PHASE TRANSITIONS, METALLIZATION, SUPERCONDUCTIVITY AND MAGNETIC
ORDERING IN DENSE CARBON DISULFIDE AND CHEMICAL ANALOGS
By
LIYANAGAMAGE RANGANATH PRABASHWARA DIAS
A dissertation submitted in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
WASHINGTON STATE UNIVERSITY Department of Physics and Astronomy
July 2013
i
To the Faculty of Washington State University:
The members of the Committee appointed to examine the dissertation of
LIYANAGAMAGE RANGANATH PRABASHWARA DIAS find it satisfactory and recommend that it be accepted.
______Choong-Shik Yoo, Ph.D., Chair
______Matthew D. McCluskey, Ph.D.
______Gary S. Collins, Ph.D.
ii
ACKNOWLEDGEMENTS
I am deeply indebted to my advisor, Prof. Choong-Shik Yoo, more than he knows. His constant encouragement, support, and invaluable suggestions made me to grow into the researcher I wanted to be. He has been everything that one would want in an advisor. His unparalleled knowledge of the subject has always inspired me. He tolerated the mistakes I made and devoted a lot of time to answer my questions, often from the most basic principles. His guidance was indispensable for the successful completion of my research project. He showed me different ways to approach a research problem and the need of being persistent to accomplish the goal. He taught me how to write manuscripts with special emphasis on the organization, and effective communication of the main message, as well as how to prepare presentations. I am very grateful to him and will not be able to pay back the debt I owe him. I can only say ‘Thank you’, from the very depth of my heart. I would also like to thank my dissertation committee, Prof.
Matthew D. McCluskey and Prof. Gary Collins for their invaluable and helpful suggestions.
I offer my sincere thanks to Dr. Mathew Debessai, an excellent scientist and a great friend, for teaching me high pressure experiments. It has been a privilege to work with him. I cannot thank him enough for his constant advice, encouragement, and discussions. I would like to extend my gratitude to Dr. Minseob Kim for many informative discussions, help with x-ray diffraction analysis and band structure calculations. I am also grateful to Dr. Viktor V. Struzhkin, for generously donating his time, equipment and expertise to make the magnetic susceptibility measurement possible.
I would like to acknowledge Prof. John Tse for the work on the theoretical calculations for CS2. I am particularly grateful to the Director of the Institute for Shock Physics, Dr.
iii Yogendra Gupta, for introducing me to the research at the Institute for Shock Physics and providing insight into choosing one’s area of research.
My sincere thanks also goes to my co-workers of the Yoo group past and present with whom I have had the opportunity to work, Dr. Jing-Yin Chen, for her assistance with scientific software, Dr. Amartya Sengupta, for his expertise to align the Raman system, Dr. Haoyan Wei, and my fellow graduate students, especially Gustav Borstad, for very exciting discussions on physics and many fine cups of coffee.
I thank the engineering and administrative staff of the Institute for Shock Physics, especially Kurt Zimmerman for his technical assistance and behind-the-scenes of work. I am very grateful for the help of the administrative staff in the Department of Physics, especially
Sabreen Dodson for her commitment to my well being. I am also indebted to Sheila Heyns and the administrative staff of the Institute for Shock Physics for excellent assistance through out all the paperwork associated with my graduate research work.
Most of all, I would like to render my deepest gratitude to my mother and late father,
Champika Dias and Bandula Dias, for their continued support and encouragement; providing me a solid foundation in life, sending me care packages when I thought the end would never be in sight, sharing my childhood stories when I needed a laugh, and listening to me when the stresses of life became overwhelming. Without such a foundation, I would not be where I am today.
Special thanks to my brother, Sathsara, for helping me step back from the details and see the bigger picture. Also, I thank my little sister Ridma for her constant support, and Savindya, for her continued support, encouragement, and for the assistance in formatting equations for my dissertation. Finally, I am thankful to my friends spread across the globe especially Dr. Prasad
Hemantha, a great teacher as well as a great friend, who showed me the beauty of physics;
iv without his endless support and encouragement when I was an undergraduate student I would not stand where I am today.
v PHASE TRANSITIONS, METALLIZATION, SUPERCONDUCTIVITY AND MAGNETIC
ORDERING IN DENSE CARBON DISULFIDE AND CHEMICAL ANALOGS
Abstract
by Liyanagamage Ranganath Prabashwara Dias, Ph.D. Washington State University July 2013
Chair: Choong-Shik Yoo
Under high pressure, simple molecular solids transform into non-molecular (extended) solids as compression energies approach those of strong covalent bonds in constituent chemical species, often with advanced mechanical, optical, electronic, and magnetic properties. The primary goal of this research is to investigate the pressure-induced molecular to nonmolecular solids, via discoveries of new states, structures, fundamental properties, and novel phenomena in carbon disulfide and its chemical analogs under extreme conditions of pressure and temperature.
Spectral, structural, resistance, and theoretical evidences show simple molecular CS2 undergoes transformations to an insulating black polymer with three-fold carbon atoms at ~9
GPa, to a semiconducting polymer above 30 GPa, and finally to a metallic solid above 50 GPa.
The metallic phase is a highly disordered 3D network structure with four-fold carbon atoms.
Based on first-principles calculations, we consider two plausible structures for the metallic phase: α-chalcopyrite and tridymite, both exhibiting metallic ground states.
Remarkably, low-temperature, dense CS2 not only becomes metallic, but also shows the coexistence of superconductivity and spin-fluctuations. This is the first such observation of
vi superconductivity in simple diamagnetic molecular solids like CS2 at high pressure. The superconductivity in CS2 arises from a highly disordered state at a relatively high transition temperature of ~6.2 K and is, interestingly, preceded by a magnetic ordering transition at ~45.2
K. Based on the x-ray scattering data, we suggest that the local structure changes from tetrahedral to octahedral and the associated spin-fluctuations are responsible for the observed magnetic ordering and superconductivity. A number of related molecular analogs and main group IV disulfides were also studied at high pressure and revealed systematic trends.
The above-mentioned findings are important for understanding novel properties of 3D extended solids, the nature of interactions and chemical bonds, and fundamental rules of high- pressure physics and chemistry. The discovery of superconductivity in CS2 is significant for applications and justifies a search for other potential high Tc superconductors composed of low-Z
3D network structures with high phonon frequencies. This is unlike other, more typical, organic superconductors of charge-transferred salts or metal-doped carbons and, most certainly, will stimulate future experimental and theoretical studies.
vii TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS...... iii ABSTRACT ...... vi LIST OF TABLES ...... xi LIST OF FIGURES ...... xii CHAPTERS ...... 1 1. Introduction ...... 1 1.1 High Pressure Science ...... 1 1.2 Motivation ...... 4 1.2.1 Simple Molecular Solids ...... 4 1.3 Example of Pressure-Induced Transformations in Oxygen and Carbon Dioxide ...... 7 1.4 Outline of the Dissertation ...... 13 2. Scientific Background ...... 14 2.1 Electron Delocalization ...... 14 2.1.1 Molecular to Non-molecular Transition ...... 14 2.1.2 What is a Metal? ...... 17 2.1.3 Mott Insulator-Metal Transition ...... 19 2.1.4 Mott-Hubbard Transition ...... 20 2.1.5 Pressure – Induced Metallization ...... 22 2.2 Electron Correlation ...... 24 2.2.1 Magnetism at High Pressure ...... 24 2.2.2 Spin-Fluctuation and Non-Fermi-Liquid Behavior ...... 26 2.3 Electron- Phonon Coupling: Superconductivity ...... 28 2.3.1 Superconductivity ...... 28 2.3.2 The Barden Cooper Schrieffer (BCS) Theory of Superconductivity ...... 30 2.3.3 High Temperature Superconductivity ...... 35 2.3.4 Pressure Effects on Superconductivity ...... 37 3. Experimental Methods ...... 40 3.1 High Pressure Techniques ...... 40 3.1.1 Types of Anvil Cells ...... 43
viii 3.1.2 Gasket materials ...... 46 3.1.3 Pressure Media ...... 49 3.1.4 Pressure Determination ...... 50 3.1.5 Low Temperatures ...... 54 3.2 Optical Spectroscopy at High Pressure ...... 56 3.2.1 Micro-Raman Spectroscopy ...... 56 3.2.1 Micro-Raman Set-up ...... 58 3.3 Angle-Dispersive X-ray Diffraction ...... 60 3.4 Electrical Transport Measurement at High Pressure ...... 65 3.5 Susceptibility Measurements at High Pressure ...... 71 3.5.1 AC-Susceptibility Measurements ...... 71 3.5.2 Double-Frequency modulation Method...... 73 3.6 Experimental Details ...... 77
3.6.1 Carbon Disulfide (CS2) ...... 77 3.6.2 Carbonyl sulfide (OCS) ...... 78
3.6.3 Group IV Sulfides: GeS2/SnS2 ...... 78 4. Dense Carbon Disulfide ...... 79 4.1 Background ...... 79 4.2 Structural Phase Transition ...... 83 4.3 Insulator-Metal Transition ...... 91 4.4 Superconducting Transition ...... 94 4.5 Magnetic Ordering Transition ...... 99 4.6 Discussions ...... 102 4.6.1 Structural and Insulator to metal transitions ...... 102 4.6.2 Superconductivity and Magnetic Ordering ...... 107 4.6.3 X-ray scattering at low temperatures and high pressure ...... 110 4.6.4 Phase Diagram of Carbon Disulfide ...... 114 5. Chemical Analogs to Carbon Disulfide ...... 118 5.1 Molecular Analog: Carbonyl sulfide (OCS) ...... 118 5.1.1 Polymerization and Insulator - Metal Transition ...... 119
5.2 Main Group IV Disulfides: GeS2, SnS2 ...... 125
ix 5.2.1 Metallization in GeS2 and SnS2 ...... 125
5.2.2 Magnetic Ordering - GeS2 and SnS2 ...... 133 5.3 Discussions ...... 136 6. Concluding Remarks ...... 138 APPENDIX ...... 143 A. Structural and Metallic Transition in GeS ...... 143
B. Structural and Metallic Transition in g-GeSe4 ...... 151
C. Photoconductivity of SnO2 under Pressure ...... 156 D. MATLAB code - Derivative Approximation ...... 158 BIBLIOGRAPHY ...... 159
x LIST OF TABLES
2. 1. Temperature dependencies for thermodynamic and transport properties from the spin
fluctuation theories of non-Fermi-liquid behavior (modified from Ref. 58) ...... 27
4. 1. The measured and calculated (in parentheses) peak positions of pair distances at various
temperatures and pressures. Td and Oh represent respectively tetrahedral and octahedral
local configurations. Only the first nearest carbon and sulfur atoms are counted for the pair
distance calculation because of the weak scattering contribution of carbon by electron
diffusion under high coordination numbers ...... 113
xi LIST OF FIGURES
1. 1. Pressure induced transformations ...... 3
1. 2. A Conceptual generalized physical/chemical phase diagram of molecular solids at high
pressure and temperatures. [C. S. Yoo, Phys. Chem. Chem. Phys. 2013] ...... 6
1. 3. Novel extended phases of molecular solids CO2, O2, N2 ...... 7
1. 4. Diagram of oxygen. The horizontal arrow indicates the phase transformations that are
taking place at room temperature with the progression of pressure...... 8
1. 5. Carbon dioxide phase diagram showing high pressure extended solid phases [Iota et al.,
2007] ...... 12
2. 1. A schematic of molecular-to-non-molecular phase transition to show the thermodynamic
constraints. [C. S. Yoo, Phys. Chem. Chem. Phys. 2013] ...... 15
2. 2. The electrical conductivities of various elements, compounds and materials. The figure
illustrates the enormous range in electrical conductivities measured at room temperature
(Reproduced from reference (Edwards & Sienko, 1982)...... 18
2. 3. Schematic illustration of energy levels for a Mott- Hubbard model at half-filling for U/W >
1. The addition of a non-zero U causes a splitting of the d band into upper (UHB) and lower
(LHB) Hubbard bands. (Modified from reference 45)...... 21
2. 4. The metallization of elements of the periodic classification under standard temperature and
pressure conditions. The figure shows the ratio (R/V) for elements of the periodic
classification. The shaded circles represent elements for which R and V are known
xii experimentally. The open circles are for elements for which only V is known experimentally
and R is calculated. (Edwards & Sienko (1983))...... 23
2. 5. Schematic of solid at low pressure (left) and high pressure (right). Rc is the radius of the ion
core and RWS is the radius determined by the average volume available per atom in the solid.
When RWS ∼ Rc, the localized electronic orbitals of the ions begin to overlap...... 25
2. 6. Schematic illustration of the electron-phonon coupling mechanism. The small central dot
with minus sign shows an electron and the arrow shows the path of the electron. Springs
indicate restoring force bringing the cations back to their equilibrium positions...... 33
2. 7. The evolution of Tc with time from Proc. HTS Workshop on Physics, Materials and
Applications, World Scientific, Singapore, 1996...... 37
3. 1. Schematic view of the diamond-anvil cell (DAC). The DAC is composed of two opposing
diamond anvils. Between the culets is a metal gasket with a hole drilled down the center. A
sample is placed inside this hole, typically along with a pressure transmitting medium and a
pressure calibrant (in this case a ruby chip). The diamonds are supported by seats typically
made of tungsten carbide (WC)...... 43
3. 2. (a) Merrill-Bassett-type diamond-anvil cell (DAC) (b) Symmetric piston-cylinder diamond
anvil cell (c) Boehler-type (plate) diamond anvils cell...... 45
3. 3. The membrane diamond anvil cell of Professor Yoo design employed in the present study:
(a) the cross sectional view, (b) the integrated view and, (c) the exploded view of piston and
cylinder...... 47
3. 4. The high pressure gas loader...... 50
3. 5. The shift of ruby R1 and R2 fluorescence lines for sample of CS2 at 2 GPa and 20 GPa ..... 54
xiii 3. 6. Low temperature system for Raman, resistivity and susceptibility measurements...... 55
3. 7. A schematic diagram of the Raman scattering process ...... 57
3. 8. A schematic diagram of the high throughput Raman spectroscopy system used in this work.
...... 59
3. 9. X-ray scattering off of a crystal lattice ...... 61
3. 10. Setup for ADXRD at the APS ...... 62
3. 11. X-ray diffraction pattern of CS2 sample at 4.0GPa ...... 63
3. 12. (a) The CS2 sample (black), background (red) and background subtracted (blue) x-ray
scattering patterns showing the analysis procedure to get the S(Q) in (b). The background x-
ray scattering was also measured from an empty cell after the experiments and the S(Q) data
was Fourier transformed to obtain the G(r)...... 64
3. 13. The steps of four-point arrangement of the electrodes for resistivity measurement in the
DAC ...... 69
3. 14. The thickness of the sample as a function of pressure during compression and
decompression. Inset: (T) and R(T) at 70 GPa showing the similar systematic behavior as a
function of temperature. Microphotographs of reflective CS2 samples at 28 and 55 GPa
showing the experimental setup for four-probe electrical resistance measurements and the
metallic reflectivity of CS2 samples above 55 GPa similar to those of Pt probes...... 70
3.15. Two identical compensating primary/secondary coil systems for ac susceptibility
measurements. The active coil is around 16-facet diamond anvil in the middle;
compensating coil contains a dummy gasket (Debessai, Ph. D. Thesis, 2008) ...... 72
3. 16. Schematic of the double-frequency modulation setup to detect superconductivity. Modified
from (Timofeev, Struzhkin, Hemley, Mao, & Gregoryanz, 2002) ...... 75
xiv 3. 17. (a) Schematic representation of magnetic field variation with time near the sample. (b)
Signal at 2f frequency extracted from the amplitude of high-frequency signal (Timofeev,
Struzhkin, Hemley, Mao, & Gregoryanz, 2002)...... 76
4. 1. Orthorhombic structure Cmca of Carbon disulfide ...... 79
4. 2. The phase diagram of carbon disulfide from the reference (Agnew, Mischke, & Swanson,
Pressure and Temperature Induced Chemistry of Carbon Disulfide, 1988)...... 82
4. 3. Raman spectra solid Carbon Disulfide upon increasing pressure ...... 85
4. 4. Raman spectra solid Carbon Disulfide upon increasing pressure after the polymerization in
the 300-700 cm-1 region associated with the structural phase transitions at 30GPa ...... 86
4. 5. The pressure dependences of the Raman spectra of solid CS2. The blue circle indicates the
increasing pressure and red circles indicate the decreasing in pressure ...... 87
4. 6. The Raman spectra of ohmically heated carbon disulfide, showing thermal decomposition
of CS2 to carbon and sulfur (phase VI) at around 720 K at 22 GPa (a) The laser-heated
carbon disulfide, decomposes to carbon and sulfur (phase III) at 30 GPa and > 1000 K. (b).
...... 88
4. 7. The background-removed structural factor S(Q) and radial distribution function G(r) (inset)
of carbon disulfide obtained at several high pressures, showing the pressure-induced
structural changes...... 90
4. 8. Microphotographs of carbon disulfide under high pressure showing its transformation from
transparent fluid to molecular solid (Cmca) at ~1.8 GPa, to black polymer above 10 GPa ((-
S-(C=S)-)p or CS3), and eventually to a highly reflecting extended solid above 40 GPa (CS4)
at ambient temperature...... 91
xv 4. 9. Pressure-induced electrical resistance changes of carbon disulfide, showing the insulator to
metal transition ...... 92
4. 10. (a) The temperature-dependent electrical resistance of carbon disulfide at 24, 30, 37, 43
GPa on a logarithmic scale, showing a transition from insulator to semiconductor to semi-
metal. (b) The ln(ρ) against 1000/T (Arrhenius plot), showing the linearity indication above
150K in dash lines. The ln(ρ) against 1/T1/4 (VRH mechanism), showing the linearity
indication at low temperatures in dash lines (blue axis)...... 93
4. 11. Temperature-dependent electrical resistance of carbon disulfide at high pressures, showing
the superconducting transitions at several pressures that occur around 6K (TC). Inset: An
expanded view into the low-temperature region (<15K) at several pressures, showing the
sharp resistivity drop at the TC (noted by an arrow) and small drops at the TX just prior to the
TC (see arrows)...... 95
4. 12. The pressure dependence of the Tc to 180GPa, indicating a discontinuity ~100GPa. Tc
determined from both resistance (blue squares) and susceptibility (red squares) ...... 96
4. 13. Magnetic susceptibility of carbon disulfide showing the superconducting transition
(marked at TC) at 50 GPa, measured by the modulating technique. Inset: The pressure
dependence of the TC as determined by the magnetic susceptibility, showing the increase in
TC with pressure...... 98
4. 14. temperature resistivity of CS2, showing the magnetic ordering transitions at 48GPa and
110GPa. The solid lines illustrate a best fit to Eq. (2.4) describing electron-magnon
scattering from antiferromagnetic magnons with an energy gap (Δ). Inset: Temperature
dependence of the carbon disulfide temperature coefficient dρ/dT. The transition
temperature TN is defined as the temperature of the minimum in dρ/dT.. (b) Values of the
xvi energy gap (Δ) and coefficient A of the T2 contribution to as a function of pressure, as
derived from fits of Eq. (2.4) to the data...... 100
4. 15. (a) The T2 dependence of the resistivity below 100 GPa and above 40 K, showing that it is
2 consistent with the form (T) = o+AT , corresponding to the Fermi-liquid behavior. (b)
The T1.5 dependence of the resistivity under pressure above 110 GPa and above 40 K, which
1.5 shows that it is consistent with the form (T) = o+AT , signifying the departure from
Fermi-liquid behavior. The arrows indicate the temperature where the resistivity starts to
deviate from the power law behavior because of the magnetic ordering transition...... 101
4. 16. The calculated structure factors of α-chalcopyrite (I-42d, top) and α-tridymite (P212121,
bottom), showing the two major features centered around 2.8 Å-1 and 4.9 Å-1 as observed in
the experiments (The calculation was done by Prof. John Tse (2011))...... 103
4. 17. The calculated enthalpies for the chalcopyrite (I-42d) and tridymite (P212121) structure of
CS2 over a large pressure range from 20 to 60 GPa, showing that the chalcopyrite structure
is more stable by about 0.3-0.4 eV/formula unit (The calculation was done by Prof. John Tse
(2011))...... 105
4. 18. (a). The electronic band structure of the chalcopyrite showing a metallic ground state. (b)
The electronic band structure of the tridymite structure at 47 GPa showing the metallic
nature and flat and parallel bands (The calculation was done by Prof. John Tse (2011)) ... 106
4. 19. The phonon band structure and density of state for the chalcopyrite structure, showing the
major Raman-active A1 phonon mode at 500 cm-1 and other IR modes at 700-800 cm-1(The
calculation was done by Prof. John Tse (2011))...... 107
4. 20. The magnitude of the resistivity anomaly δρ plotted as a function of pressure, showing a
competing effect of magnetic ordering and superconductivity in dense carbon disulfide. In
xvii the inset the δρ is defined by extrapolating the temperature dependences above and below
the transition to TN and evaluating the difference in the resultant electrical resistivity...... 109
4. 21. The pair distribution function G(r) of highly disordered extended carbon disulfide,
showing the temperature induced structural change at 63 GPa ...... 111
4. 22. (a) The pair distribution function G(r) at ambient temperature, and (b) suggested crystal
model of polymeric CS2. Pressure increased to 68 GPa at 125K, which then maintained to
11K. Tick marks represent pair distances using the cubic-close-packed structural models of
CS4 tetrahedra and CS6 octahedra, rT and rO respectively...... 112
4. 23. The pressure-temperature phase diagram for carbon disulfide, showing the pressure-
induced insulator-to-metal transition. In the region of metallic CS4 phase, showing (i) the
magnetic antiferromagnetic (AFM) ordering transition at TN, (ii) the superconducting (SC)
transition at Tsc, and (iii) a small drop in resistance (unknown origin) at Tx prior to the
superconducting transition. The pressure dependence of the TSC was determined from both
the resistance (open blue circles) and magnetic susceptibility (open red circles). PM and DM
denotes the paramagnetic and diamagnetic...... 115
5. 1. Raman spectra of OCS phases upon increasing pressure at room-temperature, resulting in
polymeric OCS at above 20 GPa...... 119
5. 2. The pressure dependences of the Raman spectra of solid OCS, indicating the structural
changes at 8 GPa and polymerization above 22 GPa. The inset shows subtle changes in
Raman spectra in the 450-700 cm-1 region associated with the structural phase transitions at
22 and 32 GPa...... 121
xviii 5. 3. Intensity ratio of the ν2 fundamental and ν1 fundamental band (ν2/ ν1 ) with increasing
pressure indicating enhancing of the intensity of the ν2 fundamental band...... 122
5. 4. The pressure dependence of the electrical resistance of OCS at room temperature. We
observed sharp decreasing of the resistance up to 70 GPa, indication the semi-metallic state
...... 123
5. 5. Microphotographs of OCS under high pressure showing its transformation from transparent
fluid to molecular solid at ~3 GPa, to black polymer above 22 GPa ((-S-(C=O)-)p), ((a) to
(e)) and eventually to a reflecting extended solid above 95 GPa at ambient temperature((f)
taken using reflected light))...... 124
5. 6. Microphotographs of GeS2 under high pressure showing its transformation from transparent
to opaque ((a) – (c)) and then to a reflecting solid above 40 GPa. The reflectance of the
sample around 40GPa providing the visual evidence for the band gap closure...... 127
5. 7. The pressure dependence of the electrical resistance of GeS2 at room temperature. We
observed sharp decreasing of the resistance up to 40 GPa, indicating a metallic state...... 128
5. 8. The temperature-dependent electrical resistance of GeS2 at various pressures on a
logarithmic scale, showing a transition from insulator to semiconductor to metal...... 129
5. 9. The pressure dependence of the electrical resistance of SnS2 at room temperature. We
observed sharp decreasing of the resistance up to ~ 38 GPa, indication the metallic state . 131
5. 10. The temperature-dependent electrical resistance of SnS2 at various pressures on a
logarithmic scale, showing a transition to a metal...... 132
5. 11. Low-temperature resistivity of GeS2 and SnS2, showing the magnetic ordering transitions
at 55 GPa. The solid lines illustrate a best fit to Eq. (2.4) describing electron-magnon
scattering from antiferromagnetic magnons with an energy gap (Δ). Inset: Temperature
xix dependence of the carbon disulfide temperature coefficient dρ/dT. The transition
temperature TN is defined as the temperature of the minimum in dρ/dT...... 134
5. 12. (a) Values of the energy gap (Δ) and coefficient A of the T2 contribution to as a
function of pressure, as derived from fits of Eq. (2.4) to the data for GeS2 and (b) for
SnS2...... 135
5. 13. The pressure dependence of the electrical resistance of group IVA sulfides at room
temperature with increasing pressure...... 137
6. 1. The composition-pressure phase diagram of CX2 (X= O, S) and YS2 (Y=C, Ge, Sn)
systems, illustrating the concept of a molecular alloy. The red dots and solid line represent
the polymerization and the blue dots and dashed line represent the metallization and the
linear interpolation. The Shaded area represents the immiscible dome at temperature T
which gives rise to magnetic ordering and superconductivity...... 139
A. 1.(a) The Pnma (62) orthorhombic structure of GeS with unit cell. The layered character and
atomic coordination are evident. The unit cell parameters are a= 4.305Å, b=3.643Å,
c=10.495Å (Iota, Yoo, & Cynn, An Optically Nonlinear Extended Solid at High Pressures
and temperatures, 1999). The structure is completely specified by four internal atomic
positions (uGe, ¼, vGe) and (uS, ¼, vS). In (b) is shown a projection of the structure along the
b axis...... 145
A. 2. Pressure dependence of the Raman spectra of GeS, showing the Ag and Bg phonons modes
of GeS, clearly Indicating the splitting of the Ag mode and the new peak above 28GPa. The
xx close and open symbols signify, respectively, the data taken during the pressure uploading
and downloading...... 146
A. 3. Pressure-induced Raman changes of germanium sulfide, (a) showing the loading spectra
and (b) showing the unloading spectra. The spectra shows splitting in Raman spectra in the
260 cm-1 region (Ag mode) and new rather broad peak appear at ~ 331cm-1 above 28GPa
indicating a structural phase transition. The unloading spectra show the reversibility of the
pressure changes to the sample...... 147
A. 4. The pressure dependence of the electrical resistance of GeS at room temperature. We
observed sharp decreasing of the resistance up to 18GPa with a discontinuity around 12GPa,
clearly indication the metallic state. The inset show the sample becomes shiny around
15GPa providing the visual evidence for the metallization. The close and open symbols
signify, respectively, the data taken during the pressure uploading and downloading...... 149
A. 5. The temperature-dependent electrical resistance of germanium sulfide at 3, 6, 11GPa on a
logarithmic scale, showing a transition from semiconductor to semi-metal, and 16, 21, 46
GPa showing the clear metallic behavior ...... 150
B. 1. Pressure dependence of the Raman spectra of GeSe4, showing the CS and ES stretching
modes of GeSe4. It’s clearly indicate that the progressive conversion of the CS to ES around
10GPa. The close and open symbols signify, respectively, the data taken during the pressure
uploading and downloading...... 152
B. 2. Pressure dependence of the CS and ES stretching modes ratio in the GeSe4...... 153
xxi B. 3. The pressure dependence of the electrical resistance of GeSe4 at room temperature. We
observed gradual decreasing of the resistance up to 20GPa with a discontinuity around
10GPa, clearly indication the metallic state...... 154
B. 4. The temperature-dependent electrical resistance of GeSe4 at 5, 8, 13.5GPa, showing a
transition to a metal, and the insect shows the resistivity anomaly at 13.5, 16, 24GPa
indicating by arrows...... 155
C. 1. (a) Pressure dependence of the electrical resistance of SnO2. Gradual increasing of the
resistance up to 18GPa indicates the band gap opening with increasing pressure. (b)
Normalized photocurrent change vs pressure with different power density (Power density
-2 -1 varies from 5000 to 65000 Wm S ) in SnO2...... 157
xxii
Dedication
This dissertation is affectionately dedicated to
my late beloved father, Bandula Kumara Dias
xxiii Chapter 1
Introduction
1.1 High Pressure Science
The goal of fundamental research in physical science is to understand the governing laws of physics and to apply that knowledge where available and when feasible for the benefit of mankind. For that purpose, pressure has great advantages compared to other physical variables
(Jayaraman,1984). Of the three thermodynamic variables, temperature, pressure, and magnetic field, pressure has historically been the least utilized, yet it has the greatest effect on the properties of the lattice of condensed matter. One of the early triumphs of quantum mechanics was to predict how matter can exist, and in what forms, at the very high pressures found in many astronomical bodies. Moreover, the application of pressure to condensed matter brings atoms closer together, which provides an ideal means to carefully tune electronic, magnetic, structural, and vibrational properties for testing fundamental theory.
