HIGH PRESSURE STUDY OF SPINEL CHROMITE

by

ALLEN D.C. WHITE, B.S.M.E.

A THESIS

IN

MECHANICAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

MECHANICAL ENGINEERING

Approved

Yanzhang Ma Chairperson of the Committee

Atila Ertas

Valery Ilich Levitas

Accepted

John Borrelli Dean of the Graduate School

May, 2005

ii

ACKNOWLEDGMENTS

First and foremost, I would like to thank my advisor Dr. Yanzhang Ma for his

guidance, motivation, and most importantly the many hours spent in both New York and

Lubbock making this paper possible. Thank you also to Dr. Atila Ertas and Dr. Valery

Levitas for being cooperative committee members throughout this study. I would also

like to thank Resul Aksoy, Emre Selvi, and Jagdev-Singh Sandhu for their assistance in

the experiments and data processing, and also the numerous discussions in the lab. Other

thanks go to Dr. Guo, Dr. Hu, and Mr. L.A. Reis for helping out in different phases of the

study, and to the College of Engineering and the Mechanical Engineering department for

financial support of this project.

Other than academic assistance, I would like to thank my family and friends for

their love and support throughout my life, there are no words to describe my gratitude to

them and everything they have done.

iii

TABLE OF CONTENTS

ACKNOWLEDGEMENTS……………………………………………………….………ii

ABSTRACT………………………………………………………………………….…....v

LIST OF TABLES…………………………………………………………………….….vi

LIST OF FIGURES…………...........................................................................................vii

CHAPTER

I. INTRODUCTION…………………………………………….……………...…1

1.1 The Spinel Structure……………………………………………..…………..1

1.2 Chromites…………………………………………………………….....……3

II. EXPERIMENTAL METHODOLOGY………………………………….....….6

2.1 Diamond Anvil Cell…………………………………………………...…….6

2.2 Energy Dispersive X-ray Diffraction……………………………………..…8

2.3 Ruby Fluorescence, a Pressure Sensor…..………………………….……...11

III. EXPERIMENTAL SETUP…………………………………………………..14

3.1 Sample Characteristics…………………………………………………….14

3.2 Diamond Anvil Cell…………………………………………………...…..14

3.3 Gasket Preparation……………………………………………………...…15

3.4 Sample Loading………………………………………………………..….19

3.5 Pressure Medium………………………………………………...…….….21

3.6 Pressure Measurement…………………………………………...……......24

3.7 Energy Dispersive X-ray Diffraction Measurements……………………..25

iv

IV. RESULTS AND DISCUSSION………………..…………………………....29

4.1 Results and Discussion...…………………………………………….........29

4.1.1 Lattice Change of Chromite under Pressure………………….........29

4.1.2 Equation of State of the Spinel Chromite and Pressure Medium…………………………………………………………….33 4.1.3 Pressure Induced Phase Transformation of Chromite…...………...35

4.2 Conclusion...……………………………………..…………………….….37

REFERENCES………………………………………………………………………..…39

APPENDIX…………………………………..………………………….……………….44

v

ABSTRACT

Chromite has one of the most important crystal structures, the spinel structure;

therefore its high pressure behavior has significant implications to the foundation of a

wide range of materials. It is also found throughout our Earth’s interior. These facts

make its high pressure studies important to materials science, physics, geosciences, and

crystallography. Synchrotron X-ray diffraction measurements of chromite were

performed using a symmetrical diamond anvil cell to 41.2 GPa. The data was fit using

the third order Birch-Murnaghan equation of state, and the bulk modulus KOT was

determined to be 197±19 GPa with K′OT=66±12 when fitting data to 16 GPa. Further

investigation revealed a pressure induced phase transformation at 28.2 GPa.

vi

LIST OF TABLES

2.1 Culet diameters…………………………….……………………………………..…...7

3.1 Indentation pressures……………………………………………….………………..17

3.2 Pressure media and their hydrostatic limits……………………………………….…22

4.1 Refinement results……………………………...…….………………………...……32

vii

LIST OF FIGURES

1.1 The spinel structure………………………..……………………………………..……2

1.2 The chromite structure……………………………….…………………………..……4

2.1 Diamond anvil cell; (a) disassembled; (b) assembled……………………………...….8

2.2 An X-ray diffraction pattern from an EDXRD experiment……………….……..……9

2.3 Ruby fluorescence measurement system……………..……………………………...12

2.4 Ruby spectrum under hydrostatic conditions………...……………………………....12

3.1 Unaligned and aligned DAC…………………………………………………………15

3.2 Deformation of gasket under pressure; (a) below 5 GPa; (b) above 5 GPa……….…16

3.3 Electronic drilling machine……………..……………………………………………18

3.4 Gasket; (a) before indentation; (b) after indentation; (c) with machined sample chamber……………....................................………….…19

3.5 Schematic of loaded DAC……………….…………………………………………..20

3.6 Picture of sample and ruby loaded in the gasket……….………………………….…21

3.7 Pressure medium loading apparatus……...………………………..……...……….…24

3.8 Observed ruby spectrum at 41.2 GPa……………………….……….………………25

3.9 EDXRD system……………………………….………………………………...……26

3.10 X-ray beam intensity distribution………….………………………………….....…27

3.11 Transmitted and diffracted X-ray with 2θ angle………..………………………..…28

4.1 X-ray diffraction pattern at 3.5 GPa………….……...…………………...………….30

4.2 X-ray diffraction patterns at different pressures…...……..……………………….…31

4.3 Effect of pressure on the d-spacings of spinel chromite…………….……………….31

viii

4.4 Cell parameter reduction with pressure………….…...……………………………...32

4.5 Equation of state of chromite………………………….……………………………..34

4.6 Equation of state of argon with measured volume at pressures…………..…………35

4.7 Comparison of the X-ray diffraction pattern before and after the phase transformation………..…………………………………………………..….36

4.8 d-spacings as a function of pressure, emphasizing the structural change at 28.2 GPa and above…………………..…………………………………37

