“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.
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“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.
Approved By:
_____________________________________
Adviser
_____________________________________
Adviser
Graduate Program in Materials Science and Engineering
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
By
Mohit Bhatia, M.S.
***
The Ohio State University
2007
Dissertation Committee:
Professor Suliman A. Dregia, Adviser
Professor Michael D. Sumption, Adviser
Professor John Morral
Professor Sheikh Akbar
ii
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
(>650oC) 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
iii
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.
iv
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.
v
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.
vi
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.
vii
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.
viii
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
ix
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
x
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
xi
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
xii
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
xiii
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
xiv
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 5.2Bc2 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 800C. ....... 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
xv
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
Figure 6.1 oHirr vs T for Various SiC added samples reacted at 675oC/40mins .......... 121
Figure 6.2 Normalized Fp vs h for MB30SiC5C (675oC/40min) .................................. 124
Figure 6.3 Normalized Fp vs h for MB30SiC5C plotted along with various pinning
functions .......................................................................................................................... 130
Figure 6.4 Normalized Fp vs h for binary MB675 (675oC/40min) plotted along with
various pinning functions ................................................................................................ 132
Figure 7.1 (T) for two MgB2 samples ......................................................................... 142
Figure 7.2 Temperature dependence of the mfor 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
xvi
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.
xvii
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
xviii
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
CHAPTER 1
INTRODUCTION AND REVIEW OF SUPERCONDUCTIVITY
1
2
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
3
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 625
oC for 180-360mins and
high-temperature window (>650oC) carried out at 675-700
oC 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,
4
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
5
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.
Temperature, T
Res
isti
vit
y,
(T)
Tc
Superconductor
Non-superconductor
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
6
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
g
F
E
hv
20
(1.1)
Where, vF is the Fermi velocity and Eg is the energy gap.
7
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
MHB 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 4x10-7
. Therefore, according to the Meissner effect, in a
superconductor B = 0, thus
HM (1.3)
and hence the susceptibility, , which is defined as the ratio of the change in
magnetization due to H is given by
1dH
dM
(1.4)
Transition is shown in Figure 1.2
8
Temperature, T
Su
scep
tib
ilit
y,
(T)
-1
0
Tc
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
)(
0
2
TGTGTB
snc (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
9
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
BJxL
2
0
1
(1.6)
where L can be evaluated in terms of the superconducting electron density n and is
given by
2
0ne
mL
(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.
10
Temperature, T
Ap
pli
ed F
ield
, H
Superconducting State
Normal State
Hc
Tc
Type-I
Figure 0.3 Critical field for a Type-I superconductor
Temperature, T
Ap
pli
ed F
ield
, H
Superconducting State
Normal State
Hc2
Tc
Type-II
Mixed State
Hc1
Figure 0.4 Critical fields for a Type-II superconductor
11
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
12
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 0.1V/cm for low-temperature superconductors and 1V/cm for high-temperature
superconductors. Figure 1.5 shows a typical V-I curve for a superconductor with Ic
defined by 1V/cm criterion. The V-I characteristics of a superconductor can be modeled
as
n
cc I
IEE
(1.9)
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.
13
Current, A
0 200 400 600 800 1000 1200
Vo
ltag
e/L
eng
th,
V/c
m
0
5e-6
1e-5
2e-5
2e-5
Ic
Figure 0.5 Typical V-I curve for a superconducting material
Figure 0.6 A general superconducting phase critical surface plot
J
T
B
Tc
J
c
Bc2
Jc
14
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.
15
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.
16
2.1 Electronic Structure of MgB2
MgB2 possesses a simple hexagonal structure with a = 3.05 A0, c = 3.52 A
0 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.
17
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
intended stoichiometric Mg3B2 phase for 1 hr at 800oC. Subsequent XRD analysis
confirmed the existence of the MgB2 phase rather than the hoped for Mg3B2 .
