Embed Size (px)
Citation preview
Characterizing Pressure Induced Structural Changes in Glasses and Liquids
by
Samrat A. Amin
A Dissertation Presented in Partial Fulfillmentof the Requirements for the Degree
Doctor of Philosophy
Approved March 2012 by theGraduate Supervisory Committee:
Jeffery Yarger, ChairGeorge Wolf
Robert Marzke
ARIZONA STATE UNIVERSITY
May 2012
ABSTRACT
The behaviors of various amorphous materials are characterized at high
pressures to deduce phase transitions, coordination changes, densification, and other
structural or electronic alterations in the system. Alongside, improvements on high
pressure techniques are presented to measure equations of state of glassy materials
and probe liquids using in-situ high resolution nuclear magnetic resonance (NMR)
spectroscopy.
27Al NMR is used to quantify coordination changes in CaAl2O4 glass pres-
sure cycled to 16 GPa. The structure and coordination environments remain un-
changed up to 8 GPa at which 93% of the recovered glass exists as 4-fold Al,
whereas the remaining population exists as [5,6]Al. Upon densification, [5,6]Al com-
prise nearly 30% of observed Al, most likely through the generation of 3-coordinated
oxygen.
A method to determine the volumetric equation of state of amorphous solids
using optical microscopy in a diamond anvil cell is also described. The method
relies on two dimensional image acquisition and analysis to quantify changes in
the projected image area with compression. The area analysis method is used to
determine the compression of cubic crystals, yielding results in good agreement
with diffraction and volumetric measurements.
A NMR probe capable of reaching 3 GPa is built to understand the nature of
magnetic field gradients and improve upon the resolution of high pressure studies
conducted in a diamond anvil cell. Field gradients in strength up to 6 G/cm are
caused largely by mismatches in the magnetic susceptibility between the sample
and gasket, which is proven to shift the chemical shift distribution by use of several
different metallic gaskets.
i
Polyamorphic behavior in triphenyl phosphite is studied at pressures up to
0.7 GPa to elucidate the formation of the glacial phase at high pressures. A per-
ceived liquid-liquid phase transition is shown to follow a positive Clapeyron slope,
and closely follows the predicted glass transition line up to 0.4 GPa and tempera-
tures below 270 K. A drastic change in morphology is indicative of a transformation
from liquid I to liquid II and followed by optical microscopy.
ii
ACKNOWLEDGEMENTS
I would like to thank my advisor, Jeff Yarger, for the years of insight and
knowledge, but more so for motivating me to explore my interests. I am grate-
ful to my committee members, especially Robert Marzke, for various discussions
on understanding NMR concepts and providing guidance throughout my graduate
studies. I owe a debt of gratitude to George Wolf for being the most influential
teacher I’ve known, tolerating my inabilities, and providing encouragement when I
needed it the most.
Much of my work was done with collaborators, and I would especially
like to thank Chris Benmore and Qiang Mei for teaching me various aspects of
diffraction and involving me with numerous projects. I would also like to thank the
Yarger/Angell/Buttry group members for scientific discussions and collaborations,
especially Emmanuel Soignard and Brian Cherry for various instrumentation help
throughout the years.
I am indebted to Harish Bhat for not only being a great friend, but the nu-
merous words of encouragement, guidance, and invaluable advice. I would like to
thank Ramesh Sharma for sharing my excitement and views on various projects,
and understanding my struggles better than anyone else could. I want to thank Erin
Oelker for the years of friendship and support. Also, I would like to thank Melinda
Creager for help early in my career and support thereafter.
Last, but certainly not least, I am forever grateful for my family’s support,
especially my brother Ruchik, to whom I owe greatly for this opportunity.
iii
TABLE OF CONTENTS
Page
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
CHAPTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 CHARACTERIZING PRESSURE INDUCED COORDINATION CHANGES
IN CALCIUM ALUMINATE GLASSES USING ALUMINUM NMR . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . 4
Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 4
NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 DETERMINING THE EQUATION OF STATE OF AMORPHOUS SOLIDS
AT HIGH PRESSURE USING OPTICAL MICROSCOPY . . . . . . . . 25
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3 NMR IN A DIAMOND ANVIL CELL: CHARACTERIZING FIELD
GRADIENTS, RESOLUTION ENHANCEMENTS, AND DIFFUSION . 43
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 46
iv
CHAPTER Page
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4 OBSERVING PHASE TRANSITIONS IN SUPERCOOLED TRIPHENYL
PHOSPHITE AT HIGH PRESSURES . . . . . . . . . . . . . . . . . . . 66
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3 Analysis and Discussion . . . . . . . . . . . . . . . . . . . . . . . 69
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter 1 References: . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Chapter 2 References: . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Chapter 3 References: . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Chapter 4 References: . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Appendix A References: . . . . . . . . . . . . . . . . . . . . . . . . . . 96
APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A EXPERIMENTAL METHODS . . . . . . . . . . . . . . . . . . . . . . 98
A.1 Diamond Anvil Cell . . . . . . . . . . . . . . . . . . . . . . . . . . 99
A.2 Solid State Nuclear Magnetic Resonance Spectroscopy . . . . . . . 103
A.3 High Pressure Liquid State NMR . . . . . . . . . . . . . . . . . . . 107
A.4 Equation of State Measurements . . . . . . . . . . . . . . . . . . . 110
A.5 Low Temperature Assembly . . . . . . . . . . . . . . . . . . . . . 112
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
v
LIST OF TABLES
Table Page
1.1 Pressure dependence of isotropic shifts, quadrupole products, and Al
speciation in calcium aluminate glasses. . . . . . . . . . . . . . . . . . 13
vi
LIST OF FIGURES
Figure Page
1.1 27Al (B0 = 9.4T) satellite transitions of calcium aluminate glasses pres-
sure cycled up to 16 GPa. . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Central transition NMR spectra of CA Glass . . . . . . . . . . . . . . . 9
1.3 Al-O coordination dependence on pressures up to 16 GPa determined
by fitting the central transition resonances with Czjzek models. . . . . . 10
1.4 Raman spectra of densified calcium aluminate glasses pressure cycled
to 16 GPa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5 27Al isotropic chemical shifts as a function of cycled pressure. . . . . . 14
1.6 27Al 3QMAS spectra of calcium aluminate glasses pressure cycled to
16 GPa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1 Images of amorphous red phosphorus taken at 1 GPa and 9.7 GPa. . . . 30
2.2 Equation of state measurements of cubic crystals, cesium iodide and
sodium iodide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Equation of state of As2O3 glass up to 6.5 GPa. . . . . . . . . . . . . . 35
2.4 Pressure cycling of GeSe2 glass up to 7.3 GPa. . . . . . . . . . . . . . . 36
2.5 Equation of state of red (amorphous) phosphorus. . . . . . . . . . . . . 38
3.1 B1 field homogeneity with different gasket materials. . . . . . . . . . . 48
3.2 Model of a radial field gradient compared with experimental results . . 50
3.3 Effect of gasket material on the susceptibility broadening . . . . . . . . 51
3.4 Proton chemical shifts of methanol as a function of pressure . . . . . . 53
3.5 Artifically narrowing resonances with the CPMG pulse sequence . . . . 55
3.6 Change in proton linewidth of methanol as a function of pressure . . . . 56
3.7 Self-diffusion of methanol up to 2.5 GPa . . . . . . . . . . . . . . . . . 58
3.8 2D COSY spectra of ethyl crotonate in a diamond anvil cell . . . . . . . 60
vii
Figure Page4.1 Microscopy of the glacial phase transition in TPP. . . . . . . . . . . . . 70
4.2 Change in morphology of the glacial phase of TPP. . . . . . . . . . . . 71
4.3 Quantification of the birefringence during TPP phase transformation. . . 73
4.4 Experimental phase diagram of TPP. . . . . . . . . . . . . . . . . . . . 75
A.1 Diagram of a typical diamond anvil cell. . . . . . . . . . . . . . . . . . 100
A.2 3QMAS spectrum of rubidium nitrate taken at 9.4T and 20 kHz MAS. . 106
A.3 Selection of viable areas by the MATLAB script after scanning a range
of threshold values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
A.4 Relative observed volume change as a result of blurring and threshold
changes in the image . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
A.5 Normalized difference in observed volume as a function of sample tilt
angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
A.6 Change in observed area of a flat copper sample in methanol and glyc-
erol to simulate refractive index changes with pressure . . . . . . . . . 115
A.7 A block diagram of the low temperature microscopy setup used in TPP
experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
viii
Chapter 1
CHARACTERIZING PRESSURE INDUCED COORDINATION CHANGES IN
CALCIUM ALUMINATE GLASSES USING ALUMINUM NMR
1.1 Introduction
Densification processes in network forming oxides are vital for understanding geo-
logical processes occurring at elevated temperature and pressure. The formation of
highly coordinated cation species have a direct consequence on the viscosity, chem-
ical processes and ion exchange properties of melts.1–5 Differences nearing an order
of magnitude can be realized in the viscosity of aluminosilicates by applying rela-
tively low pressures.6,7 Calcium aluminates (CA) and aluminosilicates (CAS) have
been studied extensively to better understand the role of network forming ions (Al,
Si, O) in liquids and glasses at high temperatures,8–14 although the effects of pres-
sure are less diagnosed. As a result, the correlation between pressure induced net-
work rearrangements and ion roles is not fully understood partly due to the multiple
functionality of cations (charge balancing, depolymerizing, intermediate species).
In magmatic liquids, the function of aluminum may be especially important for vis-
cosity models for its ability to undergo structural changes at pressures lower than
silicon in fully polymerized glasses.15 Thus, aside from their unique optical and
mechanical properties,16 glasses along the CaO-Al2O3 join are of fundamental in-
terest for their lack of typical glass forming cations (Si, P), allowing the exclusive
study of coordination changes around aluminum and oxygen which exhibit diverse
structural changes in the P-T space of oxide systems. The present work quantifies
the formation of highly coordinated aluminum species in densified CaAl2O4 glass
at pressures up to 16 GPa using high-field 27Al NMR.
1
Aluminosilicates have been studied extensively to characterize the role of
framework cations ([4]Al, [4]Si), network modifiers (Na+, Ca2+, K+) and degree
of polymerization (fraction of non-bridging oxygen (NBO)). Systematic variations
involving these species has revealed complex behavior under pressure, where the
formation of higher coordinated cations is heavily dependent on the composition
and has a direct consequence on the macroscopic properties of the glass. NMR has
been an exceptionally useful technique for quantifying these changes in pressure cy-
cled glasses. Recently, Kelsey et al.17have shown the amount of high-coordinated
Si and Al generated at pressure is substantially dependent on the aluminum concen-
tration, which undoubtedly affects the type of network linkages. Perhaps the most
consistent change with pressure is the decay of NBO, confirmed by Lee et al.18–20
alongside the formation of higher coordinated cation species, although further den-
sification processes occurring after their depletion are yet to be fully apprehended.
