STUDYING BONDING AND ELECTRONIC STRUCTURES OF A …zr349qb7986/Shi... · 2011-09-22 · I would also like to thank my committee members: Professors Ian Fisher, Ted Geballe, Evan Reed,

STUDYING BONDING AND ELECTRONIC STRUCTURES OF

MATERIALS UNDER EXTREME CONDITIONS

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF APPLIED PHYSICS

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Shibing Wang

August 2011

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/zr349qb7986

© 2011 by Shibing Wang. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

ii



http://purl.stanford.edu/zr349qb7986

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Wendy Mao, Primary Adviser


Ian Fisher, Co-Adviser


Anders Nilsson

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

iii

Abstract

Recent advances in high pressure diamond anvil cell techniques and synchrotron radi-

ation characterization methods have enabled investigation of a wide range of materials

properties in−situ under extreme conditions. High pressure studies have made signif-

icant contribution to our understanding in a number of scientific fields, e.g. condensed

matter physics, chemistry, Earth and planetary sciences, and material sciences. Pres-

sure, as a fundamental thermodynamic variable, can induce changes in the electronic

and structural configuration of a material, which in turn can dramatically alter its

properties. The novel phases and new compounds existing at high pressure have

improved our basic understanding of bonding and interactions in condensed matter.

This dissertation focuses on how pressure affects materials’ bonding and elec-

tronic structures in two types of systems: hydrogen rich molecular compounds and

strongly correlated transition metal oxides. The interaction of boranes and hydrogen

was studied using optical microscopy and Raman spectroscopy and their hydrogen

storage potential is discussed in the context of practical applications. The pressure-

induced behavior of the SiH4 + H2 binary system and the formation of a newly formed

compound SiH4(H2)2 were investigated using a combination of optical microscopy,

Raman spectroscopy and x-ray diffraction. The experimental work along with DFT

calculations on the electronic properties of the compound up to the possible metal-

lization pressure, indicated that there are strong intermolecular interactions between

SiH4 and H2 in the condensed phase. By using a newly developed synchrotron x-ray

spectroscopy technique, we were able to follow the evolution of the 3d band of a 3d

transition metal oxide, Fe2O3 under pressure, which experiences a series of structural,

electronic and spin transitions at approximately 50 GPa. Together with theoretical

iv

calculations we revisited its electronic phase transition mechanism, and found that

the electronic transitions are reflected in the pre-edge region.

v

Acknowledgement

The completion of this dissertation and my Ph.D. study is indebted to many people

who have guided and helped me both in academia and in life. I am immensely

grateful to my principal adviser and mentor Professor Wendy Mao, who has every

talent to revive my passion to science and make my Ph.D. journey a rewarding and

enjoyable experience, and to Ho-kwang Mao whose scientific insights always inspire

and enlighten me, and to Agnes Mao who provides her support and encouragement

along the way.

I would also like to thank my committee members: Professors Ian Fisher, Ted

Geballe, Evan Reed, Bruce Clemens and Anders Nilsson for guiding me through my

Ph.D. study, asking profound yet important questions at my defense and helping

improve the overall quality of this dissertation.

In addition, Professors Zhi-Xun Shen, Tom Devereaux, Alberto Salleo, Yi Cui,

Chi-Chang Kao, James Harris, Zhenan Bao, Mike McGehee and Kelly Gaffney have

also given me great advice at various stages of my graduate study, most of which I

have seriously taken and implemented.

Many thanks to my collaborators who have taught me enormous knowledge and

skills of research: Yang Ding, Jinfu Shu, Tom Autrey, Adam Sorini, Cheng-Chien

Chen, Xing-Qiu Chen, Yuming Xiao, Paul Chow, Alexander Goncharov, Nozomu

Hiraoka, Hirofumi Ishii, Yong Cai and Chong-Long Fu, and to Extreme Environ-

ments Laboratory members: George Amulele, Yu Lin, Maria Baldini, Maaike Kroon,

Natasha Filipovitch, Hongwei Ma, Gabriela Farfan, Yingxia Shi, Arianna Gleason,

Shigeto Hirai, Wen-Pin Hsieh and Qiaoshi Zeng.

I would also like to mention a few persons whose dedication to youth education

vi

and enchanting personalities have greatly shaped who I am now and have led to my

pursuing a scientific career. They include my high school science and math teachers

Ms. Dongyun Li, Ms. Qiuhui Xu and Ms. Dan Gao, my undergraduate physics and

math professors Bangfen Zhu, Yunqiang Yu and Shutie Xiao.

This dissertation is dedicated to my parents, who are my role models in work

and in life. Their unconditional love, encouragement and moral support are always

indispensable to me.

Finally, I am deeply grateful to my husband Diling and my son Juhua. Besides

the joyful companion inside and outside of graduate school, Diling’s high standards

and sharp critiques help me grow into a better experimentalist, while Juhua with his

courage, persistence and sheer curiosity constantly reminds me to stay young and

stay foolish.

Shibing Wang

Menlo Park, August, 2011

vii

Contents

Abstract iv

Acknowledgement vi

1 Introduction to High Pressure 1

1.1 Achieving high pressure with a diamond anvil cell . . . . . . . . . . . 3

1.2 Pressure measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Experimental methods 7

2.1 Optical microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Raman spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 X-ray diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 X-ray spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Boranes and hydrogen 16

3.1 Decaborane and hydrogen . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Ammonia borane decomposition . . . . . . . . . . . . . . . . . . . . . 27

3.3 Calculation of hydrogen storage capacity . . . . . . . . . . . . . . . . 30

3.4 Energy intensity calculation . . . . . . . . . . . . . . . . . . . . . . . 32

4 Silane and hydrogen 34

4.1 Metallization of hydrogen . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2 Phase diagram of SiH4 and H2 at lower pressure . . . . . . . . . . . . 41

4.2.1 Materials and methods . . . . . . . . . . . . . . . . . . . . . . 42

viii

4.2.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 46

4.2.3 Further discussion . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.3 Formation of SiH4(H2)2 - a new compound . . . . . . . . . . . . . . . 56

4.3.1 Calculations on SiH4(H2)2 to metallization pressure . . . . . . 57

4.3.2 Computational and experimental details . . . . . . . . . . . . 59

4.3.3 Results and discussions . . . . . . . . . . . . . . . . . . . . . . 60

4.3.4 Comparison with other calculations . . . . . . . . . . . . . . . 67

5 Transition metal oxides 69

5.1 Effects of pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.2 High pressure x-ray absorption study of Fe2O3 . . . . . . . . . . . . . 71

5.2.1 Introduction to Fe2O3 . . . . . . . . . . . . . . . . . . . . . . 71

5.2.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.2.3 Theoretical interpretation and discussion . . . . . . . . . . . . 76

5.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

A Correlation functions of hydrogen 81

A.1 Properties of solid hydrogen . . . . . . . . . . . . . . . . . . . . . . . 81

A.2 Correlation function and infrared spectra . . . . . . . . . . . . . . . . 82

A.3 Correlation function and Raman spectra . . . . . . . . . . . . . . . . 84

A.4 Comparison between infrared and Raman . . . . . . . . . . . . . . . . 86

Bibliography 88

ix

List of Tables

1.1 Gibbs free energy change for different compounds with different exter-

nal pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

4.1 Lattice parameter and atomic positions of SiH4(H2)2 . . . . . . . . . 60

5.1 Crystal field splitting energy (CFSE) of Fe2O3 as a function of pressure. 75

x

List of Figures

1.1 Ruby fluorescence spectra at high pressures . . . . . . . . . . . . . . 6

2.1 Illustration of Raman Processes . . . . . . . . . . . . . . . . . . . . . 8

2.2 Illustration of x-ray Kβ emission process. . . . . . . . . . . . . . . . . 13

2.3 Illustration of partial fluorescence yield x-ray absorption process. . . . 13

2.4 Schematics of XES experimental setup. . . . . . . . . . . . . . . . . . 15

2.5 Schematics of PFY-XAS experimental setup. . . . . . . . . . . . . . . 15

3.1 Molecular structure of decaborane . . . . . . . . . . . . . . . . . . . . 17

3.2 Optical photomicrographs of the decaborane sample in DAC . . . . . 20

3.3 Raman spectra of decaborane below 1200 cm−1 . . . . . . . . . . . . 22

3.4 Raman shifts of decaborane vibrational modes below 1200 cm−1 . . . 23

3.5 Raman spectra of decaborane B-H...bridge modes . . . . . . . . . . . 24

3.6 Raman spectra of decaborane B-H stretching modes . . . . . . . . . 25

3.7 Raman spectra of H2 vibron in decaborane sample . . . . . . . . . . . 26

3.8 Optical photomicrographs of ammonia borane sample in DAC . . . . 28

3.9 Raman spectra of AB at high pressure and varying temperature. . . . 29

3.10 Raman spectra of H2 vibron in heated AB . . . . . . . . . . . . . . . 31

4.1 Wigner and Huntington’s study on solid hydrogen . . . . . . . . . . . 37

4.2 Enthalpy curves and bandgaps of hydrogen at high pressure . . . . . 39

4.3 Enthalpy per proton as a function of pressure in hydrogen . . . . . . 40

4.4 Photomicrographs showing evolution of H2-SiH4 mixtures in DAC . . 43

xi

4.5 Linear relationship between the Raman intensity ratio and the liquid

composition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.6 Binary P − x phase diagram of H2-SiH4. . . . . . . . . . . . . . . . . 47

4.7 Representative Raman spectra for the SiH4 and H2. . . . . . . . . . . 49

4.8 Raman spectra of the fluid portion of the 5:1 H2:SiH4 sample with

pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.9 Raman spectra of the fluid portion of the 1:1 H2:SiH4 sample with

pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.10 Raman shift of SiH4 ν1 modes in H2 environment as a function of pressure. 53

4.11 Raman shift of H2 vibron in the SiH4 environment as a function of

pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.12 Raman spectra of SiH4 ν1, ν3 modes in SiH4(H2)2. . . . . . . . . . . 57

4.13 Raman spectra of H2 vibron modes in SiH4(H2)2 . . . . . . . . . . . . 58

4.14 Equation of state of SiH4(H2)2 . . . . . . . . . . . . . . . . . . . . . . 62

4.15 Electronic structure of SiH4(H2)2 . . . . . . . . . . . . . . . . . . . . 63

4.16 Crystal structure of SiH4(H2)2 . . . . . . . . . . . . . . . . . . . . . . 64

4.17 Pressure-dependent band gap sizes of SiH4(H2)2 . . . . . . . . . . . . 66

5.1 Crystal field splitting of 3d orbital and schematics of high spin and low

spin configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.2 K-edge PFY-XAS and XES spectra of Fe2O3 at high pressure . . . . 73

5.3 K-edge pre-edge of Fe2O3 at high pressure . . . . . . . . . . . . . . . 74

5.4 Calculation of Fe2O3 at high pressure . . . . . . . . . . . . . . . . . . 77

5.5 FEFF calculation of Fe K-edge XAS of Fe2O3 . . . . . . . . . . . . . . 78

xii

Chapter 1

Introduction to High Pressure

We live in an era of demanding everything to be faster and stronger. This requires

people to push materials properties to their ultimate limits, and at the same time

design and create new phases of materials that can sustain a number of extreme

conditions. From the interest of fundamental sciences, the key question is how these

extreme environments alter materials properties at the atomic and molecular level?

Only by successfully combining the techniques that generate extreme environments

with a variety of probing methods are we able to reveal the answers.

High pressure that is generated by diamond anvil cell(DAC) is an excellent exam-

ple of successful combination of extreme condition technique with versatile probing

methods. As the diamond windows and certain metal gaskets are transparent to a

wide range of electromagnetic spectrum, many optical and synchrotron x-ray probes

can be implemented.

The way a DAC generates high pressure can be simply understood by the defini-

tion: P = F/A, where P is the pressure, F is the force, and A is the area the force

exerts. By exerting force on a very small area (on the order of 10−8m2) pressures as

large as those in the core of the Earth can be generated. Depending on the size of the

culets of the diamond pair, the pressures a DAC can generate range from 0.1 GPa to

over 300 GPa.

To see how high a pressure one needs to reach in order to drastically alter ma-

terials properties, it is important to estimate the energy scale that pressure can do

1

CHAPTER 1. INTRODUCTION TO HIGH PRESSURE 2

Compound KT (GPa) ∆ P (GPa) ∆ GFe 170 100 5.6 eV per atom

Fe2O3 240 50 2.9 eV per atomH2O 8.8 1 17 KJ per mol

Table 1.1: Gibbs free energy change for different compounds with different externalpressure.

work to materials. Consider a solid undergoing an isothermal compression at room

temperature. The Gibbs free energy change is dG = -SdT+V dP , the integrated

form is ∆G =∫V (P )dP . Using the isothermal compressibility κ = − 1

V∂V∂P

, the

pressure dependent volume change can be written as V = V0e−κP . This gives us

∆G = V0

κ(1− e−κP ). Applying the relationship between bulk modulus KT and com-

pressibility κ : KT = 1/κ, the Gibbs free energy change is ∆G = V0KT (1− e−P/KT ).

We can see from Table 1.1, for Fe2O3, a 3d transition metal oxide, 50 GPa of

pressure will exert work equivalent to an average of 2.9 eV per atom, the typical

energy scale of competing energies in the strongly correlated systems. While for

the archetypal hydrogen bond compound H2O, 1 GPa will do 17 KJ per mol to the

system, comparative to the hydrogen bond energy in water: 21 KJ per mol. One

can thus predict that in the former case, electronic structure of Fe2O3 may change

significantly due to the reconfiguration of the valence electrons, and that in the latter

case, an external perturbation as strong as the bonding energy (here is the hydrogen

bond) will probably induce structural transitions resulting in a different order of H2O

molecules and also hydrogen bonds.

In fact, high pressure does change materials properties significantly. As a Mott

insulator, MnO becomes a metal at 120 GPa [1]. Alkali metal sodium turns from a

reflective metal to an optically transparent insulator at 200 GPa [2][3]. Siderite crystal

(mainly FeCO3), colorless at ambient condition, shows an intriguing green color at

50 GPa, and red at 70 GPa [4]. In the process of changing graphite to diamond, van

der Waals interactions between different layers of graphite converts to C-C covalent

bond in diamond.

This dissertation focuses on how pressure affects materials’ bonding and electronic


structures, both of which directly reflect the external work done to the system. I in-

vestigated hydrogen rich systems that can mimic pure hydrogen at relatively lower

pressure. The interaction of boranes and hydrogen was studied using optical mi-

croscopy and Raman spectroscopy and their hydrogen storage potential is discussed

in the context of practical applications. The pressure-induced behavior of the SiH4

+ H2 binary system and the formation of a newly formed compound SiH4(H2)2 were

investigated using a combination of optical microscopy, Raman spectroscopy and x-

ray diffraction. The experimental work along with DFT calculations on the electronic

properties of the compound up to the possible metallization pressure, indicated that

there are strong intermolecular interactions between SiH4 and H2 in the condensed

phase. By using a newly developed synchrotron x-ray spectroscopy technique, we

were able to follow the evolution of the 3d band of a 3d transition metal oxide, Fe2O3

under pressure, which experiences a series of structural, electronic and spin transi-

tions at approximately 50 GPa. Together with theoretical calculations we revisited

its electronic phase transition mechanism, and found that the electronic transitions

are reflected in the pre-edge region.

1.1 Achieving high pressure with a diamond anvil

cell

Of all the physical variables, pressure holds the widest orders of magnitudes in the

universe. The smallest pressure exists in the interstellar space, and is as low as 10−13

Pa. The atmosphere of the Moon is approximately 10−10 Pa. The outer space near

Earth is close to 10−4 Pa. And of course the Earth atmosphere is 1 bar, i.e. 105 Pa.

Pressure higher than our atmosphere can be found at the interior of planets, stars

and astronomical bodies with larger masses. Specifically the pressure of the core of

Earth is 364 GPa, i.e. on the order of 1011 Pa.

Pressures as high as those in the interior of planets and stars can be generated via

static and dynamic loading. The dynamic loading method uses a fast moving object

or a laser pulse to generate shock wave in the matter, and very high pressure and


temperature can be achieved simultaneously. For condensed matter physicists who

are looking for properties of the ground state and would like to eliminate thermal

factor, static pressure generation device can be of great advantages. Besides, static

compression a variety of measurements, while dynamic compression prepares materi-

als in a transient state that are too short for some probing methods. Diamond anvil

cells have been widely used in investigating materials at high pressure [5].

Diamonds, with excellent mechanical and optical properties, are the ideal anvil

material. In a DAC, a pair of diamonds with similar culet size are mounted to seats

with high-strength materials like tungsten carbide or boron nitride(transparent to

x-rays and good for x-ray diffraction experiment). The diamond anvil cell is designed

such that the two diamonds remain well aligned under maximal applied forces. In-

between the diamond anvils are the gasket and sample. When we prepare a metal

gasket between diamonds, the first step is to have them undergo plastic deformation:

the so-called pre-indentation step. Usually, a metal sheet of about 250 µm is inserted

between the two diamonds, and 10-25 GPa of pressure is applied to the metal sheet

when the target pressure is 20-50 GPa. This process deforms the metal gasket plas-

tically, and the gasket is pre-indented to approximately 30-50 µm depending on the

pre-indentation pressure and the choice of the gasket materials. In this dissertation

where pressure is not extremely high, the selection of gasket materials is limited by

the requirement of the probing techniques and the sample properties. Be-Cu gasket

is best for samples containing hydrogen as it does not react with the species. X-ray

transparent Be gasket is used for x-ray spectroscopy experiment maximizing the in-

tensity of the incident x-ray and that of the scattered x-ray. After pre-indentation,

the gasket will be drilled at the center with a diameter of 100-150 µm depending on

the size of the culet.

A device like DAC will generate uniaxial pressure unless the sample is surrounded

with pressure transmitting medium. Deviatoric stress, defined as anisotropic forces

within a sample, can cause systematic errors to the experiments, and acts against

the idea of pressure being a good thermodynamic variable. Appropriate pressure

transmitting medium will ensure a hydrostatic sample environment, and in this dis-

sertation, hydrogen and noble gases are used.


1.2 Pressure measurement

In a high pressure experiment, the important thing next to obtaining the desired

pressure is to measure the pressure accurately.

The primary gauges based on the physical definition of pressure include mercury

column height(P = ρgh)and precise measurement of force per unit area (P = F/A).

However, these methods are either difficult to integrate to pressure devices or of

limited accuracy. Therefore secondary gauges that can be readily combined with the

intended measurements are desirable.

In static high pressure diamond anvil cell studies, two methods are frequently

used as pressure gauges. One is using x-ray diffraction to measure the specific volume

of metals or other common crystalline solids and comparing them with their known

equation of states (EOS). Such EOS is derived from shock experiment data: When

a shock wave transports in a material, both P and T increases substantially. Across

the front of a shock wave, momentum, mass and energy are all conserved, giving a

shock-compression curve called Hugoniot. The curve can be reduced to an isotherm

at room temperature [6], allowing the EOS at room temperature to be determined.

The other method is ruby fluorescence, which is more commonly used with opti-

cal spectroscopy measurements. Ruby (Al2O3:Cr3+) has major fluorescence lines at

694.24 nm (R1) and 692.81 nm (R2) at ambient condition. As shown in figure 1.1, the

R1 fluorescence line shifts to longer wavelength (lower energy) as pressure increases.

