Mgb2 SUPERCONDUCTORS: PROCESSING, CHARACTERIZATION and ENHANCEMENT of CRITICAL FIELDS

Home , Lanthanum hexaboride, Omega (Cyrillic)

“I venture to define science as a series of interconnected concepts and conceptual schemes arising from experiment and observation and fruitful of further experiments and observations. The test of a scientific theory is, I suggest, its fruitfulness.” James Bryant Conant (1893-1978) U. S. Chemist and Educator.

MgB2 SUPERCONDUCTORS: PROCESSING, CHARACTERIZATION AND ENHANCEMENT OF CRITICAL FIELDS

DISSERTATION

Presented in Partial Fulfillment of the Requirements for

the Degree of Doctor of Philosophy in the

Graduate School of The Ohio State University

Mohit Bhatia, M.S.

***

The Ohio State University 2007

Dissertation Committee: Approved By:

Professor Suliman A. Dregia, Adviser ______Adviser Professor Michael D. Sumption, Adviser ______Professor John Morral Adviser Graduate Program in Materials Science and Engineering Professor Sheikh Akbar

ABSTRACT

In this work, the basic formation of in-situ MgB2, and how variations in the formation process influence the electrical and magnetic properties of this material was studied. Bulk MgB2 samples were prepared by stoichiometric, elemental powder mixing and compaction followed by heat-treatment. Strand samples were prepared by a modified powder-in-tube technique with subsequent heat-treatment. The influence of various heat- treatment schedules on the formation reaction was studied. Two different optimum heat- treatment windows were indentified, namely, low-temperature heat-treatment (below the melting point of Mg i.e. between 620 - 650oC) and high-temperature heat-treatment

o (>650 C) for the preparation of MgB2 with good transport properties. XRD was used to confirm phase formation and microstructural variations were studied with the help of

SEM. Following a study of the reaction temperature regimes, the focus turned to critical field enhancement via doping with various compounds targeting either the Mg or the B sites. The effects of these dopants on the superconducting properties, in particular the critical fields, were studied. Large increases in irreversibility field, oHirr, and upper critical field, Bc2, of bulk and strand superconducting MgB2 were achieved by separately adding SiC, amorphous C, and selected metal diborides (NaB2, ZrB2, TiB2) in bulk samples and three different sizes of SiC (~200 nm, 30 nm and 15 nm) in strand samples.

Lattice spacing shifts and resistivity measurements (on some samples) were consistent with dopant introduction to the lattice. It was also found that both oHirr and Bc2 depend

ii on the sensing current level which may be an indication of current path percolations.

These increases in the Bc2 were also complimented by an increase in the transport Jcs, especially for the SiC doped samples. It was important to differentiate between the effects on the transport properties arising from possible particulate enhanced flux pinning from that due to Bc2 enhancements, associated with smaller length scale disorder. Flux pinning analysis performed on SiC doped samples showed that while some small level of particulate-enhanced pinning was present, the majority of the pinning was associated with a grain boundary mechanism, suggesting that transport Jc increases were predominantly

Bc2 related.

Lastly, since the residual resistivity of a material is directly related to the electron scattering and hence Bc2, it can therefore be used as a measure to confirm the dopant introduction into the lattice. Normal-state resistivities were measured for various binary and doped MgB2 samples as a function of temperature. These resistivities were modeled based on the Bloch-Gruneissen equations. This allowed extraction of the residual resistivities, Debye temperatures and current carrying volume fractions for these samples, as well as providing information on the electron-phonon coupling constant. The residual resistivity was found to increase by a factor of three, Debye temperature decreased and the electron-phonon coupling constant increased marginally for the SiC doped samples as compared to the binary sample. This change in 0 and D confirmed the XRD evidence that the dopants were increasing oHirr and Bc2 by substituting on the B and Mg sites of the crystalline lattice.

iii

ACKNOWLEDGMENTS

It is a pleasure to thank the many people who made this thesis possible. First of all, I would like to express my deep and sincere gratitude to my advisor,

Professor M.D. Sumption. His wide knowledge of the subject and his logical way of thinking has been of great value for me. His understanding, encouraging and personal guidance have provided a good basis for the present thesis. I am also deeply grateful to my advisor, Professor S.A. Dregia for his detailed and constructive comments, and for his important support throughout this work.

I wish to express my warm and sincere thanks to Professor E.W. Collings. With his enthusiasm, inspiration and great efforts to explain things clearly and simply, he helped to make the subject fun for me.

I would like to thank Professor S.X. Dou, of University of Wollongong, Australia for their invaluable guidance on various issues and for providing some valuable samples for the study. Many thanks to Michael Tomsic, Mathew Reindfleisch and the entire team at The HyperTech Research Inc., Columbus, Ohio for their help with strand sample processing. I would also like to thank Dr. Bruce Brant, Dr. Scott Hannahs and

Dr. Alexey Suslov at the NHMFL, Tallahassee for providing their support for the critical field measurements during my numerous trips to the national lab.

I am indebted to my many past and present student colleagues for providing a stimulating and fun environment in which I learnt and grew. My special thanks to Dr.

Alexander Vasiliev for his help with TEM characterization. I also wish to thank the technical staff in the Materials Science and Engineering department at The Ohio State

University especially Henk Colijn, Cameron Begg, Gary Dodge, Ken Kushner and Steve

Bright who have helped me at all stages in the research.

My gratitude also goes towards the U.S. Dept. of Energy - Division of High

Energy Physics and NIH for funding this research under Grant Nos. DE-FG02-

95ER40900, DE-FG02-05ER84363, DE-FG02-07ER84914, 2R44EB003752-02,

1R44EB006652-01 and 4R44EB006652-02.

I also wish to thank my friends Srikant, Syadwad, Alex, Zaina, Ekta, Bijula,

Vivek and all others who have stood by me in good and bad times and have been like a family to me far away from the home.

Lastly, and most importantly, I wish to thank my parents, Girish and Ruchi Bhatia and my brother Madhur. I would not be where I am, without their foresight, constant support and love. To them I dedicate this thesis.

VITA

August 3, 1979 ……………………………….Born, Bharatpur, India

2002. ………………………………………….B.Tech (Honrs.) Ceramic Engineering Institute of Technology, BHU Varanasi, India 2005 ………………………………………….M.S., Materials Science and Engineering The Ohio State University, USA 2002-2007…………………………………….Graduate Research Associate The Ohio State University, USA

PUBLICATIONS

1) “Superconducting Properties of SiC Doped MgB2 Formed Below and Above Mg‟s Melting Point” Bhatia, M; Sumption, M. D.; Bohnenstiehl, S.; Collings, E. W; Dregia, S.A.; Tomsic, M.; Rindflisch, M.; submitted to IEEE Transactions on Applied Superconductivity (2006).

2) “Increases in the irreversibility field and the upper critical field of bulk MgB2 by ZrB2 addition.” Bhatia, M.; Sumption, M. D.; Collings, E. W.; Dregia, S.A.; Applied Physics Letters (2005), 87(4), 042505/1-042505/3.

3) “Effect of various additions on upper critical field and irreversibility field of in- situ MgB2 superconducting bulk material.” Bhatia, M.; Sumption, M. D.; Collings, E. W.; IEEE Transactions on Applied Superconductivity (2005), 15(2, Pt. 3), 3204-3206.

4) “Influence of heat-treatment schedules on magnetic critical current density and phase formation in bulk superconducting MgB2.” Bhatia, M; Sumption, M. D.; Tomsic, M.; Collings, E. W.; Physica C: Superconductivity and Its Applications (2004), 415, 158-162.

5) “Influence of heat-treatment schedules on the transport current densities of long and short segments of superconducting MgB2 wire.” Bhatia, M; Sumption, M. D.; Tomsic, M.; Collings, E. W.; Physica C: Superconductivity and Its Applications (2004), 407, 153-159.

6) “High Critical Current Density in Multifilamentary MgB2 Strands” Sumption, M.D.; Susner, M.; Bhatia, M.; Rindflisch, M.; Tomsic, M.;McFadden, K.; Collings, E.W.; submitted to IEEE Transactions on Applied Superconductivity (2006).

7) “Transport properties of multifilamentary in-situ route, Cu-stabilized MgB2 strands: one meter segments and the Jc(B,T) dependence of short samples.” Sumption, M.D.; Bhatia, M.; Rindfleisch, M.; Tomsic, M.; Collings, E.W.; Superconductor Science and Technology (2006), 19(1), 155-160.

8) “Magnesium diboride superconducting strand for accelerator and light source applications.” Collings, E.W.; Kawabata, S.; Bhatia, M.; Tomsic, M.; Sumption, M.D.; Proceedings MT19 (Genoa, 2005) – (submitted)

9) “Solenoidal coils made from monofilamentary and multifilamentary MgB2 strands.“ Sumption, M. D.; Bhatia, M.; Buta, F.; Bohnenstiehl, S.; Tomsic, M.; Rindfleisch, M.; Yue, J.; Phillips, J.; Kawabata, S.; Collings, E. W. Superconductor Science and Technology (2005), 18(7), 961-965.

10) “MgB2/Cu racetrack coil winding, insulating, and testing.” Sumption, M. D.; Bhatia, M.; Rindfleisch, M.; Phillips, J.; Tomsic, M.; Collings, E. W.; IEEE Transactions on Applied Superconductivity (2005), 15(2, Pt. 2), 1457-1460.

11) “Multifilamentary, in situ route, Cu-stabilized MgB2 strands.” Sumption, M. D.; Bhatia, M.; Wu, X.; Rindfleisch, M.; Tomsic, M.; Collings, E. W.; Superconductor Science and Technology (2005), 18(5), 730-734.

12) “Transport and magnetic Jc of MgB2 strands and small helical coils.”Sumption, M. D.; Bhatia, M.; Rindfleisch, M.; Tomsic, M.; Collings, E. W.; Applied Physics Letters (2005), 86(10), 102501/1-102501/3.

13) “Large upper critical field and irreversibility field in MgB2 wires with SiC additions.” Sumption, M. D.; Bhatia, M.; Rindfleisch, M.; Tomsic, M.; Soltanian, S.; Dou, S. X.; Collings, E. W. Applied Physics Letters (2005), 86(9), 092507/1-092507/3.

14) “Irreversibility field and flux pinning in MgB2 with and without SiC additions.” Sumption, M. D.; Bhatia, M.; Dou, S. X.; Rindfliesch, M.; Tomsic, M.; Arda, L.; Ozdemir, M.; Hascicek, Y.; Collings, E. W.; Superconductor Science and Technology (2004), 17(10), 1180-1184.

vii

15) “The effect of doping level and sintering temperature on Jc(H) performance in nano-SiC doped and pure MgB2 wires.” Shcherbakova, O.; Dou, S.X.; Soltanian, S.; Wexler, D.; Bhatia, M; Sumption M.D.; Collings, E.W. Journal of Applied Physics (2006), 99, 08M510-08M512.

16) “High transport critical current density and large Hc2 and Hirr in nanoscale SiC doped MgB2 wires sintered at low temperature.” Soltanian, S.; Wang, X.L.; Hovart, J.; Dou, X.L.; Sumption, M.D.; Bhatia, M.; Collings, E.W.; Munroe, P.; Tomsic, M.; Superconductor Science and Technology (2005), 18(4), 658-666.

17) “Thermally assisted flux flow and individual vortex pinning in Bi2Sr2Ca2Cu3O10 single crystals grown by the traveling solvent floating zone technique.” Wang, X. L.; Li, A. H.; Yu, S.; Ooi, S.; Hirata, K.; Lin, C. T.; Collings, E. W.; Sumption, M. D.; Bhatia, M.; Ding, S. Y.; Dou, S. X. Journal of Applied Physics (2005), 97(10, Pt. 2), 10B114/1-10B114/3.

18) “Improvement of critical current density and thermally assisted individual vortex depinning in pulsed-laser-deposited YBa2Cu3O7 thin films on SrTiO3 (100) substrate with surface modification by Ag nanodots.” Li, A. H.; Liu, H. K.; Ionescu, M.; Wang, X. L.; Dou, S. X.; Collings, E. W.; Sumption, M. D.; Bhatia, M.; Lin, Z. W.; Zhu, J. G.; Journal of Applied Physics (2005), 97(10, Pt. 2), 10B107/1-10B107/3.

FIELD OF STUDY

Major Field: Materials Science and Engineering

viii

TABLE OF CONTENTS

Abstract…………………………………………………………………………………..ii

Acknowledgements………………………………………………………………………iv

Vita……………………………………………………………………………………….vi

List of Figures…………………………………………………………………………....xii

List of Tables…………………………………………………………………………...xvii

Chapter 1 ...... 1 Introduction and Review of Superconductivity ...... 1 1.1 Introduction ...... 2 1.2 Superconductivity ...... 4

Chapter 2 ...... 15 Review of Magnesium Diboride ...... 15 2.1 Electronic Structure of MgB2...... 16 2.2 Preparation of MgB2 ...... 17 2.2.1 Introduction ...... 17 2.2.2 Thermodynamics of MgB2 ...... 18 2.2.3 Classification of Preparation Techniques (In-Situ vs. Ex-Situ) ...... 19 2.2.4 Preparation of Bulk Samples ...... 21 2.2.5 Preparation of Wire/Strand Samples ...... 23 2.2.6 Other Preparation Techniques...... 26 2.3 Characterization of MgB2 ...... 27 2.3.1 Microscopic Properties ...... 28 2.3.2 Critical Current Densities ...... 29 2.3.3 Resistivity ...... 29 2.3.4 Enhancement of Critical Fields ...... 32 2.4 Theory of Bc2 Enhancements ...... 33

Chapter 3 ...... 37 Processing and Characterization of Magnesium Diboride ...... 37 3.1 Processing ...... 38 3.2 Powders ...... 38 3.2.1 Bulk Sample Processing ...... 40 3.2.2 Strand Sample Processing ...... 42 3.3 Characterization Techniques ...... 44 3.3.1 X-ray diffraction ...... 44

3.3.2 Microstructural Analysis (SEM and TEM)...... 45 3.3.3 Differential Scanning Calorimetric (DSC) Measurements ...... 47 3.3.4 Superconducting Transition Temperature (Tc) Measurement ...... 50 3.3.5 Magnetic Critical Current Density (Jc,m) Measurements ...... 53 3.3.6 Transport Critical Current Density (Jc) Measurements ...... 56 3.3.7 Upper Critical Field (Bc2) and Irreversibility Field (oHirr) Measurements .... 58 3.3.8 Heat Capacity (Cp) Measurements ...... 60

Chapter 4 ...... 63 Effect of Reaction Temperature-Time on the Formation of Magnesium Diboride ...... 63 4.1 Introduction ...... 64 4.2 Influence of Reaction Temperature ...... 65 4.2.1 DSC Measurements and Analysis ...... 65 4.2.2 Microstructural Comparison ...... 70 4.3 Conclusion ...... 85

Chapter 5 ...... 87 Doping and its Effects on Critical Fields in Magnesium Diboride ...... 87 5.1 Introduction ...... 88 5.2 Effect of Reaction Temperature and Time on the Critical Fields of SiC Doped Samples ...... 89 5.3 Differences in the Effects of Mg and B site doping on the oHirr and Bc2 of in-situ Bulk MgB2 ...... 94 5.3.1 Doping of Bulk Samples for B and Mg Site Substitution ...... 95 5.3.2 Large Bc2 and oHirr in Doped MgB2 Bulk ...... 100 5.4 Temperature Dependence of oHirr and Bc2 with ZrB2 Additions ...... 105 5.5 Variation of oHirr and Bc2 in MgB2 wires with Sensing Current Level ...... 112 5.6 Conclusions ...... 116

Chapter 6 ...... 118 Flux Pinning Properties of SiC Doped Magnesium Diboride ...... 118 6.1 Introduction ...... 119 6.2 Flux Pinning in MgB2 ...... 126

Chapter 7 ...... 136 Electrical Resistivity, Debye Temperature and Connectivity in Bulk Magnesium Diboride ...... 136 7.1 Introduction ...... 137 7.2 Connectivity and Normal State Resistivity ...... 139 7.2.1 Sample Preparation and Resistivity Measurements ...... 143 7.3 Resistivity Analysis Using the Bloch-Grüneisen (B-G) Function ...... 143 7.4 Heat Capacity Measurement ...... 149 7.5 Conclusion ...... 152

Summary And Conclusion ...... 154

Appendix A List of Superconducting Parameters of Magnesium Diboride……………159

Appendix B Model and Calculations for Determining the Volume Fraction of the Current Carrying Matrix……………………………………………………………………...…160

Appendix C List of Symbols…………………………………………………………...163

List of References ...... 164

LIST OF FIGURES

Figure 1.1 Comparison of  vs. T for a non-superconducting and a superconducting material ...... 5

Figure 1.2 Typical  vs T plot for a superconducting material ...... 8

Figure 1.3 Critical field for a Type-I superconductor ...... 10

Figure 1.4 Critical fields for a Type-II superconductor ...... 10

Figure 1.5 Typical V-I curve for a superconducting material ...... 13

Figure 1.6 A general superconducting phase critical surface plot ...... 13

Figure 2.1 Crystal structure of MgB2. Boron planes are separated by Mg spacers. The atomic orbitals leading to σ- (inplane) and π- (out-of-plane) bonding are indicated ...... 17

Figure 2.2 Theoretical Phase Diagram of Mg-B ...... 18

Figure 3.1 Particle size distribution in the starting Mg powder ...... 39

Figure 3.2 Particle size distribution in the starting B powder ...... 39

Figure 3.3 Stainless steel die for bulk MgB2 compaction ...... 40

Figure 3.4 Step-ramp reaction tim-temperature profile for MgB2 samples ...... 41

Figure 3.5 Cross-sectional optical micrograph of a 19 filament MgB2 strand ...... 43

Figure 3.6 Schematic of the DSC apparatus ...... 48

Figure 3.7 Thermal lag for different DSC sample pan materials ...... 49

Figure 3.8 Typical DSC scan for Mg powder in the graphite pan ...... 50

xii

Figure 3.9 dc vs T for a superconducting material ...... 51

Figure 3.10 Simple schematic of a four-probe measurement, including a current source, Is, a voltmeter, V, a sample of resistance Rs, as well as current and voltage lead resistances RLI and RLV respectively...... 53

Figure 3.11 Schematic diagram of the vibrating sample magnetometer (VSM) ...... 54

Figure 3.12 Internal flux density profile in a slab of thickness D subjected to increasing field ...... 55

Figure 3.13 Typical M-H for a superconducting material ...... 56

Figure 3.14 Schematic of barrel sample holder for long length strand transport current measurements ...... 57

Figure 3.15 Schematic of the variable temperature Jc measurement probe ...... 58

Figure 3.16 Typical R vs. B curve and determination of oHirr and Bc2 ...... 59

Figure 3.17 Schematic of thermal connections for heat-capacity measurements ...... 61

Figure 3.18 Ce vs. T for a normal and a superconducting material ...... 61

Figure 4.1 DSC scan of as received Mg powder performed at four different heating rates ...... 66

Figure 4.2 DSC scan of a stoichiometric mixture of Mg and B powder performed at four different heating rates ...... 67

Figure 4.3 XRD scans performed on the mixed Mg + B powder before heating and after heating upto 625oC ...... 68

Figure 4.4 XRD scan after the complete MgB2 formation ...... 69

Figure 4.5 SEM (a) backscatter and (b) secondary electron images for sample MB30SiC10A (625oC/180min) ...... 71

Figure 4.6 SEM (a) backscatter and (b) secondary electron images for sample MB30SiC10C (675oC/180min) ...... 71

xiii

Figure 4.7  vs. T for samples MB30SiC10A and MB30SiC10C ...... 72

Figure 4.8 HR-SEM image for sample MB30SiC5C at 40K and 80K magnification ..... 75

Figure 4.9 TEM bright field image on binary bulk MgB2 sample MB700 ...... 80

Figure 4.10 EDX spectra from the pure MgB2 sample...... 81

Figure 4.11 HR-TEM image of MB700 (left), the CBED pattern (right top) and the simulated structure using the CBED pattern (right bottom) ...... 82

Figure 4.12 TEM bright field image on SiC doped bulk MgB2 sample MBSiC700 ...... 82

Figure 4.13 EDX spectra from the SiC doped bulk MgB2 sample MBSiC700...... 83

Figure 4.14 Temperature dependence of Jc vs B for sample MB30SiC10A ...... 84

Figure 4.15 Temperature dependence of Jc vs B for sample MB30SiC10C ...... 85

Figure 5.1 oHirr measurements on MgB2 strands doped with different sizes of SiC heat-treated at different temperatures...... 90

Figure 5.2Bc2 measurements on MgB2 strands doped with different sizes of SiC heat-treated at different temperatures ...... 91

Figure 5.3 Resistive transitions for fine (30nm) SiC doped MB30SiC10 strands reacted at different time-temperature schedules ...... 92

Figure 5.4 Values for 0Hirr and Bc2 vs heat-treatment time for various heat-treatment temperatures for MgB2 wires doped with 30nm SiC particles (MB30SiC10 series) ...... 93

Figure 5.5 Tc curves for the MB30SiC strands reacted for various times at 800C...... 94

Figure 5.6 XRD patterns for binary MgB2 sample (MB700) and samples doped with amorphous C (MBC700), SiC (MBSiC700), TiB2 (MBTi700), NbB2 (MBNb700) and ZrB2 (MBZr700) ...... 99

Figure 5.7 DC graph for bulk MgB2 samples with various additives showing superconducting transitions ...... 100

Figure 5.8 Tc vs oHirr for bulk MgB2 samples with various classes of additives ...... 101

xiv

Figure 5.9 Resistance as a function of applied field for bulk MgB2 samples doped with SiC and C ...... 102

Figure 5.10 V vs B for metal diboride doped bulk MgB2 samples...... 103

Figure 5.11 DC vs T for binary and ZrB2 doped bulk MgB2 samples ...... 107

Figure 5.12 XRD pattern for ZrB2 doped bulk MgB2 sample as compared to binary sample ...... 109

Figure 5.13 TEM bright field image of bulk sample MBZr700 ...... 110

Figure 5.14 EDX obtained from the selected grain of bulk sample MBZr700 ...... 110

Figure 5.15 Variation of 0Hirr with T for binary and ZrB2 doped MgB2 sample ...... 111

Figure 5.16  vs B for 15 nm SiC doped UW15SiC10A reacted at 640oC-40mins measured at 1, 10, 50, and 100mA of sensing current levels ...... 114

Figure 5.17  vs B for 15 nm SiC doped UW15SIC10C strands heat-treated at 725oC- 30mins measured at 10, 50, and 100mA of sensing current levels ...... 114

o Figure 6.1 oHirr vs T for Various SiC added samples reacted at 675 C/40mins ...... 121

o Figure 6.2 Normalized Fp vs h for MB30SiC5C (675 C/40min) ...... 124

Figure 6.3 Normalized Fp vs h for MB30SiC5C plotted along with various pinning functions ...... 130

o Figure 6.4 Normalized Fp vs h for binary MB675 (675 C/40min) plotted along with various pinning functions ...... 132

Figure 7.1 (T) for two MgB2 samples ...... 142

Figure 7.2 Temperature dependence of the mfor binary and doped MgB2 samples .... 144

Figure 7.3 (T) for binary MgB2, MgB2-TiB2 and MgB2-SiC samples ...... 145

Figure 7.4 m vs. T for all studied samples ...... 148

Figure 7.5 Total heat-capacity for pure and doped MgB2 at zero field ...... 151

Figure 7.6 Electronic heat-capacity (Cp(0T)-Cp(9T)) for pure and doped MgB2 ...... 151

Figure B.1 Effective resistivity of a material along x-axis (a) perpendicular to the layer structure; (b) parallel to the layer structure; and (c) with a dispersed second phase.

xvi

LIST OF TABLES

Table 3.1 Sample specification of all the bulk samples ...... 42

Table 3.2 Sample specifications of all the strand samples ...... 44

Table 4.1 Strand sample specifications ...... 70

Table 4.3 Average grain gize for SiC doped samples reacted at 675oC/40mins ...... 74

Table 5.1 Comparison of the critical fields for 30nm SiC doped MgB2 samples reacted at low-temperature and high-temperature window ...... 91

Table 5.2 Sample names, additives, and reaction temperatures...... 98

Table 5.3 Critical fields and temperatures for MgB2 with various additives...... 104

Table 5.4 Sample specifications for MBZr series samples ...... 106

Table 5.5 Heat-treatment schedules, compositions and measured superconducting properties for various ZrB2 doped MgB2 samples...... 108

Table 5.6 Sample specifications ...... 113

Table 5.7 Irriversibility fields (4.2K) and upper critical fields (4.2K) for UW-series strands using various sensing currents ...... 115

Table 6.1 Irreversibility fields for various SiC doped MgB2 strands ...... 120

Table 6.2 Upper critical dields for various SiC doped MgB2 strands ...... 120

Table 6.3 Comparison of superconducting properties for various SiC doped samples . 123

Table 6.4 Classification of pinning mechanisms ...... 128

xvii

Table 6.5 Flux-pinning exponents for various SiC doped MgB2 samples ...... 129

Table 7.1 Conducting volume fraction, residual resistivity, Debye temperature and coupling constant for three doped samples ...... 147

Table 7.2 Fitted parameters for all samples ...... 148

xviii

CHAPTER 1

INTRODUCTION AND REVIEW OF SUPERCONDUCTIVITY

1.1 Introduction

The existence of MgB2 as a simple hexagonal compound had been known since

1954 [1], but its superconducting properties were only discovered in 2001 [2]. Even though the transition temperature of MgB2 is mid-way between that of the high and low

Tc superconductors, MgB2 is in many ways more similar to low Tc superconductors. Its

critical temperature, Tc is 39K [2] surpasses 23.2K, of the Nb3Ge intermetallic [3] as well as 23K Tc of the YPd2B2C intermetallic borocarbide [4] compounds, the highest Tcs of the low Tc superconductors. Even though the Tc of MgB2 is almost 2-3 times lower than that of the mercury and cuprate based superconductors, which are widely available in wire and other usable shapes, there is still a wide interest in MgB2. This is because, unlike cuprates, MgB2 has a lower anisotropy in its superconducting properties, a much larger coherence length ((0K) ~ 4-5.2nm)[5, 6] penetration depth ((0K) ~ 125 –

180nm) [6, 7] and transparency of the grain boundaries to the current flow making it a suitable material for applications. Also, HTSC wires are relatively costly because they contain a large fraction of Ag (e.g. BSSCO) [6] or they require thin film deposition

(YBCO), while MgB2 is relatively easy to fabricate and the raw materials are less expensive.

Magnesium diboride has been extensively studied both theoretically and experimentally. Recent work has shown that doping as well as the addition of impurities to MgB2 can lead to better in-field properties, namely enhanced upper critical fields, Bc2, and enhanced transport critical current densities, Jc. Particularly high Bc2 improvements obtained for MgB2 thin films are a strong source of motivation for achieving similar affects in bulk and strand samples. The work on MgB2 superconductors presented focuses

2 on the processing of in-situ made MgB2 bulks and strand superconductors and characterization of their normal state and superconducting properties. In particular, phase formation, doping enhanced Bc2s and strand connectivity, are investigated for this new superconductor.

