Functional Nanomaterials Useful for Magnetic Refrigeration Systems

By Amir Aslani

B.S. in Electrical Engineering, May 2008, George Washington University M.S. in Electrical Engineering, May 2010, George Mason University

A Dissertation submitted to

The Faculty of The School of Engineering and Applied Science of The George Washington University in partial satisfaction of the requirement for the degree of Doctor of Philosophy

May 15, 2016

Dissertation directed by

Edward Della Torre Professor of Engineering and Applied Science

Lawrence H. Bennett Research Professor of Engineering and Applied Science The School of Engineering and Applied Science of The George Washington University certifies that Amir Aslani has passed the Final Examination for the degree of Doctor of

Philosophy as of March 8th, 2016. This is the final and approved form of the dissertation.

Functional Nanomaterials Useful for Magnetic Refrigeration Systems

Amir Aslani

Dissertation Research Committee:

Edward Della Torre, Professor of Engineering and Applied Science, Dissertation Co-Director.

Lawrence H. Bennett, Research Professor of Engineering and Applied Science, Dissertation Co-Director.

David Nagel, Research Professor of Engineering and Applied Science, Committee Member.

Shahrokh Ahmadi, Professor of Engineering and Applied Science, Committee Member.

Mohammadreza Ghahremani, Assistant Professor of Computer Information Sciences, Shepherd University, Committee Member.

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Dedication

I dedicate my dissertation to my family. Thanks for believing in me and for encouraging me to strive for my dreams. A special feeling of appreciation to my lovely mother and father, Dr. Ashraf Ahmadi and Iraj Aslani, who first taught me the value of education and critical thought. This became possible with their constant support, encouragement, and love. To my lovely sisters, Dr. Maryam and Dr. Marjan Aslani, who have been constant cheerleaders through every academic and personal endeavor in my life.

Acknowledgements

First and foremost, I would like to thank my advisors and mentors Professor

Edward Della Torre and Professor Lawrence H. Bennett for their leadership, support, and help throughout my research. They both have helped me achieve more than I ever thought possible over the past few years.

I would like to thank Professor David Nagel, and Professor Shahrokh Ahmadi who I am blessed to have known ever since my undergraduate studies at the George

Washington University. I have learned many valuable things from them and they have beautifully laid the foundation and passion for my doctoral studies.

I thank my dearest friend Dr. Mohammadreza Ghahremani for his encouragement and helpful discussions throughout my dissertation research.

Last but not least, many thanks to Professor Michael Wagner at the Chemistry

Department of the George Washington University and Professor Saniya Leblanc at the

Mechanical Engineering Department of the George Washington University for allowing me to utilize their laboratories in my research.

Abstract of Dissertation

Functional Nanomaterials Useful for Magnetic Refrigeration Systems

Magnetic refrigeration is an emerging energy efficient and environmentally friendly refrigeration technology. The principle of magnetic refrigeration is based on the effect of varying a magnetic field on the temperature change of a magnetocaloric material

(refrigerant). By applying a magnetic field, the magnetic moments of a magnetic material tend to align parallel to it, and the thermal energy released in this process heats the material. Reversibly, the magnetic moments become randomly oriented when the magnetic field is removed, and the material cools down. The heating and the cooling of a refrigerant in response to a changing magnetic field is similar to the heating and the cooling of a gaseous medium in response to an adiabatic compression and expansion in a conventional refrigeration system.

One requirement to make a practical magnetic refrigerator is to have a large temperature change per unit of applied magnetic field, with sufficiently wide operating temperature. So far, no commercially viable magnetic refrigerator has been built primarily due to the low temperature change of bulk refrigerants, the added burden of hysteresis, and the system’s low cooling capacity.

The purpose of this dissertation is to explore magnetic refrigeration system. First, the Active Magnetic Regenerator (AMR) system built by Shir et al at the GWU’s

Institute for Magnetics Research (IMR) is optimized by tuning the heat transfer medium parameters and system’s operating conditions. Next, by reviewing literature and works done so far on refrigerants, a number of materials that may be suitable to be used in

vi magnetic refrigeration technology were identified. Theoretical work by Bennett et al showed an enhancement in magnetocaloric effect of magnetic nanoparticles. Research was performed on functional magnetic nanoparticles and their use in magnetic refrigeration technology. Different aspects such as the size, shape, chemical composition, structure and interaction of the nanoparticle with the surrounding matrix and neighboring particles all have a profound effect on the magnetic behavior of a material. To carry out this research some nanoparticles, namely yttrium-iron and a Ni-Mn-In Heusler alloy, in the range of 10 to 200 nm were synthesized and characterized in order to determine the correlation between the size, shape, and the morphology of nanoparticles on their magnetic properties such as magnetization, magnetocaloric effect, Curie temperature, etc.

Results showed a significant improvement in the AMR cooling performance when the heat transfer fluid parameters and system’s operating conditions are optimized. In addition, the magnetization results of the yttrium-iron nanoparticles revealed more than a six-fold increase in the amount of magnetization at room temperature when their size reduced from 42 to 21 nm. For Heusler alloy sample the magnetization improvement at room temperature was more than 5-folds when the size of the nanoparticles reduced from

200 to 30 nm. Hence, a larger magnetocaloric effect can be expected by decreasing the nanoparticles’ size. Furthermore, results presented a drop in the coercivity of the nanoparticles as their size reduced, therefore a reduction in the hysteresis. Nanoparticles, as compared to their bulk counterpart, have a larger magnetocaloric effect with less hysteresis.

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Table of Contents

DEDICATION………………………………………………………………………….. iv

ACKNOWLEDGEMENTS…………………………………………………………….. v

ABSTRACT OF DISSERTATION……………………………………………………. vi

CHAPTER 1 . INTRODUCTION ...... 1

1.1 BACKGROUND ...... 1

1.2 SCOPE ...... 3

1.3 MOTIVATION ...... 3

1.4 OBJECTIVE ...... 4

1.5 ORGANIZATION OF DISSERTATION ...... 5 CHAPTER 2 . THEORETICAL ASPECTS AND BACKGROUND ...... 6

2.1 INTRODUCTION...... 6

2.2 MAGNETISM CLASSIFICATION ...... 6 2.2.1 Diamagnetism ...... 7 2.2.2 Paramagnetism ...... 8 2.2.3 Ferromagnetism ...... 10 2.2.3.1 Curie temperature ...... 11 2.2.3.2 Magnetic Hysteresis ...... 12 2.2.3.3 Thermal Hysteresis ...... 13 2.2.4 Ferrimagnetism ...... 14

2.3 MAGNETIC ANISOTROPY ...... 16 2.3.1 Magnetocrystalline Anisotropy ...... 16 2.3.2 Stress Anisotropy ...... 17 2.3.3 Shape Anisotropy ...... 17

2.4 MAGNETIC DOMAINS ...... 18 2.4.1 Single Domain (SD) ...... 23 2.4.2 Pseudo-Single Domain (PSD)...... 24 2.4.3 Superparamagnetism (SPM) ...... 24 2.4.3.1 MCE in Superparamagnetic Systems...... 29

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2.4.4 Hysteresis Properties of SD, PSD, and MD Particles ...... 32

2.5 MAGNETIC SUSCEPTIBILITY ...... 34 2.5.1 Frequency Dependence of Susceptibility...... 36

2.6 MAGNETOCALORIC EFFECT ...... 37

2.7 MAGNETIC ENTROPY ...... 38

2.8 CLASSIFICATIONS OF PHASE TRANSITION ...... 39

2.9 EXTERNAL APPLIED MAGNETIC FIELD ...... 41

2.10 MAGNETO-THERMODYNAMICS ...... 42

2.11 SOLID-STATE COOLING WITH CALORIC MATERIAL ...... 44

2.12 COMPARISON BETWEEN MAGNETIC REFRIGERATION AND CONVENTIONAL

REFRIGERATION SYSTEM ...... 45

2.13 ACTIVE MAGNETIC REGENERATION ...... 47

2.14 MODELING OF MAGNETIZATION AND DEMAGNETIZATION PROCESSES ...... 49 CHAPTER 3 . OPTIMIZATION OF MAGNETIC REFRIGERATORS BY TUNING THE HEAT TRANSFER MEDIUM PARAMETERS AND SYSTEM’S OPERATING CONDITIONS ...... 53

3.1 INTRODUCTION...... 54

3.2 EXPERIMENTAL SETUP ...... 56 3.2.1 Magnet ...... 56 3.2.2 Temperature sensors ...... 57 3.2.3 Refrigerant bed...... 59 3.2.4 Cylinder-piston displacer ...... 60 3.2.5 System setup as AMR device ...... 62

3.3 DATA ANALYSIS, RESULTS AND DISCUSSIONS...... 64

3.4 CONCLUSIONS ...... 71 CHAPTER 4 . CHARACTERIZATION METHODS ...... 73

4.1 X-RAY POWDER DIFFRACTION (XRD) ...... 73

4.2 X-RAY FLUORESCENCE (XRF) ...... 75

4.3 SCANNING ELECTRON MICROSCOPE (SEM) ...... 77

4.4 SUPERCONDUCTING QUANTUM INTERFACE DEVISE (SQUID) ...... 79

4.5 VECTOR VIBRATING SAMPLE MAGNETOMETER (V-VSM) ...... 81

4.6 ANNEALING PROCEDURE ...... 83 CHAPTER 5 . NANOMATERIALS IN MAGNETIC REFRIGERATION TECHNOLOGY ...... 85

5.1 NANOPARTICLES AS THE REFRIGERANT ...... 87

5.2 SYNTHESIS OF NANOPARTICLES ...... 90 5.2.1 Alkalide Reduction Chemical Synthesis ...... 92 5.2.2 Physical Vapor Deposition Sputtering ...... 92 5.2.3 High Energy Ball Milling ...... 95 5.2.4 Synthesis methods used in this research ...... 97

5.3 PROTECTING AIR SENSITIVE NANOSCALE MAGNETIC REFRIGERANTS ...... 98 CHAPTER 6 . MAGNETOCALORIC EFFECT AND MAGNETIC

PROPERTIES OF YTTRIUM-IRON (Y2FE17) NANOPARTICLES ...... 99 6.1 INTRODUCTION...... 99

6.2 EXPERIMENTAL ...... 102

6.3 RESULTS AND DISCUSSION ...... 105

6.4 CONCLUSIONS ...... 118 CHAPTER 7 . MAGNETOCALORIC EFFECT AND MAGNETIC

PROPERTIES OF NANOSTRUCTURED NI51MN33.4IN15.6 HEUSLER ALLOY ...... 120

7.1. HEUSLER ALLOYS ...... 120

7.2 INTRODUCTION...... 122

7.3 EXPERIMENTAL ...... 125

7.4 RESULTS AND DISCUSSION ...... 128

7.5 CONCLUSIONS ...... 137 CHAPTER 8 . CONCLUSIONS AND FUTURE RESEARCH ...... 139 PUBLICATIONS ...... 141 REFERENCES ...... 142 APPENDIX A— MAXWELL RELATIONS FOR MAGNETIC MATERIALS ...... 156

List of Figures

FIGURE 2-1: MAGNETISM CLASSIFICATION OF ELEMENTS IN PERIODIC TABLE ...... 7

FIGURE 2-2: DIAMAGNETIC MATERIALS PROPERTIES AND ATOMIC BEHAVIOR ...... 7

FIGURE 2-3: PARAMAGNETIC MATERIALS PROPERTIES AND ATOMIC BEHAVIOR...... 10

FIGURE 2-4: FERROMAGNETIC MATERIALS PROPERTIES AND ATOMIC BEHAVIOR ...... 11

FIGURE 2-5: TYPICAL FERROMAGNETIC HYSTERESIS LOOP SHOWING SATURATION

MAGNETIZATION MS, REMNANT MAGNETIZATION MR, COERCIVE FIELD HC...... 12

FIGURE 2-6: PLOT OF DIELECTRIC CONSTANT VERSUS TEMPERATURE FORA SINGLE

CRYSTAL OF BARIUM TITANATE ...... 13

FIGURE 2-7: FERRIMAGNETIC MATERIALS PROPERTIES AND ATOMIC BEHAVIOR ...... 14

FIGURE 2-8: ANTIFERROMAGNETIC MATERIALS PROPERTIES AND ATOMIC BEHAVIOR ...... 15

FIGURE 2-9: MAGNETISM CLASSIFICATIONS ...... 15

FIGURE 2-10: SCHEMATIC DEPICTION OF DOMAINS IN A FERROMAGNETIC OR

FERRIMAGNETIC MATERIAL; ARROWS REPRESENT ATOMIC MAGNETIC DIPOLES.

WITHIN EACH DOMAIN, ALL DIPOLES ARE ALIGNED, WHEREAS THE DIRECTION

OF ALIGNMENT VARIES FROM ONE DOMAIN TO ANOTHER...... 18

FIGURE 2-11: THE GRADUAL CHANGE IN MAGNETIC DIPOLE ORIENTATION ACROSS A

DOMAIN WALL ...... 19

FIGURE 2-12: GRAIN SIZE AND MAGNETIC DOMAIN...... 19

FIGURE 2-13: SCHEMATIC ILLUSTRATION OF THE BREAK-UP OF MAGNETIZATION

INTO DOMAINS: (A) SINGLE DOMAIN; (B) TWO DOMAINS; (C) FOUR DOMAINS;

(D) CLOSURE DOMAINS...... 21

FIGURE 2-14: SCHEMATIC REPRESENTATION OF A 180° DOMAIN WALL ...... 22

FIGURE 2-15: DOMAIN WALL THICKNESS...... 22

FIGURE 2-16: EXPERIMENTAL STRATEGY FOR ESTIMATING THE BLOCKING

TEMPERATURE OF MAGNETIC NANOPARTICLES...... 28

FIGURE 2-17: SCHEMATIC ILLUSTRATING THE DEPENDENCE OF MAGNETIC

COERCIVITY ON PARTICLE SIZE...... 29

FIGURE 2-18: SCHEMATIC OF MAGNETIC SPINS IN (A) PARAMAGNETIC AND (B)

SUPERPARAMAGNETIC NANOMATERIAL. THE CIRCLES IN (B) REPRESENT

MAGNETIC CLUSTERS...... 29

FIGURE 2-19: FIELD DEPENDENT MAGNETIZATION (HYSTERESIS LOOP)...... 32

FIGURE 2-20: FIELD DEPENDENT MAGNETIZATION BEHAVIOR OF FERROMAGNETIC,

PARAMAGNETIC, SUPERPARAMAGNETIC, AND DIAMAGNETIC MATERIAL ...... 33

FIGURE 2-21: COERCIVITY VS. PARTICLE SIZE ...... 34

FIGURE 2-22: MR/MS VS. HR/HC DIAGRAM AND MAGNETIC DOMAIN ...... 34

FIGURE 2-23: MAGNETIC SUSCEPTIBILITY VS. TEMPERATURE...... 36

FIGURE 2-24: PHASE DIAGRAMS DESCRIBING THE CHANGE IN MAGNETIZATION (M)

AS A FUNCTION OF TEMPERATURE (T). A, SECOND-ORDER PHASE TRANSITION,

WHEREBY M CHANGES CONTINUOUSLY WITH T UP UNTIL THE CRITICAL POINT

(TC). B, FIRST-ORDER PHASE TRANSITION WHEREBY M CHANGES

DISCONTINUOUSLY AT TC ...... 40

FIGURE 2-25: MAGNETIZATION WORK AND HEAT PROCESS IN A CONTROL VOLUME

BED OF SOLID MAGNETOCALORIC MATERIAL...... 43

FIGURE 2-26: COOLING CYCLES. (A) THE CONVENTIONAL VAPOR COMPRESSION

CYCLE USES A LIQUID–GAS PHASE TRANSITION. (B) CALORIC-MATERIAL

COOLING CYCLES USE MAGNETIC (H), ELECTRIC (E), OR STRESS (Σ) FIELDS TO

REVERSIBLY CHANGE THE ENTROPY (SHOWN AS THE VECTOR ARRAYS IN GRAY,

RED, AND BLUE) OF THE RESPECTIVE REFRIGERANT MATERIAL...... 45

FIGURE 2-27: COMPARISON BETWEEN MAGNETIC REFRIGERATION AND

CONVENTIONAL REFRIGERATION...... 46

FIGURE 2-28: SCHEMATIC VIEW OF AN AMR CYCLES. TI: INITIAL TEMPERATURE,

TF: FINAL TEMPERATURE, TC: COLD END TEMPERATURE, TH: HOT END

TEMPERATURE ...... 48

FIGURE 3-1: SCHEMATIC DIAGRAM OF THE EXPERIMENTAL APPARATUS SHOWING

SIX SENSOR LOCATIONS...... 56

FIGURE 3-2: A ROTARY TWO-CORE NESTED PERMANENT MAGNET CYLINDER...... 57

FIGURE 3-3: CERNOX TEMPERATURE SENSOR...... 58

FIGURE 3-4: GADOLINIUM TURNINGS SAMPLE ...... 59

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FIGURE 3-5: REFRIGERANT BED SET UP BY THE GADOLINIUM TURNING BEFORE

INSTALLATION TO THE MAGNET...... 60

FIGURE 3-6: DOUBLE ACTING DISPLACER SYSTEM INSTALLED PARALLEL TO THE

REFRIGERANT BED...... 61

FIGURE 3-7: PHOTOGRAPHY OF THE AMR DEVICE. THE REFRIGERANT IS LOCATED

INSIDE A CYLINDRICAL PERMANENT MAGNET ASSEMBLY...... 62

FIGURE 3-8: FRONT PANEL OF THE CONTROL SYSTEM PROGRAM WRITTEN USING

LABVIEW. THE PROGRAM HAS CAPABILITIES OF CONTROLLING AND

SYNCHRONIZING SYSTEM COMPONENTS...... 63

FIGURE 3-9: WIDE VIEW OF THE AMR SYSTEM WITH CONTROL EQUIPMENT ...... 64

FIGURE 3-10: CONFIGURATION OF SETUP 1 AND SETUP 2 FOR ONE CYCLE OF THE

EXPERIMENT...... 67

FIGURE 3-11: TEMPERATURE SPAN (훥TBH-BC) BETWEEN BH AND BC SENSORS AS A

FUNCTION OF DVR FOR DIFFERENT OPERATING FREQUENCIES IN SETUP 1...... 68

FIGURE 3-12: TEMPERATURE SPAN (훥TBH-BC) BETWEEN BH AND BC SENSORS AS A

FUNCTION OF DVR FOR DIFFERENT OPERATING FREQUENCIES IN SETUP 2...... 69

FIGURE 3-13: TEMPERATURE SPAN AS A FUNCTION OF OPERATING FREQUENCY FOR

DIFFERENT DVRS IN SETUP 2...... 70

FIGURE 3-14: TEMPERATURE SPAN AT DIFFERENT SENSOR LOCATIONS AS A

FUNCTION OF DVR FOR A FREQUENCY OF 0.09 HZ IN SETUP 2. SENSOR

LOCATIONS ARE SHOWN IN FIG. 1. SENSORS BH-BC ARE PLACED NEAREST TO

THE BED AND SENSORS H2-C2 ARE FARTHEST FROM THE BED...... 71

FIGURE 3-15: TEMPERATURE SPAN AS A FUNCTION OF FLOW RATE FOR DIFFERENT

OPERATING FREQUENCIES IN SETUP 1...... 71

FIGURE 4-1: PRINCIPLE MECHANISM DIAGRAM OF XRD ...... 74

FIGURE 4-2: XRD EQUIPMENT, MINIFLEX BY RIGAKU ...... 75

FIGURE 4-3: PRINCIPLE MECHANISM DIAGRAM OF XRF ...... 76

FIGURE 4-4: XRF EQUIPMENT, EDX-700 BY SHIMADZU ...... 77

FIGURE 4-5: PRINCIPLE MECHANISM DIAGRAM OF SEM ...... 78

FIGURE 4-6: SEM EQUIPMENT, PIONEER TWO BY RAITH ...... 79

FIGURE 4-7: PRINCIPLE MECHANISM DIAGRAM OF SQUID ...... 80

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FIGURE 4-8: MPMS XL SQUID BY QUANTUM DESIGN ...... 81

FIGURE 4-9: PRINCIPLE MECHANISM DIAGRAM OF VSM ...... 82

FIGURE 4-10: V-VSM MODEL 7410 BY LAKE SHORE ...... 82

FIGURE 4-11: V-VSM CRYOSTAT UNIT ...... 83

FIGURE 4-12: ANNEALING EQUIPMENT ...... 84

FIGURE 5-1: DIFFERENT HYSTERESIS LOOP SHAPES AND THEIR TYPICAL

APPLICATION ...... 85

FIGURE 5-2: SCHEMATIC OF A FERROIC COOLANT’S BEHAVIOR WITH PHASE

TRANSITION AS A FUNCTION OF TEMPERATURE...... 90

FIGURE 5-3: BOTTOM-UP AND TOP-DOWN APPROACH IN NANOMATERIAL

SYNTHESIS ...... 91

FIGURE 5-4: SPUTTERING TECHNIQUE SCHEMATIC (LEFT) AND SPUTTERING TARGET

(RIGHT) ...... 94

FIGURE 5-5: MAGNETRON SPUTTERING ...... 95

FIGURE 5-6: SCHEMATIC VIEW OF MOTION OF THE BALL AND POWDER MIXTURE ...... 97

FIGURE 6-1: SCHEMATIC VIEW OF ALKALIDE REDUCTION CHEMICAL SYNTHESIS ...... 102

FIGURE 6-2: NITROGEN DRY BOX ...... 103

FIGURE 6-3: SYNTHESIZED Y2FE17 NANOPARTICLES ...... 104

FIGURE 6-4: FIELD-DEPENDENT MAGNETIZATION OF THE COATED AND NON-COATED

21 NM SAMPLE (BOTH SAMPLES ARE UNANNEALED)...... 106

FIGURE 6-5: FIELD DEPENDENT MAGNETIZATION OF THE 42 NM SAMPLE ANNEALED

AT DIFFERENT TEMPERATURES (350 C, 400 C, AND 500 C) FOR 6 HOURS...... 107

FIGURE 6-6: XRD PATTERN OF ANNEALED SYNTHESIZED NANOPARTICLES ...... 107

FIGURE 6-7: FIELD DEPENDENT MAGNETIZATION OF THE ANNEALED AND

UNANNEALED 21 NM SAMPLE, MEASURE AT ROOM TEMPERATURE ...... 108

FIGURE 6-8: SOME SEM IMAGES OF Y2FE17 NANOPARTICLES. AVERAGE PARTICLE

SIZE IN (A) 42 NM, (B) 28 NM ...... 109

FIGURE 6-9: FIELD DEPENDENT MAGNETIZATION OF THE 21 NM SAMPLE, MEASURED

AT 9 DISCRETE TEMPERATURES FROM 10 TO 290 K...... 110

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FIGURE 6-10: FIELD DEPENDENT MAGNETIZATION OF THE 21 NM SAMPLE,

MEASURED AT 9 DISCRETE TEMPERATURES FROM 10 TO 290 K, SHOWN FROM

8000 TO 10000 OE...... 110

FIGURE 6-11: FIELD DEPENDENT MAGNETIZATION OF THE 21 NM SAMPLE,

MEASURED AT 9 DISCRETE TEMPERATURES FROM 10 TO 290 K, SHOWN FROM -

600 TO 600 OE...... 111

FIGURE 6-12: COERCIVITY AS A FUNCTION OF TEMPERATURE FOR THE 21 NM

SAMPLE ...... 111

FIGURE 6-13: EFFECT OF TEMPERATURE VARIATION ON THE MAGNETIZATION AND

THE COERCIVITY OF THE 21 NM SAMPLE ...... 112

FIGURE 6-14: ACCOMMODATION (REPTATION) MEASUREMENTS PERFORMED AT 292

K FOR THE 36 NM SAMPLE ...... 113

FIGURE 6-15: ACCOMMODATION (REPTATION) MEASUREMENTS PERFORMED AT 200

K FOR THE 28 NM SAMPLE ...... 114

FIGURE 6-16: TEMPERATURE-DEPENDENT MAGNETIZATION UNDER 1000 OE

APPLIED MAGNETIC FIELD FOR DIFFERENT-SIZED Y2FE17 NANOPARTICLES ...... 115

FIGURE 6-17: SIZE-DEPENDENT MAGNETIZATION OF Y2FE17 NANOPARTICLES IN TEMPERATURE RANGE FROM 10 TO 316 K UNDER 1000 OE APPLIED MAGNETIC