A detailed review on the effect of pressure on oxide glasses probed by NMR was
given recently by Lee.21
The series of (CaO)x-Al2O3(1�x) compositions are known to be fair glass-
formers depending on the viscosity, which is largely dictated by the interplay of
NBO and higher coordinated species. The role of ions is fairly well understood in
ambient CA crystals and glasses at several compositions. Ca ions act to depoly-
merize the network at low-alumina compositions (x>0.5) through the formation of
Q<4 species and NBO, where Qn describes aluminum tetrahedral units coordinated
by n bridging oxygens. Above the composition point where the molar concentra-
tion of aluminum exceeds the charge of the modifier cation (Ca2+, x<0.5), lack of
charge balancing ions forces the formation of higher coordinated aluminum species
while maintaining a polymerized network dominated by Q4 environments.22 Here,
interest lies in studying the mechanism associated with the spatial distribution of
2
higher coordinated species. A recent study by Lee et al.23 in aluminosilicate glasses
shows preferential proximity between [4]Al-[5]Al but little spatial correlation be-
tween [4,5]Al and [6]Al. However, the distribution of network forming cations in
aluminosilicates may not be directly comparable, as the inclination of forming Si-
O-Al linkages over Al-O-Al may influence this selectivity.24 Thus, the proximity
of highly-coordinated Al species may be different in CA glasses where only a fully
polymerized aluminate network exists.
Diffraction techniques show the average aluminum coordination to be ⇠4.0
for melt quenched glasses25 at x>0.5, although slight variations occur throughout
the composition range depending on quenching rates.26 Ion dynamics simulations14
suggest the existence of [5]Al and [6]Al species in CA liquids due to their positive
formation enthalpy, which are partially quenched in the glassy state as evidenced
by diffraction27 and NMR14 studies. This is also confirmed in high-alumina CA
glasses by McMillan et al.26 However, the existence of denser species has been sug-
gested by several studies even at low-alumina compositions.28–30 At x=0.5, NMR
reveals the existence of ⇠3.5-7% [5]Al, whereas only [4]Al is observed in composi-
tions of x<0.5.31
Similar to the crystal structure,32 the equimolar (x=0.5) CA glass is regarded
to be a fully polymerized network of corner-shared AlO4 tetrahedra with Ca2+
ions occupying holes for charge compensation. Upon compression, CaAl2O4 trans-
forms into four higher density polymorphs at relatively low pressures (<4 GPa).32
Diffraction on CA crystals show layers of edge-sharing AlO6 octahedra linked by
calcium ions at 3.5 GPa and 1000�C, while a transformation to a double-chained
structure of AlO6 octahedra occurs around 10 GPa and 1100�C.33 Mei et al.34 no-
ticed minimal changes in the Al-O correlation between ambient and 12 GPa den-
sified CA glass although in-situ experiments by Daniel et al.35 revealed significant
3
changes in the Al-O vibrations characteristic of forming [5,6]Al and OAl3 clusters.
This was inferred from a loss in signal intensity due to higher coordination where
overall lack of resolved band structure hindered the ability to quantify the changes
from Raman spectra, although it can be qualitatively stated that a significant ir-
reversible densification takes place in the glass at pressures up to 15 GPa. In a
similar manner, diffraction techniques pose inherent difficulties in the identification
of ion species in CA glasses where significant overlap in pair correlations impede
the ability to probe long range interactions in the network. For example, signif-
icant changes between ambient and pressure densified CA glasses are noticed in
correlations beyond the first coordination shell around 4.4 A where an ambiguity
is caused by the convolution of Ca-O and Al-O interactions.34 Furthermore, the
results are not sensitive to low abundances of Q speciation or coordination envi-
ronments. Thus, a precise determination of densification in CA glasses is yet to be
probed experimentally. This lack of detailed understanding behind aluminum spe-
ciation has influenced the current study using 27Al NMR, where recent advances in
high-fields and multiple quantum techniques alleviate some of the aforementioned
difficulties in quantification.
1.2 Experimental Details
Sample Preparation
Equimolar amounts of high purity CaCO3 and Al2O3 were used to fabricate glass
samples by melt quenching via containerless levitation using a CO2 laser.36 Glass
spheroids ranging in diameters of 1-3mm were quenched by cooling liquid droplets
over a suspension of argon gas. Densified samples were prepared at 8, 12, and
16 GPa by pressurizing glass pieces in a multi-anvil press in platinum or aluminum
capsules at ambient temperature. Samples were compressed and decompressed dur-
ing a period of 20 hours.
4
NMR
NMR experiments were done on decompressed samples at 9.4 and 18.8 T using
Varian VNMRS spectrometers operating at 27Al frequencies of 104.16 MHz and
208.37 MHz, respectively. Samples were spun in zirconia rotors at nr = 20 kHz us-
ing a 3.2 mm MAS probe at 9.4 T and nr = 35 kHz using a 1.6 mm fast-MAS probe
(Varian, Inc.) at 18.8 T. The magic angle was adjusted by narrowing the high field
satellite sidebands of 23Na in sodium nitrate. Up to 16384 scans were collected for
one dimensional experiments with recycle delays of 0.5-1 s. Short pulses of p/12
< 0.3 µs were used for non-selective excitation in all one-dimensional experiments
for proper quantitative analysis.37 3QMAS17,38 spectra were collected with a rotor-
synchronized 3-pulse sequence using 960 scans, 20 kHz spectral width with 32
points in the indirect dimension, 3.2 µs excitation and 1.2 µs reconversion pulses
with a radio-frequency (rf) power of 120 kHz followed by a 15 µs z-filter pulse40
with rf power of 16.6 kHz. All spectra were externally referenced to a 1M aqueous
solution of AlCl3 and background subtracted for small [6]Al signal from the rotors.
For quantitative analysis, the N=0 satellite transitions were subtracted beneath the
central transition resonances before fitting by estimating its intensity from immedi-
ately surrounding sidebands. Data collected with large spectral widths (1-5 MHz)
were baseline corrected with spline functions and minimally broadened by expo-
nential multiplication of 15 Hz to enhance the h±3/2$±1/2i transitions. Isotropic
shifts and quadrupole parameters were calculated with previously described proce-
dures.9,26,41–43 The accuracy of these calculations are dependent on the precision
of the data. Although definite positions of d cg3/2 can be made from the satellite side-
bands, the determination of d cg1/2 is subject to error as the observed intensity of the
tailing line is dependent on the distribution of quadrupole couplings. However, the
5
final error in determining the isotropic shift is still fairly accurate (< 0.5 ppm) as
d cg1/2 is weighed down by a factor of nine with respect to the position of d cg
3/2. Fitting
was done with a Czjzek44–46 model (using DMFIT47 and d=5).
1.3 Results and Discussion
Single pulse 27Al spectra collected at 9.4 T show a large asymmetric tailing towards
high field, thereby obscuring the weaker [5,6]Al resonances. This is evident in most
distorted aluminates and ascribed to a distribution of quadrupole coupling constants
(CQ). However, analysis of the h±3/2 $ ±1/2i SATRAS16 spectra reveal well
resolved peaks for all three sites in the 12 and 16 GPa glasses as shown in figure 1.
Formation of [5]Al is also evident in the 3QMAS spectra, although quantification is
not accurate due to differences in excitation and reconversion efficiencies between
sites, which like satellite transition spectral intensities, are also dependent on the
strength of the quadrupolar interaction,42 thus making quantification prone to large
errors unless corrections from accurately calculated CQ are made. At 18.8 T, the
central transitions are resolved enough by the inverse dependence of second-order
quadrupole coupling with B0 to make quantification possible. The range of bond
lengths and distortions in glasses also causes a distribution of CQ, warranting the
use of non-gaussian fits.
The spectra of ambient and 8 GPa glasses are nearly identical, suggesting
small changes occurring in short range order below this pressure. The samples are
composed mostly of tetrahedrally coordinated aluminum, although ⇠7% exists in
five-fold coordination. This [5]Al has been observed in CA glasses only at high
fields where the resolution is necessary to distinguish it from the tetrahedral reso-
nance and may be a consequence of the minute presence of NBO.49,50 Similarly,
the spectra of 12 and 16 GPa glasses are alike while containing much higher frac-
6
−1000-50005001000
kHz
Ambient
8GPa
*
12GPa
16GPa
Figure 1.1: 27Al (B0 = 9.4T) satellite transitions of calcium aluminate glasses pres-sure cycled up to 16 GPa.
Extracted on the right side are N=2 sidebands h±3/2 $ ±1/2i showing the reso-nances of higher coordinated species (scaled to highlight higher coordinated Al).The central transitions are removed for clarity. The asterisk represents a small im-purity of Al metal used in the multi-anvil assembly.
7
tions of [5,6]Al than the lower density glasses. Shown in figure 2 are three resolved
sites near 70, 41, and 12 ppm corresponding to 4, 5, and 6 coordinated aluminum,
respectively. The [4]Al isotropic shift is centered near 79 ppm for all the glasses, in
agreement with recent results.51 The generation of [5,6]Al is not surprising consid-
ering Al tends to accommodate higher coordinated polyhedra in multiple CA and
CAS crystals.33,52 At lower pressures, a slight decrease in Al coordination is no-
ticed at 8 GPa in comparison to the ambient glass (hnAl�Oi = 4.1). Upon further
compression, the densified samples show average coordinations around 4.3, largely
from the formation of [5]Al. Figure 3 shows the amount of [6]Al remains around 2%
for the 16 GPa glass while [5]Al further increases in population from 23% to 27% at
the expense of [4]Al. Hence, more than one mechanism may exist in the formation of
higher coordinated species, although structural and compositional heterogeneities
cannot be completely discounted to account for this behavior.
The pressure response of CA glass is consistent with the in-situ Raman
study by Daniel et al.35 as shown in figure 4. The Raman spectra of the 0 and
8 GPa samples appear to be nearly identical, suggesting full reversion to the ambi-
ent conditions upon decompression. The 12 and 16 GPa samples show a distinct
loss in overall intensity, especially of the 550 wavenumber band which is attributed
to changes in the Al-O-Al linkages. The spectra of both higher pressure samples
look appear to be nearly identical, thus no quantifiable correlations can be made
to the formation of higher coordinated species seen in the NMR results. Another
noticeable difference between the higher and lower density samples is the amount
of fluorescence, which appears to be higher in the 12 and 16 GPa glasses and been
linked broken Al-O bonds. The Raman band near 785 wavenumbers attributed to
the Al-O stretch appears to remain constant in normalized spectra, but also appears
to have a reduced absolute intensity in the densified samples.
8
−100−50050100150200
Chemical Shift (ppm)
0 GPa
8 GPa
12 GPa
16 GPa
Figure 1.2: Central transition NMR spectra of CA Glass
9
0 2 4 6 8 10 12 14 16 183.9
4.0
4.1
4.2
4.3
4.4
4.5
Pressure (GPa)
ηA
l−O
Figure 1.3: Al-O coordination dependence on pressures up to 16 GPa determinedby fitting the central transition resonances with Czjzek models.