A brief literature review and an introduction to the recent work on MgB2 superconductors is presented in Chapter 2. This is followed by a description of our sample preparation and characterization techniques in Chapter 3.

Bulk MgB2 samples were prepared by stoichometric elemental powder mixing and compaction technique while strand samples were prepared by modified powder-in- tube technique in both cases with subsequent reaction. The formation reaction of MgB2 was initially studied by the Differential Scanning Calorimetry (DSC). Two reaction time- temperature windows were indentified, namely, a low-temperature reaction window

(below the melting point of Mg, i.e. <650oC) performed at 625oC for 180-360mins and high-temperature window (>650oC) carried out at 675-700oC for 40mins. X-ray analysis was performed to confirm the phase formation. Both of these heat-treatments gave very similar irreversibility fields and upper critical fields for MgB2. The low-temperature heat- treated sample was found to be less porous with homogeneously distributed finer pores as compared to the bigger pores found in the high-temperature heat-treated samples.

Detailed results in this regard are presented in Chapter 4.

Following the heat-treatment optimization, the influence of various dopants on the superconducting properties, especially the critical fields will be discussed in Chapter 5.

Large increases in oHirr and Bc2 for MgB2 were achieved by the addition of various dopants. Silicon Carbide, amorphous Carbon, and selected metal diborides (NaB2, ZrB2,

TiB2) were used in bulk samples and three different sizes of SiC (~200 nm, 30 nm and 15 nm) were used as dopants in strands.

Additionally, increases in transport Jc were seen with SiC dopants. While some changes in the flux pinning properties were seen with dopants due to the presence of second phase the increases in Jc were almost entirely due to increases in Bc2 of already pinned samples. Flux pinning force were studied for the SiC doped samples and described with the help of various flux pinning models. Detailed results and analysis of the pinning properties of SiC doped MgB2 strand samples are presented in Chapter 6.

Lastly, the resistivity of MgB2 was measured for various binary and doped samples as a function of temperature. This was done because the dopants increase Bc2 via increasing residual resistivity. Thus, we could, in principle use these measurements to confirm dopant introduction into the MgB2 lattice and correlate it with the Bc2 increases.

We measured the normal state resistances of MgB2 bulk samples (pure and doped) and fitted the resistivity data to the Bloch-Gruneissen (B-G) equation. Data obtained from various other literature sources, both single crystal, dense strands and thin films were also analyzed in a similar manner and compared to our results. Values of residual resistivity, conducting volume fraction and Debye temperature have been obtained from the fitting and are discussed in detail in Chapter 7. These results confirmed that SiC doping was site substituting in the lattice and effectively changing the residual resistivity leading to exceptionally higher Bc2s.

1.2 Superconductivity

Superconductivity is a phenomenon, observed in certain elements and compounds, which is defined by the condensation of charge carrying fermions in to a 4

Bose-Einstein condensation. This condensate has many properties. However, the two most obvious are perfect conductivity and perfect diamagnetism.

In a superconducting material, the resistance drops to zero below a temperature known as its critical temperature, Tc. This is shown schematically in Figure 1.1, where

(T) for a superconductor is compared to that for a normal conductor. Specific value of

Tc is a characteristic of the particular material. This effect, seen first in mercury by K.

Onnes in 1911 [8] was the first observation of superconductivity.

Non-superconductor

(T) 

Superconductor

Resistivity, Resistivity,

Temperature, T

Figure 0.1 Comparison of  vs. T for a non-superconducting and a superconducting material

Many advances in the understanding of superconductivity were made subsequent to its discovery. Major among these was the microscopic understanding given by

Bardeen, Cooper and Schrieffer [9] (BCS Theory), which is a full description of low Tc superconductors. In a simple heuristic explanation, of this theory, an electron moving through a conductor will attract nearby positive charges in the lattice. This causes a

5 deformation of the lattice and in turn causes another electron, with opposite spin, to move into the region of higher positive charge density. The two electrons are then held together to form a Cooper pair through the exchange of the lattice vibration quanta (phonons). If this binding energy is high enough to overcome the columbic repulsion then the electron remain together as a pair. In fact, a Bose-Einstein condensate if formed involving all of the free electrons, and they no longer suffer scattering by the lattice, leading to a zero resistance state. This, in the BCS framework, is referred to as electron-phonon coupling and is described by a dimensionless electron-phonon coupling constant, ep

The Cooper pairs described by the BCS theory are quasi-particles and follow the

Bose-Einstein statistics and hence the exclusion principle does not apply to them. This means the Cooper pairs can collectively condense into a lower energy state, the BCS ground state or the superconducting state, as compared to the normal state of the matter.

The condensation into the superconducting state results in the formation of the energy gap, Eg, on both sides of the Fermi energy in the single electron excitation spectrum.

An important characteristic length for the description of superconductors is called the coherence length, , which can be defined in terms of the BCS theory [10]. There is a minimum length over which the superconducting quasi-particle (Cooper pair) density can change, this length is given by . This  is related to the fermi-velocity for the material and the energy gap associated with the condensation to the superconducting state by

2hv    F 0 E g (1.1)

Where, vF is the Fermi velocity and Eg is the energy gap.

The second hallmark of the superconductors, i.e. “perfect diamagnetism”, was observed in 1933 [11]. It was found out that apart from the vanishing resistivity a change in magnetic susceptibility,  value to  = -1, i.e. perfect diamagnetism (Figure 1.2), is also associated with the Tc. In other words, not only the magnetic field is excluded from entering the superconductor, as given by perfect conductivity, but also any magnetic field trapped in the originally normal conductor is expelled on cooling it below the Tc. This is known as the Meissner effect [11]. Thus, according to the constituting equation for a magnetic material

B   H  M 0   (1.2)

Where, B (T) is the magnetic field induction within the sample, M (A/m) is the magnetization due to applied magnetic field strength H (A/m) and o is permeability which is equal to 4x10-7. Therefore, according to the Meissner effect, in a superconductor B = 0, thus

M  H (1.3) and hence the susceptibility, , which is defined as the ratio of the change in magnetization due to H is given by

dM    1 dH (1.4)

Transition is shown in Figure 1.2

(T)  0

Susceptibility,

-1 Tc Temperature, T

Figure 0.2 Typical  vs T plot for a superconducting material

The Meissner state only exists below a certain critical magnetic field, Bc, which is related to the free energy difference between the normal and the superconducting state

(the condensation energy of the superconducting state). This thermodynamic critical field

Bc can be determined by equating the energy per unit volume required to exclude the field from the superconductor to the total condensation energy, i.e. the difference of the Gibbs free energy per unit volume of the two phases at the zero field. That is,

2 Bc (T)  Gn (T)  Gs (T) 20 (1.5)

Where, subscripts n and s are used to describe the normal and the superconducting states.

Within a small distance from the surface, flux can penetrate the superconductor, this characteristic depth is called the penetration depth, L, and is of the order of couple

8 of hundred Ao. The penetration depth can be estimated using the London equation [12] which relates the curl of current density, J (discussed below) to the magnetic field B by

  1  xJ   B  2 0 L (1.6)

where L can be evaluated in terms of the superconducting electron density n and is given by

m L  2 0ne (1.7)

Superconductors can be classified into two groups; namely, Type-I and Type-II

(Figure 1.3 and 1.4). In Type-I superconductors the magnetic flux is perfectly shielded from the interior of the superconductor up to Bc, beyond which the material undergoes a first order transition into the normal state, i.e., a complete penetration of the magnetic flux above Bc. Type-II superconductors, however, switch from the Meissner state into a state of partial magnetic flux penetration or the mixed state at a critical field Bc1 which is lower than Bc. This state is characterized by mixed regions of superconducting and normal material and the magnetic flux penetrates in the form of small quantized units of flux = h/2e where h is Plank‟s constant and e is the electronic charge. The density of these flux lines increases with the increasing applied magnetic fields untill the entire material transitions to the normal state at some higher field called upper critical field, Bc2.

In this case, the material undergoes a second-order phase transition between the superconducting and the normal state.

Type-I

Normal State

Superconducting State

Applied Field,

Tc Temperature, T

Figure 0.3 Critical field for a Type-I superconductor

Type-II

Hc2 Normal State

Mixed State

Applied Field, Hc1

Superconducting State

Tc Temperature, T Figure 0.4 Critical fields for a Type-II superconductor

Apart from Tc and Hc another limiting factor for the superconductors is the critical current density, Jc. This is defined as the maximum amount of current per unit area that can be passed through the superconductor without destroying the superconducting state.

As described earlier, in Type-II superconductors the magnetic flux lines start to penetrate above Bc1. The fluxons form a 2D hexagonal lattice with compression shear properties. Additionally these flux lines experience a Lorentz force, due to the current passing through the conductor which is in the direction perpendicular to both the magnetic field and the current direction and causes the fluxons to move. This movement of the fluxons leads to power dissipation in the material and destroys the zero resistivity state. However, the movement of the flux lines can be postponed up to much higher

Lorentz forces by flux “pinning”, i.e. by introducing lattice imperfections such as impurities, lattice defects, or large numbers of grain boundaries. Thus, in principle Jc can be defined as the maximum current density that is required to generate a Lorentz force large enough to overcome the opposing bulk pinning force due to lattice imperfections and cause the fluxons to move. These considerations are further complicated in high- temperature superconductors and MgB2, where a temperature for fluxon lattice melting is notably different from Bc2. At this temperature, in unpinned superconductors, the elastic properties of the fluxon lattice disappear, and it “melts”. This effect occurs over a line in

B-T space. For pinned superconductors, the effective pinning of the lattice as a whole, which relies on both the pinning of individual fluxons as well as the elastic interactions of the lattice, is greatly reduced. This, a line similar to the flux lattice melting line in unpinned materials exists for pinned materials; this is called the irreversibility line. At higher temperatures this leads to an irreversibility field, oHirr, and vise versa. As a

11 practical matter, the melting and irreversibility lines occupy a similar region of the B-T diagram.

For practical purposes the critical current density Jc(T,B) of a superconductor, which is defined as critical current per unit cross-section of the superconductor, can be measured by detecting a voltage across the sample specimen which is equivalent to the electrical resistance due to the fluxon flow at a particular temperature and applied magnetic field with increasing applied current. The critical current, Ic, is defined as the point where the detected electric field reaches a set criterion, arbitrarily defined as equal to 0.1V/cm for low-temperature superconductors and 1V/cm for high-temperature superconductors. Figure 1.5 shows a typical V-I curve for a superconductor with Ic defined by 1V/cm criterion. The V-I characteristics of a superconductor can be modeled as

n  I  E  Ec   (1.9)  Ic 

Where, Io is the critical current corresponding to the electric field Ec. The typical values of n range from 10-100. For the curve shown in Figure 1.5 the value of n is ~25.

2e-5

1e-5

Voltage/Length, V/cm 5e-6

0 Ic

0 200 400 600 800 1000 1200 Current, A Figure 0.5 Typical V-I curve for a superconducting material

T Tc

Bc2

J J Jc c

Figure 0.6 A general superconducting phase critical surface plot 13

Having defined the three critical parameters of the superconductor, namely, Tc, Jc and Bc2 we can now define a superconducting critical surface on a temperature-current- field plot. This critical surface is shown in Figure 1.6. This suggests a kind of phase boundary and any point that lies inside this curve is in the superconducting state.

Chapter 2

REVIEW OF MAGNESIUM DIBORIDE

In this chapter, we will present a brief literature review of the work done on processing and characterizing MgB2 superconductors. Since this thesis concentrates on the bulk and strand MgB2, the literature work reviewed in this chapter corresponds to the similar kind of samples. In the last section of the chapter we will also present a simplified version of Gurevich’s “selective impurity tunning” mechanism for doping related enhancements of the critical fields in MgB2. This forms the basis of the work done in this thesis.

2.1 Electronic Structure of MgB2

0 0 MgB2 possesses a simple hexagonal structure with a = 3.05 A , c = 3.52 A and c/a = 1.157 [1, 2]. This structure of MgB2 is shown in Figure 2.1a. The B atoms are arranged in the form of honeycomb layers and the Mg atoms are present above the center of the hexagonal B rings. In this way, MgB2 has an appearance of an intercalation compound with planes of small B sandwiched in between planes of larger (ratio 1:6) Mg atoms (Figure 2.1a) but it actually functions as a 3-D B lattice stabilized by the Mg layer which serves as electron donor. Figure 2.1 shows the details of the bonding structure of

MgB2. The Fermi level electronic states, which are the highest occupied electronic states, in MgB2 are mainly  or  bonding boron orbitals as shown in Figure 2.1. This figure shows the  bonding states derived from the px-y B orbitals and the  bonding states derived from the pz B orbitals. The  bonding orbitals lie in the Boron plane and provide the corresponding 2-D  band while the  space charge extends both in and out of the plane thus forming a 3-D  band. This electronic band structure results in unique distribution of the density of states on the Fermi surface giving rise to BCS type s-wave two-band superconductivity in MgB2 [13] and marked deviation from single-gap model.

Boron honeycomb plains

B orbitals with  character Mg ions B orbitals with  character

Figure 2.1 Crystal structure of MgB2. Boron planes are separated by Mg spacers. The atomic orbitals leading to σ- (inplane) and π- (out-of-plane) bonding are indicated [14]

2.2 Preparation of MgB2

2.2.1 Introduction

MgB2 was first synthesized accidentally by Jones et al. [1] in their attempt to prepare and characterize, what they expected to be Mg3B2. They used a chemical route where they heated a combination of powdered B and excess Mg above that needed for the

o intended stoichiometric Mg3B2 phase for 1 hr at 800 C. Subsequent XRD analysis confirmed the existence of the MgB2 phase rather than the hoped for Mg3B2 .

2.2.2 Thermodynamics of MgB2

Magnesium is a very volatile material and hence to understand and to optimize the synthesis of MgB2 it is very important to understand the Mg-B phase diagram. The most widely accepted theoretical Mg-B phase diagram, prepared by Liu et al. [15], is shown in Figure 1.3. This diagram predicts the formation of three intermediate compounds: MgB2, MgB4 and MgB7, in addition to the gas, liquid and solid (hcp) phases of the magnesium and the -rhombohedral B solid phase. According to the phase

o diagram, below 1545 C and for atomic Mg:B ratios greater than 1:2, the MgB2 phase coexists with the Mg rich solid, liquid or gaseous phases. Recognizing that at 1 atm Mg melts at 650oC and boils at 1100oC. Therefore, for any kind of bulk preparation technique for MgB2, (assuming the liquid phase diffusion) the sintering temperature has to be in this

2400 Gas + Liquid

2000 Gas + MgB7

C o 1600 Gas + MgB4

Gas + MgB2

4 1200 7

Temperature, Temperature,

+ MgB

4 Liquid + MgB2 2

800 + MgBB (s)

MgB

Solid + MgB2 400 0.0 0.2 0.4 0.6 0.8 1.0 Atomic Fraction of B

Figure 2.2 Theoretical Phase Diagram of Mg-B (Re-drawn after [15])

18 range. This phase diagram also predicts all of the above MgBx phases to be „line compounds‟. Thus, it is practically impossible to form a totally stoichiometric end- compound which is completely free of second phase. An excess of B in the compound will lead to the formation of small amount of MgB4 phase while an excess of Mg may remain as an impurity phase. It has been shown that MgB4 is non-superconducting and can be present in the form of an insulating layer around the MgB2 grains hence its presence can be detrimental to the properties of MgB2. However, if Mg is present in very small amount (as un-reacted particulate impurity), it may act as a flux pinning center in which case it would lead to enhancement in the critical current density. Apart from the above mentioned phases, the existence of MgB12, MgB20 and Mg2B25 have been claimed by various authors but their existence is yet to be confirmed.

2.2.3 Classification of Preparation Techniques (In-Situ vs. Ex-Situ)

In general, two basic approaches are being followed for the preparation of MgB2 superconductor in its bulk and strand forms. These are, the ex-situ approach which involves compaction and sintering of the pre-reacted MgB2 powder and the in-situ approach in which a mixture of elemental Mg and B powders is reacted in the final form, either strand or bulk.

Grasso et al. [16-18] achieved high values of transport critical current density (Jc) using the ex-situ method, in some cases even without any further sintering. Even though the ex-situ process offers some preparation and stoichiometric advantages, a major disadvantage of this process over in-situ process is the poor ability of MgB2 particles to form a bulk monolithic structure. This has so far remained an important issue for further

Jc enhancement using this fabrication technique. 19

Dou et al. [19, 20] have used a two-stage wire fabrication process involving an in-situ process followed by an ex-situ process to demonstrate the relative advantage of both. The results of this experiment indicated that wires made by the ex-situ preparation procedure are not optimal. Likewise Pan et al. [21] have prepared a series of samples containing varying proportions of mixtures of (MgB2)1-x:(Mg+ 2B)x where x varied from 0 to 1.

While, on the ex-situ side (smaller x values) of the composition the microstructure had the appearance of a relatively homogeneous compressed powder with particle size of <5

µm and homogeneous porosity, on the in-situ side (higher x values) the structure appeared to be more nearly monolithic with better connected smaller grains. This may be because the liquid phase of the Mg+2B mixture during the sintering eventually turns into a MgB2 matrix in which initial particles of pre-reacted MgB2 powder are embedded. Pan et al. also observed a number of large voids attributable to the core shrinkage during

MgB2 formation (molecular volume of MgB2 is 32% lower than the molecular volume of stoichiometric Mg+2B). As reported by Zhao et al. [22] this porosity can be reduced either by pressing or if a higher overall deformation rate is used for mechanical processing. But, for the fabrication of Fe-sheathed wires high deformation rates are undesirable since they tend to work-harden the Fe, a disadvantage for long wire manufacturing and applications. The superconductivity property measurements of Pan et al.‟s samples suggest that the critical current density (Jc) and irreversibility fields (oHirr) increased with increasing x. Dou et al. have successfully used this in-situ reaction approach, in particular with SiC nano-particle and carbon doping [23-25].

In spite of clear advantage over the ex-situ technique, in-situ preparation has its own disadvantage: the density of the MgB2 core after its formation is rather low, and its

20 microstructure is extremely porous [26, 27]. This is a consequence of the phase transformation from Mg+2B → MgB2, because the theoretical mass density of the initial

Mg+2B mixture is significantly lower than that of the MgB2 phase.

2.2.4 Preparation of Bulk Samples

The basic technique of bulk-sample preparation involves powder mixing and compaction followed by reaction of the compacted forms. Various research groups, following the above approach and its variants, have reported numerous different optimal heat-treatment schedules based on their specific preparation procedures.

Larbalestier et al. [28] reported a multi-step heat treatment which included anneals at 600, 800 and 900oC sequentially for 1 hr at each temperature, followed by crushing and compacting, and subsequent heat-treating under pressure at temperatures

o ranging from 650 to 800 C. Dou et al. [26] heat-treated their SiC-doped MgB2 for

o 950 C/3 hrs followed by liquid N2 quenching. Hinks et al. [29] studied stoichiometric variations of in-situ materials heat-treated in an Ar atmosphere for 3 hrs at 850oC.

As can be seen from above, early works on MgB2 preparation have concentrated on high temperature and aggressive heat-treatments [26, 30-32]. But following the works of Liu et al. [15] on the thermodynamics and the work of Fan et al. [33] on the decomposition of MgB2, it is now widely accepted that the more aggressive heat- treatment may lead to the decomposition of MgB2 into MgB4 (following the reaction shown in equation 2.1) at 4.6x 10-6 torr Mg vapor pressure at around 830oC [34]. This has been reported to degrade the superconducting properties [35]. Also, Bhatia et al. [27] and

Dou et al. [36] have shown that MgB2 actually can be formed at relatively low-

21 temperatures possibly by the vapor-solid reaction between Mg and B due to very high vapor pressure of Mg even under its melting point, following [35]

2MgB2(s)  Mg(g) + MgB4(s) (2.1)

Apart from the Magnesium volatility, other major factors that affect the properties of the MgB2 are the O content (leading to the formation of MgO especially at the grain boundaries) and the Stoichiometry of the compound (starting composition to be Mg rich, stoichiometric or Mg deficient).

A detailed understanding of the effect of MgO content is still under investigation but it has been shown that the presence of MgO at the grain boundaries leads to differences in the connectivity between grains [37] and hence to irregularities in the critical current density. This effect has also been seen and confirmed by Larbalestier et al. [28].

Following Cooper et al. (1970) [38], who reported that the Tc of NbB2 could be increased to 3.87 K by synthesizing B-rich composition near NbB2.5, Zhao et al. [39] investigated Mg-deficient compositions and reported that lattice parameters and Tc changed with starting composition. They explained their results on the basis of the presence of either Mg vacancies or interstitial B atoms. However, contradictions exist in their claims of vacancy formation on the Mg site. They also observed MgB4 as an impurity phase in their Mg-deficient samples, which according to the Gibb‟s phase rule

(for a two-component system) is not possible; both Mg vacancy and the expected impurity phase cannot co-exist in the two-component MgB2 system under equilibrium conditions at constant T and P. In another study, Serquis et al. [40, 41] analyzed the Mg vacancy content and lattice strain in a series of MgB2 samples and reported Mg vacancy concentrations up to 5% in their samples. They concluded that Tc scaled with both the Mg

22 vacancy concentration and strain. As opposed to this, Hinks et al. [29] investigated the possible departure from stoichiometry of MgB2 by studying a range of compositions,

“MgxB2”, made at the same synthesis temperature. They observed no striking variations on traversing the phase boundary between B rich and Mg-rich compositions that could be related to any change in stoichiometry of the MgB2 phase. Although they saw small changes in both lattice constants and Tcs with composition, they associated them with the strain and impurity effects and not with a variation in stoichiometry. As opposed to Mg deficiency, studies have shown that adding excess Mg (10 - 15 mol %) during the in-situ

MgB2 preparation leads to improved properties. This can be explained based again on high Mg volatility and presence of MgO layer on Mg which reduces the amount of Mg actually present for the reaction with B.

Numerous studies have invoked the existence of nonstoichiometry in MgB2 as an explanation for differences among samples without providing experimental evidence that nonstoichiometry actually exists. For example, Chen et al. [42] found a correlation between residual resistance ratio ((300K)/(50K)) and starting mixture compositions, from which they concluded that defect scattering, possibly disorder on the Mg site, was responsible for the sample-to-sample variation. A number of authors have speculated that

Mg deficiency could explain the depressed Tcs observed in thin films [43, 44].

2.2.5 Preparation of Wire/Strand Samples

Even though studies of bulk superconducting samples provide important insights into the properties and understanding of the basic science of the material, most practical applications of MgB2 superconductors (and superconductors in general) require the

23 fabrication of dense wires (both mono and multi-filament) with high current densities at the desired operating temperatures. Fabrication of useful strands depends on certain additional factors in addition to those needed for proper phase formation. These include high Bc2, high level of connectivity and high level of flux-pinning, all present in km-long strands.

Impressive progress has been made in the fabrication of MgB2 wires, number of techniques having been developed to improve the processing parameters for achieving high desired critical current densities [16-18, 45-60]. These include, (i) the early works by Canfield et al. [46] who prepared wire-shaped bulk MgB2 (no sheath) by exposing B filaments to Mg vapor and (ii) the widely used powder-in-tube method including different variants of it. Even though, the Canfield method resulted in strands of diameter 160μm, with more than 80% density, without external metal sheath and stabilizer they cannot be considered to result in practical wires.

Powder-in-tube method

A common procedure for processing practical superconducting strands and tapes of MgB2 is the power-in-tube (PIT) method. At the simplest level, this method, consists of filling a metal tube with a suitable pre-cursor powder and drawing it into a wire through a series of dies. The wire can be subsequently rolled to form a tape. Sumption

[48, 49, 51, 52, 61], Grasso [16-18], Glowacki [62], Dou [36, 54, 55], along with other research groups employed this method to fabricate MgB2 wires with good superconducting properties in their samples using this technique.

Sheath material for PIT MgB2 wires

The choice of suitable sheath materials is crucially important for the MgB2 wire/tape fabrication. The following criteria are generally taken into consideration for the selection of sheath materials for practical applications: (1) chemical compatibility,

(2) ductility, (3) high thermal and electrical conductivities and (4) cost. Chemical compatibility is the most important factor as it directly determines the final critical current densities. Iron had been used as a sheath material in some of the early work on

MgB2 strand preparation [54, 63-65] as it exhibits better chemical compatibility with

MgB2 than that of copper and silver. Even so, it has been also shown that iron can react with MgB2 (at high temperatures) and form an interface layer [66]. Even though this reaction is slow and occurs at high temperatures and Fe and its alloys also provide magnetic screening to reduce the effect of external applied magnetic field on the critical current density [63, 67], still, the use of Fe sheath, because of its hardness, leads to the problems in terms of ability to draw finer diameter strands.

Copper on the other hand, is another important sheath material providing thermal and magnetic stability to the wire provided it can be protected from reaction with MgB2 or Mg [68] significantly. This reaction is more vigorous as compared to Fe and Mg at similar temperatures. This reaction can be controlled and reduced to a minimum by lowering the sintering temperatures and shortening the sintering times. As copper has high thermal and electrical conductivity, and yet is extremely low in cost, it should be one of the best candidates for the sheath material for MgB2 if the reaction between Cu and MgB2 can be controlled or significantly confined to a thin interface layer. In turn this would enhance Jc to the levels required for practical applications. This problem has been

25 solved by Sumption et al. by the use of thin layer of Nb as a diffusion barrier in between

Mg powder and Cu stabilizer. In practice, this Cu layer is then surrounded by a sheath of either Glidcop (O dispersion strengthened Cu) or an alloy of Cu-Ni to act as a drawing aid.

2.2.6 Other Preparation Techniques

Apart from the in-situ and ex-situ process often other special preparation procedures have also been proposed and studied by certain research groups. Apart from thin-film techniques which are not considered in this research, they include (i) Solid-state reaction route and (ii) Reactive liquid infiltration route.