Boron honeycomb
plains
B orbitals with
character
B orbitals with
character
Mg ions
18
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
diagram, below 1545oC 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 1100
oC. Therefore, for any kind of bulk preparation technique
for MgB2, (assuming the liquid phase diffusion) the sintering temperature has to be in this
Atomic Fraction of B
0.0 0.2 0.4 0.6 0.8 1.0
Tem
per
ature
, oC
400
800
1200
1600
2000
2400
Solid + MgB2
Liquid + MgB2
Gas + MgB2
Gas + MgB4
Gas + MgB7
Gas + Liquid
Mg
B2
+ M
gB
4
Mg
B4
+ M
gB
7
B (
s) +
Mg
B7
Figure 2.2 Theoretical Phase Diagram of Mg-B (Re-drawn after [15])
19
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.
20
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
21
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
ranging from 650 to 800oC. Dou et al. [26] heat-treated their SiC-doped MgB2 for
950oC/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-
22
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
23
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
24
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.
25
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
26
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
after drying in vacuum at 60oC 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)
27
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.
28
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 inter-
granular 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.
29
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
MgB2 achieves moderate values of critical current density, up to 106 A/cm
2. In applied
magnetic fields of 6 T Jc is maintained above 104 A/cm
2, while in 10 T Jc is typically 10
2
A/cm2. 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:
30
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 1mcm have been reported, some 100 times higher than other reports of
10cm [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.
31
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
32
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.
33
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. 2kbTc<h/, where kb is Boltzmann constant, h is the plank‟s constant and
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
Tc
cc
dT
dBB
2
2 69.00 (2.4)
and
02 4
Fb
Tc
c Neck
dT
dB
(2.5)
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
34
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
DaDa
TTB c
Tcc
2
0,2
8 (2.6)
Where, 0
1
a (2.7)
0
1
a (2.8)
(2.9)
21
0 4 (2.10)
35
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
D
TTB c
Tcc 2
0,2
4
(2.11)
Also, if the interband scattering is disregarded, i.e ==0, and considering that
>> the equation reduces to
D
TTB c
Tcc 2
0,2
4 (2.12)
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
2exp
20 0
2
g
DD
TB c
c
(2.13)
wD
D
wD
D
wg 0
21
2
2
2
0 ln2
ln
(2.14)
w (2.15)
If the D= D = D, Eqn 2.13 again reduces to the single-band equation given by
D
TB c
c
20 0
2 (2.16)
36
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
wD
TB c
c2
exp2
0 002
,
wDD 0exp
(2.17)
And
wD
TB c
c2
exp2
0 002
,
wDD 0exp
(2.18)
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<<D for MgB2.
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].
37
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.
38
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 5-6m 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.
39
Diameter, m
40 30 20 15 10 8 6 5 4 3 2 1.5 0
Dis
trib
uti
on
Figure 3.1 Particle size distribution in the starting Mg powder
Diameter, m
3 2 1.5 1 0.8 0.6 0.5 0.4 0.3 0.2 0.15
Dis
trib
uti
on
Figure 3.2 Particle (agglomerate) size distribution in the starting B powder
40
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.
Figure 3.3 Steel die for bulk MgB2 compaction
Top Plunger
Bottom Plug
Stainless Steel
Die 5cm
3cm
1cm
41
Time, t, min
0 20 40 60 80 100 120 140
Tem
per
atu
re,
T,
oC
0
100
200
300
400
500
600
700
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 Omega
R 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.
42
Sample ID Additive Additive
Mole %
Reaction
Temp-Time
(oC-min)
Measurements
Bulk Samples
MB700 - 0 700-30 XRD, SEM,
TEM, Tc, oHirr,
Bc2, (T)
MBSiC700
SiC
10
700-30 XRD, Tc,oHirr,
Bc2, (T), Cp
MBSiC800 800-30 oHirr, Bc2
MBSiC900 900-30 oHirr, Bc2
MBAC800 Acetone Milled in
Acetone
800-30 Tc,oHirr, Bc2
MBAC900 900-30 oHirr, Bc2
MBC700
Amorphous
C
10
700-30 XRD, Tc,oHirr,
Bc2
MBC900 900-30 Tc, ,oHirr, Bc2
MBC1000 1000-30 oHirr, Bc2
MBZr700
ZrB2
7.5
700-30 XRD, Tc, oHirr,
Jcm, Bc2
MBZr800 800-30 Tc, Jcm
MBZr900 900-30 Tc, Jcm
MBNb700
NbB2
7.5
700-30 XRD, Tc, oHirr,
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
43
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.