10
Figure 1.4: Raman spectra of densified calcium aluminate glasses pressure cycledto 16 GPa.
11
The somewhat abrupt densification seen by NMR is the most noticeable
change with pressure, occurring within a 4 GPa region above 8 GPa. This implies
either a narrow distribution of bond lengths and angles within the ambient aluminate
network or a first-order like transition from [4]Al to [5,6]Al. This is in contrast to the
wide distribution of CQ values, but gives further credence to distortion of tetrahedra
with pressure. In comparison to CAS glasses,53 the densification in CA glass takes
place at significantly higher pressures.
27Al NMR parameters as a function of pressure are shown in table 1 for all
aluminum species. For ambient and 8 GPa glasses, the satellite transitions were
not adequately resolved to calculate the isotropic shifts for [5,6]Al. Within error,
the isotropic [4]Al resonance does not display any significant shift with pressure
up to 16 GPa, although differences up to 2 ppm are noticed in the d cg3/2 between
the 0 and 16 GPa glasses in figure 5. The full-width at half-height (FWHH) of
the central tetrahedral resonance remains at 17 ppm up to 8 GPa, but broadens
further with pressure to 20 ppm above 12 GPa. This is consistent with increasing
distortions in the local symmetry, although spatial rearrangements of tetrahedra are
also likely, and changes in Al-O-Al linkages cannot be ruled out. The results are
congruous with x-ray diffraction34 which finds minimal changes in the average Al-
O distance between ambient and pressure densified glasses. However, we note that
NMR appears to be much more sensitive to the local changes in coordination of Al
glasses than x-ray diffraction.
Variations in the isotropic chemical shift have been studied systematically
as a function of composition where the chemical shift of [4]Al tends to higher values
in depolymerized CA glass.26 Thus, the formation of NBO species with pressure
is unlikely as the isotropic resonance remains largely around 79 ppm. We expect
the fraction of NBO present in the ambient glass51 to decrease with pressure while
12
Sample Al diso CQh AreaPress. Coord. (ppm) (MHz) (%)
0 GPa [4]Al 78.9 5.8 93[5]Al n.d. n.d. 7[6]Al n.d. n.d. 0
8 GPa [4]Al 79.2 5.7 94[5]Al n.d. n.d. 6[6]Al n.d. n.d. < 1
12 GPa [4]Al 78.6 6.0 75[5]Al 46.3 5.6 23[6]Al 12.6 2.1 2
16 GPa [4]Al 78.8 6.7 71[5]Al 46.3 5.8 27[6]Al 12.6 2.7 2
Table 1.1: Pressure dependence of isotropic shifts, quadrupole products, and Alspeciation in calcium aluminate glasses.
13
0 5 10 15 20
10
20
30
40
50
60
70
80
Iso
tro
pic
Sh
ift (
pp
m)
Pressure (GPa)
Figure 1.5: 27Al isotropic chemical shifts as a function of cycled pressure.
Pressure has little effect on the shifts of [4]Al (triangles), [5]Al (circles), and [6]Al(squares). Lines are shown as a guide.
14
participating in the formation of [5,6]Al. Similar behavior has already been observed
in sodium silicate,54 borosilicate,55 and a variety of aluminosilicate glasses56, all
showing the reduction of NBO with pressure.21 Thus, we expect the aluminate net-
work of CA glass to stay intact at pressures up to 16 GPa, although it is presumably
weakened by the formation of higher coordinated Al.
Moderate quadrupole products for [4]Al ranging from 5.8-6.7 MHz are ob-
tained for all densified glasses and shown in table 1. Pressure has a modest effect
on the average CQh of the [4]Al sites, as its strength and distribution increase by
nearly 1 MHz up to 16 GPa. It is noticed from the shape of 1D spectra and the total
3QMAS isotropic projection in figure 6 that the tetrahedral resonance contains a
significant distribution of CQ even in the non-densified glass. While pressure usu-
ally narrows the distribution of bond lengths and inter-tetrahedral angles, we notice
a slight increase for CA glasses compressed above 12 GPa. The pentahedral Al
sites appear to be less distorted than [4]Al judging from relatively smaller CQh of
5-6 MHz for 12 and 16 GPa densified glasses, similar to rare earth doped alumi-
nosilicates.57
Concurrent formation of [3]O with higher coordinated Al species in CA
glasses has been suggested by Daniel et al.35 based on a mechanism involving an
attack from a bridging oxygen to an neighboring AlO4 tetrahedron. The gradual
coordination change shown in figure 3 is consistent with this model, as a higher
abundance (23%) of [5]Al is immediately noticed at 12 GPa followed by a slight
increase with pressure while the [6]Al population remains constant. The amount of
higher coordinated species reaches nearly 30% at 16 GPa, although it is primarily
due to an increase in [5]Al alone. As expected from the model proposed by McMil-
lan et al., this suggests that [5]Al acts as an intermediate in the formation of [6]Al.
The emergence of [6]Al into the network has to proceed through edge sharing to
15
10
20
30
40
50
60
Iso
tro
pic
Sh
ift (
pp
m)
MAS Dimension (ppm)
10
20
30
40
50
60
Ambient 12GPa
−50050100 −50050100
8GPa 16GPa
Figure 1.6: 27Al 3QMAS spectra of calcium aluminate glasses pressure cycled to16 GPa.
16
satisfy charge balance. Similarly, the formation of [5]Al can occur through corner
sharing or edge-sharing depending on the proximity of the attacking oxygen where
edge-sharing can only take place with neighboring tetrahedra. This can have a pro-
found impact on the final structure of the glass, as edge sharing promotes more
layered structures while corner sharing encourages the formation of channels. The
latter scenario is more likely considering the initial structure of the glass, and we
note that this may also hinder the formation of [6]Al where substantial rearrange-
ments of Ca ions would be necessary to form layered structures. This is consistent
with our NMR results in which the population of [6]Al remains nearly constant de-
spite a relatively large increase in pressure. Increasing nearest neighbor Al-O and
Ca-O interactions from x-ray results34 also suggest this, although further studies
on CA glasses using 17O and 43Ca NMR will be necessary to directly probe the
behavior of oxygen and calcium ions, especially to ascertain whether a correlation
exists between the formation of [3]O and changes in NBO. Keeping in mind the
large structural reversibility noticed by Daniel et al. during decompression, we can
estimate the average aluminum coordination to exceed 5 while pressurized above
12 GPa. Furthermore, the rate of decompression is likely to have a large impact
on the abundance of observed [5,6]Al in densified CA glasses, akin to temperature
quenching effects. We note that significant structural changes and formation of
higher coordinated species may also occur exclusively during the decompression
pathway as noticed in sodium silicate glasses,54 hence the structure of CA glasses
can be markedly different under static pressures than quenched glasses.
1.4 Conclusion
Using high resolution 27Al NMR, the average coordination of aluminum is shown
to increase above 4.35 in permanently densified CaAl2O4 glass compressed to 16
GPa. These changes take place at pressures significantly higher than seen in cal-
17
cium aluminosilicate glasses, proving the addition of Si to the network increases
the propensity to form [5,6]Al. Aside from the pronounced formation of [5,6]Al, the
isotropic chemical shift is largely unaffected by pressure, although a slight increase
in local distortion is evidenced by an increase in the quadrupole coupling strength
for densified glasses. The higher coordinated species show significantly less distor-
tion than the tetrahedra, but the deformation consistently increases with pressure.
Up to 16 GPa, the network is thought to remain completely polymerized. These
results suggest that a significant fraction of oxygen in the aluminate network may
exist in tri-coordinated environments. The formation of [5,6]Al and [3]O species
should cause a large decrease in the viscosity of the melt at higher pressures.
18
References
[1] S.A Brawer. Theory of relaxation in viscous liquids and glasses. The Journalof Chemical Physics, 81(2):954, 1984.
[2] Jonathan F. Stebbins. NMR evidence for five-coordinated silicon in a silicateglass at atmospheric pressure. Nature, 351:638–639, 1991.
[3] Michael Toplis, Donald B. Dingwell, and Tommaso Lenci. Peraluminous vis-cosity maxima in Na2O-Al2O3-SiO2 liquids: The role of triclusters in tectosil-icate melts. Geochimica et Cosmochimica Acta, 61(13):2605–2612, 1997.
[4] Harve S. Waff. Pressure-induced coordination changes in magmatic liquids.Geophysical Research Letters, 2(5):193–196, 1975.
[5] S Chakraborty, R Knoche, H Schulze, D.C Rubie, D Dobson, N.L Ross, andR.J Angel. Enhancement of cation diffusion rates across the 410-kilometerdiscontinuity in earth’s mantle. Science, 283:362–365, 1999.
[6] I Kushiro. Changes in viscosity and structure of melt of NaAlSi2O6 composi-tion at high pressures. Journal of Geophysical Research, 81(35):6347–6350,1976.
[7] I Kushiro, H.S Yoder, and B.O Mysen. Viscosities of basalt and andesite meltsat high pressures. Journal of Geophysical Research, 81(35):6351–6356, 1976.
[8] Jeffrey R. Allwardt, Brent T. Poe, and Jonathan F. Stebbins. The effect offictive temperature on al coordination in high-pressure (10 GPa) sodium alu-minosilicate glasses. American Mineralogist, 90(8-9):1453–1457, 2005.
[9] Dominique Massiot, Dominique Trumeau, Bruno Touzo, Ian Farnan, Jean-Claude Rifflet, Andre Douy, and Jean-Pierre Coutures. Structure and dynam-ics of CaAl2O4 from liquid to glass: A high-temperature 27Al NMR time-resolved study. The Journal of Physical Chemistry, 99(44):16455–16459,1995.
[10] Qiang Mei, Chris J. Benmore, J.K. Richard Weber, Martin Wilding, J Kim,and J Rix. Diffraction study of calcium aluminate glasses and melts: Ii. highenergy x-ray diffraction on melts. Journal of Physics: Condensed Matter,20(24):245107, 2008.
[11] Daniel R. Neuville, Laurent Cormier, D. De Ligny, J Roux, A-M Flank, andP Lagarde. Environments around Al, Si, and Ca in aluminate and aluminosil-icate melts by x-ray absorption spectroscopy at high temperature. AmericanMineralogist, 93:228–234, 2008.
[12] Brent T. Poe, Paul F. McMillan, Bertrand Cote, Dominique Massiot, and Jean-Pierre Coutures. Magnesium and calcium aluminate liquids: in situ high-temperature 27Al NMR spectroscopy. Science, 259(5096):786, 1993.
19
[13] Brent T. Poe, Paul F. McMillan, David C. Rubie, Sumit Chakraborty, JeffYarger, and Jason Diefenbacher. Silicon and oxygen self-diffusivities in sili-cate liquids measured to 15 gigapascals and 2800 kelvin. Science, 276:1245–1248, 1997.