1

CHAPTER I

INTRODUCTION

1.1 The Spinel Structure

A spinel material is a molecular compound with the AB2O4 formula. With the A

and B being metal ions with valences of 2+ and 3+, respectively, spinel compounds are

known to crystallize into a cubic structure with the space group Fd3m [1, 2]. There are

two types of spinel structures at ambient conditions, the normal (AB2O4) and inverse

(B2AO4) spinel. In the ideal normal spinel, A and B ions occupy the tetrahedral (T) and

octahedral (M) sites, respectively; in the inverse spinel, half of the B ions center the

fourfold coordination, with the consequent migration of all the A ions to the octahedral

sites [3, 4]. A full description of spinel structure geometry includes a cell edge, a

tetrahedral unshared edge, an octahedral unshared edge, an octahedral edge shared with

other octahedra, T-O and M-O bond distances, and an octahedral O-M-O angle [5]. An

illustration of this structure is shown in Figure 1.1 [6]. The blue spheres are oxygen

atoms, and the green and red spheres are the A and B ions, respectively.

Spinel materials are binary oxides, which occur in numerous industrial processes

and have important technological applications. Petric and Jacob reported that spinels are

formed as stable corrosion products when alloys are exposed to an oxidizing atmosphere

[7]. As such, they are beneficial in providing a protective layer between the alloy and

gas, inhibiting further corrosion. Also, fused cast spinel-type refractories show superior

erosion resistance to molten coal slag and are expected to find applications in coal

2

gasification systems [7]. In addition, owing to favorable electrical properties, certain

spinels have been considered as candidate materials for magneto hydrodynamic

electrodes and as a promising material (in particular, LiMn2O4) as a cathode for Lithium

batteries [8]. Other areas in which spinels are used are as a catalyst for the

decomposition of chlorinated organic pollutants [9], as magnetic materials [10],

superhard materials [11], high temperature ceramics [12], as well as high pressure sensors

[13]. This extensive class of structures also exists in significant abundance in the Earth’s

interior [(Mg, Fe)2SiO4 are the most common minerals in the Earth’s upper mantle [14]]

and plays an important role in determining the physical properties our planet. Due to

their importance in materials science, physics, geosciences, and crystallography; spinel

compounds have been extensively explored.

Figure 1.1. The spinel structure. The red cubes are also contained in the back half of the unit cell [6]

3

Studies have also been conducted to investigate the pressure induced phase

transformations of spinel-type structures [3, 15-19]. Results reveal two types of high

pressure behaviors: one undergoes a pressure induced phase transformation from the

spinel structure to its high pressure polymorph [3, 15, 18, 19]; and the other dissociates to

a mixture of its constituent oxides [16]. Although the spinel structure has been

extensively studied, previous high pressure investigations only focused on particular

spinels based on their geophysical significance, mostly relevant to the constituents of the

Earth’s interior, including Fe, Mg, Al, Si, and Ge [15,18,19,20]. With these scarce data,

it is hard to obtain a complete understanding of the high pressure behavior of spinels [5].

Other studies include determining equations of state for numerous spinels [21-23] as well

as theoretical calculations with the goal of describing this wide array of structures.

1.2 Chromites

Chromites, which are molecular compounds with the ACr2O4 formula, have a

normal type spinel structure [24,25], i.e., the tetrahedra of oxygen atoms surround

divalent metal ions and the octahedra of oxygen surround chromium ions [26]. An

illustration of a chromite structure is shown in Figure1.2 [6]. It should be noted that the

structure is identical to Figure 1.1, except the red spheres are chromium ions. Chromites

are considered as a significant spinel system with numerous potential applications. One

particular chromite, iron chromite (FeCr2O4), is known to occur due to different industrial

processes. It has been confirmed that FeCr2O4 can form in abundance on the surface of

stainless steels during welding, and also upon oxidation in air when stainless steel pipes

4

are exposed to high temperature steam in power plants [27]. Other reports indicate that

FeCr2O4 can be created on the surface of metals by bringing a mixture of Cr2O3 and Fe

powder in contact with a high energy laser, producing a coating on the parent metal to

meet extreme conditions of wear and corrosion resistance [28].

Chromites also occur naturally in our Earth, and are used for the production of

ferrochrome (important alloying agent in stainless steel making) [29], metallic chromium,

chromium chemicals, and refractories [30]. Another reason why chromite is important

was reported by Griffin and Ryan, stating that the evidence of chromites in the Earth’s

interior can be used in conjunction with certain methods (see reference for more details)

in order to target certain regions for diamond exploration [31].