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
Cu
Nb
MgB2
44
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'
Sample ID Additive Additive
mole %
Reaction
Temp-Time
(oC-min)
Measurements
Strand Samples
MB - - 674oC, 700
oC SEM, Fp, TEM
MB30SiC5 30nm SiC
5 (625oC-180),
(625 oC -360),
(675 oC -40),
(700 oC -40)
or
(800 oC -40)
SEMoHirr,
Bc2, Jc, Fp
MB30SiC10 10
MB15SiC5 15nm SiC
5
MB15SiC10 10
MB200SiC5 200nm SIC
5
MB200SiC10 10
MB30SiC10 30nmSiC 10 (700, 800 or
900oC) – (5, 10,
20 or 30)
Tc, oHirr, Bc2
UW30SiC10 30nmSiC 10 (640 or 725C)-
30
oHirr, Bc2, Jc
UW15SiC10 15nmSiC 10 (640, 680 or
725C) - 30
oHirr, Bc2, Jc
45
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.
sin2dn (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 2
o 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
46
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
47
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
48
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
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
release during such reaction. Since Mg melts at 650oC 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 660.33
oC ) 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,
Computer Heaters
Pan+ Sample Reference Pan
49
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 100
oC
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.
Temperature, oC
326 328 330 332 334 336 338
Hea
t F
low
, W
/g
0.0
0.2
0.4
0.6
0.8
1.0
Pb in Fe
Pb in SS
Pb in Al
Pb in Cu
Figure 3.7 Thermal lag for different DSC sample pan materials
50
Temperature, o
C
100 200 300 400 500 600 700
Heat
Flo
w,
W/g
-1.0
-0.5
0.0
0.5
1.0
1.5Endo
Exo
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
dH
dM (3.2)
51
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.
Temperature, T (K)
28 30 36 38
No
rmal
ized
d
c
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
Tce
Tcb
Tc
T
Figure 3.9 dc vs T for a slightly inhomogeneous superconducting material
52
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.
53
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.
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
RS
RLV RLV
V RV
RLI RLI
II
IV
54
calibrated using the standard room-temperature measurement of a sample of pure Ni
(NBS traceable).
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
JBx
4
0 (3.3)
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
Water Cooled Iron-core
1.7 T Magnet
Sample Holder
Vibrator
LHe Cryostat
Pick-up Coils
Hall Probe
Sample
55
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
x
BJo
4 (3.4)
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
(3.5)
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.
He
½ D -½ D
y
z
x
L
dd
MJ mc
31
2,
B Be=oHe
56
Magnetic field, T
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Magneti
zati
on,
kA
/m
-600
-400
-200
0
200
400
600
M
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 1V/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
57
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.
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.
Extended
Copper
End-rings
One meter of MgB2
sample, 0.8mm OD to
be wound on these
grooves
3.12 cm
3.15 cm
2.5 cm
Stainless Steel Barrel
58
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.
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
Stainless Steel Tube
Cu Current Leads
(220A max current)
Brass Can Encapsulating Samples
Heater and Temperature Sensor
Mounted on the Sample Holder Inside
Vacuum Valve
59
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.
B, T
14 16 18 20 22 24 26 28 30 32 34
R,
0
100
200
300
400
Bc2
oHirr
Figure 3.16 Typical R vs. B curve and determination of oHirr and Bc2
60
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
p
p dTdQ
C
(3.5)
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
3
2
0
2
3t
T
HC
c
ces
(3.6)
where, c
c
T
H
2
3 2
0 = , the unit volume electronic specific-heat coefficient. Thus,
33t
T
C
c
es
(3.7)
Agreeing with this over a limited temperature range in the BCS relationship
61
)exp(T
baT
C
c
es
(3.8)
where a and b are constants. In the BCS the relative jump at Tc is 43.1
cT
C
Figure 3.17 Schematic of thermal connections for heat-capacity measurements
T
0 1
Ce
0
1
2
3
Superconductor
Normal Material
Ce = T
Ce = e-
T
Figure 3.18 Ce vs. T for a normal and a superconducting material
Sample Connecting
Wires
Thermometer Heater
Apiezon Grease
Platform
T B
h a
e t
r h
m
a
l
T B
h a
e t
r h
m
a
l
62
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.