Solid-State Reaction Route

This process, proposed by Shi et al. [69], is a chemical route for the synthesis of ultra fine MgB2. In this process an appropriate amount of anhydrous MgCl2 and excess

NaBH4 was milled and sealed in stainless autoclave. The mixing and sealing were carried out in a dry glove box with flowing Ar. The autoclave was then maintained at 600oC for 8 hr and cooled to room temperature. The powder was then washed with absolute ethanol followed by distilled water to remove NaCl and other impurities. The remaining solution

o after drying in vacuum at 60 C for 4 h gave the required final black ultra fine MgB2 powder with a typical particle size ranging from 200-500nm. The reaction involved during the above process can be written as [70]

MgCl2 +2NaBH4  MgB2 + 2NaCl + 4H2 (2.2)

Reactive Liquid Magnesium Infiltration

Giunchi et al. [32, 70-72] proposed an in-situ variant of the powder compaction procedure namely, “reactive liquid Mg infiltration”. This technique is proposed as an alternative to high pressure sintering to produce very dense bulk MgB2. In this method, liquid Mg infiltrates a porous preform of B powder having a green density of at least 50% of B true density. The infiltrated Mg then reacts with B and produces a dense MgB2 form

(92-95% dense). This reaction is the most efficient way at the pressure and temperature where the liquid + MgB2 phases co-exist in the Mg-B P-T diagram. Two important observations of this method are that, if appropriate amount of B is packed with high green density, the liquid Mg is able to percolate in to it even against the gravity and at the end of the reaction, a large void is formed in place of the original Mg.

2.3 Characterization of MgB2

MgB2 is distinguished by its relatively high Tc, simple crystal structure, large coherence lengths, high critical current densities and fields, and transparency of the grain boundaries to the supercurrent. A summary of the generally accepted values of various superconducting properties is provided in Appendix A. Much applied research on MgB2 since 2001 has concentrated on the “end use properties” to fine-tune the preparation processes to achieve the required product properties. However, a large parallel effort focuses on the fundamentals of reaction, microstructure and structural-property relationships.

2.3.1Microscopic Properties

In marked contrast to the cuprate high temperature superconductors, where high angle grain boundaries universally act as weak links and dramatically reduce the intergranular critical currents [73, 74]. Larbalestier et al. [28] along with Kambara et al. [75], in independent studies, noticed that the grain boundaries in the polycrystalline MgB2 appear to have a greater transparency to critical current densities (Jc) and a much more forgiving angular dependence. The dominant reason for this is that the coherence length is larger than that of BSSCO or YBCO, and has less anisotropy. The actual nature of these grain boundaries is also important and has been studied by Klie et al. [76], who carried on direct atomic resolution studies of the grains and the grain boundaries in a polycrystalline MgB2. They found no oxygen within the bulk of the grains but significant oxygen enrichment at the grain boundaries. Furthermore, the boundaries were found to consist of two distinct boundary types, one boundary type containing BOx phases with a width of < 4nm (i.e. smaller than the coherence length) while a second type contained a

BOx -MgOy(B) - BOz trilayer ~10-15nm in width (i.e. larger than the coherence length).

Such boundary features lead to the conclusion that although Jc is high overall, the structure-property relationships at grain boundaries are still important to control. Grain boundary structure is expected to be a complex function of processing conditions, and the control of the oxygen content at grain boundaries is essential for attaining optimal bulk critical currents. With the fore-going observation in mind, we note that Magnetic measurements of Jc have indicated that in dense bulk samples, the microscopic current density is practically identical to the intra-granular Jc measured in dispersed powders demonstrating that it is not generally not limited by grain boundaries.

2.3.2 Critical Current Densities

As compared to the Jc(B) data for Nb-Ti and Nb3Sn at 4.2 K and self fields, bulk

6 2 MgB2 achieves moderate values of critical current density, up to 10 A/cm . In applied

4 2 2 magnetic fields of 6 T Jc is maintained above 10 A/cm , while in 10 T Jc is typically 10

2 A/cm . The numerous studies aimed at increasing Jc have included the efforts of; variations of reaction temperatures and the addition of various dopants.

Suo et al. [66] found that annealing of the tapes increased the core density and sharpened the superconducting transition, raising Jc by more than a factor of 10. Wang et al. [77] and Bhatia et al. [49, 78] studied the effect of sintering time on the critical current density of MgB2 wires. The best properties were seen at lower sintering temperatures (~

750oC) because the shorter reaction-temperatures times limit the grain growth which is beneficial in terms of effective grain boundary pinning. Jin et al. [79] showed that alloying MgB2 with Ti, Ag, Cu, Mo, Y, has an important effect upon Jc.

In order to increase Jc in wires and tapes, the fabrication process must be optimized probably by using finer starting powders or by incorporating nanoscale chemically inert particles that would inhibit the grain growth and provide the pinning centers.

2.3.3 Resistivity

Resistivity () is a materials‟ parameter defined as =RA/L where A is the cross- section area, R is the macroscopic resistance and L is the gauge length. To be determined in detail in Chapter 7,  is the sum of a residual component, o, and an “ideal component, the temperature dependent i(T). The residual component includes contributions from:

29 within the grain, grain boundaries and impurities. Grain boundary, porosity and macroscopic connectivity issues have led to widely ranging values of resistivity. Values as high as 1mcm have been reported, some 100 times higher than other reports of

10cm [80]. The resistivity of a single crystal of MgB2, measured perpendicular to the c-axis by Eltsev et al. [81], is very low. Its value at 300 K (5.3 µ cm) is comparable to the low resistivities of metallic Cu (1.7 µ cm) or Al (2.65 µ cm). At 50 K, just above

Tc, the value is 1.0 µ cm.

It has been suggested that the high values of resistivities obtained in many polycrystalline samples can be interpreted in terms of “reduced connectivity”, due to a reduction in the effective cross-sectional area of the sample, which suggests that the critical current density Jc should be decreased by the same reduction in effective area.

Such a trend, namely that Jc depends inversely on ρ, has been seen in MgB2 films by

Rowell et al. [82]. However, the „reduced area effect‟ alone is not a complete explanation of the resistivity behavior. While the „area factor‟ is responsible for large variation, and also macroscopic limitations of Jc, more microscopic limitations are also important, these include the resistivity of the grains themselves (intragrain effects), the connectivity between the grains (intergrain effects), and hence will increase the apparent resistivity of the sample. These intergrain effects can be broken down as follows.

Insulating Precipitates: Presence of MgO and BOx in the grain boundaries as insulating precipitates may have the effect of disconnecting the MgB2 grains from each other, thereby reducing the effective cross-sectional area of the sample. The apparent resistivity of the sample would increase, and Jc will be decreased by the same factor.

Porosity: Porosity has been mentioned by a number of authors as a contributor to high sample resistivities. Feng et al. and Zhao et al. have reported that doping of MgB2 with Zr [83] and Ti [84] increases the sample density, reduces the porosity and increases the Jc values. But the resistivities of these undoped and Zr or Ti-doped samples were not reported. It is possible that Ti and Zr act as „getters‟ for oxygen, but their oxides will be good insulators, if they are present in the grain boundaries.

Insulating secondary phases: Sharma et al. [85] have suggested that in their samples, which were deliberately made Mg deficient, there was a separation into Mg rich

(or „Mg vacancy poor‟) and Mg deficient („Mg vacancy rich‟) phases. The former was claimed to be a metallic and superconducting phase, while the latter was claimed to be insulating. The effect of such an insulating second phase will be identical to the presence of porosity or the presence of MgO and BOx.

On the other hand the intragrain effects can be broken down in the following way

Intragrain oxides: If MgO and BOx are present as isolated small precipitates within the MgB2 grains themselves they would increase the intragrain resistivity. In this regard, Klie et al. [76] have observed that within the grains of bulk MgB2, there are commensurate precipitates of MgBO/nMgB2/MgBO, resulting from oxygen substitution on the B site in MgB2. Such precipitates would presumably act to decrease the mean free path within the grains resulting in higher resistivities.

Substitutions or inclusions in grain: Other impurities, present either as inclusions within the MgB2 grains, or substituted in the MgB2 lattice, will increase the intragrain resistivity. Carbon is one such potential impurity. Recently, Ribeiro et al. [86] have

31 reported preparing single phase Mg(B0.8C0.2)2 with a Tc near 22 K and an increased resistivity.

All the above factors contribute to the resistance in real materials. Chapter 7 is dedicated to attempting to separate and understand these influences.

2.3.4 Enhancement of Critical Fields

Because MgB2 is electronically anisotropic, Bc2 and oHirr are also anisotropic.

Round wires of MgB2 are untextured, this leads to measured properties which are averages of the anisotropic properties, but the influence of anisotropy persists in particular. The Bc2 anisotropy is about 5 for single crystals [87] but is reportedly much less in dirty materials. 

Larbalestier et al. [88-90] have undertaken a broad investigation of the effect of alloying and resistivity on Bc2 for MgB2 films. They showed that Bc2 could be strongly enhanced by doping with oxygen [88]. Wilke [91] and Orimichi [92] have shown that carbon doping can strongly enhance the parallel upper critical field Bc2|| from about 10 to about 33T at 4K. Braccini et al. [90], have attained values of Bc2|| which are about twice the above mentioned values. C-doping was common to these highest Bc2 samples. Record high values of Bc2(4.2)  35 T and Bc2||(4.2)  52 T have been reported for C-doped films perpendicular and parallel to the a-b plane, respectively [92].

In a series of very important experiments Sumption et al. and Dou et al. [23, 27,

54, 61, 64, 93-102] have studied the effect of SiC and C addition and have reported significant increases in the pinning properties and in Bc2 which were higher than 33 T at

4.2 K for bulk and strand samples. These results would be shown in the later chapters.

Latest works of Bhatia et al. [101, 103] on the ZrB2 and NbB2 (similar crystal structure as

MgB2) additions in small quantities (7.5 mole %) have shown a pronounced increase in the irreversibility fields. The Bc2 have been seen to increase to more than 28 T with ZrB2.

Reports of increases in Bc2 values for MgB2 are continually evolving. It has already been shown that addition or doping of impurities or second phase materials lead to an increase in these critical properties in MgB2. A theory for Bc2 enhancement due to non-magnetic impurities is described below.

2.4 Theory of Bc2 Enhancements

Bc2 of a superconducting material can in general be increased by adding nonmagnetic impurities [104-106]. These are specifically effective if the material is in the dirty limit, i.e. 2kbTc

 is the elastic scattering time. For a one-gap dirty superconductor, such as Nb3Sn and

NbTi, a simple universal relationship between the zero-temperature Bc2(0) and the slope dBc2/dT at Tc can be given in terms of normal state residual resistivity, o

 dBc2  Bc2 0  0.69  (2.4)  dT Tc and

 dBc2  4eckb    NF 0 (2.5)  dT Tc 

Where, NF is the density of states at the Fermi surface and e is the electronic charge. For the case of MgB2, it has been shown that there exist two distinct s-wave superconducting

33 gaps which reside on different disconnected sheets of the Fermi surface. These gaps, namely sigma (g) and pi (g) band gap, are 7.2mV and 2.3mV respectively at 0K. It has been shown by Gurevich [107] that for such case of two-band superconductor, the Bc2 can be significantly higher than the value predicted by the above Eqn (2.4). The distinct

Fermi surface of MgB2 provides it three different channels of impurity scattering, namely, the intraband scattering within the  and the  sheets of the Fermi surface and the interband scattering between the two. It is because of these multiple scattering channels that the Bc2 of MgB2 can be increased to a much greater extent than the single- gap superconductor not only by increasing the o but also by optimizing the relative weight of  and  scattering rates by selective substitution on either the B or the Mg site

[107].

Gurevich solved the Usadel equations for an anisotropic two-gap superconductor taking in account both the interband and the intraband scattering to obtain the equations for calculating Bc2 neat the Tc. According to his calculations Bc2,Tc is given by

80 Tc  T  Bc2,Tc  2 (2.6)  a D  a D 

 Where, a  1 (2.7) 0

 a  1 (2.8) 0

     (2.9)

1 2 0    4   (2.10)

In the above equations, s are either the interband or intraband superconducting coupling constants between the bands shown by the subscripts. D and D are the normal state electron diffusivities in  and  band respectively.

If D and D are equal to D then the above Eqn 2.6 reduces to the single-gap equation given by

4 T  T  B  0 c (2.11) c2,Tc  2D

Also, if the interband scattering is disregarded, i.e ==0, and considering that

>> the equation reduces to

40 Tc  T  Bc2,Tc  2 (2.12)  D

This means that the Bc2 is determined by the electron diffusivity of the band that has higher intraband scattering.

Gurevich also solved the equations for calculating zero-temperature Bc2(0). This equation is given as

0Tc  g  Bc2 0  exp  (2.13) 2 D D  2 

1  2 D 2 D  2  g   0  ln 2    ln    0 (2.14)  2   w D w D  w

w       (2.15)

If the D= D = D, Eqn 2.13 again reduces to the single-band equation given by

 T B 0  0 c (2.16) c2 2D

But if the diffusivities are not equal then the Eqn 2.13 predicts a strong enhancement of

Bc2(0) as compared to the general Eqn 2.4. For the limiting cases of very different diffusivities, Eqn 2.13 becomes

0Tc    0   0  Bc2 0  exp   , D  D exp   (2.17) 2D  2w   w 

And

0Tc    0   0  Bc2 0  exp  , D  D exp   (2.18) 2D  2w   w 

In such a case the limiting value of Bc2(0) is determined by the minimum of the two diffusivities contrary to the case of Bc2 where the maximum of the two dominates.

This independent variation of Bc2(0) and Bc2 near Tc has been referred to as

„selective tuning‟ [107]. It can be said that according to the two band dirty-limit theory for the BCS superconductors, such as MgB2, Bc2(T) can be significantly increased at low temperatures by dirtying the  band much more than the  band since D<

For the case of MgB2 this could be achieved by doping on the Mg site and thus creating a disorder in the pz boron orbitals, which forms the  band. It should be noted that achieving higher Bc2s in principle require both the  and the  band to be in the dirty limit but making the  band dirtier leads to higher increases in Bc2s with much less Tc suppression [108].

Chapter 3

PROCESSING AND CHARACTERIZATION OF MAGNESIUM DIBORIDE

The first half of this chapter describes the in-situ processing techniques for the bulk and strand MgB2 superconductors. Details of reactions used for the MgB2 formation are described along with the other processing conditions. In the later half of the chapter, we will present various characterization techniques for both superconducting- state and normal- state property measurements. These include microstructural analysis, thermal analysis, critical temperature, critical current (magnetic and transport), critical fields, normal state resistivity and heat-capacity. All measurements in subsequent chapters are performed on samples fabricated with these processes and characterized with these techniques.

3.1 Processing

As mentioned in the previous chapter, in general, two basic approaches are being followed for the preparation of MgB2; the ex-situ approach, which involves compaction and sintering of the preformed MgB2 powder, and the in-situ approach where a mixture of elemental Mg and B powders are reacted in the final wire. Each of these choices has advantages and disadvantages. This thesis focuses on in-situ prepared bulks and strands.

The use of elemental Mg and B, as well as the small size of the B present in the in-situ reaction promotes the ease of dopant incorporation, as well as its apparently high level of distribution (if not perfect uniformity). We selected the in-situ fabrication technique because of the obvious benefits of small grain sizes in the reaction product, low reaction temperatures and what we expected would be better dopant dissolution and homogeneity.

3.2 Powders

Both bulk and strand samples were used in this study. The starting elemental powders were 99.9% pure Mg powder and amorphous, 99% pure B. These powders had an average particle size of 5-6m for Mg and 0.3-0.4 m for B. Figures 3.1 and 3.2 show the particle size distribution of these two powders. XRDs of these starting powders are shown in Chapter 4.

Distribution

40 30 20 15 10 8 6 5 4 3 2 1.5 0

Diameter, m

Figure 3.1 Particle size distribution in the starting Mg powder

Distribution

3 2 1.5 1 0.8 0.6 0.5 0.4 0.3 0.2 0.15

Diameter, m

Figure 3.2 Particle (agglomerate) size distribution in the starting B powder

3.2.1 Bulk Sample Processing

Bulk, binary MgB2 pellets were prepared by in-situ reaction of a stoichiometric mixture of pure Mg and amorphous B powders. The powders which were V-mixed and then spex milled for 48 min had an uncompacted powder tap density of 0.5039 g/cc.

When needed, dopants were added during the initial V-mixing of the powders. The milled powder was then compacted into the form of a cylindrical pellet in a steel die,

Figure 3.3. The pellets, approximately 1 cm in diameter and 0.5 cm high were then taken out of the die, transferred to another steel casing and encapsulated in a quartz tube for heat-treatment under 250 Torr of Ar. A small amount of Ta powder was added to the capsule as an oxygen getter. Step-ramp type heat-treatment schedules similar to the one shown in Figure 3.4 were employed with various soaking temperatures.

3cm

Stainless Steel Top Plunger 5cm Die 1cm

Bottom Plug

Figure 3.3 Steel die for bulk MgB2 compaction

700

600

500

, T 400

300

Temperature, 200

100

0 0 20 40 60 80 100 120 140 Time, t, min

Figure 3.4 Step-ramp reaction tim-temperature profile for MgB2 samples

The reaction was carried out in a tube furnace with a uniform temperature zone

(+5oC) of 20cm. The temperature was controlled by OmegaR temperature controller coupled with K-type thermocouple. After reaction, the capsules were opened and the pellets removed as cylinders. They were then reshaped into 5x2x2mm3 cuboids for further characterization. Table 3.1 lists all the bulk samples that were used in this thesis.

Further details and results on these samples are shown in the following chapters.

Reaction Measurements Additive Sample ID Additive Temp-Time Mole % (oC-min) Bulk Samples MB700 - 0 700-30 XRD, SEM, TEM, Tc, oHirr, Bc2, (T) MBSiC700 700-30 XRD, Tc,oHirr, SiC 10 Bc2, (T), Cp MBSiC800 800-30 oHirr, Bc2 MBSiC900 900-30 oHirr, Bc2 MBAC800 Acetone Milled in 800-30 Tc,oHirr, Bc2 Acetone MBAC900 900-30 oHirr, Bc2 MBC700 700-30 XRD, Tc,oHirr, Amorphous 10 Bc2 MBC900 C 900-30 Tc, ,oHirr, Bc2 MBC1000 1000-30 oHirr, Bc2 MBZr700 700-30 XRD, Tc, oHirr, ZrB2 7.5 Jcm, Bc2 MBZr800 800-30 Tc, Jcm MBZr900 900-30 Tc, Jcm MBNb700 700-30 XRD, Tc, oHirr, NbB2 7.5 Bc2 MBNb800 800-30 oHirr, Bc2

MBNb900 900-30 oHirr, Bc2 MBTi700 TiB2 7.5 700-30 XRD, Tc,oHirr, Bc2, (T), Cp MBTi800 800-30 oHirr, Bc2

Table 3.1 Sample specification of all the bulk samples

3.2.2 Strand Sample Processing

Monofilamentary and multifilamentary strands with various sheath materials were also prepared for this study. A modified Powder-in-Tube (PIT) process was used to produce the subelements (for multi-filament) or the monofilament for MgB2/Sheath composite strands. In the so-called “CTFF” type PIT process used by HyperTech Inc., a

Columbus company, the powder was dispensed onto a Nb strip (23mm wide 2x0.25mm

42 thick) of metal as it was being continuously formed into a tube. This tube (5.9mm outer diameter) was then fed into a full hard 101 Cu tube.

After drawing to the proper size, these monofilaments were ready for further study as such. For making multifilamentary strands these filaments were then restacked round into 7, 19, 37 or 54 sub-element arrays inside of either Cu-30 Ni or monel outer tubes and then drawn to final size. A cross-sectional optical micrograph of a 19 filament strand is shown in Figure 3.5a. The strand had an outer diameter of 0.8mm. A higher magnification micrograph is shown in Figure 3.5b, where the filament array is shown.

Here we can see that the MgB2 filament (Black) is surrounded by a Nb reaction barrier followed by Cu stabilizer and finally a monel outer layer. These strands are reacted in Ar at various time-temperature schedules, similar to those shown in Figure 3.4. Table 3.2 shows all the strand samples used in this thesis. For studying the variation of critical fields with sensing current levels, a special set of strands made using the same powder were made at the University of Wollongong, Australia. Except for UW strands all others were 0.8mm in diameter.

Cu MgB2

Figure 3.5a Cross-sectional optical Figure 3.5b Higher magnification view micrograph of a 19 filament MgB2 strand of filamentary array for a 19 filament MgB2 strand showing filament and surrounding materials

Reaction Measurements Additive Sample ID Additive Temp-Time mole % (oC-min) Strand Samples o o MB - - 674 C, 700 C SEM, Fp, TEM MB30SiC5 30nm SiC 5 (625oC-180),  o MB30SiC10 10 (625 C -360),  o MB15SiC5 15nm SiC 5 (675 C -40), SEM H , o o irr MB15SiC10 10 (700 C -40) Bc2, Jc, Fp MB200SiC5 200nm SIC 5 or o MB200SiC10 10 (800 C -40) MB30SiC10 30nmSiC 10 (700, 800 or o 900 C) – (5, 10, Tc, oHirr, Bc2 20 or 30) UW30SiC10 30nmSiC 10 (640 or 725C)- oHirr, Bc2, Jc 30 UW15SiC10 15nmSiC 10 (640, 680 or oHirr, Bc2, Jc 725C) - 30

Table 3.2 Sample specifications of all the strand types

3.3 Characterization Techniques

The bulk and strand samples described above were characterized using a variety of techniques, including X-ray diffraction, optical and electron microscopy, differential scanning calorimetry, transport Jc measurement, critical field measurement, resistivity measurement, and heat-capacity measurement. Each of these techniques is described below.

3.3.1 X-ray diffraction

X-Ray powder diffraction analysis is a method by which X-Rays of a known wavelength are passed through a sample in order to identify the crystal structure. X-Rays are diffracted by the lattice of the crystal to give a unique pattern of peaks of 'reflections'

44 of different intensities at differing angles due to the wave nature of the X-ray. The diffracted beams from atoms in successive planes cancel unless they are in phase, and the condition for this is given by the Bragg relationship.

n  2d sin  (3.1)

Where, is the wavelength of the X-Rays, d is the distance between different plane of atoms in the crystal lattice and  is the angle of diffraction.

XRD analysis for this thesis was performed using a Sintac XDS-500 using Cu K-

 radiation between 2 values of 20-90o with a typical scan rate of 2o per min. The X-

Ray detector in this instrument moves around the sample and measures the intensity of these peaks and the position of these peaks (i.e. diffraction angle 2). The highest peak is defined as the 100% peak and the intensity of all the other peaks are measured as a percentage of the 100% peak. These peaks are representative of a particular crystal structure and compound, and can be identified using the JCPDS database.

3.3.2 Microstructural Analysis (SEM and TEM)

In a standard scanning electron microscope (SEM), electrons are thermionically emitted from a tungsten or lanthanum hexaboride (LaB6) cathode and are accelerated towards an anode. In FE-SEM capable machines, electrons can be emitted via field emission (FE) allowing for much smaller beam sizes. The electron beam energies are typically a few hundred eV to 100keV. These high energy electrons are focused by condenser lenses into a beam with a very fine focal spot of size varying from 1nm to

5nm. During beam-sample interaction the electrons lose energy by repeated scattering

45 and absorption within a volume of the specimen with a diameter somewhat larger than the incident beam diameter. This region is known as the interaction volume. The interaction volume typically extends from less than 100nm to around 5µm into the surface. In detail, the size of the interaction volume depends on the beam accelerating voltage, the atomic number and the density of the specimen. The energy exchange between the electron beam and the sample results in the emission of electrons and electromagnetic radiation which can be detected and processed to form the sample image.

Two types of images can be produced depending on the type of electrons detected. If low energy (<50eV) secondary electrons are detected the image thus formed is called the secondary electron image (SE). Because of the low energy of these electrons, they originate from within a few nanometers from the sample surface and hence the contrast in

SE provides the information on the sample morphology; furthermore they have a smaller interaction region and can be used to obtain a higher resolution image when used in conjunction with the lens described below. Steep surfaces and edges tend to be brighter than flat surfaces, which results in images with a well-defined, three-dimensional appearance. On the other hand, a second kind of image known as backscattered electron image (BSE) is obtained by the detection of high energy back scattered electrons which are backscattered out of the specimen interaction volume. The contrast in this kind of image provides the elemental information of the sample. The EDS analysis of MgB2 is difficult because B is a light element and thus BSE is less useful than usual. On the other hand high resolution SE images yield structure and grain sizes information.

For this study of MgB2 samples we have used, an XL-30ESEM and a, FE-SEM

Sirion. Due to the presence of the field emission gun and a special electron detector built

46 inside the final lens of the Sirion it provided the capability of obtaining high magnification images even at low accelerating voltages. Therefore, the Sirion was specifically used for obtaining HR-SE images and grain size analysis on the fracture samples. The typical excitation voltages used were 5kV with a spotsize of 3.

Transmission electron microscope (TEM), on the other hand, is an imaging technique whereby a beam of electrons is transmitted through a specimen, after which an image is formed, magnified and directed to appear either on a fluorescent screen or layer of photographic film, or can be detected by a sensor such as a CCD camera. One of the most important requirements for the TEM imaging is to obtain a very thin specimen. For the case of MgB2, since the sample has a very low density (~60%) it was difficult to obtain a thin intact sample slice and therefore the imaging was performed using Tecnai

TF-20 TEM on fine crushed powder samples suspended in ethanol. The sample was held on ultra thin carbon coated 400 mesh Copper grids.

3.3.3 Differential Scanning Calorimetric (DSC) Measurements

Differential scanning calorimetry (DSC) is a thermo-analytical technique which is based on measuring the difference in the amount of heat required to increase the temperature of a sample and reference, measured as a function of temperature. Both the sample and reference are maintained at almost the same temperature throughout the experiment. The basic principle underlying this technique is that when the sample undergoes a physical transformation such as phase transitions more (or less) heat will need to flow to it than the reference to maintain both at the same temperature. Whether more or less heat must flow to the sample depends on whether the process is exothermic

47 or endothermic. By observing the difference in heat flow between the sample and reference, DSC are able to measure the amount of heat absorbed or released during such transitions. A simple schematic diagram of DSC apparatus is shown in Figure 3. 6

Pan+ Sample Reference Pan

Heaters Computer

Figure 3.6 Schematic of the DSC apparatus

The computer maintains a uniform heating rate for both the sample and the reference and by measuring the difference in the heater power needed to maintain that rate we can compute the heat-flow as a function of temperature.

In our study, DSC was used for the determination of the exact formation temperature, as well as thermodynamic and kinetic parameters for the reaction of Mg and

B to form MgB2. Since the formation reaction is exothermic we will see an excess heat

o release during such reaction. Since Mg melts at 650 C and the formation of MgB2 is expected to happen in the temperature range of 600-700oC the DSC instrument was calibrated using Pb (mp 327.45oC ), Al (mp 660.33oC ) and then rechecked for the calibration by Zn (mp 419.52oC). Different pan materials were tried and finally in-house made graphite foil pans were used for the purpose of this study. Graphite was chosen over other materials based on easy formability, low thermal lag, and no reaction with Mg,

B or MgB2. Figure 3.7 shows the thermal lags of various pan materials considered. DSC studies were performed at the heating rates of 5, 10, 15 and 20oC/min in between 100oC and 700oC. Figure 3.8 shows the typical DSC scan for Mg powder in the graphite pan.