The calibration was carried out by Mao and Bell [7], by measuring ruby fluorescence

under quasi-hydrostatic conditions with argon as a pressure transmitting medium

in a DAC and conducting in situ x-ray diffraction of copper metal standard at the

same time. They obtain the following equation to describe the calibrated hydrostatic

pressure as a function of ruby R1 fluorescence line:

P =A

B[(1 + (∆λ/λ0))

B − 1]

with A = 1904 GPa, B = 7.665, λ0 is R1 line at ambient condition, and ∆λ is the

deviation of the R1 fluorescence from λ0.

The work in this dissertation use ruby fluorescence as the pressure gauge.


688 690 692 694 696 698 700 702 704

R2

R2

R1

Inte

nsity

(arb

. uni

t)

wavelength (nm)

1 GPa

4.2 GPa

R1

Ruby Fluorescence spectra at high pressure

Figure 1.1: Ruby fluorescence spectra at high pressures: R1 and R2 lines shift to longerwavelength as pressure increases. The separation of R1 and R2 provides informationon hydrostaticity of sample environment.

Chapter 2

Experimental methods

The integration of probing techniques with the diamond anvil cell are essential to

study materials under extreme conditions. In this chapter experimental and theoret-

ical basis of these characterization methods are introduced. One has to be aware of

the fact that samples in the diamond anvil cell is surrounded by the diamond anvils

and the metal gasket. Therefore, the probing methods has to be far-field and non-

destructive, or more accurately, they have to be either transparent to the diamond

or to the gasket material. Fortunately, diamond is transparent to a wide spectrum of

electromagnetic waves, making a number of optical and x-ray probes excellent tools

to study vibrational, structural and electromagnetic properties.

2.1 Optical microscopy

One of the advantages that distinguish the diamond anvil cell from its previous gen-

eration high pressure vessels is that it has visual observation capability. By observing

the hundred-micron size sample directly from a microscope, scientists for the first time

can observe the pressure-induced phase transformation visually [8]. For example, the

color displayed by a sample reflects information of its dielectric constant and further

its electronic structure. Phases with different refractive index can be clearly seen

through the microscope. This feature enables scientists to identify potential phase

transitions without the assistance of other instrumentation and techniques, and thus

7

CHAPTER 2. EXPERIMENTAL METHODS 8

virtual state

Stokes anti-Stokes

vibrational states

h 1ν

h 0ν

Figure 2.1: Raman processes understood by virtual states.

serves as an initial step for high pressure materials studies. In Chapter 4 where I

discuss the study of the pressure effect on a mixed system, visual observation is a

very important tool to assist in identification of phase separation and transformation.

2.2 Raman spectroscopy

The invention of laser has made Raman spectroscopy a very convenient tool to study

the vibrational, rotational, and other low-frequency modes in a system. Because of

its transparency to optical wavelengths, DAC has the intrinsic compatibility with

Raman spectroscopy.

This spectroscopic method is based on inelastic light scattering (i.e. Raman scat-

tering). When light interacts with matters, it can be absorbed or scattered. The

majority of the scattered light keeps the original wavelength (i.e. elastic scattered),

while a small portion of it will lose or gain energy. The latter process, named Raman

scattering, was first discovered by Sir Venkata Raman in 1928 when focusing sunlight

to different liquids and observing the scattered light in frequency domain [9], who

was awarded the Nobel Prize in physics two years later. It is worth to note that these

experiments were motivated by Arthur Compton’s discovery that x-ray loses energy

when interacting with electrons (i.e. the Compton Effect).


The concept of virtual state is helpful to understand Raman scattering from the

respect of energy levels. One can visualize the process as shown in fig.2.1, an incoming

photon (hν) excite the system at level E0=hν0 to a virtual state, and then as system

decay to level E1=hν1, an photon with energy (hν − (E1 − E0)) is emitted. The

energy difference of the incoming and outgoing photon equals to energy difference

between state 0 and state 1. Stokes and anti-Stokes bands correspond to the gaining

and losing energy respectively. In the study of this thesis, we are primarily using the

Stokes bands for Raman spectroscopy.

Raman scattering measures the fluctuation of the polarizability of the system,

therefore it is active to vibrational modes that have a polarizability change. The

vibration modes of a molecule or a molecular solids are sensitive to external pressure.

In a high pressure experiment, one can follow specific vibrational modes and obtain

the mode Gruneisen parameter that reflects the materials’ thermodynamic properties.

Raman spectroscopy can also identify phase transitions from the sharp changes of the

vibrational modes.

Linear-response theory can well describe the Raman process macroscopically, be-

cause the scattering events are weak, linear and causal. The scattering cross section

can be well described by fluctuation-dissipation theorem, giving the spectrum a line

shape of Lorentzian. ∫ inf

− inf

gσ(ω)dω = 1

where gσ(ω) adopts the Lorentzian frequency dependence

gσ(ω) =Γσ/2π

(ωσ − ω)2 + (Γσ/2)2

The Full-width-half-maximum(FWHM) of the Raman peak Γσ is related to the

damping mechanism in a condensed system. The peak broadening is larger for liquid

phase and smaller for solid phase, as the collision between molecules in a liquid is

more frequent than in a solid.

A standard Raman spectroscopy system is composed of a laser, a microscope


that focuses the light to the sample, a holographic filter that selects the inelastic

portions from the backscattered light and filters out the Rayleigh scattering, and a

grating that disperses the scattered light to a CCD camera. This setup can be used to

measure fluorescence spectra without modification and is convenient for ruby pressure

measurements. One thing to note here is that the microscope needs an objective with

a long working distance (>2.5 cm) in order to focus the laser beam down to the

sample that is located in DAC.

2.3 X-ray diffraction

While Raman spectroscopy can give us information about the vibrational modes of

the compound studied, one would ultimately want to know the microscopic structure.

High energy x-ray, whose wavelength is comparable to atomic spacings is used to de-

termine material structures through x-ray diffraction (XRD). As an electromagnetic

wave, x-ray mainly interacts with the electrons in the materials. Therefore its scat-

tering cross-section is larger for high-Z (atomic number) elements, and smaller for

low-Z elements.

According to generic scattering theory, the total intensity of the scattered beam

at direction kf (defined as kf = |ki|R/R)is

I(kf ) = | Ai

4πR|2∫

dr

∫dr′e−i(kf−ki)(r−r′) < ρ(r)ρ∗(r′) >

Here ki is the wave vector of the incident beam, R is the sample to detector

distance, ρ(r) is the electron density. It is clear that x-ray scattering is probing the

electron density correlation functions

< ρ(r)ρ∗(r′) >=< ρ(r) >< ρ∗(r′) > + < δρ(r)δρ∗(r′) >

.

In a crystal where fluctuations are negligible, the second term is orders of magni-

tude small compared to the first term. Therefore, the scattered beam from a crystal


has the intensity

I(kf ) = | Ai

4πR|2|

∫dre−i(kf−ki)r < ρ(r) > |2

The integral is only non-zero when (kf − ki)r = πn, (n is integer). This condition is

equivalent to Bragg’s law

2d sin θ = nλ

where d is the spacing between different atomic planes in the crystal.

Because of the geometry of DAC, collimated x-rays with less than 100 µm across

are necessary to illuminate the sample efficiently. Therefore instead of in-house x-

ray diffractometer, third generation synchrotron x-rays are generally used. An image

plate or a CCD camera is placed downstream to collected the diffracted Bragg peaks.

High pressure XRD experiment can couple with versatile sample environments like

laser heating, resistive heating and cryostat.

2.4 X-ray spectroscopy

While altering materials’ structures, pressure also affects their electronic and mag-

netic properties. Because of the design of DAC, electron and soft x-rays that are

frequently used to probe the electronic structures cannot penetrate the cell and reach

the sample. Hard x-ray, on the other hand, has a good amount of transmission

through diamond and certain gasket materials, therefore its spectroscopy are preva-

lently used to investigate electronic properties of materials confined in DAC. The

availability of extremely intense and focused x-ray sources makes the high pressure

x-ray spectroscopy experiments possible.

For the electronic properties of transition metal oxides, we primarily use x-ray

emission spectroscopy (XES) and x-ray absorption spectroscopy (XAS) that directly

probe the valence electron. Details of the theoretical description of core-level spec-

troscopy can be found in [10], the central role in the interaction of x-rays with matter

is manifested in Fermi’s Golden Rule, which states that the transition probability W

between a system in its initial state Φi and final state Φf by absorbing the incident


photon with energy ~Ω is given by:

Wfi =2π

~| < Φf |T |Φi > |2δ(Ef − Ei − ~Ω)

Here T is the transition operator. To the first order, T is the interacting Hamil-

tonian Hint, proportional to Ep in electric dipole transitions. Angular momentum

conservation requires ∆l = ±1 (dipole selection rule), as the angular momentum of

x-ray is l = 1.

Specifically for 3d transition metal oxides, K-edge XES and XAS are in the energy

range of hard x-rays, i.e. the core-level s-p transitions. The d electrons, although not

involved in the first order transition, are interacting with the p orbitals through 3p-3d

exchange or ligand hybridization.

X-ray emission spectroscopy is well suited to study magnetism of transition metal

compound at high pressure [11]. The Kβ (3p→1s) emissioin line from the transition

metal atom is sensitive to the transition metal spin state. As shown in Chapter 5,

the line shape of the Kβ line in a transition metal consists of an intense main line

Kβ1,3 and a satellite structure Kβ′ located on the low-energy side. The satellite is

attributed to the multiplet structure and originates from 3p-3d exchange: in the final

state the hole at the 3p orbital can have either the same spin or opposite spin with

the 3d electrons resulting in different energies. The intensity of the Kβ′ satellite peak

is related to the total spin moments of the 3d electrons. The collapse of the magnetic

moments from a high spin to low spin transition will be reflected by the diminishing of

the Kβ′ satellite peak. An illustration of the Kβ XES processes is shown in Fig. 2.2.

X-ray K-edge absorption spectroscopy measures the transition probability of 1s

electron to the empty bound states and continuum. The 1s-3d transition, quadruple in

nature and much weaker than the dipole transition, is reflected in the pre-edge region.

The energy resolution of the absorption spectra is limited by the core-hole life time.

In the case of K-edge XAS of transition metal, the 1s core-hole has a very short life

time, thus the life-time broadening can be as large as Γ = 7eV . Such resolution would

most likely smear out the detailed features of d-band structure, which is no wider than

a few eV. Such large broadening can be partly overcome by introducing a final state


1s

3d

3p

1s

hν

Kβ

Figure 2.2: Illustration of x-ray Kβ emission process.

3d

1s

2p

continuum continuum continuum

hν

Kα

Figure 2.3: Illustration of partial fluorescence yield x-ray absorption process.


with a longer life-time core-hole. Instead of measuring the transmitted photon, one

measures the photons from a certain fluorescence line, also called partial fluorescence

yield (PFY). More clearly shown in Fig. 2.3 under one electron approximation: after

a 1s electron is kicked to the 3d or continuum, a 2p electron decays to the 1s orbital,

leaving a final state of a 2p core-hole. In PFY mode, the life time broadening ΓPFY

is given by

1

Γ2PFY

=1

Γ2int

+1

Γ2final

.[11]

Since the life-time broadening of the final state (e.g. a 2p core hole) is considerably

smaller than that of the intermediate state (e.g. a 1s core-hole), the final spectra

resolution is well improved.

The experimental set up of XES and XAS-PFY are very similar. In both situa-

tions, synchrotron x-rays go through monochromator and are focused by horizontal

and vertical Kirkpatrick-Baez mirrors. The focused x-rays reached the sample en-

closed in a DAC with x-ray transparent Be gasket. The scattered x-ray is then

energy-selected by an analyzer and reaches the detector. The spectrometer adopts

Rowland circle geometry, of which the sample, the analyzer and the detector sit on a

circle whose diameter corresponds to the analyzer bending radius R. For the K-edge

of 3d transition metal, the x-ray energy is usually below 10 keV, helium path ways are

utilized to minimize signal attenuation by air. Figs.2.4 and 2.5 show the schematics of

XES and XAS-PFY experimental set up of beamline 16-ID-D of HPCAT of Advanced

Photon Source, Argonne National Laboratory.


x-rays

analyzer

detector

90monochromator

KB

mirrors

Rowland circle

spectrometer

Figure 2.4: Schematics of XES experimental setup.

x-rays

analyzer

detector

90

high resolu!on

monochromator

KB

mirrors

Rowland circle

spectrometer

Figure 2.5: Schematics of PFY-XAS experimental setup.

Chapter 3

Hydrogen rich systems: Boranes

and hydrogen

One of the key challenges to realizing a hydrogen economy is finding appropriate

materials that meet the gravemetric, volumetric and cost requirements for on and off

board hydrogen storage and generation. An ideal hydrogen storage material should

have high weight percentage and a small volume.

While active research is being conducted in three major categories: metal hydrides,

chemical hydrogen storage, and physical hydrogen sorption, pressurizing hydrogen

with light elemental hydrides to form clathrate compound represents an alternative

approach [12]. A number of light-element hydrides have demonstrated capability

of binding and releasing H2. H2O bond with H2 and forms clathrate I, clathrate

II, clathrate h and filled Ice-II, at different temperature and pressure conditions

[12][13][14]. CH4 and H2 was shown to form a variety of molecular van der waals

compound with different molar ratios at high pressure [15]. Once formed, some

of these hydrogen-rich phases can store the additional H2 at ambient pressure and

low temperature. These results show potential for optimizing conditions for practi-

cal hydrogen storage applications [12][16][17]. Among the potential pressure induced

hydrogen storage materials, second-row-element hydrides are particularly attractive,

because of their light weight and large variety of possible structures.

The third section on boranes and hydrogen will present Raman spectroscopic

16

CHAPTER 3. BORANES AND HYDROGEN 17

Figure 3.1: Molecular structure of decaborane; large, dark spheres are boron andsmall, light spheres are hydrogen.

investigations on two different borane systems and their interaction with molecular

hydrogen under various P-T conditions.

Boron, the lightest non-metallic element in the second row of the Periodic Table, is

known to form a large series of hydrides (boranes, BxHy). The most common boranes

are diborane (B2H6) which is a gas at ambient conditions, pentaborane (B5H9) which

adopts a pyramid boron backbone and is a liquid, and decaborane (DB), B10H14,

whose ten boron atoms construct a distorted partial icosahedron and is a molecular

crystal. [18] The molecular structure of DB is shown in Fig.3.1.

Related to the borane hydrides are more ionic species where some of the boron has

been replaced by nitrogen, e.g. ammonia borane (AB)(NH3BH3) and polyaminob-

orane (PAB) (NH2BH2)n. Due to the hydrogen-hydrogen interaction between the

nitrogen- and boron-bonded hydrogen atoms of adjacent molecules, BxNxHy com-

pounds are all reported solids with the exception of borazine (NHBH)3 which is a

liquid at ambient conditions [19][20]. These ionic hydrides have been considered as

potential hydrogen storage materials given the low temperature for release of hy-

drogen [21][22]. It may be feasible to store additional hydrogen for conventional

applications if a particular class of boranes form intermolecular bonding with H2.


A hybrid material consisting of both chemically bonded hydrogen and physisorbed

hydrogen, e.g., borane+H2, may provide an alternate approach to meet commercially

viable targets. High-pressure spectroscopy is a powerful tool for investigating the

fundamental interactions between boranes and molecular hydrogen. In this chapter

we examine the interactions between molecular hydrogen and two different boranes:

ammonia borane, AB and decaborane, DB, by variable pressure Raman spectroscopy.

Previous Raman spectroscopy studies of AB under pressure reveal the positive

and negative frequency dependence on pressure of the BH3 and NH3 vibration modes

respectively, and confirm the existence of the dihydrogen bonds[23][24][25]. Phase

transitions at 0.5, 1.4, 5, and 12 GPa were identified[23][25]. Hess et al. performed

Raman spectroscopy of AB at low temperature, and identified an orthorhombic to

tetragonal phase transition at 225K [26]. As for DB, Nakano et al. compressed the

material to 131 GPa and used Raman and IR spectroscopy to find that its electronic

structure changes at 50 GPa and 100 GPa [27], but there are few published reports

regarding the lower pressure behavior.

In this Chapter I present our studies on the effect of saturated H2 pressure on

DB and AB 1. Exploration in the vast pressure-temperature-composition (P −T −x)

field can provide insight into interactions between H2 and possible host materials.

Our goal is to find conditions and compositions with the maximal amount of H2

and then optimize the conditions for H2 absorption, storage, and release. We per-

formed compression experiments to examine whether AB and DB can store molecular

hydrogen in addition to their chemical hydrogen storage capacity. We conducted de-

tailed diamond anvil cell studies of AB up to 3 GPa and temperatures up to 400

K and DB up to 11 GPa at ambient temperature both in a hydrogen-saturated en-

vironment. High-pressure Raman spectroscopy was used to monitor the changes of

intermolecular bonding in H2, B10H14, and NH3BH3 which provide direct evidence of

pressure-induced storage of additional H2 in hydrides and possible formation of new

high pressure phases.

1Reprinted with permission from [28]. Copyright (2009), American Institute of Physics.


3.1 Decaborane and hydrogen

For the decaborane experiment, we used technical grade decaborane purchased from

Sigma-Aldrich. In a DAC, a sample was placed in a sample chamber drilled into

a Be-Cu gasket. A small chip of ruby was added as a pressure calibrant. In DAC

experiments, gases were loaded either cryogenically or through a gas pressure vessel.

In our experiment, we utilize the gas loading system in Geophysical Laboratory at

Carnegie Institution of Washington. The DAC was inserted into a gas pressure vessel

which was pressurized to 25,000 psi with fluid H2 gas which filled the remaining space

(50-80%) of the sample chamber. The sample was then clamp-sealed in the gasket,

and the DAC was removed from the gas vessel. The H2 fluid provided a nearly

hydrostatic environment over the pressure range studied.

The initial pressure of the DB + H2 sample was 1.5 GPa. We collected Raman

spectra at each pressure point during compression and decompression. Photomicro-

graphs of the sample were also taken at each pressure point (Fig.3.2). The gasket hole

began to expand at 11.2 GPa (Fig.3.2c), and further elongated during decompression.

At the same time, the DB in the gasket hole aggregates at the center of the diamond

culet and bridges between the diamonds. This single phase DB region and the H2

region was transparent, while the mixed region between DB and H2 darkens due to

light scattering between grains of different refractive indices.

The Raman features of DB mainly lie in three spectral regions [27][29].The 200-

1400 cm−1 include three boron backbone bending modes (200-400 cm−1), twenty-one

skeletal stretching modes (400-1100 cm−1) and twenty B-H bending modes (600-800

cm−1,1100-1400 cm−1). 1400-2000 cm−1 correspond to twelve B-HB bridge modes, a

unique bonding in boron hydrides. The broad band in 2500-2700 cm−1 is the collective

contribution of ten B-H stretching modes. Figs.3.3 and 3.4 show the Raman spectra

from 150 cm−1 to 1200 cm−1, which covers lattice vibration, B-B skeleton bending

and stretching, and a portion of the B-H bending modes. We observed that low

frequency phonons related to crystal lattice vibrations start to appear at 3.5 GPa at

160 cm−1. This weak signal persists to 10.3 GPa at which point it has shifted to 220

cm−1, but is not observed in the transparent region. Two other peaks that start to


Figure 3.2: Optical photomicrographs of decaborane (DB) sample surrounded byfluid H2 (a) after loading at 1.5 GPa; (b) during compression, sample at 8.9 GPa;(c) gasket hole began to expand at 11.2 GPa; (d) during decompression at 5.7 GPa,sample in the upper left corner becomes transparent.


appear at 3.5 GPa are at 843 cm−1 and 1112 cm−1, which correspond to one of the

B-B skeletal stretching modes and one B-H bending mode. These two peaks remain in

the spectra during compression and decompression, and are also in the spectra of the

transparent region. For all the other features, only intensity variations were observed.