Under the extreme pressures of the Earth’s deep interior (on the order of 106 atmosphere
~ 100 GPa ~ 1 Mbar), the free energy change (pressure-volume work) of the system may reach
10 eV per two atoms (Hemley,2000). This imparts dramatic changes in the condensed state of molecular system. The application of low pressure drives densification (condensation, solidification) via atomic ordering. Further compression of crystalline lattices brings atoms and molecules into the repulsive region of intermolecular potentials, increases the coordination, decreases the length of covalent bonds and size of anions, and eventually promotes more
1 significant structural reorganizations and chemical bonding changes (Grochala, Hoffmann , Feng
& Neil, 2007). As the compression energy begins to approach the chemical bond energy, delocalization of electrons can be observed, and filled valence shell atoms become chemically reactive. Upon further compression, extended solids may even ionize the electrons (i.e., the pressure-induced ionization), forming an amorphous or ionic solid, as the electrostatic forces get more significant at extreme conditions. Many recent discoveries of novel bonding and properties of materials in extreme conditions indicate that our conventional descriptions of atomic and electron behaviors are wholly inadequate under these conditions.
The accelerating growth in scientific knowledge on how molecules respond to high pressures and technologic advances in high pressure research over a wide range of spatial, temporal and thermodynamic spaces enable us to observe the existence of complex structures, and novel properties, including metal-insulator transitions, Mott transition, superconductivity, spin transitions, etc. (Iota, Yoo, & Cynn, An Optically Nonlinear Extended Solid at High
Pressures and temperatures,1999) (Dias, Yoo, Kim & Tse,2011) (Gavriliuk, Trojan &
Struzhkin,2012) (Eremets, Gavriliuk, Trojan, Dzivenko, & Boehler,2004) (Degtyareva, et al.,
2005) (Struzhkin, Hemley, Mao, & Timofeev, Superconductivity at 10–17K in Compressed
Sulphur, 2001) (Yoo, et al., 2005) These advances, therefore, enable us to address very fundamental questions regarding intermolecular interactions and collective behaviors of molecules at very tight space (Fig. 1.1). To this end, we cite a phrase by Prof. Neil Ashcroft [in the 2010 lecture at the GRC conference on High Pressure Research].
‘Whatever it is, cool it’ “WHATEVER IT IS, SQUEEZE IT”
2
Pressure
Tuning of Molar Volume
Modification of Intermolecular Interactions
Destabilization of Intramolecular Bonds and the Electron- density Rearrangement
Phase Transition New Possible Atomic Arrangements in Molecular
System
Dimerization; One, two or three-dimensional polymerization (nonmolecular, extended phase); Amorphization; Dissociation; Metallization; Superconductivity; Magnetic ordering
Reversible Not Reversible
Figure 1. 1. Pressure induced transformations
3 1.2 Motivation
1.2.1 Simple Molecular Solids
Molecular solids are described in terms of strong covalent bonds within molecules
(intramolecular bonds) and weak van der Waals interactions between molecules (intermolecular bonds). The strong intramolecular bonds make these molecules extremely stable at ambient conditions; whereas, the weak intermolecular interactions make these solids highly compressible
(low bulk moduli typically less than 10GPa), at least initially at relatively low pressures. For this reason, many simple molecular solids, particularly those containing elements from the first and second row of the periodic table, such as H2, CO2, N2, O2, H2O, NH3, and other C-N-O-H compounds, are often considered “inert” at relatively low pressures. Indeed, the high stabilities of these molecules are often assumed even at very high pressures (10 – 40 GPa) and temperatures (1000-4000 K), as CO2, N2, H2O are considered to be four major detonation products of energetic molecules.
At high pressures, however, the nature of these intermolecular interactions is rapidly altered and they become highly repulsive. Electron kinetic energy dominates, and electrons localized within intramolecular bonds become unstable. Evidently at 100 GPa, localized electrons have acquired a huge kinetic energy, and an electron can therefore mix strongly with valence and core electrons of their own or nearby molecules. Such a core swelling and/or valence mixing creates an excellent environment for simple molecules to transform chemically from molecular to nonmolecular extended solids such as polymers and metals. This polymerization is particularly easy for CO, C2H2, (-C2N-)2, CS2 and similar molecules.
4 Even aromatic benzene transforms to a disordered cross-linked polymer at 30 GPa
(Pruzan, et al., 1990). Increasing coordination is an obvious way to adapt to higher density. At these pressures, the compression energy (PΔV) of molecular solids often exceeds several eV or several 100 kJ mol-1, rivaling those of the most stable chemical bonds enough to induce bond scission leading to chemical changes (Jeanloz,1989). Yet, a rapid broadening of electronic bands may lead to an insulator–metal transition, providing a competing mechanism. Surely, the kinetics associated with these pressure-induced chemical changes will play an important role. The products are governed by the collective behavior of molecules, resulting in strongly associated intermediary phases in a pressure range of 10–50 GPa, multi-dimensional polymeric products around 50 and 100 GPa, and eventually band-gap closing, resulting in molecular and atomic metals typically well above 100 GPa. At sufficiently high pressures of ~ 1TPa, most solids will lose their periodic integrities and ultimately form a plasma in which the chemical description of bonding is essentially lost. On the other hand, materials at high temperatures often transform into an open structure like bcc because of the large increase in entropy (Dias, Yoo, Kim & Tse, 2011) and may eventually ionize, dissociate or even decompose into elemental species. Therefore, the combination of high pressure and high temperature provides a way of probing the delicate balance between mechanical (PΔV) and thermal (TΔS) energies that governs melting curves, crystal structures, phase stabilities, and phase boundaries (See Fig. 1.2).
The pressure-induced electron delocalization of low-Z molecules often leads to a high- energy and high-density extended state. Low-Z extended solids are typically made of corner (or edge)- sharing polyhedra, similar to the structures found in SiO2 polymorphs and many transition-metal oxides such as perovskites (See Fig. 1.3).
5 The transformations of molecular solids to the extended phases often require relatively large positive volume changes (10-30%) and, thus, are associated with large kinetic barriers (30-
150 KJ/mol). As a result, these transitions are greatly hindered kinetically despite large thermodynamic stabilities of the final product.
Figure 1. 2. A Conceptual generalized physical/chemical phase diagram of molecular solids at high pressure and temperatures. [C. S. Yoo, Phys. Chem. Chem. Phys. 2013]
The collective behavior of such monolithic 3D network structures can result in novel electro/optical/magnetic properties such as piezoelectricity, ferromagnetism and nonlinear optical properties.
6 Furthermore, because of the high Debye temperatures, it is likely that low-Z extended solids will have low heat capacity, thermal conductivity and electron-phonon coupling.
Examples can be found in the high thermal conductivity of diamond which exceeds by three times that of copper and high Tc superconductors of MgB2 and B-doped diamond (Nagamatsu,
Nakagawa, Muranaka, Zenitani, & Akimitsu, 2011)).
Figure 1. 3. Novel extended phases of molecular solids CO2, O2, N2
1. 3 Example of Pressure-Induced Transformations in Oxygen and Carbon
Dioxide
Oxygen
Oxygen is one of the most important and abundant molecules on earth. The lowest electron configuration (π4π*2) of this homonuclear doubly-bonded diatomic system gives rise to
3 - 1 1 + three electronic states of increasing energy in the order of: ∑ g , Δg and ∑ g with equilibrium
-1 bond distances (r) of 0.12 nm and stretching frequencies (ν) of 1555 cm (Freiman & Jodl,
2004). The non-zero electronic spin (S=1) in the ground electronic state makes the oxygen molecule a magnetic system. Thus gaseous and liquid O2 are paramagnets.
7 In contrast, only the low-temperature phases of solid oxygen show magnetism. The phase diagram of oxygen shows that near room temperature, three solid oxygen phases of intense color occur on the order of 10 GPa: β-O2 (R m) around 5 GPa, δ-O2 (Fmmm) around 9GPa and ɛ-O2
(C2/m) around 10 GPa (Itie, et al., 1989). Above 96 GPa, ɛ-O2 which is an insulator transforms to ζ-O2 a molecular metal that becomes superconducting at 0.6K (Durandurdu & Drabold, 2002).
It shows that the ɛ–phase is stable over a vast P-T range. The antiferromagnetic order observed in low temperature and low pressure phases of α and δ, eventually collapses as superconducting ζ-
O2(Harbold, et al., 2002) is formed at high pressure and low temperature.
Figure 1. 4. Diagram of oxygen. The horizontal arrow indicates the phase transformations that are taking place at room temperature with the progression of pressure.
8 In addition, recent studies have shown that a new high-temperature phase η–O2 exists above 600K as shown in Fig. 1.4. The most interesting feature that can be seen with the proposed structures for the above mentioned solid oxygen phases is such a large stability field, between 17 to 100 GPa, of molecular ɛ-O2 in a very peculiar cluster form of O8 or (O2)4, which links the low-pressure magnetic phase with the high-pressure superconducting phase.
Oxygen is thus far the simplest elemental molecule that has shown superconductivity experimentally, which become superconducting only in their monatomic states (Kasap, et al.,
2007). It is also the first molecular solid that the superconductivity was experimentally confirmed, at around 1 Mbar. Yet, there has been no superconductivity found in diamagnetic molecular solids, despite scientists’ attempts over several decades. Therefore, the chemical basis giving rise to all these phenomena has yet been fully understood. Understanding the relationship between crystal structure, superconductivity and magnetic ordering in molecular solids at high pressures would reveal new insights into the pressure–induced changes that can be applicable to simple molecules in general and may lead to vital applications.
Carbon Dioxide
Among simple molecules, carbon dioxide is an excellent example to show a wide range of polymorphs that exhibit greatly diverse inter/intra-molecular interactions, chemical bondings, and crystal structures. Carbon dioxide is abundant in nature and other planets, and is also a major product of energetic materials reactions such as explosive detonation.
9 At ambient conditions, CO2 is a linear symmetric molecule with no permanent dipole moment but with a very large quadrupole moment (Battaglia, Buckingham, Neumark, Pierens, &
Williams, 1981). Given the large quadrupole moment, the molecular solid phase of CO2 has long been used as model for understanding the role of quadrupolar interactions in simple molecular solids.
Determining the stability of CO2 at high pressures and temperatures is crucial for understanding the structure, intermolecular interactions, and the chemical bonding of this important oxide under extreme conditions. Although CO2 is a simple molecule, its high pressure phase diagram is rather complex, exhibiting different solid phases (Fig. 1.5). The unambiguous determination of the respective thermodynamic (opposed to kinetic) P–T domains is difficult because of strong meta-stabilities. At relatively low pressures and temperatures, CO2 molecules are highly stable due to strong covalent intramolecular bonds and comparatively weak electrostatic interactions between molecules. At room temperature CO2 solidifies into phase I, with a cubic structure (Pa3) (Bridgeman,1940) (Hanson & Jones, 1981) ( Olinger,1982), commonly known as dry ice. This is a van der Waals crystal with strong (weak) intramolecular
(intermolecular) interactions. CO2-I is an optically isotropic, highly compressible solid (bulk modulus is 12GPa –– typical for a molecular solid) (Yoo, et al., Crystal Structure of Carbon
Dioxide at high pressure: “Superhard” Polymeric Carbon Dioxide, 1999).
When compressed above 12GPa at room temperature, phase I undergoes a transition into the orthorhombic phase III. As in the cubic phase, this orthorhombic structure is stabilized by the quadrupole-quadrupole interactions between the linear symmetric CO2 molecules (Kuckta &
Etters, 1988). CO2-III displays physical properties that are uncharacteristic for a molecular solid, such as an unusually large material strength. A recent X-ray diffraction study shows a large bulk
10 modulus for phase III of 87 GPa (Yoo,1999) (for comparison, Si – a covalent solid has a bulk modulus of 98GPa (Knittle,1995)).
This suggests that above 40GPa, CO2-III may not be entirely molecular, but that electron delocalization may occur, leading to strong intermolecular interactions or even to weak intermolecular bonding. The effect of such electron delocalization would be to extend the stability of CO2-III to higher pressures by softening the steep molecular repulsive potentials. In addition, the increased coupling between molecules would be expected to lower the activation barrier for breaking the strong C=O bonds, thereby creating the conditions for the formation of extended phases. Above 40–60 GPa, these molecular solids transform into a wide range of non- molecular extended phases, which include tetrahedral bonded polymeric CO2-V (Iota, Yoo, &
Cynn, Quartzlike Carbon Dioxide: An Optically Nonlinear Extended Solid at High Pressures and temperatures, 1999) (Yoo, Iota, & Cynn, Nonlinear Carbon Dioxide at High Pressures and
Temperatures, 2001) (Datchi, Giordano, Munsch, & Saitta, 2009), distorted octahedral CO2-VI
(Lipp, Evans, Baer, & Yoo, 2005) coesite-like c-CO2 (Sengupta & Yoo, 2010), and silica like amorphous CO2 (a-carbonia) (Santoro, et al., 2006).
Between the stability fields of the molecular and extended phases (i.e., 20–40 GPa), there are highly unusual intermediary phases of bent CO2-IV, strongly associated with CO2-II and highly strained CO2-III. All extended phases become amorphous solids above 100–200 GPa, signifying the instability of the [CO4] tetrahedral structure above 100 GPa (Yoo, Sengupta, &
Kim, Carbon Dioxide Carbonates in the Earth’s Mantle: Implications to the Deep Carbon Cycle,
2011). Upon laser heating above 75 GPa, all extended CO2 phases transform into an extended form of ionic CO2 (i-CO2). The polymeric CO2 may have very important technological implications for developing a high-power second-harmonic generator, a high-strength glass, and
11 a super-hard material. Finally, these molecular-to-extended phase transitions also provide a fundamental insight to the high-pressure science of many other simple molecular solids
Figure 1. 5. Carbon dioxide phase diagram showing high pressure extended solid phases [Iota et al., 2007]
.
12 1.4 Outline of the Dissertation
My Ph.D. research uncovers the pressure-induced structural and electronic phase transitions in carbon disulfide and its molecular analogs carbonyl sulfide and main group IV disulfides, germanium disulfide and tin disulfide. The main findings in this research include the pressure-induced structural phase transitions, metallization, superconducting transitions, and magnetic ordering transitions, which will be reported in the following five chapters and four appendices.
Following this introduction, we introduce key scientific concepts in chapter II and describe experimental techniques, apparatus and materials used in this study in Chapter III. We then present the main experimental results and discussions on carbon disulfide in Chapter IV and experimental results and discussions of chemical analogs in Chapter V. Finally, we summarize our main findings and their significance in Chapter VI. In the appendices, we present some related miscellaneous information on the following: Insulator Metal transition on GeS in
Appendix A, Insulator Metal transition on glassy-GeSe4 in Appendix B, photoconductivity measurement on SnO2 in Appendix C, and MATLAB code for derivative of the resistivity
Appendix D. The major findings of the present study have been published in:
. Dias, R. P., Yoo, C. S., Kim, M. & Tse, J. S. Insulator-metal transition of highly
compressed carbon disulfide. Phys. Rev. B. 84, 144104-1-6 (2011).
. Dias, R. P., Yoo, C. S., Struzhkin, V.V., Kim, M., Muramatsu, T., Matsuoka, T.,
Ohishi, Y. & Sinogeikin, S. Superconductivity in highly disordered dense carbon
disulfide. PNAS 110, 11720-11724 (2013).
13 Chapter 2
Scientific Background
2.1 Electron Delocalization
2.1.1 Molecular to Non-molecular Transition
Pressure-induced changes, at the most fundamental level, are the effect of compression on the energetic of electrons. The past discoveries of nonmolecular phases of simple molecular solids (Eremets, Hemley, Mao, & Gregoryanz, 2001)( Yoo, et al., Crystal structure of carbon dioxide at high pressure: "Superhard" polymeric carbon dioxide, 1999)( Iota, Yoo, & Cynn, An
Optically Nonlinear Extended Solid at High Pressures and temperatures, 1999)( Goncharov,
Gregoryanz, Mao, Liu, & Hemley, 2000) demonstrate the proof-of-the-principles for producing exotic phases by application of high pressure.
The linear CO2 molecule is known to polymerize into an extended solid (Iota, Yoo, &
Cynn, Quartzlike Carbon Dioxide: An Optically Nonlinear Extended Solid at High Pressures and temperatures, 1999). Even N2, which contains the strongest homonuclear bond, forms a polymer when sufficiently, compressed at greater than 110 GPa and 2000 K (Eremets, Hemley, Mao, &
Gregoryanz, 2001). In this new phase, each nitrogen atom is threefold coordinated in a pyramidal geometry, as in the cubic-gauche phase of phosporous. More importantly, such a transition from a molecular solid to a denser covalently bonded framework structure indicates the fundamental principle of high-pressure science. These transitions occur to soften highly repulsive intermolecular potentials via delocalization of electrons at high pressures and temperatures.
14 Considering the contributions to the energy: kinetic, coulomb, exchange, and correlation, the kinetic energy scales as r, where is the electron density, and therefore rises steeply on compression. This means, in general, a destabilization of intramolecular bonds as density (or pressure) increases and the intermolecular potential becomes highly repulsive.
The beauty of pressure is that it gives the opportunity to carefully tune the appropriate density to observe the effects. Figure 2.1 illustrates the molecular to non-molecular phase transition to show the thermodynamic constraints in a pressure/volume/energy diagram. Vo signifies the specific volume of a molecular solid at ambient conditions, whereas VMS and VES are those of the molecular solid and extended solid at the transition pressure.
Figure 2. 1. A schematic of molecular-to-non-molecular phase transition to show the thermodynamic constraints. [C. S. Yoo, Phys. Chem. Chem. Phys. 2013]
15 The pressure (or energy) offset of the transition (2-3) from the equilibrium value (the green line) signifies the presence of a large activation barrier. A similar kinetic barrier in the backward transition (3-4), on the other hand, makes it possible to recover the high-energy high- density product at ambient conditions.
However, these processes represent the collective properties of solids, strongly dependent on the intermolecular separation. Therefore, it is likely that these processes occur with increasing pressure as molecular phases go to ionic species to polymeric phases to metallic phases, in a way to produce the configuration with more itinerant electrons. Because of the large modifications in chemical bonding associated with the molecular-to-nonmolecular phase transitions, one might expect large activation energies in the reverse process and thus the monomolecular product to be metastable even at the ambient condition. Furthermore, these types of extended molecular solids, particularly those formed of low-Z first and second row elements, are an entirely new class of novel materials with properties such as nonlinear optical character (Iota, Yoo, & Cynn,
Quartzlike Carbon Dioxide: An Optically Nonlinear Extended Solid at High Pressures and temperatures, 1999), super-hardness (Yoo, et al., Crystal structure of carbon dioxide at high pressure: "Superhard" polymeric carbon dioxide, 1999, high-temperature superconductivity, unusual states of order-disorder, and high-energy density to name a few. Metallic H2 has been predicted to be a high Tc superconductor (Richardson & Ashcroft, 1997). Based on these facts, we conjecture that three fundamental mechanisms of high-pressure science are polymerization, metallization, and ionization, occurring in high-density molecular solids and fluids.
16 2.1.2 What is a Metal?
We know that more than two-thirds of elements are metals. This shows that the natural tendency of elements is to favor the metallic state. A sharp distinction exists in nature between metals and insulators for temperatures approaching absolute zero. In elemental metals and certain compounds the electrical resistivity tends to a finite value (or zero in the case of superconductors) as the temperature goes to zero (ρ finite as T→ 0K). But in insulators it tends to be infinite (ρ → ∞ as T→ 0K).
The electrical conductivity of solids ranges from at least 109 Ω−1cm−1 for a pure metal such as copper at liquid helium temperatures to at most 10−22 Ω−1cm−1 for the best insulators or non-metals at this same base temperature (Fig. 2.2).
The first successful theoretical description of metals is based on non-interacting or weakly interacting electron systems. The electronic states in a periodic atomic lattice are extended and have an energy spectrum forming energy bands. The theory makes a general distinction between metals and insulators at zero temperature based on the filling of the electronic bands: For insulators the highest filled band is completely filled; for metals, it is partially filled. In other words, the Fermi level lies in a band gap in insulators while the level is inside a band for metals.