Figure 1.2. The chromite structure. The red cubes are also

contained in the back half of the unit cell [6]

5

Although chromites are widely used, very few studies have been performed on

this structure. The first natural sample of iron chromite with the calcium ferrite (CF)

structure, which was found in the shock veins of the Suizhou meteorite, was reported by

Chen et al. [32]. They also discovered that iron chromite spinel transforms to the CF

structure at 12.5 GPa and to the calcium titanite (CT) structure above 20 GPa. The

experimentally calibrated CF and CT polymorphs of chromite could therefore be an ideal

pressure gauge not only for shock-metamorphosed terrestrial rocks and meteorites but

also for mantle rocks covering the important pressure range throughout the transition

zone [32]. Other investigations include ZnCr2O4 and MgCr2O4 chromites, where a

pressure induced phase transformation from the spinel structure to a high pressure

polymorph was observed [33, 34]. On the contrary, one ab initio calculation has been

performed to investigate the phase transformation of the chromites [16], and the

simulation predicts that they dissociate to their constituent oxides at high pressure and

room temperature, which disagree with experimental results. Due to these disagreements,

a systematical high pressure experimental study of a spinel chromite is critical to clarify

the contradiction as well as providing information that can lead to a better understanding

of the group of compounds that crystallize in spinels and similar structures.

6

CHAPTER II

EXPERIMENTAL METHODOLOGY

2.1 Diamond Anvil Cell

The diamond anvil cell (DAC) is fast becoming the most powerful ultra-high

pressure device; permitting engineers, materials scientists, physicists and chemists to

discover new states of matter and understand the physics and chemistry underlying

ultra-high pressure phenomena. The basic principle of the DAC is very simple. A sample

placed between the parallel faces of two opposed diamond anvils is subjected to

compression when opposite forces push the two opposed anvils together [35]. Since

pressure is defined as force divided by area, it is possible to reach higher pressures either

by increasing force or decreasing area. If one wishes to achieve high pressures by

decreasing area, then they must be willing to study small samples [36]. The small size of

the sample, and hence, of the anvils, reduces the requirements for large forces and large

supporting frames. The small anvil size has the additional advantage that it permits the

selection of a rather exotic material with just the right properties to be investigated. Also,

the cost of such a device is quite modest when compared with other high pressure devices

[36]. Today a DAC capable of generating pressures greater than 100 GPa can fit into the

palm of the hand and a number of sophisticated measurements, including X-ray

diffraction and a variety of spectroscopies, can be performed on materials of microscopic

dimensions [35].

7

The frame of the DAC is made of stainless steel and the supporting seats

(platens) are usually made of tungsten carbide, both of which have openings along the

axial direction in order for measurements to be performed on the sample. The anvils are

usually made of diamond, which is the hardest substance known to man and is quite

transparent to X-rays and light making it the ideal material [35]. They are usually

selected from brilliant-cut gem stones, are ground and polished into the desired shape

(8 or 16 edges) and size, depending on the pressures that are required to be achieved in a

given experiment. A list of several different flat culet diameters and their respective

pressures that can be obtained is shown in Table 2.1 [37]. A picture of a typical

symmetric DAC is shown in Figure 2.1.

Table 2.1. Culet diameters [37]

Culet dia. (µm) Highest pressure (GPa)

500 ~60

400 ~70

300 ~70-80

200 ~90

100 ~100-150

8

(a) (b)

Figure 2.1. Diamond anvil cell; (a) disassembled; (b) assembled

2.2 Energy Dispersive X-ray Diffraction

Energy dispersive X-ray diffraction (EDXRD) is a non-destructive materials

characterization technique that has been used for many years in numerous fields ranging

from engineering to biology. Buras et al. [38] were the first to use EDXRD techniques

with the DAC interfaced to synchrotron radiation. Since then synchrotron X-ray

diffraction has become a well-established technique and has long been successfully

applied in high pressure and high temperature studies in the diamond anvil cell [39], with

numerous synchrotron facilities worldwide allowing many scientists accessibility to

conduct experiments.

With synchrotron radiation, electrons or positrons are set into motion, orbiting

around a storage ring and emitting electromagnetic radiation. This radiation results from

the centripetal acceleration of the electrons by the magnetic fields in the storage ring.

High energy X-rays are produced, which can be useful for X-ray diffraction on a variety

of samples [14].

9

When performing structural determinations using a DAC, a germanium

charge-coupled device (CCD) detector is usually used for collecting the diffracted

X-rays; due to their stopping power in the 15-100 keV range which is generally the range

used by DAC users [40]. Combined with certain software, the data is displayed in

graphical form. A typical graph from an EDXRD experiment using a DAC is shown in

Figure 2.2.

10 20 30 40 50 60 70

0

1000

2000

3000

4000

Inte

nsity

(co

unts

)

Energy (keV)

Figure 2.2. An X-ray diffraction pattern from an EDXRD experiment.

Included in the graph are fluorescences of some materials.

10

When performing EDXRD for determining structures, the lattice parameters (a, b,

c, and α, β, γ) are determined through measurements of lattice spacings hkld ( h , k , l are

Miller indices) and the atom positions within the crystalline unit cell, which are derived

from the energy values of the centers of intense peaks seen in the data [41], similar to

Figure 2.2. The analysis uses Bragg’s law [42], which gives a relationship between the

interplanar lattice spacings hkld , reinforced diffracted beams of wavelength λ , and

pre-determined EDXRD angle Θ2 . It is shown in the following Equation,

Θ= sin2 hkldλ . (2.1)

Then using the relationship of the wavelength-frequency exchange, which can be

expressed as

υ

λc

= (2.2)

where c is the speed of light and υ is the frequency of the light, as well as

υhE = (2.3)

where E is the photon energy of the X-ray and h is Planck’s constant; with simple

manipulation the final form of

Θ

=Θ

=sin

Å1993.6sin2

keVhcEd (2.4)

is produced. This equation shows that if Θ2 is held constant (which is the case in

EDXRD), Ed becomes a constant. This allows one to determine lattice spacings from a

diffraction pattern similar to Figure 2.2.