63
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.
64
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 (2076
oC), and many
groups clearly form or aim to form MgB2 by a combination of liquid Mg and solid B at
about 650 – 700oC. 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
65
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
66
Temperature (o
C)
400 450 500 550 600 650 700
Heat
Flo
w, Q
, W
/g
-1
0
1
2
3 5 o
C/min
10 o
C/min
15 oC/min
20 oC/min
Endo
Exo
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 650
oC. 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.
67
Temperature (o
C)
100 200 300 400 500 600 700
Hea
t F
low
, Q
, W
/g
-7
-6
-5
-4
-3
-2
-1
0
1
05 oC/min
10 oC/min
15 oC/min
20 oC/min
Peaks 'a' and 'b'
Peak 'c'
Endo
Exo
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.
68
2
30 40 50 60 70 80
Inte
nsi
ty
Mg+2B 625oC
Mg+2B Un-Heat treated
101
110
100
002101
110 103 112201
004
MgB2 Peaks
Mg Peaks
Figure 4.3 XRD scans performed on the mixed Mg + B powder before heating and after
heating upto 625oC
69
2
20 40 60 80
Inte
nsi
ty
0
1000
2000
3000
4000
5000
6000
7000
100
101
002
110
102
111 200
201 112
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.
70
Sample ID SiC mole % SiC Size
(nm)
Reaction Temperature-Time
(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.
71
(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
72
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.
Temperature, T, K
32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0
Res
isti
vit
y,
,
-cm
0.0
0.5
1.0
1.5
2.0MB30SiC10A-
(625o
C-180min)
MB30SiC10C -
(675o
C-40min)
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
73
Mg melting, as is usually done, as well as in the 625 - 640oC 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
possible to compare the microstructures of MgB2 samples reacted at 675oC 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.
74
Further details on the pinning properties of SiC doped MgB2 samples are discussed in
Chapter 6.
Sample
Reacted at
675oC/40min
Size of SiC
nm
Amount of SiC
added
%
Avg. Grain
Size
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
75
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)
76
Figure 4.8b HR-SEM image for sample MB30SiC10Cat 40K and 80K magnification
(10 mole % of 30nm SiC doped sample reacted at 675oC-40min)
77
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)
78
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)
79
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)
80
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
81
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)
82
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
83
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
84
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.
B, T
0 2 4 6 8 10 12 14
J c,
A/c
m2
102
103
104
105
4.2K
10.0K
15.0K
17.5K
20.0K
22.5K
25.0K
30.0K
Figure 4.14 Temperature dependence of Jc vs B for sample MB30SiC10A
(625oC-180min)
85
B, T
0 2 4 6 8 10 12 14
J c, A
/cm
2
102
103
104
105
4.2K
10.0K
15.0K
17.5K
20.0K
22.5K
25.0K
30.0K
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
655oC. 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
86
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.
87
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.
88
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 Bc2 by nonmagnetic impurity dopings to values well above the predictions of one-gap
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
89
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.
90
Avg. SiC Size
15nm 30nm 200nm
Irre
ver
sib
ilit
y F
ield
,
oH
irr,
T
14
16
18
20
22
24
MBxSiC5A
MBxSiC10A
MBxSiC5C
MBxSiC10C
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.
91
Avg. SiC Size
15nm 30nm 200nm
Up
per
Cri
tica
l F
ield
,Bc2
, T
17
18
19
20
21
22
23
24
MBxSiC5A
MBxSiC10A
MBxSiC5C
MBxSiC10C
Figure 5.2Bc2 measurements on MgB2 strands doped with different sizes of SiC
heat-treated at different temperatures
Properties MB30SiC10A
625oC-180 min
MB30SiC10C
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
92
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.
B, T
16 18 20 22 24 26 28 30 32
Vo
ltag
e, V
,
V
0
2
4
6
8
700C/10
700C/20
700C/30
800C/5
800C/10
800C/20
800C/30
700C/5
900C/20
900C/10
900C/5
Figure 5.3 Resistive transitions for fine (30nm) SiC doped MB30SiC10 strands reacted
at different time-temperature schedules
93
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 700
oC or 900
oC reaction temperatures.