The peak observed at 655oC is an indication of the melting of Mg. Since the solid-liquid phase transition absorbed heat, the endothermic peak is observed in this case. Detailed results of the measurements on Mg and Mg + B powders are discussed in Chapter 4.

1.0 Pb in Fe Pb in SS 0.8 Pb in Al Pb in Cu

0.6

0.4

Heat Flow, W/g

0.2

0.0 326 328 330 332 334 336 338

o Temperature, C

Figure 3.7 Thermal lag for different DSC sample pan materials

1.5 Endo

1.0 Exo

0.5

Heat Flow, W/g 0.0

-0.5

-1.0 100 200 300 400 500 600 700

Temperature, oC

Figure 3.8 Typical DSC scan for Mg powder in the graphite pan

3.3.4 Superconducting Transition Temperature (Tc) Measurement

The transition temperature, Tc, of a superconductor is the critical temperature of the superconducting-to-normal state transition. Tc measurements were performed on the bulk samples using a EG&G Prinston Applied Research vibrating sample magnetometer

(VSM) model 4500 (see later Figure 3.9) coupled with a water cooled iron core 1.7T magnet. Tc was measured in terms of the sample‟s DC magnetic susceptibility,dc, which is the degree of the magnetization of the material in response to an applied magnetic field and is defined by the relationship

dM   (3.2) dH

Where, M (A/m) is the magnetization of the material and H (A/m) is the applied magnetic field.

dc vs T measurements were performed between 4.2K and 40K using a 50mT

field amplitude after initial zero field cooling. Figure 3.8 shows the typical dc, vs T plot for a general superconducting material. Marked in the plot are the beginning of the transition, Tcb, the end of the transition, Tce, and the midpoint, Tc. Also shown in the plot is the transition width, Tc, which is also a measure of the homogeneity of the superconducting phase. Unless mentioned otherwise, the midpoint of the transition, Tc, was used as the standard throughout this thesis.

0.2

Tce 0.0

-0.2 T

dc  -0.4 Tc

-0.6

Normalized Normalized

-0.8

Tcb -1.0

-1.2 28 30 36 38 Temperature, T (K)

Figure 3.9 dc vs T for a slightly inhomogeneous superconducting material

For strand samples the Tc measurements were performed either by dc vs T or by measuring resistance as a function of temperature using a four-point probe technique and at low sensing currents (10mA).

The four-probe technique is basically a simple technique for accurately measuring the transport properties of a sample. Four contacts must be made on the sample. For a bulk sample these contacts were made using a silver conductive compound while for the strand samples fine contacts were made using Pb-Sn solder. A simple circuit diagram shown in Figure 3.9 describes these connections. A known amount of current is passed through the outer (current) contacts and thus through the sample while the voltage drop is measured across the inner (voltage) taps. Since the voltmeter resistance is high, only a

very small amount of current actually passes in the lower half of the circuit, i.e. Iv << II,

The voltage drop thus measured by the voltmeter with high internal resistance is equal to the voltage drop across the sample, i.e. Rs. This technique is essential for accurate measurement of very small resistances in samples because, as, for the case of two-point measurement the measured voltage drop would be the total voltage drop across the sample and the current leads leading to an error in the measurement. Apart from that the gauge lengths should be no longer than 90% of the sample length to allow for the current transfer and current reversal is used at each measurement to cancel the effect of the thermal emfs.

RLI RLI

IV RLV RLV

V RV

3.3.5 Magnetic Critical Current Density (Jc,m) Measurements

The so called “magnetic critical current density”, Jc,m, can be extracted from M–H loop heights, Figure 3.13 using the Bean critical-state model. Magnetization (M-H) measurements were performed with vibrating sample magnetometer (VSM) using a field sweep amplitude of 1.7T and a temperature range of 4.2–40 K. A sweep rate of 0.07T/s was used for the M–H loops. Figure 3.11 is a sketch of the VSM. When a sample is placed in a uniform magnetic field it exhibits a magnetization and when this magnetized sample is mechanically vibrated perpendicular to the field direction there is a magnetic flux change, in the pick-up coils surrounding the sample which induces a voltage in the pick-up coils, proportional to the magnetic moment of the sample. The VSM is

53 calibrated using the standard room-temperature measurement of a sample of pure Ni

(NBS traceable).

Sample Holder Vibrator

LHe Cryostat

Pick-up Coils Sample

Hall Probe

Water Cooled Iron-core 1.7 T Magnet

Figure 3.11 Schematic diagram of the vibrating sample magnetometer (VSM)

For an irreversible type II superconductor the flux pinning creates a gradient in the fluxon line density, as described in Chapter 1. From Maxwell‟s equations; we know that

    xB  0 J (3.3) 4

Therefore, a field gradient would imply that the current would flow in a direction perpendicular to the field B. As shown in the schematic (Figure 3.12), for a slab of

54 thickness D, if B is in the z-direction and the flux gradient in the x-direction then the current would be in y-direction and would be given by

 o J  B (3.4) 4 x

z y x

B Be=oHe

-½ D ½ D

Figure 3.12 Internal flux density profile in a slab of thickness D subjected to increasing field

Following the above equation 3.4, critical current density for a long rectangular slab can be extracted from the height, M, of the M-H loop (Figure 3.13) using

Jc, m  2M   d   (3.5) d1    3L 

in SI units where J is measured in A/m2, M is measured in A/m and d and L are sample dimensions perpendicular to the field measured in m. The sample dimension along the field direction is large. (1-d/3L) is the shape factor in case the length of the slab,

L, is not infinite.

600

400

200

M 0

Magnetization, kA/m Magnetization, -200

-400

-600 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Magnetic field, T

Figure 3.13 Typical M-H for a superconducting material

3.3.6 Transport Critical Current Density (Jc) Measurements

The transport current density, Jc, was measured using the four-probe technique on both short samples and longer segments (about 1m). The short samples were 3cm in length with a voltage tap separation (gauge length) of 5mm. A 1V/cm criterion, as described in Chapter 1, was used for Ic. The longer segments were about 1 m, and were wound on a barrel-like “ITER” holders initially designed for strand testing under the

International Thermonuclear Energy Reactor, ITER, Jc-round-robin-test program (The holder specifications can be found in [109]). The measurements were performed in liq.

He at fields up to 15T. In our variant of the ITER test about one meter of wire was wound

56 onto 3.12cm diameter stainless steel barrel furnished with Cu end cylinders (Figure 3.14).

The Cu cylinders provide the current contacts and at the same time remove electrical contact generated heat to the He bath, recognizing that large currents need to be transported through the sample. These samples were wound on the sample holder and then reacted. After this the ends of the wires were soldered to the Cu cylinders, which in turn were soldered to the current probe using a Pb-Sn solder. The gauge length in this case was 50cm. The probe was capable of measuring up to 1800A. Nanovoltmeters were used for the voltage measurement along with a LabView coded user interface for the data acquisition.

3.12 cm

2.5 cm

Extended Copper Stainless Steel Barrel End-rings 3.15 cm

One meter of MgB2 sample, 0.8mm OD to be wound on these grooves

Figure 3.14 Schematic of barrel sample holder for long length strand transport current measurements

While the one meter segments were measured only at 4.2K, short sample measurements were also performed at temperatures of 4.2 - 30K. In this case the samples were mounted within a brass can which was then evacuated and back filled with a small amount of He exchange gas up to a pressure of 5x10-4 torr. A strip heater and a CernoxR temperature sensor provided sample heating and temperature measurement respectively.

A picture of the variable temperature Jc measurement probe is shown in Figure 3.15. The temperature was precisely controlled with a variation of only + 0.1K.

Vacuum Valve Stainless Steel Tube

Cu Current Leads (220A max current)

Brass Can Encapsulating Samples

Heater and Temperature Sensor Mounted on the Sample Holder Inside 

Figure 3.15 Schematic of the variable temperature Jc measurement probe

3.3.7 Upper Critical Field (Bc2) and Irreversibility Field (oHirr) Measurements

For Bc2 and oHirr four-point resistivity measurements were made on 1 cm long samples at the National High Magnetic Field Laboratory in Tallahassee, Florida.

Standard Pb–Sn solder was used for forming the contacts on the outer sheath, and the gauge length was 5mm. Sensing currents, of 1mA, 10mA, 50mA and 100mA, with current reversal were used to study the effect of current level on the measured critical

58 fields. Measurements were made at temperature ranging from 4.2 - 20K in applied fields ranging from 0 to 33T. The samples were placed perpendicular to the applied field, values of 0Hirr and Bc2 being obtained from the 10% and 90% points of the resistive transition. Figure 3.16 is a typical R-vs-B field curve. Indicated are 10% and 90% point of the resistive transition between the superconducting and the normal state corresponding to oHirr = 15.8T and c = 20.2T respectively. In following chapters we will discuss the results of critical field measurements made on various binary and doped MgB2 samples.

400

300

 200

100

oHirr Bc2 0 14 16 18 20 22 24 26 28 30 32 34 B, T

Figure 3.16 Typical R vs. B curve and determination of oHirr and Bc2

3.3.8 Heat Capacity (Cp) Measurements

Heat capacity measurements on solids can provide a considerable amount of information regarding the lattice, electronic and magnetic properties of the material.

Measurements on pure and doped MgB2 bulk samples in this study were performed on a

15T Quantum Design PPMS (Physical Properties Measurement System) with the heat- capacity option. The Cp measurements are based on the technique of carefully controlling the heat added to and removed from the sample while monitoring the resulting temperature change. During the measurement a known amount of heat is added to the sample at a fixed power which is then followed by a cooling period of the same duration.

Constant pressure heat-capacity is calculated using

dQ  Cp    (3.5)  dT  p

A schematic of the thermal connections to the sample and sample platform are shown below (Figure 3.17)

For the measurement of unit-volume superconducting specific-heat we assume that Cv = Cp. Further, the electronic specific-heat Ces in the superconducting state is approximately

2 3Hc0 3 Ces  t (3.6) 2Tc

3H 2 where, c0 = , the unit volume electronic specific-heat coefficient. Thus, 2Tc

C es  3t 3 (3.7) Tc

Agreeing with this over a limited temperature range in the BCS relationship

C es  aexp( b ) (3.8) T Tc

C where a and b are constants. In the BCS the relative jump at Tc is  1.43 Tc

Connecting Sample Apiezon Grease T B Wires T B h a h a e t e t r h r h m m a Platform a l Thermometer Heater l

Figure 3.17 Schematic of thermal connections for heat-capacity measurements

2 Superconductor C = e-T e e

Normal Material

Ce = T

0 0 1 T

Figure 3.18 Ce vs. T for a normal and a superconducting material

The heat-capacity was measured between 1.9 – 300K at both 0T and 9T. Since the lattice heat-capacity is not field dependent subtracting the 9T heat-capacity from the 0T data provided an appropriate approximation of the electronic heat-capacity, Ce, of the material which in case of a superconducting sample will show a peak at the Tc. This is because Ce is proportional to the temperature in the normal (non-superconducting) state while in the superconducting state, it varies as e−α /T for some constant α. Therefore, at the superconducting transition, Ce suffers a discontinuous jump. The sharpness of the heat- capacity jump is a measure of the cleanliness of the superconducting phase.

Apart from that the measured heat-capacity as a function of temperature can also be used to extract the D for the material which can lead to an estimation of the electron- phonon coupling constant for the superconductor. The detailed results in this regard are provided in Chapter 7. Figure 3.18 shows the Ce variation as a function of temperature for a normal and a superconducting material showing the sharp superconducting transition.

Chapter 4

EFFECT OF REACTION TEMPERATURE-TIME ON THE FORMATION OF MAGNESIUM DIBORIDE

In this chapter, the fundamental reaction of Mg and B leading to the formation of MgB2 is investigated. This is important to understand in order to improve the connectivity, dopant diffusion, and ultimately the transport properties of MgB2. DSC scans on Mg + B powder showed three exothermic peaks below the melting point of Mg, one of which was the MgB2 formation reaction, showingthat the formation of MgB2 phase was completed below the melting point of Mg (~655oC). This allowed us to define a high temperature window (above the melting pointof Mg) and a low-temperature reaction window (below the melting point of Mg). Efforts were made to characterize and understand the differences between the microstructures for samples processed within these windows. Microstructural characterization was also performed for binary and SiC doped MgB2 samples. This will be correlated to magnetic and electrical properties of these materials in Chapters 5-7.

4.1 Introduction

MgB2, as described in Chapter 2, is prepared by mixing B and Mg powders and then reacting them in temperatures between 620 – 900oC [78]. The actual temperatures and times vary considerably and to some extent are determined by the B powder used.

The melting temperature of Mg, 650oC, is much less than that of B (2076oC), and many groups clearly form or aim to form MgB2 by a combination of liquid Mg and solid B at

o about 650 – 700 C. It is also known that the MgB2 formation reaction is exothermic.

Additionally, the molar volume of MgB2 is 37% less than the total molar volumes of its constituents, so the reaction tends to generate porosity within the structure. Our present picture is that MgB2 forms by the inward diffusion of Mg into B particles with more B- rich compounds forming near the B-core at the early times, which are converted to more

Mg rich compounds at the later times reaching a stoichiometry of MgB2 as more and more Mg diffuses in. However, the details of this formation are not clear at this point, in particular how it progresses with time at different temperatures.

For MgB2 superconducting strands, the formation, porosity, and connectivity are very important properties which ultimately dictate its electrical and magnetic properties.

Therefore, for both theoretical and practical reasons, it becomes essential to understand the formation reaction mechanism to be able to further improve the connectivity of the reacted strands, achieve sufficient dopant diffusion, and hence to produce strands with better transport properties and higher Bc2s. Differential scanning calorimetry (DSC) of the

MgB2 formation reaction was chosen as the starting point, which was used for the determination of the exact formation temperature and the thermodynamics of the reaction of Mg and B to form MgB2. Exothermic peaks occurring below the melting of Mg

64 suggested that MgB2 was actually formed before Mg melting. This was subsequently confirmed by XRD. This defined two temperature windows for the formation of MgB2.

The microstructure and properties of MgB2 samples processed within these two windows were then compared and with and without dopants.

4.2 Influence of Reaction Temperature

4.2.1 DSC Measurements and Analysis

Differential scanning calorimetry (DSC) measurements were next performed first on pure, as-received Mg powders and then on Mg + 2B powders prepared as described in

Chapter 3 (Sec. 3.2.7). Figure 4.1 is the DSC scan of Mg powder in graphite pan. These scans are performed at varying heating rates. A large endothermic peak is seen at 650oC indicating the melting of Mg. Further, a small exothermic peak was seen around 500oC.

This peak shows the decomposition of a small amount of surface hydroxide leading to the formation of MgO given by the following reaction

Mg(OH)2  MgO + H2O

Endo o 3 5 C/min 10 oC/min 15 oC/min o 2 20 C/min

, W/g

Heat Flow,

-1 Exo 400 450 500 550 600 650 700 Temperature (oC)

Figure 4.1 DSC scan of as received Mg powder performed at four different heating rates

After Mg, DSC scans were performed on a stoichiometric mixture of Mg and B at four different heating rates. Noticeable are three pronounced exothermic peaks, with peaks „a‟ and „b‟ at around 550oC and peak „c‟ around 650oC. The first group is believed to arise from the Mg(OH)2 decomposition reaction described above and probably from reaction between Mg and hydrated B2O3 on the B surface leading to highly exothermic

MgO formation and a small amount of MgB2. This peak has been observed by various authors and detailed work in this field has been performed by Bohnenstiehl et al. [110].

The third exothermic peak „c‟ represents the completion of the Mg+B to MgB2 reaction.

Finally, the absence of an endothermic peak at the melting point of Mg (650oC) is evidence for the fact that there is no remnant Mg after earlier reaction and the formation reaction is completed before 650oC.

1 Endo 0

-1

-2

, W/g

Q -3 Peaks 'a' and 'b'

-4

Heat Flow, 05 oC/min -5 10 oC/min -6 15 oC/min 20 oC/min Peak 'c' Exo-7 100 200 300 400 500 600 700 Temperature (oC)

Figure 4.2 DSC scan of a stoichiometric mixture of Mg and B powder performed at four different heating rates

Figure 4.3 shows the XRD scans performed on the mixed powder before heating and after heating to 625oC, i.e. after the completion of peaks „a‟ and „b‟. The difference in the XRD scans indicates the formation of small amount of MgB2 after this first set of peaks („a‟ and „b‟) which on isothermal heating at this temperature for long time would lead to complete formation as indicated by the shifting of the peak „c‟ towards lower temperatures with reducing heating-rates as in Figure. 4.2. The XRD performed after the completion of the reaction is shown in Figure 4.4.

MgB2 Peaks Mg Peaks

101 110 Mg+2B 625oC

004 101 002 Intensity Mg+2B Un-Heat treated 100 110 103 112 201

30 40 50 60 70 80 2

Figure 4.3 XRD scans performed on the mixed Mg + B powder before heating and after heating upto 625oC

7000 101 6000

5000

4000 100

110

3000Intensity 002 112 2000 102 201 111 200 1000

0 20 40 60 80

2

Figure 4.4 XRD scan after the complete MgB2 formation

Following this a series of monofilament strand samples were prepared by the

CTFF based technique described in Chapter 3 (Sec. 3.2.1) in order to study on wire samples the effect of this low-temperature synthesis on the microstructure of the final compound and to compare it to the material formed at the higher-temperature heat- treatment. These strands have three different sizes of SiC added (15nm, 30nm and

200nm). One set was reacted, as described above, at 625oC for 180mins (low-temperature window) and another set at 675oC (high-temperature window). Details of the strands are described in Table 4.1.

SiC Size Reaction Temperature-Time Sample ID SiC mole % (nm) (oC-min) MB30SiC5A 5 30 625-180 MB30SiC5C 5 30 675-40 MB30SiC10A 10 30 625-180 MB30SiC10C 10 30 675-40 MB15SiC5A 5 15 625-180 MB15SiC5C 5 15 675-40 MB15SiC10A 10 15 625-180 MB15SiC10C 10 15 675-40 MB200SiC5A 5 200 625-180 MB200SiC5C 5 200 675-40 MB200SiC10A 10 200 625-180 MB200SiC10C 10 200 675-40

Table 4.1 Strand sample specifications

4.2.2 Microstructural Comparison

Figures 4.5 (a and b) show the SEM backscatter and secondary images respectively of samples MB30SiC10A while Figures 4.6 (a and b) show the similar images for sample MB30SiC10C. These images were taken at 10kV excitation voltage using an XL-30 ESEM. These images clearly show that both samples have porosity, visible as dark holes in the SE image, with probably a little more porosity in sample

MB30SiC10C (high-temperature) than in sample MB30SiC10A (low-temperature). The longer heat-treatment administered to sample MB30SiC10A appear to lead to slightly higher densification.

(a) (b)

Figure 4.5 SEM (a) backscatter and (b) secondary electron images for sample MB30SiC10A (625oC/180min)

(a) (b)

Figure 4.6 SEM (a) backscatter and (b) secondary electron images for sample MB30SiC10C (675oC/40min)

In addition to proper phase formation, it is important to know if the phases formed have the expected superconducting properties within the grains and that the grains are substantially connected. To prove this, resistive Tc measurements were chosen. A Tc near the normal Tc of 39K would confirm the presence of proper MgB2. The transition width is correlated to the purity of the sample, and a complete transition to the superconducting state for these polycrystalline samples indicate some level of connectivity. Resistive Tc measurements were then performed on samples MB30SiC10A and MB30SiC10C using the four probe technique mentioned in Chapter 3 (Sec. 3.2.6). Figure 4.7 shows the 71 resistivity of the composite material (MgB2 + Sheath) as a function of temperature, it can be seen that the Tc (mid-point transition) of sample MB30SiC10A, is 33.2K while that for sample MB30SiC10C, is 33.9K. The Tcs are depressed below that of the binary MgB2

(39K) because of the SiC doping; Tc values of the SiC doped samples are expected to vary from 32-36K. Even-though the Tc is slightly lower for the sample MB30SiC10A, the transition is sharper. A Tc of almost half of the sample MB30SiC10C indicated that a the sample MB30SiC10A (low-temperature window) is more homogeneous.

MB30SiC10A- 2.0 (625oC-180min) MB30SiC10C - (675oC-40min) 1.5

-cm



,  1.0

Resistivity, Resistivity, 0.5

0.0 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 Temperature, T, K

Figure 4.7  vs T for samples MB30SiC10A and MB30SiC10

Our aim in the later chapters is to study the influence of dopants on the critical fields, pinning and connectivity of MgB2. In order to do so we needed to select the best temperatures for the reaction. We chose to look both at reaction temperatures above the

o Mg melting, as is usually done, as well as in the 625 - 640 C range where we see MgB2 formation below Mg melting point. We can thus define a high-temperature reaction window (above melting point of Mg) and a low-temperature reaction window (below melting point of Mg, between 625 – 650oC). Below we study representatives of high and a low-temperature reaction for a doped strand. In this case SiC was chosen as the dopant, since it is one of the best known and most effective dopant in MgB2. In doing so, it was

o possible to compare the microstructures of MgB2 samples reacted at 675 C which incorporated different sizes and amounts of SiC (i.e. C series samples from Table 4.1).

We obtained fracture HR-SEM images of these samples using the Sirion scanning electron microscope (Ref. Chapter 3 Sec 3.3.2). The samples were fractured after etching with nitric acid. These images were obtained at different magnifications ranging up to

80,000X in order to investigate the resulting microstructure and the final grain size of the resulting MgB2. Grain size determination was performed using the line interception method whereby a series of lines are drawn horizontally over the image and the number of intercepts is counted. This was performed using a lower magnification image so as to get better statistical accuracy. Figures 4.8 (a-e) show the 40Kx and 80Kx HR-SEM images of these samples. Comparing the effect of 5% and 10% additions of either the

30nm SiC or the 200nm SiC doped samples, it can be seen that a lower amount of SiC addition gives smaller grain sizes. On the other hand, if we now compare the grain size variation due to the size of the SiC dopants, it can be seen from Table 4.3 that the smaller sized SiC additions lead to smaller grain sizes given a constant dopant level. Small grain size is one of the important factors needed in order to achieve higher flux pinning.

Further details on the pinning properties of SiC doped MgB2 samples are discussed in

Chapter 6.

Sample Size of SiC Amount of SiC Avg. Grain Reacted at nm added Size 675oC/40min % nm MB30SiC5C 30 5 53 MB30SiC10C 30 10 86 MB15SiC10C 15 10 44 MB200SiC5C 200 5 70 MB200SiC10C 200 10 130

Table 4.2 Average grain size for SiC doped samples reacted at 675oC/40mins

Figure 4.8a HR-SEM image for sample MB30SiC5C at 40K and 80K magnification (5 mole % of 30nm SiC doped sample reacted at 675oC-40min)

Figure 4.8b HR-SEM image for sample MB30SiC10Cat 40K and 80K magnification (10 mole % of 30nm SiC doped sample reacted at 675oC-40min)

Figure 4.8c HR-SEM image for sample MB15SiC10C at 40K and 80K magnification (10 mole % of 15nm SiC doped sample reacted at 675oC-40min)

Figure 4.8d HR-SEM image for sample MB200SiC5C at 40K and 80K magnification (5 mole % of 200nm SiC doped sample reacted at 675oC-40min)

Figure 4.8e HR-SEM image for sample MB200SiC10C at 40K and 80K magnification (10 mole % of 200nm SiC doped sample reacted at 675oC-40min)

Transmission electron microscopy was also performed on the binary MgB2 sample. As mentioned earlier, (Chapter 3 Sec 3.3.2) because of the porous nature of the samples, TEM was performed on the powdered samples which were made by crushing the bulk representatives of the above strand. Shown below in Figure 4.9 is the TEM image of a bulk binary MgB2 sample, MB700 (Ref. Table 3.1).

Figure 4.9 TEM bright field image on binary bulk MgB2 sample MB700 (See Table 3.1)

Figure 4.10, the EDX spectrum of this sample, shows a very low amount of O.

The Cu and C lines coming from the ultra thin carbon coated 400 mesh copper grids used as the sample holder. A high resolution atomic level image was also taken on the same sample, Figure 4.11, along with the convergent beam electron diffraction (CBED) pattern

80 obtained on the marked area. Using the CBED pattern the structure was simulated and is also shown in Figure 4.11 (right top).

Figure 4.10 EDX spectra from the pure MgB2 sample. (Cu and C lines coming from the grid sample holder)

Figure 4.11 HR-TEM image of MB700 (left), the CBED pattern (right top) and the simulated structure using the CBED pattern (right bottom)

Figure 4.12 TEM bright field image on SiC doped bulk MgB2 sample MBSiC700

A bright field TEM image taken on a SiC doped bulk sample (MBSiC700) is shown in Figure 4.12 along with the EDX spectrum collected from this sample showing the presence of Si and C in or around the imaged grain. The grain size seen in these TEM images are again 50-100nm, corresponding to the fracture SEM estimates.

Figure 4.13 EDX spectra from the SiC doped bulk MgB2 sample MBSiC700. (Cu and C lines coming from the grid sample holder)

As a final comparison of the formation of MgB2 in the high and low-temperature windows, their transport properties were compared. Transport Jcs were measured on both

MB30SiC10A and MB30SiC10C at temperatures ranging from 4.2K-30K, Figures 4.13 and 4.14. It can be observed that the low field Jc of sample MB30SiC10A

(low-temperature window) is slightly suppressed but at higher fields the Jc is slightly

83 higher than that of sample MB30SiC10C (high-temperature window). Also, the drop in Jc with the temperature is much more in case of the sample MB30SiC10C compared to that of sample MB30SiC10A. Overall, however, the properties are similar.

105

4.2K 10.0K 15.0K 2 104 17.5K 20.0K

, A/cm

c 22.5K J 25.0K 30.0K 103

102 0 2 4 6 8 10 12 14 B, T

Figure 4.14 Temperature dependence of Jc vs B for sample MB30SiC10A (625oC-180min)

105 4.2K 10.0K 15.0K 17.5K 4 2 10 20.0K 22.5K

A/cm

, 25.0K

c J 30.0K

103

102 0 2 4 6 8 10 12 14 B, T

Figure 4.15 Temperature dependence of Jc vs B for sample MB30SiC10C (675oC-40min)

4.3 Conclusion

It has been shown by DSC, performed on a mixture of Mg and B powders that after an initial reaction related to boron dehydration and partial magnesium oxidation,

MgB2 is formed completely before Mg melting point, i.e. at temperatures less than

o 655 C. It can be concluded that MgB2 can be formed by in-situ reaction not only at high- temperature window, above Mg melting, but also at a low-temperature window (between

625 - 655oC). A sample reacted in the low temperature window had slightly lower level of porosity with slightly lower Tc value but a sharper transition. Transport Jc values for these two samples were similar. Further, a series of SiC doped samples with different sizes and amounts of SiC reacted in the high-temperature window were studied for the

85 grain size variations. It was found that lower levels of smaller sized SiC powders produced the smaller average grain sizes. In Chapter 5, which follows, we will investigate the introduction of dopants, including the SiC doped samples studied here, intended to increase the oHirr and Bc2.