11

High pressure phase identification using synchrotron EDXRD techniques involves

many advanced experimental methods, so error evaluation becomes a most important

issue [43]. One possible source of error arises when using Bragg’s law (Equation 2.1),

which shows the necessity of carefully determining the diffraction angle 2Θ in order to

obtain accurate results. Another possible source of error in a high pressure EDXRD

experiment is the significant heating of the DAC which can cause a slight shift in the

lattice parameter. This occurs due to the diamond anvils and sample absorbing much of

the X-rays with energies less than 10 keV [44].

2.3 Ruby Fluorescence, a Pressure Sensor

The use of the wavelength shift of the ruby R1 fluorescence line to determine

pressure was originally developed by Forman, Piermarini, Barnett and Block [45].

The original calibration of this method involved observing the shift with pressure of the

ruby R1 line, while simultaneously measuring the specific volumes of several metals (Cu,

Mo, Pd, and Ag) by X-ray diffraction. The absolute pressure was obtained indirectly by

making reference to the isothermal equations of state of the metals derived from

shock-wave data [46]. After being revised numerous times, the ruby fluorescence

method has been widely used throughout the world as the common pressure scale for

high pressures above 10 kbar (1 GPa).

When used in a DAC, a ruby chip is placed in the sample chamber along with the

pressure medium and sample, and the fluorescence is excited by a laser or any strong

light source. An optical detector collects the signal and it is then displayed as a graph

12

showing intensity versus wavelength. A typical setup of a system with a corresponding

graph are shown in Figures 2.3 and 2.4, respectively. The R lines of ruby are quite

intense, and under hydrostatic pressure they shift linearly to higher wavelengths [35].

Figure 2.3. Ruby fluorescence measurement system

702.5 705.0 707.5 710.0 712.5300

400

500

600

700

800

900

R2 Line

R1 Line

Inte

nsity

Wavelength (nm)

Figure 2.4. Ruby spectrum under hydrostatic conditions

13

Measurement of the wavelength is commonly obtained by determining the

wavelength, λ , of the maximum intensity of the R1 line [47]. This value is then used in

conjunction with

−

−+= 11

1904

0

0

B

BP

λ

λλ (2.5)

to determine the pressure inside the sample chamber, where B is the curvature parameter

(7.665 for hydrostatic, 5 for quasi-hydrostatic), λ is the measured wavelength, and 0λ is

the wavelength of the maximum intensity of the R1 line at ambient pressure (694.24nm).

Although the ruby fluorescence scale is accurate under hydrostatic conditions,

when hydrostaticity diminishes it introduces larger error. When ruby is subjected to

non-hydrostatic stress, the R lines become broader. Pure uniaxial stress gives an even

greater broadening effect than non-hydrostaticity. This feature of increasing line width

makes ruby a useful sensor for detecting the limits of hydrostaticity under pressure [47].

14

CHAPTER III

EXPERIMENTAL

3.1 Sample Characteristics

The sample, (Fe0.44Mg0.56)(Cr0.89Al0.11)2O4, is a type of chromite which is dark

reddish brown in color and has the cubic fcc spinel structure (space group Fd3m) at

ambient conditions (see Figure 1.2) [48]. The sample is a natural mineral which

originated from the Philippines and whose composition is made up of FeO(12.27wt%),

MgO(15.85wt%), Cr2O3(64.77wt%), and Al2O3(7.23wt%); yielding the

(Fe0.44Mg0.56)(Cr0.89Al0.11)2O4 compound [49].

3.2 Diamond Anvil Cell

A symmetrical DAC with 300 µm flat culet diamonds was used in the experiment.

A picture of the DAC is shown in Figure 2.1. Before using the DAC in the experiment,

the culets were aligned to the rotational center of the cell as to eliminate any stress

concentrations which could cause the diamonds to crack under high pressure. This was

achieved by first tightening the set screws to a point where the diamonds could not come

in direct contact with each other. Next, the diamonds were aligned using the lateral

translation screws. The cylinder was then held stationary and the piston was rotated 180°.

After rotation, the diamond mounted in the piston was checked for alignment with the

cylinder diamond and, if misaligned, was translated halfway to the position of the center

of the stationary cylinder diamond via the lateral translation screws. The cell was then

15

flipped over and the cylinder diamond was aligned with the diamond in the piston. The

piston was held stationary while the cylinder was rotated 180° and, if misaligned, the

cylinder diamond was translated halfway to the center of the diamond in the piston

(similar to the above step). The process of aligning the diamonds is iterative in nature,

and the above procedure is usually repeated 3-4 times before the diamonds are perfectly

aligned to the rotational center of the cell.

After the alignment was complete, small pieces of sandpaper were used to remove

any debris, and then a q-tip soaked in ethanol was used to thoroughly clean the culets.

This was repeated several times to ensure that the culets were clean and ready for further

procedures. Figure 3.1 shows an unaligned and aligned DAC.