FIELD ...... 116

FIGURE 6-18: FIELD-DEPENDENT MAGNETIZATION OF Y2FE17 NANOPARTICLES

MEASURED AT 292 K...... 118

FIGURE 6-19: COERCIVITY OF Y2FE17 NANOPARTICLES AS A FUNCTION OF SIZE ...... 118

FIGURE 7-1: (A) L21 FULL-HEUSLER AND (B) C 1B HALF-HEUSLER ORDERED

STRUCTURES. … ...... 122

FIGURE 7-2: BULK NI51MN33.4IN15.6 HEUSLER ALLOY ...... 125

FIGURE 7-3: SPEX 8000 MIXER/MILL FROM SAMPLEPREP ...... 126

FIGURE 7-4: HARDENED STEEL GRINDING VIAL AND HARDENED STEEL BALLS ...... 127

FIGURE 7-5: ARGON FILLED GLOVE COMPARTMENT ...... 127

FIGURE 7-6: MAGNETIZATION AS A FUNCTION OF TEMPERATURE IN ZFC, FCC, AND

FCW SEQUENCES FOR NI51MN33.4IN15.6 BULK ALLOY TARGET UNDER (A) 100 OE (B) 1000 OE ...... 129

FIGURE 7-7: MAGNETIZATION AS A FUNCTION OF APPLIED FIELD RECORDED IN THE

VICINITY OF THE MARTENSITIC TRANSITION FOR NI51MN33.4IN15.6 BULK ALLOY

TARGET ...... 129

FIGURE 7-8: XRD PATTERN OF: (A) ANNEALED NANOPARTICLES, (B) COARSE-

GRAINED POWDER ...... 130

FIGURE 7-9: TEMPERATURE DEPENDENT MAGNETIZATION UNDER AN APPLIED FIELD

OF 1000 OE FOR THE 30 NM NI51MN33.4IN15.6 ALLOY, UN-ANNEALED (BLUE) AND ANNEALED AT 673 K FOR 6 HOURS (RED). THE INSET SHOWS THE M(T)

MEASUREMENT OF THE NANOPARTICLES FROM 10 TO 100 K BEFORE

ANNEALING...... 131

FIGURE 7-10: SEM IMAGES OF NI51MN33.4IN15.6 NANOPARTICLES ...... 132 FIGURE 7-11: TEMPERATURE-DEPENDENT MAGNETIZATION UNDER 1000 OE

APPLIED MAGNETIC FIELD FOR DIFFERENT-SIZED NI51MN33.4IN15.6 NANOPARTICLES ...... 133

FIGURE 7-12: SIZE-DEPENDENT MAGNETIZATION OF NI51MN33.4IN15.6 NANOPARTICLES IN TEMPERATURE RANGE OF 10 TO 316 K UNDER 1000 OE

APPLIED MAGNETIC FIELD ...... 135

FIGURE 7-13: FIELD-DEPENDENT MAGNETIZATION OF NI51MN33.4IN15.6

NANOPARTICLES AT 150 K...... 136

FIGURE 7-14: COERCIVITY OF NI51MN33.4IN15.6 NANOPARTICLES AS A FUNCTION OF

SIZE IN DIFFERENT TEMPERATURES ...... 137

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List of Tables

TABLE 2-1: SUSCEPTIBILITY OF PARAMAGNETIC AND FERROMAGNETIC MATERIAL ...... 11

TABLE 3-1: EXPERIMENTAL PARAMETERS ...... 65

TABLE 7-1: COERCIVITY OF NI51MN33.4IN15.6 NANOPARTICLES AS A FUNCTION OF SIZE AND TEMPERATURE ...... 136

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List of Symbols

AF antiferromagnetic AMR active magnetic regenerator C Curie constant (W/K) CF cooling factor CFC chlorofluorocarbon COP coefficient of performance DAQ data acquisition system cH specific heat at constant applied field (j/kg.K) f frequency (Hz) H applied field (A/m) HCFC hydro-chlorofluorocarbon HFC hydro-fluorocarbon RC refrigerant capacity RCP relative cooling power Hz Hertz H-L high to low j mechanical equivalent of heat LDA local-density approximation L-H low to high m mass M magnetization (emu/g), (Am2/kg) B magnetic flux density (T) H magnetic field strength (A/m) E Electric field strength (V/m) Oe Oersted P pressure (Pa) Q heat transfer (J) S total entropy T Tesla T temperature (K)

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T0 reference temperature (K)

TC Curie temperature (K)

TK Kittel temperature (K)

TN Néel temperature (K)

TB Blocking temperature (K) U internal energy v volume (m3) W mechanical work (J/kg) k Boltzman constant

Ku anisotropy constant

Hc coercivity

Greek ∆ change μ viscosity (N.s/m2) or (kg/m.s) μ permeability (H/m) μoH applied field (Tesla) μoHo reference applied field (Tesla) ρ density (kg/m3) σ entropy production (J/kg.K) χ susceptibility ε permittivity (F/m)

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Chapter 1 . Introduction

1.1 Background

The vapor-compression refrigerators have become ubiquitous in the large number of cooling applications. However, the use of chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) as working fluids has raised serious environmental concerns, primarily for the role in the destruction of the ozone layer and the global warming. Replacement by fluid hydro-fluorocarbons (HFCs), which contain no chlorine and therefore have no ozone depletion potential, is not without problems because the

HFCs are greenhouse gases with higher global warming potential than CO2. In addition, the efficiency of the vapor-compression refrigeration systems is not expected to be significantly improved in the future. Thus, due to slow improvement of the efficiency and serious concern for the environment, alternative technologies that use either inert gases or no fluid at all become attractive solutions to the environment problems [Brown 14].

Magnetic refrigeration is an emerging energy efficient and environmentally friendly refrigeration technology. In contrast with conventional vapor-compression refrigerator systems that work based on compression and evaporation of gas, magnetic refrigeration systems work by magnetizing and demagnetizing a magnetic material

(refrigerant). Magnetic refrigeration exploits a property of magnetic materials called the magnetocaloric effect (MCE): the temperature of most ferromagnetic materials is observed to rise upon the application of a magnetic field and fall upon its removal.

Magnetic refrigeration has been in use in scientific applications for a long time for cooling below 1 K. Even though there has been a surge in research on magnetic

1 refrigeration in the past few years, the magnetic materials available and studied by the scientific community do not have yet the needed characteristics to be used in large scale

(commercial applications) at temperatures around room temperature, due to economical and/or technological restrictions namely the low temperature change of solid bulk refrigerant, low cooling capacity, and the added burden of hysteresis. The major problem in magnetic refrigeration is still to find working materials with a large MCE in different temperature regions.

There are at least three important characteristics to consider in evaluating a good magnetocaloric material: (i) the process must be reversible with respect to changing/reversing magnetic field and show negligible hysteresis loss, (ii) the effect must occur near room temperature for room temperature application, and (iii) the MCE must be significant at reasonable applied magnetic field values.

One requirement to make a practical magnetic refrigerator is to have a large temperature change per unit of applied magnetic field, with sufficiently wide operating temperature range around room temperature. So far, no commercially viable magnetic refrigerator has been built primarily due to the low temperature change of solid bulk refrigerant, the added burden of hysteresis, and the system’s low cooling capacity.

Previous works on magnetic refrigeration technology are based on bulk refrigerants that undergo first-order transitions. Some materials yield apparently high MCE values near- room temperature due to misapplication of Maxwell’s equations. Most of the work in room-temperature magnetic refrigeration employs the so-called “giant magnetocaloric effect”, which uses hysteretic materials. This has not worked due to the fact that

Maxwell’s equations are only valid for non-hysteretic material. The correct calculation

2 produces much lower MCEs. In addition irreversibility remains an impediment by decreasing the cycle’s Carnot efficiency.

1.2 Scope

The main goals of my dissertation work are to optimize a direct magnetocaloric temperature change measurement apparatus with fully-controlled magnetic field, temperature, and time capabilities to measure ΔTad for different materials, and also study the usage of magnetic nanoparticles as refrigerant in magnetic refrigeration systems.

1.3 Motivation

The magnetocaloric effect (MCE) is the reversible temperature change of a magnetic material upon the application or removal of a magnetic ﬁeld. In the past 20 years, there has been a surge in research on the magnetocaloric response of materials, due mainly to the possibility of applying this effect for magnetic refrigeration close to room temperature. However, nowadays, the magnetic materials available and studied by the scientific community do not have yet the needed characteristics to be used in large scale, due to technological and/or economic restrictions. For a successful application, we need a material of low cost, non-toxic, and good thermal conductivity. Our research is devoted to explore and optimize the magnetocaloric properties of known materials, as well to seek for new magnetocaloric features in new materials. We also discuss the use of magnetocaloric characterization to gain fundamental insight into the nature of the underlying phase transition.

The motivation for this research is the importance of magnetic refrigeration as a good candidate for reducing our energy consumption, as it is more energetically efﬁcient

3 than the process based on the compression/expansion of gases. Magnetic refrigeration is an emerging energy efficient and environmentally friendly refrigeration technology with the following desirable design characteristics: (i) it does not use ozone depleting chemicals (CFCs), hazardous chemicals (NH3) or greenhouse gases (HCFCs and HFCs);

(ii) the cooling efficiency of magnetic refrigeration can be significantly higher than compressor-based techniques, e.g. the cooling efficiency in magnetic refrigerator working with gadolinium has been shown to reach 60% of the theoretical limit compared with only about 40% in the best gas-compression refrigerators; and (iii) the magnetic refrigerator can be built more compactly and generates much less noise.

1.4 Objective

The objective of this dissertation is to explore an energy efficient and environmentally friendly magnetic refrigeration system, and also study of different properties of magnetocaloric materials such as gadolinium, yttrium-iron, and Heusler alloys, and study of magnetic nanoparticles as refrigerant in magnetic refrigeration technology.

The tremendous interest in magnetic nanoparticles is reflected in published research that ranges from methods of synthesis of unique nanoparticle shapes and composite structures to a large number of magnetic nanoparticles characterization techniques, and finally to their use in many engineering, biomedical and nanotechnology- based applications. The complex magnetic behavior exhibited by magnetic nanoparticles is governed by many factors such as size, composition, shape, and shell-core structure; these factors can either improve or adversely affect the desired magnetic properties. The

4 unique properties of magnetic nanoparticles derive from the fact that these nanoscale magnets differ from bulk materials due to their high surface-to-volume ratios.

We show that nanomaterials usually have higher MCE temperature change per unit of applied magnetic field, and higher refrigerant capacity (RC) than that of their bulk counterparts since nanomaterials exhibit a substantial broadening of ferro-to- paramagnetic transition due to a considerable augmentation of the disordered inter-grain boundaries. In addition by utilizing a nanocomposite refrigerant, the hysteresis problem associated with materials that undergo first-order magnetostructural phase transition will be substantially reduced. These results are desirable for practical magnetic refrigeration that could cover a wide temperature span.

1.5 Organization of Dissertation

The thesis consists of eight chapters which aims to describe the road-map of the research and suggests future research work. The next seven chapters are theory and background review, optimization of magnetic refrigerators, characterization methods, nanomaterials in magnetic refrigeration technology, magnetic properties of yttrium-iron

(Y2Fe17) nanoparticles, magnetocaloric effect and magnetic properties of nanostructured

Ni51Mn33.4In15.6 Heusler Alloy, and future research.

Chapter 2 . Theoretical aspects and background

2.1 Introduction

Magnetic refrigeration is an emerging energy efficient and environmentally friendly refrigeration technology with many desirable design characteristics [Brück,

2005], [Yu, 2010]. With the push for the commercialization of the magnetic refrigerator, it is vitally important to perform evaluation of the magnetocaloric effect (MCE) of suitable magnetic refrigerants [Hansen, 2010], [Law, 2011] as well as implementing a better design and optimization of active magnetic regenerators. Before expanding the talk and going into details, it is necessary to have a brief overview to cover the fundamental of magnetism and magnetic refrigeration in this chapter.

2.2 Magnetism Classification

The best way to introduce the different types of magnetism is to describe how materials respond to magnetic fields. The magnetic behavior of materials can be classified into the following five major groups:

 Diamagnetism  Paramagnetism  Ferromagnetism  Ferrimagnetism  Antiferromagnetism

The two most common types of magnetism can be diamagnetism and paramagnetism, which account for the magnetic properties of most of the periodic table of elements at room temperature. Figure 2-1 illustrates these classifications in the periodic table.

Figure 2-1: Magnetism classification of elements in periodic table [Birmingham 15] 2.2.1 Diamagnetism

Diamagnetism is a fundamental property of all matter, although it is usually very weak. It is due to the non-cooperative behavior of orbiting electrons when exposed to an applied magnetic field. Diamagnetic substances are composed of atoms which have no net magnetic moments (ie. all the orbital shells are filled and there are no unpaired electrons). However, when exposed to a field, a negative magnetization is produced and thus the susceptibility is negative as shown in Figure 2-2. The other characteristic behavior of diamagnetic materials is that the susceptibility is temperature independent.

Figure 2-2: Diamagnetic materials properties and atomic behavior [Birmingham, 2015]. 7

2.2.2 Paramagnetism

In this class of materials, some of the atoms or ions in the material have a net magnetic moment due to unpaired electrons in partially filled orbitals. One of the most important atoms with unpaired electrons is iron. However, the individual magnetic moments do not interact magnetically, and like diamagnetism, the magnetization is zero when the field is removed. In the presence of a field, there is now a partial alignment of the atomic magnetic moments in the direction of the field, resulting in a net positive magnetization and positive susceptibility. In addition, the efficiency of the field in aligning the moments is opposed by the randomizing effects of temperature. This results in a temperature dependent susceptibility, known as the Curie Law. At normal temperatures and in moderate fields, the paramagnetic susceptibility is small (but larger than the diamagnetic contribution). Unless the temperature is very low (<<100 K) or the field is very high, paramagnetic susceptibility is independent of the applied field. Curie law is shown below in Equation 2.1, where C is a material constant called the Curie constant.

푪 흌 = (2-1) 푻 Materials which obey this law are materials in which the magnetic moments are localized at the atomic or ionic sites and where there is no interaction between neighboring magnetic moments. The hydrated salts of the transition metals, e.g.

CuSO4·5H2O, are examples of this type of behavior as the transition metal ions, which have a magnetic moment, are surrounded by a number of non-magnetic ions / atoms, which prevent interaction between neighboring magnetic moments.

In fact the Curie law is a special case of the more general Curie-Weiss law

(Equation 2.2), which incorporates a temperature constant (θ) and derives from Weiss theory, proposed for ferromagnetic materials, that incorporates the interaction between magnetic moments.

푪 흌 = (2-2) 푻−휽 In this equation θ can either be positive, negative or zero. Clearly when θ = 0 then the Curie-Weiss law equates to the Curie law. When θ is non-zero then there is an interaction between neighboring magnetic moments and the material is only paramagnetic above a certain transition temperature. If θ is positive then the material is ferromagnetic below the transition temperature and the value of θ corresponds to the transition temperature (Curie temperature, TC). If θ is negative then the material is antiferromagnetic below the transition temperature (Néel temperature, TN), however the value of θ does not relate to TN. It is important to note that this equation is only valid when the material is in a paramagnetic state. It is also not valid for many metals as the electrons contributing to the magnetic moment are not localized. However, the law does apply to some metals, e.g. the rare-earths, where the 4f electrons, that create the magnetic moment, are closely bound.

The Pauli model of paramagnetism is true for a material where the electrons are free and interact to form conduction band this is valid for most paramagnetic metals. In this model the conduction electrons are considered essentially to be free and under an applied field an imbalance between electrons with opposite spin is set up leading to a low magnetization in the same direction as the applied field. The susceptibility is independent of temperature, although the electronic band structure may be affected, which will then

9 have an effect on the susceptibility. Paramagnetic material’s properties are summarized in

Figure 2-3.

Figure 2-3: Paramagnetic materials properties and atomic behavior [Birmingham, 2015]. 2.2.3 Ferromagnetism

Unlike paramagnetic materials, the atomic moments in these materials exhibit very strong interactions. These interactions are produced by electronic exchange forces and result in a parallel or antiparallel alignment of atomic moments. Herein exchange forces are very large. The exchange force is a quantum mechanical phenomenon due to the relative orientation of the spins of two electrons. Ferromagnetic materials exhibit parallel alignment of moments resulting in large net magnetization even in the absence of a magnetic field. The elements Fe, Ni, and Co and many of their alloys are typical ferromagnetic materials.

Two distinct characteristics of ferromagnetic materials are their, (1) spontaneous magnetization and the existence of (2) magnetic ordering temperature. The spontaneous magnetization is the net magnetization that exists inside a uniformly magnetized microscopic volume in the absence of a field. The magnitude of this magnetization, at 0

K, is dependent on the spin magnetic moments of electrons. A related term is the saturation magnetization which we can measure in the laboratory. The saturation magnetization is the maximum induced magnetic moment that can be obtained in a

10 magnetic field (Hsat); beyond this field no further increase in magnetization occurs. The difference between spontaneous magnetization and the saturation magnetization has to do with magnetic domains. Saturation magnetization is an intrinsic property, independent of particle size but dependent on temperature.

There is a big difference between paramagnetic and ferromagnetic susceptibility.

As compared to paramagnetic materials, the magnetization in ferromagnetic materials is saturated in moderate magnetic fields and at high (room-temperature) temperatures.

Table 2-1 compares the susceptibility of paramagnets with ferromagnets and the properties of a ferromagnetic material are depicted in Figure 2-4.

Table 2-1: Susceptibility of paramagnetic and ferromagnetic material

-8 3 Hsat (T) T range (K) χ 10 m /kg Paramagnets >10 <<100 ~50 Ferromagnets ~1 ~300 1000-10000

Figure 2-4: Ferromagnetic materials properties and atomic behavior [Birmingham, 2015].

2.2.3.1 Curie temperature Even though electronic exchange forces in ferromagnets are very large, thermal energy eventually overcomes the exchange and produces a randomizing effect. This occurs at a particular temperature called the Curie temperature (TC). Below the Curie temperature, the ferromagnet is ordered and above it, disordered. The saturation 11 magnetization goes to zero at the Curie temperature. The Curie temperature is also an intrinsic property.

2.2.3.2 Magnetic Hysteresis In addition to the Curie temperature and saturation magnetization, ferromagnets can retain a memory of an applied field once it is removed. This behavior is called hysteresis and a plot of the variation of magnetization with magnetic field is called a hysteresis loop as shown in Figure 2-5.

Figure 2-5: Typical ferromagnetic hysteresis loop showing saturation magnetization Ms, remnant magnetization Mr, coercive field Hc. In other words, when a ferromagnetic material is magnetized in one direction, it will not relax back to zero magnetization when the imposed magnetizing field is removed. The amount of magnetization it retains at zero driving field is called its remanence. It must be driven back to zero by a field in the opposite direction; the amount of reverse driving field required to demagnetize it is called its coercivity. If an alternating magnetic field is applied to the material, its magnetization will trace out a loop called a hysteresis loop. The lack of retraceability of the magnetization curve is the property called hysteresis and it is related to the existence of magnetic domains in the material.

Once the magnetic domains are reoriented, it takes some energy to turn them back again.

One important factor is the area within the loop, since this represents the loss of energy within the specimen when it is magnetized and demagnetized. This energy is lost as heat within the specimen, and the larger the area within the loop the more energy is lost in magnetizing and demagnetizing the specimen. A soft magnetic material will have a small energy loss and therefore a narrow hysteresis loop while that for a hard magnetic material will be wider.

2.2.3.3 Thermal Hysteresis Thermal hysteresis is a phenomenon in which a physical quantity depends not only on the temperature but also on the preceding thermal history. It is usual to compare the behavior of the physical quantity while heating and the behavior while cooling through the same temperature range. Figure 2-6 shows the thermal hysteresis which has been observed in the behavior of the dielectric constant of single crystals of barium titanate. On heating, the dielectric constant was observed to follow the path ABCD, and on cooling the path DCEFG.

Figure 2-6: Plot of dielectric constant versus temperature fora single crystal of barium titanate [McGraw 03].

2.2.4 Ferrimagnetism In ionic compounds, such as oxides, more complex forms of magnetic ordering can occur as a result of the crystal structure. One type of magnetic ordering is called ferrimagnetism. Within these materials the exchange interactions lead to parallel alignment of atoms in some of the crystal sites and anti-parallel alignment of others. The material breaks down into magnetic domains, just like a ferromagnetic material and the magnetic behavior are also very similar, although ferromagnetic materials usually have lower saturation magnetizations. Properties of a ferrimagnetic material are depicted in

Figure 2-7.

Figure 2-7: Ferrimagnetic materials properties and atomic behavior [Birmingham, 2015].

2.2.5 Antiferromagnetism In the periodic table the only element exhibiting antiferromagnetism at room temperature is chromium. Antiferromagnetic materials are very similar to ferromagnetic materials but the exchange interaction between neighboring atoms leads to the antiparallel alignment of the atomic magnetic moments. Therefore, the magnetic field cancels out and the material appears to behave in the same way as a paramagnetic material. Like ferromagnetic materials these materials become paramagnetic above a transition temperature, known as the Néel temperature, TN. (Cr: TN =37ºC).

Figure 2-8: Antiferromagnetic materials properties and atomic behavior [Birmingham, 2015].

In summary magnetic classifications of materials are shown in Figure 2-9.

Figure 2-9: Magnetism Classifications [Birmingham, 2015].

2.3 Magnetic Anisotropy

The theory of ferro- and ferrimagnetism is based on electronic exchange forces.

These forces are so strong that these materials are spontaneously magnetized, even in the absence of an applied field. Yet, in the laboratory magnetic fields need to be applied to saturate a ferro- or ferrimagnetic material. The reason why all ferro- and ferrimagnetic materials are not magnetized to their saturated states, even in zero fields, is because ferromagnets are subdivided into many small sub-volumes, called domains. Each domain is spontaneously magnetized to saturation, but the direction of magnetization varies from domain to domain. The net vector sum of all the domains therefore produces a total magnetization of near zero. Before explaining domains, one needs to know about the influence of the crystal structure and the shape of grains on the direction of magnetization.