With increasing compression, some of the higher frequencies of B-B stretching modes

become more significant: the features at 750-800 cm−1 and those at 900-950 cm−1.

Although the three peaks of hydrogen rotons lie in the frequency range of 300-1100

cm−1, their intensity is quite weak compared to most of the DB peaks in the sample

we studied. The only exceptions are the two decompression points at 5.7 GPa and

6.4 GPa, where broad hydrogen rotons can be easily identified.

Fig.3.5 presents the 1400-2200 cm−1 range of the spectra of B-H...B bridge modes.

Two new peaks at 1483 cm−1 and 1585 cm−1 emerge at 3.5 GPa, and remain during

further compression. They are also observed in the transparent region formed at

decompression. The rest of the features have an average dν/dP of 7.3cm−1 /GPa.

The broad band of B-H stretching shows the most variations with pressure (Fig.3.6).

All the B-H stretching modes shift much faster with pressure than the B-B stretching

modes or B-HB features. The average dν/dP of B-H stretching modes is around

11.7 cm−1/GPa, whereas dν/dP of B-B skeletal stretching peaks is 2.1 cm−1/GPa.

Furthermore, the higher frequency peaks of B-H stretching starts to diverge from the

lower frequency group (peaks below 2656 cm−1) at 3.5 GPa upon compression. The

B-H spectra of the transparent region that developed during decompression in the

H2 environment are also of interest. Instead of the sharp peaks observed in other

spectra, these show less defined spectra features. The frequency of each feature in

the band does not shift from those interpolated from the Raman shift versus pressure

dependence from the dark regions.

We examined the hydrogen vibrons at around 4200 cm−1 within the different

region of the sample. During compression, the darker regions which represent a

mixture of loosely packed DB and hydrogen show the same H2 vibron as the free

hydrogen region near the edge of the gasket hole. During the decompression in the

transparent DB region, we found a hydrogen vibron which does not belong to free

hydrogen. The center of the peak is 15-20 cm−1 lower, and the FWHM is 5 times


Figure 3.3: Raman spectra for the B-B bending and stretching, B-H bending modesof B10H14 in H2. * indicates decompression data. All the other data are taken duringcompression. Gray lines are spectra taken from the transparent region.


Figure 3.4: Raman shift for the B-B bending and stretching, B-H bending modesB10H14 in H2 as a function of pressure. Open triangles are from the spectra taken ofthe transparent region. Vertical dashed line indicates where transition is observed.New peaks from the high pressure phase are marked by arrows.


Figure 3.5: (a) Raman spectra for the B-H...bridge modes. * indicates the data weretaken during decompression. Gray lines are those from the transparent region. Allother data are taken during compression. (b) Raman shift as a function of pressurewhere empty triangles are from spectra taken of the transparent region. Verticaldashed line indicates where transition is observed. New peaks from the high pressurephase are marked by arrows.


Figure 3.6: (a) Raman spectra for the B-H stretching modes. * indicates the datawere taken during decompression. Gray lines are those from the transparent region.All the other data are taken during compression. (b) Raman shift as a function ofpressure were open triangles are from spectra taken of the transparent region. Dashlines are guides for the eye.


Figure 3.7: The Raman spectra of H2 vibron from the transparent region of DB(gray), and from the free H2 region (black), taken at 3.7 GPa.

broader than the free hydrogen peak (Fig. 3.7), indicating H2 bonded in the DB solid.

The unique structure of DB molecule gives us an opportunity to study the pressure

effect on bulky molecular crystals. A good parameter to describe the pressure effect

on vibrational modes are the mode Grueisen parameter, defined as γi = KTd ln νidP

,

where KT is the bulk modulus at the pressure of interest [30]. Without the informa-

tion about bulk modulus of DB at high pressure, we are still able to compare d ln νidP

among each group of vibrational modes. The average d ln νidP

for B-H stretching modes

is 4.5 /103 GPa, and B-H. . . B bridge 3.4 /103 GPa. For B-B skeletal stretching modes

at 200-1100 cm−1, the d ln νidP

covers a wide range from 2.8 /103 GPa to 7.3 /103 GPa,

due to the wide spectral spreading of the modes. The dνidP

, on the other hand, remains

constant at around 2.1 cm−1/GPa for all the skeletal modes, thus is a better param-

eter describing the stretching of skeletal bonds. One can picture the DB molecule

as a partial icosahedron, with boron atoms sitting on ten of the twelve icosahedra

positions[18], as in Fig. 3.1. The resulting B-B skeletal bonds form the framework


of the molecule, with B-H bonds coming out like spines. The B-H...B bonds connect

six boron atoms to form the rim of the open icosahedron. The B-H bonds which are

sticking out are the most sensitive to pressure and show the most changes in Raman

shift. The B-H...B bonds show intermediate changes on Raman shifts with pressure.

The B-B backbone stretching modes, screened by the spines and the rim, are the least

sensitive to pressure.

We also find evidence of a possible phase transition at approximately 3 GPa. Four

new features at 843 cm−1, 1112 cm−1, 1483 cm−1 and 1585 cm−1 appear at 3.5 GPa

and persist with further compression and upon decompression (Figs. 3.43.5). These

new peaks are likely to be the new features of B-H bending modes and B-H. . . B

bridging modes. The shape of the broad B-H stretching band before 3.5 GPa and

after 3.5 GPa is also different, in that the four peaks with highest frequencies move

apart from the lower frequency ones.

3.2 Ammonia borane decomposition

NH3BH3 was purchased from Aviabor chemical company (98% purity) and purified

by sublimation [31]. After loading, the solid AB sample was surrounded by H2 fluid

at 0.7 GPa (Fig. 3.8a). All Raman spectra from the AB were taken through the

overlaying pure H2 layer and therefore also contained peaks from pure H2. The DAC

was progressively heated using a resistive heater until the melting of AB at approx-

imately 120C (Fig. 3.8b). Before melting, the N-H and B-H stretching modes were

fairly insensitive to increasing temperature (Fig. 3.9b). Melting was accompanied by

loss of the B-N stretching modes in AB and a noticeable broadening of the molecular

modes (Fig. 3.9a). The center of the broadened B-H stretching and bending modes

showed a blue shift of 34 cm−1 and 23 cm−1 respectively compared to the unmelted

sample at 0.7 GPa, while the N-H stretching modes did not shift. We heated the

sample to 140C and then cooled the sample in order to allow it to recrystallize. The

melt (or glass) did not recrystallize after slow cooling (over course of several hours)

back to room temperature. We then increased pressure to just above 3 GPa but the

AB still did not recrystallize. The B-H stretching modes of the melted AB shifted


Figure 3.8: Optical photomicrographs of ammonia borane (AB) sample surrounded byfluid H2 at 0.7 GPa viewed through diamond anvil; (a) sample at room temperature,(b) at 120C sample is beginning to react; (c) at 127C after heated to 140C, ABhas completely reacted.

to higher frequency with increasing pressure while the N-H stretching mode did not

shift (Fig. 3.9b). During pressurization from 0.7 to 3.2 GPa, some H2 dissolved into

the melted AB as evidenced by a new Raman peak which shows a 52 cm−1 red shift

compared to the H2 vibron peak from the overlaying free H2 layer at the AB region

(Fig. 3.10). As pressure increased, the intensity of this shoulder increased, indicating

increased dissolution of hydrogen. The sample was left in the DAC for a week and

no time-dependent changes were observed.

The Raman spectra of the crystalline AB in a H2 environment agree well with those

of pure AB [25]. We found the pressure dependence of the N-H modes of amorphous

AB were insensitive to pressure in contrast to the negative pressure dependence of

these modes in crystalline AB.

At ambient pressure, heating of AB to 70-110C is a complicated process which in-

volves melting, amorphization, isomerization, and decomposition [31][32][33][34][35].

It has been proposed that upon heating AB amorphizes and isomerizes to diammo-

niate of diborane ([(NH3)2BH2]+BH−

4 or DADB) [31][35], and will subsequently de-

compose to yield H2 and polyaminoborane ((NH2BH2)n or PAB) [22]. Although the

high pressure Raman spectra of DADB (the isomer of AB) and PAB (the decompo-

sition product of AB after losing a mole of hydrogen) are not available, we are able

to compare our results with Heldebrant’s work [31], where they heated the AB crys-

tal to 90C at ambient pressure and obtained the Raman spectra of the heated and

unheated region of AB. The changes in B-N stretching, B-H bending and stretching,


800 1000 1200

3 GPa 0.7 GPa

25oC

B-H bend

25oC

120oC

Inte

nsity

(arb

.uni

ts)

Raman shift (cm-1)

140oC, melt

B-N stretch

a

2200 2400 2600 3200 3400

b

N-H stretch

3 GPa 0.7 GPa

127oC, melt

100oC

Raman shift (cm-1)

B-H stretch

25oC

25oC

Figure 3.9: Raman spectra of AB at high pressure and varying temperature. (a)loss of B-N stretching modes at 800 cm−1 and reduction of B-H bending modes uponincreasing temperature. (b) broadening of B-H stretching modes and N-H stretchingmodes at 0.7 GPa (black), and 3 GPa (gray).


and N-H stretching in our high pressure sample are similar to AB heated at ambient

pressure producing DADB [31]. These observations indicate heating AB at 0.7 GPa

and at higher temperature of 120-140C is similar to heating AB at ambient pres-

sure at 30-50 degrees lower. The loss of intensity in the B-N stretching mode at 800

cm−1 after heating suggests significant weakening of this bond accompanied with the

weakening of the dihydrogen bonding. These changes can explain the insensitivity of

the N-H mode with pressure: in the heated product the NHx group decouples with

the BHx group of an adjacent molecule in the absence of strong dihydrogen bond-

ing. Fig.3.8c shows what appear to be bubbles forming in the sample consistent with

the decomposition of AB, although we did not observe an increase in pressure above

120C within the resolution of our measurement. The blue shift of B-H stretching and

bending modes, compared to AB, is consistent with the formation of PAB [36][37].

However we did not observe any noticeable features at the frequency range of 720-850

cm−1 in both the heated and quenched sample, where part of the B-N stretching

modes of PAB are located [36][37][38]. Overall, these results suggest that the behav-

ior of pressurized AB is similar to the complex melting, amorphization, isomerization

and decomposition behavior of AB heated at ambient pressure. Compression of the

quenched decomposition product with H2 is a possible route for rehydrogenation of

H2-lost AB. However our results show no spectral evidence of regeneration of AB up

to 3 GPa, so alternative routes for rehydrogenation need to be considered for practical

purpose.

3.3 Calculation of hydrogen storage capacity

It is useful to be able to quantitatively calculate the hydrogen storage capacity in

the systems we studied. In the pressure range we performed the experiments, the

intermolecular bonds of H2 dissolved in DB and AB are very weak in comparison

to the intramolecular H-H bond. The H2 can be viewed as an essentially unchanged

molecular unit, and the vibron intensity can be a good indicator of the total number of

H2 molecules. The amount of dissolved H2 can be estimated from the Raman spectra

by first determining the ratio of the integrated intensity of the dissolved H2 vibron


Figure 3.10: Raman spectra of H2 vibron in heated AB (black) at 3 GPa and in freeH2 region (gray)

shoulder compared to the intensity of the vibron in the H2 only regions. This ratio

can then be multiplied by the density of H2 which is determined from the equation

of state of H2 [39]. The density of NH3BH3 at 3 GPa was estimated to be 0.92

g/cm3 at 3 GPa 2. This gives us approximately 3 wt% in NH3BH3 at 3 GPa which

corresponds to one H2 per 2 molecules of NH3BH3 and 30 g H2/L of NH3BH3. We

estimated the density of B10H14 at 4.5 GPa to be 1.3 g/cm3 assuming it had a similar

compressibility as NH3BH3. This gives 1 wt% of dissolved H2 in B10H14 at 4.5 GPa,

which corresponds to one H2 per 2 molecules of B10H14 and 10 g H2/L of B10H14.

The Raman features for the hydrogen vibron display the effect of the boranes

on hydrogen. The red shift from the free H2 position indicates charge transfer to

the neighboring host molecules or formation of bonds that stabilized the dissolved

H2. Although DB backbone has a partial icosahedron shape with a diameter of

approximately 4.6 A (2.8 A after adjusting for the size of boron atoms) which is

larger than the free H2 diameter of 2.4 A at around 3.5 GPa, it is not known if the

dissolved H2 resides in the molecule or in between the molecules. Neutron diffraction

2J. Chen, personal communication.


is necessary to determine the distribution of the H2 in the solid (i.e. whether the H2

is dissolved in an ordered fashion or distributed randomly in the crystal), and would

also provide more accurate estimates of the H2 content stored in these materials [40].

We have demonstrated that with the application of pressure both DB and melted

AB can store a small but non-negligible amount of additional H2. AB is quite ionic and

may be able to interact with molecular hydrogen more strongly than other molecular

compounds which rely on dispersion forces (e.g. hydrogen-methane and hydrogen-

water compounds). In DB, changes in the Raman spectra above 3 GPa may be evi-

dence for a structural transition which should be investigated with neutron diffraction.

Further exploration of pressure-temperature space may find additional new structures

based on AB and borane building blocks which accommodate a larger amount of H2.

The next stage would then be optimization of the hydrogen storage and releasing

conditions.

3.4 Energy intensity calculation

When justifying the benefit of an alternative energy resource, one always wants to

quest the energy intensity of each procedure. It is therefore important to compare

the amount of energy it takes to pressurize hydrogen into these molecular compounds

with hydrogen combustion heat.

Let us take H2O as an example for the hydrogen storage material. As mentioned

in Chapter 1, compressing H2O to 1 GPa need approximately 17 KJ/mol. While

hydrogen combustion follows the reaction:

2H2(g) + O2(g) = 2H2O(l) + 572kJ(286kJ/mol)

This means as long as the H2:H2O ratio in the clathrate is higher than 1:16, the

theoretical energy gain is positive. A hydrogen clathrate reported in [13] has the

stoichiometry of H2(H2O)2, the ratio 1:2 of H2:H2O far exceeds the critical ratio.

This problem can also be estimated from the view of materials bonding. The

exerted GPa pressure can bind hydrogen to light element hydrides forming molecular


crystal. This process only changes the hydrogen bond and van der Waals bonding of

the system, and the external work shall be on the same order of these interactions.

While hydrogen combustion mainly gains energy from breaking and forming covalent

bonds, whose energy are usually orders of magnitude larger than either hydrogen

bond or van der Waals interaction. This argument presents an intrinsic advantage

for using high pressure to store hydrogen as the energy gain from hydrogen storage

to hydrogen combustion can always be positive.

Chapter 4

Hydrogen rich systems: Silane and

hydrogen

The last chapter focused on borane and hydrogen systems with an emphasis on their

potential practical application as hydrogen storage materials. This is just one of the

many reasons for the interest in studying hydrogen rich systems in extreme environ-

ments. Besides its implications in the infrastructure of hydrogen economy, hydrogen

rich systems also have implications for fundamental interests.

Hydrogen is the lightest and most abundant element in the universe. The un-

derstanding towards our nature would not have been possible without generations of

scientists studying its atomic and molecular properties under different physical and

chemical environments [41]. Being in the first column of the periodic table, hydrogen

is, however, quite different from all the alkali metals. Two hydrogen atoms form a

strong covalent bond that lowers the total energy. At atmospheric pressure, it forms

molecular liquid and solid at 20K and 14K respectively. Both condensed forms are

insulators unlike their one-valance-electron analogs.

It is therefore very intriguing to pose the question whether there can be any form

of hydrogen in high enough density to be metallic and even superconducting. In

fact, metallization of hydrogen has long been the holy grail for the high pressure

community, but has not yet observed experimentally up to the highest static pressure

people reached [42].

34

CHAPTER 4. SILANE AND HYDROGEN 35

Ashcroft proposed in [43] that group IVa hydrides (methane, silane, germane,

and stannane) at very high pressures can be considered as hydrogen dominant alloys.

Although chemically group IVa hydrides are different from hydrogen, at extreme

environments it is the k-space that matters when a system is becoming metallic. At

the pressure when the density is high enough, there are 8 valence electrons in the unit

cell, mimicking a unit cell of 4 hydrogen molecules. The electron density of a group

IVa hydride in its solid phase is higher than that of solid hydrogen, illustrating the

physics that hydrogen are precompressed in group IVa systems, thus the potential

metallization and superconductivity can happen at a lower pressure.

Hydrogen rich systems including group IVa hydrides provide an excellent platform

to study the effect of pressure on the evolution of bonding from molecular compound

to metal, during which processes electron density increases with pressure. And such

topic is the focus of the three sections of this chapter. In the first section, a review of

theoretical prediction and experimental efforts in the metallization of hydrogen will

be presented. In the second section, the changes of van der waals interaction upon

pressure are revealed by experimental study on the binary SiH4 and H2 system at lower

pressure. The third section will discuss how the bonding and electronic structure of

SiH4(H2)2 compound evolve from molecular to metallic at extreme environments by

performing ab initio calculations.

4.1 Metallization of hydrogen

The study of high density hydrogen started as early as 1920’s, the initial days of

quantum mechanics: Fowler first proposed that hydrogen would form a dense plasma

under extreme pressure conditions [44]. Later in 1935, Wigner and Huntington pre-

dicted that solid hydrogen will dissociate to atomic form and metallize at 25 GPa [45].

The development of density functional theory (DFT) thereafter and its application in

molecular dynamics empowered theorists to do more accurate calculations on dense

hydrogen. Meanwhile, experiments on this topic are advanced by the development of

high pressure techniques. Results from later-developed diamond anvil cell and shock


wave techniques for static and dynamic high pressure experiments revolutionized peo-

ple’s understanding over and over again. However, the the low-Z nature of hydrogen

poses great challenge to resolve its structure at megabar (above 100GPa) with x-ray

diffraction. Furthermore, no devices are available to perform neutron diffraction at

such high pressure. Theory remains to be the primary tool to investigate the proper-

ties of hydrogen at extreme enviornments.

The first quantitative prediction of metallic hydrogen was conducted by Wigner

and Huntington[45]. According to tight binding model, it is expected that atoms

in any lattice systems with odd number valence electrons will form a metal if the

electron-electron overlap between neighboring atoms are large enough. Hydrogen

with one electron in the valence should also be a metal at high enough density. The

authors then calculated the energy of a body-centered cubic lattice of atomic hydrogen

as a function of lattice constant, shown in Fig.4.1. They found that the cohesive

energy Ecoh is five times smaller than Ecoh for molecular solid hydrogen, indicating

that obtaining the metallic hydrogen is extremely difficult. The lattice constant

at the energy minimum of their model is at 1.67a0, where a0 is the Bohr Radius~2

mee2. In comparison, the bond length of the H-H covalent bond is 0.75A = 1.45a0

and the nearest neighbor distance in molecular solid hydrogen is at 3.3A = 6.3a0.

This means to achieve metallic atomic hydrogen, the distance between the nearest

molecules should be close to the intramolecular distance, corresponding to a density

around 4 g/cm3. The most advantageous compressibility at high pressures leads to

a lower bound for the metallization pressure: 25 GPa, not achievable at the time of

1935.