The fundamental difference that distinguishes metals from insulators and semiconductors is the absence of a gap for electron hole excitations. In metals, the ground state can be excited at arbitrarily small energies, which have profound phenomenological consequences. In the non- interacting electron theory, the formation of band structure is entirely due to the periodic lattice structure of atoms in crystals. This basic distinction between metals and semiconductors insulators was proposed and established in the early years of quantum mechanics (Bethe, 1928)(
17 Sommerfeld, 1928). By the early 1930s, it was recognized that insulators with a small energy gap between the highest filled band and lowest empty band would be semiconductors due to thermal excitation of the electrons (Fowler, 1933) (Wilson, 1931. Although this band picture was successful in many respects, many transition-metal oxides with a partially filled d-electron band were nonetheless poor conductors and indeed often insulators.
Figure 2. 2. The electrical conductivities of various elements, compounds and materials. The figure illustrates the enormous range in electrical conductivities measured at room temperature (Reproduced from reference (Edwards & Sienko, 1982).
A typical example in their report was NiO(Mott & Peierls, Discussion of The Paper by de
Boer and Verwey, 1937). The insulator-metal transition, the process of physically and chemically transforming an insulator into a metal, and vice versa, has so far proven surprisingly recalcitrant to a complete theoretical analysis.
18 2.1.3 Mott Insulator-Metal Transition
Insulators can be generally classified into two main types: The first is those systems whose insulating behaviors can be understood on the basis of the interaction of single electrons with the electric field of the ions in the crystal. Examples include (i) a band (or Bloch-Wilson) insulator, in which the electrons' behavior is mainly due to its interaction. (ii) A Peierls insulator, in which the electron-ion interaction produces a lattice distortion that changes the periodicity of the crystal and this in turn affects the electron transport. (iii) An Anderson insulator in which the insulating behavior is produced by the interaction of independent electrons with random lattice defects. The second group of insulators is the Mott insulators, in which band theory and hence the independent electron assumption fails. Instead, Mott insulators are often characterized by correlated many-electron phenomena and Coulomb interaction between the charge carriers
(Mott, Metal-Insulator Transition, 1968) (Imada, Fujimori, & Tokura, 1998). If there is no electron-electron interaction in the crystal solid, the only length scale is just the lattice spacing d.
However, if we introduce the interaction between electrons, we will also have another length scale associated with this electron-electron interaction. In 1937, de Boer and Verwey (Boer &
Verwey, 1937) reported insulating behavior for transition metal oxides like NiO and CoO even though band theory predicts these materials to be metals. CoO has a distorted rock-salt structure with one Co and one O atom in its unit cell, hence 15 electrons per unit cell. Band theory tells us that this material should be a metal since there are unfilled bands because of the odd number of electrons; however it is one of the toughest insulators known. In the early fifties, Mott explained this is due to a metal-insulator transition (MIT) arising from the strong electron-electron correlation effects. He then further predicted that the application of pressure could drive NiO through this transition by reducing the inter-atomic spacing between the Ni ions; this is known as
19 the Mott transition (Mott, Metal-Insulator Transition, 1968). This correlation is important in both phases of the transition.
2.1.4 Mott-Hubbard Transition
The Hubbard model is an approximate model to describe how the interactions between electrons can give rise to insulating, magnetic, and even novel superconducting effects in a solid.
In a solid where electrons can move around, the electrons interact via a screened Coulomb interaction. The biggest interaction will be for two electrons on the same atom. For simplicity, interactions are modeled by a term which is zero if the atom is empty of electrons or has only a single electron on it, but has the value U if the atom has two electrons.
There is no interaction between electrons on different sites. The electron hopping process
(the kinetic energy term) tends to delocalize the electrons into Bloch states and thus is conducive to metallic behavior. The correlated electron-electron interaction tends to localize the electrons into their own atomic states thus making it insulating. The Hubbard model thus can be used to understand the basic properties of correlated Fermi systems including Mott insulator transitions.
As shown in Figure 2.3 the ratio U/W determines whether the system will behave like an insulator (strongly correlated) or a metal (weakly correlated). When U/W < 1, the UHB and LHB overlaps causing an abrupt transition to the metallic state. The Hubbard U is relatively volume independent since it mostly depends on what happens on a single ion. However, the bandwidth
W is sensitive to temperature and pressure. Pressure increases W by reducing the interionic distances, thus increasing the orbital overlap integral t. When the pressure is increased to the point where U/W < 1, a Mott transition occurs. The main physical manifestation of a Mott transition is an abrupt increase in conductivity resulting from the UHB and LHB band overlap. It
20 is often difficult, however, to determine whether an insulator-metal transition is indeed a Mott transition because of the existence of other mechanisms of metallization (Imada, Fujimori, &
Tokura, 1998). Changes in the crystal field surrounding the metal ions in a material sometimes occur as a result of structural phase transitions. These changes often lead to insulator-metal transitions. In a Mott transition, however, the metallization is due to a change in electron correlation and is punctuated by a signature in the local moment on the correlated orbital. In general, metallization due to changes in correlation is accompanied by such signatures. This is because the same strong correlations that lead to the Mott insulator are also responsible for the formation of local moments (Imada, Fujimori, & Tokura, 1998).
Figure 2. 3. Schematic illustration of energy levels for a Mott- Hubbard model at half-filling for U/W > 1. The addition of a non-zero U causes a splitting of the d band into upper (UHB) and lower (LHB) Hubbard bands. (Modified from reference 45).
21 Such insulator-metal transition (IMT) is electronic in nature, which often accompanies an abrupt structural phase transition, yet it can occur without any structural change but instead through smoothly occurring spin crossovers over a wide range of lattice scale.
2.1.5 Pressure – Induced Metallization
The metallization of insulators or semiconductors are common under pressure. As early as 1935, Bernal (Wigner & Huntington, 1935) suggested that all materials should become metallic at sufficiently high pressure. Electrons in insulators under compression lead to greater overlap and, thereby greater interaction among both filled and unfilled molecular orbitals (MOs).
For classical semiconductors, the direct band gap often increases with pressure over a substantial pressure range. And there are indications that in certain metallic structures (Lei,
Papaconstantopoulos, & Mehl, 2007) bands may narrow with pressure.
The Goldhammer–Herzfeld (GH) criterion for metallization (Herzfeld, 1927) is another way to look at metallization. This criterion simply states that an insulator or semiconductor is likely to become a metal when the conditions on the density are such that the bulk polarizability diverges; that is, electrons can be ripped of the atoms or molecules with an infinitesimal perturbation. This argument is based upon the Lorenz-Lorentz or Clausius-Mossotti relation,
[2.1]
where n is the index of refraction, ε is the relative permittivity, α is the molecular polarizability,
Vm the volume per molecule in the solid, NA is Avagodro’s number and
22 R ≡ (4/3πα)NA is called the molar refractivity. Clearly, as R/ V →1, n →∞ and ε→∞; this can
only happen if electrons are no longer bound, as in a metal. Thus, the GH criterion is,
R/ V < 1 → insulating
R/ V ≥ 1 → metallic
Figure 2. 4. The metallization of elements of the periodic classification under standard temperature and pressure conditions. The figure shows the ratio (R/V) for elements of the periodic classification. The shaded circles represent elements for which R and V are known experimentally. The open circles are for elements for which only V is known experimentally and R is calculated. (Edwards & Sienko (1983)).
23 The Goldhammer–Herzfeld theory works remarkably well for many systems. Figure 2.4 underscores the accuracy of the simple GH criterion with respect to the metallic character of elemental solids. Note that as one scans from left to right across the figure, the elements of the periodic table turn from metal to non-metal around columns IIIA – VA just as the R/ V values curve below the dashed line at R/ Vm = 1.
If we define V0 as the ambient pressure volume and Vc as the critical pressure for transition to the metallic state, it is clear that metallization occurs when the relative volume Vc/V0
= R/V0. Xe provides a very good example of this. From Figure 2.3, R/V0 ~ 0.29 for Xe, thus it is expected that Xe should become metallic when compressed to the point where V/V0 ~ 0.29.
According to the measured equation of state of Xe (Jephcoat, et al., 1987), one would expect to reach this relative volume at a pressure of ~ 150 GPa. Indeed this is approximately the pressure where Xe is found to enter the metallic state (Eremets, et al., 2000).
2.2 Electron Correlation
2.2.1 Magnetism at High Pressure
Among various types of electron orders in solids, magnetism takes a special place. The theoretical understanding of magnetism has a long history and continues to present interesting challenges. Furthermore, magnetic fluctuations can couple to the electrons from which the magnetic order first arises, and thus lead to novel electronic states, such as unconventional superconductivity. Magnetism in solids demands interacting electrons. The exchange interactions which lead to magnetic coupling and magnetic ordering of diverse kinds attest to their existence.
2 For example, two electrons at a distance r repel each other via the Coulomb interaction EC = e /r.
24 1/3 -1/3 Since r α V , we have EC α V . Magnetic ordering is then possible only if the Coulomb repulsion of electrons is sufficiently strong relative to their kinetic energy or hopping energy,
-2/3 which varies with V . While both the kinetic energy Ek and the Coulomb energy EC increase as the density (or pressure) increases, Ek increases much more rapidly.
As such, at sufficiently high density the magnetic orbitals of neighboring atoms overlap and thereby the magnetism is suppressed. The degree of orbital overlap can be quantified by the ratio α ≡ RWS/Rmo where RWS was defined by equation 2.2.
The Wigner-Seitz radius is,
1/3 RWS ≈ [3Va/4π] [2.2] where Va = V/NA and Rmo is the radius of maximum charge density for the magnetic orbital (Fig.
2.5).
Figure 2. 5. Schematic of solid at low pressure (left) and high pressure (right). Rc is the radius of the ion
core and RWS is the radius determined by the average volume available per atom in the solid. When RWS ∼
Rc, the localized electronic orbitals of the ions begin to overlap.
25 One ought to expect various material properties to change significantly when the lattice is compressed to the point where ionic cores begin to overlap (RWS ~ Rc) [for more complete discussion see, Ref (Schilling J. S., Magnetism at high pressure, 1984)]. The ratio of these two length scales can be used to describe a wide variety of condensed matter properties. Below we consider three such properties that are all intimately linked to superconductivity: magnetic ordering, which generally destroys superconductivity, metallic versus insulating character and crystal structure, which is a key consideration in both the theoretical approaches to the search for new superconductors.
2.2.2 Spin-Fluctuation and Non-Fermi-Liquid Behavior
Landau theories have been highly successful at describing the properties of metals in terms of the Fermi liquid model. The model predicts certain temperature dependences at sufficiently low temperatures (often <1 K) for physically observable quantities. For example, the specific heat C follows C ~ γT, the magnetic susceptibility χ becomes independent of
2 temperature, and the electrical resistivity ρ behaves as ρ0 + AT . In systems of itinerant fermions, the relevant excitations were identified as 'quasiparticles' which are in a one-to-one correspondence with the single-particle momentum eigenstates of a non-interacting system, but which have a modified mass and a finite lifetime due to the quasiparticle interaction. In metals close to a magnetic ordering transition this interaction can be dominated by exchange of magnetic fluctuations, that is, by the effect of the time- and space-dependent magnetization induced by each quasiparticle on the others (Baym & Pethick, 1991).
While the understanding of the behavior of complex systems with strongly interacting particles is one of the major achievements in modern physics, a growing number of metals have
26 been found to show systematic deviations from the predictions of Landau Fermi-liquid theory.
The most straightforward observation was the occurrence of superconductivity (SC) in heavy
fermion compounds CeIn3 and CePd2Si2 (Mathur, et al., 1998)( Saxena, 2000), where the
antiferromagnetic (AF) order was suppressed to 0 K by the application of hydrostatic pressure.
Such systems are often referred to unconventional SC and subject to discussion of the magnetic
quantum critical point (QCP).
The most plausible scenario for unconventional SC is that the charge carriers are bound
together in pairs by the AF spin fluctuation (Moriya & Ueda, Antiferromagnetic spin fluctuation
and superconductivity, 2003). The incoherent scattering of quasiparticles via magnetic
interactions is then expected to lead to a resistivity of the form
α ρ = ρ0 + AT [2.3]
where ρ0 and A are constants and the exponent is smaller than two, that is, smaller that it is in a
conventional Fermi liquid at low T.
FM FM AFM AFM 3-dim 2-dim 3-dim 2-dim
Table 2. 1. Temperature dependencies for thermodynamic and transport properties from the spin fluctuation theories of non-Fermi-liquid behavior (modified from Ref. 58)
27
The interaction between magnons and conduction electrons in an antiferromagnet contributes to its electrical resistivity along with electron-phonon and electron-impurity scattering. When an energy gap from spin waves (magnons and electrons scattering) is present, where the ground state is still magnetically ordered, a rough temperature dependence of
2 resistivity well below TN is described by ρ = ρ0 + AT + ρsw. Here, the second term is due to scattering between the heavy quasi-particles, and ρsw is the contribution of spin waves, which depends essentially on their excitation spectrum. Usually, this last term leads to temperature dependence stronger than the common Fermi liquid behavior, T2. The resistivity dependence due to electron-spin wave scattering, ρsw = BT/ [1+2T/Δ] exp (-Δ/T) corresponding to a gapped antiferromagnetic spectrum. Therefore the resistivity dependence below TN for the spin density wave (SDW) antiferromagnet can be described by Eq. (2.4) with an energy gap (Δ) of SDW- antiferromagnet and an additional T2 term reflecting Fermi-liquid behavior(Andersen, Crystalline
Electric Field and Structural Effects in f-Electron Systems, 1980)( Dalichaouch, Andrade, &
Maple, 1992).
2 = o + BT/ [1+2T/Δ] exp (-Δ/T) + AT [2.4]
2.3 Electron- Phonon Coupling: Superconductivity
2.3.1 Superconductivity
After the first discovery of superconductivity over a century ago (Tinkham, 1996), the field of superconductivity is now mature with many excellent texts describing the properties of superconductors in great detail (Tinkham, 1996)( Kresin & Wolf, 1990)( Ashcroft & Mermin,
28 Solid State Physics, 1976). Superconductivity occurs when two electrons attract each other to form a pair that undergoes a Bose-Einstein-like condensation. At first glance, this seems to contradict the basic physics law, Coulomb repulsion. This attractive force would not happen for two electrons in a vacuum, but occurs in a medium of crystal lattice which makes the dielectric permittivity negative (Tinkham, 1996)( Kresin & Wolf, 1990). It is not surprising, therefore, that it took almost half a century to develop a basic microscopic theory to explain the nature of superconductivity. The superconducting state is an ordered state of electrons in a system.
The main characteristics of superconductivity are as follows:
1. Zero dc electrical resistivity when the current is below a certain critical value.
2. Expulsion of magnetic field from the interior of the superconductor
(Meissner-Ochsenfeld effect)
The first phenomenon means that a current can flow in the system without decaying, when the temperature of a superconductor is cooled below Tc. That resistivity is actually zero rather than being very small can be demonstrated straightforwardly by measuring the decay of a magnetic field induced by a supercurrent running in a loop. If the resistance were finite then the field would gradually decay over time. In fact, it is found that at low enough temperature, the supercurrents persist for as long as one measures (Kresin & Wolf, 1990). The Meissner-
Ochsenfeld effect was first observed in 1933 (Meissner & Ochsenfeld, 1933). The magnetic properties of superconductors are different from that of ordinary metals with perfect conductivity. The Meissner-Ochsenfeld effect demonstrates that superconductors are not only perfect conductors but also perfect diamagnets (with susceptibility, χ = −1, in MKS units). This means that the magnetic field within a superconductor is zero regardless of whether the field is
29 applied before or after the superconductor is cooled below Tc. This follows from Maxwell’s equation, that is, B cannot change with time in the interior of a perfect conductor. This is in contrast to the expectation if superconductors were merely a perfect conductor and is the piece of evidence that proves superconductivity is a phase of matter in the thermodynamic sense.
The specific heat capacity is the main experimental finding which contributes to the understanding of the nature of superconductors. For a normal metal, the specific heat has a linear temperature-dependent term arising from electronic excitations and a cubic term from lattice vibrations. At low temperatures, it is mostly the electronic term that contributes. The transition to the superconducting state is accompanied by a quite drastic change of the electronic contribution to the heat capacity. With decreasing temperature there is a sharp jump of the heat capacity of the superconductor at Tc, below which the heat capacity decays exponentially to zero. The change in the entropy from the normal to superconducting state is small enough to conclude that only a small portion of the conduction electrons participate in the ordered superconducting state (
Ashcroft & Mermin, Solid State Physics, 1976). Alternately, ultrasonic attenuation in superconductors is also used to confirm the existence of an energy gap in superconductors. A superconductor absorbs the sound wave more weakly than a normal metal would. At absolute zero temperature, there is no absorption at all (Kresin & Wolf, 1990). The values obtained from ultrasound attenuation measurements are in excellent agreement with other direct measurements like infrared spectroscopy.
2.3.2 The Barden Cooper Schrieffer (BCS) Theory of Superconductivity
According to F. London (London, 1938), the infinite conductivity in superconductors could be explained in terms of the Bose-Einstein condensation of Bosonic charge carriers.
30 However, it was not clear at that time how such a situation could arise given that the charge carriers in metals are electrons (Fermions). In 1946, R. A. Ogg, Jr. suggested that superconductivity could be explained by the Bose-Einstein condensation of trapped electron pairs (Ogg, Bose-Einstein condensation of trapped electron pairs. Phase seperation and superconductivity of metal-ammonia solutions, 1946)( Ogg, Superconductivity in solid metal- ammonia solutions, 1946). Electron pairs would have integer spin and thus be able to undergo
Bose-Einstein condensation. In the same paper, Ogg reported superconductivity at 180 K in quenched metal-ammonia solutions. Unfortunately, no other researchers were able to reproduce this spectacular result. Consequently, this early suggestion by Ogg that superconductivity could be explained by Bose-Einstein condensation of bound electron pairs was largely ignored. The main difficulty in coming up with a microscopic theory for superconductivity is in understanding the nature of the interaction responsible for this occurrence. However, in 1950 Frohlich proposed that the electron coupling in superconductors is mediated by positive ions of metallic lattice
(phonons) (Frohlich, 1950). At nearly the same time, an experimental evidence of the isotope effect when the Tc of mercury was found to depend on the atomic weight of the ions (Reynolds,
Serin, Wright, & Nesbitt, 1950)( Maxwell, 1950). Since mercury has different stable isotopes, it is more suitable to study the isotopic effect on Tc. They found that different isotopes of mercury displayed different superconducting transition temperatures, with the Tc of the lighter isotopes being slightly higher than that of the heavier isotopes. This key experimental observation indicated that the electron pairing must be occurring through some interaction with the lattice vibrations (phonons). The fact that electron-phonon scattering is one of the principal mechanisms of resistance was for many years a stumbling block, making it extremely hard to imagine that the same interaction can lead to a vanishing resistance. Using the idea of an electron-phonon
31 coupling, the seminal paper of Bardeen, Cooper and Schrieffer finally described a complete microscopic theory of superconductors known as the BCS theory (Bardeen, Cooper, &
Schrieffer, 1957). There are, however, superconductors that do not fit into the framework of the
BCS theory, namely high-Tc cuprate superconductors.
To understand the basic idea of how a phonon mediates electron coupling, consider a free electron, passing through the lattice. It attracts the positive cations causing a vibration of the lattice (phonon) as illustrated in the Fig. 2.6. As a result localized region of excess positive charge builds up. Because most of the massive cations move slower than the electrons, this region of excess positive charge remains for some time after the electron has moved on.
Sometime later, a second electron can be attracted to this same region of excess positive charge.
This leads to an effective attractive interaction between the two electrons causing them to “pair up” into a so-called Cooper pair. Note that the spacing between the two electrons in the pair is typically several hundred or a thousand times the interatomic spacing. The interaction is retarded since the attractive interaction occurs via phonons which travel with finite speed (while the
Coulomb repulsion between the electrons is nearly instantaneous). The interaction need only to be attractive in some (possibly very small) region of space-time, in order for the electrons to pair up.
32
Figure 2. 6. Schematic illustration of the electron-phonon coupling mechanism. The small central dot with minus sign shows an electron and the arrow shows the path of the electron. Springs indicate restoring force bringing the cations back to their equilibrium positions.
In the limit of weak electron-phonon coupling, the BCS theory predicts the following relationships. The critical temperature for the transition to superconductivity in zero magnetic fields is given by
[2.5]
33 where kB is the Boltzmann constant, is the density of states at the Fermi level, is the
Debye frequency and is the net attractive potential between electrons. The density of states at the Fermi level appears because only electrons within ~ of the Fermi level participate in the formation of Cooper pairs. Electrons deep within the Fermi sea cannot pair because there are no nearby unoccupied states for them to scatter into (Pauli blocking). Because it takes a finite energy to break apart a Cooper pair, an energy gap appears in the electronic excitation spectrum.
The energy gap (2 ) as a function of temperature near Tc is given by
[2.6]
The energy gap at zero temperature yields the famous BCS result (Ashcroft & Mermin, Solid
State Physics, 1976)
[2.7]
BCS also calculated the temperature dependence of the critical magnetic field (Hc). The critical field above which superconductivity is destroyed is given approximately by
[2.8]
where Hc is the critical field at temperature T and H0 is the critical temperature at T = 0K.
For the critical temperature, an empirical expression for intermediately strong interaction was found by McMillan ((McMillan, Transition Temperature of Strong-Coupled Superconductors,
34 1968), taking into account not only the strength of the interaction, but also the repulsive screened
Coulombic interaction. The McMillan equation is given by
[2.9]
where is the Coulomb pseudo potential which takes into account the screened Coulomb repulsion between the electrons and is the average phonon frequency. This equation is valid for intermediately strong coupling (λ ≤ 1.5).
2.3.3 High Temperature Superconductivity
High transition temperature superconductors represent a new class of materials which bear extraordinary superconducting and magnetic properties and great potential for wide-ranging technological applications. The discovery of superconductivity at ~30 K in the La-Ba-Cu-O system by Bednorz and Müller in 1986 (Bednorz & Müller, 1986) caused an explosion of interest in high temperature superconductivity. These initial developments rapidly evolved into an intense worldwide research effort and as a result, Tc has increased steadily since 1986 to its present value of ~133 K (above the boiling point of liquid nitrogen) for a compound in the Hg-
Ba-Ca-Cu-O system (Schilling, Cantoni, Guo, & Ott, 1993) (Chu, et al., 1993). When this compound (HgBa2Ca2Cu3O8) is subjected to a high pressure, the Tc onset increases to ~164 K
(more than half way to room temperature) at pressures ~30 GPa (Nuñez-Regueiro, Tholence,
Antipov, Capponi, & Marezio, 1993)( Putilin, Antipov, Chmaissem, & Marezio, 1993). The dramatic increases in Tc are shown in Fig. 2.6. Over the years of extensive research on this subject, significant progress has been made on both the fundamental science and technological applications fronts. For example, the symmetry of the superconducting order parameter and the
35 identity the superconducting electron pairing mechanism appear to be on the threshold of being established, and prototype superconducting wires that have current carrying capacities in high magnetic fields that satisfy the requirements for applications are being developed.
However, the cause of the cuprate superconductivity has remained a mystery. The mechanism behind “low transition-temperature” superconductivity of most sp-metals has been known in terms of the BCS theory discussed in the previous section. But, the electron-phonon mechanism cannot explain the Cooper pairing found in the high-temperature superconducting
(high-Tc) cuprates. So what makes the pairing or is there even a pairing “glue” in high-Tc superconductors? Many ideas have been suggested for how high-temperature superconductors work. Among those ideas, an electron coupling to magnetic excitations (instead of phonons), has been considered as the pairing “glue” in cuprates. The copper atoms in the cuprates have electrons with a quantum mechanical property called “spin”. The electron with spin can be thought of as a tiny bar magnet, with north and south poles. In cuprates, the spins can arrange themselves such that the spin on each adjacent copper atom is pointing in the opposite direction, i.e. alternating north and south poles. This is called an antiferromagnetic state of matter, and at temperatures above absolute zero such a state is subject to thermal fluctuations of the atomic spin direction. It is then theoretically possible for the conduction electrons to couple to these fluctuating spins and form Cooper pairs, somewhat in analogy to how Cooper pairs are formed by the coupling between phonons and electrons (Moriya & Ueda, Spin fluctuations and high temperature superconductivity, 2000). In other words it can simply be described in terms of the emission and absorption of waves of the electron spin density: that is, a type of bound state that arises because of an effective spin–spin interaction reminiscent of one of the oldest known forces
(magnetically mediated superconductivity).
36
Figure 2. 7. The evolution of Tc with time from Proc. HTS Workshop on Physics, Materials and Applications, World Scientific, Singapore, 1996.
2.3.4 Pressure Effects on Superconductivity
The primary effect of a change in temperature is to modify the occupation of the energy levels in a system while the primary effect of pressure application is to modify the energies of the levels (Bundy, Hibbard Jr, & Strong, 1960). Thus temperature and pressure studies provide complementary information. Since the critical temperature of superconductor depends on both lattice and electronic properties, one in general expects pressure to have a profound, and possibly complicated, effect on Tc.