The dependence of magnetic properties on a preferred direction is called magnetic anisotropy. There are several different types of anisotropy:

 magnetocrystalline- crystal structure

 stress- applied or residual stresses

 shape- grain shape

Magnetic anisotropy strongly affects the shape of hysteresis loops and controls the coercivity and remanence. Anisotropy is also of considerable practical importance because it is exploited in the design of most magnetic materials of commercial importance.

2.3.1 Magnetocrystalline Anisotropy

Magnetocrystalline anisotropy is an intrinsic property of a ferrimagnet, independent of grain size and shape. It can be seen by measuring magnetization curves along different crystal directions. Magnetocrystalline anisotropy is the energy necessary to rotate the magnetic moment in a single crystal from the easy to the hard direction.

2.3.2 Stress Anisotropy In addition to magnetocrystalline anisotropy, there is another effect related to spin-orbit coupling called magnetostriction. Magnetostriction arises from the strain dependence of the anisotropy constants. Upon magnetization, a previously demagnetized crystal experiences a strain that can be measured as a function of applied field along the principal crystallographic axes. A magnetic material will therefore change its dimension when magnetized.

The inverse affect or the change of magnetization with stress also occurs. A uniaxial stress can produce a unique easy axis of magnetization if the stress is sufficient to overcome all other anisotropies.

2.3.3 Shape Anisotropy The third type of anisotropy is due to the shape of a mineral grain. A magnetized body will produce magnetic charges or poles at the surface. This surface charge distribution, acting in isolation, is itself another source of a magnetic field, called the demagnetizing field. It is called the demagnetizing field because it acts in opposition to the magnetization that produces it.

For example, in a long thin needle shaped grain, the demagnetizing field will be less if the magnetization is along the long axis than if is along one of the short axes. This produces an easy axis of magnetization along the long axis. A sphere, on the other hand,

17 has no shape anisotropy. The magnitude of shape anisotropy is dependent on the saturation magnetization.

2.4 Magnetic Domains The microscopic ordering of electron spins characteristic of ferromagnetic materials leads to the formation of regions of magnetic alignment called domains. Within each of which the local magnetization is saturated but not necessarily parallel. The main implication of the domains is that there is already a high degree of magnetization in ferromagnetic materials within individual domains, but that in the absence of external magnetic fields those domains are randomly oriented. A modest applied magnetic field can cause a larger degree of alignment of the magnetic moments with the external field, giving a large multiplication of the applied field. The boundary region between domains is called domain wall. Schematic depiction of domains is shown in Figure 2-10.

Figure 2-10: Schematic depiction of domains in a ferromagnetic or ferrimagnetic material; arrows represent atomic magnetic dipoles. Within each domain, all dipoles are aligned, whereas the direction of alignment varies from one domain to another. [MuonRay 14]

Domain walls are interfaces between regions in which the magnetization has different directions. Within the wall, the magnetization must change direction from that in one domain to that in the other domain. This is shown in Figure 2-11. Domain walls have a finite width that is determined principally by exchange and magnetocrystalline energy.

Figure 2-11: The gradual change in magnetic dipole orientation across a domain wall [Kingery 76]. The magnetic behavior can be subdivided on the basis of grain size, as shown in Figure

2-12, into four ranges

1. SPM: superparamagnetic 2. SD: single domain 3. PSD: pseudo-single domain 4. MD: multidomain

Figure 2-12: Grain size and magnetic domain [Minnesota 15] 19

The maximum coercivity for a given material occurs within its SD range. For larger grain sizes, coercivity decreases as the grain subdivides into domains. For smaller grain sizes, coercivity again decreases, but this time due to the randomizing effects of thermal energy.

Domains constitute a fundamental concept in magnetism. A ferro- or ferrimagnetic material may be generally defined as one that possesses a spontaneous magnetization, Ms, dependent on temperature, but only slightly dependent on applied field. The theory of ferromagnetism, based on electronic exchange forces, predicts the magnitude of Ms, but says nothing about the direction of Ms. Experimentally, it is observed that for a homogeneous specimen at constant temperature, the magnitude of Ms is uniform but the direction of Ms is in general not uniform from one region to another

(on a scale of microns to millimeters). Uniformity of direction is attained only by applying a large enough field to drive the domains out of the sample, or by reducing the particle's dimensions to small enough size to prevent domain wall formation.

Domains are formed for the following reason. Consider a large single crystal.

Suppose it is uniformly magnetized, and hence a single domain. Surface charges will form on the ends due to the magnetization and are themselves a second source of a magnetic field (the demagnetizing field). The energy associated with the surface charge distribution is called the magnetostatic energy. It is just the volume integral of the field over all space. The magnetostatic energy can be approximately halved if the magnetization splits into two domains magnetized in opposite directions. This brings (+) and (-) charges closer together, thus decreasing the spatial extent of the demagnetizing field as shown in Figure 2-13. This subdivision into more and more domains cannot

20 continue indefinitely because the transition region between domains (called a domain wall) requires energy to be produced and maintained. Eventually an equilibrium number of domains will be reached for a given particle size. In other words, the introduction of a domain raises the overall energy of the system, therefore the division into domains only continues while the reduction in magnetostatic energy is greater than the energy required to form the domain wall. The energy associated with a domain wall is proportional to its area.

Figure 2-13: Schematic illustration of the break-up of magnetization into domains: (a) single domain; (b) two domains; (c) four domains; (d) closure domains. [Birmingham 15]

The schematic representation of the domain wall, shown in Figure 2-14, illustrates that the dipole moments of the atoms within the wall are not pointing in the easy direction of magnetization and hence are in a higher energy state. In addition, the atomic dipoles within the wall are not at 180o to each other and so the exchange energy is also raised within the wall. Therefore, the domain wall energy is an intrinsic property of a material depending on the degree of magnetocrystalline anisotropy and the strength of the exchange interaction between neighboring atoms. The thickness of the wall will also vary in relation to these parameters, as strong magnetocrystalline anisotropy will favor a narrow wall, whereas a strong exchange interaction will favor a wider wall.

Figure 2-14: Schematic representation of a 180° domain wall [Birmingham 15]. If a domain wall in which the magnetization changes by 180° is considered, the change in magnetization within the wall can be gradual as in Figure 2-15a or abrupt as in

Figure 2-15b.

Figure 2-15: Domain wall thickness [Minnesota 15] The exchange energy acts to keep spins parallel and can be kept small if the 180° rotation takes place gradually, over many atomic units. Therefore, the exchange energy is small in

(a) but large in (b). However, the spins within the wall are no longer aligned along an easy axis of magnetization. This produces an anisotropy energy, which is high in (a) but low in (b). The exchange energy tends to make the wall as wide as possible whereas the anisotropy tends to make the wall as thin as possible. As a result of this competition

22 between exchange and anisotropy energies, the domain wall has a finite width and surface energy.

Therefore, a minimum energy can be achieved with a specific number of domains within a specimen. This number of domains will depend on the size and shape of the sample (which will affect the magnetostatic energy) and the intrinsic magnetic properties of the material (which will affect the magnetostatic energy and the domain wall energy).

The interplay between long range and short range effects results in the domain states being grain-size dependent. In addition, the number of domains for a given grain size depends on the magnitudes of the exchange, magnetocrystalline, and saturation magnetization. These constants are dependent on temperature as well as composition.

Hence domain states in different magnetic material will have different grain size dependence. The domain states will also vary with temperature for a single grain size.

However, the larger the grain size the more domains it contains.

2.4.1 Single Domain (SD)

As the grain size decreases, a critical size will be reached where the grain can no longer accommodate a wall. Below this critical size, the grain contains a single domain

(SD). A SD grain is uniformly magnetized to its saturation magnetization.

The magnetization of a MD grain can be changed by translating the domain wall, an energetically easy process, which can be accomplished in relatively low fields. Thus

MD grains are magnetically soft with low values of coercivities (Hc) and remanence (Mr).

However, the only way to change the magnetization of a SD grain is to rotate the magnetization, an energetically difficult process. Thus, SD grains are magnetically hard and have high coercivities (Hc) and remanence (Mr).

The critical size for SD behavior depends on several factors including, the saturation magnetization and the shape of the grain. Most estimates of the SD-MD transition size are based on theoretical calculations.

2.4.2 Pseudo-Single Domain (PSD) The distinction between SD and MD is straightforward. However, small MD grains exhibit a mixture of SD-like (high remanence) and MD-like (low coercivity) behavior. For example in magnetite, this behavior occurs in the size range between 0.1-

20 µm.

2.4.3 Superparamagnetism (SPM) As particle size continues to decrease within the SD range, another critical threshold is reached, at which remanence and coercivity go to zero. When this happens, the grain becomes superparamagnetic.

A single domain particle of volume v has a uniform magnetization directed along the easy axis of magnetization. If v is small enough, or the temperature is high enough, thermal energy (kT) will be sufficient to overcome the anisotropy energy separating the

(+) and (-) magnetization states and cause a spontaneous reversal of magnetization.

For superparamagnetic particles, the net magnetic moment in zero field and at

T>0K, will average to zero. In an applied field, there will be a net statistical alignment of magnetic moments. This is analogous to paramagnetism, except now the magnetic moment is not that of a single atom, but to a SD particle containing 105 atoms. Hence, the term superparamagnetism, which denotes a much higher susceptibility value than that for simple paramagnetism.

Normally, any ferromagnetic or ferrimagnetic material undergoes a transition to a paramagnetic state above its Curie temperature. Superparamagnetism is different from this standard transition since it occurs below the Curie temperature of the material.

Superparamagnetism occurs in nanoparticles which are single-domain, i.e. composed of a single magnetic domain. This is possible when their diameter is below 3–50 nm, depending on the materials. In this condition, it is considered that the magnetization of the nanoparticles is a single giant magnetic moment, sum of all the individual magnetic moments carried by the atoms of the nanoparticle.

Because of the nanoparticle’s magnetic anisotropy, the magnetic moment has usually only two stable orientations antiparallel to each other, separated by an energy barrier. The stable orientations define the nanoparticle’s so called “easy axis”. At finite temperature, there is a finite probability for the magnetization to flip and reverse its direction. The mean time between two flips is called the Néel relaxation time τN. In particular, the Néel relaxation time is an exponential function of the grain volume, which explains why the flipping probability becomes rapidly negligible for bulk materials or large nanoparticles.

In response to a change in the applied field or temperature, an ensemble of SPM particles will approach an equilibrium value of magnetization with a characteristic relaxation time, first derived by Néel. The relaxation time is proportional to the probability of transversing the energy barrier (EB) produced by the uniaxial anisotropy. In the presence of an external field the Néel relaxation time is

풉 −풗푴 [ퟏ− 풆]ퟐ −푬 −풌 풗 풔 푯 ퟏ ( 푩) ( 풖 ) ( 풄 ) = 풇ퟎ풆 풌푻 = 풇ퟎ풆 풌푻 = 풇ퟎ풆 ퟐ풌푻 (2-3) 훕푵 where

25 f0: Ferromagnetic resonance frequency in the demagnetization field (of order 1 GHz)

EB: Energy barrier to moment reversal k: Boltzmann constant

T: Absolute temperature

Ku: anisotropy constant v: Particle volume

Ms: Saturation magnetization

he: External field

Hc: Coercivity If the magnetization of a single superparamagnetic nanoparticle is measured and

τm is defined as the measurement time then If τm>>τN, the nanoparticle magnetization will flip several times during the measurement, then the measured magnetization will average to zero. If τm<<τN, the magnetization will not flip during the measurement, so the measured magnetization will be what the instantaneous magnetization was at the beginning of the measurement. In the former case, the nanoparticle will appear to be in the superparamagnetic state whereas in the latter case it will appear to be “blocked” in its initial state. The state of the nanoparticle (superparamagnetic or blocked) depends on the measurement time.

In other words, grains having τN much less than a typical experimental time τm

(τm>>τN) will reach equilibrium from any initial magnetic state during time τm and will exhibit no remanence (superparamagnetic-Unblocked). In contrast, grains with τN much greater than experimental time τm (τm<<τN) will preserve the initial state after time τm and

26 their magnetization is effectively blocked. A transition between superparamagnetism and blocked state occurs when τm=τN. The blocking equation is

풉풆 ퟐ ퟐ풌푻[풍풏훕푵풇ퟎ] 풗푯풄(ퟏ − ) = (2-4) 푯풄 푴풔 In several experiments, the measurement time is kept constant but the temperature is varied, so the transition between superparamagnetism and blocked state is seen as a function of the temperature. The temperature for which τm=τN is called the blocking temperature (TB):

풌풖풗 푻푩 = (2-5) 풌풍풏(훕푵풇ퟎ) The exponential nature of the relaxation time on v and T makes it possible to define a blocking temperature, TB (at constant volume), or blocking volume vB, (at constant temperature) at which the magnetization goes from an unstable condition (τm>>τN)

(Superparamagneic-Unblocked) to a stable condition (τm<<τN) (Blocked).

Blocked Superparamagnetic Paramagnetic

0 TB Tc T

The blocking temperature corresponds to the transition under cooling from the superparamagnetic state to the blocking state, where the magnetic moments of the particles stabilize in a definite direction due to impossibility of thermal agitation energy overcoming the potential barrier created by the magnetic anisotropy energy of the superparamagnetic particle.

Above the blocking temperature (TB), both ferromagnetic and ferrimagnetic nanoparticles exhibit superparamagnetic behavior manifested by rapid random magnetic nanoparticle (MNP) magnetization reversals leading to a zero time-average magnetic moment. The value of TB, associated with the energy barrier, depends on the

27 characteristic measuring time, which can vary from 100 to 10−8 s. The magnetic behavior arises from the relative difference between the measuring time and the relaxation time. If the measuring time is greater than the relaxation time, the nanoparticles are considered to be in the superparamagnetic regime; if, however, the measuring time is less than the relaxation time, the nanoparticles are in a “blocked” (ferromagnetic) regime.

Experimentally, the value of TB typically corresponds to the “merging point” of the zero-field cooled (ZFC) and field-cooled (FC) magnetization curves. In ZFC measurements, a sample is first cooled to low temperature (e.g., 2–10 K) in the absence of an external field (zero-field). At this point, a small external field is applied, and the temperature is gradually increased while measuring the sample magnetization as a function of temperature. In FC measurements, the process is repeated, but the sample is cooled in the presence of an external field and the same external field is applied as the temperature is increased. The point where the two curves merge is the irreversibility temperature, Tirr, and the maximum on the ZFC curve is the blocking temperature, TB, as shown in Figure 2-16.

Figure 2-16: Experimental strategy for estimating the blocking temperature of magnetic nanoparticles. As shown by [Jeong 07] in Figure 2-17, in the single domain regime, the coercivity can follow either the solid curve for non-interacting particles or the dashed line

28 for particles that have coupling between them. The coercivity falls to zero for superparamagnetic colloidal particles.

Figure 2-17: Schematic illustrating the dependence of magnetic coercivity on particle size. [Jeong 07] 2.4.3.1 MCE in Superparamagnetic Systems

In works by [McMichael 92], [Shull 93] and [Bennett 94] a superparamagnetic system was taken to consist of monodisperesed and noninteracting magnetic clusters

(particles) uniformly dispersed in a nonmagnetic matrix, as shown in Figure 2-18.

Figure 2-18: Schematic of magnetic spins in (a) paramagnetic and (b) superparamagnetic nanomaterial. The circles in (b) represent magnetic clusters. Each cluster contains a certain number of magnetic atoms. The entropy change of a magnetic system can be calculated from the thermodynamic Maxwell equation,

흏푺 흏푴 ( ) = ( ) (2-6) 흏푯 푻 흏푻 푯

The magnetic entropy change under magnetization in magnetic field from H1 to H2 in the classical limit can be calculated by,

푯ퟐ 흏푴 푵흁ퟐ ∆(푯)ퟐ 횫퐒 = ∫ ( ) 풅푯 = − ퟐ (2-7) 푯ퟏ 흏푻 푯 ퟔ풌 푻 for paramagnetic; and

푵흁ퟐ ∆(푯)ퟐ 횫퐒퐌 = − ퟐ (2-8) ퟔ풌 (푻−푻푪) for a ferromagnet at T > TC, where N is the number of magnetic moments, μ is the size of magnetic moment, and k is Boltzmann’s constant.

In order to avoid the integration specified above, the magnetic entropy of N independent magnetic moments m, in a field H, at temperature T, is calculated directly through the partition function Z, assuming classical behavior of the moments:

ퟏ 푵 풁 = [ퟒ흅 퐬퐢퐧퐡 (풙)] (2-9) 풙

푚퐻 Where 푥 = . A more general consideration yields the following expression for ΔSM 푘푇 caused by magnetic field increase from zero to H in the classical limit:

퐬퐢퐧퐡 풙 횫퐒 = 퐒(퐓, 퐇) − 퐒(퐓, ퟎ) = 푵풌 [ퟏ − 풙퐜퐨퐭퐡 풙 + 퐥퐧 ] (2-10) 퐌 풙 For weak fields and high temperatures (푥 ≪ 1)

푵흁ퟐ 푯ퟐ 횫퐒 = − (2-11) 퐌 ퟔ풌 푻ퟐ

ΔSM and consequently the MCE can be made larger if μ is made larger and N is simultaneously made smaller (to keep the saturation magnetic moment M0=Nμ constant), because of the squared dependence of ΔSM on μ and only linear dependence on N. for superparamagnet it can be written as

푵 ퟐ 풏(( )흁) 푯ퟐ 횫퐒 = − 풏 (2-12) 퐌 ퟔ풌 푻ퟐ

Where n is the number of particles (cluster) and (N/n)μ=μc is the magnetic moment of the

푁 2 2 particle. The factor 푛(( ⁄푛)휇) in equation (2-12) may be much larger than 푁휇 in equation (2-11).

If there is some interaction between clusters (dipole and/or exchange interaction) the system displays behavior similar to that of ferromagnets, with an effective interaction temperature TI (a.k.a. blocking temperature), analogous to the Curie temperature TC.

Morup [Morup 93] called the system “superferromagnet”. Above TI the material is superparamagnetic and below TI long-range order between the clusters occurs. In the superparamagnetic region, ΔSM induced by the field change from 0 to H can be obtained by,

푵 풏(( )흁)ퟐ ퟐ 풏 푯 횫퐒퐌 = − ퟐ (2-13) ퟔ풌 (푻−푻푰)

2 퐼 퐼푀 TI was defined as 푇 = where I is magnetization and IM is the mean magnetic 퐼 3푘 coupling constant for interaction of neighboring particles. According to Shao [Shao 96a],

TI should be less than the TC of the particles material since IM and I have reduced values

푁 2 in this state. Analogous to the superparamagnetic case, the factor 푛(( ⁄푛)휇) in

2 equation (2-13) may become larger than 푁휇 in equation (2-8). This implies that ΔSM above TI in a system with magnetically interacting clusters can become substantially larger than that in a ferromagnet above TC.

The blocking temperature varies with the size of the ferromagnetically-aligned particles. As shown [McMichael 92], the magnetocaloric effect of a ferromagnetic material as a function of temperature, T, and magnetic field, H, is

ퟏ 푵흁ퟐ 푯푻 ∆푻풇풆풓풓풐 = ( ) 흁ퟎ푽푴 ( ) ퟐ 풅푯 (2-14) 푪푯 ퟑ풌 (푻−푻푪) the magnetocaloric effect above the blocking temperature would be expected to be

푵 풏( )ퟐ흁ퟐ ퟏ 풏 푯푻 ∆푻풏풂풏풐 = ( ) 흁ퟎ푽푴 ( ) ퟐ 풅푯 (2-15) 푪푯 ퟑ풌 (푻−푻푩) there will be N identical atoms, n ferromagnetic regions (clusters), each with an

푁 푁 푁2 independent cluster magnetic moment, 휇 = ( )휇. Since 푛( )2 = , is much larger 푐 푛 푛 푛 than N (Reminder: n is much smaller than N), ΔTNano>>ΔTFerro. Consequently, with superparamagnetic nanomaterials as the refrigerant, magnetic cooling would be practical.

2.4.4 Hysteresis Properties of SD, PSD, and MD Particles The various hysteresis parameters (as shown in Figure 2-19) are not solely intrinsic properties but are dependent on grain size, domain state, stresses, and temperature. Coercivity of remanence (Hr) is the reverse field which, when applied and then removed, reduces the saturation remanence to zero. It is always larger than the coercive force.

Figure 2-19: Field dependent magnetization (Hysteresis loop) [Csanyi 16] The shape of a hysteresis loop is determined partly by the domain state. Loops for

SD materials are typically wider than loops for MD materials. This is just a reflection of the higher coercivity and remanence in SD material. The hysteresis loop parameters,

Mr/Ms and Hr/Hc, are very useful in distinguishing domain state. For a SD material, typical values for hysteresis parameters are:

푴풓 푯풓 > ퟎ. ퟓ , = ퟏ − ퟐ (2-16) 푴풔 푯풄

For a MD material, these parameters are typically:

푴풓 푯풓 < ퟎ. ퟏ , > ퟒ (2-17) 푴풔 푯풄 And for a PSD material they are

푴풓 푯풓 < ퟎ. ퟏ − ퟎ. ퟓ , = ퟐ − ퟒ (2-18) 푴풔 푯풄 SPM particles exhibit no remanence or coercivity and have high saturation magnetization (Ms). The shape of the hysteresis loop is thus extremely thin. SPM grains show a very steep initial rise in magnetization with field and then a more gradual increase to saturation. However, in a mixture of mostly SPM grains but with some SD or MD grains, typical values for hysteresis parameters are:

푴풓 푯풓 ≪ ퟎ. ퟎퟏ , > ퟏퟎ (2-19) 푴풔 푯풄

Also temperature can affect the domain properties. Grains that are SPM at room temperature can become blocked and SD at low temperatures. Figure 2-20 illustrates field-dependent magnetization behavior of different magnetic material classes.

Figure 2-20: Field dependent magnetization behavior of ferromagnetic, paramagnetic, superparamagnetic, and diamagnetic material Coercivity as a function of particle size and its related field-dependent magnetization is shown in Figure 2-21.

Figure 2-21: Coercivity vs. particle size [Fang 16]

In summary, the Mr/Ms and Hr/Hc diagram is a useful indicator of domain states as depicted in Figure 2-22.

Figure 2-22: Mr/Ms vs. Hr/Hc diagram and magnetic domain [Minnesota 15].

2.5 Magnetic Susceptibility Magnetic susceptibility is a quantitative measure of the extent to which a material may be magnetized in relation to a given applied magnetic field. The magnetic susceptibility of a material, χm, is equal to the ratio of the magnetization M within the

푀 material to the applied magnetic field strength H, or 휒 = . This ratio, strictly 푚 퐻 speaking, is the volume susceptibility, because magnetization essentially involves a certain measure of magnetism (dipole moment) per unit volume. The magnetic induction

B is related to H by the relationship

퐁 = µ (퐇 + 퐌) = µퟎ(ퟏ + 훘퐦)퐇 = µ퐇 (2-20) where μ0 is the magnetic constant, and (1+ χm) is the relative permeability of the material.