[14] Brent T. Poe, Paul F. McMillan, Bertrand Cote, Dominique Massiot, and Jean-Pierre Coutures. Structure and dynamics in calcium aluminate liquids: High-temperature 27Al NMR and Raman spectroscopy. Journal of the AmericanCeramic Society, 77(7):1832–1838, 1994.
[15] Jeffery L. Yarger, K.H Smith, Ronald A. Nieman, J Diefenbacher, George H.Wolf, Brent T. Poe, and Paul F. McMillan. Al coordination changes in high-pressure aluminosilicate liquids. Science, 270(5244):1964–1967, 1995.
[16] Eugenie V. Uhlmann, Michael C. Weinberg, Norbert J. Kreidl, Lori L.Burgner, Raymond Zanoni, and Kenneth H. Church. Spectroscopic proper-ties of rare-earth-doped calcium-aluminate-based glasses. Journal of Non-Crystalline Solids, 178:15–22, 1994.
[17] Kimberly E. Kelsey, Jonathan F. Stebbins, Jed L. Mosenfelder, and Paul D.Asimow. Simultaneous aluminum, silicon, and sodium coordination changesin 6 GPa sodium aluminosilicate glasses. American Mineralogist, 94:1205–1215, 2009.
[18] Sung Keun Lee, George D. Cody, Yingwei Fei, and Bjorn O. Mysen. Natureof polymerization and properties of silicate melts and glasses at high pressure.Geochimica et Cosmochimica Acta, 68(20):4189–4200, 2004.
[19] Sung Keun Lee, George D. Cody, Yingwei Fei, and Bjorn O. Mysen. Theeffect of Na/Si on the structure of sodium silicate and aluminosilicate glassesquenched from melts at high pressure: A multi-nuclear (Al-27, Na-23, O-17)1D and 2D solid-state NMR study. Chemical Geology, 229:162–172, 2006.
[20] Sung Keun Lee, George D. Cody, Yingwei Fei, and Bjorn O. Mysen. Oxygen-17 nuclear magnetic resonance study of the structure of mixed cation calcium-sodium silicate glasses at high pressure: Implications for molecular link toelement partitioning between silicate liquids and crystals. Journal of PhysicalChemistry B, 112:11756–11761, 2008.
[21] Sung Keun Lee. Effect of pressure on structure of oxide glasses at high pres-sure: Insights from solid-state NMR of quadrupolar nuclides. Solid StateNuclear Magnetic Resonance, 38(45-57), 2010.
[22] Jonathan F. Stebbins, Scott Kroeker, Sung Keun Lee, and T.J. Kiczenski.Quantification of five-and six-coordinated aluminum ions in aluminosilicateand fluoride-containing glasses by high-field, high-resolution 27Al NMR.Journal of Non-Crystalline Solids, 275:1–6, 2000.
20
[23] Sung Keun Lee, Michael Deschamps, Julien Hiet, Dominique Massiot, andSun Young Park. Connectivity and proximity between quadrupolar nuclidesin oxide glasses: Insights from through-bond and through-space correlationsin solid-state NMR. Journal of Physical Chemistry B, 113(15):5162–5167,2009.
[24] Sung Keun Lee and Jonathan F. Stebbins. The degree of aluminum avoidancein aluminosilicate glasses. American Mineralogist, 84:937–945, 1999.
[25] Chris J. Benmore, J.K.Richard Weber, Sujatha Sampath, Joan Siewenie,J Urquidi, and J.A Tangeman. A neutron and x-ray diffraction study of cal-cium aluminate glasses. Journal of Physics: Condensed Matter, 15:S2413,2003.
[26] Paul F. McMillan, William T. Petuskey, Bertrand Cote, Dominique Massiot,Claude Landron, and Jean-Pierre Coutures. A structural investigation ofCaO-Al2O4 glasses via 27Al MAS-NMR. Journal of Non-Crystalline Solids,195:261–271, 1996.
[27] Qiang Mei, Chris J. Benmore, Joan Siewenie, J.K. Richard Weber, and MartinWilding. Diffraction study of calcium aluminate glasses and melts: I. high en-ergy x-ray and neutron diffraction on glasses around the eutectic composition.Journal of Physics: Condensed Matter, 20(24):245106, 2008.
[28] Laurent Cormier, Daniel R. Neuville, and Georges Calas. Structure andproperties of low-silica calcium aluminosilicate glasses. Journal of Non-Crystalline Solids, 274(1-3):110–114, 2000.
[29] Eun-Tae Kang, Seong-Joo Lee, and Alex C. Hannon. Molecular dynamicssimulations of calcium aluminate glasses. Journal of Non-Crystalline Solids,352(8):725–736, 2006.
[30] H Morikawa, F Marumo, T Koyama, M Yamane, and A Oyobe. Structuralanalysis of 12CaO.7Al2O3 glass. Journal of Non-Crystalline Solids, 56:355–360, 1983.
[31] Daniel R. Neuville, Laurent Cormier, and Dominique Massiot. Al coordina-tion and speciation in calcium aluminosilicate glasses: Effects of compositiondetermined by 27Al MQ-MAS NMR and Raman spectroscopy. Chemical Ge-ology, 229(1-3):173–185, 2006.
[32] S Ito, K Suzuki, M Inagaki, and S Naka. High-pressure modifications ofCaAl2O4 and CaGa2O4. Materials Research Bulletin, 15:925–932, 1980.
[33] B Lazic, V Kahlenberg, J Konzett, and R Kaindl. On the polymorphism ofCaAl2O4-structural investigations of two high pressure modifications. SolidState Sciences, 8:589–597, 2006.
21
[34] Qiang Mei, Chris J. Benmore, Sujatha Sampath, J.K. Richard Weber, KurtLeinenweber, Samrat A. Amin, Paul Johnston, and Jeffery L Yarger. Thestructure of permanently densified CaAl2O4 glass. Journal of Physics andChemistry of Solids, 67(9-10):2106–2110, 2006.
[35] Isabelle Daniel, Paul F. McMillan, Philippe Gillet, and Brent T. Poe. Ramanspectroscopic study of structural changes in calcium aluminate (CaAl2O4)glass at high pressure and high temperature. Chemical Geology, 128(1-4):5–15, 1996.
[36] J.K. Richard Weber, J.J Felten, and Paul C. Nordine. Laser hearth melt pro-cessing of ceramic materials. Review of Scientific Instruments, 67(2):522–524,1996.
[37] D Massiot, C Bessada, J.P Coutures, and F Taulelle. A quantitative study of27Al MAS NMR in crystalline YAG. Journal of Magnetic Resonance, 90:231–242, 1990.
[38] Lucio Frydman and John S. Harwood. Isotropic spectra of half-integerquadrupolar spins from bidimensional magic-angle spinning NMR. Journalof the American Chemical Society, 117(19):5367–5368, 1995.
[39] Ales Medek, John S. Harwood, and Lucio Frydman. Multiple-quantummagic-angle spinning NMR: a new method for the study of quadrupolar nu-clei in solids. Journal of the American Chemical Society, 117:12779–12787,1995.
[40] Jean-Paul Amoureux, Christian Fernandez, and Stefan Steuernagel. Z filter-ing in MQMAS NMR. Journal of magnetic resonance. Series A, 123(1):116,1996.
[41] E Lippmaa, A Samoson, and M Magi. High-resolution 27Al NMR of alumi-nosilicates. Journal of the American Chemical Society, 108(8):1730–1735,1986.
[42] A Samoson. Satellite transition high-resolution NMR of quadrupolar nucleiin powders. Chemical Physics Letters, 119(1):29–32, 1985.
[43] Jorgen Skibsted, Eric Henderson, and Hans J. Jakobsen. Characterization ofcalcium aluminate phases in cements by 27Al MAS NMR spectroscopy. Inor-ganic chemistry, 32:1013–1027, 1993.
[44] G Czjzek, J Fink, F Gotz, H Schmidt, J Coey, J-P Rebouillat, and A Lienard.Atomic coordination and the distribution of electric field gradients in amor-phous solids. Physical Review B, 23(6):2513–2530, 1981.
[45] G Le Caer and R. A. Brand. General models for the distributions of electricfield gradients in disordered solids. Journal of Physics: Condensed Matter,10:10715–10774, 1998.
22
[46] Jean Baptiste d’Espinose de Lacaillerie, Christian Fretigny, and DominiqueMassiot. Mas NMR spectra of quadrupolar nuclei in disordered solids: TheCzjzek model. Journal of Magnetic Resonance, 192(2):244–251, 2008.
[47] Dominique Massiot, Franck Fayon, Mickael Capron, Ian King, Stephanie LeCalve, Bruno Alonso, Jean-Olivier Durand, Bruno Bujoli, Zhehong Gan, andGina Hoatson. Modelling one-and two-dimensional solid-state NMR spectra.Magnetic Resonance in Chemistry, 40:70–76, 2002.
[48] Christian Jager. How to get more from 27Al MAS NMR by high-speedsatellite-transition spectroscopy. Journal of Magnetic Resonance, 99(2):353–362, 1992.
[49] Jonathan F. Stebbins, Sung Keun Lee, and Jane V. Oglesby. Al-O-Al oxy-gen sites in crystalline aluminates and aluminosilicate glasses; high-resolutionoxygen-17 NMR results. American Mineralogist, 84(5-6):983, 1999.
[50] Daniel R. Neuville, Grant S. Henderson, Laurent Cormier, and DominiqueMassiot. The structure of crystals, glasses, and melts along the CaO-Al2O3join: Results from Raman, Al l- and k-edge x-ray absorption, and 27Al NMRspectroscopy. American Mineralogist, 95:1580–1589, 2010.
[51] Dinu Iuga, Claudia Morais, Zhehong Gan, Daniel R. Neuville, LaurentCormier, and Dominique Massiot. NMR heteronuclear correlation betweenquadrupolar nuclei in solids. Journal of the American Chemical Society,127:11540–11541, 2005.
[52] Volker Kahlenberg, Reinhard X. Fischer, and Cliff S.J. Shaw. High-pressureCa4Al6O13: An example of a calcium aluminate with three different types ofcoordination polyhedra for aluminum. American Mineralogist, 85(10):1492–1496, 2000.
[53] Jeffrey R. Allwardt, Jonathan F. Stebbins, Burkhard C. Schmidt, Daniel J.Frost, Anthony C. Withers, and Marc M. Hirschmann. Aluminum coordina-tion and the densification of high-pressure aluminosilicate glasses. AmericanMineralogist, 90:1218–1222, 2005.
[54] George H. Wolf, Dan J. Durben, and Paul F. McMillan. High-pressure Ramanspectroscopic study of sodium tetrasilicate (Na2Si4O9) glass. The Journal ofChemical Physics, 93(4):2280–2288, 1990.