In 1968, Ashcroft proposed that the hypothetical form of metallic hydrogen can

be superconducting when predicted by BCS theory, which imply that the substantial

magnetic field of planet Jupiter may partly attribute to the superconducting hydro-

gen interior [41]. Later calculations by Brovman et al. took into account both the

static lattice energy and zero point vibration energy [46]. They were able to find the

equation of states (EOS) and thermodynamic potential of a number of phases that

can be favorable under high pressure. These enabled them to find the pressure of the

transition from molecular to metallic phase to be 100-250 GPa. They also proposed,


Figure 4.1: After [45]: Energy of the lattice as a function of lattice constant. Lowest

curve, for flat wave functions; second curve with all corrections except zero-point

energy of the nuclei; the dotted lines contain the zero-point energy, the lower for

deuterium, and upper for ordinary hydrogen.


for the first time, that the metallic hydrogen phase has similarity to a liquid.

With the development of diamond anvil cell techniques, experiments can achieve

the pressure that was considered insurmountable in the 1930’s. More than 250 GPa

static pressure could be applied to different materials including hydrogen [47]. How-

ever, people have not found any sign of metallic hydrogen at room temperature up

to 342 GPa [42]. These findings challenged the previous theoretical predictions, and

excited new interest in the theoretical communities.

Enlightened by the experimental findings, Johnson and Ashcroft took a different

approach. Instead of trying to find the atomic metallic phase of hydrogen, they

preserved the pairing of protons and aimed at finding molecular metallic hydrogen,

the metallization mechanism of which is bandgap closure upon pressure[48]. Starting

from the favored structures of previous calculations using quantum Monte Carlo and

molecular dynamics, Johnson and Ashcroft used density functional theory with local

density approximation (LDA) to select a number of orthorhombic phases that are

energetically competitive. In Fig.4.2 the enthalpy curves as functions of pressure

and the bandgap vs density are displayed for a number of molecular and atomic

structures. It shows that the P21/c phase yields to Cmca phase (both molecular) at

an LDA pressure of about 135 GPa and the latter phase prevails over a wide range

of pressures until 425 GPa (LDA) when the molecular phase turns into monatomic

Cs-IV phase. The authors pointed out that LDA usually underestimates the pressure

in solid hydrogen, which means the molecular to atomic transition might happen at

a pressure higher than 425 Ga. The bandgap closure occurs, however, at a much

lower LDA pressure: when the P21/c changes to Cmca the latter is metallic at the

corresponding density.

In addition to Johnson and Ashcroft’s work introduced above, Pickard and Needs

also conducted DFT calculations to determine the structure of the high pressure

phase (above 250 GPa, phase III) of solid hydrogen[49]. In contrast to the previ-

ous approach, Pickard and Needs did not restrain the structure to be orthorhombic.

Instead, they relax many random structures to minima in the enthalpy at fixed pres-

sure, and then calculate the enthalpies of the most stable phases at a larger pressure

range, shown in Fig.4.3. Searching a larger pool of candidate structure candidate


Pressure (GPa)

50–0.30

–0.25

–0.20

–0.15

–0.10

–0.05

0.00

0.05

150

∆H

(e

V p

er

pro

ton

)

250

P2 1/c

Pca2 1

Cmc2 1

Cmca

Cs–IV

β–Sn

350 450 550

Density (mol cm –3)

0.00–2.0

2.0

6.0

10.0

mhcp-c (LDA)

mhcp-c (eGW)

Cmc21 (LDA)

Cmc21 (eGW)

P21/c (LDA)

P21/c (eGW)

14.0

18.0

0.10

Ba

nd

ga

p (

eV

)

0.20 0.30 0.40 0.50

Figure 4.2: After: [48]. Left: Enthalpy curves of solid hydrogen relative to the

monatomic diamond structure as functions of LDA pressure for the molecular and

monatomic structures in Johnson and Ashcroft’s study. Right: Bandgaps as a func-

tion of density for the mchp − c, Cmc21, and P21/c structures of dense hydrogen.

Open symbols are bandgaps using LDA, close symbols represent empirically corrected

bandgaps (eGW).


100 150 200 250 300 350 400

Pressure (GPa)

En

tha

lpy

di

ere

nce

pe

r p

roto

n (

me

V)

–30

–20

–10

0

10

–30

–20

–10

0

75 100 125 150

Cmca

Pa3

Pca21 Cmcm

High-Cmca

Ibam

Cmca-12

Pbcn

C2

C2/c

P63/mmc

P21/cP63/m

Figure 4.3: After:[49]. Enthalpy per proton as a function of pressure. Static lattice

enthalpies relative to the Cmca phase. Inset: Enthalpies including zero-point motion

relative to the Pa3 phase. Solid lines indicate new structure from [49], dashed lines

are for previously considered structures.


allowed them to find new structures that have lower energy than those reported by

Johnson and Ashcroft. The two structures that are favored between 105 - 385 GPa

are Cmca − 12, C2/c. The Cmca structure considered in the previous work wins

between 385 - 490 GPa.

Hydrogen is a quantum material. The small mass of proton leads to a large zero-

point energy (~ω) within the harmonic approximation. In fact these energies are so

large that they can significantly affect the relative stabilities of the structure and their

vibrational properties [49]. In both works, the authors have included the zero-point

energy of the proton. However, noticeable anharmonic effects make estimating the

energy accurately quite difficult. According to Fig. 4.3, the difference of energy per

proton between different phases are as small as 2-5 meV, the same order of magnitude

as the error in calculating the zero point energy per proton. Therefore, although

some phases might seems unfavorable in the enthalpy-pressure diagram, they might

be favored in reality over a wide range of pressure. Total calculated energy is not the

only criterion.

Pickard and Needs also calculated the infrared spectra of the candidate phases,

and found that vibrational spectra of C2/c structure agrees best with experiments,

making C2/c structure the best candidate for phase III solid hydrogen. Density of

states calculation for this phase shows that metallic transition occurs at 300 GPa.

Adjusting the 2eV error DFT usually made on bandgaps, they predict metallization

C2/c will occur at 410 GPa. Clearly, the electron-electron correlation exerts a huge

problem when calculating the bandgap of dense hydrogen. Methods beyond the local

density approximation is necessary to resolve the structure and electronic properties.

4.2 Phase diagram of SiH4 and H2 at lower pres-

sure

As previously mentioned in the beginning of the chapter, group IVa hydrides (i.e.

CH4, SiH4, GeH4, SnH4) have the highest atomic fraction (80%) of hydrogen among

elemental hydrides and were predicted to metallize into hydrogen dominant metallic


alloys at lower pressures compared to pure hydrogen [43]. Recent experiments on

silane (SiH4) have confirmed such predictions: Synchrotron infrared reflectivity and

electrical conductivity measurements indicate its metallization at around 50-60 GPa

[50][51], and SiH4 becomes superconducting at a transition temperature of 17 K at

96 GPa [51]. Interactions between elemental hydrides and additional molecular hy-

drogen at high pressure are a rapidly growing area of research [16][13]. Formation of

numerous stoichiometric compounds demonstrates the complicated interactions be-

tween hydrogen and other molecular species in condensed phases. H2 and H2O form

clathrates and filled ices that can be quenched to ambient pressure at low temperature

[13]. Methane (CH4) was discovered to form at least four stoichiometric compounds

with hydrogen at pressures up to 10 GPa [15]. This section devotes to constructing

the pressure-composition (P -x) phase diagram of H2-SiH4 systems to 6.5 GPa at room

temperature.

4.2.1 Materials and methods

Samples with two premixed starting compositions, 5:1 and 1:1 molar H2:SiH4 ratios,

were loaded as a well mixed fluid phase in a DAC and were monitored in-situ using

optical microscopy and Raman spectroscopy.

Diamond anvil cell sample loading

Two gas mixtures of SiH4 and H2 gas with 50 and 83 mol% of H2 (corresponding to

H2:SiH4 molar ratios of 1:1 and 5:1 molar ) were premixed by Voltaix Product and

certified with ±1% composition accuracy. They were loaded in DAC using the gas

loading system at the Geophysical Laboratory. Small pieces of ruby were placed in

the sample chamber for pressure calibration, and the entire DAC was placed in a

large gas pressure vessel. The highly uniform gas mixture was pumped into the vessel

to a nominal pressure of 100 MPa which fills the DAC sample chamber (which was

left slightly opened) as well as its surroundings. A feed-through mechanism was then

applied to close the DAC sample chamber and seal the gas samples inside the gasket.

The gaskets were made of a Be-Cu alloy which was chosen for its superior ability in


Figure 4.4: Photomicrographs showing evolution of H2-SiH4 mixtures with pressurein a DAC at 300K: Left panels (A), (B), and (C) show the sample with 5:1 H2:SiH4

starting composition. Right panels (D), (E), and (F) show 1:1 H2:SiH4 sample. Aspressure was increased (B) an H2-dominant phase (H-solid) and (E) SiH4-dominantphase (S-solid) solidified from the initially fluid samples. (C) and (F) show the com-pletely solidified samples above the eutectic point.


preventing H2 loss. After loading, venting of the excess flammable silane-hydrogen

gas mixture in the gas loading vessel was controlled by passing the exhaust through

water. After sealing the samples in the gasket, the DACs were removed from the gas

vessel. Both samples started as well mixed fluid phase, as in Fig. 4.4A, 4.4D. The

diamonds in both cells had culets 0.5 mm in diameter, and the diameter of the sample

chamber was approximately 150 µ m.

Raman spectroscopy and optical microscopy measurements

We used Raman spectroscopy to quantitatively monitor the behavior of two compo-

nents in the systems. Raman intensity has been used successfully for determinations

of composition for the H2-CH4 fluid [15] and the (H2)4CH4 crystalline solid [52]. This

method depends on using molecular Raman modes whose intensity is insensitive to

the chemical environment that is a good assumption for the high frequency H-H

molecular vibration and the Si-H stretch in the fluid phase using the calibration. The

spectra were measured in a back scattering geometry with excitation wavelength of

487.987 nm. The energy resolution for all the spectra is 4 cm−1. Pressure is deter-

mined by the shift of the ruby R1 fluorescence line [7] using the same system. Since

the peak intensity for a specific Raman feature is proportional to the amount of that

component in the phase being measured, we estimated the composition of the solid

and fluid SiH4 and H2 phases by comparing the intensity (integrated area) ratio for

the Si-H stretching modes of SiH4 and Q1 vibron of H2 with that of a known com-

position, i.e. the starting compositions (Fig. 4.5). The SiH4/H2 Raman intensity

ratio (RIR) was fit to a linear relationship with the SiH4/H2 molar ratio of liquid

composition (C) of the starting samples, and the calibration line was found to be:

RIR = 11.63C

If the molecular polarizability of these molecular vibration chances drastically in

S- and H-solids, the calibration slope may change. However, our observations of

relative concentration change within each solid are still valid. The shift of the Raman

peaks (Figs. 4.10 and 4.11) is also consistent with the composition determination

from the peak intensities (Fig. 4.6). Due to the difference in refractive indices of the

solid and fluid phases, they can be clearly distinguished using optical microscopy. We


0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

10

12

14

SiH

4/H2 R

aman

inte

nsity

SiH4/H

2 molar ratio

RIR = 11.63 x C

Figure 4.5: Calibration for the linear relationship between the Raman Intensity Ratio(RIR) and the SiH4/H2 molar ratio of liquid composition (C) of the starting samples.Filled circles (blue in the case of 5:1 H2:SiH4 and red for 1:1) are the data point forthe sample before crystallization. Unfilled circles are data whose compositions hasbeen determined with the RIR. The uncertainty for the H2 molar fraction is 1.5%.


used direct visual observation to determine the pressure at which phase separation

occurred and when the eutectic point was reached.

4.2.2 Results and discussion

The 5:1 H2:SiH4 sample starts as a homogeneous, colorless fluid at 1 GPa (Fig. 4.4A),

a hydrogen-dominant phase (H-solid) first appears when pressure was raised to 5.8

GPa, higher than the freezing pressure for pure H2 of 5.5 GPa [53]. As the H-

solid grows from the fluid with further pressure increase (Fig. 4.4B), the H2 content

(initially 83.3 mol%) of the fluid decreases to a minimum value of 64 mol% (estimated

from the Raman spectra, see Materials and Methods). At pressures above 6.5 GPa,

the remaining fluid suddenly and completely solidifies (Fig. 4.4C), into a mixture of a

SiH4-dominant phase (S-solid) and H-solid, clearly indicating the eutectic behavior.

The darkened appearance is due to light scattering off the grain boundaries between

the two different phases which have different refractive indices. The 1:1 H2:SiH4

sample also starts as a homogeneous, colorless fluid (Fig. 4.4D). The S-solid first

crystallizes from the fluid at 5.4 GPa, significantly higher than the freezing pressure

reported for pure SiH4 at 4 GPa [50]. With increasing pressure, the remaining fluid

phase becomes increasingly H2 rich as more S-solid crystallizes (Fig. 1E), indicating

behavior on the other side of the eutectic from the 5:1 H2:SiH4 sample. At 6.4 GPa,

the remaining fluid suddenly and completely solidifies (also with darkened appearance,

Fig. 4.4F).

The observations for these two compositions indicate that SiH4-H2 system is con-

sistent with a simple binary eutectic phase diagram (Fig. 4.6). Kinetics effects were

found to be significant in the solidification process. We observed super-pressurization

phenomenon in our system whereby we had to increase pressure by 0.2 - 0.4 GPa

above the eutectic pressure before the entire system crystallized, analogous to the su-

percooling effect observed in the freezing of fluids. The two liquidus curves actually

cross, i.e. the H2-rich liquidus extends to as low as 62 mol% H2 and the H2-poor

liquidus extends to as high as 74 mol% H2 before the second solid appears. From the

point where the pressure-composition (P -x) liquidus curves of the two fluid intersect


Figure 4.6: Binary P-x phase diagram of H2-SiH4. Circles are measured from liquidphase, and diamonds are from solid. Red symbols show data for the 5:1 H2:SiH4

sample, and blue symbols are from 1:1 sample. Data above the eutectic pressureare a result of super-pressurization of the sample. Possible extension to the freezingpressures for pure H2 [53] and SiH4 [50] are shown by dashed lines.


we were able to determine the eutectic pressure and composition as being, 6.1(±.1)

GPa and 72(±2) mol% H2 at 300K.

The main Raman features for SiH4 are the ν1(A1) and ν3(F2) vibrational modes of

SiH4 that overlap at around 2200 cm−1 and the ν2(E) mode at around 900 cm−1 [50][54].

These features become much sharper when SiH4 solidifies. Representative spectra of

SiH4 are shown in Fig. 4.7A: the S-solid contains 1.3 mol% H2, the liquid phase at

4.1 GPa 50 mol% H2, and the H-solid 99.6 mol% H2. Fig. 4.7B shows the high pres-

sure H2 vibrons in the H-solid (98.5 mol% H2, 6 GPa), H2-SiH4 fluid (83.3 mol% H2,

5.2 GPa) and the S-solid (0.6 mol% H2, 5.6 GPa). The Raman spectra of the liquid

phases of H2-SiH4 for the two samples are shown in Fig. 4.8 (5:1 H2:SiH4) and Fig. 4.9

(1:1 H2:SiH4). The peak intensities in the spectra are normalized to the acquisition

time (laser power was held constant in our experiments).

Figs. 4.8 and 4.9 present the evolution of the fluid Raman peaks as a function

of pressure. The H2 Q1(1) vibron of both fluid samples broadens with increasing

pressure, and reaches 30 cm−1 at 6 GPa. It sharpens greatly in the crystalline H-

solid (FWHM = 7 cm−1 with instrument resolution of 4 cm−1. Compared with the

corresponding pure H2 liquid (15 cm−1) and solid (5.6 cm−1) [53], our observation

suggests the strong interaction between the SiH4 and H2 components. Likewise in

both fluid samples, the SiH4 ν1 and ν3 modes broaden and diverge from each other

as pressure increases leading to the broadening of the feature at around 2200 cm−1.

The behavior of the hydrogen rotons in our samples were consistent with that of pure

hydrogen, and were not affected by the SiH4 composition within measurement error.

The Raman intensity, frequency, and FWHM of the SiH4 ν1, ν3 and H2 Q1(1)

modes are highly characteristic of the solid and fluid phases and their compositions.

For the fluid across the H2-SiH4 binary system, the SiH4 ν1, ν3 frequency decreases

and H2 Q1(1) vibron frequency increases with increasing H2 content (Figs. 4.10 and

4.11).The liquidus pressure of 5.8 GPa for the 5:1 H2:SiH4 sample can thus be precisely

identified by intensity and frequency decrease of the H2 vibron and intensity increase

and frequency decrease of SiH4 ν1,ν3. Conversely, the liquidus pressure of 5.4 GPa

for the 1:1 H2:SiH4 sample can be precisely identified by intensity and frequency

increase of the H2 vibron and intensity decrease and frequency increase of SiH4 ν1,


800 1000 2200 2400

H2-SiH4

4.1 GPa

H-solid6.1 GPa

S-solid6.1 GPa

x5x10

x10

x10

Raman Shift (cm-1)

A

4000 4200

B

Q1(1)

S-solid5.6 GPa

H2-SiH4

5.2 GPa

H-solid6.0 GPa

x6

Raman Shift (cm-1)

Figure 4.7: Representative Raman spectra for the SiH4 ν1,ν2, and ν3 modes andH2 Q1(1) vibron in both fluid and solid H2-SiH4 phases of the 5:1 and 1:1 H2:SiH4

samples. (A) from bottom to top shows Si-H stretching modes for the SiH4 in H-solidat 6.1 GPa which contains 0.4 mol % SiH4, in the 50 mol % SiH4 fluid at 4.1 GPa,and in S-solid at 6.1 GPa with 98.7 mol % SiH4. (B) from bottom to top show showsH2 vibron for the H2 in S-solid at 5.6 GPa with 0.6 mol % H2, the 5:1 H2:SiH4 fluidat 5.2 GPa which contains 83.3% H2, and the H-solid at 6.0 GPa which contains 98.5mol % H2.


Figure 4.8: Evolution of the Raman spectra of the fluid portion of the 5:1 H2:SiH4

sample with increasing pressure. Left series shows the SiH4 ν1, ν3 modes, right seriesthe H2 vibron. The sample hits the liquidus line just above 5.8 GPa.


Figure 4.9: Evolution of the Raman spectra of the fluid portion of the 1:1 H2:SiH4

sample with increasing pressure. Left series shows the SiH4 ν1, ν3 modes, right seriesthe H2 vibron. The sample hits the liquidus line just above 5.4 GPa.


ν3. The sharp change in the slopes of the pressure dependence with Raman shift

can be readily observed at the liquidus pressures (Figs. 4.10 and 4.11), above which

the fluids no longer remain at the original bulk composition, but change with the

fractionation of the H-solid or S-solid. The fractionating fluid curves for the two

compositions intersect at the eutectic point, providing additional strong support to

the binary eutectic at 6.1±0.1 GPa, and then continue to cross over as a result of the

metastable super-pressurization phenomenon (Figs. 4.10 and 4.11).