Thus the volume magnetic susceptibility χm and the magnetic permeability µ are related by the following formula:

µ = µퟎ(ퟏ + 흌풎) (2-21) Magnetic materials may be classified as diamagnetic, paramagnetic, or ferromagnetic on the basis of their susceptibilities. Diamagnetic materials, such as bismuth, when placed in an external magnetic field, partly expel the external field from within themselves. Diamagnetic materials are characterized by constant, small negative susceptibilities, only slightly affected by changes in temperature.

Paramagnetic materials, such as platinum, increase a magnetic field in which they are placed because their atoms have small magnetic dipole moments that partly line up with the external field. Paramagnetic materials have constant, small positive susceptibilities, less than 1/1,000 at room temperature, which means that the enhancement of the magnetic field caused by the alignment of magnetic dipoles is relatively small compared with the applied field. Paramagnetic susceptibility is inversely proportional to the value of the absolute temperature. Temperature increases cause greater thermal vibration of atoms, which interferes with alignment of magnetic dipoles.

Ferromagnetic materials, such as iron and cobalt, do not have constant susceptibilities; the magnetization is not usually proportional to the applied field strength.

The reason that there is no one-to-one correspondence between M and H is because of magnetic hysteresis. Measured ferromagnetic susceptibilities have relatively large positive values, sometimes in excess of 1,000. Thus, within ferromagnetic materials, the magnetization may be more than 1,000 times larger than the external magnetizing field,

35 because such materials are composed of highly magnetized clusters of atomic magnets

(ferromagnetic domains) that are more easily lined up by the external field.

Ferromagnetic and ferrimagnetic compounds also show a decrease in magnetic susceptibility with increasing temperature. However, a plot of magnetic susceptibility vs. temperature shows a different line shape for these compounds than for paramagnetic compounds. A rough sketch of the shapes of these curves is shown in Figure 2-23.

Figure 2-23: Magnetic susceptibility vs. temperature. Above a critical temperature (Curie point) the ferromagnetic and ferrimagnetic material displays paramagnetic behavior and below the Curie point the material displays magnetic properties. For antiferromagnetism, above the Neel point the material displays paramagnetic behavior. Below the Neel point the material displays weak magnetic properties which at lower and lower temperatures can become essentially diamagnetic.

A small fraction of SPM particles can contribute significantly to the room- temperature susceptibility of SD or MD grains. SPM susceptibility can be 10-100 times that of an equivalent amount of SD grains.

2.5.1 Frequency Dependence of Susceptibility Susceptibility can be measured as a function frequency of the applied oscillating field. Superparamagnetic behavior depends on the time scale of observation (the choice

36 of τ) so grains may behave superparamagnetically at one frequency, but not at another.

Frequency dependent susceptibility χfd can therefore be used to constrain grain size / domain state of magnetic materials. SPM grains show the most pronounced frequency dependence of low-field susceptibility.

2.6 Magnetocaloric effect

The magnetocaloric effect is defined as the thermal response of a magnetic material to an applied magnetic field and is apparent as a change in its temperature.

Magnetic cooling and heating effects are possible because a magnetic solid, which is a collection of atomic magnetic dipoles, can exist in various states of order and disorder. If the atomic dipoles are randomly oriented, then the magnetic entropy, or degree of disorder, has its maximum possible value. If by lowering the temperature or by applying a strong magnetic field or both, we bring the dipoles to the maximum possible degree of alignment, then the magnetic disorder or entropy is minimized [Brown 81]. Thus the externally controlled parameter, field strength, has the same kind of influence on the thermodynamic state of a magnetic solid that pressure has on a gas.

Magnetocaloric effect (MCE), or adiabatic temperature change, which is detected as the heating or the cooling of magnetic materials due to a varying magnetic field, was originally discovered [Pecharsky 99a] in iron by Warburg. The MCE is intrinsic to all magnetic materials and is due to the coupling of magnetic sub lattice with the magnetic field, which changes the magnetic part of the entropy of a solid. Similar to the compression of a gas, the isothermal magnetizing of a magnetocaloric material reduces the entropy and, in the reverse process, demagnetizing (which is similar to the expansion of a gas) restores the zero-field magnetic entropy of a system. In the MCE, when a

37 volume of material containing individual magnetons, initially oriented so that no net magnetization is present, experiences an applied field, the magnetons tend to line up with the external field. In adiabatic systems, the energy of magnetization is transferred to the lattice as thermal energy and the material becomes heated [Hull 89]. When the applied field is removed from the aligned system, spin-lattice coupling transfers thermal energy from lattice vibration to the randomization of the magnetons and, thus, cools the lattice.

This effect is greatest near the Curie temperature, TC, where the ordering influence of the ferromagnetic exchange interaction and the disordering effect of thermal agitations are in approximate balance. At higher temperatures the material responds only paramagnetically, and at significantly lower temperatures the spontaneous magnetization approaches saturation, such that applying an external field has little effect on the magnetic order.

Study of the MCE is of particular interest from two points of view. First, it is a research technique for phase transitions in various magnets, and second, it is a means for investigating materials that show promise as working substances for the AMR system.

2.7 Magnetic entropy

The entropy change associated with temperature and magnetic field can be considered in three respects: lattice entropy, electronic entropy, and magnetic entropy

[Chen 91]. To evaluate the performance of a magnetic refrigeration system, all three entropy components must be considered. These three entropies are defined as follows.

 Lattice entropy: the entropy associated with the vibration of the molecules, which

is also a function of temperature.

 Electronic entropy: the kinetic entropy of the electrons. It is a function of

temperature.

 Magnetic entropy: the entropy change caused by the spin of the molecules when

the material is magnetized under the magnetic field. It involves the strength of the

magnetic field, material properties, temperature, and Curie point.

2.8 Classifications of phase transition

The magnetocaloric effect is an adiabatic process that occurs without an exchange of heat with the surrounding environment taking place. Consequently, when an applied magnetic field is cut off, the entropy associated with the magnetic moments of a material increases and, in turn, its lattice entropy must decrease, resulting in a drop in temperature of the material. This effect is largest close to the transition temperature of ferromagnets, where the magnitude of the magnetization changes most rapidly with temperature.

Gadolinium has been widely studied as a magnetocaloric material because it is ferromagnetic at room temperature and has a sizeable magnetic moment. However, as for all materials undergoing continuous (or in the language of thermodynamics, second order) phase transitions, its magnetocaloric effect is rather modest: the governing parameter is the change of the magnetization with temperature, and this is limited by the fundamental fact that the magnetization decays continuously to zero as the transition temperature is approached (Figure 2-24a).

The effect is significantly enhanced in materials undergoing discontinuous (or first order) phase transitions. Gd5Si2Ge2 [Pecharsky 97] was the first of a series of gadolinium-based materials found to display a first-order magnetic phase transition and, as a result of the abrupt jump in the magnetization near the transition temperature (Figure

2-24b), a giant magnetocaloric effect.

Typically the magnetization jump at first-order phase transitions is accompanied by a change in the lattice parameters, which may cause a structural transition. This magnetoelastic coupling complicates matters, and makes the indirect derivation of the magnetocaloric effect unreliable [Nordblad 13]: the adiabatic temperature change associated with the applied magnetic field is not merely a function of the magnetization.

A drastic example of this ambiguity is given by the Heusler alloy NiMnIn(Co) [Liu 12],

[Fähler 12], in which the magnetization increases on heating as a result of a structural transition, leading to an inverse magnetocaloric effect. Nevertheless, direct measurements of the magnetocaloric adiabatic temperature change are possible, and this structural contribution can be used to enhance it.

Figure 2-24: Phase diagrams describing the change in magnetization (M) as a function of temperature (T). a, Second-order phase transition, whereby M changes continuously with T up until the critical point (Tc). b, First-order phase transition whereby M changes discontinuously at Tc [Nordblad 13].

Materials undergoing the first-order magnetostructural phase transition, exhibit a large and narrow peak magnetic entropy change accompanying a magnetostructural phase transition, but this is often accompanied by undesirable thermal hysteresis [Provenzano

04], [Krenke 05]. Materials with a second-order magnetic phase transition usually show a lower peak entropy change but with a broader peak, which results in an enhanced refrigerant capacity [Skorvanek 04], [Franco 06a]. Moreover, these materials present

40 reduced hysteresis loss and tunable Curie temperatures [Franco 06b], [Ipus 09]. As a result materials that undergo a second-order magnetic transition are very favorable to be used in magnetic refrigeration applications.

The development of order in the system at the transition temperature can be gradual or abrupt. This leads to a convenient classification of phase transitions into two types, namely, discontinuous and continues. Second-order transition is a continuous transition. In continuous transition, entropy changes continuously, and hence the growth of order below TC is also continuous. There is no latent heat involved in a continuous transition. The paramagnetic-to-ferromagnetic transition in magnetic materials is an example of such a transition. First-order transitions are also called discontinuous transition. Discontinuous transition involves a discontinuous change in the entropy at the transition temperature. This is characterized by the amount of latent heat that must be extracted from the material for it to be ordered.

2.9 External applied magnetic field

In a magnetic refrigeration system, change in magnetic field causes the MCE. A cycle can be realized by moving either the magnetic field or the refrigerant material.

Basic methods of moving the magnetic field include: physically moving the magnet that produces the field; moving a shield between the magnet and the magnetic material; dissipation the field through resistance heating; and switching the magnetic field to another indicator by means of an electric circuit. Methods of moving the magnetic material include: reciprocating motion of a piston of magnetic material in and out of a constant field; and continuous rotation of a disk, with a portion of the disk passing through the field.

Based on these approaches, systems have been designed to utilize the change of the magnetic field in magnetic refrigeration system. A summary of methods that have been used in performing magnetic field change in various magnetic refrigeration systems is as follows. Solid bed can be in a reciprocating movement into and out of a constant field magnet [Kral 00], [Hirano 02] immersed in a column of fluid and moving from high field to low field, moved with respect to the superconducting magnetic field [DeGregoria

90], and be exposed to a constant field while a cylindrical wheel rotates the material in and out of a constant field magnet [Bohigas 00], [Mills 84], [Ingebretsen 01]. Also, systems have been designed in which the refrigerant material is permanently mounted and the magnetic field is charged rapidly. This field change can be based on changing current in a superconducting magnet [Jeong 92], [Green 88], [Blumenfeld 02], creating a quasipulse field by discharging a battery of capacitors into the solenoid having a large induction [Dankov 97], or moving the superconducting magnets with constant field through a fixed solid bed [Zimm 92], [DeGregoria 92].

In all of these approaches, motion generates irreversible losses, the minimization of which plays a major role in determining the viability of a given approach. These losses can be in the form of eddy currents and hysteresis or through friction.

2.10 Magneto-thermodynamics

Altering the thermodynamic state of a magnetic material by performing heat and magnetic work processes is known as the magnetocaloric effect (depicted in Figure 2-25).

The MCE is essentially the application of the first and second laws of thermodynamics to a magnetic system. Consider that a magnetic refrigerant system consists of a magnetocaloric material that undergoes a magnetic work process as a result of changing

42 magnetic field and a reversible heat processes as shown in the following figure.

Figure 2-25: Magnetization work and heat process in a control volume bed of solid magnetocaloric material. If a control volume, V is drawn around the system, the first law of thermodynamics relates the change in the internal energy, U of the solid material to the work performed on the magnetocaloric material, W and the heat transferred through the control volume, Q,

푑푈 = 푑푄 − 푑푊 (2-22)

The reversible work on the control volume can be in the form of mechanical, chemical, and magnetic work process. These three forms of work are expanded in

Equation 2-23,

dW = dWmech + dWchem + dWmag (2-23)

푑푊 = 푃푑푉 − ∑ 휇푖푑푁푖 − 푉휇0퐻푑푀 (2-24)

th where P is the pressure, Ni is the chemical potential of i species, μ0 is the magnetic permeability of free space, H is magnetic field intensity, and M is magnetization per unit volume.

With constant volume and in the absence of chemical reaction, Equation 2-24 reduces to

풅푾 = −푽흁ퟎ푯풅푴 (2-25) Substituting this relation in Equation 2.22 results

풅푼 = 풅푸 + 푽흁ퟎ푯풅푴 (2-26) An entropy balance on the control volume for the reversible process by applying the second law of thermodynamic yields

dQ dS = (2-27) T where dS is the differential change in the total entropy of the solid material at temperature T, that heat transferred from the material. Substituting Equation 2-27 in 2-26 results the combined first and second law in relation to the reversible heat and magnetic work process on the control volume,

풅푼 = 푻풅푺 + 푽흁ퟎ푯풅푴 (2-28) 2.11 Solid-state cooling with caloric material

In a vapor compression cycle, as seen in Figure 2-26a, pressure converts the refrigerant gas to a liquid state and latent heat associated with the phase transition is unleashed. When the pressure is released and the refrigerant changes back to the gaseous state, the latent heat is reabsorbed, drawn in from the environment to be cooled.

However, the environmental impact of the high global-warming potential (GWP) of vapor compression refrigerants based on hydrofluorocarbons and hydrochlorofluorocarbons, as well as the low cooling efficiency of the conventional cooling technology calls for an alternative energy efficient and environmentally friendly cooling technology.

Caloric-material cooling cycles use magnetic, electric or stress fields to reversibly change the entropy, as shown in Figure 2-26b. If the change in the entropy is caused by changing a stress field, it is called elastocaloric. If the change is caused by an electric field, it is electrocaloric, and if the change happens due to changing the magnetic field, it is magnetocaloric.

Figure 2-26: Cooling cycles. (a) The conventional vapor compression cycle uses a liquid–gas phase transition. (b) Caloric-material cooling cycles use magnetic (H), electric (E), or stress (σ) fields to reversibly change the entropy (shown as the vector arrays in gray, red, and blue) of the respective refrigerant material. [Takeuchi 15] To compare cooling devices, one can compare their overall system efficiency measured in coefficient of performance (COP). System efficiency can be expressed as the ratio of the delivered cooling energy per cycle to the total input wattage for the machine’s operation. The current state-of-the-art commercial vapor compression cycle has a COP of about 3.6 [Takeuchi 15]. Among the three classes of caloric materials discussed here, magnetocaloric materials have the largest COP, a result of the large entropy change that is attainable by a magnetic field.

2.12 Comparison between magnetic refrigeration and conventional refrigeration system

The magnetic cycles are generally composed of the process of magnetization and

45 demagnetization, in which heat is discharged or absorbed in four steps as depicted by

Figure 2-27. From thermodynamic point of view, the magnetic cooling can be realized by: Carnot, Stirling, Ericsson and Brayton, where the Ericsson and Brayton cycles are believed to be the most suitable for such medium or room temperature cooling. Such cycles are predisposed to yield high cooling efficiency of the magnetic materials [Rafik,

12], [Bouchekara 08].

(a) (b)

Step 1: Magnetize Step 1: Compress the solid thereby gas thereby increasing its increasing its temperature temperature

Step 2: Remove Step 2: Remove Heat with a Heat with a Cooling fluid. Cooling fluid.

Step 3: Demagnetize Step 3: Expand and and cool solid. cool gas.

Step 4: Absorb Step 4: Absorb heat from cooling heat from cooling load. load.

Figure 2-27: Comparison between magnetic refrigeration and conventional refrigeration. Figure 2-27a shows the magnetic refrigeration cycle while Fig 2-24b shows the conventional gas compression process that is driven by continuously repeating the four different basic processes shown. The steps of the magnetic refrigeration process are analogous to those of the conventional refrigeration. By comparing (a) with (b) in Figure

2-27, one can see that the compression and expansion are replaced by adiabatic magnetization and demagnetization, respectively. These processes change the

46 temperature of the material and heat may be extracted and injected just as in the conventional process.

2.13 Active Magnetic Regeneration

The direct exploitation of the giant MCE around the room temperature is limited by the fact that existing MCE materials do not achieve high temperature differences

[Lebouc 05]. For example, a sample of gadolinium around room temperature produces an

MCE of approximately 10 K in a magnetic field of 5 T.

Since the gadolinium is considered as one of the best magnetocaloric materials currently available, the MCE corresponds to the absolute maximum value that can be obtained between the hot tank and cold tank. Thus it is obviously hard to imagine the exploitation of the MCE in most refrigeration applications [Rafik 12], [Engelbrecht 05].

This technical barrier has been overcome by the application of the Active

Magnetic Regenerative (AMR) [Engelbrecht 05]; [Lebouc 05]; [Tura 07]; [Barclay 82].

Regeneration in magnetic refrigeration systems allows the heat rejected by the network in any step of the cycle to be restored and returned to the network in another step in the same cycle [Yu 03]. Thus, the capacity used for cooling the network load can be used effectively to increase the actual change of entropy and the obtained temperature difference [Rafik 12], [Yu 03].

The regenerative bed consists of MCE material bed that initially has an equal temperature profile between the hot and cold end. The bed itself acts as a regenerator.

The different solid parts of the regenerator are connected by the fluid, so the heat does not need to be transferred between two solid parts separated, but on the same block.

Figure 2-28 shows the principle of an AMR cycles [Aprea 12]; the dashed line

47 represents the initial temperature profile of the bed in each process while the solid line represents the final temperature profile of that process. An AMR cycle consists of the four following processes: (1) bed magnetization; (2) iso-field cooling; (3) bed demagnetization; (4) iso-field heating.

Figure 2-28: Schematic view of an AMR cycles. Ti: initial temperature, Tf: final temperature, Tc: cold end temperature, Th: hot end temperature [Aprea 12]. Initially the porous regenerator bed is at a steady state condition with the hot heat exchanger at Th and the cold heat exchanger at Tc. In the magnetization process, the magnetic field in the bed is increased with no fluid flow, which causes the temperature of material to increase due to the magnetocaloric effect. The temperature of the magnetic material at the hot end of the bed rises above the hot heat exchange temperature Th. In the iso-field cooling process, with the high magnetic field, the fluid is blown from the cold end to the hot end of the bed. The magnetic material temperature decreases because the fluid absorbs heat from the bed and after expels heat at a temperature higher than Th in the hot heat exchanger. In the bed demagnetization the magnetic material temperature

48 decreases with no fluid flow. Finally, in the last step, with a zero field, the fluid is blown from the hot end to the cold end of the bed. The magnetic material temperature increases because the fluid expels heat to the bed and after absorbs heat at a temperature lower than

Tc in the cold heat exchanger, producing the cooling load.

Each particle of the bed undergoes a regenerative Brayton cycle and the entire bed undergoes a cascade Brayton cycle [Yu 03]. This cycle is repeated ‘n’ times and the ΔT generated is amplified at each cycle to reach the temperatures limits of hot and cold sources (steady state). This ΔT is higher than the adiabatic temperature change of refrigerant material (MCE). In addition, the regenerator bed can be achieved by superposing different materials of different composition to expand the temperature’s range of variation and thus to extend the utilization range of the system [Rafik 12].

2.14 Modeling of magnetization and demagnetization processes

During the process of magnetization or demagnetization in an AMR cycle, the magnetic field strength is changed to utilize the MCE of the refrigerant bed. In each half cycle of the inner magnet rotation, the magnetocaloric material experiences a change of field and as the result of the MCE heat is transferred in or out of the solid bed. During this process, the entropy of the solid material changes with time as a function of the applied field H and its temperature T,

s = s(H,T). (2-29)

Taking the exact differential from this equation results

흏푺 흏푺 풅푺 = ( ) 풅푻 + ( ) 풅푯 (2-30) 흏푻 푯 흏푯 푻 The specific heat at constant applied field for a magnetocaloric material is defined as

흏푺 푪 = 푻( ) (2-31) 푯 흏푻 푯

In this equation, the change in entropy vs. field strength at constant temperature is related to the magnetic field by applying the Maxwell relation (Appendix A)

흏푺 흏푴 ( ) = 흁 푽( ) (2-32) 흏푯 푻 ퟎ 흏푻 푯 By substituting Equations 2-31 and 2-32 in Equation 2-30, change in the entropy of the solid refrigerant during this process can be derived as

푪 흏푴 풅푺 = 푯 풅푻 + 흁 푽( ) 풅푯 (2-33) 푻 ퟎ 흏푻 푯 If we assume that magnetization or demagnetization processes are reversible adiabatic processes, i.e. no heat loss to the surroundings, based on the second law of thermodynamics the total change in the entropy of the system consists of the magnetocaloric solid refrigerant bed and the entrapped gas in the bed will be zero

(2-34) dStotal = (mds)solid + (mds)gas = 0.

In the porous bed of refrigerant solid with much higher density than the entrained gas, we can ignore the mass of the gas compared to the mass of solid bed. Based on this assumption Equation 2-34 results that change of the entropy of the solid refrigerant during magnetization or demagnetization steps is zero, ds =0

Therefore, Equation 2-33 can be simplified to

푻 흏푴 풅푻 = − 흁ퟎ푽( )푯풅푯 (2-35) 푪푯 흏푻 It should be noted that in this equation, Temperature (T), specific heat at constant applied

휕푀 field (C ), change in magnetic field with respect to temperature ( ) , and the magnetic H 휕푇 퐻 field strength (H) are functions of time and as the magnetic field is changed with time, these values change. The next chapter will discuss the methods that each of these terms can be evaluated.

Equation 2-35 has been reported [Bozorth 51], [Martin 74], [Vonsovslii 74] for physics of the magnetocaloric effect of a solid magnetocaloric material without considering the effect of the exchange gas that we ignored in Equation 2-34.

For a time increment of dt, Equation 2-35 can be written as

풅푻 푻 흏푴 풅푯 = − 흁ퟎ푽( )푯 (2-36) 풅풕 푪푯 흏푻 풅풕 Equation 2-37 shows the change in the temperature of magnetic refrigerant bed in the presence of a changing field. This first-order differential equation governing the magnetization and demagnetization steps in the process can be solved as an initial-value problem using Euler’s or Runge-Kutta methods. In other words integration of Equation 2-

36 can result in temperature of the solid bed at any desired time.

풕 푻 흏푴 풅푯 푻(풕) = 푻(ퟎ) − ∫ 흁ퟎ푽( )푯 풅풕 (2-37) ퟎ 푪푯 흏푻 풅풕 In order to solve Equation 2.37 the rate of change of magnetic field strength with time needs to be known. Our test bed is unique in design as a permanent adjustable-field rotating magnet generates the change in the magnetic field. Equation 2-38 shows the dependency of the magnetic field strength to time and the inner magnet rotational frequency, f.

푯 = ퟐ풄풐풔ퟐ(흅풇풕) (2-38) It should be noted that Equations 2-36 and 2-37 can evaluate the temperature of the magnetocaloric material, but due to the set up and presence of resistance between the pieces of the refrigerant bed and thermocouple, there is a difference between the multimeter-recorded temperature and the material actual temperature. This difference is commonly known as thermal lag and is proportional to the rate at which the temperature rises. Improper contact between the thermocouple and the surface of the material,

51 existence of oxidants layer such as gadolinium oxide on the surface of gadolinium turnings and presence of an exchange gas such as helium or air between the thermocouple and the surface of the gadolinium can cause this resistance in measuring temperature by thermocouple.