Chapter 5

DOPING AND ITS EFFECTS ON CRITICAL FIELDS IN MAGNESIUM DIBORIDE

Effects of dopants on the superconducting properties, in particular the critical fields of MgB2 superconductors will be discussed in this chapter. Large increases in the oHirr and Bc2 of bulk and strand superconducting MgB2 were achieved by the addition of the following dopants. While, SiC, amorphous C and selected metal diborides (NaB2, ZrB2, TiB2) were used in bulk samples and three different sizes of SiC (~200 nm, 30 nm and 15 nm) were used as dopants in the strand samples. For bulk samples, we achieved C doping through acetone milling as well as SiC dopant decomposition-and-C-subsitution on the B site. Additionally we were able to substitute Nb, Zr, and Ti on the Mg site separately through metal diboride additions to bulk MgB2. Substantial increases in oHirr and Bc2 were achieved in both cases with Bc2 reaching higher than 33T at 4.2K. It was observed that different doping sites (B vs Mg) have different characteristics and lead to different relative increases in oHirr and Bc2. Also, it was found out that both oHirr and Bc2 depend on the sensing current level which may be an indication of current path percolation.

5.1 Introduction

Since the discovery of superconductivity in MgB2 [2], many groups have worked to enhance its 0Hirr and Bc2. Methods such as proton irradiation which introduce atomic disorder [111], as well as dopant introduction which increases lattice distortions and electronic scattering [22, 23, 25, 26, 99, 103, 112-122] have been employed with good effect. It has been demonstrated that in the case of “dirty” MgB2 thin films, 0Hirr and Bc2 are substantially higher than those of the pure binary films [90]. This has been most evident in C doped thin films where 0Hc2s can reach 49 T at 4.2 K. Explanations of this effect are based on the generalized two-gap Usadel equations [90, 107]. According to this treatment, the impurity scattering is accounted for by the intraband electron diffusivities

Dσ and Dπ, and intraband scattering rates σ and π leading to pronounced enhancements of B by nonmagnetic impurity dopings to values well above the predictions of one-gap c2 theory.

Replicating these large increases in oHirr and Bc2 in metal-sheathed PIT strands has not yet been achieved. However, Bhatia et al. [27, 98, 101, 102] and Dou et al. [25,

97, 123] have shown that SiC doping can significantly improve oHirr and Bc2 of metal- sheathed PIT strands to values as high as 33 T [98, 101]. Matsumoto et. al. [124] doping with SiO2 and SiC in the in-situ process, increased oHirr from  17 T to  23 T at 4 K.

In Chapter 4, we described the formation of MgB2 noting the best conditions for its formation from our particular starting materials. In this chapter we focus on doping

MgB2 with materials intended to increase the upper critical field, Bc2. We begin with SiC dopants, processing the resulting bulk material in both the high- and low-temperature reaction windows discovered in Chapter 4. After showing the effect of SiC on oHirr and

Bc2, we go on to describe the effects of doping on B site using different sources of C and on

Mg site with several metal diborides (ZrB2, TiB2, NbB2). We will then discuss in detail about the ZrB2 doping of MgB2 bulks and the SiC doping of MgB2 strands. Finally we will describe some measurements that reveal the intrinsic inhomogenieties in MgB2 strands and comment on the implications.

5.2 Effect of Reaction-Temperature and Time on the Critical Fields of SiC Doped

Samples

It has been shown in the previous chapter that high quality MgB2 superconductors can be formed within two distinct reaction-temperatures windows (i.e. below the melting point of Mg and another one above it). It then becomes important to compare the effects of these two reaction schedules on the critical field properties of the samples thus formed.

Monofilament PIT strand samples (Ref. Sec. 3.2.2) described in previous chapter were measured in both perpendicular magnetic field and in the “force-free” (field-parallel) orientation at the NHMFL. Figures 5.1 and 5.2 show the variation of 4.2K perpendicular field oHirr and Bc2, respectively, as a function of reaction and doping. The results for

30nm SiC doped sample are given in Table 5.1. The force-free-orientation measurements led to similar trends but with slightly higher values.

, T

irr

o  20

18 MBxSiC5A MBxSiC10A Irreversibility Field, Irreversibility 16 MBxSiC5C MBxSiC10C

14 15nm 30nm 200nm Avg. SiC Size

Figure 5.1 oHirr measurements on MgB2 strands doped with different sizes of SiC heat-treated at different temperatures.

Figures 5.1 and 5.2 show that the highest oHirr and Bc2 values are seen for the smaller particle sized dopants (30nm and 15nm). This can be correlated with the grain size measured on the same strands where smaller SiC particles led to smaller grain sizes while larger dopants formed larger grain sizes. Additionally we can see that higher concentration of dopants (10%) lead to higher critical fields.

, T 22

MBxSiC5A 19 Upper Critical Field, Upper Critical MBxSiC10A MBxSiC5C 18 MBxSiC10C

17 15nm 30nm 200nm Avg. SiC Size

Figure 5.2Bc2 measurements on MgB2 strands doped with different sizes of SiC heat-treated at different temperatures

MB30SiC10A MB30SiC10C Properties 625oC-180 min 675oC-40 min c2,|| T 24.85 24.45 c2,perp, T 23.66 23.50 irr,||, T 22.46 22.53 irr,perp, T 21.49 21.48

Table 5.1 Comparison of the critical fields for 30nm SiC doped MgB2 samples reacted within low-temperature and high-temperature windows

It has been shown that 10mole% of 15nm or 30nm SiC in MgB2 strands lead to enhanced critical fields. Further, we also showed that in terms of reaction temperatures both the heat-treatment windows produce almost identical enhancements in oHirr and

Bc2. It should be noted that the low-temperature reaction is carried out at 625oC which is not only below the m.p. of Mg but also below the m.p. of Al. This opens the doors to the

91 possibility of fabricating light-weight strands for specific applications, Al being much less dense than Cu can be used as a stabilizer for these superconducting strands.

We then went on to studying the effect higher reaction temperatures on the critical fields of 30nm SiC doped MgB2 strands. For this purpose a series of strand samples with 10% of 30nm SiC additions, MB30SiC10 series samples, were reacted for varying times at temperatures of 700-900oC.

Figure 5.3 shows variation of the resistive transitions for these MB30SiC10 series strands with reaction temperature-time. It can be clearly seen that both 0Hirr and Bc2

(measured at the 10% and 90% point of the transition) increase with increasing heating time at any given reaction temperature.

8 700C/10 700C/20 700C/30 6 800C/5 800C/10

V 800C/20



, 800C/30

V 4 700C/5 900C/20 900C/10

Voltage, 900C/5 2

0 16 18 20 22 24 26 28 30 32

B, T

Figure 5.3 Resistive transitions for fine (30nm) SiC doped MB30SiC10 strands reacted at different time-temperature schedules

Curves of 0Hirr and Bc2 values for these strand heated at various temperatures are plotted vs heating time in Figure 5.4. In this case, it can be seen that the critical fields are highest for 800oC reacted sample as compared to 700oC or 900oC reaction temperatures.

Reacting at 800C for 30 minutes gave the highest values, 29.4T and 31.3T for 0Hirr and

Bc2 respectively.

30 700C oHirr 800C  H 28 o irr 900C  H 26 o irr 700C Bc2

, T 24 800C B

B c2

22 900C Bc2

14 5 10 15 20 25 30 Reaction time, t, mins

Figure 5.4 Values for 0Hirr and Bc2 vs heat-treatment time for various heat-treatment temperatures for MgB2 wires doped with 30nm SiC particles (MB30SiC10 series)

Figure 5.5 shows the Tc curves (resistive transitions under self field) for the

MB30SiC10-series samples heated for various times at 800C. Tc midpoints of 34.2, 34.4,

37.8 and 34.4 were found for heating times of 5, 10, 20, and 30 minutes respectively, with transition widths (as measured from 10% to 90% of the transition) of 1.2 to 1.4K.

However, the fact that the overall resistivity of the strand is not changing drastically,

93 along with the fact that the strand heated for 20 minutes has a Tc of 36.2K suggests significant homogeneity in this strand. It is likely that various current paths exist in the other strands (with 5, 10 or 30 min reaction), some of which have different compositions, and no doubt various orientations are being probed as well. This would be further discussed in detail in the later section of this chapter.

10 800C/05 800C/10 800C/20 8 800C/30

 6



Resistivity, Resistivity,

0 20 25 30 35 40 45 50 Temperature, T, K

Figure 5.5 Tc curves for the MB30SiC strands reacted for various times at 800C.

5.3 Differences in the Effects of Mg and B site doping on the oHirr and Bc2 of in-situ

Bulk MgB2

Various authors have presented evidence supporting the hypothesis that C substitutes for B in the B-lattice. Significant drops in Tc have been reported for C additions, especially relatively aggressive additions, particularly where elemental C is

94 added directly to the MgB2. In the same way it is believed that the major influence of SiC additions is effected by the donation of C to the B sub-lattice due to SiC decomposition, parallel to the direct elemental C substitution, leading to moderate amounts of C-doping combined with slightly reduced Tc values and good transport properties.

On the other hand, efforts have also been aimed at finding the appropriate dopants for site substitution for the Mg atoms. Such substitutions are expected to lead to scattering in the  band rather than the  band, and to thus lead to both smaller Tc reductions as well as possibly better 0Hirr and Bc2 properties. Increase in the Bc2 through the  band should also be less anisotropic since the band itself is less anisotropic. Rather than using metallic additions directly, however, we chose to add the metal diborides. The rationale for this was that the lattice constants for the metal diborides used were very close to the lattice constants of MgB2 and they have the same crystal structure

(hexagonal) and crystal symmetry (P6/mmm) and hence should more readily form solid solution with MgB2. Thus, in this chapter we have investigated six different types of dopants, either C-bearing or from the metal diboride family.

5.3.1 Doping of Bulk Samples for B and Mg Site Substitution

Bulk samples with compositions (MgB2)0.9(SiC)0.1, (MgB2)0.9C0.1, and

(MgB2)0.925(XB2)0.075 where (X= Zr, Nb and Ti) along with a MgB2 control sample were prepared by the in-situ bulk sample preparation technique mentioned in Chapter 3 (Sec

3.2.1). The MBSiC series of samples were doped with ~200 nm SiC. For MBC series of samples, amorphous C from Alfa Aesar was used, a third series of samples, MBAC, was prepared by milling stoichiometric Mg and B with small amount of acetone in order to

95 achieve C addition. Lastly, MBZr, MBNb, MBTi series samples were doped with ZrB2,

NbB2, TiB2 powders obtained from Alfa Aesar. The samples in this study were heat- treated at temperatures between 700-800C for 30 minutes (high-temperature window) so as to achieve more homogeneous incorporation of the dopants. XRD measurements were taken with a Sintac XDS-500 between 2 values of 20-90 degrees (Chapter 3 Sec 3.3.1).

XRD patterns for samples including the control sample (MB700), the metal diboride doped samples (MBZr700, MBNb700 and MBTi700) and the C-based doped samples

(MBCSiC700 and MBAC800), the results are shown in Figure 5.6. The details of the heat treatment and the lattice parameter calculations are presented in Table 5.2. The lattice parameter calculations were performed using (100), (101), (002) and (110) peaks indexed within space group P6/mmm. As can be seen from the table, a positive a-lattice parameter change is seen for samples MBZr700 and MBNb700 and a negative change is seen for

MBTi700 as compared to control sample MB700. These trends are consistent with the lattice parameter differences between those of ZrB2, NbB2 and TiB2 respectively and

MgB2. Changes were also seen in c-lattice parameter of the metal diboride doped samples. This indicates that we were successful in introducing the dopants into the crystal structure. For SiC doped sample, MBSiC700, almost no change in „a’ and a slight decrease in „c’ were noted. This is consistent with the trend seen by Dou et al. [16], where they did not see an appreciable change in „a’ and systematic decrease in „c’ while increasing the SiC doping percentage from 0-34%. However, we have noted that for C doped sample, MBAC800, the decrease in „a’ was more than that seen for MBSiC700 sample while the change in „c’ was similar. For all samples, small amounts of secondary phase were also present, as can be seen in Figure 5.6. The DC-susceptibility, DC, as

96 described in the next section also showed the evidence of the presence of a small amount of secondary phase. These samples were then studied for their oHirr and Bc2 values.

Table 5.2 Bulk sample names, additives and reaction temperatures

MBC700

MBSiC700

MBTi800

MBNb700

MBZr700

Figure 5.6 XRD patterns for binary MgB2 sample (MB700) and samples doped with amorphous C (MBC700), SiC (MBSiC700), TiB2 (MBTi700), NbB2 (MBNb700) and ZrB2 (MBZr700). Star symbols indicate the corresponding ZrB2 or NbB2 or TiB2 peaks for metal diborides doped samples and SiC peaks for MBSiC700 sample (distinct second phase peaks)

5.3.2 Large Upper Critical Field and Irreversibility Field in Doped MgB2 Bulk

Resistive transitions vs. applied field measurements as described in Chapter 3

(Sec 3.3.7) were used to determine oHirr, and c2 for all samples. Figure 5.7 shows the variation of normalized susceptibility of various samples with temperature (not all reaction temperatures for all samples are shown). Full flux exclusion is seen below Tc, along with acceptable Tc and transition widths, suggesting complete or nearly complete superconducting phase formation. The Tc values; onset completion and midpoint, extracted from the curves are tabulated later in Table 5.3 along with the oHirr and c2 values for the control and the doped samples.

0.0 MB700 MBSiC700

 / MBAC800

 -0.2 MBC700 MBC900 -0.4 MBZr700 MBNb700 MBTi800 -0.6

-0.8

Normalized Susceptability, Susceptability, Normalized

-1.0

0 10 20 30 40

Temperature, T, K

Figure 5.7 Normalized DC graph for bulk MgB2 samples with various additives showing superconducting transitions

100

The relation between the Tc drop and Hirr increase of the doped samples is shown in Figure 5.8. It can be seen that the Tc drop is much more for the case of C doped samples in comparison to the metal doped samples. This is consistent with Gurevich‟s theory where he predicted that the low-temperature critical fields can be enhanced with

Mg-site substitutions with much less drop in Tc as compared to B-site substitutions.

39 Binary 38 Diborides C - doping 37 SiC

T 35

32 14 16 18 20 22 24 26  H , T o irr

Figure 5.8 Tc vs oHirr for bulk MgB2 samples with various classes of additives (See Figure 5.7)

The resistance vs. applied magnetic field curves for these first set of samples, that include SiC and C doped samples, are shown in Figure 5.9. It can be seen that the c2 of all the SiC and C doped samples are more than 33T. The exact values of c2 for these samples could not be obtained because the magnetic field was limited to 33 T in the resistive magnet at the NHMFL in Florida. Also, it can be seen that the oHirr for these

101

SiC doped bulk samples increased from 24.5 to 28 T with increase in reaction

o o temperature from 700 C to 900 C. This increase in the oHirr with reaction temperature is in accordance with the results obtained for the SiC doped strand samples (these results presented in the next section). In contrast, for C-doped samples, no significant change in

oHirr was seen with the heat-treatment temperature. This is because of the saturation of carbon substitution in MgB2.

10 MBAC800 MBSiC700 8 MBC700 MBC1000

 MBSiC800 -4 6 MBC900

, 10 R 4 MB700 MBSiC900

Resistance, 2

15 20 25 30 35 40 Magnetic Field, B, T

Figure 5.9 R vs B for bulk MgB2 samples doped with SiC and C

Corresponding curves for the boride doped samples, i.e. with ZrB2, NbB2 and

TiB2 doping, are shown in Figure 5.10. It can be seen from these curves that even though,

Hirr and Bc2 values for this set are lower than first set of samples with SiC and C doping, they are significantly higher than the pure MgB2 control sample. The highest vales in the metal diboride substitution set, 24.0 and 28.6 T, for oHirr and Bc2

102 respectively, are achieved by ZrB2 doping. Detailed results for the MBZr700 sample are presented in the following sections of this chapter. For NbB2 and TiB2, the highest

o values of oHirr and Bc2 were obtained for the samples reacted at 700 C/30 mins. and a decrease in the critical fields were observed on increasing the reaction temperature.

5 MBTi700

MBNb700

4  MB700 -4 MBNb800

, 10 R 3

MBTi800 2 MBNb900

Resistance,

1 MBZr700

15 20 25 30 35 Magnetic Field, B, T

Figure 5.10 R vs B for metal diboride doped bulk MgB2 samples

These results are summarized in Table 5.3 which shows that the ratio of 0Hirr and Bc2 and the difference between 0Hirr and Bc2, B, varies based on the kind of doping.

These values can be classified into different groups: control sample, C-based samples and metal doped samples. For metal-doped samples the values of Hirr/Bc2 are >0.8, which is slightly higher than the pure sample, while, for the C-doped samples these values are much lower than the control sample. Similarly, B for metal-doped samples varies from

3.5 to 5, which is close to the pure sample value of 4.5, while for the C-based samples the

103

Bs are almost twice as high as that of the pure sample. This means that while both metal and the carbon doping are increasing the 0Hirr and Bc2 but the increase in oHirr in case of metal doping is more pronounced. This is interpreted in the following way: with C doping the substitution takes place at the B lattice leading to a more pronounced change in the phonon scattering of the  band and hence, decreasing the electronic diffusivity,

D, in  band with metal-doping the substitution is done on to the Mg lattice increasing scattering in the  band rather than  band and so it decreases D more strongly than D leading to an increase in -band oHirr and Bc2. Since the spread in the 10% and 90% line is controlled by anisotropy and connectivity, the increase in Bc2 and also oHirr of a more isotropic component should lead to less apparent spread, which is what is seen for these samples.

Sample oHirr, Bc2,  irrc c, c,on, c,com, c Name T T K K K K MB700         MBSiC700         MBSiC800         MBSiC900         MBC700        

MBC71000 ~20.0 >33 >13 <0.60 32.4   

MBAC800         MBZr700 24.0 28.6 4.6 0.84 35.6 36.4 33.0 3.4 MBNb700 20.5 25.5 5 0.80 36.1 36.4 35.1 1.3 MBNb800 18.5 22.8 4.3 0.81 - - - - MBNb900 18.0 21.6 3.6 0.83 - - - - MBTi700 19.0 22.5 3.5 0.84 - - - - MBTi800 18.0 22.6 4.6 0.80 36.3 36.5 35.7 0.8

Table 5.3 Critical Fields and Temperatures for bulk MgB2 with various additives.

104

In conclusion to the section, we have doped C on to the B site via acetone mixing as well as SiC additions and on the other hand dopants on the Mg site using Nb, Zr, and

Ti metal diboride additions. In both the cases this has led to increases in the 0Hirr and

Bc2. Even though the increases in both the cases have been substantial, different doping sites have different characteristics and lead to different relative increases in 0Hirr and

Bc2.

5.4 Temperature Dependence of oHirr and Bc2 with ZrB2 Additions

Having shown the positive effects of metal diboride doping in MgB2 in terms of increase in the critical fields and noting that ZrB2 additions gave the best results, we further studied the effect of various heat-treatment temperatures on the properties of ZrB2 doped MgB2 bulk samples. In addition we studied the dependence of the properties on the temperature of the measurements. ZrB2 was in particular selected for the detailed study because it was the best in terms of maximum increase in Bc2 with minimum Tc drop and hence the material of choice. Bulk samples with compositions MgB2 and

(MgB2)0.925(ZrB2)0.075, similar to the ones in the previous section were prepared by an in- situ reaction (Ref. Chapter 3 Sec 3.2.1) and reacted at temperatures of 700oC, 800oC and

900oC for 30 min. Details of the sample composition, and heat-treatment are given in

Table 5.4.

105

Sample Name Reaction Temp Reaction Time Tc, K (OC) (min) MB700 700 30 38.2 MBZr700 700 30 35.7 MBZr800 800 30 36.5 MBZr900 900 30 36.5

Table 5.4 Sample Specifications for bulk MBZr Series Samples

At 4.2 K, oHirr, and Bc2 were determined by resistive transitions with applied field, with the measurements being performed at the National High Magnetic Field

Laboratory (NHMFL) Tallahassee (Ref. Chapter 3 Sec 3.3.7). At higher temperatures (20

K and 30 K) 0Hirr was calculated two different ways. Magnetization measurements were performed from 4.2 K to 40 K on these samples using a VSM (Ref. Chapter 3 Sec 3.3.5).

At higher temperatures where M-H loop closure could be observed, the loop closure itself defined 0Hirr. When loop closure could not be directly observed (e.g., at somewhat lower temperatures) the quantity M1/2B1/4 was plotted vs B and extrapolated to the horizontal axis to obtain an estimate of 0Hirr. This technique (a Kramer extrapolation) is usually a very good estimate of where transport current vanishes (i.e., oHirr) for conductors where the pinning is occurring at the grain boundaries, although significant inhomogeneities may cause concave or convex curvature at very low currents [16].

Nevertheless, the numbers so extracted are representative of the majority of current paths in the material. XRD analysis was also performed on these samples between the 2 values of 30-70o (Ref. Chapter 3 Sec 3.3.1).

106

In the present experiment the previously mentioned binary sample, reacted at

o 700 C/30 min was used as the reference material. Figure 5.11 shows the plot of DC vs T for these samples in comparison with the binary sample. It can be seen that the Tc drops by 2.5 K for sample MBZr700 as compared to MB700. Comparing this to the results of

Ma et al [115] we note that while they see a drop of only 1 K, their binary sample has a lower Tc than the present binary. Thus, the midpoint Tc values for our ZrB2 samples are very similar to that of Ma et al.

0.0 MB700 MBZr700

DC  -0.2 MBZr800 MBZr900 -0.4

-0.6

-0.8

Normalized Susceptibility, Susceptibility, Normalized -1.0

-1.2 5 10 15 20 25 30 35 40 Temperature, T, K

Figure 5.11 DC DC vs T for binary and ZrB2 doped bulk MgB2 samples (See Table 3.1)

107

Table 5.5 correlated the heating schedules and compositions of the samples along with the measured critical fields. It can be seen that the Bc2 of the doped sample, reacted at 700oC, is found to be 28.6 T as compared to 20.5 T for the binary sample.

Additionally, oHirr has also been found to increase from 16 T to 24 T at 4.2 K with ZrB2 doping followed by reacting at 700oC.

Sample Name HT Tc, K 0Hirr Bc2 (OC/Min) T T MB700 700/30 38.2 16.0 20.5 MBZr700 700/30 35.7 24.0 28.6 MBZr800 800/30 36.5 23.2 27.6 MBZr900 900/30 36.5 23.0 27.5

Table 5.5 Reaction temperature-time schedules, compositions and measured superconducting properties for various ZrB2 doped bulk MgB2 samples

This increase in the critical fields is believed to be due to the small substitution of

Zr on the Mg sites as evidenced by the change in the lattice parameter, Figure 5.12, the effects of which are believed to be changes in the electron diffusivities in the  and  band as described above. As can be seen from the XRD patterns, Figure 5.12, of control sample and MBZr700 sample the shift in [002] and [110] peaks to a lower angle in the doped sample suggest an increase in both a and c lattice parameter possibly due to the uniform stress induced in the lattice by Zr substitution on the Mg site. Also shown in

Figure 5.13 is the TEM bright field image of a grain of MBZr700 sample. The EDX obtained from the section of this image is shown in Figure 5.14 and shows the presence of Zr in the grain.

108

MB700 101 MBZr700

Count 100

002 110

30 40 50 60 70 2 Theta

Figure 5.12 XRD pattern for ZrB2 doped bulk MgB2 (MBZr700) sample as compared to binary sample (MB700)

109

Figure 5.13 TEM bright field image of bulk sample MBZr700

Figure 5.14 EDX obtained from the selected grain of bulk sample MBZr700

110

Based on the tendency for the Zr to substitute on the Mg site, and our understanding of the  and the  band properties, it was expected that the Zr doped sample would have some increase in the oHirr and Bc2 at the elevated temperature but a major effect at the low temperatures.

At higher temperatures, direct M-H loop closure was used to determine oHirr, the results are shown in Figure 5.15. At intermediate T, the Kramer extrapolation described before was used to determine oHirr, these are also shown in Figure 5.12, where the 4.2 K resistance measurements are also included. An increase in the oHirr with ZrB2 doping of

MgB2 was observed over the entire temperature range with a much larger increase at lower temperatures as compared to temperatures near Tc.

25 From I-V curve

(T) 20

irr

o  15

10 From Kramer Plot 5 From M-H loop Irreversibility Field, MBZr700 MB700 0

0 5 10 15 20 25 30 35 40

Temperature, T(K)

Figure 5.15 Variation of 0Hirr with T for binary and ZrB2 doped MgB2 sample 111

Additions of 7.5 mol% of ZrB2 into MgB2 enhanced oHirr at all temperatures. At

4.2, via resistive transitions, c2 was found to increase from 20.5T for binary sample to

28.6T for the doped sample and oHirr from 16T to 24T. At higher temperatures oHirr increased as well. A Tc midpoint depression of 2.5K was seen as compared to the binary sample.

5.5 Variation of Upper Critical Field and irreversibility Field in MgB2 wires with

Sensing Current Level

It has been shown experimentally in strands, and bulks, that dopants can improve the irreversibility field, 0Hirr, and upper critical field, Bc2, of MgB2, as well as high field transport Jc. In metal sheathed strands Bc2 values of up to 33T have been obtained and

5 2 transport Jc values of 10 A/cm at 4.2K have been achieved.

On the other hand, the problem of connectivity and inhomogeneity in MgB2 remains unsolved (connectivity to be discussed in the Chapter 7). In the following section, we have tried to quantify the variation in 0Hirr and Bc2 with sensing current, as well as transport Jc variation in nominally similar PIT MgB2 strands. These transport signatures are interpreted in terms of sample inhomogeneity and anisotropy.

Apart from the SiC doped strands that were studied and presented in Sec 5.1, a series of very similar strands were also prepared at University of Wollongong, Australia

(UW). These samples were chosen for the study since they had the highest known Bc2s of the MgB2 strand samples and hence were most susceptible to the presence of inhomogeneities. These strands also had small size SiC (15nm or 30nm) additions.

Further sample details are given in Table 5.6.

112

Sample Series Reaction Temp.-Time SC SiC size, SC area, (C/min) Fraction nm mm2 UW15SiC10A 640/30 47.30 15 0.637 UW30SiC10B 680/30 38.87 30 0.524 UW30SiC10C 725/30 47.80 30 0.644 UW15SIC10C 725/30 40.05 15 0.539

Table 5.6 Sample specifications for UW series strand MgB2 samples

Figure 5.16 shows the resistivity vs field for sample UW15SiC10 series sample

o reacted at 640 C/30min (15nm SiC doped MgB2). Resistive transitions are shown for sensing current levels of 1, 10, 50, and 100mA. As usual, Bc2 is taken to be the field at

90% of the normal state response and 0Hirr is defined as the field at 10% of normal state as described earlier ( see Chapter 3 (Sec.3.3.7)). A decrease in both 0Hirr and Bc2 can be seen as the sensing current is increased from 1 to 100mA. Specific values are listed in

Table 5.7, with a difference in Bc2 of 1.3T, and a difference in 0Hirr of 1.4 T between the

1 and 100 mA sensing current measurements, respectively. Similar measurements (but restricted to 10 and 50mA) were made for UW30SiC10 series strands reacted at

o o 680 C/30min (30nm SiC doped MgB2) and 725 C/30min (30nm SiC doped MgB2), with the results given in Table 5.7.