37 Therefore to understand the effect of pressure on the superconducting transition temperature, it is important to analyze the pressure dependence of Tc (Schilling,2006).
Differentiating the McMillan equation (2.9) with respect to volume gives:
[2.10]
where ≡ / is the Grüneisen parameter, ≡ is the Hopfield parameter, Δ ≡ −1.04λ/(λ − μ (1 + 0.62λ)), and ᴧ ≡ [1.04λ(1 + λ)(1 − 0.62μ ]/[λ −
μ (1 + 0.62λ)]2. It is assumed that the effective electron-electron Coulomb repulsion μ is pressure independent as compared to the electron-phonon coupling parameter λ (Seiden, 1969).
Further simplification of the term yields −1.04λμ [1+0.62λ(0.62μ − 1)]/[λ − μ (1
+ 0.62λ)]2. μ is of the order of 0.1 and the electron-phonon coupling is less than 1.5 for moderately strong interactions (Hamlin, Tissen, & Schilling, 2007), making the term negative. Hence, the pressure dependence of Tc is mainly determined by the volume derivative of the Hopfield parameter and the Grüneisen parameter. Several groups have calculated η from band structure under pressure (Evans, Ratt, & Gyorffy, 1973) (Kmetko, 1971) (Anderson,
Papaconstantopoulos, & McCaffrey, 1973). Although the value of η changes under pressure, its volume derivative tends to remain somewhat constant. For instance, for many of the transition
metals, the term lies between -3 to -5. This large negative value in transition metals is
believed to relate to the broadening of the d-band under pressure (Evans, Ratt, & Gyorffy, 1973).
38 If the lattice term γ is between 1.5 and 2.5, then the pressure dependence of Tc will be positive.
This positive value of dTc/dP, however does not apply to the majority of transition metals which show either a decrease of Tc with pressure or a complex dependence. The complex nature of Tc could be due to the pressure effects on electronic structure, pressure-driven charge transfer from s to d bands, or a pressure-induced structural phase transitions (Schilling,2006) (Ross &
McMahan, 1982). For many simple metals, Tc decreases with pressure, mainly due to the weakening of the electron-phonon coupling. This weakening is itself caused due to phonon
stiffening. Electronic structure calculations for this class of materials show is smaller,
around – 1 (Evans, Ratt, & Gyorffy, 1973). However, there are some exceptions to this general trend. Neaton and Ashcroft have predicted that under sufficiently high pressure the simple metals lithium (Neaton & Ashcroft, Pairing in dense lithium, 1999) and sodium (Neaton & Ashcroft, On the constitution of sodium at higher densities, 2001) exhibit quite complex electronic behavior due to the overlap of the ionic cores. This in conjunction with a lattice softening seen especially in high-pressure phase of fcc lithium yields an increase of transition temperature with pressure
(Shimizu, Ishikawa, Takao, Yagi, & Amaya, Superconductivity in compressed lithium at 20K,
2002) ( Struzhkin, Eremets, Gan, Mao, & Hemley, 2002). Furthermore, among the s, p metals which exhibit a similar anomalous electronic behavior are sulfur and phosphorus. Sulfur becomes metallic above 85 GPa with a superconducting transition temperature as high as 17 K at
165 GPa (Hanfland, Syassen, Christensen, & Novikov, 2000), whereas phosphorus has a Tc value of 18 K at 30 GPa (Shirotani, et al., 1988).
39 Chapter 3
Experimental Methods
3.1 High Pressure Techniques
Pressure is the force divided by the area to which this force is applied and this definition sums up the underlying approach to designing high-pressure equipment. The basic considerations are: (i) how the force is generated, and (ii) how the surface is defined. Use of two opposed anvils is by far the most common way of generating the load. In the early days, pressure devices used tapered “anvils” made of hard metal alloys such as steel or tungsten carbide. However, these devices were large and the anvils opaque, preventing the vast number of characterization methods such as optical spectroscopy and x-ray diffraction.
The first diamond anvil cell (DAC) was made by Weir et al.( Weir, Lippincott, Van
Valkenburg, & Bunting, 1959) to perform infrared spectroscopic measurements, but the widespread use started only from the early 1970s on. By that time, the ruby fluorescence method had been introduced to determine the pressure in-situ. Since then, the DAC has remained the only device for exerting ultra-high static high pressure. The advantages of this technique are several; Diamond is the strongest material known, and is transparent to a wide range of electromagnetic waves from x-rays to the far infrared, which makes possible to use the diamond anvil cell with a wide range of in-situ laser spectroscopic methods and synchrotron x-ray diffractions. Combining with laser-heating methods, the DAC is capable of achieving the pressure-temperature condition at the center of Earth.
40 Figure 3.1 illustrates the basic construction and operation of the DAC. The two brilliant cut diamonds with flat tips (culets) of typically 0.3 mm in diameter squeeze on a metallic gasket, which has a hole of typically 0.1 mm in diameter. The hole is filled with the sample and a few particles of ruby crystals for pressure measurements. Traditionally, anvils of either 8 or 16 facets are used. For anvils with a flat culet of diameter d, the maximum pressure Pmax which can be
“safely” obtained is given by Pmax = 10/d (d in mm Pmax in GPa) (Debessai, Ph. D. Thesis, 2008).
This relation is correct for gems of approximately 60mg (0.3 carat) and table size of 3mm, and between ~ 5 to 50GPa. The majority of diamonds used in DACs are naturally gem quality
(ranging from 0.16 to 0.5 carat) and brilliant cut, which contain impurities. These gems can be classified as type I and type II. Type I contains a small amount of nitrogen, which gives an intense infrared absorption between 1100 and 1500 cm-1. Type II diamonds contain no nitrogen.
The luminescence of diamonds anvils can be a serious problem for Raman measurements. The diamonds are glued onto a backing material with Stycast (2850 FT Black).
Pressure is exerted when the opposing anvils are pushed together. The diamond anvils sit atop a backing material (seats). Backing seats are necessary to transfer the load, typically 0-5kN, from the metallic load frame onto the anvils. Without the backing plates the anvils would indent the metal contact surface. Backing plates are therefore made of hard materials with a compressive strength well beyond those of metals. These seats are typically made from tungsten carbide
(WC). For the X-ray spectroscopy, beryllium (Be and pressed cubic boron nitride (c-BN)) are also used. With 0.1 mm culet size the application of 1000kg (or 1 ton) generates 1 Mbar of the sample. There are a few transparent hard materials that can replace diamond for certain experiments. Those include sapphire, moissanite and zirconia.
41 The main consideration to reach Mbar pressure regime lies in the quality and alignment of the diamond anvils. The most delicate region of the diamond is the culet area(Adams, Christy, &
Norman, Optimization of diamond anvil cell performance by finite element analysis, 1993) (
Adams & Shaw, A computer-aided design study of the behavior of diamond anvils under stress,
1982). The maximum pressure attained in the DAC depends on the culet diameter. Eremets
(Eremets M. , 1996) suggested that a culet diameter of 0.6 mm works below 50 GPa, while a diameter of 1 mm can only reach 20 GPa. Using two flat anvils of 0.3mm can generate the maximum pressure of 100 GPa, for pressures above 100 GPa, even smaller flats often in beveled anvils are used (Mao & Bell, High-Pressure Physics: Sustained Static Generation of 1.36 to
1.72Megabars, 1978).
The main drawback of beveled anvils is the appearance of circular ring cracks at the culet when pressures near or above 1 Mbar are released. To prevent this, R. Boehler (Boehler, Private
Communication) used a fine diamond powder in between the metal gasket and the diamonds.This tends to overcome the cold welding of the gasket to the diamond, allowing pressure to be released from 130 GPa without ring cracks appearing. In the present research, a
0.5 mm culet is used as high as 50 GPa, a 0.3 mm culet is used to 98 GPa. For pressures above
100 GPa, a 0.18 mm culet beveled at 7o out to 0.3 mm and 0.1 mm culet beveled at 7o out to 0.3 mm are used. The highest pressure achieved in the present study is 204 ± 8 GPa using a pair of
0.18 mm culet beveled anvils. Materials under pressure can be studied either under uniaxial strain, where the sample is directly pressed upon without any pressure medium, or under hydrostatic (quasi-hydrostatic) conditions, where a pressure medium is used. In this thesis work, experiments under pressure have been made both with and without a pressure medium.
42
Figure 3. 1.Schematic view of the diamond-anvil cell (DAC). The DAC is composed of two opposing diamond anvils. Between the culets is a metal gasket with a hole drilled down the center. A sample is placed inside this hole, typically along with a pressure transmitting medium and a pressure calibrant (in this case a ruby chip). The diamonds are supported by seats typically made of tungsten carbide (WC).
43 3.1.1 Types of Anvil Cells
There are many types of diamond anvil cells; listing a few includes the piston- cylinder
Mao-Bell cell, Merril-Bassett-type Diamond cell and Boehler-type cell (Fig. 3.2). The most important consideration designing any DAC is that diamond culets must remain as close to parallel as possible in order to achieve the maximum possible pressure. Early designs used hemispherical seats that allowed independent adjustment of each diamond anvil to correct for imperfections in the seat construction. However, modern machining techniques have rendered this all but obsolete. Most cells now employ tapered cylinder seats made of WC. Another equally important consideration is the diamond culets must be aligned and stay aligned as the load is increased. To ensure stable alignment of the diamond culets, the difference in diameter between piston and the cell bore should be less than a few µm. Over time the piston and cylinder are gradually worn away, resulting in a poor fit between the piston and cylinder. Although there are many types of DACs are in existence, for the highest pressure, the piston-cylinder style DAC is considered the most effective.
Almost all the experiments described in this dissertation were carried out using piston- cylinder type membrane diamond anvil cell designed by Professor Yoo. The membrane DAC
(Figure 3.3), a pressure membrane assembly is screwed onto the DAC, replacing the manual pressure adjusting screws. A metered amount of inert gas is introduced into a chamber, causing the membrane to expand and tightening the cell.
44
Figure 3. 2. (a) Merrill-Bassett-type diamond-anvil cell (DAC) (b) Symmetric piston-cylinder diamond anvil cell (c) Boehler-type (plate) diamond anvils cell.
45 This method is not only very precise and systematic, but it also allows for remote pressure application. This is a major advantage when performing synchrotron experiments where the sample must be enclosed inside a hutch while being exposed to x-rays. The membrane loading has the advantage that pressure may be changed at any temperature above the melting point of the loading gas (helium). Mechanical loading methods often require that the clamp be removed from the cryostat in order to change the pressure. The applied force is determined very accurately by the gas pressure applied to the membrane. A needle valve allows fine control of the pressure applied to the membrane. A reservoir volume at room temperature insures that the pressure applied to the membrane changes by less than 1% between room temperature and 5 K.
3.1.2 Gasket materials
The use of good gaskets is essential for achieving the maximum possible pressure of
DAC. The gasket reduces the strain in diamond culets and makes it possible to load the sample with a pressure medium. Metallic gaskets for use in high pressure experiments were introduced by Alvin Van Valkenburg, in 1962 (Valkenburg, 1962). The ideal gasket material should have high strength and high ductility, as well as be chemically inert and non-magnetic and non- superconducting for magnetic measurements.
Generally ductility decreases with increasing hardness. If the gasket’s ductility is too low, it can suffer brittle failure under pressure, resulting in destruction of the diamonds. On the other hand, if the gasket is too ductile with low hardness, then the gasket is unable to contain extreme pressures. The magnetic response of a gasket on cryogenic is also important in ac susceptibility measurements. A gasket that has a very steep magnetic response will make detection of superconductivity from a small sample very difficult.
46
a
Figure 3. 3. The membrane diamond anvil cell of Professor Yoo design employed in the present study: (a) the cross sectional view, (b) the integrated view and, (c) the exploded view of piston and cylinder.
47 Moreover, the magnetism can interfere with the superconductivity of the sample. If a gasket becomes superconducting, observation of superconductivity from a sample will be impossible, as the gasket signal is at least three orders of magnitude larger than that of the sample. Resistivity measurements do not put any restriction on the superconductivity of the gasket as the sample is electrically insulated from the gasket. Metal foils (Re) with thickness ~200 μm were used for all the experiments in this dissertation as the gasket material. With 51 HRC (HRC is the Rockwell c-scale hardness unit. 1 HRC = 2.16 Tonnes/in2), it is superior in hardness and also has low magnetic response. Rhenium superconducts at 1.4 K (Hulm & Goodman, 1957) under ambient pressure, but under strain Tc increases to ~4 K, restricting the measurement of superconductivity to temperatures above this temperature. Our low temperature system can only reach 4.5K. The foils are first pre-indented to a thickness dependent on the diameter of the diamond culet (see
Fig.3.1). The pre-indented thickness should be approximately 1/9 of the culet diameter and 1/3 of the hole diameter (Debessai, Private Communication, 2009). The hole is drilled through the center of the pre-indented area by electro-discharge machining (EDM). Depending on the sample and pressure medium, the initial diameter of the hole should be adjusted so that it reaches 1/3 of the culet diameter at high pressure. When using highly compressible He pressure medium the initial hole diameter should be 1/2 the culet diameter (Debessai, Private Communication, 2009); at high pressure the hole diameter then shrinks to ~ 1/3 of the culet diameter. This is also the case when one uses no pressure medium, where usually, as much as 70% of the cell volume is initially empty.
Smaller diamond culets allow higher pressures with lower applied force. Many of the rhenium foils we used worked very well as gaskets, but some of the foils were highly granular and displayed significant cracking on pre-indentation, making them unsuitable as gaskets. Under
48 magnification, small microcracks on the order of 100 μm long are visible in the rhenium foils that develop cracks during pre-indentation. Pre-indented gaskets should always be examined carefully for cracks before use.
3.1.3 Pressure Media
Bridgman stated, “The most important immediate problem of technique in this field is to find methods of producing stress systems which are truly hydrostatic” (Bridgman, Solid under pressure, 1963) except carbon disulfide and carbonyl sulfide the other materials examined here were all in the form of a powder or polycrystalline solid. In general, when loading a solid sample, it is necessary fill the remaining space with a pressure medium (a soft and inert material) so that the bidirectional stress from the diamonds anvils is distributed relatively homogeneously onto the sample. An ideal pressure-transmitting medium would have zero shear strength
(liquids). But most of the liquids solidify at relatively low pressures. However, 4:1 mixture of methanol and ethanol remains a liquid up to 10 GPa (Piermarini, Block, & Barnett, 1973) at room temperature.
One potential drawback of this mixture is a glass transition above 10 GPa which allows the buildup of large shear stresses on the sample. Some samples, however, are very sensitive to non-hydrostatic stresses (GeS for example). In these cases, a medium that stays quasi-hydrostatic at higher pressures is required. The noble gases make very good hydrostatic pressure media because their solid phases are still very soft. They are also chemically inert and do not readily fluoresce under Raman laser excitation. However, they are gases at ambient conditions.
Therefore we loaded as pressurized gas using high-pressure gas loader (Fig. 3.4) also designed
49 by Professor Yoo at WSU. The pressures required to reach liquid density at ambient temperature are around 28,000 psi. We used mostly Helium as the pressure medium in this work.
Figure 3. 4. The high pressure gas loader
3.1.4 Pressure Determination
The history of high-pressure research reveals that much early effort was devoted to the development of practical and accurate methods for measuring the applied pressure (Bridgman,
The Physics of High Pressure, 1949). Many traditional manometers could not be adapted to diamond anvil cells, and the applied pressure was only estimated based on a rough calculation of load-vs-area or from the known equation of state of the pressure standard. However, the unit cell
50 volume can only be obtained through x-ray diffraction. This method is not useful for optical spectroscopy. Emission spectroscopy offers a more convenient way of measuring pressure without the need of an x-ray diffractometer. The luminescence spectrum of ruby (Al2O3 doped with Cr3+) exhibits exceptionally strong, sharp peaks that display a large, linear red-shift under pressure (Forman, Piermarini, Barnett, & Block, 1972. Piermarini et al. (Forman, Piermarini,
Barnett, & Block, 1972) published the first calibration of the R1 fluorescence line of ruby (up to about 19.5 GPa) in 1975 using the known EOS of NaCl based on previous dynamic shock measurements. Ruby fluorescence, allowing the pressure measurement with only a small ruby chip (1-2 μm) placed in the sample chamber. The pressure-induced shift of the R1 fluorescence line, ΔλR1, was later calibrated to almost 1 MBar by Mao et al. (Mao, Xu, & Bell, Calibration of the Ruby Pressure Gauge to 800 kbar Under Quasi-hydrostatic Conditions, 1986).
Recently, evidence has accumulated that the earlier ruby pressure scales systematically underestimated pressures in the upper pressure range and new calibrations have been suggested
(Holzapfel, 2005) (Silvera, Chijioke, Nellis, Soldatov, & Tempere, 2007). At this time the most comprehensive and accurate pressure calibration appears to be that of Chijioke et al. (Silvera,
Chijioke, Nellis, Soldatov, & Tempere, 2007), which takes into account the results of many hydrostatic calibrations. Indeed the simplicity of the ruby luminescence method for in situ pressure calibration is without question a contributing factor to the widespread application of diamond anvil cell techniques and, as such, was the subject of an extensive review by Syassen in
2008 (Syassen, 2008). Pressure versus the wavelength of the R1 line, λ is given by, where λ0 is the wavelength of the R1 line at ambient pressure.
[3.1]
51 The ruby luminescence method also allows one to qualitatively determine the degree of hydrostaticity in the sample chamber by observing the line widths of the R1 and R2 lines. Under hydrostatic compression the R1 and R2 lines remain well resolved and pressure measurement is straightforward. The R1–R2 separation has been shown to be strongly dependent on the presence of any deviatoric stresses within the sample chamber.
In experiments where non-hydrostatic conditions are being investigated it is therefore common to see these spectral lines overlapping, and the uncertainty in the pressure measurement is significantly increased. A comparison of the ruby fluorescence spectra obtained under hydrostatic and quasi-hydrostatic conditions can be found in Fig. 3.5. This is a qualitative measurement, however, and a more informative method of determining the condition in the sample chamber would involve placing multiple pieces of ruby at the center of the sample and near the edges to determine the pressure gradient across the sample. Because of a small energy difference between the R1 and R2, the intensities of the two are roughly similar in magnitude at
-1 room temperature (~200cm ). As temperature is decreased, the population of the R2 states
(higher energy) becomes small compared to that of the R1 state (lower energy). This results in a substantially greater intensity of the R1 line at low temperature, with the R2 line nearly disappearing at liquid He temperatures. The temperature dependence of the R1 line was found by
Buchsbaum et al. (Buchsbaum, Mills, & Schiferl, 1984) to be given by
[3.2]
-1 where (t) is given in cm , t = T/(300K).
52 Above 1 Mbar, several effects make it difficult to measure the ruby lines (Syassen, 2008).
For example, the absorption band of ruby line shifts out of the laser excitation line (typically 514 nm), greatly decreasing the intensity of the R1 and R2 lines. Above 120 GPa, the diamond itself begins to fluoresce, giving rise to a broad background with increased intensity at shorter wavelengths. The increasing width of ruby line at high pressures makes it difficult to resolve. A convenient alternative to the ruby luminescence is to use the Raman spectrum of the diamond anvil to determine pressure. The first-order Raman spectrum of diamond consists of a single peak (vibron) located at 1333.1 cm−1 at room temperature, shifting slightly to 1333.3 cm−1 at 15
K (Syassen, 2008). The pressure throughout the anvil varies from zero at the table in the optical port up to the maximum pressure at the center of the culet. Since the diamond vibron shifts monotonically to higher frequency under pressure, the high-frequency edge of the anvils Raman spectrum gives the pressure at the center of the culet where the sample is located. The most recent calibration of the high-frequency edge of the diamond Raman spectrum of the diamond anvil is that of Akahama et al. (Akahama & Kawamura, Pressure calibration of diamond anvil raman gauge to 310 GPa, 2006) up to 310 GPa using the equation of state of platinum as a standard and found that the calibration is nearly independent of the gasket material, sample or pressure medium. They found that the pressure is given by
[3.3]
−1 where =1334 cm , =547 GPa and =3.75. The diamond vibron was used as the pressure standard in this work above Mbar pressure. It’s useful in the case of studies such as resistance which often use no pressure medium; in this situation large pressure difference may exist between the sample and ruby if they are not directly on top of each other.
53
R1
R2
(a.u.) Intensity
2 GPa 20 GPa
690 695 700 705 Wavelength (nm)
Figure 3. 5. The shift of ruby R1 and R2 fluorescence lines for sample of CS2 at 2 GPa and 20 GPa
3.1.5 Low Temperatures
To obtain low temperatures, we used a closed-cycle refrigerator (ColdEdge-SDRK-408D), custom designed for low vibration and for use with our membrane-DAC, and which has two stages to cool down the cell to liquid He temperature (a photograph of the low-temperature system is shown in Fig. 3.6). The way the refrigerator operates is by first compressing helium gas to about 300 psi and then allowing this compressed gas to expand via a two-stage cold head.
The cold head uses helium gas and consists of two physically separated stages for low vibration,
54 providing cooling to 25-45 K at the first stage and to 3.5-4.2 K at the second. A small amount of helium (less than 1 psi) is introduced to fill the space between the two stages for heat exchange.
Temperature can be controlled by running a compressor and heaters that are placed around the cold head or in the sample space. Lower temperatures can be reached by pumping on the sample space. The coldest part of the cryostat is 5 cm above the top of the pressure cell. Two thermometers are placed at the top and the middle of the DAC to measure the sample temperature. The difference between these two points is less than 1 K. While warming up, a temperature gradient of 50 mK can be maintained between the top and middle thermometers which are around 3 cm apart in the He-gas pressure system.
Cryost Lock-in at Amplifier
micro-Raman
Setup
Figure 3. 6. Low temperature system for Raman, resistivity and susceptibility measurements.
55 3.2 Optical Spectroscopy at High Pressure
Optical spectroscopies, including Raman and infrared, have been major tools for many decades, to investigate the physical and chemical properties of molecules under high pressure.
Raman and IR spectroscopies probe characteristic molecular vibrations, providing direct information on inter-molecular interactions, chemical bondings, and local structures. On the other hand, these interactions depend on the inter-atomic distances, and therefore vibrational spectroscopies also provide an indirect probe of the pressure-induced microscopic structural changes and therefore reveal phase transitions. The vibrational spectroscopies provide a unique tool to unveil the unknown structure of new materials and are commonly used in investigation of the phase diagram of solids.
3.2.1 Micro-Raman Spectroscopy
The vibrational modes involving the internal and external degrees of freedom of the molecules, in molecular crystals, are usually classified as vibrons and lattice phonons, respectively. Raman scattering probes the time fluctuations of total electric polarizability driven by the different modes. This phenomena first observed by Indian physicist Chandrasekhara
Venkata Raman who awarded the 1930 Nobel Prize in Physics for his work on the scattering of light in liquids and gases. By chance, he discovered that incident monochromatic light passing through certain materials was shifted to lower energy, an effect which becomes known as the
“Raman effect”. The Raman scattering is an inelastic scattering process. The monochromatic lights with energy hν0 of the incident beam are sufficient to excite vibrations or rotations of the atoms or molecules in the solid around their equilibrium positions. Every periodic solid has a
56 certain set of possible vibrations or rotations that can be excited, which are related to the symmetry of the crystal. The incident photon (if it is not scattered elastically – Rayleigh scattering) will excite the atom or molecule to a virtual energy state (which is lower in energy than the lowest unoccupied electronic state), immediately followed by de-excitation and emission of a photon (see Fig. 3.7). In the case of Stokes scattering, the emitted photon is of lower energy than the incident; the energy difference being equal to the energy of the particular vibration or rotation excited in the solid (hν0 – hνm). If the atom or molecule is already in an excited vibrational state, Anti-Stokes scattering occurs, where the emitted photon is of a higher energy than the incident, is possible (hν0 + hνm). The intensity of emitted photons is plotted as a function of wavelength shift from the elastic line, which is measured in units of wave number.