If TG is the temperature of the gadolinium, TT is the temperature of the thermocouple, and

G is the thermal conductivity between the gadolinium and the thermocouple, the rate of heat transfer between the two is given by

풅푸 = 푮(푻 − 푻 ) (2-39) 풅풕 푮 푻 The amount of the heat transferred to the temperature sensor is proportion to its heat capacity CT and rate of change of temperature in the sensor

풅푸 = 푪푻풅푻푻 (2-40) Combining Equations 2-39 and 2-40 results

풅푻푻 푪 = 푮(푻 − 푻 ) (2-41) 푻 풅풕 푮 푻 This first order differential equation can be solved for the recorded temperature of the thermocouple TT assuming the temperature of the solid refrigerant is a known value based on Equation 2-36. As mentioned previously thermal lag can be caused by various sources that contribute in thermal conductivity of the media between the thermocouple and the magnetocaloric material. One way to evaluate the thermal conductivity G is to match the calculated values for temperature to the experimental results.

Chapter 3 . Optimization of Magnetic Refrigerators by Tuning the Heat Transfer Medium Parameters and System’s Operating Conditions

Abstract: A new experimental test bed has been designed, built, and tested to evaluate the effect of the system’s parameters on a reciprocating Active Magnetic

Regenerator (AMR) near room temperature. Bulk gadolinium was used as the refrigerant; silicon oil as the heat transfer medium, and a magnetic field of 1.3 T was cycled. This study focuses on the methodology of single stage AMR operation conditions to get a high temperature span near room temperature. Herein, the main objective is not to report the absolute maximum attainable temperature span seen in an AMR system, but rather to find the system’s optimal operating conditions to reach that maximum span. The results of this research show that there is a optimal operating frequency, heat transfer fluid flow rate, flow duration, and displaced volume ratio in an AMR system. By optimizing these parameters the refrigeration performance increased by 24%. The optimized values are system dependent and need to be determined and measured for any AMR system by following the procedures that are introduced in this research. It is expected that such optimization will permit the design of a more efficient magnetic refrigeration system.

Aim of research: So far many groups have designed and built different magnetic refrigeration prototypes. However, they run their systems as if and not at an optimal point. In this research we have demonstrated experimentally that any magnetic refrigeration system can be optimized to get a higher temperature difference between the hot and cold side of the AMR.

3.1 Introduction

In contrast with conventional vapor-compression refrigerator systems that work based on compression and evaporation of gas, magnetic refrigeration systems work based on magnetizing and demagnetizing a magnetic material (refrigerant). Magnetic refrigeration exploits a property of magnetic materials called the magnetocaloric effect

(MCE): the temperature of ferromagnetic materials is observed to rise upon the application of a magnetic field and fall upon its removal. When a material is magnetized, its magnetic moments are aligned, leading to a reduction in its magnetic entropy. If this process is done adiabatically and reversibly, the total entropy is constant. Thus, a reduction in magnetic entropy is compensated by an increase in lattice entropy resulting in a temperature increase. MCE can be defined as adiabatic temperature change due to magnetization or demagnetization, or, alternatively, as an isothermal magnetic entropy change.

Magnetic refrigeration systems have many advantages compared to conventional refrigerators. They do not use hazardous and ozone-depleting chemicals, greenhouse gases, and are an environmentally friendly cooling technology. Magnetic refrigeration can be more energy efficient than convectional refrigerators. The cooling efficiency of magnetic refrigerators working with gadolinium has been shown to reach a theoretical limit of 60%, while the cooling efficiency of the best gas-compression refrigerators is approximately 40% [Bruck 05], [Gschneidner 05], [Yu 10], [Ghahremani 12].

The Active Magnetic Regenerator (AMR) cycle uses a heat transfer fluid to transport the heat generated or absorbed from MCE in the refrigerant to the hot and cold ends of an AMR device. The AMR cycle consists of four processes: magnetization, hot

54 blowing, demagnetization, and cold blowing. During magnetization, the temperature of the refrigerant increases, then fluid is pumped from the cold end to the hot end in order to absorb the magnetic work (hot blowing). The regenerator is then demagnetized, causing a decrease in temperature, and a cooling load is absorbed from the refrigerant by pumping fluid from the hot end across the regenerator toward the cold end (cold blowing). The four processes need not be discrete, and the fluid flow may coincide with magnetization and demagnetization depending on a system’s design.

With the push for the commercialization of the magnetic refrigerator, it is vitally important to evaluate AMR performance. In recent years several AMR experimental systems have been designed and tested [Engelbrecht 12], [Tuŝek 12], [Trevizoli 11],

[Lozano 12], [Bahl 08], [Richard 04], [Okamura 06], [Li 06], [Balli 11]. Most of these focused on the evaluation of the AMR performance by studying different refrigerant materials and multistage systems. Although there are a few researches reporting the effect of a system’s parameters on the performance of AMR theoretically, through numerical simulations and modeling [Aprea 11], [Roudaut 09], [Tagliafico 12], [Nielsen 10],

[Dikeos 13], they did not perform any optimization experimentally on their system’s parameters.

Three aspects influence the maximum attainable temperature span seen in an

AMR device: system, refrigerant material, and thermofluid. Any improvement or optimization done in these categories can result in a higher temperature span seen between the hot and the cold ends of an AMR. The variables for the thermofluid are: type, viscosity, heat conductivity, specific heat capacity, and the tuning of heat transfer

55 fluid and its operating conditions such as frequency, flow rate, flow duration, displaced volume, pressure, etc.

In this work, refrigerant porosity, shape and type, field intensity and distribution, and heat transfer fluid type are fixed parameters, while the experimental focus is on understanding how tuning the heat transfer medium and its operating conditions affect

AMR cooling performance.

3.2 Experimental setup

The schematic design of the AMR system is shown in Figure 3-1. The AMR system consists of four main components: a rotary two-core nested permanent magnet cylinder producing a variable field up to 1.3 T, a core glass tube housing the refrigerant bed in the middle of it, six temperature sensors in different distances from the bed, and a reciprocative pump to move the heat transfer fluid through the system between magnetic cycles in order to absorb or release the generated heat by the refrigerant during

(de)magnetization.

Figure 3-1: Schematic diagram of the experimental apparatus showing six sensor locations. 3.2.1 Magnet

A permanent adjustable-field rotating magnet generates the change in the

56 magnetic field in the solid refrigerant bed. This magnet that commercially is called Magic

Ring Magnet (shown in Figure 3-2) produces a magnetic field with a magnitude varying between 0 and 2 Tesla at various frequencies. Two nested permanent magnet cylinders generate the magnetic field, each of these producing a 1 T field. A stepper motor rotates the inner cylinder in order to vary the magnitude of the field. The outer cylinder is fixed, which means that the resulting field is rotating. The frequency of rotating can be selected between 0.2 and 1.6 Hz.

Figure 3-2: A rotary two-core nested permanent magnet cylinder. 3.2.2 Temperature sensors

The direct measurement of the temperature of the magnetocaloric sample is obtained by the Cernox temperature sensors from Lakeshore. The thermistor Cernox is a temperature sensitive resistor that changes resistance with changes in temperature non- linearly. Most thermistors have a negative temperature coefficient therefore, as temperature increases, resistance decreases. The sensor can quickly detect minute changes in temperature. Cernox thin film resistance cryogenic temperature sensors offer significant advantages over comparable bulk or thick film resistance sensors. The smaller package size of these thin film sensors makes them useful in a broader range of 57 experimental mounting schemes, and they are also available in a chip form. They are easily mounted in packages designed for excellent heat transfer, yielding a characteristic thermal response time much faster than possible with bulk devices requiring strain-free mounting. Additionally, they have been proven very stable over repeated thermal cycling and under extended exposure to ionizing radiation.

Figure 3-3 shows schematic and different packaging of Cernox sensors. Cernox sensor was selected over thermocouple sensors because of its low magnetic field-induced errors over the 0.3 K to 420 K temperature range with accuracy of 0.001 K and time resolution of 1 ms. In addition, the Cernox sensor offers high sensitivity and negative temperature coefficient resistance temperature detector.

One of the advantages of this system compared to previous magnetocaloric temperature measurement systems [Kuz’min 11], [Franco 09] is the use of thermistor based temperature sensors, Cernox, instead of thermocouples, because alternating magnetic fields affect thermocouple based temperature sensors and cause errors in the recorded temperature [Shir 05b], while Cernox sensors can be used in alternating magnetic fields. The Cernox magneto-resistance is typically negligible above 30 K and is not significantly affected by orientation relative to the magnetic field.

Figure 3-3: Cernox temperature sensor.

3.2.3 Refrigerant bed

Our designed system has the ability to measure adiabatic temperature change of magnetic refrigeration with various shapes. We used gadolinium turnings for the adiabatic temperature change measurements in gadolinium as shown in Figure 3-4.

Figure 3-4: Gadolinium turnings sample Commercial gadolinium powder was the alternative choice for the test bed.

Applying gadolinium powder as the bed refrigerant has some advantages. The heat transfer surface area for the powder is the best among the other shapes of metal. Also, there will be less resistance inside the material to transfer heat or cold energy that is generated by the MCE to the surface. On the other hand, the powder refrigerant can cause blockage of the flow of the heat transfer medium. Proper filters needed to be installed on both ends of the bed that permit heat transfer medium to pass the bed while keeping the refrigerant material inside the refrigerant bed. Additionally, as gadolinium powder is extremely reactive and can cause explosion upon exposure to air, the bed set up and operation of the test system needs to be performed in absence of air and presence of an inert gas such as helium. In consideration of all of these factors, along with the high price of gadolinium powder, we decided to use gadolinium chops in the form of turnings, which were made by the rounded plate of the metal, and bulk gadolinium. This shape of

59 commercial gadoliniums have a relatively good surface area for heat transfer to the medium, is not reactive to air, and allows the flow through the regenerative bed without significant resistance and pressure built up. Figure 3-5 shows an illustration of the refrigerant bed set up by the gadolinium turning before installation to the magnet.

Figure 3-5: Refrigerant bed set up by the gadolinium turning before installation to the magnet. 3.2.4 Cylinder-piston displacer

In the AMR setup of the test bed system, we used a gas displacer sealed rod-less cylinder from Festo Company in order to move the heat transfer medium liquid through the refrigerant bed in the refrigeration setup. In the adiabatic temperature measurement setup, the refrigerant’s heat is transferred by the liquid following in the glass tubes channel.

A double acting displacer system installed parallel to the refrigerant bed is used to provide reciprocating motion for the gas. The servo pump system consists of two magnetically coupled actuators, one belt drive, one servomotor, and one control enclosure. The servomotor actuates the pumping system. It is programmable to achieve various moves and motion profile. The motor control includes provisions for several input/output that can be used with the servo system. The main advantage of this system is double- action movement of rod less piston that its speed can be controlled in various rates by its software and it is relatively sealed.

The displacer is made to reciprocate around its center position by coupling to the drive motor through a gearbox. Since it is mechanically coupled to the drive shaft, the phasing between the blow wave front and the regenerator position is ensured. The phasing can be adjusted by changing the angular position of the displacer crank-arm. The stroke length of the gas displacer can also be adjusted by changing the throw on the crank.

The double-acting piston displacer moves the heat transfer medim through the bed. The displacer system motion is synchronized with the rotation of the inner magnet by the LABVIEW software. If we setup the system in AMR mode, at the time that the magnet is in the maximum field position, which corresponds to the refrigerant’s hottest temperature, the piston moves in the direction to send the heat transfer medium to the hot reservoir through the bed. As soon as the magnet is in the lowest field position, which corresponds to the coldest temperature of the refrigerant material, the piston moves in the opposite direction, in order to transfer the exchange liquid to the cold reservoir through the refrigerant bed. Figure 3-6 shows cylinder piston displacer in the test bed system.

Figure 3-6: Double acting displacer system installed parallel to the refrigerant bed.

3.2.5 System setup as AMR device

Temperature sensors are mounted on holder rods made of Polylactide (PLA) material produced by a 3D printer. Thermocouple readings are disturbed by the proximity of a varying magnetic field [Shir 05a]. Because sensors BH and BC are exposed to the magnetic field, two resistance temperature sensors (Cernox RTD) from

Lakeshore Cryotronics are used to carry out the measurements at these locations due to their low magnetic field-induced errors. The other sensors (H1, H2, C1, and C2) are outside of magnetic field range; therefore thermocouples were placed at these locations.

A picture of the AMR system and the core of the experimental setup are shown in Figure

3-7.

Figure 3-7: Photography of the AMR device. The refrigerant is located inside a cylindrical permanent magnet assembly. The volume of the bed is 48cm3 in which 2/3 is filled by gadolinium turnings and

1/3 by heat transfer fluid. In many of the previous studies [Engelbrecht 12], [Tuŝek 12],

[Trevizoli 11], [Okamura 06], the heat transfer fluid was water. However, based on the fact that gadolinium is electropositive and reacts with water to form gadolinium

62 hydroxide and hydrogen gas, it is not a good heat transfer medium candidate. Even though there are corrosion inhibitors that can be added to water to prevent this chemical reaction, silicone oil has additional advantage as its specific heat is about one fourth of that of water which makes it more suitable since less energy per unit mass is required to raise its temperature by 1 K. In general, the higher the specific heat of a material, the more heat is needed to change the temperature of the material itself, taking away from the latent heat that can be used to cool a medium. Hence, to avoid this chemical reaction and to improve performance, silicone oil is used as the heat transfer medium.

The system control program was written with LabVIEW software. The program allows remote control and synchronization of the test system components and gathers measured signals from the temperature sensors, which are then evaluated and analyzed.

By using this program, the applied magnetic field can be set between 0 T to 2 T in intervals of 1 mT, the sample’s ambient temperature can be set between (-40 C or 233.15

K to 200 C or 473.15 K) with accuracy of 0.01 C or 0.01 K; and the time is set in intervals of 0.1 s. The front panel of the control system program is shown in Figure 3-8.

Figure 3-8: Front panel of the control system program written using LabVIEW. The program has capabilities of controlling and synchronizing system components.

In the upper-left side of the panel, the communication protocol between main program and system components control unit (permanent magnets, cylinder displacer, temperature sensor and LabVIEW interface) are defined. In the upper-right side of the panel, the permanent magnet (Halbach) parameters are defined such as sample field value and sweep rate. The magnetic field value can be set between 0T – 2T with an accuracy of

1mT and the sweep rate can be set from 20 mT/s to 2 T/s.

The lower part of the panel shows measured temperature by sensors and has the capability to display and record temperatures from two Cernox sensors and four thermocouples simultaneously. The vertical axis of the chart is temperature and the horizontal axis is time. Control System Program gathers the measured direct temperature from sensors and logs them for further processing.

Figure 3-9: Wide view of the AMR system with control equipment 3.3 Data analysis, results and discussions

A number of tests were performed on 140 grams of gadolinium turnings. The temperature span (ΔT) between the hot and cold side of the AMR was measured at multiple operation conditions defined by different operating frequencies, fluid flow

64 durations, and flow rates. Experimental parameters are presented in Table 3-1.

Table 3-1: Experimental parameters

The utilization factor (휑) is defined as the ratio between the thermal capacity rate of the fluid and that of the solid [Trevizoli 11], [Richard 04], [Tagliafico 12], [Nielsen

10],

풎̇ 푪풑흉풃풍풐풘 흋 = (3-1) 푴푪푯(흁ퟎ푯=ퟎ) where 푚̇ is the pumped mass flow rate, Cp is the specific heat capacity of the working fluid, τblow is the time period for fluid flow, M is the mass of magnetic material, and CH is the specific heat of the refrigerant at μ0H = 0 T.

In this research a new concept, displaced volume ratio (DVR) is defined as the ratio of the fluid volume that flows through the AMR bed to the volume of the AMR bed occupied by the fluid in the hot and cold blowing cycles,

푽̇ 흉풃풍풐풘 푫푽푹 = (3-2) 푽풃풆풅

-1 where 푉̇ is the fluid volume flow rate (ml.s ), τblow is the time period for fluid flow, and

푉푏푒푑 is the volume of AMR bed occupied by fluid. The utilization factor is dependent on

65 the mass and the specific heat of the refrigerant and heat transfer fluid used in the system, whereas the concept of DVR is completely independent of the type and properties of the refrigerant and is solely dependent on the heat transfer medium movement parameters.

In this study, two different setups for each AMR cycle have been introduced as follow. Figure 3-10 shows these setups as well as one cycle of the experiment. Regions

A, B, C, and D are ramp-up, magnetization, ramp-down, and demagnetization, respectively. In both setups the flow rate is kept constant in intervals B and D. In Setup

1 the flow rate for each frequency and DVR is calculated as

푽풃풆풅 푽풃풆풅 푭풍풐풘푹풂풕풆 = × 푫푽푹 = ퟏ × 푫푽푹 (3-3) 풕풎풂품 − 풕 ퟐ풇 푹 where Vbed is the volume of AMR bed occupied by fluid, tmag= tdemag is the magnetization or demagnetization time, f is the operating frequency, and tR is ramp-up or ramp-down duration.

In Setup 2, for each frequency the flow rate is kept constant at its maximum amount and the fluid flow duration varies to generate the desired DVRs. In this setup, right after the beginning of regions B and D there is a delay time (tw) before fluid flow starts. As DVR increases the delay time decreases. During the delay time, there is no fluid movement through the bed. It should be noted that there is no delay time in Setup 1 in which fluid flow starts immediately at the beginning of regions B and D.

Each operating frequency is obtained by changing the duration of regions A, B, C and D. The maximum operating frequency for the system is determined with respect to the maximum allowable fluid flow rate in the apparatus before the seals fail due to excess pressure build up.

Figure 3-10: Configuration of Setup 1 and Setup 2 for one cycle of the experiment.

Figure 3-11 and 3-12 show the temperature difference between BH and BC sensors versus DVR for different operating frequencies in the two experimental setups respectively. If the value of DVR is too small, only a part of the energy generated by the magnetocaloric effect can be utilized. In addition, too big of a DVR causes the fluid from the hot end of the AMR to flow into the cold end and vice versa, causing a decrease in the

ΔT at these locations. The quantity “temperature span” considered herein refers to a single-stage refrigeration cycle and is a property of the refrigerant material rather than of the cooling device. The latter can be multistage, with wider temperature spans [Zverev

10], [Richard 04], [Aprea 11].

Figure 3-11 shows ΔT as a function of DVR in Setup 1. There is a DVR of 0.625 for each operation frequency in which the maximum ΔT occurs. Increasing the frequency causes a decrease in the maximum temperature change. This is because at higher

67 operating frequencies there isn’t sufficient time to transfer the amount of energy generated by the magnetocaloric effect. In contrast, lower operating frequencies (longer fluid flow durations) provide sufficient time for heat to be transferred from the refrigerant to the fluid (and vice versa) in any cycle, resulting in a higher ΔT. At this optimum

DVR, a 24% increase in the performance is achieved by changing the operating frequency.

Figure 3-11: Temperature span (훥TBH-BC) between BH and BC sensors as a function of DVR for different operating frequencies in Setup 1. The temperature span as a fucntion of DVR in Setup 2 is shown in Figure 3-12.

The result is that the maximum ΔT occurs at a DVR of 0.3 for all operating frequencies.

In Setup 2, unlike Setup 1, as operating frequency increases, ΔT increases. In Setup 2, due to a varying frequency and based on the presence of a delay time for heat exchange between the refrigerant and the fluid, the ΔT is affected by heat losses to the surroundings. As the operating frequency increases, the heat loss during one period decreases, hence ΔT increases. At this optimum DVR, the performance is increase by

22% when varying the operating frequency.

However, as the operating frequency increases, the delay time diminishes and eventually after some higher DVRs the flow occupies the entire region (there will not be a 68 delay time anymore), therefore the two setup configurations exhibit the same behavior (as seen in Figure 3-10 at DVR=3α). For instance in Figure 3-12 the ΔT curves for frequencies 0.09 Hz and 0.11 Hz cross each others at DVR=2. After this point the delay time for f=0.11 Hz is reduced to zero, therefore the results for Setup 2 are similar to those for Setup 1 and the ΔT curve for f=0.11 Hz falls below that of f=0.09 Hz. A similar trend occures for the other frequencies at different DVRs and these can be seen in Figure 3-12.

Figure 3-12: Temperature span (훥TBH-BC) between BH and BC sensors as a function of DVR for different operating frequencies in Setup 2. Figure 3-13 shows the temperature span as a function of frequency for different

DVRs in Setup 2. Result shows the ΔT increases as the operation frequency increases and peaks at an optimal frequency of 0.2 Hz. It is worth noting that the optimal frequency is related to the geometry of the refrigerant used in the AMR bed. At this optimum frequency, a 20% increase in the performance is achieved by varying the DVR.

Figure 3-13: Temperature span as a function of operating frequency for different DVRs in Setup 2. Figure 3-14 shows the temperature change at different sensor locations as a function of DVR for the operation frequency of 0.09 Hz. This figure illustrates that the maximum ΔT at various sensor locations occurs at different DVRs. For instance, at locations BH-BC (closest distance to the bed) the peak is reached at DVR=0.3, at locations H1-C1 the peak occurs at DVR=2, and at locations H2-C2 (farthest distance to the bed) the peak is yet to be observed at some DVR higher than 3. Similar trends take place for other tested operating frequencies. This is due to a need for pumping more fluid in order for it to reach sensors which are located further from the AMR bed. This result implies that the performance of an AMR system is dependent on the cooling load placement and its distance from the bed.

Figure 3-14: Temperature span at different sensor locations as a function of DVR for a frequency of 0.09 Hz in Setup 2. Sensor locations are shown in FIG. 1. Sensors BH-BC are placed nearest to the bed and sensors H2-C2 are farthest from the bed. Figure 3-15 shows ΔT as a function of flow rate in Setup 1. Result shows that different optimal values of the fluid flow rate can be identified at a given frequency with respect to ΔT in order to maximize the performance of the AMR.

Figure 3-15: Temperature span as a function of flow rate for different operating frequencies in Setup 1. 3.4 Conclusions

In this thesis, several significant system parameters that affect the cooling performance of an AMR system have been studied. This research provides the

71 experimental optimization procedure that must be applied to any AMR system in order to improve that system’s performance. Herein, a single stage AMR test bed using a stationary permanent magnet assembly allowing control of a number of experimental parameters (such as operating frequency, heat transfer medium flow rate, flow duration, and displaced volume ratio) has been designed and evaluated. Two AMR setup configurations were introduced and experiments were performed at different operating conditions.

The results show that the configuration in Setup 1 is more suitable for systems that are operating with lower frequencies, whereas the configuration in Setup 2 is more appropriate for systems that are operating with higher frequencies. It is shown that the performance of an AMR system is dependent on the cooling load placement and its distance from the bed. There were optimal DVRs of 0.625 and 0.3 in Setup 1 and Setup 2, respectively. The optimum operating frequency of the system in Setup 2 was 0.2 Hz in which the highest ΔT occurred at any DVR. Lastly, an optimal value of heat transfer fluid flow rate was identified for any operating frequency. The results of this work demonstrate a significant increase of performance in magnetic refrigeration system (about 24%) by varying and optimizing the AMR parameters. These optimized values are system dependent and need to be determined and measured for any AMR system by following the procedures that were introduced in this research. It is expected that such optimization will permit the design of a more efficient commercially viable magnetic refrigeration system.