Figure 5.17 shows the results for UW15SiC10C (15nm SiC doped MgB2)

o 725 C/30min strand. Generally, both 0Hirr and Bc2 decrease with increasing sensing current level. This decrease does not seem to be present, or at least is very much smaller, for UW15SiC10C 725oC/30min sample (Table 5.7).

113

5 1mA 10mA 50mA 4 100mA

cm 3

 

Resistivity, Resistivity,

0 18 20 22 24 26 28 30 32 B, T

Figure 5.16  vs B for 15 nm SiC doped UW15SiC10A reacted at 640oC-40mins measured at 1, 10, 50, and 100mA of sensing current levels

0.8

10 mA 50 mA 100 mA 0.6

  0.4

Resistivity, Resistivity, 0.2

0.0 20 22 24 26 28 30 32

B, T

Figure 5.17  vs B for 15 nm SiC doped UW15SIC10C strands heat-treated at 725oC- 30mins measured at 10, 50, and 100mA of sensing current levels

114

Table 5.7 0Hirr (4.2K) and Bc2 (4.2K) for UW-series strands using various sensing currents

115

The general reduction of 0Hirr and Bc2 with sensing current is not unexpected, and can be interpreted in terms of the number of available current paths with sufficiently high 0Hirr and Bc2. A typical sample can be imagined to consist of a number of parallel current paths, each with a different 0Hirr and Bc2. These differences are expected to stem either from anisotropy, or inhomogeneity, either of the underlying binary compound, or the level of C-doping generated by the SiC. A statistical distribution of 0Hirr and Bc2 among the current paths would lead to the current level sensitivity seen here. All samples in this work except for UW15SiC10C series 725oC/30min heat-treated sample have

0Hirr and Bc2 values which change noticeably as the sensing current changes (about 0.5T when going from 10mA to 50mA), while those for the above mentioned strand change negligibly. The fact that one of the samples has a much smaller difference in 0Hirr and

Bc2, suggests that diffusion-related inhomogeneities may be important. Inhomogeneity should also influence the high field transport Jc response.

5.6 Conclusions

MgB2 strands with SiC additions reacted at low-temperature and high-temperature reaction window were measured for 0Hirr and Bc2 and both were found to behave identically. Also, comparing between additions of different amounts of SiC it was found that 10% additions of SiC always produced samples with much higher critical fields as compared to 5% additions, keeping the size constant on the other hand out of all three different sizes of SiC powders, 15nm or 30nm SiC additions let to much higher Bc2s and

oHirrs as compared to 200nm SiC. Further, on studying the effect of reaction temperature and time (high-temperatures) on the properties of 10% 30nm SiC doped

116 sample it was found out that both oHirr and Bc2 got better with longer soaking time at fixed temperatures and also got better with increasing reaction temperatures up to 800oC beyond which both oHirr and Bc2 decreased with increasing temperature.

Apart from SiC doped strand samples we have also studied the effect of doping at different sites in bulk MgB2. C doping on to the B site was achieved via acetone mixing as well as SiC additions and on the other hand, doping was done on the Mg site using Nb,

Zr, and Ti metal diboride additions. In both the cases this has led to increases in the 0Hirr and Bc2. Even though the increases in both the cases have been substantial, different doping sites have shown different characteristics and lead to different relative increases in

0Hirr and Bc2.

Since SiC doping, both in bulk and strand, led to large increases in critical fields which might as well be accompanied by an increase in anisotropy and inhomogeneity in the current paths, we have, therefore, tried to quantify the variation in 0Hirr and Bc2 with sensing currents. The SiC strands, which were relatively high performance, showed transport current and irreversibility field signatures suggesting material based inhomogeneities. All but one sample had differences in 0Hirr and Bc2 values as determined from resistive transitions as the sensing current level was varied. This variation can be interpreted in terms of sample inhomogeneity and anisotropy.

Since it was evident from the XRDs that all these dopants also leave a small amount of second phase in the sample, it becomes important at this point to investigate other effects due to these additions. Therefore, in the following chapters we will study the pinning properties in these SiC doped strands and make an attempt to understand the origin of the high transport Jcs also seen in these stands.

117

Chapter 6

FLUX PINNING PROPERTIES OF SiC DOPED MgB2

In this chapter, the flux pinning properties of SiC doped MgB2 strands are explored. A series of SiC doped MgB2 monofilament strands were studied to determine the influence of the amount and the size of SiC dopants on the flux pinning properties, Samples were prepared with either 5 at% or 10 at% of different particle sizes (15nm, 30nm or 200nm) of SiC added to stoichiometric Mg and B powders. A large increase in the critical fields was earlier observed for 15nm and 30nm doped samples while an increase in the Jc was also observed for these doped samples. Changes in the flux pinning force’s functional form, associated with various pinning mechanisms, are observed for these samples. This suggests doping/additions are causing some small amount of direct pinning but the major influence in Jc increases are found to be not pinning related. Microstructural changes due to doping, which were earlier were observed using HR- SEM imaging, are correlated with the transport properties enhancements.

118

6.1 Introduction

After a basic study of reaction and microstructure in Chapter 4, we went on to study oHirr and Bc2 enhancements due to doping in Chapter 5. In some cases these dopants, while they increased Bc2, degraded the transport Jc, possibly because of dopant collection at the grain boundaries and reduction of the effective connectivity. However, in the case of SiC additions to MgB2, large increases in the critical fields are accompanied by significant increases in the transport currents. While of course some increase in Jc will be seen as a direct influence of increasing Bc2, either by increasing the regime of the B-T space where it is superconducting, or by increasing the condensation energy and thus scaling the pinning force. However, it is important to see if additional pinning centers are created as well. Therefore, we investigate the pinning properties in these MgB2 samples doped with different amount and sizes of SiC and also compare them to the pinning properties of the pure samples. For this purpose a series of strand samples were selected from the previously measured samples (Table 4.1). These samples were reacted at different time-temperature schedules using our regular step-ramp heat-treatment profile.

Further, oHirr and Bc2 of these samples were measured at the NHMFL using a four-point probe technique (Chapter 5 Sec. 5.2) at 10mA, 50mA and 100mA current levels. Current reversal was also employed. Tables 6.1 and 6.2 show oHirr and Bc2 for these samples measured in a perpendicular field at 50mA sensing current along with the detailed samples description, dopant size, percentage and reaction temperatures.

119

Strand Mole % SiC dia. Irreversibility Fields, oHirr, T Sample of SiC nm 625/180 625/360 675/40 700/40 800/40 MB30SiC5 5 30 20.5 20 19.5 20 20 MB30SiC10 10 30 20.5 21 20 20.5 21 MB15SiC10 10 15 21 20.75 20.5 21 21 MB200SiC5 5 200 16 16 16.5 16 16 MB200SiC10 10 200 16.5 16.5 17 17 18

Table 6.1 Irreversibility fields for various SiC doped MgB2 strands

Strand mole % SiC dia. Upper Critical Field, c2, T Sample of SiC nm 625/180 625/360 675/40 700/40 800/40 MB30SiC5 5 30 23.5 23 22.5 22 23 MB30SiC10 10 30 24 24.5 22.5 23 24.5 MB15SiC10 10 15 24 24 23.25 23 24 MB200SiC5 5 200 18 18 18.25 18.5 19 MB200SiC10 10 200 19.5 19.5 19.25 19 20

Table 6.2 Upper critical fields for Various SiC doped MgB2 strands

For this study we have picked five samples which were heat-treated at 675oC/40 min, i.e., C-series samples from Table 4.1 (See Chapter 4), to investigate the effect of dopant size and amount.

The transport critical current of all of these five samples was measured as a function of temperature (4.2-30K) using four-probe short sample measurement technique mentioned previously in Chapter 3 (Sec. 3.3.7). Unfortunately the 4.2K measurements for these samples could not be effectively obtained because of the current limitations on our short sample probe (I< 200A). Therefore, the Fp analysis would be carried out at temperatures of 10K and higher. The transport critical current curves as a function of applied field were used to calculate the irreversibility fields of these samples at different

120

2 temperatures using a 100A/cm definition of oHirr. Figure 6.1 shows the variation of

oHirr for these samples as a function of temperature.

22 MB30SiC5C 20 MB30SiC10C MB15SiC10C 18

, T MB200SiC5C

irr MB200SiC10C

H 16

 14

Irreversibility Field 8

4 5 10 15 20 25 30

Temperature, T, K

o Figure 6.1 oHirr vs T for Various SiC added samples reacted at 675 C/40mins

The Jc curves were also used to obtain the flux pinning force for these samples using

F B  J B p c (6.1)

As is known, the pinning function obtained from the above equation should vanish at both B = 0 and Jc = 0 (B = oHirr) and has a maxima somewhere in between.

Below we will investigate the details of Fp more in depth, but the simplest analysis consists of finding the maxima of the pinning force (in GN/m3) and at what fraction of

121

Bc2 this maxima occurs. According to the models of flux pinning, normalized pinning force Fp is a function of reduced field, h (oH/Hirr) and is given by

F p  h p 1 hq Fp,max (6.2)

Table 6.3 details the maximum value of the pinning force for each sample along with the grain sizes obtained from the previous analysis (Chapter 3). These are compared to the critical current at 10K and 5T along with the oHirr from the Jc plot obtained at

10K for the sample set. Binary MgB2 is thought to be dominated by grain boundary pinning. If the present set of samples, which include SiC doping, were also dominated by

G-B pinning we should expect an increase in Fp,max with reducing grain size. However, no such correlation is seen in Table 6.3. Additionally, increases in oHirr seen with SiC in

Table 6.3 should lead to corresponding Bc2 increases, which should lead (see below) to increased Fp,max through the condensation energy. Again no such correlation is seen in

Table 6.3. Figures 6.2 (a-e) show the normalized pinning functions, Fp/Fp,max plotted against the reduced field, h. It can be noted that the graphs at different temperature do not scale into one function as has been seen for many other type-II superconductors. This non-scaling or partial scaling (separate scaling at low-temperature, below 20K, and high- temperature, above 20K) has been observed previously as well by Susner et. al. [125] and

Senatore et. al. [126] during their analysis of the pinning properties in doped MgB2. To understand and explain this behavior of MgB2 it becomes important to look more closely at the various models of flux pinning mechanisms in type-II superconductors [127].

122

Sample Avg. Grain Fp,max at 10K oHirr at 10K Reaction- Size using 100A/cm2 temperature criterion 675oC/40min Nm GN/m3 T MB30SiC5C 53.31 4.53 17.11 MB30SiC10C 86.04 3.91 15.40 MB15SiC10C 44.7 3.09 18.07 MB200SiC5C 70.5 3.24 14.84 MB200SiC10C 130.8 3.99 15.05 MB675 87 2.98 8.42

Table 6.3 Comparison of superconducting properties for various SiC doped samples compared to a binary strand sample

123

1.0

10 K 12.5 K 0.8 15 K 17.5 K 20 K 22.5 K 0.6 25 K 27.5 K

p max

F 0.4

0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0 h

o Figure 6.2a Normalized Fp vs h for MB30SiC5C (675 C/40min)

1.0 10 K 15 K 17.5 K 0.8 20 K 22.5 K 25 k

0.6

pmax

F 0.4

0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0 h

o Figure 6.2b Normalized Fp vs h for MB30SiC10C (675 C/40min)

124

1.0 10 K 12.5 K 15 K 0.8 17.5 K 20 K 22.5 K 25 K 0.6 27.5 K

p max

F 0.4

0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0 h

o Figure 6.2c. Normalized Fp vs h for MB15SiC10C (675 C/40min)

1.0 10 K 12.5 K 15 K 0.8 17.5 K 20 K 22.5 K 25 K 0.6 27.5 K

p max 30 K

p 32.5 K

F 0.4

0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0 h

o Figure 6.2d Normalized Fp vs h for MB200SiC5C (675 C/40min)

125

1.0 10 K 12.5 K 15 K 0.8 17.5 K 20 K 22.5 K 0.6 25 K 27.5 K

p max

F 0.4

0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0

B/Birr

o Figure 6.2e Normalized Fp vs h for MB200SiC10C (675 C/40min)

6.2 Flux Pinning in MgB2

According to the models of flux-pinning in type-II superconductors, eight basic pinning functions have been proposed. These are divided into magnetic and core interactions. Magnetic interactions are dominant when both the pin size, a, and pin spacing, l, are greater than .  is of course the distance over which the local induced field, B, can undergo an appreciable change within a superconductor. Because of the above condition (a and l > ), B can adjust everywhere to a local equilibrium value giving rise to a flux barrier at the interfaces of pins and the matrix. Core interactions dominate when either a or l is less than . In this case the local B cannot achieve an

126 equilibrium value and can be considered as an average value. The dominant contribution to the energy difference is then the condensation energy within the flux lines.

The magnetic and core interactions are further classified into either volume, surface or point pins based on the size of interacting pinning centers as compared to the inter-flux-line spacing, d. These are also classified into either normal or  pinning based on the fact that the pinning centers can either be non-superconducting particles, such as normal metals, insulators or voids, or the pinning might arise because of the small fluctuations in the Ginsberg-Landau respectively. Table 6.4 shows the complete classification as described in [127]. These eight kinds of pinning mechanisms are mathematically described by distinct combination of exponent values (ps and qs) as shown in Eqn 6.2 earlier. These values for all eight expressions are also shown in Table

6.4.

Following these pinning function equations we fitted our pinning force data to the above equation 6.2. The values of the exponents p and q obtained for the data for our samples have been tabulated in Table 6.5. These values of the exponents do not follow any of the prescribed pinning mechanism in the above model. Various authors have also proposed using a summation equation with all eight functions for the cases where multiple pinning mechanisms are active over the entire curve. This analysis was also performed and it did not provide any satisfactory results in our case. On looking at the Fp data analytically by plotting it on a curve with the six core pinning functions in the background an interesting trend can be observed in the sample set. The Figures 6.2 (a-e) are replotted as Figures 6.3 (a-e) with six more functions for the comparison plotted along with.

127

Interaction Types of Pins Types of Pinning Pinning Location of Type Centers Function Maximum Exponents Pinning Force Normal p = 1/2, q = 1 h = 0.33 Magnetic Volume  p = 1/2, q = 1** h = 0.17, 1  h1/2(1-2h)] Normal p = 0, q = 2 ----- Volume  p = 2, q = 1 h = 0.5 Normal p = 1/2, q = 2 h = 0.2 Core Surface  p = 3/2, q = 1 h = 0.6 Normal p = 1, q = 2 h = 0.33 Point  p = 5/2, q = 1 h = 0.67

Table 6.4 Classification of pinning mechanisms

128

Temperature, Fp,max, A P q K GN/m3 Sample: MB30SiC5C (675oC/40min) 10.0 4.53 19.82 1.259 4.384 12.5 3.72 13.34 1.090 3.795 15.0 2.94 9.936 0.965 3.407 17.5 2.12 8.260 0.8759 3.114 20.0 1.47 7.797 0.889 2.746 22.5 1.16 11.78 1.203 2.973 25.0 0.90 23.94 1.598 3.583 27.5 0.68 26.51 1.614 3.737 Sample: MB30SiC10C (675oC/40min) 10.0 3.91 17.29 1.202 4.127 15.0 2.42 12.93 1.109 3.533 17.5 1.62 10.48 1.025 3.189 20.0 0.94 8.394 0.9664 2.642 22.5 0.51 12.93 1.266 2.885 25.0 0.23 12.27 1.220 2.923 Sample: MB15SiC10C (675oC/40min) 10.0 3.09 11.32 0.9707 3.799 12.5 2.51 9.446 0.9213 3.332 15.0 1.90 8.331 0.8972 2.980 17.5 1.40 10.68 1.056 3.072 20.0 1.01 13.57 1.185 3.414 22.5 0.72 15.01 1.270 3.416 25.0 0.48 21.69 1.363 4.140 27.5 0.30 19.38 1.298 3.931 Sample: MB200SiC5C (675oC/40min) 10.0 3.24 10.51 0.8531 4.562 12.5 3.01 19.15 1.150 5.139 15.0 2.64 26.10 1.303 5.353 17.5 1.95 16.94 1.133 4.459 20.0 1.38 9.751 0.9180 3.562 22.5 0.92 8.125 0.8797 3.020 25.0 0.69 24.13 1.437 4.208 27.5 0.55 28.45 1.525 4.472 30.0 0.45 36.42 1.741 4.481 32.5 0.36 65.09 2.003 5.169 Sample: MB200SiC10C (675oC/40min) 10.0 3.98 13.95 1.050 4.200 12.5 3.40 11.20 0.9653 3.940 15.0 2.68 10.12 0.9100 3.906 17.5 1.92 6.696 0.7513 3.164 20.0 1.22 6.748 0.7568 2.966 22.5 0.81 25.41 1.390 4.515 25.0 0.53 14.62 1.133 3.975 27.5 0.34 14.24 1.424 2.719

Table 6.5 Flux-pinning exponents for various SiC doped MgB2 samples

129

1.0

1. p = 0, q = 2 (Normal, Volume Pinning) 0.8 2. p = 1, q = 1 ( Pinning, Volume Pins) 3. p = 1/2, q = 2 (Normal, Surface Pinning) 4. p = 3/2, q = 1 ( Pinning, Surface Pins) 0.6 5. p = 1, q = 2 ((Normal, Point Pinning) 6. p = 2, q = 1 ( Pinning, Point Pins)

pmax

/F Low Temperature

F 0.4 Intermediate Temperature 3 5 2 4 6 1 High Temperature

0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0 h

Figure 6.3 a Normalized Fp vs h for MB30SiC5C plotted along with various pinning functions

1.0

0.8 1. p = 0, q = 2 (Normal, Volume Pinning) 2. p = 1, q = 1 ( Pinning, Volume Pins) 3. p = 1/2, q = 2 ((Normal, Surface Pinning) 0.6 4. p = 3/2, q = 1 ( Pinning, Surface Pins) 5. p = 1, q = 2 ((Normal, Point Pinning)

pmax

/F 6. p = 2, q = 1 ( Pinning, Point Pins)

F 0.4 Low and Intermediate Temperature 3 5 2 4 6 1 High Temperature

0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0 h

Figure 6.3 b Normalized Fp vs h for MB30SiC10C plotted along with various pinning functions

130

1.0 1. p = 0, q = 2 (Normal, Volume Pinning) 2. p = 1, q = 1 (Pinning, Volume Pins) 0.8 3. p = 1/2, q = 2 ((Normal, Surface Pinning) 4. p = 3/2, q = 1 ( Pinning, Surface Pins) 5. p = 1, q = 2 ((Normal, Point Pinning) 6. p = 2, q = 1 ( Pinning, Point Pins) 0.6 10K

pmax 12.5K

p 15K F 0.4 17.5K 3 5 2 4 6 1 20K 22.5 0.2 25K 27.5K

0.0 0.0 0.2 0.4 0.6 0.8 1.0 h

o Figure 6.3 c Normalized Fp vs h for MB15SiC10C (675 C/40min) plotted along with various pinning functions

1.0 1. p = 0, q = 2 (Normal, Volume Pinning) 2. p = 1, q = 1 ( Pinning, Volume Pins) 0.8 3. p = 1/2, q = 2 ((Normal, Surface Pinning) 4. p = 3/2, q = 1 ( Pinning, Surface Pins) 5. p = 1, q = 2 ((Normal, Point Pinning) 6. p = 2, q = 1 (Pinning, Point Pins) 0.6 10K

pmax 12.5K

p 15K

F 0.4 17.5K 3 5 2 4 6 1 20K 22.5 25K 0.2 27.5K 30K 32.5K

0.0 0.0 0.2 0.4 0.6 0.8 1.0 h

o Figure 6.3 d Normalized Fp vs h for MB200SiC5C (675 C/40min) plotted along with various pinning functions

131

1.0

1. p = 0, q = 2 (Normal, Volume Pinning) 0.8 2. p = 1, q = 1 ( Pinning, Volume Pins) 3. p = 1/2, q = 2 ((Normal, Surface Pinning) 4. p = 3/2, q = 1 ( Pinning, Surface Pins) 0.6 5. p = 1, q = 2 ((Normal, Point Pinning) 6. p = 2, q = 1 (Pinning, Point Pins)

pmax 10K

p 12.5K

F 0.4 15K 3 5 2 4 6 1 17.5K 20K 22.5 0.2 25K 27.5K

0.0 0.0 0.2 0.4 0.6 0.8 1.0 h

o Figure 6.3 e Normalized Fp vs h for MB200SiC10C (675 C/40min) plotted along with various pinning functions

1.0

p,max 6. p = 2, q = 1 ( Pinning, Point Pins)

/F 4.2K

F 0.4 10K 15K 20K 25K 0.2 30K

0.0 0.0 0.2 0.4 0.6 0.8 1.0 h

o Figure 6.4 Normalized Fp vs h for binary MB675 (675 C/40min) plotted along with various pinning functions

132

From Figures 6.3 (a-e) it can be seen that there exist 4 different regions in the graphs

(very clear in Figures 6.3 a and d and not so obvious in the rest of them). These regions are:

1. Low Temperatures (T < 20K), Low Fields (h < 0.3)

2. High Temperatures (T > 20K), Low Fields (h < 0.3)

3. Low Temperatures (T < 20K), High Fields and (h > 0.3)

4. High Temperatures (T > 20K), High Fields (h > 0.3). and the pinning force curve behaves very differently in these regions. In region 1, i.e. at low temperatures and low fields it is obvious that the surface pinning (grain boundry) is the major contributor to the transport properties of the samples and as the temperature increases there seem to be a mixed contribution from both surface and point pins.

For all the doped samples it can be seen that around 10K the major contribution to the peak pinning force, Fp,max, is coming from the surface pins (maxima at h ~ 0.2) and as we move towards region 2 the maxima shifts towards the point pinning mechanism

(maxima at h ~ 0.33) and at highest temperatures of measurement (T = 30 or 32.5K) point pins become the major contributors. This distinction is much more obvious in the 30nm doped SiC samples as compared to the other three samples and is not seen at all in the binary sample shown in Figure 6.4 where the pinning functions rides on the surface pinning over the entire range of temperature and fields.

In the high field regions, i.e. regions 3 and 4, it can be observed from the graphs that an obvious deviation from either the surface or the point pinning occurs and the function tends to move towards the volume pinning curve and riding perfectly on the

133 volume pinning function at much higher fields. This phenomenon could be explained based on a combination of two very different possibilities.

The first possibility is that a compositional inhomogenety that might be present in these doped samples would lead to a series of local oHirrs fields rather than a distinct

oHirr value. This has been earlier observed and computed by Cooley et al. for Nb3Sn samples [128] and also documented by Godeke [129]. The presence of such compositional inhomogenety will lead to an error in the estimation of oHirr and Jc at higher fields. This would not be the case for the binary sample and hence there would not be too much deviation from the basic surface pinning curve.

The second explanation is based on flux pinning models whereby, at higher fields as the d (inter-flux-line spacing) decreases the pinning centers which earlier acted as the surface pins (either a or l < d) or the point pins (a and l < d) now satisfy the condition of the volume pins (a and l > d) and hence a shift to the volume pinning mechanism.

Since both of these are possible in our doped samples, the exact reason for the Kramer non-linearity and hence the deviation from the basic surface pinning curve it is not clear at this point. It is possible that a combination of both of these possibilities is leading to the seen effect.

Overall, there seems to be an increase in th 10K Fp from the binary value at

2.98GN/m3 to values from 3-4.5 GN/m3 for the SiC doped samples. The fact that the value of h = 0.2 at temperatures from 4.2-20K suggest that the pinning remains dominated by grain boundary pinning, at least at these lower temperatures. This suggests that at least in 4.2-20K regime, SiC additions are not adding much in the way of additional pinning centers (e.g. particulate pins). Thus they either increase Fp via

134 increases in condensation energy or by grain boundary refinement. The near doubling of moHirr would suggest a four-fold increase in Fp (since condensation energy goes as

Bc22, see Eqn 6.2)

The increase seen in Fp is much weaker than this. On the other hand, no correlation with grain size is seen in Fp data either. These two observations are likely result of the large problem in connectivity known to exist in MgB2. In the next chapter we address this issue.

The higher temperature results on the other hand, suggest some shift from grain boundary pinning to particulate or volume pinning may be present. This is not too surprising because a small level of volume and particulate pins should be generated by the un- reacted (residual) SiC. However, these pins are too sparse to be very effective, or even observable except where grain boundary pinning is weak – at higher temperatures and fields. This is just what is seen.

135

Chapter 7

ELECTRICAL RESISTIVITY, DEBYE TEMPERATURE AND CONNECTIVITY IN BULK MgB2 SUPERCONDUCTORS

It is understood that the Jc, of MgB2 superconductor falls short of the intrinsic Jc because of the problems of grain connectivity, grain boundary blockages, and high porosity. It is important to understand the degree of connectivity in order to be able to improve Jcs. In this Chapter we have attempted to build up on the model of connectivity proposed by Rowell et al [1]. We have measured the normal state resistances of MgB2 bulk samples (pure and doped) in the temperature range of 40 - 300K and fitted the resistivity data to the Bloch-Gruneissen (B-G) equation. Data obtained from various other literature sources, both single crystal and thin films as well as dense strands were also analyzed in the similar manner and compared to the measured binary samples. Values of residual resistivity, connectivity, electron-phonon coupling constant, and Debye temperature have been obtained from the fitting. These values of Debye temperature will also be measured using the Quantum design PPMS in order to further validate the model.