Reacting at 800C for 30 minutes gave the highest values, 29.4T and 31.3T for 0Hirr and
Bc2 respectively.
Reaction time, t, mins
5 10 15 20 25 30
B,
T
14
16
18
20
22
24
26
28
30
32
34
700C oH
irr
800C oH
irr
900C oH
irr
700C Bc2
800C Bc2
900C Bc2
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 800C. 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,
94
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.
Temperature, T, K
20 25 30 35 40 45 50
Res
isti
vit
y,
cm
0
2
4
6
8
10800C/05
800C/10
800C/20
800C/30
Figure 5.5 Tc curves for the MB30SiC strands reacted for various times at 800C.
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
95
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
96
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 700-800C 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
97
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.
98
Table 5.2 Bulk sample names, additives and reaction temperatures
99
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)
MBZr700
MBNb700
MBTi800
MBSiC700
MBC700
100
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.
Temperature, T, K
0 10 20 30 40
No
rmal
ized
Su
scep
tab
ilit
y,
/o
-1.0
-0.8
-0.6
-0.4
-0.2
0.0MB700
MBSiC700
MBAC800
MBC700
MBC900
MBZr700
MBNb700
MBTi800
Figure 5.7 Normalized DC graph for bulk MgB2 samples with various additives showing
superconducting transitions
101
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.
oH
irr, T
14 16 18 20 22 24 26
Tc,
K
32
33
34
35
36
37
38
39
Binary
Diborides
C - doping
SiC
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
102
SiC doped bulk samples increased from 24.5 to 28 T with increase in reaction
temperature from 700oC to 900
oC. 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.
Magnetic Field, B, T
15 20 25 30 35 40
Res
ista
nce
, R
, 1
0-4
0
2
4
6
8
10
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
MBAC800
MBSiC700
MBC700
MBC1000
MBSiC800
MBC900
MB700
MBSiC900
103
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
values of oHirr and Bc2 were obtained for the samples reacted at 700oC/30 mins. and a
decrease in the critical fields were observed on increasing the reaction temperature.
Magnetic Field, B, T
15 20 25 30 35
Res
ista
nce
, R
, 1
0-4
0
1
2
3
4
5
6
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
MBTi700
MBNb700
MB700
MBNb800
MBTi800
MBNb900
MBZr700
104
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
Name oHirr,
T
Bc2,
T irrc c,
K
c,on,
Kc,com,
Kc
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.
105
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, 800
oC and
900oC for 30 min. Details of the sample composition, and heat-treatment are given in
Table 5.4.
106
Sample Name Reaction Temp
(O
C)
Reaction Time
(min)
Tc, K
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 M1/2
B1/4
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).
107
In the present experiment the previously mentioned binary sample, reacted at
700oC/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.
Temperature, T, K
5 10 15 20 25 30 35 40
No
rmal
ized
Su
scep
tib
ilit
y,
DC
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0 MB700
MBZr700
MBZr800
MBZr900
Figure 5.11 DC DC vs T for binary and ZrB2 doped bulk MgB2 samples
(See Table 3.1)
108
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
(O
C/Min)
Tc, K 0Hirr
T
Bc2
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.
109
2 Theta
30 40 50 60 70
Co
un
t
MB700
MBZr700101
002 110
100
Figure 5.12 XRD pattern for ZrB2 doped bulk MgB2 (MBZr700) sample as compared to
binary sample (MB700)
110
Figure 5.13 TEM bright field image of bulk sample MBZr700
Figure 5.14 EDX obtained from the selected grain of bulk sample MBZr700
111
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.
Temperature, T(K)
0 5 10 15 20 25 30 35 40
Irre
ver
sib
ilit
y F
ield
,
oH
irr
(T)
0
5
10
15
20
25
30
MBZr700
MB700
Figure 5.15 Variation of 0Hirr with T for binary and ZrB2 doped MgB2 sample
From I-V
curve
From M-H
loop
From Kramer
Plot
112
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
transport Jc values of 105 A/cm
2 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.