Chapter 4 . Characterization Methods

Before presenting the results of this research on magnetic nanoparticles, first we explain the methods and experiments that were used to characterize nanoparticles properties. To determine the chemical structure, morphology, microstructure and composition the following procedures were performed. The powder X-ray diffraction

(Rigaku MiniFlex) measurement at room temperature has been carried out to study the crystal structures using Cu-Kα radiation. Surface morphology of the synthesized powder alloy was characterized by scanning electron microscopy (Raith PIONEER Two) technique. The composition of the powders was determined from energy dispersive X-ray fluorescence spectrometer (Shimadzu EDX-700). Magnetization measurements were performed using vector vibrating sample magnetometer (Lake Shore VVSM 7410) and superconducting quantum interface devise (Quantum Design SQUID MPMSXL) with standard zero field cooling (ZFC), field cool cooling (FCC), and field cool warming

(FCW) techniques.

4.1 X-ray Powder Diffraction (XRD)

X-ray powder diffraction (XRD) is an analytical technique primarily used for phase identification of a crystalline material and can provide information on unit cell dimensions. The analyzed material is finely ground and homogenized. X-ray diffraction is now a common technique for the study of crystal structures and atomic spacing. X-ray diffraction is based on constructive interference of monochromatic X-rays and a crystalline sample. The principle mechanism is illustrated in Figure 4-1. These X-rays are generated by a cathode ray tube, filtered to produce monochromatic radiation, collimated

73 to concentrate, and directed toward the sample. The interaction of the incident rays with the sample produces constructive interference (and a diffracted ray) when conditions satisfy Bragg's Law (nλ=2d sin θ). This law relates the wavelength of electromagnetic radiation to the diffraction angle and the lattice spacing in a crystalline sample. These diffracted X-rays are then detected, processed and counted. By scanning the sample through a range of 2θ angles, all possible diffraction directions of the lattice should be attained due to the random orientation of the powdered material. Conversion of the diffraction peaks to d-spacings allows identification of the mineral because each mineral has a set of unique d-spacings. Typically, this is achieved by comparison of d-spacings with standard reference patterns. All diffraction methods are based on generation of X- rays in an X-ray tube. These X-rays are directed at the sample, and the diffracted rays are collected. A key component of all diffraction is the angle between the incident and diffracted rays.

X-ray powder diffraction is most widely used for the identification and characterization of unknown crystalline materials, identification of fine grained minerals that are difficult to determine optically, determination of unit cell dimensions, and determination of crystal structures.

Figure 4-1: Principle mechanism diagram of XRD 74

The XRD measurements in this research were carried using MiniFlex by Rigaku shown in Figure 4-2. MiniFlex is a general purpose X-ray diffractometer that can perform qualitative and quantitative analysis of polycrystalline materials.

Figure 4-2: XRD equipment, MiniFlex by Rigaku 4.2 X-ray Fluorescence (XRF)

XRF spectrometer is a non-destructive analytical technique used to determine the elemental composition of materials. XRF analyzers determine the chemistry of a sample by measuring the fluorescent (or secondary) x-ray emitted from a sample when it is excited by a primary x-ray source. Each of the elements present in a sample produces a set of characteristic fluorescent x-rays (“a fingerprint”) that is unique for that specific element, which is why XRF spectroscopy is an excellent technology for qualitative and quantitative analysis of material composition.

The analysis of major and trace elements in geological materials by x-ray fluorescence is made possible by the behavior of atoms when they interact with radiation.

When materials are excited with high-energy, short wavelength radiation (e.g., X-rays),

75 they can become ionized. If the energy of the radiation is sufficient to dislodge a tightly- held inner electron, the atom becomes unstable and an outer electron replaces the missing inner electron. When this happens, energy is released due to the decreased binding energy of the inner electron orbital compared with an outer one. The emitted radiation is of lower energy than the primary incident X-rays and is termed fluorescent radiation. Because the energy of the emitted photon is characteristic of a transition between specific electron orbitals in a particular element, the resulting fluorescent X-rays can be used to detect the abundances of elements that are present in the sample. The principle mechanism is portrayed in Figure 4-3.

Figure 4-3: Principle mechanism diagram of XRF

The energy dispersive XRF measurements in this research were carried using

EDX-700 by Shimadzu shown in Figure 4-4. The EDX-700 was designed for an even greater level of sensitivity, and enabling both trace and rapid analysis that goes beyond the limits of screening analysis.

Figure 4-4: XRF equipment, EDX-700 by Shimadzu 4.3 Scanning Electron Microscope (SEM)

SEM uses a focused beam of high-energy electrons to generate a variety of signals at the surface of solid specimens. The signals that derive from electron-sample interactions reveal information about the sample including external morphology (texture), chemical composition, and crystalline structure and orientation of materials making up the sample.

The SEM is an instrument that produces a largely magnified image by using electrons instead of light to form an image. The principle working mechanism is shown in Figure 4-5. A beam of electrons is produced at the top of the microscope by an electron gun. The electron beam follows a vertical path through the microscope, which is held within a vacuum. The beam travels through electromagnetic fields and lenses, which focus the beam down toward the sample. Once the beam hits the sample, electrons and X- rays are ejected from the sample. Detectors collect these X-rays, backscattered electrons,

77 and secondary electrons and convert them into a signal that is sent to a screen similar to a television screen. This produces the final image.

Figure 4-5: Principle mechanism diagram of SEM [Purdue 14]

The SEM measurements in this research were carried using PIONEER Two by

Raith shown in Figure 4-6. PIONEER Two is ultra-high resolution electron beam lithography (EBL) and an analytical scanning electron microscope (SEM) imaging integrated into a single system.

Figure 4-6: SEM equipment, PIONEER Two by Raith 4.4 Superconducting Quantum Interface Devise (SQUID)

SQUID magnetometer is a very sensitive device for measuring magnetic field.

Using a device called a Josephson junction, a SQUID can detect a change of energy as much as 100 billion times weaker than the electromagnetic energy that moves a compass needle. A Josephson junction is made up of two superconductors, separated by an insulating layer so thin that electrons can pass through. A SQUID consists of tiny loops of superconductors employing Josephson junctions to achieve superposition. A direct current (DC) SQUID, consists of two Josephson junctions employed in parallel so that electrons tunneling through the junctions demonstrate quantum interference, dependent upon the strength of the magnetic field within a loop. The mechanism is as follow: In the absence of any external magnetic field, the input current I splits into the two branches equally. If a small external magnetic field is applied to the superconducting loop, a screening current, Is, begins circulating in the loop that generates a magnetic field 79 canceling the applied external flux. The induced current is in the same direction as I in one of the branches of the superconducting loop, and is opposite to I in the other branch; the total current becomes I/2 + Is in one branch and I/2 - Is in the other. As soon as the current in either branch exceeds the critical current, Ic, of the Josephson junction, a voltage appears across the junction which is proportional to sample’s magnetic moment.

The mechanism is illustrated in Figure 4-7.

Figure 4-7: Principle mechanism diagram of SQUID [Georgia 15]

The magnetometer is also commonly equipped with a variable temperature control that consists of vital units like a liquid helium Dewar, a heater, and a temperature sensor. Part of the magnetic measurements done in this research was carried using MPMS

XL SQUID by Quantum Design shown in Figure 4-8.

Figure 4-8: MPMS XL SQUID by Quantum Design 4.5 Vector Vibrating Sample Magnetometer (V-VSM)

VSM is a sensitive device for measuring magnetic field. The principle of mechanism is as follow. A sample is placed inside a uniform magnetic field to magnetize the sample. The sample is then physically vibrated sinusoidally. The induced voltage in the pickup coil is proportional to the sample's magnetic moment, but does not depend on the strength of the applied magnetic field. In a typical setup, the induced voltage is measured through the use of a lock-in amplifier using the piezoelectric signal as its reference signal. By measuring in the field of an external electromagnet, it is possible to obtain the hysteresis curve of a material. The vibrating sample magnetometer measures the magnetization of a small sample of magnetic material placed in an external magnetizing field by converting the dipole field of the sample into an ac electrical signal.

Figure 4-9: Principle mechanism diagram of VSM [Georgia 15]

Most of the magnetic measurements done in this research were carried using V-

VSM model 7410 by Lake Shore with a cryostat unit as shown in Figures 4-10 and 4-11.

Figure 4-10: V-VSM model 7410 by Lake Shore

Figure 4-11: V-VSM cryostat unit 4.6 Annealing procedure

Salt-matrix annealing procedure was carried to anneal synthesized nanoparticles.

The basic process is to mix nanoparticles with salts and do heat treatments of the mixture below melting points of the salts. After the heat treatments, the salts with high water or solvent solubility can be completely removed by washing the mixture in water or solvent and the heat treated nanoparticles can be recovered with retained nanoscale morphology. Table salt, NaCl, is the most suitable salt for the treatments.

The sample was grinded with a mixture of 2g of dried KCl and 2g of dried NaCl for 5 minutes. The resultant powder was then transferred to an alumina boat, which was placed in a quartz annealing tube. The tube was then sealed, vacuumed, and heated at given temperature for 6 hours. Upon completion of annealing, the quartz tube was

83 allowed to cool down to room temperature. The heated powder was then washed with water and centrifuged at 10,000 rpm for 6 times to remove KCl and NaCl, then dried in the air. The annealing equipment is shown in Figure 4-12.

Figure 4-12: Annealing equipment

Chapter 5 . Nanomaterials in Magnetic Refrigeration Technology

Some of the main impediments and challenges on the way of magnetic refrigeration to become commercially feasible are refrigerant magnetic hysteresis, low cooling capacity, and finding suitable materials as refrigerant that can be used in room temperature with sufficiently wide operating temperature range. Previous works on magnetic refrigeration technology are based on bulk refrigerants. Over the past 35 years, many groups both in the United States and abroad have dedicated considerable effort both in developing effective magnetic refrigerants and in prototype development of magnetic refrigerators, heat pumps, and air conditioners. However, to this date, no one has built a successful commercial refrigerator because most of the work in room- temperature magnetic refrigeration employs the so-called “giant” magnetocaloric effect, which uses hysteretic materials [Liu 12]. The apparent colossal results are due to the inappropriate use of Maxwell’s equations, which are not valid in hysteretic systems. The direct measurements produce much lower MCEs. In addition irreversibility remains an impediment by decreasing the cycle’s Carnot efficiency.

Figure 5-1: Different hysteresis loop shapes and their typical application [Georgia 15] 85

A main reason for the failure was that a major amount of effort was dedicated to materials that undergo first-order transitions some of which yield artificially high MCE values near-room temperature. In addition, the hysteresis accompanying these first-order transitions makes these materials unsuitable for magnetic refrigerants. None of the wide range of bulk materials proposed by the different organizations mentioned above for near-room or above temperature magnetic refrigeration has a cooling capacity significantly greater than that of the benchmark gadolinium.

It has been shown that nanostructures are the best choice for magnetic refrigeration systems [Bennett 95], [Della Torre 12], [Shir 03], [Shull 91]. Nanostructures have a higher MCE over a temperature distribution so they exhibit more cooling efficiency as compared to bulk materials. The magnitude of entropy change varies for different materials based on the number of particles per unit volume, magnetic moment of the particles, and the order parameter [Shir 03]. Magnetocaloric properties of a nanostructure can be tuned and optimized by controlling its properties such as size, shape, morphology, etc. Therefore, the MCE peak can be displaced to other temperatures, broadened, or made sharper. Curie temperature, TC, scales with size of the nanoscale magnetic material offering the opportunity to tune the transition temperature, lowering it or raising it by varying material dimensions. Hence, the Curie temperature of bulk alloys that have good MCE properties at temperatures higher than room temperature can be tuned by decreasing their size. In addition, the reduction of the Curie temperature is dependent not just on size but shape as well, the reduction being less pronounced as the aspect ratio of the nanoparticles is increased [Lung-fei 07]. We believe that by utilizing

86 nanostructural material as refrigerant the adiabatic temperature change (∆Tad) per unit of applied magnetic field is increased and the hysteresis is minimized.

Aim of research: to investigate magnetic and magnetocaloric properties of nanoparticles. Nanoparticles are synthesized and characterized in order to determine the correlation between their size, shape, and morphology on their magnetic properties such as magnetization, magnetocaloric effect, Curie temperature, etc.

5.1 Nanoparticles as the refrigerant

Magnetic refrigeration is based on the magnetocaloric effect (MCE) in magnetic materials that causes the entropy to change with the external field. In a single magnetic material, the MCE is usually most pronounced near the magnetic phase transition temperature, and is smaller further away. An ideal refrigerator requires a material with the MCE over a large range of temperatures. Nanomaterials are promising alternatives as room temperature refrigerants.

Nanoparticles are of great scientific interest as they are, in effect, a bridge between bulk materials and atomic or molecular structures. A bulk material should have constant physical properties regardless of its size, but at the nano-scale size-dependent properties are often observed. Thus, the properties of materials change as their size approaches the nanoscale and as the percentage of atoms at the surface of a material becomes significant. For bulk materials larger than one micrometer (or micron), the percentage of atoms at the surface is insignificant in relation to the number of atoms in the bulk of the material. The interesting and sometimes unexpected properties of

87 nanoparticles are therefore largely due to the large surface area of the material, which dominates the contributions made by the small bulk of the material.

The magnetic properties of nanoparticles are determined by many factors, the key of these including the chemical composition, the type and the degree of defectiveness of the crystal lattice, the particle size and shape, the morphology (for structurally inhomogeneous particles), the interaction of the particle with the surrounding matrix and the neighboring particles. By changing the nanoparticle size, shape, composition and structure, one can control to an extent the magnetic characteristics of the material based on them. However, these factors cannot always be controlled during the synthesis of nanoparticles nearly equal in size and chemical composition; therefore, the properties of nanomaterials of the same type can be markedly different.

In terms of the potential interest for application in magnetic refrigeration, the maximum |∆SM| value is not the exclusive parameter to be taken into account for considering a material attractive. The temperature at which MCE occurs defines the technological field, and the temperature range in which it can operate is also of much importance. In order to predict and evaluate the MCE of a material, refrigerant capacity

(RC) [also known as relative cooling power (RCP)] can be considered as the basis for calculating the temperature behavior of the material. RC indicates how much heat can be transferred from the cold end to the hot end of a refrigerator describing a thermodynamic cycle. RC is defined as the product of the peak entropy change times the full width at half

pk maximum (FWHM) of the peak ∆T, RCFWHM = |∆SM | ∆TFWHM. The higher the ∆TFWHM value is, the larger the temperature difference between the hot and the cool ends of the cycle that can be used for operation.

Increasing the RC not only increases the amount of refrigeration obtainable from the particular refrigerant and field excursion, but also tends to increase the thermodynamic efficiency of the cycle, thus measuring how well a particular volume or quantity of refrigerant is utilized. Improvement in RC mainly relies on broadening the magnetic entropy change by coupling two phases of magnetic materials with desirable properties through alloying, changing the composition or field. Some materials exhibit tricritical points where a first-order transition becomes second-order as a function of composition or applied field, as seen in Figure 5-2a. At such a point, one can utilize the entropic benefits of the first-order transition without the punishing energy loss associated with circling the hysteresis loop: Thermal hysteresis in a second order transition is, in principle, zero [Takeuchi 15].

Another method of broadening the magnetic entropy change, therefore improve

RC, is nanostructure synthesis with the main motivation rooted in their inherent tendency to have distributed exchange coupling, which will broaden the magnetic entropy curve

[Ucar 12]. The significance of nanostructured powders is the fact that these powders have a broader temperature dependence of magnetic entropy change, giving larger temperature span in magnetic refrigeration.

Figure 5-2: Schematic of a ferroic coolant’s behavior with phase transition as a function of temperature. (a) The change from first- to second-order behavior, through a tricritical point, may be induced by a change of composition or applied field. (b) A first-order transition (left panels) results in a larger transition entropy change ΔS than in the second-order case (right panels), albeit over a narrower temperature window. Tt,↓ and Tt,↑ are transition temperatures for decreasing and increasing T respectively. Thermal hysteresis is clearly present in the first-order case. [Takeuchi 15] 5.2 Synthesis of Nanoparticles

Many different approaches to magnetic ordered nanostructure synthesis and processing have been developed till now [Campbell 13]. These strategies can be categorized as either “top-down” or “bottom-up” approach as shown in Figure 5-3. There are various top-bottom methods for fabricating arrays of magnetic nanostructures. These include different lithography methods such as electron beam lithography, focused ion

90 beam irradiation etching, and sputtering. Bottom-up processes are based on the synthetic and assembling chemical-physical approaches.

Figure 5-3: Bottom-Up and Top-Down approach in nanomaterial synthesis [Saravanan 08] Bottom-up and top-down approaches each have their advantages and disadvantages. Top-down approaches can be extremely effective at reproducibly defining nanostructure dimensions. An example of this is the lithography technique which is the foundation of the microelectronic industry. However, lithography fundamental limitation in defining features smaller than 10 nm in diameter. Bottom-up routes to nanostructure, on the other hand, such as colloidal synthesis, are inexpensive. These methods have the

91 potential to produce nanoparticles with characteristic dimensions less than 10 nm with low cost.

5.2.1 Alkalide Reduction Chemical Synthesis

In chemical synthesis, metal salt, a reducing agent and a stabilizer are mixed to produce metal nanoparticles. The reducing agent detaches metal from the salt and the stabilizer passivates the nanoparticle to suppress further growth of the nuclei. Alkalide reduction is a low temperature solution phase synthesis method capable of producing wide range of single element nanomaterials, binary and ternary nanoparticles. Alkalides are crystalline ionic salts consisting of crown ether or cryptand complexed alkali metal cations charged balanced by a stoichiometric number of alkali metal anions. Alkalides produce alkali metal anions when dissolved in nonreducible solvents. Upon dissolution in ethers, solvated alkali anions are formed. Alkali anions are one of the most powerful reducing agents in any given solvent. Alkalide reduction of metal salts results in the formation of metal colloids consisting of nanoscale particles. Variation of alkalide salt to metal cation ratio can result in nanoscale materials with different structures, thus enabling access to metastable phases that are not easily accessible by other synthesis methods. Co- reduction of two metal salts can result in binary nanoscale alloys. Following aggregation and removal of the solvent, the byproducts can be washed away, recovering the crown ether and leaving bare metal nanoparticles. The method is general across the periodic table, including the lanthanides.

5.2.2 Physical Vapor Deposition Sputtering

Sputter deposition is a physical vapor deposition (PVD) method of thin film deposition by sputtering. This involves ejecting material from a "target" that is a source 92 onto a "substrate" such as a silicon wafer. This is done by first creating a gaseous plasma and then accelerating the ions from this plasma into some source material (“target"), the source material is eroded by the arriving ions via energy transfer and is ejected in the form of neutral particles - either individual atoms, clusters of atoms or molecules. As these neutral particles are ejected they will travel in a straight line unless they come into contact with something - other particles or a nearby surface. If a "substrate" such as a Si wafer is placed in the path of these ejected particles it will be coated by a thin film of the source material. The principle mechanism is portrait in Figure 5-4.

Sometimes described as the "fourth state of matter" (the first three being solid, liquid, gas), a gaseous plasma is actually a "dynamic condition" where neutral gas atoms, ions, electrons and photons exist in a near balanced state simultaneously. An energy source is required to "feed" and thus maintain the plasma state while the plasma is losing energy into its surroundings. One can create this dynamic condition by metering a gas

(e.g. Ar) into a pre-pumped vacuum chamber and allowing the chamber pressure to reach a specific level (eg. 0.1 Torr) and introducing a live electrode into this low pressure gas environment using a vacuum feedthrough.

Powering the electrodes with DC voltage will result:

1- Ever present "free electrons" will immediately be accelerated away from the

negatively charged electrode (cathode). These accelerated electrons will approach

the outer shell electrons of neutral gas atoms in their path and, being of a like

charge, will drive these electrons off the gas atoms. This leaves the gas atom

electrically unbalanced since it will have more positively charged protons than

negatively charged electrons - thus it is no longer a neutral gas atom but a

positively charged "ion" (e.g. Ar +).

2- At this point the positively charged ions are accelerated into the negatively

charged electrode (cathode) striking the surface and "blasting" loose electrode

material (diode sputtering) and more free electrons by energy transfer. The

additional free electrons feed the formation of ions and the continuation of the

plasma.

3- All the while, free electrons find their way back into the outer electron shells of

the ions thereby changing them back into neutral gas atoms. Due to the laws of

conservation of energy, when these electrons return to a ground state, the resultant

neutral gas atoms gained energy and must release that same energy in the form of

a photon. The release of these photons is the reason the plasma appears to be

glowing.

Figure 5-4: Sputtering technique schematic (left) and sputtering target (right) [M-Systems 10] The "diode sputtering" example given above has proven to be a useful technique in the deposition of thin films when the cathode is covered with source material

("sputtering target"). Diode sputtering however has two major problems - the deposition

94 rate is slow and the electron bombardment of the substrate is extensive and can cause overheating and structural damage.

Magnetron sputtering: The development of magnetron sputtering deals with both of these issues simultaneously. By using magnets behind the cathode to trap the free electrons in a magnetic field directly above the target surface, these electrons are not free to bombard the substrate to the same extent as with diode sputtering. At the same time the extensive, circuitous path carved by these same electrons when trapped in the magnetic field, enhances their probability of ionizing a neutral gas molecule by several orders of magnitude. This increase in available ions significantly increases the rate at which target material is eroded and subsequently deposited onto the substrate. The procedure is shown in Figure 5-5.

Figure 5-5: Magnetron sputtering [Farotex 16] 5.2.3 High Energy Ball Milling

Mechanical alloying (MA) is a solid-state powder processing technique involving repeated welding, fracturing, and rewelding of powder particles in a high-energy ball

95 mill. In this process a powder mixture placed in the ball mill is subjected to high-energy collision from the balls. The alloying process can be carried out using different apparatus, mixer mill, planetary mill or a horizontal ball mill. However, the principles of these operations are same for all the techniques.

Planetary ball mill is a most frequently used system for mechanical alloying since only a very small amount of powder is required. The centrifugal forces, created by the rotation of the vial around its own axis together with the rotation of the turn disc, are applied to the powder mixture and milling balls in the vial. The powder mixture is fractured and cold welded under high energy impact.

Figure 5-6 shows the motions of the balls and the powder. Since the rotation directions of the vial and turn disc are opposite, the centrifugal forces are alternately synchronized. Thus friction resulted from the hardened milling balls and the powder mixture being ground alternately rolling on the inner wall of the bowl and striking the opposite wall. During the high-energy ball milling process, the powder particles are subjected to high energetic impact. The impact energy of the milling balls in the normal direction attains a value of up to 40 times higher than that due to gravitational acceleration.

Special mills have been developed in the USA under the trade name Spex mills.

The common variety of the mill has one vial containing the sample and milling balls, secured in the clump and swung energetically back and forth several thousand times a minute. The back- and- fourth shaking motion is combined with lateral movements of the end of the vial, so that the vial appears to be describing a figure eight or infinity sign as it moves. The vial is vibrated with amplitude of 50 mm and a frequency of 20 Hz.

Figure 5-6: Schematic view of motion of the ball and powder mixture [Cao 15]. 5.2.4 Synthesis methods used in this research

To synthesis yttrium-iron nanoparticles, alkalide reduction chemical synthesis technique has been used. This procedure was carried at Dr. Wagner’s laboratory at the

Chemistry Department of the George Washington University. To synthesis Heusler alloy nanoparticles, high-energy ball milling technique has been carried at Dr. LeBlanc’s laboratory at the Mechanical Engineering Department of the George Washington

University.