136

7.1 Introduction

The special electronic and phononic structures of MgB2 have been the subject of numerous studies and reviews in the last six years. In MgB2, layers of Mg atoms stabilize planes of hexagonally connected B atoms. In fact MgB2 could be usefully described as

Mg-stabilized allotrope of B, since it is the B lattice that controls its electronic and vibrational properties. The transport properties of MgB2 both above and below its critical temperature, Tc, have been described in terms of a two-band electronic structure. In-plane and inter-planar bonding between the B atoms gives rise to an electronic band structure consisting of a 2D so-called “σ band” (deriving from the in-plane B-B bonds) and a 3D

“π band” (deriving from both in-plane and inter-plane B-B bonds). MgB2‟s moderately high Tc stems from the large ep (electron-phonon coupling constant) caused by the presence of holes in the B-B-bonding in-plane σ band and the relative softness of B-B- bond-stretching vibration modes [130, 131]. It is generally agreed that MgB2 is an electron-phonon moderated BCS-like s-wave superconductor [130, 132] but with two distinct energy gaps: a main gap, Eg(0)  7.2 mV, located in the 2D σ band, and a secondary gap, Eg(0)  2.3 mV, in the π band. Initially rather low, MgB2s anisotropic upper critical fields, Bc2 and Bc2||, can be substantially increased by introducing dopants, hence disorder, into the π and σ bands, and its critical current density, Jc , can be increased through the introduction of flux pinning centers. Above Tc the normal state properties of MgB2, metallic in nature, are dominated by the 3D π band [133], interband

- scattering playing an insignificant role [134]. But however we choose to describe these, what might be termed intrinsic, properties of the MgB2 crystal, the

137 superconducting and normal-state transport properties of practical polycrystalline bulk specimens or wires produced by some form of powder compaction process we will have to take into account the influences of extrinsic macroscopic artifacts such as: (i) porosity,

(ii) “sausaging” in the case of a wire and, (iii) the presence of intergranular blocking phases.

Together these will govern the sample‟s effective cross-sectional area for electrical transport and hence its Jc, for a given critical current, and its resistivity, , for a given resistance/unit length. Both superconductivity and normal electrical conductivity will be moderated by the same effective cross-sectional area. For this reason, measurements of the normal-state  can lead to estimates of effective cross-sectional area for supercurrent transport [82]. Rowell, in a seminal article on the subject [82], has defined a quantity 1/F (< 1), the fractional cross-sectional area for current transport, or connectivity, and shows how a reasonable value for connectivity can be extracted just from measurements of the sample‟s resistances at two temperatures: 300K and about

40K. It turns out that the Rowell model is restricted to samples that do not deviate too much from clean stoichiometric MgB2. Accordingly we have found it necessary to develop an extension of the Rowell approach in order to quantify the connectivity of heavily doped MgB2 samples. Our method, which makes use of the Bloch-Grüneisen function, yields not only a connectivity parameter but also values for residual resistivity,

Debye temperature and through it an electron-phonon coupling parameter. Finally, we propose a “generalized porosity model” to describe the sample‟s connectivity and identify its effective resistivity as that of a heterogeneous composite consisting of a high resistivity dispersion in a low resistivity matrix [135]. In case of MgB2 these dispersions

138 include the volume occupied by: (i) porosity, (ii) high resistivity second phase material and (iii) isolated MgB2 particles encapsulated in a high resistivity oxide film. By way of the resistively measured F-parameter, this model based on [135] allows us to express the effective volume fraction of the current carrying matrix, Cin the form C = [3/(2F+1)]

(Ref. Appendix B for details).

7.2 Connectivity and Normal State Resistivity

The transport J, of a superconducting sample is, as a practical matter, specified as the Ic divided by some defined sample cross-sectional area – usually the area of the superconductor. The Jc so obtained is usually less than the intrinsic Jc of the superconductor, due either to restrictions, cross-sectional area oscillations along the conductor length, (“sausaging”), or porosity. In the case of MgB2, several authors have

8 2 calculated the depairing Jcd. This Jcd is accepted to be of the order of 10 A/cm . The measured Jc of any practical sample is only about 5% of this highest local Jc for two primary reasons. These include the above mentioned sausaging and local Jc inhomogeneities and potentially other causes. But in well-made strands the primary causes which are dominant are: (i) The core of a powder-in-tube sample is only about

50% dense, in as-drawn PIT strands, usually about 80%, a consequence of powder packing density and another 37% porosity coming from shrinkage during the in-situ

Mg+2B  MgB2 reaction if that processing route is employed. (ii) Imperfect connectivity between the resulting MgB2 grains, due for example to the presence of insulating grain-boundary films. Without any change in the connectivity mechanism, full densification by mechanical compaction would be expected to double Jc simply from a

139 geometrical standpoint. However, significant improvements in intergrain connectivity will in principle lead to manifold increases in Jc. It turns out that the grains of polycrystalline MgB2 are usually poorly connected. In attempting to correct the problem it is important to have a measure of the degree of connectivity. As first pointed out by

Rowell [82], normal state resistivity measurement provides the needed connectivity gauge.

Rowell proposed to determine a sample‟s connectivity by comparing its resistivity at some low temperature with that of a single (hence perfectly connected) crystal. The intragranular resistivity of a conductor is the sum of the “residual” value, 0, (which is subject to extreme variability from sample to sample independent of connectivity) and the

“ideal” electron-phonon-scattering component, i(T). The former is caused by defects and dopants, essentially non-phononic contributions to electron scattering within a grain and is independent of connectivity The latter is also connectivity independent, since it is due to electron-phonon scattering but the total measured resistivity of a sample is connectivity dependant and has been used as the connectivity gauge by Rowell, who assumed that

i(T) over some fixed wide temperature range (in particular between about 40K and

300K) was invariant from sample to sample and equal to 4.3 μcm, based on single- crystal data [81]. Therefore, according to Rowell approach

m, polyT   F0  i T  (7.1)

Where m,poly is the measured resistivity of a polycrystalline sample. For a pure single crystal sample limiting F=1 (100% connected) and thus,

m,scT   0  i T  (7.2)

140

Now subtracting the 50K measured resistivity from the 300K resistivity for both the samples. Eqn. 7.1 becomes

m, poly300  50  Fi 300  50 (7.3)

and Eqn. 7.2 becomes

 300  50   300  50  4.3cm [82] (7.4) m,sc    i  

Now, if i(T) is assumed to be invariant from sample to sample then equation 6.3 and

6.4 can be equated to obtain the value of F.

Δρ 300  50 F  m (7.5) 4.3cm

As demonstrated below, this invariance of i(T), the central assumption of the

Rowell method, has been validated for two binary fairly clean samples. Shown in the

Figure 7.1 are (i) a binary MgB2 sample prepared at OSU as described in Chapter 3

(Table 3.1) and (ii) a binary sample from The Naval Research Lab with 10% extra Mg,

NRLHR10Mg. Figure 7.1a shows the temperature dependent part of the measured resistivities, m1(T) and m2(T), for MB700 and the NRLHR10Mg sample respectively while Figure 7.1b shows these resistivities after being normalized by their connectivities.

The F values for the two samples were obtained by the above described Rowell analysis.

141

50 MB700 NRLHR10Mg 40

 30



i 

Resistivity, 10

0 50 100 150 200 250 300 Temperature, T, K

Figure 7.1a (T) for two MgB2 samples

5 MB700 F = 10.4 NRLHR10Mg F= 2.3 4

-cm 3



(T)

i  2

1/F(

0 50 100 150 200 250 300 Temperature, T, K

Figure 7.1b Invariance of (T) for two MgB2 Samples

142

In what follows we describe the resistivity measurements on a series of bulk doped MgB2 samples and then go on to analyze the results using a modified Rowell approach appropriate to heavily doped material.

7.2.1 Sample Preparation and Resistivity Measurements

Four-terminal resistivity measurements were made between 50 K and 273 K on bulk pellets of binary MgB2 and MgB2 doped with TiB2 and SiC respectively using the fabrication method described in Chapter 3 (Sec 3.2.1). The samples are listed in

Table 7.1. Resistivity measurement was performed using the four-probe measurement technique as described in Chapter 3. A fixed current of 10 mA was used with current reversalsand the voltage taps‟ separation in this case was about 3 mm.

7.3 Resistivity Analysis Using the Bloch-Grüneisen (B-G) Function

Figure 7.2 shows the temperature dependence of the resistivities of three different samples. A large difference in the 50K baseline value is apparent by the visual inspection.

We could interpret this to be due to a difference in level of F. Figure 7.3a shows the spread of i(T) for these samples. This data set was subsequently analyzed using the

Rowell method, to get the value of the connectivity parameter F, and contrary to the data in Figure 7.1 and [82] this data does not scale on to one curve after being converted to

100% connectivity (shown in Figure 7.3b). In this case, we must allow both i(T) and o to vary. Functionally, allowing i(T) to be no longer invariant accounts for its overall slope changes from sample to sample. The departure of the i(T) invariance implicit in the Rowell approach can be expressed in terms of a varying Debye temperature, D, from

143 sample to sample. The permitted variation of o, (not a feature of Rowell analysis) allows the effect of doping to be explicitly accounted for in the resistivity measurement.

400

300 MB700 MBTi800 MBSiC700

 200

(T)

m 

100

0 50 100 150 200 250 300 Temperature, T, K

Figure 7.2 Temperature dependence of the mfor binary and doped MgB2 samples

144

100

MB700 MBTi800 80 MBSiC700





i  40

0 50 100 150 200 250 300 Temperature, T, K

Figure 7.3a (T) for binary MgB2, MgB2-TiB2 and MgB2-SiC samples

Single Crystal Data [81] 4 MB700 MBTi800 MBSiC700



(T), (T),   2

(1/F).

0 50 100 150 200 250 300 Temperature, T, K

Figure 7.3b Demonstration of varying i(T)

145

The more straight forward way to allow for the non-scaling is to introduce a

Debye temperature, D, that is allowed to vary from sample to sample. Hence, we replace

the sample invariant i(T) with the true Debye function i(T,D).

Several authors have reported excellent agreement between the measurement resistivity temperature dependence and the standard Bloch-Grüneisen (B-G) function

[130, 136] or a variation of it [137, 138]. Following this approch [130, 136-138] we have adopted the standard form of the B-G function in order to allow for a variation in D. The standard B-G form of the ideal (electron-phonon) resistivity is

 m D k  T  T ez zmdZ  T     (7.6) i    z 2 D D  0 e 1 in which k is a materials constant to be selected or determined and m = 5. In variants of

B-G that were found to provide satisfactory fits to the experimental data m was given the values 3 [137] and 3-5 [138]. As well as enabling a connectivity parameter to be extracted from the (T)s of doped samples and the very important o, which correlates to the level of doping and Bc2 enhancement, it also provides a value for D which together

with Tc enables a value for the electron-phonon coupling constant, ep, to be derived with the aid of the McMillan formula (eqn. 7.7). However, the coupling constant thus obtained is fairly limited by the choice of coulombic psudo potential, * (See. Chapter 1). For the calculation here we have taken the value to be 0.05 as calculated by Bohnen et al [139].

D 1.04(1 ) Tc  exp * (7.7) 1.45 (  (1 0.62  )

146

With this in mind our extension of the Rowell approach consisted of fitting the experimental data to:

 5 R  T z 5   k  T  e z dz   (T )  F     (7.8) m  o    z 2  R R  0 e 1   in which, m(T) is the measured resistivity as a function of temperature and o, R and F were free parameters, the constant k having been pre-determined by fitting the single- crystal (hence F = 1) data of Eltsev et al. [81] to Eqn.(7.8). Table 7.1 lists the values of

F, a derived volume percent of the current carrying matrix, C, (see Appendix A for calculations), and the other important extracted parameters, o, R, and ep obtained by fitting the experimental data to Eqn 7.8.

Sample F % C 0 R ep (B-G Method) (cm) (K) =0.05) MB700 4.32 31.1 11.29 677 0.8365 MBTi800 9.50 15.0 9.49 764 0.7574 MBSiC700 7.39 19.0 38.56 593 0.8665

Table 7.1 Conducting volume fraction, residual resistivity, Debye temperature and coupling constant for three doped samples

Similar analysis was also performed on other data sets obtained from the literature

[134] which was collected on dense wire made with boron coated tungsten filament [46] and c-axis oriented thin films [140] and also on the data obtained by Naval Research

Labs (NRL-HR samples) on two different MgB2 samples. The results of the analysis are shown in Table 7.2 and the complete set of data along with the fitting curve is shown in

Figure 7.4 (a and b) for all measured and literature data that was used.

147

Sample % C o R ( D ) (B-G Method) (-cm) (K) Single Crystal [134] --- 1.04 949 MB700 31.1 11.29 677 (653) MBTi800 15.0 9.49 764 (745) MBCSiC700 19.0 38.56 593 (600) NRLHR10Mg 86.5 2.12 695 NRLHR 96.5 1.97 739 Dense Wire [46] 67.9 0.31 839 Thin Film [140] 23.6 4.05 858

Table 7.2 Fitted parameters for all samples

400

MBSiC700 300 MBTi800 MB700

cm c-axis Oriented Thin Film



, Tu et. al. [140]  200 NRLHR10Mg NRLHR Dense Wire Canfield et. al. [46]

Resistivity, Resistivity, 100 Single Crystal [134]

0 50 100 150 200 250 300 Temperature, T, K

Figure 7.4 a m vs. T for all studied samples (Solid Lines Represent the Fitting Curve)

148

12 NRLHR10Mg NRLHR Dense Wire -

cm 10 Canfield et al [46]



, Single Crystal [134]  8

Resistivity, Resistivity, 4

0 50 100 150 200 250 300

Temperature, T, K

Figure 7.4 b m vs. T for samples with low resistivities (an expansion of the lower data set of the Figure 7.4 a)

Our new fitting function describes well the measured or reported values.

Connectivity values ranging from 96.5% for the purest NRL sample to 15.0 % for TiB2 doped sample have been obtained. Finally we emphasize that the B-G analyzed method led for the first time for the values of the residual resistivities to be extracted. It is these values that provide the measure of the -band scattering and hence correlate with the low-temperature Bc2s

7.4 Heat Capacity Measurement

Following the above analysis, heat-capacity measurements as a function of temperature ranging between 2 - 300K were also performed, using Quantum Design

PPMS system (ref. Chapter 3 for details), on the binary and doped bulk samples. These

149 measurements were performed at both 0T and 9T. In contrast to the low-temperature specific heat of the low-temperature superconductors (Tc ~ 4 -9K) the heat-capacity jump in MgB2 (Tc ~ 39K) takes place in the presence of a relatively large lattice heat-capacity,

Figure 7.5. Therefore, in order to improve the presence of the heat-capacity jump at Tc it is needed to subtract the lattice heat-capacity, leaving only the electronic component.

This is done by subtracting the measurement at 9T, above Bc2 of MgB2 in the tested temperatures, from the data at 0T. The curves for all three samples show the superconducting transitions between 35 - 40K. The 0T heat capacity and the difference of the 0T and the 9T are shown in Figure 7.5 and 7.6 respectively.

Heat-capacity measurement as a function of temperature also provides the Debye temperature by using the following formula:

3 D C  T  T x4ex  9  dx (7.9) Nk    x 2  D  0 e 1 w here, C is the total heat-capacity of the material i.e. sum of both electronic and the lattice heat-capacity. Heat-capacity variation as a function of temperature for these samples was fitted to Eqn. 7.9 and the D obtained for all three bulk samples was in close agreement with the D obtained by the resistivity data fitting. Values of D measured by heat-capacity are shown in parenthesis in Table 7.2.

150

200

150

100

, mJ/mol-K

(0T)

p C MB700 50 MBSiC700 MBTi800

0 0 50 100 150 200 250 300

T, K

Figure 7.5 Total heat-capacity for pure and doped MgB2 at zero field

80 MB700 MBSiC700 MBTi800 60

mJ/mol-K 40

(9T), (9T),

(0T)-C

C 20

0 20 25 30 35 40

T, K

Figure 7.6 Electronic heat-capacity (Cp(0T)-Cp(9T)) for pure and doped MgB2

151

7.5 Conclusion

To conclude, we have been able to measure the variation of normal state resistivity with temperature for both pure and doped/dirty MgB2 bulk samples using the four-point contact method. It was shown that Rowell‟s model fits binary MgB2 samples well but not doped samples. A proposed refinement of Rowell‟s analysis using B-G function fits the measured data very well and provides information about the current carrying volume fraction, along with the o and D which, in-turn can be used to obtain the ep. Several other data sets obtained from various references have also been fitted by this method and show the applicability of this method.

Thus two new parameters are obtainable with this new model. The first o, describes the amount of non-phononic, i.e. residual, scattering within the grain. We can associate this with doping related electron scattering and Bc2 enhancements. The second is D, which indicates a change in the phonon spectrum.

The connected volume fraction of the binary MgB2 sample, MB700, was found to be around 31% and it further decreased on adding dopants. Except for the highly dense samples prepared by the NRL by hot-rolling and Canfield et al. using dense B filaments rest of the bulk samples had %C ranging between 15-30%. This suggest that even though these samples had high Bc2s and reasonable transport properties, their Jcs would in principle be improved by a factor of three or four just by radically increasing the connectivity. Also, looking at the residual resistivities, o, in Table 7.2 it can be seen that the o increased by a factor of three for the SiC doped sample as compared to the our binary MgB2 sample. This is an indication of the enhanced electron scattering caused due to the C substitution in MgB2 lattice. This was not the case for the TiB2 doping and hence

152 it did not give higher Bc2 (Ref. Table 5.3). Apart from that, the D, for all the samples was found to be lower than that for the single crystal MgB2 and decreased further with successful SiC doping. Also, the ep got marginally increased by SiC doping while it reduced a little with the TiB2 addition.

153

SUMMARY AND CONCLUSIONS

In this work, the basic formation of in-situ MgB2, and how variations in the formation process as well as selected dopant additions influence the electrical and magnetic properties of this material were studied. Bulk MgB2 samples were prepared by stoichometric elemental powder mixing and compaction followed by heat-treatment.

Strand samples were prepared by a modified powder-in-tube technique with subsequent heat-treatment. The influence of numerous reaction temperature-time schedules on the formation of MgB2 was studied. The phase formation of MgB2 during the in-situ reaction was initially studied using DSC. Two groups of exothermic peaks were found below the

o melting temperature of Mg with the one just below 650 C corresponding to the MgB2 formation. Based on this, two heat-treatment windows were identified, namely: a low- temperature reaction window (between 620-650oC) and a high-temperature reaction window (>650oC). X-ray analyses were performed on both high and low-temperature reacted samples to confirm the complete phase formation. SEM micrographs were used to determine the level of porosity, connectivity, and the presence of secondary phase for the samples which contained additional dopants. XRD was additionally used to confirm the solution of dopants into the MgB2 lattice and the presence of any second phases.

Fracture SEMs were used to determine the grain sizes on both binary and the doped samples. TEM bright field imaging coupled with EDX was also used to confirm the presence of these dopants into the host MgB2 grains. Both of the above mentioned heat-

154 treatment windows gave very similar oHirr and Bc2s for MgB2 but the low-temperature heat-treatment was found to be slightly better in terms of high field transport critical currents. The low-temperature heat-treated sample was found to be less porous with homogeniously distributed finer pores as compared to the bigger pores found in the high- temperature heat-treated samples.

Following the reaction studies, the effects of various dopants on the superconducting properties, especially the critical fields were studied. Large increases in

oHirr, and Bc2 of bulk and strand superconducting MgB2 were achieved by adding the dopants. SiC, amorphous C, and selected metal diborides, NbB2, ZrB2, TiB2, (in bulk samples) and three different sizes of SiC, ~200 nm, 30 nm and 15 nm, (in strands). MgB2 strands with SiC additions, reacted in both low-temperature and high-temperature reaction windows and measured for 0Hirr and Bc2, were found to behave identically. It was found that 10% additions of SiC always produced much higher Bc2s as compared to

5% additions, at fixed particle size. On the other hand, the 15nm or 30nm SiC additions led to much higher Bc2s and oHirrs than did the 200nm SiC powder addition. Further, on studying the effect of reaction temperature and time (high-temperatures) on the properties of 10% 30nm SiC doped sample it was found out that both oHirr and Bc2 improved with longer soaking time at fixed temperatures and also improvrd with increase of the reaction

o temperatures up to 800 C. Both oHirr and Bc2 decreased with increasing reaction temperature beyond 800oC.

Apart from SiC doping, which was aimed at dirtying the  band, the effect of doping onto different sites in bulk MgB2 was also studied. C doping onto the B site was achieved via acetone mixing as well as SiC additions. Doping onto the Mg site, for

155 selectively dirting the  band was achieved, using NbB2, ZrB2, and TiB2. Increases in

0Hirr and Bc2 were seen in both the cases. Even though the effective increases in both the cases have been substantial, different doping sites showed different characteristics and lead to different relative increases in 0Hirr and Bc2. In case of metal diboride dopants,

ZrB2 was found to be most effective, leading to large increases in Bc2 at low temperatures, as proposed by the theory of “selective impurity tuning” for the case of the dirty  band.

For SiC doped samples, efforts were also made to quantify the variation in 0Hirr and Bc2 with sensing currents in order to probe the current-dependent variations in the current paths due to possible material inhomogenieties. The SiC strands, which were relatively high performance, showed transport current and 0Hirr signatures suggesting material based inhomogeneities. All but one sample had differences in 0Hirr and Bc2 values as determined from resistive transitions as the sensing current level was varied.

This variation which can be interpreted in terms of sample inhomogeneity and anisotropy was also observed in the electronic specific-heat signature in terms of the decrease in the sharpness of the heat-capacity jump at Tc.

Additionally, increases in transport Jc were seen with SiC dopants. Some small flux pinning changes were seen, but most increase could be attributed to Bc2 improvements. Such changes in the flux pinning strength were studied for the SiC doped samples and explained with the help of flux pinning models. From the maxima in the flux pinning curves, Fp,max, of the binary sample and the SiC doped samples it was noticed that

3 the Fp,max of 10% 30nm SiC sample, (at 3.9GN/m ) was higher than that of the binary sample (at 2.9GN/m3). No direct correlation was seen between the grain size and the

156 pinning force. However, as compared to the un-doped sample, an apparent increase in Jc was seen for the 30nm and 15nm SiC doped samples which also had higher oHirr and

Bc2s. The lack of direct correlation between Jc and either grain size or oHirr can be attributed to the fact that the measured Jc for these samples is not the intrinsic Jc but some connectivity reduced fraction of it. This led us to the study of connectivity in these doped samples.

Connectivity was deduced from measurements of the normal-state resistivities of these doped and un-doped samples as a function of temperature. These measurements, in principle, could also be used to confirm the substitution of depant elements into the MgB2 lattice whose presence lead to proportional increases in the impurity scattering and hence residual resistivity. In order to be able to extract residual resistivities from the measured data we needed to include in our analysis the influence of connectivity, porosity and dopants as a function of Debye temperature, D. This was done by fitting m(T) to the

Bloch-Gruneissen equation. By doing so we were able to extract the residual resistivities,

D and current carrying volume fractions for these samples. As an added bonus the D determined in this way provides information on the electron-phonon coupling constant.

Debye temperatures extracted by the heat-capacity measurements were seen to agree with the resistivity determined values. Comparing between the SiC doped samples as compared to the binary sample, the residual resistivity was found to increase three fold,

D decreased and the electron-phonon coupling constant increased. The increase in residual resistivity for the SiC doped sample led us to conclude that the SiC was substituting into the MgB2 lattice, presumably in the form of C and hence effectively changing the scattering behavior in MgB2 leading to exceptionally high Bc2s.

157

It can therefore be concluded that MgB2 can be effectively doped with SiC, C or metal diborides and enhanced oHirr and Bc2 values can be achieved based on Gurevich‟s

“selective impurity tuning” mechanism. Even though, Bc2s as high as 33T have been achieved there still lies room for further improvements as shown in the case of thin films

6 (Bc2||=60T). On a separate note the 4.2K Jc of the material is still of the order of 2x10

2 8 2 A/cm which is only a fraction of the depairing Jc (~10 A/cm ), i.e., the ultimate achievable Jc. This achievable Jc is limited due to the problems of connectivity (as shown in Chapter 7) and therefore efforts should be made to prepare samples with higher density and cleaner grain boundaries which are free from the oxide insulating phases. One such way can be to use clean MgB4 and Mg as the starting powders for the final MgB2 preparation. It should also be helpful to co-dope MgB2 with SiC (or other forms of C) and nonmagnetic hard nanoscale particulates in order to achieve higher flux pinning along with the positive effects of C substitution on the B lattice and hence achieving higher Bc2 along with much higher Jcs making MgB2 an ideal material for practical applications.

158

APPENDIX A

LIST OF SUPERCONDUCTING PARAMETERS OF MAGNESIUM DIBORIDE

Parameter Values

Critical Temperature Tc = 39 - 40K Hexagonal Lattice a = 0.3086nm Parameters c = 0.3524nm Theoritical Density d = 2.55g/cm3 Pressure Coefficient dTc/dP = -1.1 - 2K/GPa 23 3 Carrier Density ns = 1.7-2.8 x10 holes/cm Isotope Effect T = B + Mg = 0.3 – 0.02 Resistivity at 40K m(40K) = 0.1 – 300cm Coherence Length ab(0K) = 3.7 - 12nm c(0K) = 1.6 - 3.6nm Penetration Depth nm Energy Gap Eg = 7.2mV Eg = 2.3mV Debye Temperature D = 600 – 900 K 8 2 Depairing Current Density Jd = 10 A/cm Irreversibility Field oHirr (polycrystalline) = 11 – 16T Upper Critical Field Bc2 (polycrystalline) = 14 – 19T

159

APPENDIX B

MODEL AND CALCULATIONS FOR DETERMINING THE VOLUME FRACTION

OF CURRENT CARYING MATRIX

For determining effective resistivity of a composite, certain mixture rules can be applied depending on the mixture geometry and resistivity of the constituent phases. Following

Figure 1 describes three possible cases. Case 1 (Figure 1a) and Case 2 (Figure 1b) are two extreme cases where the two phases in the composite ( and ) are in the layers making them effectively either series or parallel connections in terms of individual resistivities ( and ) for effective resistivity (m) measured in x-direction. Case 3

(Figure 1c), on the other hand, is the case where  phase is randomly dispersed in the matrix of .

 

(a) (b) (c)

Figure B.1 Effective resistivity of a material along x-axis (a) perpendicular to the layer structure; (b) parallel to the layer structure; and (c) with a dispersed second phase. 160

For Case 1,

 m  x   x   (1)

Where, x and x are the area fractions of phases  and  respectively.

Since,

x  1 x (2)

Therefore,

 m     x      (3)

For Case 2,

1 x x     (4)  m   

Therefore, from eqn. 4 and 2,

     m   if (<<) (5) x    x  x

In case of MgB2, Rowell analysis provided a method to estimate the connectivity in the sample. This connectivity is equivalent to the area fraction of the connected MgB2 phase

( phase) or the effective current carrying cross-section. The porosity and blocked current paths are taken to be high resistivity  phase and hence eqn. 5 can be applied to a good approximation with the quantity F (defined in the Rowell analysis) being equal to inverse of x.

Considering Case 3, on the other hand, gives an even better approximation, since these paths are not always ideally parallel. This case considers a heterogeneous material with a dispersed phase  in a continuous matrix phase . Following that, the effective resistivity

161 of the composite (measured resistivity, m) is given in terms of the volume fractions of the two phases, namely C and Cif (<<) then this m is equal to,

 1  1 C   2   m     if (<<) [135] (6)  1 C      

And since,

C  1 C (7)

Therefore,

3  C  m     (8)  2C  

Now,

3  C  F   (9) 2C 

And if we now define connectivity to be more accurately the volume fraction of the current carrying phase, i.e. C, it then will be equal to,

3 C  (10)  2F 1

Further details can be found in [135, 141].