[55] L-S Du, J.R Allwardt, B.C Schmidt, and J.F Stebbins. Pressure-induced struc-tural changes in a borosilicate glass-forming liquid: boron coordination, non-bridging oxygens, and network ordering. Journal of Non-Crystalline Solids,337:196–200, 2004.
23
[56] Sung Keun Lee. Simplicity in melt densification in multicomponent mag-matic reservoirs in earth’s interior revealed by multinuclear magnetic reso-nance. Proceedings of the National Academy of Sciences, 108(17):6847–6852,2011.
[57] P. Florian, N. Sadiki, D. Massiot, and J.P. Coutures. 27Al NMR study of thestructure of lanthanum- and yttrium-based aluminosilicate glasses and melts.Journal of Physical Chemistry B, 111:9747–9757, 2007.
24
Chapter 2
DETERMINING THE EQUATION OF STATE OF AMORPHOUS SOLIDS ATHIGH PRESSURE USING OPTICAL MICROSCOPY
2.1 Introduction
Understanding how the molar volume changes as a function of pressure is a key as-
pect in understanding the thermodynamic state of a system. The structural and elec-
tronic response to stress often dictates the physical properties of materials. Funda-
mental pressure-volume relations were first investigated decades ago,1,2 primarily
relying on the experiments pioneered by P. Bridgman using large volume presses.3,4
With the advent of diamond anvil cells (DAC), high pressure experimentation has
become routine using less intricate equipment while allowing access to a larger ther-
modynamic space. Hence, a large amount of experimental work at high pressure
is conducted in DACs despite the limitations imposed by minute sample volumes.
These size constraints become a significant hinderance for visible microscopy under
pressure, where volume measurements are important to characterize the structural
response of a system to static stress.
Most prominently seen in crystalline compounds, densification with pres-
sure can be easily elucidated by diffraction methods which give a direct measure-
ment of the unit cell volume. In contrast, amorphous solids pose a challenge due
to their lack of periodic structure, thus rendering diffraction to be ineffectual aside
from pair distribution function analysis, which itself relies on knowing the atomic
number density for scaling diffuse scattering. Consequently, several studies have
relied on other techniques to determine the equation of state of amorphous solids
and liquids under pressure. Most notably, image shearing or splitting techniques
have proven to give accurate measurements exceeding the resolving power of the
optics.5 A similar video image shearing technique6 was used to precisely gauge
the distance between lines deposited on the sample, allowing resolution on par with25
x-ray diffraction.7 This principle was extended8 to quantify the changes in GeO2
glass by imaging photochemically etched lines on the surface of a polished sam-
ple. Although the modification of the latter study resulted in a lower resolution,
the imaging apparatus required a much simpler setup. Ultimately, the accuracy of
optical measurements are limited by the finite resolution of optics. Thus, imaging
techniques cannot match the resolution of diffraction as the sample size approaches
the micrometer scale. However, optical measurements can successfully yield accu-
rate results using interference effects. Using the parallel surfaces of diamond culets
as an etalon, the equation of state of solid H2 has been measured9 in a DAC by
determining the thickness with interference from white light, provided the pressure
dependence of the index of refraction is known. Several studies have also utilized
x-ray absorption as a tool to measure density changes at high pressure in large vol-
ume presses.10–12 With advances in synchrotron sources, x-ray absorption has been
used to profile the volume of the sample chamber in a diamond anvil cell by scan-
ning through the gasket with a micro-focused beam.13 X-rays also permit the use
of tomography at the micro scale.14 In this work, we further simplify the visible
microscopy method8 by employing high pixel density cameras and image process-
ing software to simplify sample preparations and experimentation to measure the
equation of state of amorphous solids in a diamond anvil cell under hydrostatic
conditions.
2.2 Experimental Details
Piston-cylinder and Merrill-Bassett7 design diamond anvil cells were utilized for
the pressure studies. Diamonds with culet diameters of 300-500 µm were used to
load large samples while allowing pressures over 10 GPa to be generated. Hydro-
static compression9 was achieved by using methanol:ethanol:water (16:3:1) for red
phosphorus and pentane:isopentane (1:1) for cesium iodide and sodium iodide. A
26
4:1 methanol:ethanol mixture was used for As2O3 and GeSe2 glasses. Samples
were monitored over time at constant pressure to confirm that solvation was incon-
sequential. Pressure was determined using the ruby fluorescence method.10–12 For
gold coated samples, flat pieces of glass were selectively coated using a sputter-
ing technique similar to that used for scanning electron microscopy (SEM) sample
preparation.
Samples with a thickness less than 30 µm were selected to avoid bridging
between the diamond culets. Pieces with areas over 10,000 µm2 were individually
chosen to ensure an area to thickness ratio greater than 300 in order to avoid tilting
from irregular surfaces. High resolution images were taken with 5.1 megapixel
Olympus C5060WZ and 8.0 megapixel Sony DSC-F828 cameras. The maximum
magnification, limited by the optics, was used to ensure the sample region was
dispersed over 50,000 or more pixels to make accurate measurements.
A custom script (MATLAB 2010a) was used to calculate the area of the
solid within the sample chamber by detecting the edges via image processing al-
gorithms based on the Canny method.20 Several pictures were taken while rotating
the cell, refocusing the image, and adjusting the amount of transmitted light for
proper contrast. Errors were calculated based on the spread of areas during these
alterations under various threshold values. The script systematically calculated a
mean area from a range of acceptable values whereas outliers were rejected. Fur-
ther error analysis and testing of the script was done by methodically manipulating
a single image where gaussian blurring and rotation were varied to study its effects
on the area calculations. The consequence of these perturbations are shown in the
appendix.
27
2.3 Results and Discussion
Densification of amorphous versus crystalline solids differ in two important aspects:
i) The compression in amorphous solids is isotropic whereas that of non-cubic crys-
talline lattices varies independently in various crystallographic directions, allowing
distinct strain distribution along dissimilar lattice planes. ii) The densification of
amorphous solids can vary with the distribution of void spaces, which are largely
dependent on synthetic or hysteretic conditions. Because amorphous solids com-
press isotropically, the change in area of a sample under pressure can be followed
directly by optical microscopy. This area is directly related to the volume change of
the material. A MATLAB image processing script capable of edge detection using
the Canny algorithm20 is used to define a perimeter of the sample of interest. For
consistency, the region of interest is chosen by the user through a graphical interface
after which the script calculates the area in pixels within the boundary and returns
acceptable values for further analysis.
The compression measurements are performed with a few key assumptions:
i) Under hydrostatic conditions, the compression is completely isotropic. ii) The
change in refractive index of diamond due to culet deformation is negligible. iii)
The change in refractive index of the liquid medium surrounding the sample has
an negligible effect of image magnification. iv) The largest area of the sample is
measured confocally due to the large area to thickness ratio. v) Changes in the
tilting of the sample are insignificant during the evolution of the experiment. These
assumptions are reasonably deduced from the pressure range of the experiment and
geometry of the sample. The first assumption allows the relation of volume and
area through a cubic model using the relation
VV0
=AA0
rAA0
(2.1)
28
where the length change of the unobservable dimension is assumed to be equal to
those observed.
Typical results of bright field analysis are shown in figure 1 where images
of amorphous red phosphorus at 1 GPa and 9.7 GPa are overlaid to highlight the
change in area due to densification. Observing the general shape of the sample in
both images, it is apparent that compression is largely isotropic, thus validating our
first assumption.
Following the conditions mentioned in the experimental section, consis-
tent data can be obtained throughout multiple runs. However, several non-ideal
image conditions such as blurring, sample tilting, and lack of contrast can arise
from improper imaging or sample loading. The two former conditions can be
avoided by careful selection of the sample and correct focusing, whereas the lat-
ter is highly dependent on the refractive index difference between the sample and
pressure medium. In the scenario where these indices are equivalent, a transpar-
ent sample cannot be distinguished visually from the medium and edge detection is
likely to fail. The performance of the program can be tested independently on these
perturbations, of which the results are shown in the supplemental section. Taking
the mean area given from edge analysis, the maximum calculated error in volume is
approximately ± 2% over a wide range of threshold values and pixel blurring with
a 15 pixel radius, all simulated using the image processing toolbox of MATLAB.
Another problem also arises due to compression where the refractive index of the
medium is highly dependent on the pressure. In the case of methanol and ethanol,
the refractive indices change non-linearly to pressures up to 20 GPa and a Dn = 0.3
is realized by 7 GPa.21 The independent change in refractive indexes of the sam-
ple and pressure medium thus cause enhancements or degradations in edge contrast
depending on the difference between the two indices. Furthermore, the same effect
29
1 GPa
9.7 GPa
100 μm
Figure 2.1: Images of amorphous red phosphorus taken at 1 GPa and 9.7 GPa.
30
can also be responsible for slight differences in magnification of the sample. In
order to quantify these effects, flat samples of copper were loaded in air, methanol,
and glycerol under identical conditions used in high pressure experiments. With re-
spect to the errors obtained from edge detection, those introduced by changes in the
refractive index are measured to be minor in cases where the difference in refractive
index between the sample and pressure medium is large enough to properly define
edges. Hence, errors arising from changes in the refractive index are regarded to be
insignificant as shown in the supplemental information.
The orientation of the sample with respect to the chamber can also yield
errors in the area/volume measurements. Tilting of the sample is constrained by the
dimensions of the sample chamber and results in a perceived area smaller than the
actual value. While the error varies depending on the tilt in more than one dimen-
sion, the maximum loss in observed area can be calculated by a rotation around a
single axis during which a plane is approximated by a line equal to the diameter
or edge contingent on the geometrical model. Assuming a square geometry, the
discerned area can be calculated as
A(L,a) = L2cos(amax) (2.2)
where L denotes the length of an edge and amax is constrained by the spacing be-
tween the diamond culets (D) through the relation
a = sin�1(D/L). (2.3)
In actuality, the a ⌧ amax as most experiments can be performed in the a < 5�
using proper sample selection. Furthermore, the error due to tilt can be considered
insignificant if the tilt persists throughout the experiment. Performing this calcula-
tion on a square test piece with an edge L = 100 µm, the observed area as a function
of tilt angle is shown in the supplemental information and deemed inconsequential31
with respect to the errors in threshold and blurring up to a tilt angle of 8 degrees
where a 2% difference in A/A0 can be realized. However, when using confocal
microscopy, the resultant errors are nonindependent as tilting of the sample conse-
quently leads to blurring in adjacent planes above and below the focal plane.
Measurements using bright field microscopy are ultimately limited to the
resolving power of the microscope assembly. Assuming optical aberrations to be
negligible, the diffraction limited resolution (R) of an objective can be approxi-
mated22 by
Rdi f f ⇡l
2NA(2.4)
where l is the wavelength of light and NA is the numerical aperture of the objective.