Figure 3.1. Unaligned and aligned DAC

3.3 Gasket Preparation

The introduction of a gasket into the diamond anvil apparatus, which was first

demonstrated by Van Valkenburg [50], is a very important development in the history of

the DAC; for it is this discovery which allows the use of the DAC as a quantitative tool

for high pressure research. The gasket performs two functions in a high pressure

16

experiment. With a hole pierced it provides a chamber for the sample to be studied, and

also gives lateral support to the diamond anvils [51]. This support is given by the gasket

extruding from the sample chamber around the side of the diamond anvils. The

extrusion, acting as a supporting ring, creates stress concentrations towards the sample at

the edge of the culets that prevent the motion of the gasket material between the anvils as

well as anvil failure [35]. Below ~5 GPa, the gasket does not display significant

deformation and beyond ~5 GPa, the gasket material yields and undergoes large

deformation and flows out of the sample chamber to form a curved feature. The flow rate

decreases after ~50 GPa due to the bending of the diamond anvils [37]. This process is

illustrated in Figure 3.2.

(a) (b)

Figure 3.2. Deformation of gasket under pressures during indentation; (a) below ~5 GPa; (b) above ~5 GPa

The first step in preparing the gasket was to create an indentation at its center by

subjecting the gasket to a pressure predetermined by the designated maximum pressure in

the experiment. This was done by using the DAC in conjunction with a small ruby chip

to measure the indentation pressure. A table showing desired pressures to be obtained in

an experiment with their corresponding indentation pressures is displayed on the

17

following page [37]. With the maximum pressure being 41 GPa in this experiment, the

indentation pressure was 20 GPa. After the gasket was indented, it was removed from

the DAC and a hole was drilled in the center of the indentation as the sample chamber.

This was performed with an electronic drilling machine (EDM)

Table 3.1. Indentation pressures [37]

Maximum Pressure (GPa) Indentation Pressure (GPa)

<30 1/2 Pmax

>30 20

>50 30

An EDM uses electricity as opposed to mechanical methods to machine metals.

In this process, a spark is created between a tool (tungsten bit) and a sample (gasket) of

different voltage polarity when they are brought into close proximity. This spark, which

occurs when a tool discharges current to the sample through a dielectric medium, can

melt a small portion of the sample with sufficient energy [52]. Since the process can be

applied to either soft or hard metals the EDM is ideally suited for drilling high pressure

gasket materials such as rhenium, stainless steel, and inconel with 2-3 µm tolerances [52].

A picture of an EDM is shown in Figure 3.3.

18

Figure 3.3. Electronic drilling machine

In preparation for drilling the hole with the EDM, the indented gasket was placed

on the stage and secured with a small metal mount (positive side of the electric circuit).

Then the wire drilling tool (negative side of the electric circuit) was lowered (z-direction)

until it almost touched the gasket, and the stage was translated (x and y-directions) until

the tool was aligned with the center of the indentation. Off-center alignment could have

19

caused the sample to migrate under load from the center to the edge of the culet, limiting

the highest pressures of the experiment and possibly causing premature failure of the

anvils [52]. After centering, a dielectric organic solvent (ethanol) was dropped onto the

stage and the tool was brought close enough to the gasket to start the spark. The

machining process lasted approximately 3-4 minutes. Figure 3.4 shows the gasket at

different stages of the process.

(a) (b) (c) Figure 3.4. Gasket; (a) before indentation; (b) after indentation;

(c) with machined sample chamber

3.4 Sample Loading

The sample, (Fe0.44Mg0.56)(Cr0.89Al0.11)2O4, was ground into fine grains and

compressed to form a large flake before it was loaded into the sample chamber. This was

done using 1 in3 tungsten carbide blocks. With a pre-drilled gasket centered on the

bottom culet (piston side) and secured with a small piece of wax (which creates no

diffraction peaks), the sample flake was placed in the center of the gasket hole avoiding

contact with the gasket. A small ruby chip was then placed on the culet between the

sample and the gasket in order to measure the pressure during the experiment (see section

2.3). After placement of the sample and ruby, the cylinder side of the DAC was carefully

20

lowered onto the piston, avoiding any impact of the top culet with the sample and ruby.

A diagram explaining this along with a picture of the sample and ruby loaded into the

gasket in this experiment are shown in Figures 3.5 and 3.6, respectively.

Figure 3.5. Schematic of loaded DAC

21

Figure 3.6. Picture of sample and ruby loaded in the gasket

3.5 Pressure Medium

The next step in the experimental procedure is to load the pressure transmitting

medium into the sample chamber. The pressure medium completely fills the spatial voids

in the sample chamber left after loading the sample and pressure calibrator (ruby). The

purpose of the pressure medium is to convert the axial forces applied by the squeezing

mechanism of the DAC to hydrostatic pressure on the sample. It is required to have a

low shear strength (minimizing deviatoric stresses in the sample chamber) and chemical

inertness (non-reactive with the sample). Ideal pressure media are the noble gases, which

fulfill all requirements [14]. Several acceptable pressure media and their respective

hydrostatic limits are listed in Table 3.2 [37].

22

Table 3.2. Pressure media and their hydrostatic limits [37]