The compositions of the H-solid and S-solid are close to the end-members but

contain a small and variable amount of the opposite components. The H2 content

of the S-solid in equilibrium with the fluid below 6 GPa is 1.5 mol%. This drops

to 0.5mol% in equilibrium with the H-solid above 6.1 GPa. Conversely, the SiH4

content in the H-solid in equilibrium with the fluid below 6 GPa is 2 mol%. This

drops to 0.5 mol% in equilibrium with the S-solid above 6.1 GPa. These small but real

variations are significant. The H2 vibron frequency shift of the S-solid as a function

of pressure shows a sharp kink at the eutectic pressure (Fig. 4.11), confirming the

small compositional change in the S-solid at the eutectic. The addition of the minor

components has a remarkable impact on the crystalline phases making S-solid and H-

solid significantly different from the pure SiH4 and H2 solids. Pure silane crystallizes

at 4 GPa into solid phase III and transforms to solid phase IV at 6.5 GPa which

is stable up to 10 GPa [50].When the S-solid began to crystallize at 5.4 GPa from

the 1:1 H2:SiH4 fluid, however, the Raman spectra of the SiH4 ν1, ν3 and ν2 modes

were similar to the pure SiH4 phase IV [50]. We did not observe the equivalent phase

III spectra over the range studied. The Raman vibron frequency of the minor H2

component in the S-solid is 30-40 cm−1 lower than that of pure H2 (Fig. 4.11). These

distinctive features make it very easy to characterize that S-solid as a new compound

of silane and hydrogen, rather than a mixture of two end-member phases.

The ν1, ν3 and ν2 modes of the minor SiH4 component in the H-solid that crys-

tallized from the 5:1 H2:SiH4 sample are similar to that of the S-solid or pure silane

phase IV in terms of peak shape, but are 30 cm−1 higher in frequency (Fig. 4.10), and

thus clearly distinguishable from S-solid and SiH4 phase IV. The minor SiH4 compo-

nent also has a significant effect on Raman vibron of the H2 vibron of the H-solid as


0 1 2 3 4 5 6 72180

2190

2200

2210

2220

2230

2240

2250

Pure SiH4

1:1 H2:SiH4 sample

5:1 H2:SiH4 sample

Ram

an S

hift

(cm

-1)

Pressure (GPa)

Figure 4.10: Raman shift of SiH4 ν1 modes in the H2 environment as a function ofpressure. Circles represent liquid phase, diamonds refer to solid. Red data are for the5:1 H2:SiH4, blue for the 1:1 sample. Vertical blue and red lines indicate the pressurewhere the first solid forms. Vertical black line indicates the crossover in the liquidphase data which occurs at the eutectic pressure. Fluid data above this pressure is aresult of super-pressurization. Black symbols show pure fluid SiH4 data [50].


0 1 2 3 4 5 6 74150

4160

4170

4180

4190

4200

4210

4220

Pure H2

1:1 H2:SiH4 sample

5:1 H2:SiH4 sample

Ram

an s

hift

(cm

-1)

Pressure (GPa)

Figure 4.11: Raman shift of H2 vibron in SiH4 environment as a function of pressure.Circles represent liquid phase, diamonds refer to data from solid. Red data are for the5:1 H2:SiH4 sample, blue for the 1:1 sample. Vertical blue and red lines indicate thepressure where the first solid forms. Vertical black line indicates the crossover in theliquid phase data which occurs at eutectic pressure. Fluid data above this pressureis a result of super-pressurization. For comparison, data for pure H2 [53] are shownin black with dashed line representing liquid and solid black line for the solid.


shown in its frequency decrease of 6 cm−1 in comparison to the pure solid H2. Again,

these features establish the distinction between the H-solid and pure H2 solid.

4.2.3 Further discussion

We used optical microscopy and Raman spectroscopy to study the H2-SiH4 binary

system at pressures up to 6.5 GPa. Crystallization from the fluid, the H2-SiH4 system

shows an apparently simple binary eutectic phase diagram consisting of a fluid and

two near-end-member solids, S-solid and H-solid with limited solid solubility between

SiH4 and H2. No solid phases with intermediate composition are observed within

the pressure range studied. Monitoring the Raman peaks of H2 and SiH4 in different

fluids and solids visible through optical microscopy, in two samples with starting

compositions of 5:1 and 1:1 molar ratios, we determined its P -x phase diagram with

liquidus curves leading to the binary eutectic point at 6.1(± 0.1) GPa and 72(± 2)

mol% H2 at 300K. The eutectic pressure determination based on the change of H-

H and Si-H Raman peaks intensity ratio is in agreement with several independent

determinations from kinks in the Raman shifts of the H-H vibron frequency and Si-H

Raman frequencies in the two liquids and the kink in the Raman shifts of the H-H

vibron frequency in the S-solid with pressure. Super-pressurization is significant when

the mixtures fully solidify, indicating important kinetics effects in the H2-SiH4 system.

Overshooting of the eutectic by 0.2-0.4 GPa is evident as shown by the crossovers

of P -x plot and P -ν plots of the Si-H stretching modes and H2 vibron for the 5:1

and 1:1 H2:SiH4 starting compositions. Metastability and sluggish reaction kinetics

are a key favorable condition for the possible existence and retention of additional

phases in the system for potential applications. Strong intermolecular interaction

between the two species was observed. The Raman spectra for the H2 vibron in

both the H2-SiH4 fluid and solid phases show substantial red shift and broadening

compared to pure H2. This softening becomes larger with increasing SiH4 content.

Conversely the ν1, ν3 Si-H stretching modes show substantial blue shift compared to

pure silane in an H2 rich environment. Most intriguingly, the H-solid and S-solid are

different from the respective end-member solids. In both phases, addition of minor


components of the opposite compound has a substantial effect on the bonding and

phase stability. The original Ashcroft concept [43] only requires a hydrogen-dominant

material which may become a metallic alloy and the second component (or dopant)

may participate in the common overlapping bands. It has been well established that a

minor composition change can have major effects on electron properties. For instance,

YH3−δ can be switched back-and-forth sharply between insulator and metal by the

hydrogen content change (δ) of several percent which triggers a phase change [55],

and the diamond goes through an insulator-superconductor transition by doping with

percent-level boron without a structure change[56]. Both the H-solid and S-solid are

more hydrogen-dominant than pure Group IV hydrides, and the 0.5-2% dopants are

sufficient to contribute to overlapping bands, making them interesting candidates

for further investigation of hydrogen metallization and superconductivity at higher

pressure.

4.3 Formation of SiH4(H2)2 - a new compound

Bringing the SiH4 and H2 mixture to pressure above 6.8 GPa, a new molecular com-

pound composed of SiH4 and H2 is formed. This is evidenced by the very different

SiH4 ν1 and ν3 and H2 vibron Raman features (Figs. 4.12 and 4.13). For the H2

vibron, the spectra change from a single peak at 6 GPa to a much lower-frequency

main peak with multiple satellites: the main peak redshifts to 4139 cm−1 at 8.6 GPa

from 4205 cm−1 at 6 GPa, and further shifts to 4129 cm−1 at 15 GPa. The SiH4

ν1 and ν3 modes remain hardening upon compression, however the spectra shape are

different from that of pure SiH4 or S-solid. Clearly, intermolecular interaction is much

stronger in the new phase than in the mixed liquid phase. X-ray diffraction on this

new compound shows a face-centered cubic structure. Further comparison between

the Si equation of state and H2 equation of state shows that the molar volume of

the compound is between the sum of one SiH4 and two H2 and the sum of one crys-

talline Si(V) and four H2. The composition of the compound is thus determined to be

SiH4(H2)2. Rietvield refinement resolves the space group to be F43m [57], however

the exact positions of the molecular hydrogen could not be resolved. It is also unclear


2100 2200 2300 2400

Si-H

Raman Shift (cm-1)

15 GPa

13 GPa

11 GPa

8.6 GPa

Figure 4.12: Raman spectra of SiH4 ν1, ν3 modes in SiH4(H2)2.

why the compound is stable above 6-7 GPa. In the following section I will present

the computational result of the high pressure behavior of SiH4(H2)2. This work1 is in

collaboration with Dr. Chen from Institute of Metal, Chinese Academy of Science,

and Dr. Fu from Oak Ridge National Laboratory.

4.3.1 Calculations on SiH4(H2)2 to metallization pressure

In this section, we investigated the possible hydrogen positions and analyzed the elec-

tronic structure of SiH4(H2)2 through first-principle calculations within the framework

of density functional theory (DFT). We explored the mechanism for the stabilization

of SiH4(H2)2 under pressure. The electronic structure demonstrated that this new

compound is a wide gap insulator at lower pressure and undergoes bandgap closure

at 200 GPa. The hydrogen molecules in the compound have a small induced dipole

1Reprinted with permission from [58]. Copyright (2010), American Physical Society.


4050 4100 4150 4200 4250 4300

6 GPa

H2 vibron

15 GPa

13 GPa

11 GPa

Raman Shift (cm-1)

8.6 GPa

Figure 4.13: Raman spectra of H2 vibron modes in SiH4(H2)2 and compared withthat of H-solid.


moment that decreases with pressure. These results provide insight into the effect of

pressure on hydrogen-dominant materials and has implications for the metallization

of pure hydrogen.

4.3.2 Computational and experimental details

First-principles calculations were performed using the Vienna ab initio Simulation

Package (VASP) [59] with the ion-electron interaction described by the projector aug-

mented wave potential (PAW) [60]. We used the generalized gradient approximation

for the exchange-correlation functional. Brillouin-zone integrations were performed

for special k points according to Monkhorst and Pack technique. The energy cutoff

for the plane-wave expansion of eigenfunctions was set to 500 eV. The generalized

gradient approximation based on the Perdew-Burke-Ernzerhof (PBE) pseudopoten-

tials [61] are used for Si and H (only s and p electrons are included).The core radii

of Si and H potentials are chosen to be 2.944 A (PAW-PBE Si 05Jan2001) and

2.174 A (PAW-PBE H 15Jun 2001), respectively. For calculations at low pressure

we also checked the energy cutoff of 700 eV and found the obtained results are al-

most unchanged in comparison with the value of 500 eV. Optimization of structural

parameters was achieved by minimizing forces and stress tensors. Highly converging

results were obtained utilizing a dense 11×11×11 k-point grid for the Brillouin zone

integration. To calculate charge transfer, we used the code of Bader charge analysis

including both valence and core charges [62][63] obtained within a grid of 300 × 300

× 300 (27 millions grid points). This grid is dense enough to correctly reproduce

the core electron charge of both Si and H atoms. For the proposed structure, Ra-

man spectra under pressure have been calculated using Quantum-ESPRESSO [64].

A series of self-consistent total energies calculations were performed to determine

the equilibrium lattice parameters within the norm-conserving pseudopotentials be-

fore conducting the Raman calculations. The experimental data in this work was

collected in a diamond anvil cell. Synchrotron X-ray diffraction was carried out at

HPCAT, Advanced Photon Source, Argonne National Laboratory.


Table 4.1: DFT optimized structural parameters at 6.8 GPa for the F43m structureof SiH4(H2)2. Lattice parameters are given in A.

Space group F43ma in A 6.279 (expt: 6.426 [57])

Si in 4a sites (0, 0, 0)H in 16e sites (0.1348, 0.1348, 0.1348)

eight H-H pairsH-H pair1 (0.5441, 0.0015, 0.9601)H-H pair1 (0.4559, 0.0040, 0.0404)H-H pair2 (0.9675, 0.4495, 0.9878)H-H pair2 (0.0304, 0.5496, 0.0034)H-H pair3 (0.0433, 0.9952, 0.5413)H-H pair3 (0.9575, 0.9990, 0.4586)H-H pair4 (0.4974, 0.5517, 0.5298)H-H pair4 (0.4942, 0.4482, 0.4709)H-H pair5 (0.2242, 0.2929, 0.7412)H-H pair5 (0.2902, 0.2014, 0.7817)H-H pair6 (0.7800, 0.7973, 0.7061)H-H pair6 (0.7476, 0.7105, 0.7823)H-H pair7 (0.2046, 0.7944, 0.2750)H-H pair7 (0.2887, 0.7113, 0.2543)H-H pair8 (0.7755, 0.2850, 0.2654)H-H pair8 (0.7068, 0.2029, 0.2113)

4.3.3 Results and discussions

We performed a series of searches for the possible hydrogen positions within the

face centered cubic (fcc) F43m space group proposed from experiments [57]. The

tetrahedra SiH4 unit occupies the fcc lattice sites. The positions of eight H2 pairs are

at two nonequivalent sites. Four equivalent pairs are at the middle of each axis of the

cubic structure and in the center of the cube. The other four pairs of H2 are at the

1/4 or 3/4 position of the four body diagonal lines forming a tetrahedron. The latter

four are the nearest neighbors of a SiH4 molecule. The optimized lattice parameters

at 6.8 GPa for the lowest-energy configuration are compiled in Table 4.1.

Fig. 4.14 shows the calculated volumes as a function of pressure together with


previous experimental results [57] and our new data point. The theoretical equa-

tion of state (EOS) is consistent with the experimental findings, especially at higher

pressures. Below 15 GPa, the calculated volumes are 3-6% smaller than the corre-

sponding experimental values. This discrepancy may be attributed to the fact that

at low pressures intermolecular van der Waals interactions are significant, given that

there is a large separation between the H2 and the SiH4 units, and DFT methods are

known to have limited accuracy describing long range interactions. Temperature may

also be a source for the discrepancy in the lattice constants at low pressures. Our cal-

culated data were performed at absolute zero temperature whereas the experimental

measurements were collected at 300K.

We derived a zero-pressure bulk modulus K0 = 5.3 GPa with K′ = 3.76 from a fit

to a third order Birch-Murnaghan EOS, compared to the experimental values of K0

= 6.8 GPa and K′ = 4 [57].

The Raman spectra of SiH4 and H2 can provide important information for under-

standing the property change of SiH4(H2)2 under compression. A detailed description

of the vibrational modes for pure H2 and pure SiH4 can be found in previous high pres-

sure Raman spectroscopy work [53][50]. We calculated the Raman spectra at 9 GPa

and 25 GPa. From the 9GPa data (shown in Fig. 4.14), we see that the major repre-

sentative experimental Raman features (ν2(E), ν1(A1) and ν3(F2) stretching modes

in SiH4 and the H2 vibron) have been qualitatively reproduced in our theoretical cal-

culations, especially the multiple peaks in hydrogen vibron region. At 9 GPa, our

calculations revealed that the SiH4 ν1(A1) feature is at 2201 cm−1, and the H2 vibron

is at 3940 cm−1. Increasing pressure up to 25 GPa, their positions shift to 2412 cm−1,

and 3866 cm−1. Comparing with the experimental measurement [57], our theoretical

values are underestimated by 5∼ 6%, due to the overestimation of the bond length.

Despite the underestimation, the qualitative trend for our calculated Raman shifts

with pressure are consistent with experimental observations [57][65]. The most intense

peak from the ν1(A1) and ν3(F2) stretching modes of the SiH4 unit shows substantial

blue shift with increasing pressure (Fig. 4.14). Conversely, the pressure-dependent

vibron mode from H2 in SiH4(H2)2 exhibits strong red shifts. This softening becomes

larger with increasing pressure. We also find that the low-frequency ν2(E) mode


Expt (This work)Calc

(a)

Expt(Strobel et. al. )

(b)

Figure 4.14: Panel (a), Comparison of the calculated pressure-dependent volumes(equation of state) with available experimental data. Panel (b), calculated and ex-perimental Raman spectra at 9 GPa and 8.6 GPa respectively.


-12 -8 -4 0 40

0.20.40.60.8

1

DO

S (

stat

es e

V-1

f.u.

-1)

Si-sSi-pHSi

HH

-30 -20 -10 0Energy (eV)

0

0.5

1.0

1.5

0.20.40.60.8

1

0 50 100 150 200Pressure (GPa)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Cha

rge

tran

sfer

q (

e)

0 GPa

6.8 GPa

200 GPa

[SiH4]q+

[(H2)2]q-

(a)

(b)

(c)

(d)

Figure 4.15: Electronic structure of SiH4(H2)2, panels (a to c): the calculated totaland local density of states (DOS) at three pressures of 0 GPa, 6.8 GPa, and 200GPa, respectively. HSi and HH denote the H atom from the units of SiH4 and H2

molecule, respectively. The Fermi level is set to zero. Panel d: the calculated pressure-dependent intermolecular charge transfer, q, between the SiH4 and the H2 molecules,defined as [SiH4]

q+[(H2)2]q−.

(approximately 940 cm−1) is insensitive to pressure. Alltogether, our results indicate

there are strong intermolecular interactions in SiH4(H2)2 under pressure.

Studying the pressure-dependent electronic structures provides insight into the

stabilization mechanism of the compound SiH4(H2)2. Fig. 5.3(a, b and c) compares

the calculated densities of states (DOS) at 0 GPa, 6.8 GPa and 200 GPa. The band

structures that the DOS is based on was calculated according to the experimentally

extracted volume [57] of 410.12 A3. The 0 GPa DOS represents the simple mixed

phase of SiH4 and H2, where the energy level of hydrogen from SiH4 (denoted as HSi)

and that of the hydrogen from H2 (denoted as HH) do not overlap significantly. As

pressure increases to 6.8 GPa, the energy band from the hydrogen atom in the H2


Figure 4.16: The crystal structure of SiH4(H2)2: panel (a) two-dimensional structuralprojection and panel (b) a three-dimensional structure. Large and small balls denoteSi and H, respectively. Panel (c): Contour plot of the charge difference in the (006)plane as marked in panel (b). Positive values (red) denotes the charge accumulationand negative value (blue) charge depletion. * marks the region of charge accumulationin the interstitial spaces.

molecule starts to overlap with the band of the SiH4 hydrogen atoms. This indicates

there will be hybridized states between HSi from SiH4 and HH from H2 molecule.

The hybridization is accompanied by charge accumulation at two sites (c.f., Fig.

4.16): one is the interstitial space between HSi and HH , the other is on the HSi

site of SiH4. The former bridges the HSi and HH , and thus is a direct evidence

of strong interaction between SiH4 and H2 units. The effect of the latter charge

accumulation may have contributed to the change of the Si-H bond strength. The

charge maxima between the HSi and HH atoms is consistent with the site-l-projected

density of states (Fig. 5.3(b)). It is also interesting to note that the charge distribution

anomaly in the interstitial space does not exist below 5.4 GPa. Thus, the stabilization

of the compound SiH4(H2)2 arises from the overlapping of valence electrons in the

interstitial spaces bridging the HSi and HH . The spatial overlap of the hydrogen

atoms is consistent with the their DOS overlap in energy as pressure changes from

ambient pressure to 6.8 GPa, shown in Fig. 5.3b.

SiH4(H2)2 consists of two sublattices, one occupied by SiH4 tetrahedra and the

other by molecular H2 pairs. In order to clearly identify the intermolecular character,

we calculated the magnitude of the intermolecular charge transfer between the unit

of SiH4 and the H2 molecule using the Bader technique [62][63]. Our results reveal


that the SiH4 tetrahedra and H2 pairs play the roles of electron donor and electron

acceptor respectively. The charge transfer between the constituent clusters stabilizes

this fcc-type SiH4(H2)2 in a weak ionic form, [SiH4]q+[(H2)2]

q−, as the Coulombic

attraction substantially enhances the thermodynamic stabilization. In terms of our

projector augmented wave (PAW) calculations within the denser 300 × 300 × 300

k-mesh (27 millions grid points), charge transfer, q, is displayed in Fig. 5.3(d) as a

function of pressure. Interestingly, with increasing pressure we observed two obvious

jumps from the pressure-dependent charge transfer curve. Before the first jump occurs

at 5.4 GPa, there is a constant charge transfer q of approximately 0.01e. Above 5.4

GPa, the magnitude of q suddenly increases to about 0.04e. Eventually, it reaches

0.18e at 199 GPa. The pressure range above 5.4 GPa agrees with the experimental

region where SiH4(H2)2 becomes stable. The likely mechanism that contributes to

the increase in charge for the H2 units above 5.4 GPa are: (1) the contraction of the

hydrogen wave function more closely into the nuclei region as the bonding between HH

and HSi is developed [also see Fig. 4.16(c)], and (2) the increase in charge transfer (or

extension) from the SiH4 tetrahedra to the H2 units as the intermolecular distance

decreases. We found that the pressure-induced charge increase (or distortion) for

the hydrogen molecule has an effect on weakening the H-H bond, which results in

softening of the H2 vibron. This is similar to what has been found in pure H2 both

experimentally [47] and theoretically at pressures as high as 200 GPa [49] and in the

recently discovered Xe-H2 compound [66].