113
Sample Series Reaction Temp.-Time
(C/min)
SC
Fraction
SiC size,
nm
SC area,
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
reacted at 640oC/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
680oC/30min (30nm SiC doped MgB2) and 725
oC/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)
725oC/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).
114
B, T
18 20 22 24 26 28 30 32
Res
isti
vit
y,
cm
0
1
2
3
4
51mA
10mA
50mA
100mA
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
B, T
20 22 24 26 28 30 32
Res
isti
vit
y,
cm
0.0
0.2
0.4
0.6
0.8
10 mA
50 mA
100 mA
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
115
Table 5.7 0Hirr (4.2K) and Bc2 (4.2K) for UW-series strands using various sensing
currents
116
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
117
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.
118
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.
119
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.
120
Strand
Sample
Mole %
of SiC
SiC dia.
nm
Irreversibility Fields, oHirr, T
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
Sample
mole %
of SiC
SiC dia.
nm
Upper Critical Field, c2, T
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
121
temperatures using a 100A/cm2 definition of oHirr. Figure 6.1 shows the variation of
oHirr for these samples as a function of temperature.
Temperature, T, K
5 10 15 20 25 30
Irre
ver
sib
ilit
y F
ield
oH
irr,
T
4
6
8
10
12
14
16
18
20
22
MB30SiC5C
MB30SiC10C
MB15SiC10C
MB200SiC5C
MB200SiC10C
Figure 6.1 oHirr vs T for Various SiC added samples reacted at 675oC/40mins
The Jc curves were also used to obtain the flux pinning force for these samples
using
BJBF cp
(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
122
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
qp
p
phh
F
F 1
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].
123
Sample
Reaction-
temperature
675oC/40min
Avg. Grain
Size
Nm
Fp,max at 10K
GN/m3
oHirr at 10K
using 100A/cm2
criterion
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
124
h
0.0 0.2 0.4 0.6 0.8 1.0
Fp/F
p m
ax
0.0
0.2
0.4
0.6
0.8
1.0
10 K
12.5 K
15 K
17.5 K
20 K
22.5 K
25 K
27.5 K
Figure 6.2a Normalized Fp vs h for MB30SiC5C (675
oC/40min)
h
0.0 0.2 0.4 0.6 0.8 1.0
Fp/F
pm
ax
0.0
0.2
0.4
0.6
0.8
1.0
10 K
15 K
17.5 K
20 K
22.5 K
25 k
Figure 6.2b Normalized Fp vs h for MB30SiC10C (675
oC/40min)
125
h
0.0 0.2 0.4 0.6 0.8 1.0
Fp/F
p m
ax
0.0
0.2
0.4
0.6
0.8
1.0
10 K
12.5 K
15 K
17.5 K
20 K
22.5 K
25 K
27.5 K
Figure 6.2c. Normalized Fp vs h for MB15SiC10C (675oC/40min)
h
0.0 0.2 0.4 0.6 0.8 1.0
Fp/F
p m
ax
0.0
0.2
0.4
0.6
0.8
1.0
10 K
12.5 K
15 K
17.5 K
20 K
22.5 K
25 K
27.5 K
30 K
32.5 K
Figure 6.2d Normalized Fp vs h for MB200SiC5C (675
oC/40min)
126
Figure 6.2e Normalized Fp vs h for MB200SiC10C (675
oC/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
B/Birr
0.0 0.2 0.4 0.6 0.8 1.0
Fp/F
p m
ax
0.0
0.2
0.4
0.6
0.8
1.0
10 K
12.5 K
15 K
17.5 K
20 K
22.5 K
25 K
27.5 K
127
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.