Figure 3. 7. A schematic diagram of the Raman scattering process
57 3.2.1 Micro-Raman Set-up
In this section we will briefly discuss the main aspects of Raman set-up. Because of the small sample volume, to obtain Raman spectra in DAC experiments require microscope optics to not only focus the incident beam down below the sample size but also to collect the Raman scattered light. Figure 3.8 shows a schematic diagram of the con-focal micro Raman set-up used in this work employed with DAC. A lasers such as an Ar+ ion laser or a Nd:Yag solid state laser is typically used as the excitation source. The Raman scattering intensity goes as ~ 1/λ4 where λ is the excitation wavelength. Thus, the Raman signal can be increased by moving toward shorter wavelength or higher energy. Yet, the availability of different excitation lines is also crucial for a number of reasons. It allows one to discriminate between Raman and fluorescence peaks when new, unknown materials or phases are produced at high pressure. In this work, 514nm laser line was used. The output beam at 514.5nm has very low divergence (0.5mrad) and for our purposes is considered collimated (Spectra-physics Stabilite Series Laser Beam Specifications, 2001). In order to obtain a micro-focused laser beam, it is necessary to expand the laser beam first to make a relatively large diameter collimated beam. Then, using a high magnitude objective lens, the laser beam is focused onto the sample. This stems from the relationship that beam-waist, w, of a
Gaussian beam of diameter D focused by a lens of focal length f is given by the expression w =
1.27 λ f/ D. Therefore both a shorter focal length objective and a larger diameter beam will produce a smaller beam-waist. In this study, we used a 5x beam expander to expand from the initial laser beam diameter of 1.4mm to ~8mm beam (Spectra-physics Stabilite Series Laser
Beam Specifications, 2001). Then we used a Mitutoyo infinity corrected 20X microscope objective, with a large working distance of 32.0 mm to focus the beam to an approximate spot
58 size of w ~ 3 μm at the sample and to collect the Raman scattering signals in a coaxial, backscattering configuration.
L2 L1
Figure 3. 8. A schematic diagram of the high throughput Raman spectroscopy system used in this work.
Also, we used a holographic bandpass cube (Kaiser Optical Systems, Inc.) to diffract the incoming laser down the axis of the main objective. The configuration allowed the selection of different laser lines by rotation of the mirror/cube assembly. The bandbass cube also removed the laser plasma lines and much of the Rayleigh scattered light from the sample.
Diamond fluorescence is always a problem in Raman measurement. We usually used low fluorescence diamonds, but not always sufficient enough, in reducing the background during optical spectroscopy experiments at high pressure. Hence, a spatial filter (con-focal arrangement) was used to discriminate against diamond fluorescence. This consisted of a pair of achromatic
59 lenses (L1 and L2 in Fig. 3.8) of focal lengths f, placed a distance 2f apart to preserve collimation. An adjustable aperture was then placed at the focal point between L1 and L2. Light coming from in front of and behind the object plane, i.e. fluorescence from the diamond anvils, will not be in focus. These non-parallel rays of light are focused either behind or in front of the aperture. In this way, most of the light entering the microscope objective, not emanating from the sample, is blocked by the aperture. A smaller aperture rejects more stray light at the expense of sample signal. The spatial filter was positioned before the flip mirror, making sure the image of the sample and aperture are in focus at the same time. The aperture size was set by closing the aperture until only the sample region we wish to probe was visible in the CCD image. The notch filter is essential to remove the quasi-elastic Rayleigh component of the scattered signal which, otherwise, overwhelms the weak, inelastic signal.
3.3 Angle-Dispersive X-ray Diffraction
X-ray diffraction (XRD) technique is the primary technique for the determining the crystal structure. When an x-ray radiation is scattered off of the atoms, the superposition of scattered rays produces constructive and destructive interference depending on where in the lattice they originate. For a crystalline material, the condition for the diffraction was first described in 1913 by Bragg’s Law:
nλ d [3.4] hkl 2sin hkl
60 Where λ is the wavelength of the incident x-ray beam, dhkl is the spacing between the lattice planes (Figure 3.9) and Θ is its angle of incidence. As illustrated in the Figure 3.9, x-ray beam to be reflected there must be constructive interference between photons reflected off two successive surfaces. This will occur when the path length difference (2dhklsinΘ), between the two photons are nλ (Bragg’s Law).
Figure 3. 9. X-ray scattering off of a crystal lattice
Angle dispersive XRD (ADXRD), using a monochromatic x-ray beam and an area detector is now more common due to the introduction of synchrotron radiation which is able to produce much more intense sources of monochromatic x-rays. HPCAT at the Advanced Photon
Source (APS) at Argonne National Laboratory has advanced and refined ADXRD with a small focused x-ray beam (3-5 µm) of sufficient flux suitable for performing XRD experiments. It
61 offers a wide energy range (12-70 keV) focused beam, and detector selections of CCD, imaging plate, or Pilatus (see Figure 3.10).
Figure 3. 10. Setup for ADXRD at the APS
The x-ray diffraction pattern is made up of rings of diffracted rays, called the Debye-
Scherrer rings, instead of individual spots as in single-crystal diffraction.
62
Figure 3. 11. X-ray diffraction pattern of CS2 sample at 4.0GPa
Figure 3.11 shows a portion of the raw diffraction image of carbon disulfide sample at 4
GPa. Angle-resolved x-ray scattering data were collected at room temperature using micro- focused (~10x10 μm) monochromatic synchrotron x-ray at 16 ID-B /HPCAT (λ=0.3682 Å) at the Advanced Photon Source and BL10XU (λ=0.4136 Å) at the SPring-8 for both room temperature and low temperature. The x-ray scattering intensities were recorded on high- resolution 2D image plates over a large 2θ range between 0 and 40 degrees and then converted to
1D profiles using the Fit2D program. To investigate the structure in the amorphous phase, pair distribution function (PDF) analysis was performed on room temperature x-ray data by using the
PDFGetX2. The background x-ray scattering was also measured from an empty cell after the experiments and was subtracted from the data to obtain the S(Q) of the sample as shown in figure 3.12. The S(Q) data was then Fourier transformed to obtain the g(r).
[3.5]
According to
-1 where Q is the amplitude of scattering vector and Qmax=25 Å was applied.
63
Figure 3. 12. (a) The CS2 sample (black), background (red) and background subtracted (blue) x-ray scattering patterns showing the analysis procedure to get the S(Q) in (b). The background x-ray scattering was also measured from an empty cell after the experiments and the S(Q) data was Fourier transformed to obtain the G(r).
64 3.4 Electrical Transport Measurement at High Pressure
Electrical resistivity experiments have dominated in the study of many interesting high pressure phenomena including; the pressure-induced superconductivity, insulator-to-metal transitions, and quantum critical behaviors. Performing resistivity measurements in the DAC is, however, technologically challenging as it is difficult to make electrical contact to a tiny sample and keep it insulated from the metallic gasket. A large number of different approaches have been developed over the years to address this problem.
One solution is to replace the metal gasket with an insulating gasket. Mica-MgO composite gaskets, for example, have been successfully used to 40 GPa (Reichlin, 1983). The metal gasket can also be coated with an electrically insulating layer by either sputtering
(Gonzalez, Besson, & Weill, 1986) or by coating the gasket with mixture of alumina, diamond or cubic boron nitride mixed with epoxy (Eremets, Struzhkin, Mao, & Hemley, 2001). However, in order to overcome the random movements of leads in the sample chamber under high pressure, thin film fabrication and photolithography technology have been used to integrate the probes onto a diamond anvil directly (Eremets, Struzhkin, Mao, & Hemley, 2001). Recently, Weir et al.
(Weir, Akella, Aracne-Ruddle, & Vohra, 2000) encapsulated a microcircuit on a diamond anvil with epitaxially grown diamond films, and determined the electrical resistance and magnetic susceptibility under high pressure. Although these previous works promote the techniques greatly, there are many problems yet to be resolved, such as how to determine exact and reproducible resistivity under high pressure, how to perform the resistivity measurement at high temperatures using either externally heated or laser heating DAC, and how to conduct the impedance measurement in a DAC at pressures beyond Mbars of pressure.
65 There are several ways to make electrical contacts between the sample and the conductive wires.
Simple pressed contacts are often sufficient to ensure good electrical contact between the wires and the sample, provided that the sample’s surface is clean. In situations where secure contacts are required, small amounts of silver paste or silver epoxy can be used to bond the wire to the sample. These contacts may be applied directly to the sample, but contact resistances can often be reduced if thin-film metal contact pads (Au, Pt) are first evaporated or sputter deposited onto the sample. If the sample is a semiconductor, depositing metal contact films onto it is also beneficial to overcome the “Shottky” contacts. Generally, non-rectifying or “ohmic” contacts are desirable for delivering electrical currents to semiconductors and getting voltage signals out of them. The spark welding is also used to make contacts to samples.
The van der Pauw method (Van der Pauw, 1958) is used for measuring the resistivity of arbitrarily shaped samples. There are several requirements associated with the Van der Pauw method.
. Contacts are at the circumference of the sample
. Contacts are sufficiently small
. Sample is homogeneous in thickness
. Surface of the sample is singly connected
If these conditions are satisfied, the Van der Pauw method is a powerful technique for determining the sample resistivity of samples of arbitrary shape (subject to the restriction that the thickness is uniform and known).
66 Electrical contacts are made at four points A, B, C, and D, on the periphery of the sample, a current IAB can be applied from contact A to contact B while measuring the voltage drop VD-VC.
If we define RAB,CD = (VD-VC)/IAB and, analogously, RBC,DA = (VA-VD)/IBC then the resistivity is given by the equation
[3.6]
where, is the sample thickness. The resistivity cannot be solved from the equation, but the resistivity can be calculated by numerically for given values of resistance. But if it is assumed that the sample is symmetrical, then above equation reduces to
[3.7]
Even though this is a very simple technique, in practice, however, is difficult to apply to
DAC experiments. The contact areas are often a significant fraction of the sample size, the samples are often irregular in shape, and the in situ thickness of a high pressure is usually very difficult to determine with much accuracy. However, a rough estimate of the absolute resistivity can usually be made based on the sample dimensions and the locations of the contact points by using 4-wire resistance measurements.
67 Here we describe in detail how we performed the resistivity measurement in DAC in the present study. A metallic gasket is first pre-indented and a sample hole is drilled. A strip of Scotch tape is used to insulate the whole gasket except the pre-indented area (see Fig. 3.13 (a)). Then a mixture of diamond or alumina powder with Stycast epoxy is placed on top of the pre-indented area to insulate the gasket. The insulation powder is then pressed to about 15 - 20 GPa. Crazy glue is then used on the edges of the pre-indented area to keep the insulation powder intact (see
Fig. 3.13 (b) and (c)). A sample chamber is then drilled into the insulating material by hand using an acupuncture needle (see Fig. 3.13 (d)). Platinum electrodes, 5 μm thick, are cut with a sharp razor blade with a tip of 5 to 10 μm and held in place using a small piece of Scotch tape. This tape also helps to guide the direction of the electrodes onto the sample chamber (see Fig. 3.13 (e) and (f)). The electrodes are then pressed to a few GPa for at least half an hour so that the electrodes will stick to the insulation powder (see Fig. 3.13 (g) and (h)).
As the culet size decreases, four-point resistivity measurements get very difficult, and the electrode configuration takes a quasi four-point arrangement. In resistivity measurements, the challenge is to not touch the electrodes when loading the sample or ruby. The best way is to load the sample in the sample chamber and place the ruby on the upper diamond. Ac-resistivity measurement was carried out using the lock-in amplifier. The frequency, 13 Hz, was chosen such that the signal coming from the oscillator of the lock-in is a smooth sinusoidal wave. Below 10
Hz the oscillator signal has noise incorporated with the sinusoidal wave. The frequency has to be small to ideally reproduce a DC-like measurement. The sample thickness was determined by measuring the distance between the back surfaces of two diamond anvils.
68
Figure 3. 13. The steps of four-point arrangement of the electrodes for resistivity measurement in the DAC
69 As we described above, the Van der Pauw’s technique is used to measure resistivity in arbitrarily shaped samples. But, the contacts to the sample must be located on the boundary of the sample and the contacts areas should be small in comparison with the sample size in order to use this technique with a uniform thickness. In this regard, at pressures of 60-200 GPa the situation is less than ideal and leaves a small residual resistance. Furthermore, the plastic deformation of diamond at these pressures is significant to affect the sample thickness (Huang, et al., 2007).
60
35 2.8 70 GPa 30 50 2.4
25
2.0
) ) m 20 Loading
1.6 (
m)
(
R R
40 Unloading
15 1.2
10 0.8 30 CS2 5 0.4
Thickness ( Thickness 0 50 100 150 200 250 300 T (K) 20
10 0 20 40 60 80 100 P (GPa)
Figure 3. 14. The thickness of the sample as a function of pressure during compression and decompression. Inset: (T) and R(T) at 70 GPa showing the similar systematic behavior as a function of temperature. Microphotographs
of reflective CS2 samples at 28 and 55 GPa showing the experimental setup for four-probe electrical resistance measurements and the metallic reflectivity of CS samples above 55 GPa similar to those of Pt probes. 2
70 We measured sample thickness in both the compression and decompression processes, as shown in Fig. 3.10. The electric probes remain stable in shape and position above 40-50 GPa. However, because of the relatively small sample size above 50 GPa, the situation in DAC is quite complex and a geometric correction (Huang, et al., 2007) is necessary for sample thickness. We estimated the uncertainty introduced by this correction to be no more than 10% in resistivity, estimated according to the finite element analysis of resistivity measurement with four point probes in a diamond anvil cell (Huang, et al., 2007). Furthermore, this correction does not strongly affect the systematic of (T) as a function of temperature as shown in Fig. 3.14 inset.
3.5 Susceptibility Measurements at High Pressure
3.5.1 AC-Susceptibility Measurements
This technique measures the Meissner effect of superconductors. This simple yet important property is extensively used to detect bulk superconductivity. The sample is surrounded by a secondary (pick-up) coil and a separate coil (primary) subjects the sample to an alternating magnetic field. The secondary (pick-up) coil and a field generating primary coil wound on top of the secondary coil and two pairs of identical coils are used. The primary coils of each pair are connected in series in the same direction so that the field generated in the middle of both will be the same. However, the secondary coils are connected in the opposite direction so that the induced voltage in one of the secondary coils will be canceled out by the other. The coils are wound from 60 μm insulated copper wire and each consist of 6 layers with 30 turns per layer.
The inner diameter of the pickup coil is ~3.4 mm and the height of the coils is ~2 mm (see Fig.
3.15).
71 The alternating flux through the pickup coil produces an ac voltage which is the measured signal.
Above Tc, the applied field penetrates the sample. When the sample is cooled below Tc, the field is expelled from the sample due to the superconducting shielding effect, forcing some of the flux lines out of the pickup coil. This leads to a reduction in the induced voltage in the pickup coil.
Thus, a sudden drop in the pickup coil voltage is expected when the sample becomes superconducting. The crucial point is to balance the secondary coils at room temperature so that the response from the secondary coils is as small as possible. The balancing of the coil system does not guarantee negligible temperature-dependent background, but minimizes the response to the lowest value possible.
Figure 3.15. Two identical compensating primary/secondary coil systems for ac susceptibility measurements. The active coil is around 16-facet diamond anvil in the middle; compensating coil contains a dummy gasket (Debessai, Ph. D. Thesis, 2008)
72 In practice, there is a residual temperature dependent background due to slight differences in the magnetic environments of the pick-up coil. In order to minimize this temperature-dependent background, one must choose a gasket material that is non-magnetic down to the lowest measurement temperatures. In addition, the gasket should have low enough conductivity that eddy currents do not significantly shield the applied field. A Lock-in amplifier (SR830) is used to generate an ac magnetic field through the primary coil and to detect the drop in the induced voltage through the secondary coil. The lock-in amplifier is used to detect a very small signal embedded in a noisy background. This technique is capable of measuring superconducting transitions in samples with dimensions less than 100μm.
3.5.2 Double-Frequency modulation Method
The technique that we described in 3.5.1 is a single-frequency standard technique often used at ambient pressure and adapted for diamond anvil cell experiments. However, detecting small signals becomes increasingly difficult and impossible for the sample sizes less than 80µm in diameter. But using a double-frequency modulation method, can detect signals from samples as small as 10 µm in diameter (Timofeev, Struzhkin, Hemley, Mao, & Gregoryanz, 2002)
(Timofeev Y. A., 1992). The technique is based on the fact that the magnetic susceptibility of the superconducting materials depends on the external magnetic field enclosed in the volume of the sample. When the magnetic field is high enough to quench the superconductivity, the Meissner effect is suppressed and the magnetic field penetrates the sample volume. In contrast, the susceptibility of metallic parts of the high pressure cell (diamagnetic and paramagnetic) is essentially independent of the external magnetic field. In his way the background remains
73 practically constant and allows the separation of the signal arising from the sample from that of the background.
The exciting coil creates an alternating magnetic field which produces electromotive forces in both the signal and compensating coils. These coils are included in the electrical circuit in such a manner that their electromotive forces act in opposite directions and nearly compensate for each other. The difference between the two electromotive forces determines the background signal (see Fig. 3.16). We apply the low-frequency (f=22 Hz) magnetic field with an amplitude up to tens of Oersted, which causes the destruction of the superconducting state near the superconducting transition. This in turn leads to a change in the magnetic susceptibility of the sample from -1 to 0 twice in a given period, and produces a modulation of the signal amplitude in the receiving coils at a frequency 2f.
The subsequently amplified signal from the lock-in amplifier is then recorded as a function of the temperature on the computer. The critical superconducting temperature Tc is then identified as the point where the signal goes to zero due to the disappearing of the diamagnetic signal at Tc. The signal starts first appears when Hc1 [Hc1(T1) = H0] is equal to the amplitude of the low-frequency magnetic field where the temperature is T1 (see Fig. 3.17) and reaches its maximum at temperature Tmax. The signal drops to zero at Tc because the magnetic field penetrates the sample volume at all the times; thus there is no variation of high-frequency signal amplitude with time.
In this research work we used double modulation methods to detect the superconducting signal. Samples were loaded in a Be-Cu diamond anvil cell using nonmagnetic Ni-Cr alloy gaskets. The background signal in our measurements appeared to be that of paramagnetic; its phase is approximately opposite to that of the signal from the sample. We interpolated the
74 background in the range of the superconducting transition with a smooth polynomial function.
iφ The total signal can be represented as the complex variable U = AT e T and the interpolated
iφ iφ background as B = AB e B; our signal is then S = AS e S = U-B, the difference of two complex variables.
Figure 3. 16. Schematic of the double-frequency modulation setup to detect superconductivity. Modified from (Timofeev, Struzhkin, Hemley, Mao, & Gregoryanz, 2002)
75
Figure 3. 17. (a) Schematic representation of magnetic field variation with time near the sample. (b) Signal at 2f frequency extracted from the amplitude of high-frequency signal (Timofeev, Struzhkin, Hemley, Mao, & Gregoryanz, 2002).
76 3.6 Experimental Details
All the Raman spectroscopy, Resistivity measurement and laser/internal/external heating were described in this dissertation were performed at Prof. Yoo’s Static High Pressure
Laboratories at Washington State University. Synchrotron x-ray diffraction experiments were done at sectors 16 ID-B, APS at Argonne National Laboratory, Japan Synchrotron Radiation
Research Institute (SPring-8) and Advanced Light Source, Lawrence Berkley National
Laboratory. The magnetic susceptibility was performed at Geophysical Laboratory and Center for High Pressure Research Washington D.C. The entire sets of samples were loaded at WSU, but a few CS2 samples were also loaded at the Geophysical Laboratory for magnetic susceptibility measurements. The following sections describe each individual experiment as well as sample loading details.
3.6.1 Carbon Disulfide (CS2)
This study was based on a large number of experiments, more than fifty samples, all providing a consistent and reproducible set of Raman, electric resistance, magnetic susceptibility and synchrotron x-ray scattering data. The sample was liquid CS2 (99.99% from Sigma-Aldrich) loaded onto a membrane-driven diamond-anvil cell (m-DAC), using 1/3-carat, type Ia diamond anvils with a 0.3 (or 0.18 and 0.1 for higher pressures) mm culet. A 0.2 mm thick rhenium gasket was pre-indented to 30 µm and 130 (or 100) µm hole was electro-spark drilled at the center of the gasket. Direct current electrical resistance measurements were performed with 3 mA current,
LACKSHORE 120 current source with switching polarity, and the voltage readout from Keithley
2000 DVM was recorded on a computer.
77 For low resistance values AC technique was used at 13 Hz frequency with a 3 mA current from a Stanford Research SR830 digital lock-in amplifier. The electrical resistivity was then calculated through Van der Pauw’s equation. We measured the thickness of the sample for both the compression and decompression processes. Low-temperature Raman spectroscopy and resistance measurements were performed by custom designed vibration-free close-cycle cryostat
(Cold-Edge Tech, PA) up to 4.5K. The magnetic susceptibility performed by continuous flow cryostat using a highly-sensitive modulation technique; samples were loaded in a Be-Cu diamond anvil cell, using nonmagnetic Ni-Cr alloy gaskets.
3.6.2 Carbonyl sulfide (OCS)
The sample was gas (>99% from Sigma-Aldrich). OCS samples were loaded onto a membrane-driven diamond-anvil cell (m-DAC) by condensing OCS gas to −50 °C and 10 atmospheres, using 1/3-carat, type IA diamond anvils with a culet size of 300 µm in a sealed environment. A rhenium gasket was pre-indented to 40–50 µm thickness and a small hole of 120
µm was drilled using an electric discharge micro drilling machine. A few micrometer-sized ruby chips were scattered inside the cell for in situ pressure measurements.
3.6.3 Group IV Sulfides: GeS2/SnS2
All samples were crystalline powder loaded onto a membrane-driven diamond-anvil cell
(m-DAC), using 1/3-carat, type Ia diamond anvils with a 0.3 mm culet. A 0.2 mm thick rhenium gasket was pre-indented to 40 µm and 120 µm hole was electro-spark drilled at the center of the gasket. We used Helium as a pressure transmitting medium and chip of ruby for pressure calibration.
78 Chapter 4
Dense Carbon Disulfide
4.1 Background
Carbon disulfide is a centro-symmetric linear tri-atomic molecule with a similar valence electronic structure as of CO2. Liquid CS2 crystallizes at 161.7 K at ambient pressure or above
~1.8 GPa at room temperature. The structures of the low-temperature (148 and 133 K) solid phases of CS2 were determined by single crystal x-ray diffraction (Baenziger & Duax, 1968) and neutron diffraction on polycrystalline samples (Powell, Dolling, & Torrie, 1982). The crystal structures belong to the orthorhombic space group Cmca with Z= 4 molecules in the unit cell on
C2h sites. High pressure and at room temperature, the crystal structures were also determined to be Cmca up to 12 GPa by powder x-ray diffraction (Akahama, Minamoto, & Kawamura, X-ray powder diffraction study of CS2 at high pressures, 2002).
Figure 4. 1. Orthorhombic structure Cmca of Carbon disulfide
79 X-ray and neutron scattering studies showed a remarkable anisotropy in the thermal expansion, with the lattice parameter c increasing with decreasing temperature. The linear centro symmetric molecules S ═ C ═ S lie in layers parallel to the bc planes perpendicular to the a axis
(Fig. 4.1). They are tilted with respect to the b axis by an angle 43.21° at 150 K (Powell, Dolling,
& Torrie, 1982). Crystallographic study of a single crystal of CS2 in the vicinity of 3 GPa and
243 K, indicate that there is probably an additional crystalline solid (Weir, Piermarini, & Block,
Crystallography of some High-pressure Forms of C6H6, CS2, Br2, CCl4, and KNO3, 1968) isostructural to that of CO2-III (Cmca). It is interesting to note that the cubic Pa-3 structure seen in CO2-I is absent in the phase diagram of CS2. Nevertheless, it is still consistent with the periodic structural variation with pressure; for example, the absence of the graphite structure in silicon and the second-row CO2 transforming to the structures of the third-row compound SiO2 at high pressures. Furthermore, as in the cases of CO2-III, CS2 molecules in the Cmca phase behave cooperatively and lead to strong chemical reactions at high pressures and high temperatures.
Upon increasing pressure, CS2 produced a irreversible black product knows as Bridgman’s black.
Bridgman was the first to report the chemical transformation of carbon disulfide to a black polymer under static high pressure-temperature condition (~5.5 GPa and 450 K)
(Bridgman, Freezing parameters and compressions of Twenty-One Substance to 50,000 Kg/cm2,
1942). However, Agnew and coworkers (Agnew, Mischke, & Swanson, Pressure and
Temperature induced Chemistry of Carbon Disulfide, 1988) later found that the chemistry of CS2 is actually substantially more complicated at high pressures and temperatures as illustrated in
Fig. 4.2. Several reaction zones were identified, all of which contain the mixtures of multimer products of carbon disulfide. According to Agnew and coworkers, CS2 polymerizes at 8.3 GPa and room temperature to form Bridgeman's Black polymer and the CS2 dimer, but they observed
80 at least three other species among the products when the sample was subjected to higher temperature at lower pressure. One of these species has the same infrared features observed for the (C3S2); polymer of carbon subsulfide, suggesting that it is the same material. Note that at the ambient temperature carbon disulfide transforms into a dimeric product above 9GPa, signifying the dimeric pairing of the Cmca structure.