Material Hydrostatic Limit (GPa) Condition

Ar2 ~60 Hydrostatic

He ~100 Quasi-hydrostatic

N2 ~13 Hydrostatic

Xe2 ~100 Quasi-hydrostatic

Methanol/Ethanol (4:1) ~12 Hydrostatic

Al2O3 ~100 Quasi-hydrostatic

NaCl ~28 Quasi-hydrostatic

In this experiment, liquefied argon was used, allowing hydrostatic conditions to

be achieved up to 60 GPa. The pressures reached throughout the experiment were well

within the hydrostatic limits of the pressure medium. When loading the pressure

medium, the first step was to loosen the set screws and slightly tighten the main screws,

allowing the culets to come in contact with the sample. At this point reference guidelines

were marked on each screw, with four matching lines being marked on the DAC. These

later allowed the pressure medium inside the sample chamber to be secured without

applying any initial pressure. Next, the main screws were loosened, turning them 180°,

and one set screw was tightened until a slight gap was observed between the culets and

the gasket. If this gap was too large, the sample may have been lost when the pressure

medium filled the sample chamber. The set screw was then loosened to allow the

pressure medium to be contained inside the sample chamber when the main screws were

tightened later in the procedure. The DAC was gently placed in a container which could

withstand cryogenic conditions, avoiding any impulse forces on the sample. This

23

container was placed in an insulating shell, and a helical shaped copper tube which was

connected to an argon tank at one end and entered the container at the other end was

inserted between them. The tank valve was opened and the argon was allowed to flow

inside the container for several minutes. Next, a cover was placed over the container to

isolate the DAC from dry air (completely exhausted from the container by having a lower

molecular weight than argon, 28.97g/mol and 39.94g/mol, respectively), which could

have condensed upon cryogenic cooling and entered the sample chamber. Liquid nitrogen

was poured between the two containers submerging the copper tube. At this point the

argon began to liquefy due to conductive heat transfer with the liquid nitrogen, and was

allowed to flow until the entire sample chamber was submerged. After submersion was

complete, the liquefied argon continued to flow until boiling (caused by the room

temperature DAC) stopped. Then the main screws were tightened 180° to their original

position, containing the pressure medium inside the sample chamber. Finally, the DAC

was removed from the container and allowed to reach room temperature. A 2-d

cross-sectional schematic of the pressure medium loading apparatus is shown in

Figure 3.7.

24

Figure 3.7. Pressure medium loading apparatus

3.6 Pressure Measurement

A small ruby chip was placed in the sample chamber and was used to measure the

pressure throughout the experiment. The value of the wavelength of the ruby R1 line was

used before each diffraction measurement in conjunction with Equation 2.5 (see section

2.3) to determine the pressure for that particular run. The resolution of the R1 and R2

lines together with their intensity ratio can give a good measure of hydrostaticity. In an

ideal hydrostatic condition the distance between the R1 and R2 lines is 1.5 nm, and the

intensity ratio

15

2

1 =R

R

I

I. (3.1)

When pressure becomes non-hydrostatic, the two peaks begin to overlap until

only one peak is observed. Figure 3.8 shows the measured ruby spectrum at 41.2 GPa in

25

this experiment. It should be noted that although this does not meet the criteria for ideal

hydrostatic conditions, due to both peaks being present with minimal overlap at the

highest pressure reached, that hydrostatic conditions were achieved throughout the

experiment.

702.5 705.0 707.5 710.0 712.5300

400

500

600

700

800

900

R2 Line

R1 Line

In

tens

ity

Wavelength (nm)

Figure 3.8. Observed ruby spectra at 41.2 GPa

3.7 Energy Dispersive X-ray Diffraction Measurements

The sample was probed using EDXRD techniques at the superconducting wiggler

beam line X17B3, National Synchrotron Light Source, Brookhaven National Laboratory.

A schematic of the system is shown in Figure 3.9. The X-ray was focused to

approximately 25 µm x 30 µm using two pairs of tungsten slits. In order to align the

sample with the X-ray beam, the horizontal and vertical X-ray beam intensity

26

distributions transmitted through the DAC were measured as a function of motor position

by scanning the DAC stage. The position of the sample and the gasket hole were shown

in the obtained two dimensional maps of the transmitted X-rays. An example of the

transmission curve during a scan is shown in Figure 3.10. Using this method the center

of the gasket hole could be determined, which was used as a reference position, according

to which the desired position could be located to the X-ray. The accuracy of the motor

used is 1µm, which is sufficient for the experimental requirements.

Figure 3.9. EDXRD system

The data was collected with a solid-state germanium CCD detector with a 2θ

angle of 8° being used throughout our experiment. Figure 3.11 illustrates the transmitted

X-ray beam being reflected from the sample with the corresponding diffracted beam and

2θ angle. Data accumulation times were approximately 12 minutes. Crystals have a

tendency to orient along certain directions in a DAC at elevated pressures [53]. When

this occurs, the diffraction signal may be partially or completely lost. Using the

27

continuous rotation method allowed an average diffraction spectrum to be collected

within the covered angles. The DAC was continuously rotated (0.5°/second)

perpendicular to the X-ray beam while diffraction patterns were recorded to overcome the

coarse crystal effect. In our experiment, the rotation stage had 0.023° on-axis and

70 µrad tilt angle accuracies, which was sufficient to keep the sample precisely aligned

with the X-ray beam [53].

-5.0 -4.9 -4.8 -4.7 -4.6 -4.50

1000

2000

3000

4000

5000

diameter

diamond anvil culet diameter

gasket hole

Inte

nsity

(co

unts

)

Distance (mm)

Figure 3.10. X-ray beam intensity distribution

28

Figure 3.11. Transmitted and diffracted X-ray with 2θ angle

29

CHAPTER IV

RESULTS AND DISCUSSION

4.1 Results and Discussion

4.1.1 Lattice Change of Chromite under Pressure

From the EDXRD measurements, we collected the X-ray diffraction patterns to

41.2 GPa. An X-ray diffraction pattern of chromite at 3.5 GPa is shown in Figure 4.1.

We observed (3 1 1), (2 2 2), (4 0 0), (5 1 1), (3 3 3), (6 0 0), and (4 4 2) peaks in our

measurements as shown in the figure. Figure 4.2 shows diffraction patterns at 3.5, 9.7,