When using digital cameras with a CCD array, this resolution is usually dictated by
the aperture in the lens assembly where smaller circular openings lead to overlap-
ping of Airy disks at the sensor at which point the Rayleigh criterion dictates the
distinguishability of focal points. In the case where the diameter of the Airy disk
surpasses the edge length of an individual pixel, the resultant setup is limited in
resolution by the aperture. Hence, edge detection experiments should be performed
using a large aperture to ensure the resolution is limited by the size of pixels instead.
For imaging in diamond anvil cells, this approach has no disadvantage since depth
of field is not of concern. Using a halogen bulb and NA ⇡ 0.15, the wavelength of
the lowest energy transmitted light (⇠800 nm) gives a resolution of 2.66 µm and
nearly matches the pixel size of the CCD detector at 2.76 µm. Hence, our optical
edge detection resolution is dictated mainly by the size of the pixels on the CCD
considering lmax ⇡ 600 nm.
The equation of state of cesium iodide and sodium iodide were measured to
validate the assumption of isotropic compression on cubic lattices while allowing
direct comparison to volume changes deduced by measurements in large volume
32
0 1 2 3 4 5 6 7 80.7
0.75
0.8
0.85
0.9
0.95
1
V/ V
0
Pressure (GPa)
a) b)
0.7
0.75
0.8
0.85
0.9
0.95
1
V/ V
0
0 1 2 3 4 5 6 7 8
Pressure (GPa)
Figure 2.2: Equation of state measurements of cubic crystals, cesium iodide andsodium iodide.
Shown on the left is (a) cesium iodide and on the right (b) sodium iodide. Blackdata points designate measurements in a diamond anvil cell using the microscopictechnique described in this work. The red line represents data from Bridgman usinga large volume press.3
33
presses. Figure 2 shows the densification being consistent with the results of Bridg-
man.3 Larger errors are noticed in these measurements due to the transparency of
the samples where edge detection is hampered at higher threshold values. Such
cases may require the sample surface to be coated with a thin layer of gold for better
contrast, which was shown to provide more accurate results on transparent glasses
in our previous studies.23 This technique is essential when the indices of refrac-
tion are nearly identical between the sample and pressure medium as the similarity
negates the appearance of a boundary defining their separation. This scenario is
shown in figure 3 for As2O3 glass coated with a thin (⇠ 10 nm) layer of gold which
greatly increases the contrast between sample and pressure medium. Nevertheless,
additional preparations are often unnecessary as the technique is robust for opaque
samples.
Compaction of As2O3 glass was measured up to 6.5 GPa in a methanol:ethanol
pressure medium where the volume collapses below 80% of the initial value by 6.5
GPa. Gold coating was required for further contrast to distinguish the sample from
the pressure medium. Shown in figure 3, the slope agrees well with studies to higher
pressures,24 proving that gold has a negligible effect on the final measurement while
providing adequate contrast. The sample shown in figure 3 also has a nonuniform
color distribution due to unpolished faces where nearly a quarter of the sample ap-
pears to be dark with respect to flatter regions. Throughout the sample, ridges can
be noticed where the sample cleaves. In combination, these effects would have no
effect on the perimeter detection, whereas traditional filtering by color or threshold
would yield completely inaccurate results. Furthermore, the edge detection script
is written to exclude non-enclosed objects lacking a complete boundary, making it
agile enough to exclude artifacts surrounding the region of interest.
34
0 1 2 3 4 5 6 7 80.7
0.75
0.8
0.85
0.9
0.95
1
Pressure (GPa)
No
rma
lize
d V
olu
me
(V
/V0
)
Figure 2.3: Equation of state of As2O3 glass up to 6.5 GPa.
A 3rd order Birch-Murnaghan equation of state is fitted to the data to give K0 = 11.3and K0’ = 6.7. Inlay: Picture of gold coated As2O3 glass. A thin layer of sputtercoated gold helps enhance the contrast between the glass and pressure mediumwhen their refractive index and transparency are similar.
35
Figure 2.4: Pressure cycling of GeSe2 glass up to 7.3 GPa.
Compression is shown as circles and decompression as squares. A 3rd order Birch-Murnaghan equation of state is fitted to the data to give K0 = 14.2 and K0’ = 2.6.
36
The equation of state of GeSe2 glass is shown in figure 4 and coincides
well with simulations.25 By 7 GPa, the glass compresses to 73% of the ambient
volume while undergoing an electronic change that converts the glass from semi-
transparent red to an opaque black color, although no discontinuity is observed in
the data. Upon decompression, a large hysteresis exists down to 1 GPa after which
the sample volume reverts back to its initial value. Within error, this is consis-
tent with densification results based on the Archimedes method which show a 4%
densification in pressure cycled glasses.25
The isothermal equation of state of amorphous red phosphorus was mea-
sured up to 10 GPa in hydrostatic medium of methanol:ethanol:water. The normal-
ized volume change is shown in figure 5 alongside the densification of black phos-
phorus from previous studies.26,27 The relative volumes of both species are scaled
to the ambient density of amorphous red phosphorus (rred = 2.34), resulting in an
ambient volume difference of 13.4% between the red and crystalline black phases.
As expected, the compressibility of red phosphorus is larger than crystalline black
up to 8 GPa where a pressure induced crystallization converts the sample to black
phosphorus.28 In contrast, black phosphorus converts from an orthorhombic to a
rhombohedral structure around 5 GPa and upon further compression to a simple
cubic phase near 11 GPa. Interestingly, the measured density of red phosphorus is
nearly identical to that of the orthorhombic phase near 5 GPa, although a transfor-
mation to a denser state is not noticed until 8 GPa. Differing by ⇠2 GPa with the
results of Zaug et al,29 this difference may be attributed to experimental differences
affecting nucleation probability.
37
0 2 4 6 8 10 12
0.9
1
V/V
0
Pressure (GPa)
0.8
0.7
0.6
a-P compression
3rd Order B-M fit
Orthorhombic black-P
Rhombohedral black-P
Cubic black-P
Figure 2.5: Equation of state of red (amorphous) phosphorus.
Multiple compression/decompression cycles were performed up to 10 GPa at 298K. The black lines represent a 3rd order Birch-Murnaghan fit. The discontinuityaround 8 GPa is a result of the phase transition from red to black phosphorus. Alarge hysteresis is noticed for both forms upon decompression.
38
2.4 Conclusion
Using the recent progress in digital imaging, accurate density measurements of
amorphous solids can be made at high pressures using simple image processing
scripts capable of edge detection. This technique allows a convenient and simple
way to determine the equation of state in diamond anvil cells as demonstrated by
the comparison to cubic crystals. The pressure-volume relations of several glasses
also agree well with previous studies. Furthermore, the image processing script
proves to be robust to small artifacts introduced by optics, focusing errors, and re-
fractive index changes with pressure. Advancement in optics, digital cameras and
computing power can undoubtedly improve on the resolution and accuracy in future
studies.
39
References
[1] Francis Birch. Finite elastic strain of cubic crystals. Physical Review,71(11):809–824, 1947.
[2] F.D. Murnaghan. The compressibility of media under extreme pressures. Pro-ceedings of the National Academy of Sciences, 30(9):244–247, 1944.
[3] P.W. Bridgman. The compression of twenty-one halogen compounds andeleven other simple substances to 100,000 kg/cm2. Proceedings of the Amer-ican Academy of Arts and Sciences, 76(1):1–7, 1945.
[4] P.W. Bridgman. The compression of sixty-one solid substances to 25,000kg/cm2, determined by a new rapid method. Proceedings of the AmericanAcademy of Arts and Sciences, 76(1):9–24, 1945.
[5] J. Dyson. Precise measurement by image-splitting. Journal of the OpticalSociety of America, 50(8):754–757, 1960.
[6] Charles Meade and Raymond Jeanloz. Frequency-dependent equation of stateof fused silica to 10 GPa. Physical Review B, 35(1):236–244, 1987.
[7] Cassie Scott and Raymond Jeanloz. Optical length determinations in thediamond-anvil cell. Review of Scientific Instruments, 55(4):558–562, 1984.
[8] K.H. Smith, E. Shero, A. Chizmeshya, and G.H. Wolf. The equation of stateof polyamorphic germania glass: A two-domain description of the viscoelasticresponse. Journal of Chemical Physics, 102(17):6851–6857, 1995.
[9] Joop van Straaten and Isaac F. Silvera. Equation of state of solid molecular h2and d2 at 5 k. Physical Review B, 37(4):1989–2000, 1988.
[10] Yoshinori Katayama, Kazuhiko Tsuji, Osamu Shimomura, Takumi Kikegawa,Mohamed Mezouar, Domingo Martinez-Garcia, Jean Michel Besson, DanielHausermann, and Michael Hanfland. Density measurements of liquid un-der high pressure and high temperature. Journal of Synchrotron Radiation,5:1023–1025, 1998.
[11] Y. Katayama, K. Tsuji, J.-Q. Chen, N. Koyama, T. Kikegawa, K. Yaoita, andO. Shimomura. Density of liquid tellurium under high pressure. Journal ofNon-Crystalline Solids, 156-158:687–690, 1993.
[12] Y. Katayama, K. Tsuji, H. Kanda, H. Nosaka, K. Yaoita, T. Kikegawa, andO. Shimomura. Density of liquid tellurium under pressure. Journal of Non-Crystalline Solids, 205-207:451–454, 1996.
[13] Xinguo Hong, Guoyin Shen, Vitali B. Prakapenka, Mark L. Rivers, andStephen R. Sutton. Density measurements of noncrystalline materials at
40
high pressure with diamond anvil cell. Review of Scientific Instruments,78(10):103905, 2007.
[14] Yanbin Wang, Takeyuki Uchida, Frank Westferro, Mark L. Rivers, NorimasaNishiyama, Jeff Gebhardt, Charles E. Lesher, and Steve R. Sutton. High-pressure x-ray tomography microscope: Synchrotron computed microtomog-raphy at high pressure and temperature. Review of Scientific Instruments,76:073709, 2005.
[15] Leo Merrill and William A. Bassett. Miniature diamond anvil pressure cellfor single crystal x-ray diffraction studies. Review of Scientific Instruments,45(2):290–294, 1974.
[16] Ross J. Angel, Maciej Bujak, Jing Zhao, G. Diego Gatta, and Steven D. Ja-cobsen. Effective hydrostatic limits of pressure media for high-pressure crys-tallographic studies. Journal of Applied Crystallography, 40:26–32, 2007.
[17] H.K. Mao, J. Xu, and P.M. Bell. Calibration of the ruby pressure gauge to 800kbar under quasi-hydrostatic conditions. Journal of Geophysical Research,91(B5):4673–4676, 1986.
[18] J.D. Barnett, S. Block, and G.J. Piermarini. An optical fluorescence systemfor quantitative pressure measurement in the diamond anvil cell. Review ofScientific Instruments, 44(1):1–8, 1973.
[19] Wilfried B. Holzapfel. Refinement of the ruby luminescence pressure scale.Journal of Applied Physics, 93(3):1813–1818, 2003.
