ray from The resulting diffractogram is provided in Figure

100 Figure 38: Diffractogram of for Fe 77Ni 5.5Co 5.5Zr 7B 4Cu 1 magnetic powders using Cr-Kα source As can be seen in the Figure 39, all samples were comprised of solely alpha-fe phase except for Powder 1. Powder 1 was produced by dry milling, allowing oxidation and therefore resulting in a zirconium oxide, ZrO2, phase. The powders were then analyzed for magnetic properties using the LakeShore VSM. The hysteresis loops are provided in the Figure

101 Figure 39: Room temperature magnetic hysteresis of Fe 77Ni 5.5Co 5.5Zr 7B 4Cu 1 magnetic powders and ribbons As can be seen from the hysteresis loops, the powders have a sheared loop due to demagnetization caused by the shape of the powders. As is known for magnetic powders, the coercivities are greatly increased 9,30. This is also the case for these powders studied; however, there is also a large unexpected decrease in saturation magnetization. This was later determined to be caused due to a chromium contamination from the stainless steel ball-milling medium. A summary of the structural and magnetic properties of these powders is shown in Table

102 Sample ID ID # M s (A m 2 /kg) H c (Oe) H c (A/m) ao (nm) D (nm) Powder 1 BD-013-TF Powder 2 BD-005-TF Powder 3 BD-003-TF Powder 4 BD-007-TF Ingot 13_AS Ingot 13_AS X X Ingot 13_HT Ingot 13_HT Table 16: Saturation specific magnetization (M s), coercivity (H c), lattice parameter (a o) and crystallite size (D) of Fe 77Ni 5.5Co 5.5Zr 7B 4Cu 1 magnetic powders and ribbons The lowered saturation magnetization of the nanocrystalline powders compared to that of the nanocrystalline ribbons was due to the chromium contamination. Powders have also been processed with a post stress relaxing anneal. By annealing the powders after processing them, residual stresses may be relieved. These residual stresses are believed to be one of the main contributors to the higher coercivity by providing pinning sites for domain wall motion during magnetization. These powder also had a chromium contamination. The processing conditions are provided in Table 17. Sample ID HT ( C) HT (s) Milling Type Milling (s) SA ( C) SA (s) Powder 1_ Wet Ball Methanol Powder 2_ Wet ball Methanol Powder 3_ Wet ball Methanol Powder 4_ Wet ball Methanol Powder 5_ Wet ball Methanol Powder 6_ Wet ball Methanol Table 17: Stress annealed (SA) and milling conditions for Fe 77Ni 5.5Co 5.5Zr 7B 4Cu 1 magnetic powder The stress annealed (SA) magnetic powders were all subject to the same heat treatment (HT) and milling conditions. Half of the samples were SA at 200 C and half at 400 C. The powders were stress annealed at times of 600, 3600, and s (10, 60, and 360 minutes). The resulting magnetic hysteresis loops are shown in Figure

103 Figure 40: Room temperature magnetic hysteresis of Fe 77Ni 5.5Co 5.5Zr 7B 4Cu 1 stress annealed magnetic powders and ribbons As can be seen from the hysteresis loops, the saturation magnetization was still significantly lower than that of the heat-treated ribbon; again due to chromium contamination. The saturation magnetization and coercivity were analyzed as a function of stress relieving anneal time and temperature. These graphs can be seen in Figure 41 and Figure 42. Here, a red line is used to show results of a powder processed with similar conditions but with no stress anneal. 101

104 Figure 41: Magnetization vs stress anneal time for Fe 77Ni 5.5Co 5.5Zr 7B 4Cu 1 SA magnetic powders Figure 42: Coercivity vs stress anneal time for Fe 77Ni 5.5Co 5.5Zr 7B 4Cu 1 SA magnetic powders From Figure 41 and Figure 42, it is seen that as post stress anneal time increases so does the magnetization. The coercivity on the other hand varies non-linearly with time. A maximum magnetization and minimum coercivity exist with a 400 C SA for s (360 min). A summary of the magnetic properties of the post stress annealed powders is shown in Table

105 Sample ID SA ( C) SA (s) M s (A m 2 /kg) H c (Oe) H c (A/m) Powder 1_ Powder 2_ Powder 3_ Powder 4_ Powder 5_ Powder 6_ Table 18: Saturation specific magnetization (M s) and coercivity (H c) of Fe 77Ni 5.5Co 5.5Zr 7B 4Cu 1 stress annealed (SA) magnetic powders Finally, powders have also been prepared from ribbons melt spun at NASA GRC. This NASA facility has an open-air melt spinner that can produce greater than 3 kilograms of ribbon in a single run. Due to a technical malfunction during spinning, the first batch of ribbon resulted in poor quality. Two powder samples have been produced from this poor quality ribbon with ceramic ball-mill media. The processing conditions and resulting hysteresis loops are provided in Table 19 and Figure 43. Sample ID ID # HT ( C) HT (s) Milling Milling (s) Powder 1_3 NASA NSG Wet ball Methanol Powder 2_3 NASA NSG Wet ball Methanol Table 19: Processing conditions including heat treat (HT) for NASA spun Fe 77Ni 5.5Co 5.5Zr 7B 4Cu 1 magnetic powders 103

106 Figure 43: Room temperature magnetic hysteresis of NASA spun Fe 77Ni 5.5Co 5.5Zr 7B 4Cu 1 magnetic powders As can be seen from the hysteresis loop, the saturation magnetization is not as drastically reduced from that of the heat-treated ribbons (no longer Cr contamination) however there is still a significant decrease. This decrease is most likely due to oxidation due to the malfunction during spinning. A summary of the magnetic properties of these powders is provided in Table 20. Sample ID ID # Milling (s) M s (A m 2 /kg) H c (Oe) Hc (A/m) Powder 1_3 NASA NSG Powder 2_3 NASA NSG Ingot 13_AS AS Ribbon X Ingot 13_HT HT Ribbon X Table 20: Saturation specific magnetization, M s, and coercivity, H c, of Fe 77Ni 5.5Co 5.5Zr 7B 4Cu 1 NASA spun magnetic powders 104

107 The chromium contamination appears to be solved from the more reasonable magnetization in these powders. This has been confirmed from X-Ray Energy Dispersive Spectroscopy (XEDS) performed at CWRU. This analysis technique allows for the elemental composition of a sample to be determined. The results of this analysis are shown in Figure 44 and Table Figure 44: Scanning Electron Microscope image of NASA spun powder showing areas used for energy dispersive x-ray spectroscopy analysis Table 21: Atomic fraction of elements in NASA spun Powder 2_3 This analysis was completed on Powder 2_3 at two points. Pt1 analysis was performed on a large powder particle (blue square) while pt2 analysis was performed on a cluster of small 105