The collective behavior and polymerization of CS2 molecules are in a way analogous to those of CO2. Yuan and coworkers have studied the phase transition of CS2 at high pressures and high temperatures by ab initio method (Yuan & Ding, High Pressure Phase transition of carbon disulfide, 2007). They found pieces of polymer structure at 300K and 10 GPa in the molecular dynamics run and predicted existence of extended structure with four-fold carbon atoms for carbon disulfide above 20 GPa (Agnew, Mischke, & Swanson, Pressure and Temperature induced Chemistry of Carbon Disulfide, 1988) and was found in its chemical analog, CO2, above
40 GPa (Iota, Yoo, & Cynn, An Optically Nonlinear Extended Solid at High Pressures and temperatures, 1999). In their study, the CS4 tetrahedral structure appeared initially at 300K and
20GPa. The decomposition of CS2 at 20 GPa and at different high temperatures, starting from
1000K into C and S atoms also predicted.
81
Figure 4. 2. The phase diagram of carbon disulfide from the reference (Agnew, Mischke, & Swanson, Pressure and Temperature Induced Chemistry of Carbon Disulfide, 1988).
A few high-pressure investigations on solid CS2 were carried out using Raman, Infrared spectroscopic methods (Agnew, Mischke, & Swanson, Pressure and Temperature induced
Chemistry of Carbon Disulfide, 1988)( Bolduan, Hocheimer, & Jodl, 1986)( Whalley, 1960).
Here we summarize the Raman study done prior to this study. Since carbon disulfide has an inversion center the Raman active modes are IR inactive and vice versa. Three sharp Raman bands were found at 664, 648, and 654 cm-1 in the frequency region of the symmetrical
32 32 33 stretching vibration ν1. This is caused by isotopomers like C S2(90%), C S S(1.4%), and
32 34 C S S(4%), their intensities match with the isotopic abundance. The νs mode is comparatively less affected by compression so that the rate of increasing frequency with respect to pressure is less, indicating the strengthening of the bond. Two bands at 787 (broader less intense line) and
82 802 (narrow intense line) cm-1 were observed in the overtone region. The bending modes are degenerate. This mode appears due to Fermi resonance coupling with nearby νs vibration. Only the more intense peak has the appropriate symmetry and energy with that of ν1 mode for Fermi resonance interaction. Here the splitting between vs fundamental and 2vb overtone is much less than the intramolecular coupling. Therefore the interacting modes do not mix completely. Due to this weak mixing 2vb and vs modes retain their original character unlike CO2. Upon increasing the pressure, both the peaks shift to lower frequency with broader peak having strong pressure dependence. According to literature 4 lattice vibrations were expected ( Bolduan, Hocheimer, &
Jodl, 1986). But at low pressures only two lines were observed. As pressure increased 3 lines were observed. It is also stated in literature that these lines serve as a criterion for crystal quality.
Gradual darkening of CS2 sample was observed above 6GPa. Between 7 and 9GPa the sample further turned dark and above 9GPa it became completely Black ( Bolduan, Hocheimer, & Jodl,
1986)( Whalley, 1960).
4.2 Structural Phase Transition
Both Raman and X-Ray studies were carried out on CS2 over a wide P-T region.
Pressure-induced Raman changes (Fig. 4.3) indicate dramatic transformations of molecular carbon disulfide (Cmca) (Powell, Dolling, & Torrie, 1982) to a previously known disordered 1D black polymer (Agnew, Mischke, & Swanson, Pressure and Temperature induced Chemistry of
Carbon Disulfide, 1988) of (-S-(C=S)-)p with three-folded carbon atoms bonded to sulfur atoms at 10 GPa (depicted as CS3 phase). The Raman spectrum of molecular CS2 consists of a
83 -1 -1 symmetric stretching mode νs at 650 cm , an overtone of S=C=S bending νb at 800 cm , and a lattice mode at 100 cm-1 as shown in Figure 4.3 upon increasing pressure.
The pressure-dependent Raman changes of carbon disulfide can be summarized in Figure
4.4, signifying the molecular to nonmolecular phase transitions. Above 9 GPa, all of these modes disappear and, instead, two new broad peaks appear at ~430 cm-1 and 500 cm-1, representing, respectively, the bending and stretching modes of (S-(C=S)-S) in a 1D polymeric configuration.
Above 30GPa, these two features merge into a single band at ~470 cm-1, which can be attributed to the S-C-S bending mode in a 3D network structure made of CS4 tetrahedra (Fig. 4.4). The existence of this type of extended structure with four-fold carbon atoms was predicted for carbon disulfide above 20GPa (Yuan & Ding, High Pressure Phase transition of carbon disulfide, 2007) and was found in its chemical analog, CO2, above 40 GPa (Iota, Yoo, & Cynn, An Optically
Nonlinear Extended Solid at High Pressures and temperatures, 1999). We, therefore, attribute the
Raman change at 30GPa to a structural phase transition to an extended carbon disulfide solid made of CS4 tetrahedra (depicted as CS4 phase). Figure 4.5 summarized the Raman peak shift upon increasing pressure, which noticeably indicating the structural changes at around 10 GPa and 30 GPa. Upon decreasing pressure CS4 phase transform back to CS3 phase but not to the molecular CS2 (see Fig. 4.5). Not that those high pressure phases are highly disordered.
84
Figure 4. 3. Raman spectra solid Carbon Disulfide upon increasing pressure.
85
Figure 4. 4. Raman spectra solid Carbon Disulfide upon increasing pressure after the polymerization in the 300-700 cm-1 region associated with the structural phase transitions at 30 GPa.
86 Figure 4. 5. The pressure dependences of the Raman spectra of solid CS2. The blue circle indicates the increasing pressure and red circles indicate the decreasing in pressure.
At ambient pressure CS2 decomposes to C and S above ~ 562K. To understand the stability field of high pressure phases of CS2, we performed heating experiments at 22, 30, and 50 GPa. The decomposition of carbon disulfide to carbon and sulfur at high pressures and temperatures were observed. The data at 710 K and 22 GPa signifies carbon disulfide decomposition to carbon and sulfur (S-VI phase (Degtyareva, et al., Vibrational dynamics and stability of the high-pressure chain and ring phases in S and Se, 2007)), which is confirmed by its characteristic Raman peak in the present resistive-heating experiments (Fig. 4.6a).
87 However, we confirmed that the CS4 phase at 50 GPa was not decomposed to 725 K, the maximum temperature of the present resistive-heating experiments, but decomposes to carbon and S-III (Degtyareva, et al., Vibrational dynamics and stability of the high-pressure chain and ring phases in S and Se, 2007) upon laser-heating to higher temperatures as well at 30 GPa (well above 1000 K) (Fig. 4.6b).
Figure 4. 6. The Raman spectra of ohmically heated carbon disulfide, showing thermal decomposition of
CS2 to carbon and sulfur (phase VI) at around 720 K at 22 GPa (a) The laser-heated carbon disulfide, decomposes to carbon and sulfur (phase III) at 30 GPa and > 1000 K. (b).
88 The present x-ray diffraction data support the structural phase transitions of carbon disulfide to the 1D (CS3) and 3D (CS4) extended solids (Fig. 4.7). Below 10 GPa, the polycrystalline diffraction pattern of solid CS2 is poor due to its large crystal grains with highly preferred orientations. Nevertheless, all the observed peaks can be indexed with the previously known Cmca structure of molecular CS2 (Baenziger & Duax, 1968). At higher pressures, those sharp diffraction peaks weaken and broaden, becoming a few broad features centered at around
-1 2.5, 3.3 and 4.3 Å , indicating the transformation of CS2 to a highly disordered solid. No diffraction feature is discernable for the presence of either sulfur or carbon, confirming that CS2 does not decompose chemically. Note that all solid phases of sulfur (including S-II and III phases relevant to this pressure range) maintain high crystallinity well above 35GPa (nearly to
200 GPa) at ambient temperatures (Degtyareva, et al., Vibrational dynamics and stability of the high-pressure chain and ring phases in S and Se, 2007).
The pair distribution function (PDF) profiles reveal the local structures of semiconducting CS3 and metallic CS4 phases (see the inset in Fig. 4.7). The first dominant peak can be assigned to the nearest carbon-sulfur distance (r1) (Powell, Dolling, & Torrie, 1982). For example, the peak at 1.32 (±0.05) Å at 9 GPa can be assigned to the C=S double bonds in molecular CS2. The observed peak at around 1.70 (±0.05) Å at 27, 46 and 55 GPa can be assigned to the C-S single bonds in CS4 tetrahedral with some partial C=S double bond characters (Frapper & Saillard, 2000). The second dominant peak, on the other hand, can be assigned to the neighboring sulfur-sulfur distance (r2), which decreases from 4.08 and 3.25 Å at
9 GPa, corresponding to the two nearest S..S interatomic distances in the Cmca phase (Labes &
Nichols, 1979), to 2.99 and 3.15 Å at 27 GPa, corresponding to two different S..S distances in the CS3 phase. It then collapses to 2.77 Å at 47-55 GPa. Interestingly, the ratio of r1 and r2, is
89 ~1.63 at 55 GPa and is close to the ideal close-pack hexagonal structure c/a = 1.63, signifying its
3D network structure (Ichikawa, 1973).
Figure 4. 7. The background-removed structural factor S(Q) and radial distribution function G(r) (inset) of carbon disulfide obtained at several high pressures, showing the pressure-induced structural changes.
90 4.3 Insulator-Metal Transition
Organic molecules are typically electric insulators because of hybridization resulting in a filled close-shell configuration. Carbon disulfide is a transparent fluid at ambient conditions. The most dramatic change in carbon disulfide under pressure is in its visual appearance (Fig. 4.8) from a transparent fluid to a molecular solid (Cmca) at 1.8 GPa to a 1D black polymer of (-S-
(C=S)-)p with three-folded carbon atoms bonded to sulfur atoms at 10 GPa, and to a reflecting polymer above 40-50 GPa.
Figure 4. 8. Microphotographs of carbon disulfide under high pressure showing its transformation from transparent fluid to molecular solid (Cmca) at ~1.8 GPa, to black polymer above 10 GPa ((-S-(C=S)-)p or CS3), and eventually to a highly reflecting extended solid above 40 GPa (CS4) at ambient temperature.
91 The pressure-induced structural phase transitions accompany a large, seven-order, drop in
electric resistance over a pressure range of 10 to 50 GPa, clearly suggesting an insulator-metal
transition at ~50 GPa (Fig. 4.9). The conducting phase of carbon disulfide, especially in the CS4
phase above 50 GPa, is opaque and highly reflective approaching the level of Pt metal (see the
insect of Fig. 4.9). The measured resistance of the CS4 phase at 50 GPa is less than 20 Ω which
is typical for metals at this pressure in a DAC. The metallic nature of the CS4 phase is consistent
with its high optical reflectivity.
Figure 4. 9. Pressure-induced electrical resistance changes of carbon disulfide, showing the insulator to metal transition.
92 Figure 4. 10. (a) The temperature-dependent electrical resistance of carbon disulfide at 24, 30, 37, 43 GPa on a logarithmic scale, showing a transition from insulator to semiconductor to semi-metal. (b) The ln(ρ) against 1000/T (Arrhenius plot), showing the linearity indication above 150K in dash lines. The ln(ρ) against 1/T1/4 (VRH mechanism), showing the linearity indication at low temperatures in dash lines (blue axis).
The resistance of the low-pressure CS3 and CS4 phase as a function of temperature further
suggest a gradual insulator-to-metal transition (Fig. 4.10a). The temperature dependence of
resistance, however, does not follow a single activated dependence, as illustrated by the ln(ρ)
against 1/T plot (Fig. 4.10b), and exhibits a considerable deviation from linear 1/T dependence
below ~150K or 1000/T > ~6.6 (see red line in Fig. 4.10b). Instead, it follows the 1/T1/4
dependence (see the blue axis in Fig. 4.10b), consistent with a “variable range hopping” model of
a Mott insulator (Sage, Blake, & Palstra, 2008). Its metallic nature is retained up to 202 GPa
93 (±6 GPa), the highest pressure studied at ambient temperature. In summary, Carbon disulfide shows extremely high metallic conductivity above 50 GPa, following a series of structural phase transition from transparent molecular CS2 phase, to the threefold CS3 phase at 10 GPa, and to a highly disorder fourfold CS4 phase at ~ 30 GPa.
4.4 Superconducting Transition
Efforts to identify and develop new superconducting materials continue to increase rapidly, motivated by both fundamental science and the prospects for application. High pressure plays an increasingly important role in such efforts. However, highly compressed low-Z molecular solids become extended solids in three-dimensional network structures of polymeric and/or metallic states, as found in their periodic high- Z counterparts. A relevant question is then, can these extended forms of simple molecular solids give rise to novel properties such as superconductivity and magnetism, as often found in sp/spd-elemental metals and metallic alloys at low temperatures (Schilling J. S., Handbook of High Temperature Superconductivity: Theory and Experiment, 2007) (Schilling J. S., 2007). The theoretical prediction of high temperature
(possibly 300 K) superconductivity in metallic hydrogen at high pressure is stimulating in this regard (Ashcroft, Metallic Hydrogen: A High-Temperature Superconductor?, 1968); yet, the superconductivity in simple molecular solids has only been observed in paramagnetic oxygen at
TC ~ 0.6K above 100 GPa (Shimizu, Suhara, Ikumo, Eremets, & Amaya, 1998).
Although, highly disordered, CS4 phase exhibits a remarkably low electrical conductivity of ~5 µΩ/m at ambient temperatures, similar to that of an elemental metal (rather than an organic polymer or a polymeric metal) (Kaye & Laby,1993). In this section, we further show that the CS4
94 phase undergoes a superconducting state at ~6.2K, observed over a large pressure range from 50
Figure 4. 11. Temperature-dependent electrical resistance of carbon disulfide at high pressures, showing the
superconducting transitions at several pressures that occur around 6K (TC). Inset: An expanded view into the
low-temperature region (<15K) at several pressures, showing the sharp resistivity drop at the TC (noted by
an arrow) and small drops at the TX just prior to the TC (see arrows).
95 to 172 GPa (the maximum pressure studied) and exhibits the characteristics of a correlated intermetallic molecular” alloy. Evidence for superconductivity in carbon disulfide is found in both the electrical resistance and magnetic susceptibility data (Fig. 4.11). The superconducting transition, for example, is clearly recognized at the onset of the sharp resistance drop at 4.91K at
60 GPa in Fig. 4.11. The transition temperature TC increases to 6.01 K at 90 GPa at a rate of
+32mK/GPa and to 6.23K at 140 GPa at +4.2mK/GPa, then decreases to 5.82K at 172 GPa (Fig.
4.12).
Figure 4. 12. The pressure dependence of the Tc to 180GPa, indicating a discontinuity ~100GPa. Tc determined from both resistance (blue squares) and susceptibility (red squares).
96 The resistance drop is nearly 60% within 0.1 degrees of the transition. This is a very sharp drop, considering the disordered nature of this material and compared with other superconducting transitions in organic superconductors (Hebard, et al., 1991) and pure elemental solids at high pressures (Yabuuchi, Matsuoka, Nakamoto, & Shimizu, 2006)( Shimizu, Ishikawa,
Takao, Yagi, & Amaya, Superconductivity in compressed lithium at 20K, 2002). It is not uncommon to observe a small residual resistance (0.4-0.7µ) in the superconducting state, likely arising from the contact resistance between the Pt electrical lead and the CS2 sample.
Interestingly, the sample resistance at 48GPa increases slightly below 6K, showing the typical behavior of disordered metals in the presence of weak localization effects (Patrick &
Ramakrishnan, Disordered electronic systems , 1985) (Mott, Metal-Insulator Transition, 1968).
Note on a small but consistent drop in the measured resistance just prior to the superconducting transition (depicted as TX in Fig. 4.11 inset), interestingly exhibits similar pressure dependence to the TC.
The Electrical resistance is a sensitive technique for detecting superconductivity, but weakly suitable to establish whether or not a material is a bulk superconductor. In this regard magnetic susceptibility is far better technique. The superconducting transition is also apparent from the abrupt change in magnetic susceptibility at the onset of TC (Fig. 4.13), as measured by a modulation method (see chapter 3). The transition temperature TC is seen at the onset of the susceptibility signal on the high temperature side, where the magnetic flux completely enters the sample. Both the magnetic susceptibility and the electrical resistance data yield the consistent TC of around 6 K (Fig. 4.12). For a phonon-mediating superconductor with small Coulomb repulsion [150], the superconducting temperature can be approximated by TC = (θD/1.45) exp(-
1.04(1+λ)/λ), where θD is the Debye temperature and λ is the electron-phonon coupling constant.
97 -1 Using TC = 6K and θD = 700K, based on the single vibron at 500cm of CS4 phase, we estimate
λ= 0.31, indicating relatively weak electron-phonon coupling. For comparison, paramagnetic
(SN)x shows a similar value of λ=0.31 but only at a substantially lower TC = 0.26K (Andersen,
Crystalline Electric Field and Structural Effects in f-electron Systems, 1980).
Figure 4. 13. Magnetic susceptibility of carbon disulfide showing the superconducting transition (marked at TC) at 50 GPa, measured by the modulating technique. Inset: The pressure dependence of the TC as determined by the magnetic susceptibility, showing the increase in TC with pressure.
98 4.5 Magnetic Ordering Transition
Intriguingly, we find CS4 phase have a new magnetic state as evident from the unusual resistance plateau (Fig. 4.14) around ~ 45K and is characteristic of a spin density wave (SDW) antiferromagnet (see chapter 3 for more details) but the exact nature of magnetic state is not known. The critical temperature TN is then defined by the inflection point at the minimum of dρ/dT, as illustrated in Fig. 4.14a inset. The resistivity values below TN (between 7K and 35K) can be described by Eq. (2.4) with an energy gap (Δ) of antiferromagnet and an additional T2 term reflecting Fermi-liquid behavior (Andersen, Crystalline Electric Field and Structural Effects in f-Electron Systems, 1980).
2 = o + BT/ [1+2T/Δ] exp (-Δ/T) + AT [4.1]
The best fit at 48 GPa (red solid line in Fig. 4.12a), for example, gives Δ=53K, A= 0.125
-2 -1 cmK o = 17m, B = 304cmK . As illustrated in Fig. 4.14b, the energy gap Δ increases linearly with pressure from 50K at 50 GPa to 75 K at 100 GPa (at the rate of 0.42K/GPa), where it jumps to 150 K and shifts at the rate of 0.66 K/GPa to 180 GPa. The coefficient A, on the other hand, rapidly decreases with pressure and becomes nearly independent of pressure above
100 GPa. Note that the rate of the pressure shift of the TC also drops sharply at around 100 GPa from TC/P = 32 mK/GPa to 4.2 mK/GPa (Fig. 4.12). The value of Δ (P=0) obtained from this fitting is 2.65meV (or 30.7 K) – consistent with those of heavy fermions systems such as UT2Al3 and URu2Si2 (~5.5 meV or 70 K) (Dalichaouch, Andrade, & Maple, Superconducting and
Magnetic Properties of the Heavy-Fermion Compounds UT2A13 (T=Ni, Pd), 1992)( McElfresh,
2 et al., 1987). The resistivity change above TN shows the T dependence of a typical Fermi-liquid behavior to ~100 GPa (Fig. 4.15a). The T2 dependence has also been observed in amorphous or
99 disordered metals (Ohkawa, 1978). Above this pressure, however, the resistivity dependence deviates from the normal metallic T2 dependence and follows the T1.5 (Fig. 4.15b).
Figure 4. 14. temperature resistivity of CS2, showing the magnetic ordering transitions at 48GPa and 110GPa. The solid lines illustrate a best fit to Eq. (2.4) describing electron-magnon scattering from antiferromagnetic magnons with an energy gap (Δ). Inset: Temperature dependence of the carbon
disulfide temperature coefficient dρ/dT. The transition temperature TN is defined as the temperature of the minimum in dρ/dT.. (b) Values of the energy gap (Δ) and coefficient A of the T2 contribution to as a function of pressure, as derived from fits of Eq. (2.4) to the data.
100
Figure 4. 15. (a) The T2 dependence of the resistivity below 100 GPa and above 40 K, showing that it is 2 1.5 consistent with the form (T) = o+AT , corresponding to the Fermi-liquid behavior. (b) The T dependence of the resistivity under pressure above 110 GPa and above 40 K, which shows that it is 1.5 consistent with the form (T) = o+AT , signifying the departure from Fermi-liquid behavior. The arrows indicate the temperature where the resistivity starts to deviate from the power law behavior because of the magnetic ordering transition.
101 This unusual T1.5 dependence of resistivity has been observed in strongly correlated systems
(Varma, Nussinov, & Saarloos, 2002)( Khalifah, et al., 2001)( (Rivadulla, Zhou, & Goodenough,
2003). Thus, the abrupt changes in the temperature-dependent resistivity, the pressure-dependent superconductivity, and the band-gap energy Δ of two spin states – all observed between 90 and
120GPa – seem to signify an electron correlation-driven phase transition (or spin cross-over) in dense carbon disulfide from an itinerant metal to a correlated metal.
4.6 Discussions
4.6.1 Structural and Insulator to metal transitions
The present spectroscopic and diffraction results indicate the pressure-induced metallization of carbon disulfide at ~50 GPa, following a series of structural phase transitions from transparent molecular CS2 phase to three-fold CS3 phase at 10 GPa to four-fold CS4 phase at ~30 GPa. The insulator-to-metal transition is not due to CS2 decomposition or elemental sulfur, but occurs well in the stability field of highly disordered CS4 phase.
To investigate further using first-principles density functional theory calculations, in collaboration with Prof. John Tse at University of Saskatchewan in Canada, we determined the crystal and electronic structures of two plausible structures for highly disordered metallic CS4 phase: those are, making the analogy with CO2, the predicted chalcopyrite (I-42d) and observed tridymite (P212121) structures of extended CO2-V (Yoo, et al., Crystal structure of carbon dioxide at high pressure: "Superhard" polymeric carbon dioxide, 1999)( Sera, Corazon, Chiarotti,
Scandolo, & Tossatti, 1999). At ~50 GPa, the optimized tridymite and chalcopyrite structures have a similar density of 4.22 g/cm-3 well within the expected density range between extended
3 3 CO2 or diamond of ~3.56 g/cm and sulfur-II of 4.26 g/cm at 50 GPa (Sera, Corazon, Chiarotti,
102 Scandolo, & Tossatti, 1999)( Degtyareva, et al., Vibrational dynamics and stability of the high- pressure chain and ring phases in S and Se, 2007).
The calculated diffraction profiles for both structures (tridymite at 55 GPa and chalcopyrite at 50 GPa in Fig. 4.16) reproduced the observed major bands at Q =2.7 Å-1 and 4.5 to 5.5 Å-1. However, the agreement is slightly better for the distorted tridymite structure because the asymmetry of the band profile from 4.5 to 5.5 Å-1 is correctly modeled. The chalcopyrite structure is composed solely of the CS4 tetrahedra with one unique C-S bond of 1.74 Å. The S-C-
S valence angles from 103o – 107o are close to the ideal tetrahedron (Fig. 4.16a).
Figure 4. 16. The calculated structure factors of α-chalcopyrite (I-42d, top) and α-tridymite (P212121, bottom), showing the two major features centered around 2.8 Å-1 and 4.9 Å-1 as observed in the experiments (The calculation was done by Prof. John Tse (2011)).
103 The tridymite structure, on the other hand, is highly distorted and consists of corner-sharing four (C1)- and three (C2)-fold coordinated carbon atoms at 52 GPa (Fig. 4.16b). At 52 GPa, the
C-S bond lengths vary between 1.68 and 1.86 Å with S-C-S angles from 100o to 120o. It is also significant that the CS4 tetrahedra contain a relatively long C1-S bond of 1.86 Å as compared to the remaining 1.71, 1.75 and 1.78 Å. The trigonal arrangement around C2 is almost planar with two C2-S bonds of 1.71 Å and slightly shorter bond of 1.68 Å. The nearest C2…S contact distance is 2.10 Å at 52 GPa, which rapidly decreases with increasing pressure and collapses to
1.90 Å at 78 GPa. Thus, above 78 GPa the tridymite structure is expected to become a fully four- coordinated structure made of highly distorted CS4 tetrahedra with one long (1.9 Å) and three short (~1.7 Å) C-S bonds. Similarly, mixed three- and four-fold CO2 layer structures have been proposed to be energetically competitive with fully four-fold structures at high pressures (Deng,
Simon, & Kohler, 2005)( Montoya, Rousseau, Santoro, Gorelli, & Scandolo, 2008).