[20] John Canny. A computational approach to edge detection. IEEE Transac-tions on Pattern Analysis and Machine Intelligence, PAMI-8(6):679–698, Apr1986.
[21] Jon H. Eggert, Liwen Xu, Rongzheng Che, Liangchen Chen, and Jifang Wang.High pressure refractive index measurements of 4:1 methanol:ethanol. Jour-nal of applied physics, 72(6):2453–2461, 1992.
[22] D.W. Piston. Choosing objective lenses: The importance of numerical aper-ture and magnification in digital optical microscopy. The Biological Bulletin,195(1):1–4, 1998.
[23] C.J. Benmore, E. Soignard, M. Guthrie, S.A. Amin, J.K.R. Weber, K. McKier-nan, M.C. Wilding, and J.L. Yarger. High pressure x-ray diffraction measure-ments on Mg2SiO4 glass. Journal of Non-Crystalline Solids, 357(14):2632–2636, Jan 2011.
[24] E. Soignard, S.A. Amin, Q. Mei, C.J. Benmore, and J.L. Yarger. High-pressure behavior of As2O3: Amorphous-amorphous and crystalline-amorphous transitions. Physical Review B, 77(14):144113, Apr 2008.
41
[25] Q Mei, C.J. Benmore, R.T. Hart, E. Bychkov, P.S. Salmon, C.D. Martin,F.M. Michel, S.M. Antao, P.J. Chupas, P.L. Lee, S.D. Shastri, J.B. Parise,K. Leinenweber, S. Amin, and J.L. Yarger. Topological changes in glassyGeSe2 at pressures up to 9.3 GPa determined by high-energy x-ray and neu-tron diffraction measurements. Physical Review B, 74(1):014203, 2006.
[26] L. Cartz, S.R. Srinivasa, R.J. Riedner, J.D. Jorgensen, and T.G. Worlton. Ef-fect of pressure on bonding in black phosphorus. The Journal of ChemicalPhysics, 71(4):1718–1721, 1979.
[27] Takumi Kikegawa and Hiroshi Iwasaki. An x-ray diffraction study of latticecompression and phase transition of crystalline phosphorus. Acta Crystallo-graphica Section B: Structural Science, B39:158–164, 1983.
[28] Erin N. Oelker, Emmanuel Soignard, Keri A. McKiernan, Chris J. Benmore,and Jeffery L. Yarger. Pressure-induced crystallization of amorphous redphosphorus. Solid State Communications, in press, 2011.
[29] Joseph M. Zaug, Alan K. Soper, and Simon M. Clark. Pressure-dependentstructures of amorphous red phosphorus and the origin of the first sharpdiffraction peaks. Nature Materials, 7(11):890–899, 2008.
42
Chapter 3
NMR IN A DIAMOND ANVIL CELL: CHARACTERIZING FIELDGRADIENTS, RESOLUTION ENHANCEMENTS, AND DIFFUSION
3.1 Introduction
High-resolution NMR spectroscopy has become the standard characterization tech-
nique for small molecules in the liquid state. Its ability to elucidate structure and
dynamics at the molecular level can provide a definite advantage when probing
the intermolecular interactions or transport properties at high pressures. However,
the inherent insensitivity of the technique coupled with technical difficulties often
negates the practicality of its use for high pressure studies, especially modern exper-
iments that rely heavily on the use of diamond anvil cells (DAC) where minuscule
sample sizes and spatial constraints greatly hinder the ability to perform routine
NMR without heavy modifications.
The most successful implementation of high pressure NMR has been shown
by Jonas et al1–23 using custom made large volume probes typically operating be-
low 1 GPa. While the complexity of its design and setup ultimately hinders its
widespread use, these probes provided resolution comparable to conventional liq-
uids probes (i.e., line widths < 1 Hz). In contrast, DAC NMR provides incom-
parable ease of setup and a much higher pressure limit, although it significantly
compromises on resolution as typical line widths are found to be 2 orders of mag-
nitude larger.24–29 This difference in observed line width is a direct consequence
of magnetic susceptibility broadening, which is much more prominent in the DAC
due to its smaller sample size. This phenomenon has also been observed in capillary
tubes where broadening is inversely proportional to the tube diameter and sample
volume.30
43
The hardware requirements for each high pressure apparatus is also markedly
different, owing mostly to the method in which pressure is generated. The large
volume probes utilized fluid pumps to pressurize vessels larger than standard 5 mm
NMR tubes. Consequently, these probes require detailed construction and careful
operation as catastrophic blowouts are often encountered. A benefit of the sample
size and cylindrical geometry is the allowed use of helmholtz type coils for sam-
ple excitation and observation, making the construction similar to liquids probes.
In contrast, DACs impose large geometrical constraints on the construction of the
probe, especially in the design and placement of the coil. Whether using a Merrill-
Bassett or cylindrical type DAC, the largest hindrance is caused by the diamond
anvils and sample gasket, also limiting the filling factor. In addition, the metallic
gasket is thought to shield much of the RF signal while inducing magnetic field
gradients around the sample. Finally, the backing plates of the cell also limit the
geometry of the coil and while possibly inducing eddy currents near the sample.
Considering these restrictions, its not surprising that most DAC probe designs uti-
lize similar construction, although various coil designs and arrangements have been
attempted. One of the first DAC NMR attempts27 utilized a split coil design and a
resonator constructed from the gasket itself to measure T1 and T2 relaxation times
at pressure up to 52 kbar. An improved ”hairpin” resonator was later constructed
for collecting free induction decays of solid H2 at 16 kbar.31 Flat inductor coils
consisting of a single turn have been successfully used32 to obtain spectra at 10
GPa and cryogenic temperatures. A split coil based low temperature apparatus has
also been constructed to measure the pressure dependence of the Knight shift in
lithium and sodium.28 Diamond cells specially designed for housing RF coils have
also been constructed for improved sensitivity.33 While earlier DAC NMR attempts
were geared towards improving the hardware and studying solid samples,34 more
recent studies25,26 have focused on the pressure dynamics of liquids where higher44
resolution is required. These studies have been largely directed towards under-
standing the hydrogen bonding networks in liquids by use of 1H NMR, although
13C NMR spectra have also been recorded for glycerol in a DAC,24 giving a wider
chemical shift range at the expense of sensitivity.
3.2 Experimental
Experiments were performed on a 9.4 T Varian VNMRS spectrometer operating at
a 1H frequency of 400 MHz. A single channel probe was constructed to house a
Merrill-Basset type diamond anvil cell made entirely of a beryllium-copper alloy.
Inserts for the probe allowed the cell to be mounted in two orthogonal geome-
tries with respect to the static magnetic field. Single spectra were collected with a
spin-echo18 pulse sequence to allow excess eddy currents to dissipate before sig-
nal collection. CPMG19,20 spectra were collected with a single pulse sequence in
which up to 12 echoes were collected following each p pulse. Phase alternation20
was used to compensate for imperfect p pulses. For tap water samples, a 10 s recy-
cle delay was used while 3-15 s was used for methanol depending on the pressure.
COSY spectra were collected with a 2-pulse (90-t-90) sequence with proper phase
cycling. 80 scans were taken at each increment in the indirect dimension along with
a 8 kHz sweep width, 128 increments, and a 5 s recycle delay. The COSY pulse
sequence was tested with the same hardware configuration with an ethyl crotonate
sample in a 2 mm capillary tube in place of the DAC.
Gaskets of beryllium-copper were punched to 5 mm diameter and typically
indented below 100 microns in thickness. For placing the coil closer to the sample,
rectangular gaskets were also cut, but limited the pressure range of the study. The
thickness of the gasket indentation was adjusted depending on the desired pressure
range of the experiment in order to ensure maximum sample volume. Diamond
45
anvils with culets of 1 mm diameter were employed for experiments below 3 GPa
while 650 micron diameter cults were used for higher pressures. Two small pieces
of ruby (Cr:Al2O3) were loaded with the sample to determine pressure using the
ruby fluorescence scale.10–12
A round shaped 4-turn split solenoid copper coil was used for excitation and
signal recovery. The coil was hand fabricated to a diameter of 2 mm with a space of
approximately 5 mm to accommodate the gasket. The coil was connected to a pair
of variable trimming capacitors by a coaxial wire, allowing the circuitry to be placed
outside the diamond cell plates and enabling the probe to be tuned externally by
rods protruding from the body. A spectrum analyzer and oscilloscope were used to
initially tune and match the circuit to the experimental proton frequency and finely
set by reducing the amount of reflected power from the probe. Excitation pulses
of p/2 = 6 µs in length were calibrated by nutating the proton signal from a large
sample volume (unindented gasket) containing water loaded in a DAC. Shimming
was attempted on the sample by several methods, although none affected the overall
lineshape or width.
3.3 Results and Discussion
Design of the electrical components is a crucial part of NMR experimentation where
the RF characteristics of the circuitry often dictates the quality and reliability of the
data. Generating large B1 fields allow uniform excitation over a large spectral range,
which is necessary for nuclei with large chemical shift ranges. Beyond single pulse
NMR, the necessity of generating a homogeneous B1 field becomes increasingly
important. For example, even in a two pulse spin-echo sequence, the inclusion of
heterogeneity in the p pulses causes the refocusing to be imperfect, thus altering the
echo amplitude. Being imposed by the spatial constraints of the DAC, the circuit
46
(see supplemental) used in this study was still capable of generating large B1 fields
of 40 kHz due to the small coil diameter. The homogeneity of the B1 field is largely
affected by the gasket material as shown in figure 1. Using a teflon gasket with
a similar sample chamber volume, the homogeneity of the the transverse field is
nearly perfect through a rotation of 2520�. This less than 5% change over 7 rotation
cycles outperforms most commercial probes, owing largely to the miniscule sample
size. Even with a split coil design, the size of the sample is extremely small with
respect to the generated B1 field, thus making DB1 negligible over the sample vol-
ume. In contrast, the shielding by a metallic BeCu gasket causes enough distortions
in the B1 field to create a >5% difference after a rotation through 720�. Through
2520�, the nutation amplitude has lost over 50% of its initial intensity. The 90�
pulse time was measured over various sample thicknesses and found to be invariant
within the determination error.
An added benefit of modern day NMR is the increased sensitivity of the
spectrometer’s electronics. While earlier designs24,27,31 tried to place discrete com-
ponents as close to the coil as possible to avoid added noise, we have found this
factor to be insignificant in the design of the circuitry. Using sample volumes capa-
ble of reaching 1.5 GPa, spectra with a signal to noise ratio of 10 could be obtained
within 128 scans.
The most noticeable trait of a spectrum generated from a DAC sample is
the broad linewidth in comparison to standard liquids NMR. Its clear that a het-
erogeneous broadening is caused by the magnetic susceptibility distortions near the
sample, resulting in resonances that are over 200-700 Hz broad at the base. The
broadening appears to be largely due to a radial gradient, and its strength can be
estimated by
G =2G
g1HD(3.1)
47
Figure 3.1: B1 field homogeneity with different gasket materials.