Last year our group, the institute for magnetics research, was chosen by the

Center for Functional Nanomaterial (CFN) of the DOE’s Brookhaven National

Laboratory (BNL) to use their clean room. CFN is capable of fabricating thin films using sputtering techniques. Even though using their facility was free of charge to our group, we had to obtain the alloy of interest (as a 3” sputtering target) by ourselves for deposition. After contacting a few vendors, Kurt Lesker Company was capable of making some of our alloys. Depending on the alloy, the cost ranged from $8000 to $14000. This venue of synthesizing nanoparticles will be carried in our future research once we secure adequate funding. 97

5.3 Protecting Air Sensitive Nanoscale Magnetic Refrigerants

Some of the materials that are excellent candidates for nanoscale magnetic refrigerants are air sensitive. For instance, at very small nanocrystallite size (2 – 10 nm), lanthanide metal nanocrystals spontaneously combust when exposed to air. Larger nanocrystals with consequently lower surface area react less violently and less reactive metals, alloys and compounds may only surface oxidize. In some cases, simply bonding the powdered bulk form with a protective coating might mitigate this issue. However, it may be desirable to provide nanocrystal level protection to more sensitive materials, preventing oxide surface growth by producing core-shell nanocrystals. This can be readily accomplished with alkalide reduction by first reducing the “core” (magnetic) element to provide “seeds” and then slowly adding the “shell” (protective) element to be reduced on the surface of the “core”. In this research we have protected the yttrium-iron nanoparticles by Gold coating and the Heusler alloy nanoparticles by keeping them in

Argon atmosphere.

Chapter 6 . Magnetocaloric Effect and Magnetic Properties of Yttrium-Iron (Y2Fe17) Nanoparticles

6.1 Introduction

The research efforts concerning magnetocaloric materials can be classified in: (a) the search for higher performance materials and (b) reduction of materials cost. The first one is usually centered around rare earth alloys, while the second is accomplished by substituting rare earth elements by transition metals. Substitution for scarce and strategic elements, environmental considerations, and cost considerations all speak to potential contributions of these new materials to sustainability. The cost associated with the production of magnetocaloric refrigerants is a big barrier against industrial scale-up.

Therefore, in recent years, research on magnetocaloric materials has shifted toward finding the most economically advantageous magnetic refrigerant with the highest performance.

During the last decade, one of the most exciting yet challenging endeavors in applied materials science and engineering has been the search for new materials or the processing of existing ones, modifying the microstructure and/or the size with the aim of tailoring and controlling their physical/chemical properties in such a way that functionality could be enhanced. The study of metallic alloys is one of the main fields of research in Material Science. In this case, Fe- based alloys attract a great interest because of the number of applications in which they can be used, and its commercial value [Tegus 02], [Franco 06a] and they are believed to be promising magnetic refrigerants [Ucar 12].

A wide family of magnetic intermetallic compounds arises from the alloy of rare- earth (R) and 3d transition metals (M). Localized magnetism of rare-earth sublattice with an itinerate magnetism 3d sublattice, makes these magnetic intermetallics very attractive for commercial applications. The unpaired 3d electrons of the transition metal component give rise to a net magnetic moment. In this family of compounds, the magnetic behavior is determined mainly by the Fe sublattice. The magnetic coupling of the Fe magnetic moments depends on the Fe-Fe interatomic distance. For distances lower than 2.45 Å, the exchange coupling favors an antiparallel alignment of the magnetic moments, whereas for longer distances they are parallel [Kraiem 05]. Moreover, these alloys can exhibit different magnetic behavior: ferromagnetism (e.g. Pr2Fe17), ferrimagnetism (e.g.

Tb2Fe17), etc. The majority of the alloys of this family present a magnetic ordering temperature close to room temperature. Furthermore, TC is well below to that of pure Fe

(1073 K).

At constant pressure, the total entropy of a magnetic solid, S(T,H), consists of magnetic (SM), lattice (SLat) and electronic (SEl) contributions and can be written as

푆(푇, 퐻) = 푆푀(푇, 퐻) + 푆퐿푎푡(푇) + 푆퐸푙(푇) (6-1)

The value of the isothermal magnetic entropy change, ΔSM, due to the change in magnetic field from H1 to H2 is given by the expression [Morrish 65]

푯ퟐ 흏푴(푻,푯) 휟푺푴(푻, 휟푯) = ∫ ( ) 풅푯 (6-2) 푯ퟏ 흏푻 푯

On withdrawing the magnetic field under adiabatic conditions, the adiabatic temperature change, ΔTad, is given by

푯ퟐ 푻 흏푴(푻,푯) 휟푻 (푻, 휟푯) = − ( ) ( ) 풅푯 (6-3) 풂풅 ∫푯ퟏ 푪(푻,푯) 푯 흏푻 푯

100

From the Curie–Weiss law, the susceptibility of a ferromagnetic material at high temperatures and low magnetic fields can be written as [Shao 96a]

푴 푪 푵품ퟐ푱(푱+ퟏ)흁ퟐ 흌 = = = 푩 (6-4) 푯 푻−푻푪 ퟑ푨풌푩(푻−푻푪)

where N, g, J , kB, μB and A stand for the number of magnetic atoms per unit volume, gyromagnetic ratio, angular momentum, Boltzmann constant, Bohr magneton and atomic weight, respectively. Substituting the expression for M from equation (6-4) in the equation (6-2), the expression for ΔSM can be written as

ퟐ ퟐ ퟐ ퟐ ퟐ 푵품 푱(푱+ퟏ)흁푩푯 푵품 푱(푱+ퟏ)흁푩푯 휟푺푴 = − ∫ ퟐ 풅푯 = − ퟐ (6-5) ퟑ풌푩(푻−푻푪) ퟔ풌푩(푻−푻푪)

The magnetic entropy change, ΔSM, attains a maximum when the temperature, T, approaches the Curie temperature, TC, as observed in equation (6-5). Therefore, for application at around room temperature, MCE materials with TC close to room temperature should be selected. The selection of a material with a large angular momentum, J, will also satisfy the need for sufficient change in entropy. Alloys and compounds using rare-earth elements such as Gd, Tb, Dy and Ho might be suitable for this purpose due to their large angular momentum. But these materials are expensive for commercial use. Low-cost Fe-rich materials would be a good choice as MCE materials in our daily life refrigerators because of the large g and J value in iron. But the Curie temperature of Fe is 1073 K, much higher than the room temperature, and the MCE effect of iron is also not significant at room temperature. Therefore, attempt has been made to prepare and study the MCE in inexpensive iron-rich binary alloys R2Fe17 (R = Y, Pr, Nd)

[Valdes 14], [Alvarez 10]. The TC of these alloys has been found to be close to room temperature [Kirchmayr 79].

101

6.2 Experimental

A sample of Y2Fe17 alloy nanoparticle with gold coating was synthesized through alkalide reduction chemical synthesis. The procedure is as follow. Yttrium (III) chloride,

YCl3 (99.99%, Alfa Aesar), Iron (III) chloride, FeCl3 (99.9%, Aldrich), and Gold (III) chloride, AuCl3 (99.99%, Aldrich) were purchased and used without further purification.

100 ml of solvent tetrahydrofuran (THF) solution of YCl3 (1 mmol/L) and FeCl3 (8.5 mmol/L) was prepared and hand poured into a 100 ml THF solution of the reducing agent

+ - K (15-Crown-5)2Na (20 mmol/L) under vigorous magnetic stirring in a few seconds.

The mixture colloid was allowed to stir for 2 minutes, and then 100 ml THF solution of

AuCl3 (3.5 mmol/L) was slowly added in 3 minutes. A schematic of this procedure is shown in Figure 6-1. The synthesis was performed in Nitrogen dry box shown in Figure

6-2. The products were transferred into an air-tight solvent bottle for storage. Y2Fe17@Au nanoparticles were extracted by vacuum removal of solvents, washed with water, centrifuged, and dried in the air. The final product is a dark brown powder shown in

Figure 6-3.

Figure 6-1: Schematic view of alkalide reduction chemical synthesis 102

Figure 6-2: Nitrogen dry box

103

Figure 6-3: Synthesized Y2Fe17 nanoparticles The particle sizes of nanoparticles can be controlled by systematically adjusting the reaction parameters, such as time, temperature, and the concentrations of reagents and stabilizing surfactants. In general, particle size increases with increasing reaction time, because more monomeric species are generated, and with increasing reaction temperature because the rate of reaction is increased. In this research, to obtain different-sized nanoparticles the concentration of the salts were varied and new samples with 1.5, 2, and

3 times the concentration of the original sample were synthesized. Nanoparticles are air sensitive, hence to prevent oxidation they were coated with gold. Finally, resultant powders were annealed at 673 K for 6 h.

To determine the chemical structure, morphology, microstructure and composition the following procedures were performed. The powder X-ray diffraction

(Rigaku MiniFlex) measurement at room temperature has been carried out to study the

104 crystal structures using Cu-Kα radiation. Surface morphology of the synthesized powder alloy was characterized by scanning electron microscopy (Raith PIONEER Two) technique. The composition of the powders was determined from energy dispersive X-ray fluorescence spectrometer (Shimadzu EDX-700). Magnetization measurements were performed in the temperature range of 10 to 316 K using vector vibrating sample magnetometer (Lake Shore VVSM 7410) with standard zero field cooling (ZFC), field cool cooling (FCC), and field cool warming (FCW) techniques. Before the magnetization

M(T) measurements were made, the samples were cooled from 300 K to 9 K at 0 applied external magnetic field. A non-zero magnetic field was then applied and the measurements were done from 10 K to 316 K (ZFC) and then without removing the filed from 316 K to 10 K (FCC). Subsequently, without removing the field, the measurements were done from 10 K to 316 K (FCW).

6.3 Results and Discussion

As the size of magnetic materials reduces in to nano range they become more air sensitive. For instance, at very small nanocrystallite size (2 – 10 nm), lanthanide metal nanocrystals spontaneously combust when exposed to air. Larger nanocrystals with consequently lower surface to volume ratio react less violently and may only surface oxidize. Adding a protective coating to nanoparticles is a way to mitigate this issue.

However, the shell coating might reduce the net magnetization since nanoparticles are surrounded by the coating material (eg. gold, silver, and silica). Therefore, the coating shell should be thick enough to prevent oxidation and at the same time does not degrade the total magnetization by much. Two samples of the 21 nm nanoparticles were synthesized, one with gold (Au) coating and one without coating. Their field dependent

105 magnetization measured at 292 K is plotted in Figure 6-4. It is obvious that the non- coated sample had less magnetization which indicates surface oxidations. Because of this, all the samples in this research were coated by gold.

Figure 6-4: Field-dependent magnetization of the coated and non-coated 21 nm sample (both samples are unannealed) The XRD pattern of synthesized sample revealed the existence of some disordered (amorphous) phase in the structure. To store the crystallinity of the nanoparticles all sampled were annealed. The annealing temperature and the annealing time are the two parameters that need to be determined for each alloy to obtain the optimum result. Work by [Fleet 12] studied the variation of the annealing time and temperature on the magnetic properties of Co2FeSi Heusler alloy thin films. To determine the proper annealing temperature of nanoparticles, the 42 nm sample was divided in to four portions. The first, second and the third portions were annealed at 350 C, 500 C and

400 C, respectively. The forth portion remained unannealed. The annealing time in all cases was 6 hours. The field dependent magnetization of portions was measure at room temperature and is shown in Figure 6-5. Result suggested that the 400 C annealing

106 temperature was the most suitable one; hence all samples were annealed at 400 C for 6 hours to restore crystal structure of the synthesized nanoparticles.

Figure 6-5: Field dependent magnetization of the 42 nm sample annealed at different temperatures (350 C, 400 C, and 500 C) for 6 hours. The XRD measurements of annealed samples are shown in Figure 6-6. The patterns fit the yttrium-iron crystal structure.

Figure 6-6: XRD pattern of annealed synthesized nanoparticles 107

By annealing the nanoparticles the crystal structure becomes ordered and this leads to an improvement in the magnetic properties of the synthesized nanoparticles. As an example the room temperature field dependent magnetization of the 21 nm sample annealed at 400 C for 6 hours versus the unannealed sample is shown in Figure 6-7.

Annealing procedure improved the magnetization significantly by about 8 folds. This however, increased the coercivity a little bit. This is because amorphous alloys have reduced hysteresis loses [Ucar 12].

Figure 6-7: Field dependent magnetization of the annealed and unannealed 21 nm sample, measure at room temperature The morphology of the synthesized nanoparticles was observed with SEM shown in Figure 6-8. The average sizes of synthesized nanoparticles were estimated to be 21, 28,

36 and 42 nm. This is in good agreement with crystallite size estimated from XRD data using well-known Scherrer relation,

ퟎ.ퟗퟒ흀 푫 = (6-6) 풑 휷 퐜퐨퐬 Ѳ

108 where λ is wavelength of X-ray source, β is the full width at half maximum (FWHM) of diffraction peak, and θ is the Bragg angle.

Figure 6-8: Some SEM images of Y2Fe17 nanoparticles. Average particle size in (a) 42 nm, (b) 28 nm Figure 6-9 shows the magnetization as a function of applied field for the 21 nm sample; measured at 9 discrete temperature points from 10 K to 290 K. Zooming in this figure helped us determine the effect of the temperature on the magnetization and the coercivity.

109

Figure 6-9: Field dependent magnetization of the 21 nm sample, measured at 9 discrete temperatures from 10 to 290 K. Figure 6-10 shows the M(H) curves of Figure 6-9 plotted from 8000 Oe to 10000

Oe. Results show that by increasing the temperature there is a reduction in magnetization.

This occurs because as temperature increases, more thermal energy is supplied and individual electron spins become more likely to be in higher energy states, pointing opposite to their neighbors and less lined up, leading to a reduction in the total magnetism.

Figure 6-10: Field dependent magnetization of the 21 nm sample, measured at 9 discrete temperatures from 10 to 290 K, shown from 8000 to 10000 Oe.

110

Figure 6-11 shows the M(H) curves of Figure 6-9 plotted from -600 Oe to +600

Oe. Results show that by increasing the temperature there is a reduction in the amount of coercivity. This is because as temperature increases, more thermal energy is supplied and individual electron spins become more likely to be in higher energy states, pointing randomly, opposite to their neighbors and less lined up, therefore a smaller field is required to reduce the remnant magnetization to zero, hence reduction in the coercivity.

Figure 6-12 shows the coercivity as a function of temperature for the 21 nm sample.

Figure 6-11: Field dependent magnetization of the 21 nm sample, measured at 9 discrete temperatures from 10 to 290 K, shown from -600 to 600 Oe.

Figure 6-12: Coercivity as a function of temperature for the 21 nm sample

111

Figure 6-13 summarizes the effect of the temperature on the amount of magnetization and coercivity for the 21 nm sample.

Figure 6-13: Effect of temperature variation on the magnetization and the coercivity of the 21 nm sample. Accommodation (reptation) is a magnetizing process which occurs when the field is cycled between two extrema. Accommodation is different from magnetic aftereffect

(viscosity). Magnetic aftereffect is measured by observing the magnetization as a function of time with the applied field held constant. In magnetic accommodation the magnetization is observed as the field repeatedly traverses the same minor loop. Such measurements involve both time and interaction effects [Bennett 96]. For the 36 nm sample, five M(H) measurements at room temperature were performed consecutively and the resulting hysteresis loops are shown on the same plot in Figure 6-14. There was no

112 movement or shifts from one loop to the other, therefore sample showed no accommodation at room temperature.

Figure 6-14: Accommodation (reptation) measurements performed at 292 K for the 36 nm sample. To determine thermal stability of a sample at low temperature, accommodation measurements were performed on the 28 nm sample at 200 K following this procedure:

1) Sample was cooled down from room temperature (292 K) to 200 K, under zero

field.

2) At 200 K the temperature was kept constant and two M(H) loops were measured

(as shown in Figure 6-15, Loop 1-1, and Loop 1-2)

3) Immediately after M(H) measurements, the temperature was raised up to 292 K

with a rate of 4 K per minute.

4) Sample was cooled down once again to 200 K under zero field and after keeping

the temperature constant, another two M(H) measurements were performed (as

shown in Figure 6-15, Loop 2-1, and Loop 2-2)

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Aftereffect measurements of the 28 nm sample following the abovementioned procedure are shown in Figure 6-15. Because of thermal variation the loops did not overlap each other. The saturation magnetization of the second loops (Loop 2-1, 2-2) decreased from the ones in the first loops (Loop 1-1, 1-2) by 2.1%, falling from 13.19 emu/g in first loops to 12.91 emu/g in second loops. In addition, the average coercivity of second loops increased by 150%, rising up from 9 Oe in the first loops (Loop 1-1, 1-2) to 22.5 Oe in the second loops (Loop 2-1, 2-2).

Figure 6-15: Accommodation (reptation) measurements performed at 200 K for the 28 nm sample.

Figure 6-16 shows the temperature-dependent magnetization measurement of the synthesized nanoparticles measured in ZFC, FCC, and FCW sequences in a temperature range of 10 to 316 K under a magnetic field of 1000 Oe. Results show an increase in the magnetization of the nanoparticles as their size reduces. The 21 nm and 42 nm samples had the highest and the least amount of magnetization in this temperature span, respectively. The magnetization of the 21 nm sample is about five times than that of the

114

42 nm sample. The samples were magnetic at room temperature which indicates that the

Curie temperature must be above room temperature.

Figure 6-16: Temperature-dependent magnetization under 1000 Oe applied magnetic field for different-sized Y2Fe17 nanoparticles. When domains are formed, the magnetostatic energy decreases, and the wall energy and the magnetocrystalline anisotropy energy increase. The transition point from superparamagnetic to single-domain to multi-domain for each type of nanoparticles depends upon the size and geometry of the nanoparticles. In addition, temperature can influence the transition. Even though there is no definite point between each transition region, these can be approximated.

115 due to the band narrowing caused by the lack of orbital overlap. On the other hand, the surface anisotropy makes the surface layer magnetically harder than the core of the particle. At low temperature, this can result in the magnetization enhancement.

Size-dependent magnetization in temperature span of 10 to 316 K under an applied magnetic field of 1000 Oe was measured and is shown in Figure 6-17. It is clear that at any given temperature there is an inverse correlation between the nanoparticles size and the amount of magnetization. At any temperature, by reducing the size the magnetization increases. In addition, for a given size by increasing the temperature the magnetization reduces. This happens because as temperature increases, more thermal energy is supplied and individual electron spins become more likely to be in higher energy states, pointing opposite to their neighbors and less lined up, leading to a reduction in the total magnetism.

Figure 6-17: Size-dependent magnetization of Y2Fe17 nanoparticles in temperature range from 10 to 316 K under 1000 Oe applied magnetic field.

116

The hysteresis is an important parameter in evaluating the performance of the refrigerant materials. Hysteresis losses must be minimized to achieve a higher refrigeration capacity which is a key criterion in distinguishing a suitable refrigerant material. Figure 6-18 shows the field-dependent magnetizations of the four different- sized Y2Fe17 nanoparticle samples measured at room temperature (292 K). The coercivity reduces as particle size gets smaller from 42 nm to 36 nm to 28 nm, but it increases for the 21 nm sample. This is shown in Figure 6-19. Two main factors relate to coercivity: particle size and shape anisotropy. The relationship of HC ~ ΔNMS (where ΔN is the diversity of demagnetization factor in different direction) may explain why the 21 nm sample has higher coercivity. In addition, as shown by [Jeong 07] in Figure 2-17, the coercivity depends on the size of nanoparticles involved, and that for series of magnetic nanoparticles over a range of sizes, nanoparticles go through two maxima in the 2 separate regimes (single-domain and multi-domain).

117

Figure 6-18: Field-dependent magnetization of Y2Fe17 nanoparticles measured at 292 K.

Figure 6-19: Coercivity of Y2Fe17 nanoparticles as a function of size. 6.4 Conclusions

The yttrium-iron Y2Fe17 nanoparticles were successfully synthesized through chemical synthesis. The XRD analysis revealed the transformation of disordered crystal

118 structure to Y2Fe17 structure during the post-annealing process. The SEM analysis showed a formation of nanoparticles with an average size of 21, 28, 36 and 42 nm which were in close agreement with crystallite size estimation from XRD. The effects of temperature and size on the magnetic properties were examined. The magnetic characterization of the samples revealed a significant improvement in the magnetic properties of the nanoparticles. The magnetization increased with the reduction in particle size. The hysteresis first decreased by reducing the size of nanoparticles and then increased for the smallest sample. Results show that nanoparticles, as compared to their bulk counterpart, have a larger magnetocaloric effect with less hysteresis which is especially important in the magnetic refrigeration technology. Furthermore, for any sample, both the saturation magnetization and the coercivity decreased by an increase in temperature.

In the future we intend to vary the annealing temperature and the annealing time to see their effect on the magnetic properties, and we intend to measure M(T) at higher temperatures by implementing an oven attachment to our vector VSM.

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Chapter 7 . Magnetocaloric Effect and Magnetic Properties of Nanostructured Ni51Mn33.4In15.6 Heusler Alloy

Abstract: A systematic study of the size effect on the magnetic and structural properties of a Ni51Mn33.4In15.6 Heusler alloy converted to nanoparticles has been performed. We present new data to explain the enhanced magnetic and magnetocaloric properties of nanostructured Heusler alloy synthesized through high-energy ball-milling technique. The properties of the particles were characterized by x-ray diffraction, electron microscopy, and magnetometer techniques. Isothermal magnetic field variation of magnetization exhibits field hysteresis in bulk Ni51Mn33.4In15.6 alloy across the martensitic transition. As the size of the nanoparticles is reduced, there is an increase in magnetization, generating a higher magnetocaloric effect per unit of applied magnetic field, and a decrease in the coercivity and a substantial reduction in hysteresis.

7.1. Heusler alloys

A Heusler alloy is a ferromagnetic metal alloy based on a Heusler phase. Heusler phases are intermetallic with particular composition and face-centered cubic crystal structure. They are ferromagnetic (even though the constituting elements are not) as a result of the double-exchange mechanism between neighboring magnetic ions. The latter are usually manganese ions, which sit at the body centers of the cubic structure and carry most of the magnetic moment of the alloy.