128
Interaction
Type
Types of Pins Types of Pinning
Centers
Pinning
Function
Exponents
Location of
Maximum
Pinning Force
Magnetic
Volume
Normal p = 1/2, q = 1 h = 0.33
p = 1/2, q = 1**
h1/2
(1-2h)]
h = 0.17, 1
Core
Volume
Normal p = 0, q = 2 -----
p = 2, q = 1 h = 0.5
Surface
Normal p = 1/2, q = 2 h = 0.2
p = 3/2, q = 1 h = 0.6
Point
Normal p = 1, q = 2 h = 0.33
p = 5/2, q = 1 h = 0.67
Table 6.4 Classification of pinning mechanisms
129
Temperature,
K
Fp,max,
GN/m3
A P q
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
130
h
0.0 0.2 0.4 0.6 0.8 1.0
Fp
/Fp
ma
x
0.0
0.2
0.4
0.6
0.8
1.0
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)
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)
Low Temperature
Intermediate Temperature
High Temperature123 45 6
Figure 6.3 a Normalized Fp vs h for MB30SiC5C plotted along with various pinning
functions
h
0.0 0.2 0.4 0.6 0.8 1.0
Fp
/Fp
ma
x
0.0
0.2
0.4
0.6
0.8
1.0
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)
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)
Low and Intermediate Temperature
High Temperature123 45 6
Figure 6.3 b Normalized Fp vs h for MB30SiC10C plotted along with various pinning
functions
131
h
0.0 0.2 0.4 0.6 0.8 1.0
Fp
/Fp
ma
x
0.0
0.2
0.4
0.6
0.8
1.0
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)
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)
10K
12.5K
15K
17.5K
20K
22.5
25K
27.5K
123 45 6
Figure 6.3 c Normalized Fp vs h for MB15SiC10C (675oC/40min) plotted along with
various pinning functions
h
0.0 0.2 0.4 0.6 0.8 1.0
Fp
/Fp
ma
x
0.0
0.2
0.4
0.6
0.8
1.0
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)
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)
10K
12.5K15K
17.5K
20K
22.5
25K
27.5K
30K
32.5K
123 45 6
Figure 6.3 d Normalized Fp vs h for MB200SiC5C (675oC/40min) plotted along with
various pinning functions
132
h
0.0 0.2 0.4 0.6 0.8 1.0
Fp
/Fp
ma
x
0.0
0.2
0.4
0.6
0.8
1.0
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)
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)
10K
12.5K15K
17.5K
20K
22.5
25K
27.5K
123 45 6
Figure 6.3 e Normalized Fp vs h for MB200SiC10C (675oC/40min) plotted along with
various pinning functions
h
0.0 0.2 0.4 0.6 0.8 1.0
Fp
/Fp
,ma
x
0.0
0.2
0.4
0.6
0.8
1.0
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)
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)4.2K
10K
15K
20K
25K
30K
Figure 6.4 Normalized Fp vs h for binary MB675 (675
oC/40min) plotted along with
various pinning functions
133
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
134
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/m
3 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
135
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.
136
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.
137
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
138
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
139
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, Cin 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
calculated the depairing Jcd. This Jcd is accepted to be of the order of 108A/cm
2. 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
140
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 μcm, based on single-
crystal data [81]. Therefore, according to Rowell approach
TFT ipolym 0, (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,
TT iscm 0, (7.2)
141
Now subtracting the 50K measured resistivity from the 300K resistivity for both the
samples. Eqn. 7.1 becomes
5030050300, ipolym F (7.3)
and Eqn. 7.2 becomes
cmiscm 3.45030050300, [82] (7.4)
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.
cm
ΔρF m
3.4
50300 (7.5)
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.
142
50 100 150 200 250 300
0
10
20
30
40
50
MB700
NRLHR10Mg
Res
isti
vit
y,
i
cm
Temperature, T, K
Figure 7.1a (T) for two MgB2 samples
50 100 150 200 250 300
1/F
(i(
T))
,
-cm
0
1
2
3
4
5
MB700 F = 10.4
NRLHR10Mg F= 2.3
Temperature, T, K
Figure 7.1b Invariance of (T) for two MgB2 Samples
143
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
144
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.
Temperature, T, K
50 100 150 200 250 300
m(T
)
cm
0
100
200
300
400
MB700
MBTi800
MBSiC700
Figure 7.2 Temperature dependence of the mfor binary and doped MgB2 samples
145
Temperature, T, K
50 100 150 200 250 300
i
cm
0
20
40
60
80
100
MB700
MBTi800
MBSiC700
Figure 7.3a (T) for binary MgB2, MgB2-TiB2 and MgB2-SiC samples
Temperature, T, K
50 100 150 200 250 300
(1/F
).(
T),
cm
0
1
2
3
4Single Crystal Data [81]
MB700
MBTi800
MBSiC700
Figure 7.3b Demonstration of varying i(T)
146
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
T
z
mzm
DD
i
D
e
dZzeTkT
0
21
(7.6)
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].