16, 20.2, and 25.3 GPa. It should be noted that the indexed peaks shift linearly with

pressure to 25.3 GPa. A Peakfit program (Peakfit v4.11) was used to analyze the

diffraction patterns and determine peak positions at different pressures. After

determining the peak positions in keV (energy), the lattice spacings of the peaks were

obtained using the procedure in section 2.2. Within this pressure range (<25.3 GPa) the

diffraction patterns can all be indexed into the face centered cubic (fcc) structure, with

the cell parameter varying in response to pressure. The relationship of the d-spacings of

these peaks with pressure measured to 25.3 GPa is shown in Figure 4.3. Using the

d-spacings of the (3 1 1), (2 2 2), (4 0 0), (5 1 1), (3 3 3), (6 0 0), and (4 4 2) planes in

conjunction with a refinement software (Robert Downs, University of Arizona); the cell

parameter, a, and volume of the unit cell, V, of chromite were determined to different

pressures. These values are shown in Table 4.1. The numbers in parentheses are the

30

error that correlate to the last digit. The relationship of the cell parameter, a, with

increasing pressure is shown in Figure 4.4.

30 40 50 60 70

0

500

1000

1500

2000

(Ar)

(Ar)

(600

,442

)

(511

,333

)

(400

)

(222

)(3

11)

Inte

nsity

Energy (keV) Figure 4.1. X-ray diffraction pattern at 3.5 GPa. Numbers in the brackets represent the (h k l) values of the corresponding peaks. Peaks not marked are from the X-ray diffraction

system.

31

3.5 GPa

(6 0

0,4

4 2

)

(5 1

1,3

3 3

)

(3 1

1)

Energy (keV)

9.7 GPa

20.2 GPa

16 GPa

25.3 GPa

40 50 60 70

(2 2

2)

(4 0

0)

Inte

nsity

Figure 4.2. X-ray diffraction patterns at different pressures. Numbers in the brackets

represent the (h k l) values of the fcc chromite.

5 10 15 20 251.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

(600),(442)

(511),(333)

(400)

(222)

(311)

d-sp

acin

g (Å

)

Pressure (GPa)

Figure 4.3. Effect of pressure on the d-spacings of the spinel chromite

32

Table 4.1. Refinement results

Pressure (GPa) Cell Parameter: a (Å) Unit Cell Volume: V (Å3)

0.0001 8.3106(28) 573.98(58) 3.5 8.2968(36) 571.14(75)

5.2 8.2696(44) 565.53(92)

9.7 8.243(11) 560.2(23)

12.7 8.216(14) 554.6(29) 16 8.2112(73) 553.6(14)

18.2 8.2255(68) 556.5(13) 20.2 8.2265(88) 556.7(18) 22.9 8.1931(61) 549.9(12) 25.3 8.209(16) 553.3(32)

0 5 10 15 20 258.18

8.20

8.22

8.24

8.26

8.28

8.30

8.32

cell

para

met

er: a

(Å

)

Pressure (GPa)

Figure 4.4. Cell parameter reduction with pressure

33

4.1.2 Equation of State of the Spinel Chromite and Pressure Medium

The bulk modulus is defined as the measure of compressibility of a material and

its first pressure derivative is the measure of the rate at which it becomes stiff as it is

compressed [36]. The bulk modulus of spinel chromite (Fe0.44Mg0.56)(Cr0.89Al0.11)2O4

was calculated using the third order Birch-Murnaghan equation of state (EOS)

( )

−

−−

−

= 14'

43

123 3

2

03

5

03

7

0

v

vK

v

v

v

vKP OTOT . (4.1)

After refinement was performed, the values of pressure (with error approximated at 0.05

GPa) and their corresponding volumes were input into BULK software (Robert Downs,

University of Arizona), which was used to obtain the bulk modulus KOT and it’s first

pressure derivative K′OT. These values were found to be KOT =197±19 GPa with

K′OT=66±12 when fitting data to 16 GPa, and KOT =260±22 GPa with K′OT =51±9 when

fitting data to 25.3 GPa. These values when fit to the experimental data are shown in

Figure 4.5. The large difference in bulk moduli when fitting data to 16 and 25.3 GPa can

be attributed to the increase in volumes at 18.2 and 20.2 GPa. This could possibly be due

to a phase transition initiating at 18.2 GPa. Thus, we believe that the KOT =197±19 GPa

reflects the bulk modulus of the low pressure chromite phase.

34

0 5 10 15 20 25545

550

555

560

565

570

575

Fit data below 16 GPa

Fit data below 25.3 GPa

Vol

ume(

Å3 )

Pressure (GPa) Figure 4.5. Equation of state of chromite. The dashed line shows the EOS using

data to 16 GPa, the solid line shows the EOS using data to 25.3 GPa.

The compressibility of the pressure medium, argon, was also investigated. This

was done with the same procedure as for chromite, but with the (1 1 1) and (2 0 0) planes

being used. Argon is known to transform from a liquid to a single crystal solid at

1.15±.05 GPa [54]. Using Equation 4.1, the equation of state of argon was determined to

20.2 GPa. The bulk modulus was found to be KOT=2.97 GPa when K′OT =9, which agrees

with previous literature [54, 55]. The equation of state is shown in Figure 4.6, with

measured volumes at pressures.