We also observed that the charge on each HH of H2 is different. This charge asym-

metry in hydrogen molecule results in a small dipole moment. The nearest H2 to SiH4

carries a charge asymmetry between 0.02 and 0.04e, whereas the charge asymmetry of

the next-nearest H2 is between 0.01 and 0.02e. Furthermore, these charge asymmetry

for all H2 pair decreases with increasing pressure, consistent with the reduced H2 IR

intensity at higher pressure observed in the SiH4(H2)2 IR experiment [57].

We also note that, after 199 GPa, charge transfer q suddenly increases to 1.02e,

accompanied by metallization of the compound. This is partly due to the change in

the locations of the Si atoms from their face-centered 4a position, implying that the

compound is in a different structure above this pressure. Also, at this high pressure,


0 40 80 120 160 200Pressure (GPa)

0

1

2

3

4

5

6

7

8

9

10

Ban

d ga

p (E

g, eV

)

Γ X LW Γ

-20-15-10-505

Γ X LW Γ

-20-15-10-505

Γ X LW Γ

-20-15-10-505

6.8 GPa 199 GPa 200 GPa

Figure 4.17: Pressure-dependent band gap sizes (Eg in eV). Inset from left to right:the calculated electronic band structures at 6.8 GPa, 199 GPa, and 200 GPa, respec-tively. Red dashed lines indicate the top of valence band.

the electrons become more delocalized as evidenced in the increasingly parabolic

behavior of the band dispersion. Metallization is accompanied by the occupation of

antibonding orbitals.

We have calculated the electronic band structures of SiH4(H2)2 at 0 K. The results

indicate that the new compound is a transparent indirect wide-gap insulator with a

large band gap of about 6.1 eV at 6.8 GPa. With increasing pressure, the gap de-

creases, and the dispersion of each band increases indicating an increasing intermolec-

ular interaction. At 200 GPa, the bandgap closes and SiH4(H2)2 becomes metallic

(c.f., Fig. 4.17) because of a structural transformation. Normally, standard density

functional theory underestimates band gap, implying the real pressure-dependent

gaps are larger than predicted in our PBE-GGA approximations. The predicted met-

allization pressure is lower than that of pure H2 again demonstrating that the addition


of a group IV hydride can lower the metallization pressure compared to pure hydro-

gen. In our calculation (c.f., Fig. 4.17) the compound has a band gap of about 4.3

eV at 35 GPa, which implies that experimentally observed sample darkening might

be due to hydrogen reaction with gasket material, a concern addressed in Ref. [57].

The metallization scheme of bandgap closure in SiH4(H2)2 is consistent with the

prediction for molecular metallic hydrogen [48], and the possibility of superconduc-

tivity at relatively high temperature [67]. The present compound inherits many of

the electronic and vibrational features of the dense solid superconducting phases of

both SiH4 [51] and H2 [43][48].

4.3.4 Comparison with other calculations

In our work we have performed first-principles calculations to investigate the pressure-

dependent behavior of the structural and electronic properties of the SiH4(H2)2 and

its stability mechanism. We determined the positions of the hydrogen atoms and

explicitly calculated the pressure-induced charge transfer from the SiH4 tetrahedra to

molecular H2 units. Besides the small partially ionic feature, the compound is also

stabilized by the charge accumulation at the interstitial position between HSi from

SiH4 and HH from H2. Our results are further supported by the calculated Raman

spectra which are in good qualitative agreement with experimental observations. In

the SiH4(H2)2, the H2 vibron shows substantial red shift whereas the stretching modes

from SiH4 exhibit strong blue shift with increasing pressure. We also show that the

compound is a wide-gap insulator at low pressure and eventually becomes metallic

above 200 GPa, accompanied by a large charge transfer from SiH4 to H2 during

metallization.

Concurrently, a number of theoretical work using different computational methods

address the high pressure structural, bonding and electronic properties of SiH4(H2)2

[68] [69][70][71] [72]. Ramzan et al. used DFT calculations to investigate the metal-

lization of SiH4(H2)2 and found that it occurs at 145 GPa and 160 GPa with GGA

and GW methods respectively [68]. Yao et al. predicted the metallization to be at


120 GPa [70]. The difference compared to our results might be due to the selec-

tion of pseudopotentials and the scheme of structural relaxation. However all works

confirmed that at 35-50 GPa the SiH4(H2)2 is still a wide gap insulator and the

metallization occurs at a much higher pressure via bandgap closure.

The theoretical communities also have an consensus of the nature of the unusually

strong intermolecular interaction. Yim et al. performed first-principles molecular

dynamic calculations and calculated a structure with orientationally disordered silane

and hydrogen [69]. As the H2 molecules occupies the tetrahedral and octahedral sites

of a distorted fcc the two types of H2 behaves differently. While the H-H bond length

of H2 at octahedral sites shortened with pressure, that of the H2 at the tetrahedral

sites (closer to SiH4) lengthened with pressure: the bond weakens. With natural

bond orbital analysis, they showed that the weakenning of the H-H bond is due to

perturbative donor-acceptor interactions between localized occupied and unoccupied

antibonding orbitals of SiH4 and H2. This is consistent with our finding through

Bader charge analysis that there are charge decrease in SiH4 unit and increase in H2

unit. Such charge transfer is the major contribution to the intermolecular interaction

that leads to an inverse pressure dependence of H2 vibron, which occurs at much

lower pressure in SiH4(H2)2 than in pure H2.

Chapter 5

Transition metal oxides: Fe2O3 as

an archetypal example

In previous chapters, the materials systems I have studied are all main group front row

molecular compounds. The hydrides and hydrogen itself can all be described as closed

shell systems, and the dominant interaction is dispersive van der waals interaction.

Further down the periodic table and in between the main groups are transition metal

elements, where their compounds’ properties depend on d-electron configurations.

Extremely interesting physics phenomena often emerge in these strongly correlated

systems, with potential applications in the areas of superconductivity, colossal mag-

netoresistance and spintronics. Due to the strong correlation of the valence electrons,

the failure of the single electron approximation poses many challenges for theoreti-

cal calculations. To distinguish the different effects and resolve the physics in these

systems, pressure is a fundamental and complimentary parameter in addition to tem-

perature and doping. High pressure itself has a number of attractive advantages: 1) a

DAC can input sufficient energy into the system to induce structural, electronic and

magnetic phase transitions; 2) pressure is a clean perturbation, basically reducing the

lattice parameters, and it is straight-forward to compare theoretical simulations on

materials properties with experimental results. Only thanks to the recent develop-

ments of high pressure techniques, people are able to add a new dimension to the

phase diagram and discover new state of matter therein.

69

CHAPTER 5. TRANSITION METAL OXIDES 70

t2g t2g

eg

eg

High spin Low spin Octahedral crystal !eld splitting

Energy

dz² dx²-dy²

dxy dxz dyz

Figure 5.1: Crystal field splitting of 3d orbital and schematics of high spin and lowspin configurations

5.1 Effects of pressure

The effects of pressure on the electronic structure of 3d transition metal oxides are

usually reflected by the change in conductivity and magnetic moment. It is well known

that many of them are Mott insulators at ambient conditions, due to the localized

nature of d-electrons. As pressure brings the ions and thus valence electrons closer

to each other, an insulator to metal transition can occur. The magnetic moment

(or zero moment) of a 3d transition metal oxide is mostly from the unpaired d-

electrons. As the metal ion is in an non-spherically symmetric environment (e.g. MO6

octahedron coordination), its angular dependent d orbital’s five-fold degeneracy is

reduced. Crystal field theory and ligand field theory (an extension of molecular orbital

theory) are used to explain the reduction of degeneracy in such systems. For a typical

octahedral environment, the 3d orbital are split to higher 2-fold eg levels (dz2 ,dx2−y2)

and lower 3-fold t2g levels (dxy,dyz,dxz). The differences in energy, the so-called crystal

field splitting energy, is determined by the strength of the interaction between the

ligand and the metal valence electron and varies with different metals and ligands.

This energy competes with the electron pairing energy, and favors different spin state

(see Fig. 5.1). Pressure reduces the size of the MO6 octahedron, strengthening the

interaction between the metal and the ligand, triggering a spin transition.

In this chapter I will present the study of an example of pressure induced insulator

to metal and high spin to low spin transition the high pressure evolution of the


electronic structure of Fe2O3 using x-ray absorption1.

5.2 High pressure x-ray absorption study of Fe2O3

5.2.1 Introduction to Fe2O3

An archetypal 3d transition metal oxide and important geological compound, α-Fe2O3

(hematite) undergoes a series of structural and electronic transitions at high pressure.

At ambient conditions, Fe2O3 is an antiferromagnetic insulator, and adopts the corun-

dum structure. This structure is maintained until approximately 50 GPa whereupon

it transforms to a Rh2O3(II)-type structure [74], accompanied by a 10% drop in

volume. The structural transition is associated with changes in magnetic and elec-

tronic structures. X-ray Kβ emission at ambient pressure and 72 GPa show that the

magnetic moment drops from high-spin (HS) to low-spin (LS) at high pressure [75].

Conductivity measurements indicate that an insulator to metal transition occurs be-

tween 40− 60 GPa [76]. Mossbauer spectroscopy up to 82 GPa [76] and synchrotron

Mossbauer spectroscopy at 70 GPa [77] imply the collapse of the magnetic moments

and a nonmagnetic nature of the HP phase.

The nature of these transitions has been a popular research topic over the past

decade. Based on their structural study of the Rh2O3-II phase, Rozenberg et al.

have suggested that the charge-transfer gap closure is responsible for metallization

and concurrent spin moment transition [74]. Combined local density approximation

and dynamical mean-field theory calculations by Kunes et al. have implied that

the reduction of the Mott gap with pressure drives the volume collapse and struc-

ture change [78]. This idea appears to be at odds with experimental observations

of a metastable state in which the HS and high pressure structure occur simultane-

ously [79]. Thus, despite many studies of the transitions in Fe2O3, the nature of the

evolution of the electronic structure with pressure remains unresolved. In this arti-

cle, we implemented new experimental method and theoretical approaches bringing

valuable information to the problem.

1Reprinted with permission from [73]. Copyright (2010), American Physical Society.


A number of spectroscopic techniques have been applied to investigate the elec-

tronic configuration of 3d transition metal compounds. Photoemission and x-ray L-

edge absorption provide useful information on the 3d-levels of transition metals, but

unfortunately, these probes cannot penetrate the high pressure cells. X-ray absorp-

tion spectroscopy (XAS) at the K-edge of 3d transition elements, however, operates in

the hard x-ray regime, allowing the study of the electronic structure at high pressure.

The pre-edge region of the K-edge absorption spectrum can be used to investigate

3d-electrons of transition metal compounds. In Fe-bearing compounds, the pre-edge

spectra contain information about the oxidation state and local coordination [80].

However, limited by the 1s core-hole lifetime broadening, the energy resolution using

a transmission geometry is not sufficient to resolve the detailed structure of the pre-

edge region. Therefore we use the partial fluorescence yield method for measuring

absorption. Instead of collecting the transmitted x-ray, the Kα1 emission line is

measured. This method thus has a 2p core hole lifetime broadening of about 0.3 eV,

resulting in much higher energy resolution.

In the next section I will present the first high pressure XAS measurement in

partial fluorescence yield on Fe2O3 up to 64 GPa. The improved resolution of the

resulting spectra shows the evolution of the Fe3+ 3d electronic structure as the ma-

terial undergoes its complex pressure-induced transitions. Previously, Caliebe et al.

applied this technique to Fe2O3, and assigned the double-peak structure of the pre-

edge to the t2g and eg components of the 3d band [81] as suggested previously [82].

Similar methods have been used to study orbital hybridization and spin polarization

of Fe2O3 [83] and pre-edges of other Fe-containing compounds [84].

5.2.2 Experiments

Fe2O3 powder was loaded in a hydrostatic pressure transmitting medium (He or Ne) in

an X-ray transparent Be gasket. Ruby fluorescence was used for pressure calibration.

High pressure XAS spectra of Fe2O3 were collected at two 3rd generation synchrotron

facilities. In both setups, monochromatic X-rays focused by Kirkpatrick-Baez mirrors

were directed through a panoramic DAC, and the analyzer was fixed at 90 from the


7100 7120 7140 7160

A64 GPa

In

tens

ity (a

rb. u

nit)

Incident Energy (eV)

11 GPa

7020 7040 7060 7080

K '

K 1,3

0 GPa [2]

64 GPa

B

Inte

nsity

(arb

. uni

t)

Emission Energy (eV)

0 20 40 60

7122.5

7123.0

7123.5

7124.0

7124.5

Ked

geE

nerg

y (e

V)

Pressure (GPa)

Figure 5.2: A: X-ray K-edge absorption spectra of Fe2O3 in partial fluorescence yieldgeometry at 11 GPa and 64 GPa; Inset: Fe K-edge position at different pressures. Theedge is determined by the maximum of the first derivative of the absorption spectra.B: X-ray Kβ emission spectra of Fe2O3 at 64 GPa and 0 GPa from [75], showing thereduction of the spin moment. Red: high spin state; blue: low spin state.

incident beam.

In the SPring-8 XAS experiment conducted at BL12XU, we scanned the incident

X-ray energy from 7110 to 7145 eV with a step size of 0.1 eV and over the smaller

range of 7112 to 7115 eV at 0.05 eV step size. In the APS setup at HPCAT 16-IDD,

the entire edge was scanned from 7100 to 7160 eV with a step size of 0.25 eV. The

pre-edge was scanned from 7108 to 7118 eV (7109 to 7119 eV for 56 and 64 GPa)

with a step size of 0.2 eV. For both measurements, the partial fluorescence yield was

collected with the analyzers set at the Fe Kα1 energy (6405.6 eV).

Figure 1A shows the representative Fe K-edge XAS spectra for Fe2O3. The partial


7110 7112 7114 7116 7118

0GPa

17GPa

29GPa

40GPa

48GPa

56GPa

64GPa

t2g

eg

Incident Energy (eV)

Nor

mal

ized

Inte

nsity

(ar

b.un

it)

Figure 5.3: X-ray K-edge pre-edge of Fe2O3 at 0, 17, 29, 40, 48, 56 and 64 GPa. Thebottom 3 spectra are from SPring-8 using high resolution monochromator, and thetop 4 spectra are from APS using diamond monochromator.


Pressure (GPa)CFSE (eV)

01.41

61.44

171.59

291.73

401.82

481.85

Table 5.1: Crystal field splitting energy (CFSE) of Fe2O3 as a function of pressure.

fluorescence yield geometry allows us to resolve the pre-edge features. At the highest

pressure in our study, we collected the Kβ emission spectrum of the sample shown in

Figure 1B. Compared with the 0 GPa spectrum of Badro et al., there is a dramatic

reduction in the Kβ′ satellite peak intensity in the 64 GPa spectrum, indicating a LS

ground state [75][11].

As shown in Fig.5.2A inset, it is also observed that the K-edge blue shifts with

pressure until the phase transition region, and remain approximately constant there-

after. This shift of K-edge with pressure is also observed in other 3d transition metal

oxides [85], a result of the increase of electron density upon compression.

Fig. 5.3 shows the Fe K-edge pre-edge spectra of the sample from ambient pressure

to 64 GPa. The tail of the main absorption edge was subtracted for each spectrum

by removing the K-edge absorption spectrum of Fe in the Be gasket. The pre-edge

features at ambient pressure are associated with excitations to t2g and eg orbitals, split

by the octahedral crystal field. Our ambient pressure data can be fit with a crystal

field splitting energy (CFSE) of 1.4 eV, consistent with previous observation [81][82].

The two-peak feature in the pre-edge persists until 48 GPa, just before the phase

transitions occur. By fitting the pre-edge spectra we estimate a monotonic increase

of the CFSE to 1.85 eV at 48 GPa, as shown in Table 5.1. This increase is expected

as the FeO6 octahedra shrink with pressure, and the shorter metal-ligand distance

elevates the eg level relative to the t2g level.

The pre-edge spectra above the phase transitions (i.e. above 48 GPa) are more

complicated to interpret. The FWHM of the pre-edge features significantly broadens

and a simple assignment in terms of single particle t2g and eg transitions is inconsis-

tent; at such pressures, Fe2O3 is in the LS state in which eg should be empty and five

of the six t2g states occupied. Such a single particle configuration should lead to rel-

atively small (large) t2g (eg) amplitudes, unlike the features observed in the pre-edge

spectra at 56 and 64 GPa.


5.2.3 Theoretical interpretation and discussion

To understand the pressure dependence of the XAS, we first used crystal-field atomic

multiplet theory to calculate the electronic structure. The relevant parameters are

the atomic t2g-eg energy level spacing 10Dq [86], and the “Racah parameters” B and

C associated with d-d interactions [87]. We fix Racah B = 0.075eV and C = 0.346eV

appropriate for solid-state Fe3+ systems [88][89], and perform calculations for a range

of 10Dq.

The lowest two eigenenergies for the (1s)2(3d)5 configuration are shown in Fig. 5.4(a)

from which a HS-LS transition is evident near 10Dq = 2.2eV. For low pressure (low

Dq) the ground state has 6A1 character (HS) and crosses over at high pressure to a

state of 2T2 character (LS) [90].

While the critical value of 10Dq determined by the atomic multiplet calculation

is larger than that suggested by the experimental t2g-eg peak splitting in Fig. 5.3, it

is well-known that the critical 10Dq for the HS-LS transition is reduced by the Fe-O

charge-transfer processes. We perform calculations on a FeO6 octahedral cluster that

explicitly includes multiplets, ligand hybridization and charge-transfer via the Slater-

Koster matrix elements [91], Racah parameter A, and charge-transfer gap energy ∆.

At ambient pressure, the values of the parameters are (in units of eV): Vpdσ = −1.13,

Vpdπ = 0.65, Vppσ = 0.56, and Vppπ = −0.16, A = 5.0, 10Dq = 0.96, and ∆ = 2.7 [91].

We have used the smaller value of Vpdσ from [91].

The lowering of the critical 10Dq is illustrated in Fig. 5.4(a), which shows the

energies of the HS and LS states calculated in the FeO6 cluster compared to atomic

multiplet theory as a function of 10Dq. The HS to LS transition occurs at smaller

10Dq since the hybridization most strongly couples the d5 LS state with the d6L LS

state, lying lower in energy than the d6L HS state.