162

APPENDIX C

LIST OF SYMBOLS

Symbols Description

Tc Critical Temperature  Coherence Length  Penetration Depth Ec Critical Electric Field Ic Critical Current Jc Critical Current Densiy oHirr Irreversibility Field Bc2 Upper Critical Field H Applied Field M Magnetization B Field Inside the Conductor m Measured Resistivity o Residual/Impurity Resistivity D Electron Diffusivity ep Electron-Phonon Coupling Constant Fp Flux-Pinning Force C Current Carrying Volume Fraction D Debye Temperature Cp Total Heat-Capacity Ce Electronic Heat-Capacity Eg Superconductor Energy Gap DC DC Susceptibility e Electronic Charge C Speed of Light kb Boltzman‟z Constant H Plank‟s Constant

163

LIST OF REFERENCES

[1] M. Jones, R. Marsh, J. Amer. Chem. Soc., vol. 76 p. 1434 1954.

[2] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akimitsu, Nature, vol. 410 pp. 63-64 2001.

[3] J. R. Gavaler, M. A. Janocko, C. Jones, J.Appl. Phys., vol. 45 p. 3009 1974.

[4] R. J. Cava, H. Takagi, B. Batlogg, H. W. Zandbergen, J. J. Krajewski, W. P. Peck, D. R.B., Nature, p. 372245 1994.

[5] D. C. Larbalestier, L. D. Cooley, M. O. Rikel, A. A. Polyanskii, J. Jiang, S. Patnaik, X. Y. Cai, D. M. Feldmann, A. Gurevich, A. A. Squitieri, M. T. Naus, C. B. Eom, E. E. Hellstrom, R. J. Cava, K. A. Regan, N. Rogado, M. A. Hayward, T. He, J. S. Slusky, P. Khalifah, K. Inumaru, M. Haas, Nature, vol. 410 pp. 186-189 2001.

[6] D. K. Finnemore, J. E. Osbenson, S. L. Bud‟ko, G. Lapertot, P. C. Canfield, Phys. Rev. , vol. 86 p. 2420 2001.

[7] X. H. Chen, Y. Y. Xue, R. L. Meng, C. W. Chu, Phys. Rev. B, vol. 64 p. 172501 2001.

[8] H. Kemerlingh Onnes, Leiden Comm., vol. 120b 1911.

[9] J. Bardeen, L. N. Cooper, R. Schrieffer, Phys. Rev., vol. 108 p. 1175 1957.

[10] L. Ginzburg, L. D. Landau, Zh. Eksperim. i Teor. Fiz., vol. 20 p. 1064 1950.

[11] W. Meissner, R. Ochsenfeld, Naturwissenschaften, vol. 21 p. 787 1933.

[12] F. London, H. London, Proc. Roy. Soc. (London), vol. A149 p. 71 1935. 164

[13] T. W. Heitmann, S. D. Bu, D. M. Kim, J. H. Choi, J. Giencke, C. B. Eom, K. A. Regan, N. Rogado, M. A. Hayward, T. He, J. S. Slusky, P. Khalifah, M. Haas, R. J. Cava, D. C. Larbalestier, M. S. Rzchowski, Supercond. Sci. Tech., vol. 17 pp. 237-242 2004.

[14] H. Schober, B. Renker, R. Heid, Institut Laue-Langevin Annual Report 2002.

[15] Z. K. Liu, D. G. Scholm, Q. Li, X. X. Xi, Appl. Phys. Lett., vol. 78 p. 3678 2001.

[16] G. Grasso, A. Malagoli, C. Ferdeghini, S. Roncallo, V. Braccini, A. S. Siri, M. R. Cimberle, Appl. Phys. Lett., vol. 79 pp. 230-232 2001.

[17] G. Grasso, A. Malagoli, D. Marre, E. Bellingeri, V. Braccini, S. Roncallo, N. Scati, A. S. Siri, Physica C, vol. 378 pp. 899-902 2002.

[18] G. Grasso, A. Malagoli, M. Modica, A. Tumino, C. Ferdeghini, A. S. Siri, C. Vignola, L. Martini, V. Previtali, G. Volpini, Supercond. Sci. Tech., vol. 16 pp. 271-275 2003.

[19] S. X. Dou, S. Zhou, A. V. Pan, H. Liu, Physica C p. 382 349 2002.

[20] S. X. Dou, S. Zhou, A. V. Pan, H. Liu, J. Horvat, Supercond. Sci. Technol. , vol. 15 p. 1490 2002

[21] A. V. Pan, Supercond. Sci. Technol., vol. 16 pp. 639-644 2003.

[22] S. Zhou, A. V. Pan, M. Ionesc, H. Liu, S. X. Dou, Supercond. Sci. Technol., vol. 15 p. 236 2002.

[23] S. X. Dou, W. K. Yeoh, J. Horvat, M. Ionescu, Appl. Phys. Lett., vol. 83 pp. 4996- 4998 2003.

[24] S. K. Chen, K. S. Tan, B. A. Glowacki, W. K. Yeoh, S. Soltanian, J. Horvat, S. X. Dou, Appl. Phys. Lett., vol. 87 2005.

[25] S. X. Dou, S. Soltanian, W. K. Yeoh, Y. Zhang, IEEE Trans. Appl. Supercond., vol. 15 pp. 3219-3222 2005.

165

[26] S. P. Dou, AV; Zhou, S; Ionescu, M; Liu, HK; Munroe, PR, Supercond. Sci. Technol., vol. 15 pp. 1587-1591 2002.

[27] M. Bhatia, M. D. Sumption, E. W. Collings, IEEE Trans. Appl. Supercond., vol. submitted 2006.

[28] D. C. Larbalestier, L. D. Cooley, M. O. Rikel, A. A. Polyanskii, J. Jiang, S. Patnaik, X. Y. Cai, D. M. Feldmann, A. Gurevich, A. A. Squitieri, M. T. Naus, C. B. Eom, E. E. Hellstrom, R. J. Cava, K. A. Regan, N. Rogado, M. A. Hayward, T. He, J. S. Slusky, P. Khalifah, K. Inumaru, M. Haas, Nature, vol. 410 p. 6825 2001.

[29] D. G. Hinks, J. D. Jorgensen, H. Zheng, S. Short, Physica C vol. 382 p. 166 2002

[30] R. A. Ribeiro, S. L. Bud‟ko, C. Petrovic, P. C. Canfield, Physica C, vol. 382 pp. 194-202 2002.

[31] S. L. Bud‟ko, G. Lapertot, C. Petrovic, C. E. Cunningham, N. Anderson, P. C. Canfield, Phys. Rev. Lett. , vol. 86 p. 1877 2001.

[32] G. Giunchi, S. Ceresara, L. Martini, V. Ottoboni, S. Chiarelli, S. Spadoni, Paper presented at the Conference SATT11, Vietri S.M.(SA) Italy, 2002

[33] Z. Y. Fan, D. G. Hinks, N. Newman, J. M. Rowell, Appl. Phys. Lett. , vol. 79 p. 87 2001

[34] S. Brutti, A. Ciccioli, G. Balducci, G. Gigli, P. Manfrinetti, A. Palenzona, Appl. Phys. Lett. , vol. 80 p. 2892 2002.

[35] M. E. Yakinci, Y. Balci, M. A. Aksan, H. I. Adiguzel, A. Gencer, J. Supercond., vol. 15 pp. 607-611 2002.

[36] S. X. Dou, E. W. Collings, O. Shcherbakova, A. Shcherbakov, Supercond. Sci. Tech., vol. 19 pp. 333-337 2006.

[37] R. F. Klie, J. C. Idrobo, N. D. Browning, A. Serquis, Y. T. Zhu, X. Z. Liao, F. M. Mueller, Appl. Phys. Lett., vol. 80 pp. 3970-3972 2002.

166

[38] A. S. Cooper, E. Corenzwit, L. D. Longinotti, B. T. Matthias, W. H. Zachariasen, Proc. Natl. Acad. Sci. , vol. 67 p. 313 1970

[39] Y. G. Zhao, X. P. Zhang, P. T. Qiao, H. T. Zhang, S. L. Jia, B. S. Cao, M. H. Zhu, Z. H. Han, X. Wang, B. L. Gu, Physica C, vol. 366 p. 1 2001

[40] A. Serquis, Y. T. Zhu, E. J. Peterson, J. Y. Coulter, D. E. Peterson, F. M. Mueller, Appl. Phys. Lett., vol. 79 p. 4399 2001

[41] A. Serquis, X. Z. Liao, Y. T. Zhu, J. Y. Coulter, J. Y. Huang, J. O. Willis, D. E. Peterson, F. M. Mueller, N. O. Moreno, J. D. Thompson, V. F. Nesterenko, S. S. Indrakanti, J. Appl. Phys., vol. 92 pp. 351-356 2002.

[42] X. H. Chen, Y. S. Wang, Y. Y. Zue, R. L. Meng, Y. Q. Wang, C. W. Chu, Phys. Rev. B vol. 65 p. 024502 2001.

[43] H. M. Christen, H. Y. Zhai, C. Cantoni, M. Paranthaman, B. S. Sales, C. Rouleau, D. P. Norton, D. K. Christen, D. H. Lowndes, Physica C vol. 353 p. 157 2001.

[44] S. R. Shinde, S. B. Ogale, R. L. Greene, T. Venkatesan, P. C. Canfield, S. L. Bud‟ko, G. Lapertot, C. Petrovic, Appl. Phys. Lett., vol. 79 p. 227 2001

[45] Y. Ma, X. Aixia, L. Xiaohang, Z. Xianping, A. Satoshi, W. Kazuo, Jap. J. Appl. Phys., vol. 45 pp. L493-L496 2006.

[46] P. C. Canfield, D. K. Finnemore, S. L. Bud'ko, J. E. Ostenson, C. Lapertot, C. E. Cunningham, C. Ptrovic, Phys. Rev. Lett. , vol. 86 p. 2423 2001

[47] C. E. Cunningham, C. Petrovic, G. Lapertot, S. L. Bud'ko, F. Laabs, W. Strazheim, D. K. Finnemore, P. C. Canfield, Physica C vol. 353 p. 5 2001

[48] E. W. Collings, E. Lee, M. D. Sumption, M. Tomsic, X. L. Wang, S. Soltanian, S. X. Dou, Physica C, vol. 386 pp. 555-559 2003.

[49] M. Bhatia, M. D. Sumption, M. Tomsic, E. W. Collings, Physica C, vol. 407 pp. 153-159 2004.

167

[50] M. D. Sumption, M. Bhatia, F. Buta, S. Bohnenstiehl, M. Tomsic, M. Rindfleisch, J. Yue, J. Phillips, S. Kawabata, E. W. Collings, Supercond. Sci. Tech., vol. 18 pp. 961-965 2005.

[51] M. D. Sumption, M. Bhatia, X. Wu, M. Rindfleisch, M. Tomsic, E. W. Collings, Supercond. Sci. Tech., vol. 18 pp. 730-734 2005.

[52] M. D. Sumption, M. Bhatia, M. Rindfleisch, M. Tomsic, E. W. Collings, Supercond. Sci. Tech., vol. 19 pp. 155-160 2006.

[53] A. Malagoli, V. Braccini, N. Scati, S. Roncallo, A. S. Siri, G. Grasso, Physica C, vol. 372 pp. 1245-1247 2002.

[54] S. X. Dou, J. Horvat, S. Soltanian, X. L. Wang, M. J. Qin, S. H. Zhou, H. K. Liu, P. G. Munroe, IEEE Trans. Appl. Supercond., vol. 13 pp. 3199-3202 2003.

[55] S. Soltanian, J. Horvat, X. L. Wang, M. Tomsic, S. X. Dou, Supercond. Sci. Tech., vol. 16 pp. L4-L6 2003.

[56] M. A. Aksan, M. E. Yakinci, Y. Balci, Physica C, vol. 408-10 pp. 132-133 2004.

[57] P. Kovac, T. Melisek, M. Dhalle, A. den Ouden, I. Husek, Supercond. Sci. Tech., vol. 18 pp. 1374-1379 2005.

[58] C. Fischer, Appl. Phys. Lett., vol. 83 pp. 1803-1805 2003.

[59] J. H. Kim, S. Zhou, M. S. A. Hossain, A. V. Pan, S. X. Dou, cond-mat/0607350; Presented at ASC2006, 2006.

[60] T. Nakane, H. Kitaguchi, H. Kumakura, Appl. Phys. Lett., vol. 88 2006.

[61] M. D. Sumption, M. Bhatia, M. Rindfleisch, M. Tomsic, E. W. Collings, Appl. Phys. Lett., vol. 86 2005.

[62] B. A. Glowacki, M. Majoros, M. Vickers, J. E. Evvets, Y. Shi, I. McDougall, Supercond.Sci. Technol., vol. 14 p. 193 2001

168

[63] J. Horvat, S. Soltanian, X. L. Wang, S. X. Dou, IEEE Trans. Appl. Supercond., vol. 13 pp. 3324-3327 2003.

[64] S. H. Zhou, A. V. Pan, M. J. Qin, H. K. Liu, S. X. Dou, Physica C, vol. 387 pp. 321- 327 2003.

[65] A. V. Pan, S. H. Zhou, S. X. Dou, Supercond. Sci. Tech., vol. 17 pp. S410-S414 2004.

[66] H. L. Suo, Appl. Phys. Lett. , vol. 79 p. 3116 2001

[67] A. V. Pan, S. H. Zhou, H. K. Liu, S. X. Dou, Supercond. Sci. Tech., vol. 16 pp. L33- L36 2003.

[68] X. L. Wang, L. Q. Yao, J. Horvat, M. J. Qin, S. X. Dou, Supercond. Sci. Tech. , vol. 17 p. L24 2004

[69] L. Shi, Y. Gu, T. Qian, X. Li, L. Chen, Z. Yang, J. Ma, T. Qian, Physica C, vol. 405 p. 271 2004.

[70] G. Giunchi, S. Ginocchio, S. Raineri, D. Botta, R. Gerbaldo, B. Minetti, R. Quarantiello, A. Matrone, IEEE Trans. Appl. Supercond., vol. 15 pp. 3230-3233 2005.

[71] G. Giunchi, G. Ripamonti, T. Cavallin, E. Bassani, Cryogenics, vol. 46 pp. 237-242 2006.

[72] G. e. a. Giunchi, Supercond. Sci. Technol., vol. 16 pp. 285-291 2003.

[73] D. Dimos, P. Chaudhari, J. Mannhart, Phys. Rev. B vol. 41 p. 4038 1990

[74] N. D. Browning, J. P. Buban, P. D. Nellist, D. P. Norton, S. J. Penny, Physica C vol. 294 p. 183 1998

[75] M. Kambara, N. H. Babu, E. S. Sadki, J. R. Cooper, H. Minami, D. A. Cardwell, A. M. Campbell, I. H. Inoue, Supercond. Sci. Technol. , vol. 14 2001

169

[76] R. F. Klie, J. C. Idrobo, N. D. Browning, A. C. Serquis, Y. T. Zhu, X. Z. Liao, F. M. Mueller, Appl. Phys. Lett. , vol. 80 p. 3970 2002

[77] S. X. Dou, X. L. Wang, J. Horvat, D. Milliken, E. W. Collings, M. D. Sumption, Physica C vol. 361 p. 79 2001

[78] M. Bhatia, M. D. Sumption, M. Tomsic, E. W. Collings, Physica C, vol. 415 pp. 158-162 2004.

[79] S. Jin, H. Mavoori, R. B. van Dover, Nature vol. 411 p. 563 2001.

[80] J. M. Rowell, S. Y. Xu, X. H. Zeng, A. V. Pogrebnyakov, Q. Li, X. X. Xi, R. J.M., W. Tian, P. Xiaoqing, cond-mat/0302017, 2003

[81] Y. Eltsev, S. Lee, K. Nakao, N. Chikumoto, S. Tajima, N. Koshizuka, M. Murakami, Phys. Rev. B vol. 65 p. 140501(R) 2002

[82] J. M. Rowell, Supercond. Sci. Technol., vol. 16 pp. R17-R27 2003.

[83] Y. Feng, Y. Zhao, Y. P. Sun, F. C. Liu, B. Q. Fu, L. Zhou, C. H. Cheng, N. Koshizuka, M. Murakami, Appl. Phys. Lett., vol. 79 p. 3893 2001

[84] Y. Zhao, Y. Feng, C. Cheng, L. Zhou, Y. Wu, T. Machi, Y. Fudamoto, N. Koshizuka, M. Murakami, Appl. Phys. Lett., vol. 79 p. 1154 2001

[85] P. A. Sharma, N. Hur, Y. Horibe, C. H. Chen, B. G. Kim, S. Guha, M. Z. Cieplak, S. W. Cheong, Phys. Rev. Lett. , vol. 89 p. 167003 2002.

[86] R. A. Ribeiro, S. L. Bud‟ko, C. Petrovic, P. C. Canfield, Physica C, vol. 384 p. 227 2003.

[87] C. Buzea, T. Yamashita, Supercond. Sci. Tech., vol. 14 pp. R115-R146 2001.

[88] C. B. Eom, M. K. Lee, J. H. Choi, L. J. Belenky, X. Song, L. D. Cooley, M. T. Naus, S. Patnaik, J. Jiang, M. Rikel, A. Polyanskii, A. Gurevich, X. Y. Cai, S. D. Bu, S. E. Babcock, E. E. Hellstrom, D. C. Larbalestier, N. Rogado, K. A. Regan, M. A. Hayward, T. He, J. S. Slusky, K. Inumaru, M. K. Haas, R. J. Cava, Nature, vol. 411 pp. 558-560 2001. 170

[89] V. Braccini, L. D. Cooley, S. Patnaik, D. C. Larbalestier, P. Manfrinetti, A. Palenzona, A. S. Siri, Appl. Phys. Lett., vol. 81 pp. 4577-4579 2002.

[90] V. Braccini, A. Gurevich, J. E. Giencke, M. C. Jewell, C. B. Eom, D. C. Larbalestier, A. Pogrebnyakov, Y. Cui, B. T. Liu, Y. F. Hu, J. M. Redwing, Q. Li, X. X. Xi, R. K. Singh, R. Gandikota, J. Kim, B. Wilkens, N. Newman, J. Rowell, B. Moeckly, V. Ferrando, C. Tarantini, D. Marre, M. Putti, C. Ferdeghini, R. Vaglio, E. Haanappel, Phys. Rev. B, vol. 71 2005.

[91] R. H. T. Wilke, S. L. Bud'ko, P. C. Canfield, D. K. Finnemore, S. T. Hannahs, Physica C, vol. 432 pp. 193-205 2005.

[92] E. Ohmichi, T. Masui, S. Lee, S. Tajima, T. Osada, cond-mat/0312348, 2003

[93] S. X. Dou, A. V. Pan, S. Zhou, M. Ionescu, X. L. Wang, J. Horvat, H. K. Liu, P. R. Munroe, J. Appl. Phys., vol. 94 pp. 1850-1856 2003.

[94] S. Soltanian, M. J. Qin, S. Keshavarzi, X. L. Wang, S. X. Dou, Phys. Rev. B, vol. 68 2003.

[95] S. Soltanian, X. L. Wang, J. Horvat, M. J. Qin, H. K. Liu, P. R. Munroe, S. X. Dou, IEEE Trans. Appl. Supercond., vol. 13 pp. 3273-3276 2003.

[96] X. L. Wang, S. H. Zhou, M. J. Qin, P. R. Munroe, S. Soltanian, H. K. Liu, S. X. Dou, Physica C, vol. 385 pp. 461-465 2003.

[97] S. X. Dou, V. Braccini, S. Soltanian, R. Klie, Y. Zhu, S. Li, X. L. Wang, D. Larbalestier, J. Appl. Phys., vol. 96 pp. 7549-7555 2004.

[98] M. D. Sumption, M. Bhatia, S. X. Dou, M. Rindfliesch, M. Tomsic, L. Arda, M. Ozdemir, Y. Hascicek, E. W. Collings, Supercond. Sci. Tech., vol. 17 pp. 1180-1184 2004.

[99] X. L. Wang, S. Soltanian, M. James, M. J. Qin, J. Horvat, Q. W. Yao, H. K. Liu, S. X. Dou, Physica C, vol. 408-10 pp. 63-67 2004.

[100] Y. Zhao, M. Ionescu, J. Horvat, A. H. Li, S. X. Dou, Supercond. Sci. Tech., vol. 17 pp. 1247-1252 2004.

171

[101] M. Bhatia, M. D. Sumption, E. W. Collings, IEEE Trans. Appl. Supercond., vol. 15 pp. 3204-3206 2005.

[102] M. D. Sumption, M. Bhatia, M. Rindfleisch, M. Tomsic, S. Soltanian, S. X. Dou, E. W. Collings, Appl. Phys. Lett., vol. 86 2005.

[103] M. Bhatia, M. D. Sumption, E. W. Collings, S. Dregia, Appl. Phys. Lett., vol. 87 2005.

[104] N. R. Werthamer, E. Helfand, P. C. Hohenburg, Phys. Rev., vol. 147 p. 295 1966.

[105] K. Maki, ibid., vol. 148 p. 392 1966.

[106] W. A. Fietz, W. W. Webb, Phys. Rev., vol. 161 p. 4231 1967.

[107] A. Gurevich, Phys. Rev. B, vol. 67 2003.

[108] A. Gurevich, Cond-mat/0701281v1, 2007.

[109] L. F. Goodrich, HEP Conductor Workshop (unpublished), 2002.

[110] S. Bohnenstiehl, Private Comunication, 2007.

[111] A. D. Caplin, Y. Bugoslavsky, L. F. Cohen, L. Cowey, J. Driscoll, J. Moore, G. K. Perkins, Supercond. Sci. Technol., vol. 16 pp. 176-182 2003.

[112] S. X. Dou, S. Soltanian, Y. Zhao, E. Getin, Z. Chen, O. Shcherbakova, J. Horvat, Supercond. Sci. Tech., vol. 18 pp. 710-715 2005.

[113] O. de la Pena, A. Aguayo, R. de Coss, Phys. Rev. B, vol. 66 2002.

[114] J. Wang, Y. Bugoslavsky, A. Berenov, L. Cowey, A. D. Caplin, L. F. Cohen, J. L. M. Driscoll, L. D. Cooley, X. Song, D. C. Larbalestier, Appl. Phys. Lett., vol. 81 pp. 2026-2028 2002.

172

[115] Y. W. Ma, H. Kumakura, A. Matsumoto, H. Hatakeyama, K. Togano, Supercond. Sci. Tech., vol. 16 pp. 852-856 2003.

[116] P. P. Singh, Sol. St. Comm., vol. 127 pp. 271-274 2003.

[117] S. Agrestini, C. Metallo, A. Filippi, G. Campi, C. Sanipoli, S. De Negri, M. Giovannini, A. Saccone, A. Latini, A. Bianconi, J. Phys. Chem. Sol., vol. 65 pp. 1479- 1484 2004.

[118] W. K. Yeoh, J. Horvat, S. X. Dou, V. Keast, Supercond. Sci. Tech., vol. 17 pp. S572-S577 2004.

[119] W. K. Yeoh, J. Horvat, S. X. Dou, P. Munroe, IEEE Trans. Appl. Supercond., vol. 15 pp. 3284-3287 2005.

[120] Y. W. Ma, X. P. Zhang, A. X. Xu, X. H. Li, L. Y. Xiao, G. Nishijima, S. Awaji, K. Watanabe, Y. L. Jiao, L. Xiao, X. D. Bai, K. H. Wu, H. H. Wen, Supercond. Sci. Tech., vol. 19 pp. 133-137 2006.

[121] O. Perner, W. Habler, R. Eckert, C. Fischer, C. Mickel, G. Fuchs, B. Holzapfel, L. Schultz, Physica C, vol. 432 pp. 15-24 2005.

[122] A. Yamamoto, J. Shimoyama, S. Ueda, I. Iwayama, S. Horii, K. Kishio, Supercond. Sci. Tech., vol. 18 pp. 1323-1328 2005.

[123] S. Soltanian, X. L. Wang, J. Horvat, S. X. Dou, M. D. Sumption, M. Bhatia, E. W. Collings, P. Munroe, M. Tomsic, Supercond. Sci. Tech., vol. 18 pp. 658-666 2005.

[124] A. Matsumoto, H. Kumakura, H. Kitaguchi, H. Hatakeyama, Supercond. Sci. Technol., vol. 16 pp. 926-930 2003.

[125] M. Susner, M. D. Sumption, M. Bhatia, E. W. Collings, Presented at ICMC-CEC 2007, 2007.

[126] C. Senatore, P. Lezza, R. Flukiger, Adv. In Cryog. Eng. (materials), vol. 52 p. 654 2006.

[127] D. Dew-Hughes, Phil. Mag. B, vol. 30 pp. 293-305 1974. 173

[128] L. D. Cooley, P. J. Lee, D. C. Larbalestier, Adv. Cryog. Eng. (Materials), vol. 48B p. 925 2002.

[129] A. Godeke, Performance Boundaries in Nb3Sn Superconductors in: vol PhD, University of Twente, 2005.

[130] Y. Kong, O. V. Dolgov, O. Jepson, Phys. Rev. B, vol. 64 pp. 020501-020501 2001.

[131] A. Y. Liu, I. I. Mazin, J. Kortus, Phys. Rev. Lett. , vol. 81 p. 087005 2001.

[132] Y. Wang, T. Plackowski, A. Junod, Physica C, vol. 355 p. 179 2001.

[133] S. D. Kaushik, S. Patnaik, Physica C, vol. 442 pp. 73-78 2006.

[134] I. I. Mazin, O. K. Andersen, O. Jepsen, O. V. Dolgov, J. Kortus, A. A. Golubov, A. B. Kuz'menko, D. van der Marel, Phys. Rev. Lett., vol. 89 2002.

[135] J. A. Reynolds, J. M. Hough, Proc. Phy. Soc., vol. 70 p. 769 1957.

[136] A. Bharathi, S. J. Balaselvi, S. Kalavathi, G. L. N. Reddy, V. S. Sastry, Y. Hariharan, T. S. Radhakrishnan, Physica C, vol. 370 pp. 211-218 2002.

[137] A. V. Sologubenko, J. Jun, S. M. Kazakov, J. Karpinski, H. R. Ott, Phys. Rev. B, vol. 65 2002.

[138] M. Putti, E. G. d‟Agliano, D. Marrè, Eur. Phys. J. B vol. 25 p. 439 2002.

[139] K. P. Bohnen, R. Heid, B. Renker, Phy. Rev. Lett., vol. 86 p. 5771 2001.

[140] J. J. Tu, Phys. Rev. Lett., vol. 87 p. 277001 2001.

[141] S. O. Kasap, Principles of Electrical Engineering Materials and Devices, McGraw- Hill, 1997.

174