35

0 5 10 15 2070

80

90

100

110

120

130

140

150

160

KOT

=2.97 GPaK'

OT=9

Vol

ume

(Å3 )

Pressure (GPa)

Figure 4.6. Equation of state of argon with measured volume at pressures

4.1.3 Pressure Induced Phase Transformation of Chromite

(Fe0.44Mg0.56)(Cr0.89Al0.11)2O4 is known to have a cubic fcc structure at ambient

conditions with space group Fd3m [56]. We found that the indexed peaks shift linearly

with pressure to 25.3 GPa. At 28.2 GPa, the diffraction patterns change abruptly and can

no longer be indexed into the fcc structure. Figure 4.7 shows the change of the pattern

when pressure increased to 28.2 GPa. Figure 4.8 shows the relation of the d-spacings of

the indexed peaks with pressure. It should be noted that the d-spacings change drastically

at 28.2 GPa, indicating a structural phase transition at this pressure. These new d-

spacings can fit to two different orthorhombic structures, the CF and CT structures,

36

which spinels have been established to transform to at high pressures [32]. However, our

current data cannot distinguish the structures. Further investigation is required for

clarification.

16 GPa

(6 0

0,4

4 2

)

(5 1

1,3

3 3

)

(3 1

1)

Energy (keV)

28.2 GPa

30.1 GPa

40 50 60 70

(2 2

2)

(4 0

0)

Inte

nsity

Figure 4.7. Comparison of the X-ray diffraction pattern before and after the phase

transformation

37

5 10 15 20 25 30 35 40 45

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

(600,442)

(511,333)

(400)

(222)

(311)

d-sp

acin

g (Å

)

Pressure (GPa)

Figure 4.8. d-spacings as a function of pressure, emphasizing the structural

change at 28.2 GPa and above

4.2 Conclusion

A high pressure energy dispersive X-ray diffraction study was carried out

to explore the isothermal compressibility and possible pressure-induced phase

transformation of (Fe0.44Mg0.56)(Cr0.89Al0.11)2O4 spinel chromite. The sample, which is an

fcc structure at ambient conditions [56], was able to be indexed into the fcc structure

using the (3 1 1), (2 2 2), (4 0 0), (5 1 1), (3 3 3), (6 0 0), and (4 4 2) planes in

conjunction with a refinement software to 25.3 GPa. The values of the d-spacings of the

38

indexed peaks shift linearly to 25.3 GPa, as seen in Figure 4.3. Then, using BULK

software (Robert Downs, University of Arizona), two bulk modulus values for the sample

were obtained. The bulk modulus was calculated to be KOT =197±19 GPa with

K′OT=66±12. This values when transposed on the experimental data is shown in Figure

4.5. Due to the increase in the volume of the unit cell at 18.2 and 20.2 GPa, we believe

that KOT =197±19 GPa is the accurate value of the bulk modulus for the low pressure

phase of the spinel chromite. It was also found that (Fe0.44Mg0.56)(Cr0.89Al0.11)2O4

transforms to another structure at 28.2 GPa. As evidenced by the pattern, the sample can

be indexed into two different orthorhombic structures, the CaFe2O4 and CaTi2O4 type

structures. The abrupt shifts in the d-spacings of the diffraction peaks are shown in

Figure 4.8. In order to properly identify the structure that (Fe0.44Mg0.56)(Cr0.89Al0.11)2O4

spinel chromite transformed to in this experiment, further investigations need to be done.

Furthermore, for better understanding the mechanisms of the spinel structure, an

extensive study of the structural, magnetic, and thermodynamic properties of numerous

spinels should be performed.

39

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44

APPENDIX

OTHER WORKS BY THE AUTHOR

A. White, Y. Ma, R. Aksoy, E. Selvi, and J. Sandhu, X-ray Diffraction Measurements of

Chromite to 41 GPa, Journal of Physics and Chemistry of Solids, submitted (2005). A. White, Y. Ma, R. Aksoy, E. Selvi, and J. Sandhu, High Pressure X-ray Diffraction

Study of Chromite [(Fe0.44Mg0.56) (Cr0.89Al0.11)2O4] to 41 GPa, ASME International Southwest Region X 2005 Graduate Student Technical Conference, submitted. Y. Ma, J. Liu, C. Gao, and A. White, An in situ high pressure X-ray Diffraction Study of

CaCu3Ti4O12 Perovskite: Evidence of a stiffer Grain Surface, Physics Review Letter, submitted (2005). C. Gao, Y. Han, Y. Ma, A. White, and G. Zou, High Pressure in situ Resistivity

Measurement in a Diamond Anvil Cell, Review of Scientific Instruments, submitted (2005). E. Selvi, Y. Ma, R. Aksoy, A. Ertas, A. White, and J. Sandhu, High Pressure X-ray

Diffraction Study of WS2, Journal of Physics and Chemistry of Solids, submitted (2005). R. Aksoy, Y. Ma, E. Selvi, M. Chyu, A. Ertas, and A. White, Equation of State

Measurement of Molybdenum Disulfide to 38.8 GPa, Journal of Physics and Chemistry of Solids, submitted (2005). E. Selvi, Y. Ma, R. Aksoy, A. Ertas, A. White, and J. Sandhu, Equation of State

Measurement of Tungsten Disulfide to 25 GPa, ASME International Southwest Region X 2005 Graduate Student Technical Conference, submitted. R. Aksoy, Y. Ma, M. Chyu, A. Ertas, and A. White, High Pressure X-ray Diffraction

Study of Molybdenum Disulfide, ASME International Southwest Region X 2005 Graduate Student Technical Conference, submitted.

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