Over the pressure range from 20 – 60 GPa, the calculated enthalpy of tridymite is 0.3 to 0.4 eV/CS2 higher than that of the chalcopyrite structure, but the energy difference decreases with increasing pressure (Fig. 4.17). The both structures have a metallic ground state (Figs. 4.18a and
4.18b) as observed in experiments and are found to be dynamically stable. We found that the calculate electron-phonon parameter of the chalcopyrite structure is very small (Fig. 4.19). The low symmetry and large number of atoms in the tridymite unit cell preclude calculations on the electron-phonon coupling parameter. However, the electronic band structure of the tridymite at
47 GPa, on the other hand, reveals two interesting features (Fig. 4.18b): (i) the simultaneous presence of flat and dispersive bands near the Fermi level and (ii) a set of parallel bands alongY that may lead to possible nesting of the Fermi surface. These features have been suggested to favor superconductivity ( Sun, et al., 2009).
104
Figure 4. 17. The calculated enthalpies for the chalcopyrite (I-42d) and tridymite (P212121) structure of CS2 over a large pressure range from 20 to 60 GPa, showing that the chalcopyrite structure is more stable by about 0.3-0.4 eV/formula unit (The calculation was done by Prof. John Tse (2011)).
105
Figure 4. 18. (a). The electronic band structure of the chalcopyrite showing a metallic ground state. (b) The electronic band structure of the tridymite structure at 47 GPa showing the metallic nature and flat and parallel bands (The calculation was done by Prof. John Tse (2011))
106
Figure 4. 19. The phonon band structure and density of state for the chalcopyrite structure, showing the major Raman-active A1 phonon mode at 500 cm-1 and other IR modes at 700-800 cm-1(The calculation was done by Prof. John Tse (2011)).
4.6.2 Superconductivity and Magnetic Ordering
The present structural model that described in chapter 4, clearly reflects an increase in the first nearest coordination number, most likely arising from the contribution of sulfur 3d bands in
CS bonds. The enhanced d-band character, then, results in relatively narrow itinerant bands; whereas, the local structural change introduces a mixed valence state. Therefore, we conjecture that the observed electron correlation, both below ~45K at 63GPa and above 100 GPa at ambient temperature, is due to the cooperative fluctuation in CS bond lengths and spin states in this narrow-band mixed valence states.
107 In fact, pure sulfur, which becomes superconducting above 93 GPa and further transforms to another superconducting phase (-Po like, six-folded) above 157 GPa with a sudden jump in the
TSC (from 14 K to 17 K) (Struzhkin, Hemley, Mao, & Timofeev, Superconductivity at 10–17 K in Compressed Sulphur, 2001) (Gregoryanz, et al., 2002), is also stabilized by the 3d hybridization with the core electrons (Rudin & Liu, 1999). Furthermore, similar magnetic ordering transitions in GeS2 and SnS2 observed in the present study further signify a more general periodic behavior of sulfur-containing group IV-VI compounds as correlated intermetallic alloys.
On the other hand, the persistent electrical resistivity anomaly near 45 K in Fig. 4.14a may provide insights into the interplay between magnetic ordering and superconductivity. Figure
4.20 plots the magnitude of the resistivity anomaly δρ as a function of pressure. As shown in the inset, the δρ is obtained by extrapolating the temperature dependences above and below the transition to TN and evaluating the difference in the resultant electrical resistivity. The plot clearly shows a noticeable difference in δρ between the non-superconducting state at 48 GPa and the superconducting state at 60 GPa. The quantity δρ in the superconducting state steadily decreases with pressure to ~100 GPa, above which it drops abruptly and then decreases again steadily above 120 GPa. This behavior can be understood within the context of the fraction of gapped (or ungapped) Fermi Surface (FS) spins. As pressure increases, the fraction of gapped spins decreases and reduces the number of available states into which quasiparticles can scatter.
Thus, it results in the reduction in δρ as observed. This result is then consistent with the fact that the superconductivity and antiferomagnetism is mutually exclusive.
108 Furthermore, it is important to note that the spin transition with an abrupt drop in δρ occurs at the onset of the local structural change and the electron-correlation change from the
Fermi-liquid (FL) to non-FL transition, all at around 100 GPa. Therefore, these results seem to indicate that CS2 indeed undergoes a magnetic ordering transition prior to the superconducting state.
Figure 4. 20. The magnitude of the resistivity anomaly δρ plotted as a function of pressure, showing a competing effect of magnetic ordering and superconductivity in dense carbon disulfide. In the inset the δρ is
defined by extrapolating the temperature dependences above and below the transition to TN and evaluating the difference in the resultant electrical resistivity.
109 4.6.3 X-ray scattering at low temperatures and high pressure
To understand the structural origin of superconductivity and magnetic odering , we have also examined the local structural change of CS4 phase under extreme conditions (Figs. 4.21).
T The pair distribution function G(r) at low temperatures and 63 GPa (denoted as r2 in Fig. 4.21) shows a dominant peak at ~2.8A of the S-S distance. The overall shape of the peak remains
T similar to ~70 K. The first peak (r1 ) at ~1.7 Å of the C-S distance, on the other hand, disappears or merges into the second peak with lowering temperatures (as well as increasing pressures in
Fig. 4.22a), probably due to either a relatively small x-ray scattering cross section of carbon or a disorder in the first shell structure of CS4 phase, or both. Importantly, the dramatic change in the
G(r) occurs both below 50 K (near the TN) and above 100 GPa (near the transition in the TC),
O O emerging in two new peaks at ~ 2.1 and ~ 6.2 Å (denoted as r1 and r5 , respectively). This results in an abrupt change of the first nearest distance from 1.7Å to 2.1Å. The second nearest distance (r2), however, changes only slightly within an experimental uncertainty of ±0.1Å. Then, below 50 K or above 100 GPa, the r2/r1 ratio collapses from ~1.67 of a close-packed tetrahedral packing, to ~1.43 (i.e., r2 = √2 * r1) of an octahedral packing similar to that observed in molten six-folded FeS [159,160]. In fact, all other observed peaks in the G(r) can be modeled reasonably well in terms of the present close-packed polyhedral models (Fig. 4.20b and Table 4.1), within
O O 5% for tetrahedral and even better for octahedral including the two new features (r1 and r5 ).
This model yields the density of 4.28 (or 4.75) g/cm3 at 58 (or 100) GPa, consistent with the previous estimation of 4.22 g/cm3 at 50 GPa. The increase in the coordination number leading to enhanced magnetic interaction is also consistent with the two-fold increase of the energy gap Δ observed in the resistivity above 100 GPa.
110
Figure 4. 21. The pair distribution function G(r) of highly disordered extended carbon disulfide, showing the temperature induced structural change at 63 GPa
111
Figure 4. 22. (a) The pair distribution function G(r) at ambient temperature, and (b) suggested crystal model of polymeric CS2. Pressure increased to 68 GPa at 125K, which then maintained to 11K. Tick marks represent pair distances using the cubic-close-packed structural models of CS4 tetrahedra and CS6 octahedra, rT and rO respectively.
112 Td Oh Td Oh
125K at 63GPa 40K at 63GPa 58GPa at 300K 100GPa at 300K
r1 1.67 (1.69) 2.14 (2.09) 1.68 (1.73) 1.91 (1.71)
r2 2.85 (2.76) 3.03 (2.96) 2.80 (2.82) 2.70 (2.79)
r3 4.20 (3.90) 4.16 (4.18) 4.58 (4.00) 3.84 (3.95)
r4 5.14 (4.77) 5.13 (5.12) 5.43 (4.89) 4.71(4.83)
r5 6.28 (6.16) 6.15 (5.91) 6.67 (6.32) 5.73 (5.58)
r6 6.97 (7.29) 7.10 (6.61) 7.34 (7.48) 6.80 (6.84)
Density (g/cm3) 4.93 4.90 4.25 4.75
Table 4. 1. The measured and calculated (in parentheses) peak positions of pair distances at various temperatures and pressures. Td and Oh represent respectively tetrahedral and octahedral local configurations. Only the first nearest carbon and sulfur atoms are counted for the pair distance calculation because of the weak scattering contribution of carbon by electron diffusion under high coordination numbers
.
113 4.6.4 Phase Diagram of Carbon Disulfide
The main findings in our research on carbon disulfide can be summarized in the phase diagram as shown in Fig. 4.23. First to recognize in the present phase diagram is the chemical analogy between carbon disulfide and carbon dioxide, sharing a similar polymorph in Cmca for molecular CS2-I (or CS2) and CO2-III phases and its transformation to non-molecular solids likely in tridymite-like structures. However, there exist some significant differences between the two. For example, molecular CS2 transforms into highly disordered three- and four-fold polymers above 10 GPa, which eventually metallizes above 50 GPa. The disordered structure of
CS2 with mixed three- and four-fold structures stays over a large pressure range (40 – 70 GPa), underscoring a substantial degree of ionic character in C-S bonds. On the other hand, CO2-III transforms to various extended solids with primarily four-fold coordinated carbon atoms above
40 GPa and high temperatures; then, those extended solids transform into non-metallic amorphous solids above 80-200 GPa or extended ionic solids at high temperatures (Yoo, Iota, &
Cynn, Nonlinear Carbon Dioxide at High Pressures and Temperatures, 2001) ( Yoo, Sengupta, &
Kim, Carbon Dioxide Carbonates in the Earth’s Mantle: Implications to the Deep Carbon Cycle,
2011). The structures of amorphous extended CO2 solids have been suggested to have carbon atoms with mixed three- and four-fold coordination (Iota, Yoo, & Cynn, An Optically Nonlinear
Extended Solid at High Pressures and temperatures, 1999)( Iota, Yoo, & Cynn, An Optically
Nonlinear Extended Solid at High Pressures and temperatures, 1999) (Montoya, Rousseau,
Santoro, Gorelli, & Scandolo, 2008). Therefore, the nature of structural disorder seems to be similar between the two, but their electronic structures are quite different (metallic vs. insulator with Eg>3.5 eV).
114 The atomic radii of carbon and oxygen and sulfur atoms in fully covalent bonds are: 0.77 Å for carbon, 0.66 Å for oxygen and 1.02 Å; whereas, those in fully ionic bonds are: 1.24 Å for O2- ,
0.16 Å for C+4 and 1.84Å for S2- ( Nicol & Syassen, 1983). Therefore, a natural way to increase the packing density at high pressures is to increase the ionic character in C–O or the C-S bonds so that the substantially smaller carbon atoms can be fit into the interstitial sites of close packed oxygen and sulfur atoms.
Figure 4. 23. The pressure-temperature phase diagram for carbon disulfide, showing the pressure-induced insulator-to-metal transition. In the region of metallic CS4 phase, showing (i) the magnetic antiferromagnetic
(AFM) ordering transition at TN, (ii) the superconducting (SC) transition at Tsc, and (iii) a small drop in resistance
(unknown origin) at Tx prior to the superconducting transition. The pressure dependence of the TSC was determined from both the resistance (open blue circles) and magnetic susceptibility (open red circles). PM and DM denotes the paramagnetic and diamagnetic.
115 Carbon disulfide transforms into nonmolecular, highly disordered metallic phase III [CS4 phase] at around 45-50 GPa, which are superconducting at low temperatures (see Fig. 4.23).
Remarkable, the highly disordered CS4 phase shows extremely high metallic conductivity, similar to those of elemental metals. This is in a stark contrast to the most “metallic” organic polymers that exhibit barely metallic conductivity (Heeger, 2001). The poor conductivity in organic polymers is due to the fact that their electronic structures are dominated by disorder with short mean free paths approaching the atomic separation (i.e., Ioffe-Regel criterion) (Ioffe &
Regel, 1960). In this regard, the origin of high metallic conductivity in highly disordered CS4 phase is quite puzzling - not to even mentioning its collective intermetallic behaviors of superconductivity, magnetic ordering, and non-Fermi liquid like behaviors. We conjecture that this highly unusual behavior of carbon disulfide is due to a collective lattice distortion arising from the local structural change from a tetrahedral to octahedral configuration (as shown in Fig.
4.23) that may occur dynamically. Such dynamic local structure change can then cause the valence change causing the spin to fluctuate and the bond distance change creating new lattice phonon to more effectively mediate the electrons.
Understanding the interplay of superconductivity, magnetism, and structural disorder is an intriguing scientific challenge for many decades (Goldman & Markovic, 1998)( Anderson P. W.,
1959). Although structural disorder enhances electrical resistance and decreases Tc, superconductivity do exists in many disordered systems, as previously observed in Ge (Barkalov, et al., 2010) and MZr metallic glasses (M=Cu, Ni, Co, and Fe) (Altounian & Strom-Olsen,
1983). In fact, high Tc superconducting oxides and metal-doped carbons are intrinsically disordered. In this regard, the present observation of superconductivity and magnetic ordering in highly disordered carbon disulfide is not surprising, but offers insights into correlated metallic or
116 intermetallic behaviors of extended carbon disulfide and motivates a systematic search for other highly conducting states of simple molecular systems with high phonon frequencies at high pressures. Therefore, both magnetic and superconducting properties of simple organic molecules like carbon disulfide certainly are significant in fundamental science and technology applications.
117 Chapter 5
Chemical Analogs to Carbon Disulfide
5.1 Molecular Analog: Carbonyl sulfide (OCS)
The series of related triatomic linear molecules CO2, OCS and CS2 is of fundamental interest in various aspects in high pressure science. High-pressure spectroscopic studies give the first insight of rich chemistry of those molecules, like pressure dependent intra-molecular forces and their anharmonicities (Fermi resonance interactions) as well as the pressure-dependent intermolecular forces and the formation of various crystalline phases. Over the past decades
Raman scattering of CO2 and CS2 have been extensively studied but until now only one high- pressure Raman study on solid carbonyl sulfide (OCS) has been reported(Shimizu, Ikeda, &
Sasaki, 1990). At ambient conditions OCS is a colorless, flammable gas with an unpleasant odor.
It is a linear triatomic molecule like CO2 or CS2 but unlike CO2 and CS2 it is non-centro- symmetric possessing a dipole moment of 0.715 D (Tanaka, Ito, Harada, & Tanaka, 1984). At atmospheric pressure below 134 K it forms a solid of rhombohedral structure with space group
5 R3m (C 2v) and one molecule per unit cell (Overell, Pawley, & Powell, 1982). The previous high-pressure study reveals that OCS changes irreversibly with a dark red appearance above 17
GPa (Shimizu, Ikeda, & Sasaki, 1990). In the present study, we found the spectroscopic evidence of a new phase arising above 9 GPa and a pressure induced polymerization above 21 GPa. We also found that the latter polymerization accompany the electronic insulator metal transition.
118 5.1.1 Polymerization and Insulator - Metal Transition
Pressure-induced Polymerization
The Raman spectra of OCS indicate that it became a molecular solid above 2.8 GPa.
Unlike CO2 and CS2, all three fundamentals are Raman active as well as infrared active. The typical Raman spectrum of solid OCS is shown in Fig. 5.1. The band near 870 cm-1 and 1986cm-1 can be ascribed to the ν1 - stretching mode and the ν3 - asymmetric-stretching mode, respectively.
-1 -1 -1 The band near 517 cm , 1023cm , and 1035 cm can be ascribed to the O=C=S bending (ν2),
-1 and the first over-tone of the bending mode 2ν2, respectively and lattice mode at 138 cm (Fig.
5.1).
Figure 5. 1. Raman spectra of OCS phases upon increasing pressure at room-temperature, resulting in polymeric OCS at above 20 GPa.
119
The appearance of the 2ν2 is interesting due to the unexpectedly strong intensity of the Raman
-1 band 2ν2 due to Fermi resonance between the frequencies ν1 and 2ν2. The band at 1035 cm is very sharp and strong, the band at 1023 cm-1 is very broad and less intense and because of its being at 12 cm-1 lower frequency relative to the other peak it cannot be assigned to the overtone of the isotopomers C=34S . Therefore the more likely possibility for the origin of two bands is that the vibrational level of the frequency ν2 splits into two levels (which is observed as shown in
Fig. 5.2) as a result of the crystal field and their overtones appear in the spectrum through Fermi resonance with the frequency ν1. In OCS though much weaker than in CO2, 2ν2 and ν2 exhibit
Fermi resonance. In both OCS and CS2, however, it has a very similar intensity of about one-
34 32 tenth that of ν1. The doublet structure in the ν1 is caused by the isotopomers C= S and C= S.
The relative intensities of those bands are consistent with the natural abundance of the isotope molecules (C=34S – 90% and C=32S – 8%). Three bands were observed at 1980cm-1, 1986cm-1 and the broad peak 2015 cm-1. The band at 1986 cm-1 is very sharp. These three bands are interpreted as the components of the antisymmetric stretching vibration arising from the factor group splitting by the crystal field. Upon increasing pressure those peaks show a blue shift up to
9 GPa and above 9 GPa the peak around 1980 cm-1 disappears as well as the intensities and the broadness of the other two peaks change dramatically. Above 9 GPa all the bands show red shift upon increasing pressure. The low-frequency Raman band at 142 cm-1 is due to lattice vibration.
It has been found that the frequency of this intermolecular mode shows remarkable pressure dependence with a slope of dν/dp ~ 9.76cm-1/GPa. Upon increasing pressure this lattice mode starts to split above 8 GPa as shown in figure 5.2, indicating a structural change. From our
Raman spectra we are seen a structural change above 8 GPa.
120 Another interesting observation was that in OCS, the intensity of the ν2 fundamental increased compare to the ν1 fundamental band (see Figure 5.3).
Figure 5. 2. The pressure dependences of the Raman spectra of solid OCS, indicating the structural changes at 8 GPa and polymerization above 22 GPa. The inset shows subtle changes in Raman spectra in the 450-700 cm-1 region associated with the structural phase transitions at 22 and 32 GPa.
121 Above 21 GPa, all of these modes disappear and, instead, two new broad peaks appear at ~547 cm-1 and 574cm-1 (see the inset of Fig. 5.2), representing, respectively, the bending and stretching modes of (S-(C=O)-S) in polymeric configuration. Above 32 GPa, these two features
-1 merge into a single band at ~570 cm like CS2, which can be attributed to the O-C-S bending mode in a 3D network structure made of tetrahedra. We, therefore, attribute the Raman change at
32 GPa to a structural phase transition to an extended solid made of O2CS2 tetrahedra.
Figure 5. 3. Intensity ratio of the ν2 fundamental and ν1 fundamental band (ν2/ ν1 ) with increasing
pressure indicating enhancing of the intensity of the ν2 fundamental band.
122 Insulator to Metal Transition
The pressure variation of electrical resistance measurement is shown on Fig. 5.4. The resistance of OCS undergoes a sharp decrease by six orders of magnitude, when the pressure increased from 50 to ~70 GPa, clearly suggesting a band gap closure. Above 70 GPa resistance drops slowly from ~100 Ω to ~10 Ω at 95 GPa suggesting an insulator to metal transition. The conducting phase of OCS is opaque and to some extent reflective (see inset Fig. 5.4). The measured resistance of the OCS at 95 GPa is less than 13 Ω which is typical for metals at this pressure in a DAC. The metallic nature of the OCS is consistent with its visual appearance (Fig.
5.5).
Figure 5. 4. The pressure dependence of the electrical resistance of OCS at room temperature. We observed sharp decreasing of the resistance up to 70 GPa, indication the semi-metallic state
123 The insets show the reflectance of the sample around 78 GPa providing the visual evidence for the band gap closure.
Figure 5. 5. Microphotographs of OCS under high pressure showing its transformation from transparent fluid to molecular solid at ~3 GPa, to black polymer above 22 GPa ((-S-(C=O)-)p), ((a) to (e)) and eventually to a reflecting extended solid above 95 GPa at ambient temperature((f) taken using reflected light)).
124 5.2 Main Group IV Disulfides: GeS2, SnS2
5.2.1 Metallization in GeS2 and SnS2
Comparing germanium disulfide, tin disulfide and silicon disulfide with CS2 provides opportunities to exploit the periodic relationship between the structural phase transitions and the electronic metallization. SiS2 is highly reactive with moisture and decomposes; therefore, we have limited our studies on GeS2 and SnS2.
During the last few years, semiconducting layered compounds and alloys have been investigated intensively and their optical properties have been of particular interest. Among the layered semiconducting compounds, special attention has been paid to group IV disulfides. The series of related triatomic solids SiS2, GeS2 and SnS2 belongs to the family of layered semiconductors of MX2-type (M – metal, X – chalcogen) possessing a number of unique properties is of fundamental interest in various aspects in high pressure science. For example, we have witnessed a simple molecular solid such as CS2 transform into non-molecular (extended) solids with more itinerant electrons, which softens repulsive interatomic interactions at high density. As a result, it gives rise to various properties like insulator-to-metal transitions, superconductivity, magnetic ordering, and deviation from Fermi liquid behaviors. On the other hand, nonmolecular phases of carbon dioxide transform into either amorphous solids at ambient temperature or ionic solids at high temperatures, but not to metallic phase. In this regard, the systematic studies of sulfur-containing chemical analogs of GeS2 and SnS2 complement the earlier described studies of CO2, CS2, and OCS.
125 Germanium disulfide is a polymorphous compound displaying three main modifications at ambient conditions (Dittmar & Schifer, H.T.-GeS2, 1975)( Dittmar & Schifer, The crystal structure of Germanium disulfide, 1976)( (Popovic & Stolz, Infared and Raman spectra of
Germanium Dichalcogenides-I: GeS2, 1981)( Popovic, Consideration of the Vibrational
Properties of Germanium Dichalcogenides on Base of Vibrational Properties of GeX (X=S,Se) tetrahedra, 1983)( Pauling & Am, 1929); three dimensional crystalline structure (3D-GeS2) which the dominant Raman band corresponding to symmetric stretch vibrations of S atoms in
-1 chains of corner-sharing tetrahedra ~342 cm , a layered crystalline structure (2D-GeS2), and an amorphous phase.
We have studied 3D-GeS2 and under pressure its transforms to low density amorphous phase at around 6 GPa and to a high density amorphous phase above 15 GPa. Upon decompression this low-density, amorphous phase is stable to ambient pressure. The 3D crystalline structure has never been recovered on release. The pressure-induced structural changes accompany a large, seven-order drop in electric resistance over a pressure range of 10 to
50 GPa, clearly suggesting an insulator-metal transition at ~40 GPa (See Fig. 5.7). The conducting phase of germanium disulfide, especially in the above 40 GPa, is opaque and highly reflective. The metallic nature of the amorphous phase is consistent with its high optical reflectivity (Fig. 5.6). The resistance as a function of temperature further suggests a gradual insulator-to-metal transition (Fig. 5.8).
126
Figure 5. 6. Microphotographs of GeS2 under high pressure showing its transformation from transparent to opaque ((a) – (c)) and then to a reflecting solid above 40 GPa. The reflectance of the sample around 40GPa providing the visual evidence for the band gap closure.
127
Figure 5. 7. The pressure dependence of the electrical resistance of GeS2 at room temperature. We observed sharp decreasing of the resistance up to 40 GPa, indicating a metallic state.
128
Figure 5. 8. The temperature-dependent electrical resistance of GeS2 at various pressures on a logarithmic scale, showing a transition from insulator to semiconductor to metal.
129 A characteristic feature of the layered SnS2 crystals is their polytypism, arising due to the infinite number of possible layer alternations which differ in the sequence of the constituent atoms (Bletskan, 2004). Tin disulfide, for example, consists of two layers of hexagonal closed packed sulfur anions with sandwiched tin cations which are octahedrally coordinated by six nearest-neighbor sulfur atoms (Wang, Tang, Yang, Qian, & Xu, 2001). The atoms within the layers are connected via strong covalent bonding (12% ionic), adjacent layers are only weakly bonded by van-der-Waals forces. Each S is nested at the top of a triangle of Sn atom. Adjacent
S–Sn–S layers are bound by weak van der Waals interactions (Wells, 1975).
Most of the physical properties of semiconductors (optical and photoelectric properties, photoemission, photoluminescence, etc.) can be explained on the basis of their energy band
-1 structure. Raman spectrum of SnS2 shows a strong peak around 318 cm (A1g), weak peak around 221 cm-1 and a wide peak between 450 and 650 cm-1 at 0.5GPa. At high pressures above
40 GPa it becomes amorphous with one broad peak. As we observed in GeS2, SnS2 undergoes a similar pressure-induced metallic transition above 37 GPa (Fig 5.9) with eight-order drop in electrical resistance over the pressure range of 10 to 40 GPa. The conducting phase is opaque and highly reflective. The metallic nature of the amorphous phase is consistent with its high optical reflectivity. The resistance as a function of temperature further suggests a gradual metallic transition (Fig. 5.10). Finally, it is remarkable to observe that GeS2 and SnS2 show extremely high metallic conductivity, similar to those of elemental metals.