These parameters yield the ambient pressure spectra shown in Fig. 5.4(c), which

is in good agreement with experiment (cf. Fig.5.3 and Table 5.1). The two spectral

peaks separated by ∼ 1.4 eV correspond to excitations into the t2g and eg orbitals

respectively and indicate a HS ground state, with the observed CFSE coming from

10Dq plus a 0.45 eV covalent contribution. Thus while the critical 10Dq is reduced by

the Fe-O charge transfer processes, the ligand field splitting due to covalency pushes


Figure 5.4: (a) Energy of LS state for the single atom multiplet calculation (dottedline) compared with the FeO6 cluster diagonalization (dashed line) relative to theHS state (solid line). (b) HS-LS Phase diagram for Fe2O3. The dotted line showsthe probable trajectory of (10Dq, Vpdσ) with increasing pressure (see text). (c)-(e)K-edge pre-edge XAS spectra from the FeO6 cluster calculation at various pressures;EA is the Fe K-edge absorption energy. At ambient pressure (c), the spectrum showsdistinct t2g-eg absorption peaks separated by 1.4 eV, indicating a high-spin groundstate. At 48 GPa (d), the peak separation is 1.6 eV, and the ground state still residesin the high-spin sector. At 76 GPa (e), the spectrum shows broad, multiple peaks,indicating a low-spin ground state. All the spectra were broadened with a 0.3 eVLorentzian.


Figure 5.5: ab initio calculations with the FEFF software of the pre-edge region ofthe Fe K-edge XAS spectra for the high pressure metallic Rh2O3(II)-type structureof Fe2O3. EF is the fermi level.

up the spectral t2g-eg peak separation of the XAS spectra [81].

With parameters set to reproduce ambient spectra, we consider the pressure evo-

lution of the HS-LS transition and the XAS spectra. As the pressure increases, both

10Dq and the hopping integrals increase, respectively having ∼ d−5 and ∼ d−4 Fe-O

bond length dependence [86][91]. The combined effect of pressure-dependent hop-

ping and 10Dq is explained in the phase diagram of Fig. 5.4(b). We consider several

variations of Vpdσ with d as shown in Fig. 5.4(b), which all indicate that the critical

pressure occurs between 52 and 55 GPa. Although variation of the exponent of Vpdσ

induces a variation on the order of 5% in the predicted critical pressure it is striking to

observe that the experimentally observed limits on the critical pressure are in general

agreement with theoretical predictions.

Figures 5.4(c)-(e) show the calculated pre-edge XAS spectra from the FeO6 cluster

at various pressures. The spectrum at 48 GPa (Figure 5.4(d)) shows a clear two peak

structure in the HS state, with a t2g-eg peak separation of ∼1.6 eV. The calculated

CFSE is ∼ 15% smaller in energy than experiment, which may be in part due to

structural deviations from octahedral symmetry giving inequivalent Fe-O bonds not

included in the cluster calculation [74], as well as the overall uncertainty in cluster

parameters. Figure 5.4(e) shows the calculated XAS spectra at 76 GPa. The high


pressure spectra has multiple-peak features indicating a LS ground state; this quali-

tative change in character of the ground state is reflected as a qualitative change in

the calculated spectra. It is the simple transformation properties (A1) of the HS state

that allow the XAS to be interpreted in terms of single particle t2g and eg levels; the

final state, with one additional d-electron, transforms as A1 ⊗ (T2 ⊕ E) = T2 ⊕ E

mimicking the single particle t2g and eg levels. On the other hand, addition of a

d-electron to the LS state yields T2⊗ (T2⊕E) = A1⊕E⊕T1⊕T2⊕T1⊕T2 resulting

in more peaks than would be expected based on a single particle interpretation.

While an insulator-metal transition is not necessarily concomitant with a change

in the local spin configuration (and vice versa), a low spin metallic state is always

expected at a high enough pressure. In this regime, we use the all-electron FEFF

code [92][93] to calculate the high pressure Fe K-edge XAS for a large cluster of 152

atoms in the high pressure structure. Figure 5.5 shows the calculated pre-edge XAS,

having broad pre-edge features in qualitative agreement with the experiment at and

above 56GPa.

We last turn to the electronic phase transition mechanism. Badro et al. have

shown the coexistence of HS and Rh2O3-II structure indicating that the electronic

transition can not drive the structural transition. Kunes et al. divided the elec-

tronic transition into a Mott gap closing and a HS-LS gap closing, and estimated

the respective regimes of stability via a local “density-based interaction”. Here we

have indicated the importance of atomic multiplets and ligand hybridization. Our

results indicate the location of the HS-LS transition can be well-described within

the charge-transfer multiplet-hybridization cluster approach and reasonable choices

for the pressure-dependence of the cluster parameters. The reduction of the critical

pressure for the HS-LS transition in comparison with atomic multiplet theory due to

ligand hybdrization is seen to be significant. These results lead to the prediction that

the critical pressure occurs between 52 and 55 GPa, at values of 10Dq much smaller

than would be expected from atomic multiplet theory based on the experimental

spectra. While our cluster calculation cannot address in detail the closing of a bulk

Mott gap, the observed reduction of the HS-LS transition pressure leads us to suggest

that the physics of a local HS-LS transition should be strongly reconsidered as the


key ingredient giving the evolution of spectral features observed in the pre-edge XAS

spectra with pressure.

5.2.4 Summary

We measured x-ray absorption spectra of Fe2O3 up to 64 GPa. The narrowing effect

of resonant emission and the symmetry properties of the 3d5 configuration allow us

for the first time to experimentally resolve the crystal field splitting and its pressure

dependence through the metal-insulator transition. The CFSE increases from 1.41

eV at ambient conditions to 1.85 eV at 48 GPa. The pre-edge features change dras-

tically at higher pressures corresponding to the range where a number of electronic

and structural transitions have been reported. We constructed the phase diagram for

Fe2O3 which shows that the changes in multiplet structure and hybridization are im-

portant for a quantitative estimate of the critical pressure. Based on considerations of

local cluster physics, excellent agreement between the observed pressure-dependence

of the experimental and calculated spectra were obtained.

Appendix A

Correlation functions of hydrogen

and its infrared and Raman spectra

A.1 Properties of solid hydrogen

At ambient condition hydrogen exists in the gas phase, and most of the bulk properties

can be described by the simple molecular model. As a linear homonuclear diatomic

molecule, hydrogen’s vibrational behavior in low energy is well described by a quan-

tum mechanical harmonic oscillator, with energy (ν + 12)~ω0, ν = 0, 1, 2, .... Its rota-

tion is similar to all other linear molecules defined by quantum number J = 0, 1, 2, ...,

and the energy is J(J + 1)~2/(2µR2), µ means reduced mass (only in this section).

The spins of the two electrons of hydrogen molecule can have S = s1 + s2 = 0 or

S = s1 + s2 = 1, named para-hydrogen and ortho-hydrogen respectively. The con-

version rate between the two species are very low, so the para-ortho ratio of a given

sample is usually unchanged at the time scale of interests. Para- and ortho- hydrogen

have slightly different IR and Raman spectra, but we are not distinguishing them

here.

Two thermal dynamic parameters can be tuned to achieve the condensed phase of

hydrogen: temperature and pressure. At atmospheric pressure, hydrogen gas liquifies

at 20 K, and solidifies at 14 K. The initial efforts to study solid hydrogen were mostly

done cryogenically. Later on, as the high-pressure technique develops, solid hydrogen

81

APPENDIX A. CORRELATION FUNCTIONS OF HYDROGEN 82

is more and more investigated at room temperature under significant pressure(tens

of thousands of atmospheric pressure). Specifically, hydrogen solidifies at 5.5 GPa at

300 K. Crystal solid hydrogen always adopts a close-packed structure, depending on

the temperature and pressure condition, it can be either hcp or fcc.

Solid hydrogens are also the simplest and most fundamental molecular solids.

Even under moderately high pressure (lower than hundreds of GPa), it remains good

molecular crystals, where the properties of hydrogen molecules are not quite different

from those of free molecules. The discussion in the following sections relies heavily

on the molecular nature of this solid.

A.2 Correlation function and infrared spectra

Infrared spectroscopy can be well described by the linear response theory of energy

absorption. Under IR radiation, the system’s Hamiltonian becomes H = H0(Γ) −E(t)µ(Γ), and µ(Γ) is the electric dipole moment of the system at Γ state. There-

fore, the rate at which the energy is absorbed is −E(t)⟨µ⟩t. Each frequency of the

electric field can be written as E(t) = E0 cos(ωt)n, and the response of µ to the

electromagnetic field is thus:

⟨µ⟩t = E0[cos(ωt)χ′µµ(ω) + sin(ωt)χ′′

µµ(ω)]

Averaging −E(t)⟨µ⟩t over an oscillating cycle, we have energy absorption rate:

R(ω) = E20ωχ

′′µµ(ω)/2

Even if solid hydrogen can be well described by quantum mechanics, we will

show that classical description is sufficient to show the density dependence of its

IR absorbance. Under classical mechanics, χ′′µµ(ω) is proportional to the oscillation

frequency of the external field and the correlation function of the fluctuation of the

dipole moment of the system: χ′′µµ(ω) = ω/(2kBT )Cδµδµ(ω). So the rate of absorption

is

R(ω) = E20ω

2/(4kBT )Cδµδµ(ω)


Due to the symmetry it has, an isolated hydrogen molecule does not have any

dipole moment, not to mention its time correlation. However, as the density of

hydrogen gas increases, the charge distribution of each molecule is affected by the in-

creasing intermolecular interaction, and pressure-induced IR absorption was observed

in hydrogen gas compressed to 0.2 GPa [94]. The induced absorption persists in the

liquid and first solid phase in hydrogen as the pressure increases or temperature lowers

[95] [96], because the intermolecular interaction are enhanced as the matter becomes

denser.

Let us now focus on the induced dipole moment, and assume that in the condensed

phase, each molecule has an induced dipole moment of µi(t)ui(t) (both the amplitude

and the orientation of the dipole are changing with time). Then the total dipole

moment of the system under illumination is

µ(Γ) =N∑i=1

µiui

and the dipole moment that interacts with the external field is

µn(Γ) =N∑i=1

µiui · n =N∑i=1

µiuin

The correlation function follows:

Cµnµn(t) = ⟨µn(t)µn(0)⟩ = ⟨N∑

i,j=1

µi(t)uin(t)µj(0)ujn(0)⟩ =N∑

i,j=1

⟨µi(t)uin(t)µj(0)ujn(0)⟩

It is reasonable to assume that the amplitude and the orientation fluctuate indepen-

dently, as experiments found that the hydrogen molecule rotates quite freely even in

the high pressure liquid and solid phase [53]. So we further have

Cµnµn(t) =N∑

i,j=1

⟨µi(t)µj(0)⟩⟨uin(t)ujn(0)⟩

as always we can divide the sum into two parts: one is the self correlation the other


is the collective correlation.

Cµnµn(t) =N∑i=1

⟨µi(t)µi(0)⟩⟨uin(t)uin(0)⟩+N∑

i=j=1

⟨µi(t)µj(0)⟩⟨uin(t)ujn(0)⟩

= N⟨µ1(t)µ1(0)⟩⟨u1n(t)u1n(0)⟩+N(N − 1)⟨µ1(t)µ2(0)⟩⟨u1n(t)u2n(0)⟩

In solid hydrogen, the intermolecular correlation is non-negligible. So, the second

term that describe the intermolecular correlation is important here. Let us assume

that in the fcc solid hydrogen, only nearest neighbor interaction contribute to the

orientational intermolecular correlation and that the amplitude correlation maybe

long range. Denote a as lattice constant, then√2a is the nearest neighbor distance,

therefore the 12 nearest neighbors occupy a volume of a3 out of the whole volume V .

Let us assume the amplitude correlation µ1(t)µ2(0) = µ2(t), and average orientational

product u1n(t)u2n(0) = c(t), c(t) < 1/3. The second term can now be approximated

as following:

N(N − 1)⟨µ1(t)µ2(0)⟩⟨u1n(t)u2n(0)⟩ = N(N − 1)a3µ2(t)c(t)/V ≈ V n2a3µ2(t)c(t)

It is clear that the collective correlation term is proportional to the square of the

number density (n2), i.e. proportional to the square of the density (ρ2) of solid

hydrogen. The dependence on density of the total absorption intensity should be

more than linear.

A.3 Correlation function and Raman spectra

Although Raman spectroscopy is always considered as an alternative method to study

the vibrational characteristic of a material , it is intrinsically a very different approach

from infrared spectroscopy. IR is a first order absorption (transmission) experiment

that records the energy absorption rate of a certain frequency, while Raman experi-

ment is a frequency resolved measurement of a scattering process, and is second order

in nature.

In a high pressure Raman experiment, the sample confined between two diamonds


are illuminated by a laser, and the back scattered light goes through a grating, and

collected by a CCD camera. The grating together with other factors determines

the frequency resolution. The direction of the incident and scattered light satisfies

ni · nf = −1. The wave equation to describe the light is Maxwell equation in a

material with dielectric constant ϵ(r, t) = ϵI+ δϵ(r, t):

ϵ0(ω)

c2∂2E

∂t2= ∇2E+

ω2

c2δϵ(r, t) · E(r, t)

The frequency resolved intensity of the scattered light is proportional to the space

and time Fourier transform of ⟨(nf · δϵ(r, t) · ni)(nf · δϵ(0, 0) · ni)⟩, in short as

⟨δϵ(r, t)δϵ(0, 0)⟩. To first order approximation, the intensity of the scattered light

is

I(ω) = | E0

4πR|2 Rω

4

2πc4

∫dr

∫ ∞

−∞dte−i(kf−ki)·r+i(ω−ωi)t⟨δϵ(r, t)δϵ(0, 0)⟩

R is the illuminated region. We can see that scattering intensity increases with ω4,

indicating that the shorter the wavelength of the incident beam is, the higher the

output intensity is. This is why we use optical laser to conduct Raman experiments.

For a second order effect, this increase of intensity is very important to achieve decent

signal to noise ratio.

The polarizability αi of a molecule i and macroscopic dielectric constant has a sim-

ple relation derived from D = ϵE = E+4πP and P =∑

αiE(ri)δ(r− ri): The space

time fluctuation of dielectric constant is no more than the spatial distribution and

time fluctuation of the polarizability of each molecule constituting the bulk material.

The correlation function can now be written as

⟨(∑j

nf · α(j, t) · niδ(r− rj(t)))(∑l

nf · α(l, 0) · niδ(r− rl(0)))⟩

simplified as

⟨(∑j

α(j, t)δ(r− rj(t)))(∑l

α(l, 0)δ(r− rl(0)))⟩


the spatial fourier transform is

⟨(∑j

α(j, t)eik·rj(t))(∑l

α(l, 0)eik·rl(0))⟩

Let us only consider the self correlation term (reasons to be discussed later), the

correlation function simplifies to be

⟨∑j

α(j, t)α∗(j, 0)eik·(rj(t)−rj(0))⟩ =∑j

⟨α(j, t)α∗(j, 0)⟩ = N⟨α(t)α∗(0)⟩

as in solid hydrogen, to the first order the position of each molecule does not change

from time, so r(j, t)− r(j, 0) ≈ 0. With this, we can find the time Fourier transform

of polarizability correlation function in the quantum mechanical regime.∫ ∞

−∞dtei(ω−ωi)tN⟨α(t)α∗(0)⟩ = 2πN

∑i,j

ρii|αi,j|2(δ(ω − ωij)− δ(ω + ωij))

where i, j are the quantum number of the vibrational states solid hydrogen has, and

αij is polarizability matrix element. For the fundamental band of hydrogen vibron

the transition corresponds to the ν = 0 → 1 transition, i.e. ρ00|α01|2(δ(ω − ω01) −δ(ω+ω01)). It is also worth to note that with such assumption the intensity of Raman

spectra is proportional to the total number of molecules N involved in the scattering

process, thus proportional to number density n and density ρ.

A.4 Comparison between infrared and Raman

The above derivation shows that in a molecular solid IR spectroscopy measures the

time correlation function of the fluctuation of the total dipole moment, and that

Raman scattering measures the time correlation of the fluctuation of the ”total”

molecular polarizability.

Specifically for solid hydrogen, I use different assumptions when treating the self

correlations and collective correlations of dipole moment and polarizability. For the

correlation function of the dipole moment, the collective correlations are considered to


be important. While for polarizability fluctuations, the collective term is dropped. In

another word, the self-collective ratio of the fluctuation of the dipole moment is much

smaller than that of the fluctuation of the polarizability. This is reasonable since

the hydrogen molecule has an intrinsically non-zero polarizability, and the induced

dipole moment is of a second order. In fact, experiments have observed that the IR

signal of solid hydrogen is indeed more sensitive to density than its Raman signal

[47], demonstrating to first order the validity of the assumptions.

There are other factors that contribute to the IR and Raman vibrational bands,

e.g. fluctuation of the quadruple moment of hydrogen molecules to IR, and vibration-

rotation coupling to both IR and Raman. These factors contribute to the spectra in

a similar fashion as the two correlation functions in Section 2 and 3.

Bibliography

[1] C. S. Yoo, B. Maddox, J.-H. P. Klepeis, V. Iota, W. Evans, A. McMahan, M. Y.

Hu, P. Chow, M. Somayazulu, D. Hausermann, R. T. Scalettar, and W. E.

Pickett, “First-order isostructural mott transition in highly compressed mno,”

Phys. Rev. Lett. 94, 115502 (2005).

[2] Y. Ma, M. Eremets, A. R. Oganov, Y. Xie, I. Trojan, S. Medvedev, A. O.

Lyakhov, M. Valle, and V. Prakapenka, “Transparent dense sodium,” Nature

458, 182–U3 (2009).

[3] A. Lazicki, A. F. Goncharov, V. V. Struzhkin, R. E. Cohen, Z. Liu, E. Grego-

ryanz, C. Guillaume, H. K. Mao, and R. J. Hemley, “Anomalous optical and

electronic properties of dense sodium,” Proceedings of the National Academy of

Sciences of the United States of America 106, 6525–6528 (2009).

[4] B. Lavina, P. Dera, R. T. Downs, V. Prakapenka, M. Rivers, S. Sutton, and

M. Nicol, “Siderite at lower mantle conditions and the effects of the pressure-

induced spin-pairing transition,” Geophysical Research Letters 36 (2009).

[5] A. Jayaraman, “Diamond anvil cell and high-pressure physical investigations,”

Rev. Mod. Phys. 55, 65 (1983).

[6] A. D. Chijioke, W. J. Nellis, and I. F. Silvera, “High-pressure equations of state

of al, cu, ta, and w,” Journal of Applied Physics 98, 073526 (2005).

[7] H. K. Mao, J. Xu, and P. M. Bell, “Calibration of the ruby pressure gauge to

800 kbar under quasi-hydrostatic conditions,” Journal of Geophysical Research

91, 4673–4676 (1986).

88

BIBLIOGRAPHY 89

[8] W. A. Bassett, “Diamond anvil cell, 50th birthday,” High Pressure Research:

An International Journal 29, 163–186 (2009).

[9] C. Raman and K. Krishnan, “A new type of secondary radiation,” Nature 121,

501–502 (1928).

[10] A. K. Frank de Groot, Core Level Spectroscopy of Solids (CRC Press, Boca

Raton, 2008).

[11] J.-P. Rueff and A. Shukla, “Inelastic x-ray scattering by electronic excitations

under high pressure,” Rev. Mod. Phys. 82, 847–896 (2010).

[12] V. V. Struzhkin, B. Militzer, W. L. Mao, H.-k. Mao, and R. J. Hemley, “Hydro-

gen storage in molecular clathrates,” Chemical Reviews 107, 4133–4151 (2007).

[13] W. L. Mao, H.-k. Mao, A. F. Goncharov, V. V. Struzhkin, Q. Guo, J. Hu, J. Shu,

R. J. Hemley, M. Somayazulu, and Y. Zhao, “Hydrogen Clusters in Clathrate

Hydrate,” Science 297, 2247–2249 (2002).