*
1.04(1 )exp
1.45 ( (1 0.62 )
DcT
(7.7)
147
With this in mind our extension of the Rowell approach consisted of fitting the
experimental data to:
T
z
z
RR
om
R
e
dzzeTkFT
0
2
55
1)( (7.8)
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
(B-G Method) % C 0
(cm)
R
(K)
ep
=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.
148
Sample % C
(B-G Method)
o
(-cm)
R ( D )
(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
Temperature, T, K
50 100 150 200 250 300
Res
isti
vit
y,
,
cm
0
100
200
300
400
MBSiC700
MBTi800
MB700
c-axis Oriented Thin FilmTu et. al. [140]
NRLHR10Mg
NRLHR
Dense Wire Canfield et. al. [46]
Single Crystal [134]
Figure 7.4 a m vs. T for all studied samples
(Solid Lines Represent the Fitting Curve)
149
Temperature, T, K
50 100 150 200 250 300
Res
isti
vit
y,
,
cm
0
2
4
6
8
10
12
14
NRLHR10Mg
NRLHR
Dense Wire - Canfield et al [46]
Single Crystal [134]
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
150
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:
T
x
x
D
D
dxe
exT
Nk
C
0
2
43
19 (7.9)
where, 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.
151
T, K
0 50 100 150 200 250 300
Cp (
0T
), m
J/m
ol-
K
0
50
100
150
200
MB700
MBSiC700
MBTi800
Figure 7.5 Total heat-capacity for pure and doped MgB2 at zero field
T, K
20 25 30 35 40
Cp
(0T
)-C
p(9
T),
mJ/
mo
l-K
0
20
40
60
80
MB700
MBSiC700
MBTi800
Figure 7.6 Electronic heat-capacity (Cp(0T)-Cp(9T)) for pure and doped MgB2
152
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
153
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.
154
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
melting temperature of Mg with the one just below 650oC 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-
155
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
temperatures up to 800oC. 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
156
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
the Fp,max of 10% 30nm SiC sample, (at 3.9GN/m3) was higher than that of the binary
sample (at 2.9GN/m3). No direct correlation was seen between the grain size and the
157
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.
158
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
(Bc2||=60T). On a separate note the 4.2K Jc of the material is still of the order of 2x106
A/cm2 which is only a fraction of the depairing Jc (~10
8 A/cm
2), 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.
159
APPENDIX A
LIST OF SUPERCONDUCTING PARAMETERS OF MAGNESIUM DIBORIDE
Parameter Values
Critical Temperature
Tc = 39 - 40K
Hexagonal Lattice
Parameters
a = 0.3086nm
c = 0.3524nm
Theoritical Density d = 2.55g/cm3
Pressure Coefficient dTc/dP = -1.1 - 2K/GPa
Carrier Density ns = 1.7-2.8 x1023
holes/cm3
Isotope Effect T = B + Mg = 0.3 – 0.02
Resistivity at 40K m(40K) = 0.1 – 300cm
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
Depairing Current Density Jd = 108 A/cm
2
Irreversibility Field oHirr (polycrystalline) = 11 – 16T
Upper Critical Field Bc2 (polycrystalline) = 14 – 19T
160
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.
161
For Case 1,
xxm (1)
Where, x and x are the area fractions of phases and respectively.
Since,
xx 1 (2)
Therefore,
xm (3)
For Case 2,
xx
m
1
(4)
Therefore, from eqn. 4 and 2,
xxxm
if (<<) (5)
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
162
of the composite (measured resistivity, m) is given in terms of the volume fractions of
the two phases, namely C and Cif (<<) then this m is equal to,
C
C
m1
2
11
if (<<) [135] (6)
And since,
CC 1 (7)
Therefore,
C
Cm
2
3 (8)
Now,
C
CF
2
3 (9)
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,
12
3
FC (10)
Further details can be found in [135, 141].
163
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
164
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