The discovery of Heusler alloys dates back to 1903 when Friedrich Heusler reported that the addition of sp elements (Al, In, Sn, Sb or Bi) in a Cu-Mn alloy turn it into a ferro-magnetic material, even though no ferromagnetic element was contained

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[Heusler 03]. The basic understanding of crystal structure and composition of these alloys remained unknown for a long time. In 1929 X-ray measurements of Potter

[Potter 29] on a Cu-Mn-Al alloy revealed that all constituents of this system were ordered in a fcc lattice. Bradley and Rodgers [Bradley 34] investigated the Cu-Mn-Al system in detail using X-ray and anomalous X-ray scattering. They established a relationship between composition, chemical order and magnetic properties. After a successful interpretation of the crystal structure numerous investigations were made on these systems. It was found that the Heusler structure is formed essentially from the ordered combination of two binary B2 compounds XY and XZ. Both compounds may have the CsCl type crystal structure, for instance CoMn and CoAl yield

Co2MnAl. Thus the ability of compounds to form B2 structure indicates the possibility of forming new Heusler compounds. It was also discovered that it is possible to leave one of the four sublattices unoccupied (C 1b structure). The latter compounds are often called half- or semi-Heusler alloys, while the L21 compounds, where all four sublattices are occupied are referred to as full-Heusler alloys. Extensive experimental studies showed that the majority of Heusler compounds order ferromagnetically in stoichiometric composition. Crystal structure, composition and heat treatment were found to be important parameters for determining magnetic properties. With the discovery of half-metallic ferromagnetism in NiMnSb and the observation of shape memory effect in Ni2 MnGa compound, Heusler alloys received tremendous experimental and theoretical interest. The crystal structure is shown in

Figure 7-1.

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Figure 7-1: (a) L21 full-Heusler and (b) C 1b half-Heusler ordered structures. The structure consists of 4 interpenetrating fcc lattices. In the case of the half-Heusler alloys one of the four sublattices is empty. One notices that if all atoms are identical, the lattice is simply bcc. Disordered Heusler phases: (c) B2 disorder due to the Y-Z exchange and (d) A2 disorder caused by the X-Z or X-Y intermixing [vadalá, 2008]. 7.2 Introduction

(MCE): the temperature of most ferromagnetic materials is observed to rise upon the application of a magnetic field and fall upon its removal. Magnetic refrigeration is energy efficient and environmentally friendly preferred alternative for the compressor-based cooling systems. As a result, room-temperature MCE has attracted a lot of research interest in the last few years.

Majority of the magnetocaloric materials studied so far,[Gschneidner 00],[Khattak

15],[Tishin 03], are based on rare-earth compounds and some of which show a so called

122

“giant” MCE due to misappropriate use of Maxwell relations. Because of the presence of first order magnetostructural transition in these materials they show hysteretic behavior and Maxwell relations are inapplicable in calculating the ΔTad and the entropy change since they are valid only at the thermal equilibrium. Therefore, direct methods for measuring ΔTad must be performed [Ghahremani 12].

Recently rare-earth-free refrigerant materials have stimulated researcher’s interest and among them Heusler alloys are a promising candidate because of the fairly low-cost of the material and their large value of MCE as an outcome of martensitic phase transformation that takes place in a magnetically ordered state [Paramanik 15]. The structure and magnetic properties of the Heusler alloys have been studied because of their several technological implications and multifunctional properties [Pramanick 13] leading to a variety of research such as magnetic shape memory effect [Sutou 04],[Krenke 06], magnetoresistive behavior [Samanta 14],[Yu 06], barocaloric effect [Manosa 10] , magnetocaloric effect [Pathak 08],[Chattopadhyay 10], etc.

One technological potential for Ni-Mn-In Heusler alloys are in magnetic refrigeration technology due to a presence of large magnetocaloric effect. The adiabatic temperature changes (ΔTad) for these alloys are strongly dependent on the alloy composition and on the characteristic martensitic transformation temperature [Dubenko

15]. To date, refrigerants used in magnetic refrigeration technology do not have yet the needed characteristics to be used in large scale, due to technological restrictions namely the low adiabatic temperature change of bulk refrigerant, and the added burden of hysteresis.

123

Magnetic nanoparticles have attracted a lot of interest and research attention due to their potential application in the fields of material science, medicine, engineering, electronics, information technology, etc. [Abedini-Nassab 15], [Horrocks 12]. There are several top-down and bottom-up methods in synthesizing nanoparticles [Gubin 05]. The complex magnetic behavior exhibited by nanoparticles is governed by many factors, including their size, composition, shape, and shell-core structure. The increased surface to volume ratio and tailored structure in nanoparticles introduces many size dependent phenomena which may be used to optimize the physical and chemical properties.

Sequence of phase transformation and magnetic properties may be effectively controlled by adjusting the particle size and atomic packing. Theoretically, nanoscale magnetic materials have been shown to be a good candidate in magnetic refrigeration due to a presence of a large MCE in the superparamagnetic system [McMichael 92],[ Bennett 94].

This effect is observed not only in the systems consisting of magnetic nanoparticles, but also in magnetic molecular cluster systems [Spichkin 01]. Work by [Provenzano 03] and

[Yamamoto 00] showed MCE enhancement in superparamagnetic gadolinium gallium iron garnet and an enhancement of magnetic entropy change in superparamagnetic iron nitride nanograins, respectively. Work by [Shao 96b] showed that Gd0.85Y0.15 nanopowders displayed 15% increase of the MCE when compared with bulk alloy of the same stochiometry due to superparamagnetic behavior of the nanopowders in contrast to the ferromagnetic behavior of the bulk alloy.

These have motivated us to study the size-dependent magnetization behavior in

Ni51Mn33.4In15.6 Heusler alloy as a function of both temperature and applied magnetic field. In this thesis we report a significant increase in the amount of magnetization and a

124 reduction in magnetic hysteresis as the size of the refrigerant reduces in nano range.

These appealing results can be the key to increase the low adiabatic temperature change per unit of applied magnetic field and eliminating the irreversible burden of the hysteresis seen in magnetocaloric materials. It is expected that this would eventually lead to a design of more efficient commercially viable magnetic refrigeration systems.

7.3 Experimental

High purity elements nickel, manganese, and indium were used to prepare polycrystalline Ni51Mn33.4In15.6 alloy using induction melting technique in Argon (Ar) atmosphere. A rectangular prism specimen, with dimensions of 25 mm × 11 mm × 10 mm, was cut from the ingot. The specimen was heat treated in an Ar atmosphere at 1173

K for 8 h, aged at 773 K for 48 h, and then quenched in water. Figure 7-2 shows a photograph of the bulk sample.

Figure 7-2: Bulk Ni51Mn33.4In15.6 Heusler alloy The ingot was mechanically crushed in size followed by high energy ball milling to achieve nanoparticles. High energy mixer/mill SPEX 8000 from SamplePrep was utilized to mill the alloy at 1725 RPM and is shown in Figure 7-3. Alloy was milled in hardened steel grinding vial with hardened steel balls as shown in Figure 7-4. Ball to

125 powder ratio was 10:1. To minimize cold welding between powder particles and thereby inhibits agglomeration, 1 wt% methanol was used as a process control agent. The powders were milled, extracted and kept under Ar atmosphere to prevent any reaction with air. This was done in sealed glove compartment by vacuuming and refilling the glove with argon 4 times as shown in Figure 7-5.

To alleviate the excess amount of heat that is generated during the ball milling process, the milling was carried intermittently in 5 minutes intervals; milled for 5 minutes and rest for 5 minutes, so on and so forth. To obtain different-sized nanoparticles the milling time varied at 4, 7, and 15 hours, resulting in samples with an average particle size of 200, 65, and 30 nm, respectively. This is in agreement with other literatures on the synthesis of nanoparticles by high energy ball milling technique [Rajkumar 08],[Wang

07],[Nirmala 11],[Alvarez 10],[Chaudhary 14]. Finally, resultant powders were annealed at 673 K for 6 h to remove internal stresses which are created during the milling process.

Figure 7-3: SPEX 8000 mixer/mill from SamplePrep

126

Figure 7-4: hardened steel grinding vial and hardened steel balls

Figure 7-5: Argon filled glove compartment To determine the chemical structure, morphology, microstructure and composition the following procedures were performed. The powder X-ray diffraction

127 milled powders is less than 0.25%. Magnetization measurements were performed in the temperature range of 10 to 316 K using vector vibrating sample magnetometer (Lake

Shore VVSM 7410) with standard zero field cooling (ZFC), field cool cooling (FCC), and field cool warming (FCW) techniques. Before the magnetization M(T) measurements were made, the samples were cooled from 300 K to 9 K at 0 applied external magnetic field. A non-zero magnetic field was then applied and the measurements were done from

10 K to 316 K (ZFC) and then without removing the filed from 316 K to 10 K (FCC).

Subsequently, without removing the field, the measurements were done from 10 K to 316

K (FCW).

7.4 Results and discussion

Before synthesizing Ni51Mn33.4In15.6 nanoparticles, the magnetic properties of the bulk sample were characterized. The temperature dependence of the magnetization for

Ni51Mn33.4In15.6 bulk alloy from 10 to 316 K under an applied magnetic field of 100 Oe and 1000 Oe is shown in Figure 7-6. Results show the martensitic phase transformation occurs around 290 K. The splitting between ZFC and FCW magnetization data signifies the presence of magnetic frustration. This difference at low temperatures is a signature of the antiferromagnetic correlations and of the antiferromagnetic exchange interactions in the martensitic phase, which also manifest themselves in the existence of the exchange bias in these alloys [Dubenko 12].

128

Figure 7-6: Magnetization as a function of temperature in ZFC, FCC, and FCW sequences for Ni51Mn33.4In15.6 bulk alloy target under (a) 100 Oe (b) 1000 Oe Figure 7-7 illustrates field dependent magnetization in the neighborhood of the martensitic phase transformation. Measurements showed hysteresis in the temperature regime across the martensitic transition. This is related to field induced first order martensitic to austenite phase transition.

Figure 7-7: Magnetization as a function of applied field recorded in the vicinity of the martensitic transition for Ni51Mn33.4In15.6 bulk alloy target The XRD pattern of ball milled powders showed that the milling process induced a phase transformation and disordered the crystal structure due to excess amount of mechanical stress imported during the milling procedure. To offset this effect all samples

129 were annealed at 673 K for 6 h and a new set of XRD measurements is shown in Figure

7-8. The disordered crystal structure transformed to Heusler structure after heat treating the samples.

Figure 7-8: XRD pattern of: (a) annealed nanoparticles, (b) coarse-grained powder In addition, annealing the milled powders enhanced the magnetic properties of the samples. As seen Figure 7-9 the temperature dependent magnetization of the annealed 30 nm sample is much higher than that of the un-annealed sample. The inset in this figure presents the magnetization in ZFC and FCW of the un-annealed sample from 10 to 100 K showing a blocking temperature, TB, of 45 K.

130

Figure 7-9: Temperature dependent magnetization under an applied field of 1000 Oe for the 30 nm Ni51Mn33.4In15.6 alloy, un-annealed (blue) and annealed at 673 K for 6 hours (red). The inset shows the M(T) measurement of the nanoparticles from 10 to 100 K before annealing. The morphology of the synthesized powder samples were observed with SEM shown in Figure 7-10. The average sizes of synthesized nanoparticles were estimated to be 200, 65, and 30 nm. This is in good agreement with crystallite size estimated from

XRD data using well-known Scherrer relation,

ퟎ.ퟗퟒ흀 푫 = (7-1) 풑 휷 퐜퐨퐬 Ѳ where λ is wavelength of X-ray source, β is the full width at half maximum (FWHM) of diffraction peak, and θ is the Bragg angle.

131

Figure 7-10: SEM images of Ni51Mn33.4In15.6 nanoparticles Figure 7-11 shows the temperature-dependent magnetization measurement of the synthesized nanoparticles measured in ZFC, FCC, and FCW sequences in a temperature range of 10 to 316 K under a magnetic field of 1000 Oe. Results evidently show an increase in the magnetization of the nanoparticles as their size reduces. The 30 nm and

200 nm samples had the highest and the least amount of magnetization in this temperature span, respectively. The magnetization of the 30 nm sample is about four times than that of the 200 nm.

132

Figure 7-11: Temperature-dependent magnetization under 1000 Oe applied magnetic field for different-sized Ni51Mn33.4In15.6 nanoparticles The microscopic ordering of electron spins characteristic of ferromagnetic materials leads to the formation of magnetic domains; within each the local magnetization is saturated but not necessarily parallel. The main implication of the domains is that there is already a high degree of magnetization in ferromagnetic materials within individual domains, but that in the absence of external magnetic fields those domains are randomly oriented. A modest applied magnetic field can cause a larger degree of alignment of the magnetic moments with the external field, giving a large magnification of the applied field. Within domain walls, interfaces between regions in which the magnetization has different directions, the magnetization must change direction from that in one domain to that in the other domain. Domain walls have a finite width that is determined principally by exchange and magnetocrystalline energy.

Magnetic material forms domains to minimize the magnetostatic energy. This subdivision into more and more domains cannot continue indefinitely because domain 133 wall requires energy to be produced and maintained. Eventually an equilibrium number of domains will be reached for a given particle size. When domains are formed, the magnetostatic energy decreases, and the wall energy and the magnetocrystalline anisotropy energy increase. The transition point from superparamagnetic to single- domain to multi-domain for each type of nanoparticles depends upon the size and geometry of the nanoparticles. Even though there is no definite point between each transition region, these can be approximated. For example Fe3O4 is estimated [Guardia

11] to be superparamagnetic for a particle size of less than 25 nm, single domain within

25 to 87 nm and multi domain above 87 nm; and these values in nickel are, superparamagnetic for particle size of less than 30 nm, single domain between 30 to 83 nm and multi domain above 83 nm [He 12].

As particle size becomes smaller, the role of particle’s core and surface region becomes comparable. Now the surface region essentially modifies magnetization configuration of the particles and has an effect on its magnetic characteristics. For ferromagnetic nanoparticles, pure finite-size effects are expected to enhance the Ms value with respect to the bulk. Metal atoms at the surface present a higher magnetic moment due to the band narrowing caused by the lack of orbital overlap. On the other hand, the surface anisotropy makes the surface layer magnetically harder than the core of the particle. At low temperature, this can result in the magnetization enhancement.

Size-dependent magnetization in temperature span of 10 to 316 K under an applied magnetic field of 1000 Oe was measured and is shown in Figure 7-12. It is clear that at any given temperature there is an inverse correlation between the nanoparticles size and the amount of magnetization. At any temperature, by reducing the size the

134 magnetization increases. In addition, for a given size by increasing the temperature the magnetization reduces. This happens because as temperature increases, more thermal energy is supplied and individual electron spins become more likely to be in higher energy states, pointing opposite to their neighbors and less lined up, leading to a reduction in the total magnetism.

Figure 7-12: Size-dependent magnetization of Ni51Mn33.4In15.6 nanoparticles in temperature range of 10 to 316 K under 1000 Oe applied magnetic field The hysteresis is an important parameter in evaluating the performance of the refrigerant materials. Hysteresis losses must be minimized to achieve a higher refrigeration capacity which is a key criterion in distinguishing a suitable refrigerant material. Therefore, magnetic coercivity that describes magnetic hysteresis of ferromagnetic materials is an object of this research. Field-dependent magnetizations of the three different-sized nanoparticle samples were measured. Figure 7-13 illustrates

M(H) measurements at 150 K. It is apparent that the amount of coercivity (Hc) reduces as nanoparticles become smaller of the samples measured. At this temperature the 200 nm

135 sample had the highest amount of coercivity (42 Oe) and the 30 nm sample had the least

(2 Oe).

Figure 7-13: Field-dependent magnetization of Ni51Mn33.4In15.6 nanoparticles at 150 K. The magnetic hysteresis loops were measured at two other temperatures, 220 and

290 K as well. At each temperature for anyone of the samples, the coercivity was measured and is tabulated in table 7-1.

Table 7-1: Coercivity of Ni51Mn33.4In15.6 nanoparticles as a function of size and temperature

136

Results prove that coercivity of ferromagnetic particles is size dependent. As shown in Figure 7-14, at any temperature the coercivity (Hc) reduces by decreasing the nanoparticles size, therefore a reduction in magnetic hysteresis losses. This phenomenon occurs because as the size of magnetic nanoparticles increases, the nanoparticles become pseudo single domain and then multi domain structures in which the moments of each domain may not be aligned. After applying a magnetic field some of the non-parallel vector magnetic moments cancel, leading to a reduction in the amount of coercive field required to reduce the magnetization to zero. For small nanoparticles hysteresis losses are absent or negligible. Kneller [Kneller 63] related the decrease in coercivity with decreasing particle size to thermal effect in superparamagnetic particles.

Figure 7-14: Coercivity of Ni51Mn33.4In15.6 nanoparticles as a function of size in different temperatures 7.5 Conclusions

The Heusler alloy Ni51Mn33.4In15.6 nanoparticles were successfully synthesized with the same composition as the bulk target by high energy ball milling method. The

137

XRD analysis revealed the transformation of disordered crystal structure to Heusler structure during the post-annealing process. The SEM analysis showed a formation of nanoparticles with a mean size of 30, 65, and 200 nm which was in close agreement with crystallite size estimation from XRD. The nanoparticles undergo a structural phase transitions, tailored by their size, atomic order, and intrinsic magnetic structure, different from their bulk counterpart. The magnetic characterization of the samples revealed a significant improvement in the magnetic properties of the nanoparticles, namely the magnetization increased and the hysteresis decreased by reducing the size of nanoparticles. Results show that nanoparticles, as compared to their bulk counterpart, have a larger magnetocaloric effect with less hysteresis which is especially important in the magnetic refrigeration technology.

138

Chapter 8 . Conclusions and Future Research

Paving the path for making magnetic refrigeration technology to reach its full potential and become commercially viable is a multi-disciplinary research. To name a few this involves magnetization physics, metallurgy, nanostructures, quantum effects, etc.

Broadly, the research can be categorized in system design and magnetocaloric material selection.

In this research we optimized the active magnetic regenerator system at the IMR group by tuning the heat transfer medium and system’s operation conditions. We proposed experimental optimization procedure that must be applied to any AMR system in order to improve its performance. The results of this work demonstrated a significant performance increase in the magnetic refrigeration system by varying and optimizing the

AMR parameters. The optimized values are system dependent and need to be determined and measured for any AMR system by following the procedures that were introduced in this research.

The focus in magnetocaloric research is shifting toward materials with nanoscale structures because they exhibit a distributed magnetic transition, which leads to broader magnetic entropy curves with better magnetocaloric refrigerants. However, a good understanding of disorder, surfaces, interfaces, and their role in determining the distribution of magnetic exchange interactions in nanostructures is important, as it will allow tenability of the refrigerant capacity in magnetic nanostructures. This will eventually impact applications in magnetocaloric cooling near room temperature.

We investigated the effect of the size and temperature on the magnetic and magnetocaloric properties of magnetic nanoparticles. We performed experimental

139 research on two magnetocaloric materials, namely yttrium-iron (Y2Fe17) and Heusler alloy (Ni51Mn33.4In15.6). Results demonstrated that nanomaterials have higher magnetocaloric properties and less hysteresis compared to their bulk counterpart.

The area of magnetocaloric nanoparticles is still young and more research is required to understand different phenomena when the size of material reduces and varies in nano range. Among the future research to be conducted is further analysis of other interesting nanostructured magnetic materials, effect of different annealing time and temperature on magnetic behavior of nanoparticles, effect of different synthesis methods on magnetic properties of nanoparticles, etc.

It is expected that the optimization method introduced here and the results of the research done on magnetic nanoparticles will permit the design of a more efficient commercially viable magnetic refrigeration system.

140

Publications

Related to Dissertation:

1. Amir Aslani, Mohammadreza Ghahremani, Ming Zhang, Lawrence H. Bennett,

and Edward Della Torre. “Magnetocaloric Effect and Magnetic Properties of

Ni51Mn33.4In15.6 Heusler Alloy Nanoparticles.” IEEE Transactions on Magnetics,

under review (2016).

2. Mohammadreza Ghahremani, Amir Aslani, Abid Siddique, Lawrence H. Bennett,

and Edward Della Torre. “Optimization of Magnetic Refrigerators by Tuning the

Heat Transfer Medium and Operating Conditions.” AIP Advances, under review

(2016).

3. Khurram Khattak, Amir Aslani, Chidubem Nwokoye, Abid Siddique, Lawrence

H. Bennett and Edward Della Torre. “Magnetocaloric Properties of Metallic

Nanostructures.” Cogent Engineering (2015), 2: 1050324.

Other:

4. Mohammadreza Ghahremani, Amir Aslani, Lawrence H. Bennett, and Edward

Della Torre. “Magnetic State Stabilization in Ni51Mn33.4In15.6 Heusler Alloy.”

Cogent Physics (2015), 2: 1109019.

5. Abid Siddique, Shu Gu, R. Witte, Mohammadreza Ghahremani, Chidubem

Nwokoye, Amir Aslani, R. Kruk, Virgil Provenzano, Lawrence H. Bennett and

Edward Della Torre. “Electric Field-Controlled Magnetization Switching in Co/Pt

Thin Film Ferromagnets.” Cogent Physics (2016), 3: 1139435.

141

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Appendix A— Maxwell relations for magnetic materials

The derivation of the Maxwell relations for a magnetic material undergoing a magnetic work process is analogous to that for a material undergoing a pdv work process. The applied magnetic field H is analogous to the pressure p, and the quantity -μ νM is 0 analogous to v. The differential magnetic work is

(A.1) where μ0 is the permeability of free space, v is specific volume, and dM is the differential change in magnetization.

The differential combined first and second law for a magnetic material undergoing a reversible heat and magnetic work process, derived in chapter 2, is

(A.2) where umag is the specific internal energy, T is the temperature, and s is the specific entropy. The magnetic enthalpy is defined as

(A.3)

The differential magnetic enthalpy, dhmag, is then

(A.4)

The Helmholtz free energy for a magnetic system is defined as

(A.5)

156

The differential Helmholtz free energy, df, is then

(A.6)

The Gibbs free energy for a magnetic system is defined as

(A.7)

The differential Gibbs free energy, dgmag, is then

(A.8)

The differential internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy may also be expressed as the exact differentials

æ ¶umag ö æ ¶umag ö dumag = ç ÷ ds + ç ÷ dM (A.9) è ¶s ø M è ¶M ø S

æ ¶hmag ö æ ¶hmag ö dhmag = ç ÷ ds + ç ÷ dH (A.10) è ¶s ø H è ¶H ø S

æ ¶fmag ö æ ¶fmag ö dfmag = ç ÷ dT + ç ÷ dM (A.11) è ¶T ø M è ¶M ø T

æ ¶gmag ö æ ¶gmag ö dgmag = ç ÷ dT + ç ÷ dH. (A.12) è ¶T ø H è ¶H ø T

By comparing Equation A.2 to Equation A.9, Equation A.4 to Equation A.10, Equation

A.6 to Equation A.11, and Equation A.8 to Equation A.12, the following relationships

157 can be determined:

æ ¶umag ö æ ¶hmag ö T = ç ÷ = ç ÷ (A.13) è ¶s ø M è ¶s ø H

æ ¶umag ö æ ¶fmag ö H = ç ÷ = ç ÷ (A.14) è ¶M ø S è ¶M ø T

(A.15)

(A.16)

Equations A.13 – A.16 are sometimes called the thermodynamic definitions of T, H, -s, and –μ0vM.

Because dumag, dhmag, dfmag, and dgmag are exact differentials, their mixed second order partial derivatives are equal. That is, given a property z = z(x,y),

(A.17)

Equating the mixed second order partial derivatives of umag, hmag, fmag, and gmag we get

2 ¶ umag æ ¶T ö æ ¶H ö = ç ÷ = ç ÷ (A.18) ¶s¶M è ¶M ø S è ¶s ø M

(A.19)

(A.20)

158

(A.21)

Equations A.18 - A.21 are the Maxwell relations.

159