[14] W. L. Vos, L. W. Finger, R. J. Hemley, and H.-k. Mao, “Novel h2-h2o clathrates

at high pressures,” Phys. Rev. Lett. 71, 3150–3153 (1993).

[15] M. S. Somayazulu, L. W. Finger, R. J. Hemley, and H. K. Mao, “High-Pressure

Compounds in Methane-Hydrogen Mixtures,” Science 271, 1400–1402 (1996).

[16] W. L. Mao and H.-k. Mao, “Hydrogen storage in molecular compounds,” Pro-

ceedings of the National Academy of Sciences of the United States of America

101, 708–710 (2004).

[17] W. L. Mao, C. A. Koh, and E. D. Sloan, “Clathrate hydrates under pressure,”

Physics Today 60, 42–47 (2007).

[18] J. S. Kasper, C. M. Lucht, and D. Harker, “The crystal structure of decaborane,

B10H14,” Acta Crystallographica 3, 436–455 (1950).

BIBLIOGRAPHY 90

[19] C. F. Hoon and E. C. Reynhardt, “Molecular dynamics and structures of amine

boranes of the type r 3 n.bh 3 . i. x-ray investigation of h 3 n.bh 3 at 295k and

110k,” Journal of Physics C: Solid State Physics 16, 6129 (1983).

[20] J. Li, S. M. Kathmann, G. K. Schenter, and M. Gutowski, “Isomers and con-

formers of h(nh2bh2)nh oligomers: understanding the geometries and electronic

structure of boronnitrogenhydrogen compounds as potential hydrogen storage

materials,” The Journal of Physical Chemistry C 111, 3294–3299 (2007).

[21] T. B. Marder, “Will we soon be fueling our automobiles with ammoniaborane?”

Angewandte Chemie International Edition 46, 8116–8118 (2007).

[22] G. Wolf, J. Baumann, F. Baitalow, and F. P. Hoffmann, “Calorimetric process

monitoring of thermal decomposition of b-n-h compounds,” Thermochimica Acta

343, 19 – 25 (2000).

[23] S. Trudel and D. F. R. Gilson, “High-pressure raman spectroscopic study of the

ammoniaborane complex. evidence for the dihydrogen bond,” Inorganic Chem-

istry 42, 2814–2816 (2003). PMID: 12691593.

[24] R. Custelcean and Z. A. Dreger, “Dihydrogen bonding under high pressure: a

raman study of bh3nh3 molecular crystal,” The Journal of Physical Chemistry

B 107, 9231–9235 (2003).

[25] Y. Lin, W. L. Mao, V. Drozd, J. Chen, and L. L. Daemen, “Raman spectroscopy

study of ammonia borane at high pressure,” The Journal of Chemical Physics

129, 234509 (2008).

[26] N. J. Hess, M. E. Bowden, V. M. Parvanov, C. Mundy, S. M. Kathmann, G. K.

Schenter, and T. Autrey, “Spectroscopic studies of the phase transition in am-

monia borane: Raman spectroscopy of single crystal nh[sub 3]bh[sub 3] as a

function of temperature from 88 to 330 k,” The Journal of Chemical Physics

128, 034508 (2008).

BIBLIOGRAPHY 91

[27] S. Nakano, R. J. Hemley, E. A. Gregoryanz, A. F. Goncharov, and H. kwang

Mao, “Pressure-induced transformations of molecular boron hydride,” Journal

of Physics: Condensed Matter 14, 10453 (2002).

[28] “Bonding in boranes and their interaction with molecular hydrogen at extreme

conditions,” The Journal of Chemical Physics 131, 144508 (2009).

[29] W. E. Keller and H. L. Johnston, “A note on the vibrational frequencies and the

entropy of decaborane,” The Journal of Chemical Physics 20, 1749–1751 (1952).

[30] A. M. Hofmeister and H.-k. Mao, “Redefinition of the mode gruneisen parameter

for polyatomic substances and thermodynamic implications,” Proceedings of the

National Academy of Sciences of the United States of America 99, 559–564

(2002).

[31] D. J. Heldebrant, A. Karkamkar, N. J. Hess, M. Bowden, S. Rassat, F. Zheng,

K. Rappe, and T. Autrey, “The effects of chemical additives on the induction

phase in solid-state thermal decomposition of ammonia borane,” Chemistry of

Materials 20, 5332–5336 (2008).

[32] M. Hu, R. Geanangel, and W. Wendlandt, “The thermal decomposition of am-

monia borane,” Thermochimica Acta 23, 249 – 255 (1978).

[33] M. T. Nguyen, V. S. Nguyen, M. H. Matus, G. Gopakumar, and D. A. Dixon,

“Molecular mechanism for h2 release from bh3nh3, including the catalytic role of

the lewis acid bh3,” The Journal of Physical Chemistry A 111, 679–690 (2007).

[34] C. W. Hamilton, R. T. Baker, A. Staubitz, and I. Manners, “B-n compounds for

chemical hydrogen storage,” Chem. Soc. Rev. 38, 279–293 (2009).

[35] A. C. Stowe, W. J. Shaw, J. C. Linehan, B. Schmid, and T. Autrey, “In situ solid

state 11b mas-nmr studies of the thermal decomposition of ammonia borane:

mechanistic studies of the hydrogen release pathways from a solid state hydrogen

storage material,” Phys. Chem. Chem. Phys. 9, 1831–1836 (2007).

BIBLIOGRAPHY 92

[36] D.-P. Kim, K.-T. Moon, J.-G. Kho, J. Economy, C. Gervais, and F. Babonneau,

“Synthesis and characterization of poly(aminoborane) as a new boron nitride

precursor,” Polymers for Advanced Technologies 10, 702–712 (1999).

[37] J. Baumann, F. Baitalow, and G. Wolf, “Thermal decomposition of polymeric

aminoborane (h2bnh2)x under hydrogen release,” Thermochimica Acta 430, 9

– 14 (2005).

[38] R. Komm, R. A. Geanangel, and R. Liepins, “Synthesis and studies of

poly(aminoborane), (h2nbh2)x,” Inorganic Chemistry 22, 1684–1686 (1983).

[39] R. J. Hemley, H. K. Mao, L. W. Finger, A. P. Jephcoat, R. M. Hazen, and C. S.

Zha, “Equation of state of solid hydrogen and deuterium from single-crystal x-ray

diffraction to 26.5 gpa,” Phys. Rev. B 42, 6458–6470 (1990).

[40] K. A. Lokshin, Y. Zhao, D. He, W. L. Mao, H.-K. Mao, R. J. Hemley, M. V.

Lobanov, and M. Greenblatt, “Structure and dynamics of hydrogen molecules

in the novel clathrate hydrate by high pressure neutron diffraction,” Phys. Rev.

Lett. 93, 125503 (2004).

[41] N. W. Ashcroft, “Metallic hydrogen: A high-temperature superconductor?”

Phys. Rev. Lett. 21, 1748–1749 (1968).

[42] J. O. C. Narayana, H. Luo and A. Ruoff, “Solid hydrogen at 342 gpa: no evidence

for an alkali metal,” Nature 393, 46–49 (1998).

[43] N. W. Ashcroft, “Hydrogen dominant metallic alloys: High temperature super-

conductors?” Phys. Rev. Lett. 92, 187002 (2004).

[44] R. H. Fowler, “On dense matter,” Mon. Not. R. Astron. Soc. 87, 114–122 (1926).

[45] E. Wigner and H. B. Huntington, “On the possibility of a metallic modification

of hydrogen,” The Journal of Chemical Physics 3, 764–770 (1935).

[46] E. Brovman, Y. Kagan, and A. Kholas, “Propoerties of metallic hydrogen under

pressure,” Sov. Phys. JETP 35, 783 (1972).

BIBLIOGRAPHY 93

[47] H.-k. Mao and R. J. Hemley, “Ultrahigh-pressure transitions in solid hydrogen,”

Rev. Mod. Phys. 66, 671–692 (1994).

[48] K. Johnson and N. Ashcroft, “Structure and badgap closure in dense hydrogen,”

Nature 403, 632 (2000).

[49] C. J. Pickard and R. J. Needs, “Structure of phase III of solid hydrogen,” Nature

Physics 3, 473–476 (2007).

[50] X.-J. Chen, V. V. Struzhkin, Y. Song, A. F. Goncharov, M. Ahart, Z. Liu, H.-k.

Mao, and R. J. Hemley, “Pressure-induced metallization of silane,” 105, 20–23

(2008).

[51] M. I. Eremets, I. A. Trojan, S. A. Medvedev, J. S. Tse, and Y. Yao, “Supercon-

ductivity in hydrogen dominant materials: Silane,” 319, 1506–1509 (2008).

[52] W. Mao, V. Struzhkin, H. Mao, and R. Hemley, “Pressure-temperature stability

of the van der Waals compound (H2)4CH4,” Chemical Physics Letters 402, 66–70

(2005).

[53] S. K. Sharma, H. K. Mao, and P. M. Bell, “Raman measurements of hydrogen

in the pressure range 0.2-630 kbar at room temperature,” Phys. Rev. Lett. 44,

886–888 (1980).

[54] R. P. Fournier, R. Savoie, N. D. The, R. Belzile, and A. Cabana, “Vibrational

spectra of sih4 and sid4csih4 mixtures in the condensed states,” Canadian Jour-

nal of Chemistry 50, 35–42 (1972).

[55] J. Huiberts, R. Griessen, J. Rector, R. Wijnaarden, J. Dekker, D. deGroot,

and N. Koeman, “Yttrium and lanthanum hydride films with switchable optical

properties,” Nature 380, 231–234 (1996).

[56] E. Ekimov, V. Sidorov, E. Bauer, N. Mel’nik, N. Curro, J. Thompson, and

S. Stishov, “Superconductivity in diamond,” Nature 428, 542–545 (2004).

BIBLIOGRAPHY 94

[57] T. A. Strobel, M. Somayazulu, and R. J. Hemley, “Novel pressure-induced inter-

actions in silane-hydrogen,” Phys. Rev. Lett. 103, 065701 (2009).

[58] X.-Q. Chen, S. Wang, W. L. Mao, and C. L. Fu, “Pressure-induced behavior of

the hydrogen-dominant compound sih4(h2)2 from first-principles calculations,”

Phys. Rev. B 82, 104115 (2010).

[59] G. Kresse and J. Furthmller, “Efficiency of ab-initio total energy calculations

for metals and semiconductors using a plane-wave basis set,” Computational

Materials Science 6, 15 – 50 (1996).

[60] G. Kresse and D. Joubert, “From ultrasoft pseudopotentials to the projector

augmented-wave method,” Phys. Rev. B 59, 1758–1775 (1999).

[61] J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation

made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).

[62] W. Tang, E. Sanville, and G. Henkelman, “A grid-based bader analysis algorithm

without lattice bias,” Journal of Physics: Condensed Matter 21, 084204 (2009).

[63] E. Sanville, S. D. Kenny, R. Smith, and G. Henkelman, “Improved grid-based

algorithm for bader charge allocation,” Journal of Computational Chemistry 28,

899–908 (2007).

[64] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni,

D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. D. Corso, S. de Giron-

coli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj,

M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini,

A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seit-

sonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, “Quantum espresso: a

modular and open-source software project for quantum simulations of materials,”

Journal of Physics: Condensed Matter 21, 395502 (2009).

[65] S. Wang, H.-k. Mao, X.-J. Chen, and W. L. Mao, “High pressure chemistry in

the h2-sih4 system,” Proceedings of the National Academy of Sciences of the

United States of America 106, 14763–14767 (2009).

BIBLIOGRAPHY 95

[66] M. Somayazulu, P. Dera, A. F. Goncharov, S. A. Gramsch, P. Liermann,

W. Yang, Z. Liu, H.-k. Mao, and R. J. Hemley, “Pressure-induced bonding

and compound formation in xenon-hydrogen solids,” Nature Chemistry 2, 50–53

(2010).

[67] C. F. Richardson and N. W. Ashcroft, “High temperature superconductivity in

metallic hydrogen: Electron-electron enhancements,” Phys. Rev. Lett. 78, 118–

121 (1997).

[68] M. Ramzan, S. Lebegue, and R. Ahuja, “Electronic structure and metalization

of a silane-hydrogen system under high pressure investigated using density func-

tional and gw calculations,” Phys. Rev. B 81, 233103 (2010).

[69] W.-L. Yim, J. S. Tse, and T. Iitaka, “Pressure-induced intermolecular interac-

tions in crystalline silane-hydrogen,” Phys. Rev. Lett. 105, 215501 (2010).

[70] Y. Yao and D. D. Klug, “Silane plus molecular hydrogen as a possible pathway

to metallic hydrogen,” 107, 20893–20898 (2010).

[71] Y. Li, G. Gao, Q. Li, Y. Ma, and G. Zou, “Orientationally disordered h2 in

the high-pressure van der waals compound sih4(h2)2,” Phys. Rev. B 82, 064104

(2010).

[72] Y. Li, G. Gao, Y. Xie, Y. Ma, T. Cui, and G. Zou, “Superconductivity at 100k

in dense sih4(h2)2 predicted by first principles,” 107, 15708–15711 (2010).

[73] S. Wang, W. L. Mao, A. P. Sorini, C.-C. Chen, T. P. Devereaux, Y. Ding, Y. Xiao,

P. Chow, N. Hiraoka, H. Ishii, Y. Q. Cai, and C.-C. Kao, “High-pressure evolution

of fe2o3 electronic structure revealed by x-ray absorption,” Phys. Rev. B 82,

144428 (2010).

[74] G. K. Rozenberg, L. S. Dubrovinsky, M. P. Pasternak, O. Naaman, T. Le Bihan,

and R. Ahuja, “High-pressure structural studies of hematite fe2o3,” Phys. Rev.

B 65, 064112 (2002).

BIBLIOGRAPHY 96

[75] J. Badro, V. V. Struzhkin, J. Shu, R. J. Hemley, H.-k. Mao, C.-c. Kao, J.-P.

Rueff, and G. Shen, “Magnetism in feo at megabar pressures from x-ray emission

spectroscopy,” Phys. Rev. Lett. 83, 4101–4104 (1999).

[76] M. P. Pasternak, G. K. Rozenberg, G. Y. Machavariani, O. Naaman, R. D.

Taylor, and R. Jeanloz, “Breakdown of the mott-hubbard state in fe2o3: A first-

order insulator-metal transition with collapse of magnetism at 50 gpa,” Phys.

Rev. Lett. 82, 4663–4666 (1999).

[77] S.-H. Shim, A. Bengtson, D. Morgan, W. Sturhahn, K. Catalli, J. Zhao,

M. Lerche, and V. Prakapenka, “Electronic and magnetic structures of the

postperovskite-type fe2o3 and implications for planetary magnetic records and

deep interiors,” 106, 5508–5512 (2009).

[78] J. Kunes, D. M. Korotin, M. A. Korotin, V. I. Anisimov, and P. Werner,

“Pressure-driven metal-insulator transition in hematite from dynamical mean-

field theory,” Phys. Rev. Lett. 102, 146402 (2009).

[79] J. Badro, G. Fiquet, V. V. Struzhkin, M. Somayazulu, H.-k. Mao, G. Shen, and

T. Le Bihan, “Nature of the high-pressure transition in fe2o3 hematite,” Phys.

Rev. Lett. 89, 205504 (2002).

[80] M. Wilke, F. Farges, P. Petit, G. Brown, and F. Martin, “Oxidation state and

coordination of Fe in minerals: An FeK-XANES spectroscopic study,” American

Mineralogist 86, 714–730 (2001).

[81] W. A. Caliebe, C.-C. Kao, J. B. Hastings, M. Taguchi, A. Kotani, T. Uozumi,

and F. M. F. de Groot, “1s2p resonant inelastic x-ray scattering in α− fe2o3,”

Phys. Rev. B 58, 13452–13458 (1998).

[82] G. Drger, R. Frahm, G. Materlik, and O. Brmmer, “On the multipole character

of the x-ray transitions in the pre-edge structure of fe k absorption spectra. an

experimental study,” Physica Status Solidi (b) 146, 287–294 (1988).

BIBLIOGRAPHY 97

[83] P. Glatzel, A. Mirone, S. G. Eeckhout, M. Sikora, and G. Giuli, “Orbital

hybridization and spin polarization in the resonant 1s photoexcitations of

α− fe2o3,” Phys. Rev. B 77, 115133 (2008).

[84] J.-P. Rueff, L. Journel, P.-E. Petit, and F. Farges, “Fe k pre-edges as revealed

by resonant x-ray emission,” Phys. Rev. B 69, 235107 (2004).

[85] A. Y. Ramos, H. C. N. Tolentino, N. M. Souza-Neto, J.-P. Itie, L. Morales, and

A. Caneiro, “Stability of jahn-teller distortion in lamno3 under pressure: An

x-ray absorption study,” Phys. Rev. B 75, 052103 (2007).

[86] J. H. V. Vleck, “The jahn-teller effect and crystalline stark splitting for clusters

of the form xy6,” The Journal of Chemical Physics 7, 72–84 (1939).

[87] G. Racah, “Theory of complex spectra. ii,” Phys. Rev. 62, 438–462 (1942).

[88] D. Sherman and T. Waite, “Electronic-Spectra Of Fe3+ Oxides And Oxide Hy-

droxides In The Near Ir To Near Uv,” American Mineralogist 70, 1262–1269

(1985).

[89] S. Brice-Profeta, M.-A. Arrio, E. Tronc, N. Menguy, I. Letard, C. C. dit Moulin,

M. Nogus, C. Chanac, J.-P. Jolivet, and P. Sainctavit, “Magnetic order in γ-fe2o3

nanoparticles: a xmcd study,” Journal of Magnetism and Magnetic Materials

288, 354 – 365 (2005).

[90] Y. Tanabe and S. Sugano, “On the absorption spectra of complex ions ii,” Journal

of the Physical Society of Japan 9, 766–779 (1954).

[91] W. Harrison, Elementary Electronic Structure (World Scientific, Singapore,

2004).

[92] A. L. Ankudinov, B. Ravel, J. J. Rehr, and S. D. Conradson, “Real-space

multiple-scattering calculation and interpretation of x-ray-absorption near-edge

structure,” Phys. Rev. B 58, 7565–7576 (1998).

BIBLIOGRAPHY 98

[93] A. L. Ankudinov, C. E. Bouldin, J. J. Rehr, J. Sims, and H. Hung, “Parallel

calculation of electron multiple scattering using lanczos algorithms,” Phys. Rev.

B 65, 104107 (2002).

[94] W. F. J. Hare and H. L. Welsh, “Pressure-induced infrared absorption of hy-

drogen and hydrogen-foreign gas mixtures in the range 1500-5000 atmospheres,”

Canadian Journal of Physics 36, 88 (1958).

[95] H. P. Gush, W. F. J. Hare, E. J. Allin, and H. L. Welsh, “The infrared funda-

mental band of liquid and solid hydrogen,” Canadian Journal of Physics 38, 176

(1960).

[96] M. Hanfland, R. J. Hemley, H. K. Mao, and G. P. Williams, “Synchrotron in-

frared spectroscopy at megabar pressures: Vibrational dynamics of hydrogen to

180 gpa,” Phys. Rev. Lett. 69, 1129–1132 (1992).

Documents

STUDYING BONDING AND ELECTRONIC STRUCTURES OF A …zr349qb7986/Shi... · 2011-09-22 · I would also like to thank my committee members: Professors Ian Fisher, Ted Geballe, Evan Reed,