130
Figure 5. 9. The pressure dependence of the electrical resistance of SnS2 at room temperature. We observed sharp decreasing of the resistance up to ~ 38 GPa, indication the metallic state.
131
Figure 5. 10. The temperature-dependent electrical resistance of SnS2 at various pressures on a logarithmic scale, showing a transition to a metal.
132 5.2.2 Magnetic Ordering - GeS2 and SnS2
Remarkably, both GeS2 and SnS2 show not only the metallization but also new magnetic states as evident from the unusual resistance plateau (Fig. 5.11) around ~ 35 K and 30 K respectively. The resistance plateau, is analogous to that observed in CS2 arising from a magnetic ordering transition (see chapter 3 for more details). The critical temperature TN is then defined by the inflection point at the minimum of dρ/dT, as illustrated in Fig. 5.11 inset. The resistivity values below TN can be described by Eq. (2.4) with an energy gap (Δ) of antiferromagnet and an additional T2 term reflecting Fermi-liquid behavior (Andersen, Crystalline Electric Field and
Structural Effects in f-Electron Systems, 1980).
The best fit at 55 GPa (black dash line for GeS2 and red dash line for SnS2 in Fig. 5.11), for
-2 -1 example, in GeS2, gives Δ=153 K, A= 0.024 cmK o = 8m, B = 254cmK . As illustrated in Fig. 5.12a, the energy gap Δ increases linearly with pressure from 67 K at 45 GPa to 78 K at
50 GPa (at the rate of 2.2 K/GPa), where it jumps to 153 K and shifts at the rate of 3.85 K/GPa to
55 GPa. The coefficient A, on the other hand, rapidly increases at 50 GPa and suddenly decreases again and becomes nearly independent of pressure above 55 GPa. In SnS2, we never observed any jump in energy gap and also an unusual increment in A. The value of Δ (P=0) obtained from this fitting is 32 K for GeS2 and 48 K SnS2 – consistent with those of heavy fermions systems such as UT2Al3 and URu2Si2 (~5.5 meV or 70 K) (Dalichaouch, Andrade, &
Maple, 1992) (McElfresh, et al., 1987). However we did not observe any superconducting transition up to the 4.5 K minimum temperature measured, but decreases in magnetic ordering temperature in systematically may indicate that superconductivity arises at below 4.5 K, which deserves further experimental and theoretical studies on these solids beyond 4.5 K.
133
Figure 5. 11. Low-temperature resistivity of GeS2 and SnS2, showing the magnetic ordering transitions at 55 GPa. The solid lines illustrate a best fit to Eq. (2.4) describing electron-magnon scattering from antiferromagnetic magnons with an energy gap (Δ). Inset: Temperature dependence of the carbon disulfide temperature coefficient dρ/dT. The transition temperature TN is defined as the temperature of the minimum in dρ/dT.
134
Figure 5. 12. (a) Values of the energy gap (Δ) and coefficient A of the T2 contribution to as a function of pressure, as derived from fits of Eq. (2.4) to the data for GeS2 and (b) for SnS2.
135 5.3 Discussions
The carbonyl sulfide (OCS) shows a greater degree of similarity with carbon disulfide. It is the intermediate state and the only one to possess a dipole moment of 0.715 D (Tanaka, Ito,
Harada, & Tanaka, 1984). The molecular OCS transforms to black OCS2 phase like, (S-(C=O)-
S) and then to a four-folded extended solid which eventually becomes metallic. Clearly, these results highlight how the presence of ionicity, can collectively give rise to greatly different chemical behaviors at high pressures.
Raman study of GeS2 indicates that there is a low-density amorphous to high-density amorphous transition upon increasing pressure around 15 GPa. This can interpreted as the conversion from a tetrahedral glass to a mainly octahedrally coordinated amorphous state. In a-
GeO2 the fourfold-to-sixfold nature of the transition seems well established at low pressures, at least by comparison with analogous behavior in crystalline quartz like GeO2 ( Durandurdu &
Drabold, 2002). The metallization occurs within the high density amorphous phase, we point out that the band gap closing is associated with structural transition, indicating the resistance changes onset of this structural transition. However, simulation studies observed AAT in GeSe2 as well but at much higher pressures (60 GPa) ((Harbold, et al., 2002). Therefore, we might argue that the family of tetrahedral GeX2 (X=O, S, Se) systems the pressure range of transition at which the fourfold to sixfold change takes place increases with X atomic radii. Usually, elements behave at high pressure like the elements below them in the periodic table at lower pressures. Also, bond covalency of Ge-X increases with increasing X atomic radii, which would lead one to expect the metallization pressure to decrease with increasing X atomic radii(Fig. 4.13.).
136 On the other hand YS2 (Y= C, Ge, Sn) materials are characterized by a different degree of
Y-S bond covalency and bond ionicity. In view of their very different bond ionicity and polyhedral connectivity, the metallization pressure decreases with increasing Y atomic radii.
Figure 5. 13. The pressure dependence of the electrical resistance of group IVA sulfides at room temperature with increasing pressure.
137 Chapter 6
Concluding Remarks
Pressure allows the basic electronic properties and lattice structures to be tuned by shortening distances between atoms, and it can induce a rich variety of phenomena. Simple molecular solids, such as carbon disulfide, beautifully illustrate these kinds of transformations which form the main findings reported in this dissertation. In particular, we report the transformation under pressure of linear CS2 first into a ID black polymer (-S-(C=S)-)n) and then to a denser covalently bonded network structure made of CS4 tetrahedra. These structural changes are accompanied by dramatic changes in the electrical transport properties, with the electric resistance by seven orders of magnitude from 10 GPa, where the 1D black polymer forms to 50 GPa, well in the stability region of the fourfold coordinated CS4, which exhibits metallic properties. Upon cooling at high pressures, CS4 first undergoes a magnetic ordering transition at 45.2K, and then becomes a superconductor at 6.2K, the first simple, diamagnetic molecular solid to exhibit these transformations. The system undergoes further electronic and structural changes at 1 Mbar, from typical Fermi liquid behavior with a local tetrahedral structure to non-Fermi liquid behavior with a local octahedral structure.
These changes are consistent with a transformation from a itinerant metal to a correlated metal. It is known that the electron-phonon mechanism cannot explain the Cooper pairing found in the high Tc superconductors.
138 Some recent theories have opposed electron coupling to the magnetic excitations of the material (spin-fluctuations in antiferromagnetic state), rather than phonons, as the pairing “glue” in cuprates.
Figure 6. 1. The composition-pressure phase diagram of CX2 (X= O, S) and YS2 (Y=C, Ge, Sn) systems, illustrating the concept of a molecular alloy. The red dots and solid line represent the polymerization and the blue dots and dashed line represent the metallization and the linear interpolation. The Shaded area represents the immiscible dome at temperature T which gives rise to magnetic ordering and superconductivity.
139 Since a magnetic ordering transition was observed in the CS4 phase, this system may provide a suitable case to further examine these recent ideas regarding unconventional superconductivity, in the Cooper pairing may mediated magnetically by fluctuation spins. Thus, it is hoped that a better understanding of the magnetic ordering and the structure could provide further insight into the behavior and properties of unconventional superconductors.
The changes that were observed in CS2 suggested examining molecular and chemical analogs to examine the systematic trends in these simple molecular solids. Like CS2, the linear molecular OCS transforms under pressure gradually to a black polymer (-S-(C=O)-)n) and then to a denser covalently bonded network structure made of tetrahedra. This phase, like CS4, also undergoes a large, seven-order drop in electric resistance, over a pressure range of 50 to 100
GPa, clearly suggesting an insulator-metal transition at ~95 GPa, almost twice the metallization pressure of CS4. This can be understood as being caused by the ionicity of oxygen. This has implications for the possible metallization of CO2, which is reported to still be transparent at 220
GPa (Yoo, Sengupta, & Kim, Carbon Dioxide Carbonates in the Earth’s Mantle: Implications to the Deep Carbon Cycle, 2011) (see Fig. 6.1). For the chemical analogs, metallization is also observed, with the insulator-metal transition occurring at ~40 GPa in GeS2, ~35 GPa in SnS2.
Remarkably, both metallic GeS2 and SnS2 show a magnetic ordering transition at 35K and 30K, respectively. Both were cooled to 4.5 K, however, no superconductivity was observed in either molecular solid. The similarities between these systems suggest that they should exhibit superconductivity, and further studies to temperatures below 4.5 K could be possible future experiments.
140 Extended states of molecular solids, polymeric or metallic alike can be considered as molecular alloys of constituent elemental solids. Fig. 6.1 illustrates this concept on the system of carbon-oxygen, carbon-sulfur, germanium-sulfur, and tin-sulfur. Note that the transition pressures for the pressure-induced polymerization to 3D network structures increases as the ionic character in carbon–oxygen bonds increases and decreases with the increasing of cation radii of group IV elements. These pressure-induced polymerizations to mostly wide-band gap network structures retard the occurrence of metallization.
Chemical transformations of highly compressed low-Z molecular solids at their bond energies have opened up new avenues of inquiry. Much fundamental research interest has been focused on resolving crystal structures of novel extended states and understanding the driving forces behind the bonding changes that lead to the formation of new materials. Yet, from a practical perspective, low-Z extended solids such as CS2 exhibit intriguing metallic, magnetic, superconductive properties, which make them an extremely attractive material for future technological needs. Furthermore, there are many candidates of such materials that can be stabilized into novel 3D network structures at high pressures, including nearly all low-Z molecular solids that make of first and second row elements. Combined with the concept of novel molecular alloys, one can begin to design (or imagine) novel low-Z extended materials of the sp- or spd-counterpart metals that often exhibit superconductivity, magnetism and novel optical/electronic properties, but only with substantially enhanced thermal/chemical/mechanical properties.
While the significant findings were made in the present research regarding the pressure- induced structural and electronic phase transitions, especially the superconductivity and magnetic ordering in carbon disulfide, understanding the detailed relationship between crystal
141 structures and electronic correlations in this highly disordered system requires further studies – both theoretical and experimental. Directly probing the exact nature of structural disorder and magnetic states in dense carbon disulfide and its chemical analogs should be emphasized, utilizing modern high-pressure technologies and advanced light sources such as neutron scatterings, synchrotron x-rays, and high-field magnetic sources, over the extended region of pressure and temperature in particular. Extending the concept of molecular alloys, it would also be interesting to investigate sulfur-containing composites as well as other binary mixtures of light elements, over an extended pressure range altering both chemical and structural miscibilities in significant ways.
142 Appendix A
Structural and Metallic Transition in GeS
The compounds consisting of group-IV elements (Ge, Sn) and group-VI elements (S, Se) are in many respects an interesting group of compounds. They are known as narrow-gap semiconductors or semimetals which have a potential for various optoelectronic applications. At ambient pressure those compounds adopt an orthorhombic structure with eight atoms per unit cell forming double-layer planes normal to the longest axis, which closely related to that of black phosphorous (Jayaraman,1984)( Hemley, 2000)( Grochala, Hoffmann , Feng & Neil,2007). At the present time, experimental structural, spectral and electrical studies have been performed on several members of the IV-VI family (Iota, Yoo, & Cynn, An Optically Nonlinear Extended
Solid at High Pressures and temperatures, 1999)( Dias, Yoo, Kim & Tse, 2011). However, the presence or absence of the phase transitions in some of these compounds is still uncertain
(Gavriliuk, Trojan, & Struzhki, 2012). It is well known that shear deformations alter the stability of phases and change the mechanism of phase transition. Therefore the controversies on those studies might arise from non-hydrostaticity of the applied pressure because the two compounds are made up of puckered layers structures very sensitive to shear stress(Eremets, Gavriliuk,
Trojan, Dzivenko, & Boehler, 2004)( Degtyareva, et al., 2005). On the other hand electrical resistance measurement on GeSe showed monotonically decreases with increasing pressure and it suggest that GeSe has become metallic above 25GPa (Struzhkin, Hemley, Mao, & Timofeev,
Superconductivity at 10–17K in Compressed Sulphur, 2001). The presence of metallization reflects weakening of the strong covalent nature of the Ge-Se bonds. It is also well known that the vibrational spectra of layered crystals are characterized by low frequency optical phonons.
143 They can attribute to rigid layer modes, which adjacent rigid layers move parallel to each other and compressive vibration in which layers vibrate against each other.
Relatively little studies has been done on the GeS. It is of great interest to know how the structural, vibrational, and electrical properties will change upon application of pressure. It is the least anisotropic member of the series of orthorhombic IV-VI compounds and behaves as if it were in some sense an intermediate case between the two dimensional (layer type) and three dimensional crystals. Earlier x-ray diffraction studies of GeS have shown that its sable upto
34GPa (Iota, Yoo, & Cynn, An Optically Nonlinear Extended Solid at High Pressures and temperatures, 1999). However recent theoretical studies (ab initio simulation) shows, that GeS indeed undergo a gradual phase transition to an orthorhombic state with space group Cmcm above 34GPa and also the metallization of GeS prior to transformation into the Cmcm phase
(Yoo, et al., 2005). The importance of understanding pressure induced electronic, structural, and vibrational effects in layered semiconductors, provides the motivation for the present work. In the present study, we report a structural and electronic phase transitions of GeS to metallic phase above 14GPa, using Raman spectroscopy, electrical resistance.
16 A factor-group analysis of the three dimensional space group D2h reveals 24 vibrational modes (Zha, Liu, & Hemley, 2012)( Eremets, Hemley, Mao, & Gregoryanz, 2001). Their representation at the center of the Brillouin zone is Γ = 4Ag + 2B1g + 4B2g + 2B3g + 2Au + 4B1u +
2B2u + 4B3u. Apart from three acoustic vibrations, there are 21 optical phonons and two are inactive (2Au) seven are infrared active (3B1u, 3B3u, 1B2u) and 12 are Raman active (4Ag, 2B1g,
4B2g, 2B3g). The structure contains double layer (perpendicular to c axis) in each layer covalently bonded and form a zigzag chain along the direction of the minor axis of the crystal in which atoms are threefold coordinated (Fig. A1). Materials with this structure are expected to exhibit
144 three zone centre rigid-layer optical vibrations. One of the modes is a rigid-layer mode which individual layers move each other as a unit and the other two
Figure A. 1.(a) The Pnma (62) orthorhombic structure of GeS with unit cell. The layered character and atomic coordination are evident. The unit cell parameters are a= 4.305Å, b=3.643Å, c=10.495Å (Iota, Yoo, & Cynn, An Optically Nonlinear Extended Solid at High Pressures and temperatures, 1999). The structure is completely specified
by four internal atomic positions (uGe, ¼, vGe) and (uS, ¼, vS). In (b) is shown a projection of the structure along the b axis.
145 are shear displacement in which the layers slide over each other by bond bending and covalent bond length changing in the a and b directions (Fig. A1). Also the degeneracies due to layer symmetry are lifted when coupling between layers in introduced (Davydov splitting) as the modes split into Raman active doublets.
Figure A. 2. Pressure dependence of the Raman spectra of GeS, showing the A and B phonons modes of GeS, g g clearly Indicating the splitting of the Ag mode and the new peak above 28GPa. The close and open symbols signify, respectively, the data taken during the pressure uploading and downloading.
146
Figure A. 3. Pressure-induced Raman changes of germanium sulfide, (a) showing the loading spectra and (b) showing the unloading spectra. The spectra shows splitting in Raman spectra in the 260 cm-1 region (Ag mode) and new rather broad peak appear at ~ 331cm-1 above 28GPa indicating a structural phase transition. The unloading spectra show the reversibility of the pressure changes to the sample.
147 The Raman spectra of GeS under hydrostatic pressure are presented in Fig. A3 and the pressure dependence of the Raman active modes shows in Fig. A2. According to the previous reports
(Yoo, et al., Crystal structure of carbon dioxide at high pressure: "Superhard" polymeric carbon dioxide, 1999) at ambient conditions Raman frequencies could be grouped into three lowest frequencies (~52 cm-1, ~64 cm-1, ~77 cm-1), somewhat higher frequencies (ranging from `88 cm-1 to ~133 cm-1) and considerably higher frequencies (ranging from ~210 cm-1 to ~300 cm-1 ). The
-1 lowest frequency modes we collected in our experiment occur at 111 cm (Ag shear mode).
However we observed Ag modes and B3g mode only due to the anisotropic nature of the sample.
The observed Raman modes show the increasing frequencies with increasing pressure as expected. However one of the higher frequency shear mode (bond stretching type) which occur around 269cm-1 shows the clear discontinuity of the rate of change of the frequency above 8GPa from 2.949 cm-1/GPa to 4.176 cm-1/GPa (Fig. A3). Also a splitting of the one of the Ag mode above 8GPa observed. Above 30GPa, one new rather broad peak appear at ~ 331cm-1, indicating a structural phase transition.
The pressure variation of electrical resistance measurement is shown on Fig. A4. The resistance of GeS undergoes a sharp decrease by seven orders of magnitude with a slight discontinuity ~12GPa when the pressure was increased from 0 to 18GPa, clearly suggesting a metallic transition at ~ 16GPa (Fig. A4). The conducting phase of germanium sulfide is opaque and highly reflective approaching the level of Pt metal (see inset Fig. A4). The measured resistance of the GeS at 16GPa is less than 10Ω which is typical for metals at this pressure in a
DAC. During decompression, following a hysteresis cycle, the resistance of the sample returns to its original value. The metallic nature of the germanium sulfide is consistent with its high optical reflectivity and its calculated electronic band structure later discussed. The resistance of the low
148 pressure GeS as a function of temperature further suggesting a gradual transition from semi- conductor to a metal (Fig. A5).
Figure A. 4: The pressure dependence of the electrical resistance of GeS at room temperature. We observed
sharp decreasing of the resistance up to 18GPa with a discontinuity around 12GPa, clearly indication the metallic state. The inset show the sample becomes shiny around 15GPa providing the visual evidence for the metallization. The close and open symbols signify, respectively, the data taken during the pressure uploading and downloading.
149
Figure A. 5: The temperature-dependent electrical resistance of germanium sulfide at 3, 6, 11GPa on a logarithmic scale, showing a transition from semiconductor to semi-metal, and 16, 21, 46 GPa showing the clear metallic behavior.
The present spectroscopic and resistance results indicate the pressure-induced
metallization of germanium sulfide at ~16 GPa, and possible structural phase transition.
However according to the present experimental data GeS doesn’t transform to predicted Cmcm
phase instead rock salt structure. It’s because likely through the shearing of layers relative to
each other along the c direction. We also observed a significant change of the pressure
-1 -1 dependence of the high frequency Ag mode from 2.949 cm /GPa to 4.176 cm /GPa.
150 Appendix B
Structural and Metallic Transition in g-GeSe4
Chalcogenide glasses that are primarily sulfides, selenides, or tellurides of Group III, IV, and V elements have found important and wide-ranging applications in photonics and telecommunication technologies owing to their unique optical properties including infrared transparency, large optical nonlinearity, and strong photosensitivity (Jayaraman,1984) ( Hemley,
2000). Germanium selenides represent the archetypal chalcogenide glass-forming system and their structural characteristics have been studied extensively over the last two decades using a wide range of spectroscopic and diffraction techniques. In that regard, germanium selenium system exhibits properties, which are unusual, and possibly unique, relative to other semiconductors. These unusual characters have obviously added much flavor to stimulated study. The results change with atomic configuration, and a subsequent change in the physical properties such as structure, optical and electrical properties of the material (Iota, Yoo, & Cynn,
Quartzlike Carbon Dioxide: An Optically Nonlinear Extended Solid at High Pressures and temperatures, 1999)( Dias, Yoo, Kim & Tse,2011). Here we summarized the results of Raman spectroscopic study of the structural rearrangement in the tetrahedral backbone consisting of corner and edge-sharing GeSe4 glass, as a function of pressure (denoted as CS and ES, respectively). Pressure-dependent structural changes in the tetrahedral backbone in terms of its
ES:CS ratio is investigated. Finally, the resistance measurement indicated that metallic transition above 20GPa and, interestingly low temperature resistance shows an anomaly with clear pressure dependence, which can be a magnetic ordering transition.
151
Figure B. 1. Pressure dependence of the Raman spectra of GeSe4, showing the CS and ES stretching modes of GeSe4. It’s clearly indicate that the progressive conversion of the CS to ES around 10GPa. The close and open symbols signify, respectively, the data taken during the pressure uploading and downloading.
Raman band near 197 cm-1 corresponds to the symmetric stretching of Se atoms in Ge-Se-Ge
linkage that are corner-shared (CS) between GeSe2 tetrahedra while the 214 cm-1 band
corresponds to the breathing mode of pair of Se atoms that are edge-shared between two
neighboring GeSe4 tetrahedra (Fig. B1). As shown in the Fig. B1, clearly indicate a structural
phase transition at around 10-11 GPa, which occurs reversibly. The high-pressure phase can be
signified by the progressive conversion of the CS to ES around 10GPa (see Fig. B2) in GeSe4
and two new Raman features, one of which exhibits a softening behavior (band at 210cm-1).
152 Note that it is not Se-Se vibration in pure Se, but perhaps a similar mode in GeSe4, as we have compared in the figure (green line).
Figure B. 2. Pressure dependence of the CS and ES stretching modes ratio in the GeSe4.
The pressure variation of electrical resistance measurement is shown on Fig. B3. The resistance of GeSe4 undergoes a sharp decrease by seven orders of magnitude with a slight discontinuity ~10 GPa (inset of Fig B3) indicating the metallic state above 20 GPa. The resistance of the low pressure GeSe4 as a function of temperature further suggesting a gradual transition from to a metal (Fig. B4).
153
Figure B. 3. The pressure dependence of the electrical resistance of GeSe4 at room temperature. We observed gradual decreasing of the resistance up to 20 GPa with a discontinuity around 10 GPa, clearly indication the metallic state.
154
Figure B. 4. The temperature-dependent electrical resistance of GeSe4 at 5, 8, 13.5 GPa, showing a transition to a metal, and the insect shows the resistivity anomaly at 13.5, 16, 24 GPa indicating by arrows.
155 Appendix C
Photoconductivity of SnO2 under Pressure
Tin oxide (SnO2) is a wide band gap (Eg=3.6 eV) n-type semiconductor used in many applications such as gas sensors and as anode material in Li-based batteries (Jayaraman,1984)
( Hemley, 2000). Usually, this material is crystallized in rutile (TiO2) structure. The unit cell contains two formulas; the cations are located on D2h sites and the oxygens are on C2v sites.
Nanocrystalline materials are the ones whose properties can be tuned by varying their grain sizes. As it is a semiconductor, its resistance and photoconductivity properties are two important factors to characterize this material. In the present work, we report, electrical resistivity and photoconductivity of nanocrystalline SnO2 with different power density under high-pressure.
The Fig. C1a gives the typical resistance vs pressure plot for nanocrystalline SnO2 up to
18 GPa. As shown in the figure, resistance increased upon increasing pressure, indicating the band gap opening. Unfortunately we were not able to get the resistance at low pressures but from the resistance value its convincing that initially resistance drop and then increased. (In another words first bad gap closed and then increased upon increasing pressure). High pressure photoconductivity data is sometimes used to complement electrical resistivity data when studying materials which may be in the vicinity of an expected insulator-to-metal transition or vise versa. Here we performed photoconductivity measurements with a 100 mW green laser
(514.5 nm) on SnO2, to confirm the band gap opening upon increasing pressure. The figure C1b show the photocurrent of the SnO2 sample with increasing pressure and different power density.
156
Figure C. 1. (a) Pressure dependence of the electrical resistance of SnO2. Gradual increasing of the resistance up to 18 GPa indicates the band gap opening with increasing pressure. (b) Normalized photocurrent change vs -2 -1 pressure with different power density (Power density varies from 5000 to 65000 Wm S ) in SnO2.
157 Appendix D
MATLAB code - Derivative Approximation
%------% Code : Derivative Approximation % Description : This code will make 2 plots; % Temperature(T)vs Resistance(R)and Temperature vs Derivative of R w.r.t T %------[T]=importdata('CS275T.txt'); [R]=importdata('CS275R.txt'); n=6;% order of fit p=polyfit(T,R,n);% find polynomial coefficients Ti=linspace(100.0096,6.025869,9400); Ri=polyval(p,Ti);% evaluate polynomial plot(T,R,'b',Ti,Ri,'r') xlabel('T(K)'), ylabel('R(Ohms)') pd = polyder(p); dyp=polyval(pd,T);% poly derivative for comparison dy=diff(R)./diff(T);% compute differences and use array division plot(T,dyp,'-') ylabel('dR/dT'), xlabel('T') save('dypfile.txt','dyp','-ASCII')
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