48
where g is the gyromagnetic ratio, G is the full linewidth at the base of the resonance,
and D is the diameter of the sample chamber. In comparison to a model utilizing
a chemical shift distribution convoluted by a radial volume function, the resultant
line shape is nearly identical to the observed spectrum as shown in figure 2. Doing
a similar comparison with a linear gradient would result instead in a chemical shift
distribution taking the shape of the sample chamber. Using equation 1 and a typical
proton linewidth of G ⇡ 350 Hz, a gradient value of approximately 2.5 G/cm is ob-
tained and scales linearly with the pressure. This derivation is oversimplified as it
doesn’t account for non-circular alterations of the sample volume and the complex
susceptibility distortions in multiple dimensions caused by both the gasket material
as well as the surrounding diamonds. Thus, it may be difficult to accurately calcu-
late the magnetic field gradients since they are irreproducible due to experimental
deformations of the sample volume during pressure generation. This effect is easily
noticeable from spectra collected at different pressures as the linewidth of the res-
onance increases significantly with pressure. As expected, the closer proximity of
the diamonds and irregularities in the shape of the hole will cause larger magnetic
field deviations over a smaller sample volume.
Broadening due to magnetic susceptibility is further verified by the use of
various metals or alloys for the gasket material. Shown in figure 3, the distribution
width and direction is largely dependent on the difference between the magnetic
susceptibilities of the gasket (cg) and the sample (cs). In the case where cg > cs
a broadening towards higher (positive) chemical shift is noticed, while a tail in the
opposite direction is observed when cg < cs. The widths and general shape are
not directly comparable as we were not able to test gaskets with equal thicknesses
without further indenting the metal, which would change the density, and thus af-
fect the susceptibility. However, it can be qualitatively stated from the results that
49
−50005001000
0
0.2
0.4
0.6
0.8
1.0
1.2
Hz
No
rma
lize
d In
ten
sity
Figure 3.2: Model of a radial field gradient compared with experimental results
50
−5000−4000−3000−2000−1000010002000300040005000
BeCu
Zinc
Silver
Gold
Chemical Shift (Unreferenced / Hz)
Figure 3.3: Effect of gasket material on the susceptibility broadening
51
the small volume to surface area of the sample chamber has a drastic effect on the
distribution of magnetic gradients which would otherwise be unobservable in larger
samples where the volume experiencing a homogenous field would greatly outnum-
ber the surface area. Hence, this broadening phenomenon is likely one that cannot
be circumvented for static high pressure experiments which employ minute sample
volumes approaching the nanoliter scale.
The susceptibility effect also points out the importance of sample orienta-
tion with respect to the static magnetic field for DAC NMR studies. The crystalline
nature of some metals can produce an anisotropic field distribution depending on
its orientation with the B0 field. In the case of BeCu gaskets, a face centered cubic
lattice ensures that the susceptibility tensors are equivalent among the axes, making
comparisons to previous experiments24 using a different geometry easier, although
it should be noted that the field interaction with diamond also changes with orienta-
tion. Still, the observed shape, width, and direction of the broadening is comparable
to that shown in previous studies24.
Despite the broadening, accurate measurements of the chemical shift were
made up to 3 GPa for methanol as shown in figure 4. The chemical shift difference
between the methyl and hydroxyl protons increases linearly from 1.6 ppm to 2.45
ppm at 3 GPa, in contrast with previous results which show a non-linear behavior
beyond 7 kbars,25 although the lower field results of the previous study clearly
indicate a lesser resolution and sensitivity than our experiments.
In order to obtain higher resolution spectra from the current apparatus, the
B1 inhomogeneity caused by the gasket may be used to obtain higher resolution
spectra by the use of spin-echo type experiments where incomplete refocusing can
help eliminate part of the heterogeneous broadening. This may require the use of
larger gasket volumes, which were determined to have a larger B1 inhomogeneity.
52
0 0.5 1 1.5 2 2.5 3 3.51.6
1.8
2
2.2
2.4
2.6
Pressure (GPa)
Pe
ak
Se
pa
ratio
n (
CH
3 −
OH
) (p
pm
)
Figure 3.4: Proton chemical shifts of methanol as a function of pressure
53
While this approach is not an ideal solution to gain resolution as it discards part
of the signal, it may be advantageous in the case of DAC NMR where removal of
the gradient is not possible due to hardware limitations and technical difficulties.
The results of this approach are shown in figure 5 from a methanol sample using
a Carr-Purcell-Meiboom-Gill (CPMG)19,20 pulse train. At 1.5 GPa, the linewidth
of the methyl resonance can be reduced from 206 Hz to 46 Hz by taking the data
after 4 echoes with a t = 30 ms. Even after discarding over half of the area in a
compromise for resolution, a signal to noise ratio of 10 can be achieved at 1.5 GPa
with 2k scans. This resolution is enough to baseline resolve a 13C-1H J-coupling
(150 Hz) in a diamond anvil cell as shown in figure 5.
When using smaller diameter culets smaller sample chambers, the B1 ho-
mogeneity is noticeably improved and the linewidth cannot be reduced by the tech-
nique mentioned above. However, the B0 field gradient is still present and can be
used to measure diffusion effects instead. Using the CPMG pulse train, the change
in intensity of each echo can be described by
M(2nt) = M0 exp�2nt
T2+�Dg2G2(2nt)t2
3
�(3.2)
where D is the diffusivity, G represents the magnitude of the field gradient and g is
the gyromagnetic ratio. The values of T2 and D can be extracted by performing sev-
eral CPMG experiments using differing t values. A detailed analysis of diffusion
data is further discussed in the appendix. In ideal experiments, the magnitude of
the gradient remains constant, thus the t value is the only variable in the data sets.
However, the densification and spatial changes that occur within the gasket during
pressure changes significantly alters the gradient, and this is easily apparent in the
resultant linewidth as shown in figure 6. The estimated gradient is likely overes-
timated with this technique, especially in the case where gasket deformation takes
place and the radius is not uniform, although the scaling of the gradient with pres-54
Tau = 10ms
Tau = 20ms
Tau = 30ms
Tau = 40ms
Tau = 50ms
Tau = 10ms
Tau = 20ms
Tau = 30ms
12C MeOH CPMG with 4 Echoes
FWHM ~ 30 Hz
Figure 3.5: Artifically narrowing resonances with the CPMG pulse sequence
55
Figure 3.6: Change in proton linewidth of methanol as a function of pressure
56
sure is still determined and useful in calculations. Thus, a multiplication correction
factor of 0.33 is introduced to scale the 0.4 GPa gradient to match the diffusivity
of methanol to that determined by Jonas and Akai.42 The same correction factor is
applied to each calculated gradient value. Using these values, the calculated self-
diffusivity values of methanol are determined up to 2.5 GPa and shown in figure 7.
On a logarithmic scale, the diffusion values follow the same slope determined up to
0.5 GPa by Jonas and Akai.42 On a linear scale, an exponential decrease is noticed
up to 2.5 GPa where the diffusivity is .02*D1atm.
Its clear from the data obtained that the orientation of the sample also plays
a large role in the susceptibility gradient over the sample. Previous DAC NMR
work43 has been performed primarily with the B0 field lines crossing the narrow
axis of the gasket where the gasket disc is perpendicular to the field lines. In this
geometry, it is assumed that the field gradient caused by susceptibility is radial in
nature and a separate field gradient caused by the diamonds is along the thickness
of the gasket. In this work, the DAC is oriented 90 degrees with respect to the pre-
vious setups, resulting in static field lines going through the long axis of the gasket.
The end result is a different distribution of the magnetic field lines that is appar-
ent in the line shape of the spectra. Unsurprisingly, changing the orientation has
the same effect as changing the gasket material, where the difference in suscepti-
bility between the gasket and diamond ultimately dictate the effective field felt by
the sample. Hence, changing the orientation leads to the creation of different gra-
dients over the sample. However, the broadness of the resonances remains nearly
the same, although there may be an ideal orientation for narrower resonances. This
change in gradients with orientation can have a significant impact on the type of
experiments that can be performed. For example, Raffaelle et al43 didn’t notice a
change in the gradient with pressures up to 2 GPa, and was thus able to calculate
57
Figure 3.7: Self-diffusion of methanol up to 2.5 GPa
58
diffusion parameters with the use of a static field gradient throughout the experi-
ment. By rotating the cell 90 degrees, the results obtained in this work show that
the field gradients are much more reliant on the spacing between the diamonds as
well as the shape of the container, and thus change significantly with pressure. The
tradeoff is a simpler probe design in which the cell can simply be inserted without
large configurational changes in the probe body, although corrections have to be
employed to account for the changes in the field gradient.
With an increase in resolution and sensitivity, perhaps the most useful im-
plementation of NMR is through 2-dimensional correlation techniques. Although
this has been shown extensively by Jonas et al, no 2D NMR in a diamond anvil cell
has been published to our knowledge. This is largely due to the limitations imposed
by the sample volume and sensitivity, which ultimately make 2D techniques unfea-
sible due to time constraints. Using volumes capable of reaching 2 GPa, we have
recorded 2D COSY spectra of ethyl crotonate in a DAC within 15 hours. Shown in
figure 8, the five resonances of ethyl crotonate are subject to the same broadening
issues, although the cross correlations quickly reveal the correct J-coupling con-
nectivity within the molecule. Although the resolution is not adequate to perform
studies on systems with more than a few resonances, the effects of bonding changes
such as dimerization can be probed easily using the technique.
3.4 Conclusion
Performing high pressure NMR studies remains challenging due to the technical
requirements for generating pressure. While the diamond anvil cell affords con-
venience in generating large pressures without the need for complex assemblies,
a clear hindrance is imposed by the minuscule sample volumes and magnetic sus-
ceptibility gradients which ultimately restrict high resolution work. Despite these
59
O
O
1
2
3
4
5
1234567
Small Capillary
F2 (ppm)
15
2
34
F2 (ppm)
123456789
Diamond Anvil Cell
1
5
2
34
2.1 GPa 80 scans/indirect point8KHz indirect dim s/w
Figure 3.8: 2D COSY spectra of ethyl crotonate in a diamond anvil cell
60
problems, accurate chemical shift measurements can still be obtained to pressures
above 3 GPa reproducibly. The increased sensitivity of modern electronics allows
the collection of adequate (S/N = 10) spectra within minutes from a diamond anvil
cell. With the use of artificial narrowing pulse sequences, higher resolution spectra
can be acquired at the expense of signal. While the linewidths are still an order of
magnitude larger than typical liquids resonances, enough resolution is gained to ob-
serve baseline resolved C-H J-couplings. The increased sensitivity and resolution
also make it possible to measure intramolecular correlations in a diamond anvil cell
using a COSY pulse sequence, which can be useful in elucidating bonding changes
at higher pressures.
Results indicate that the use of non-metallic elements may be extremely
advantageous for excitation and collection of RF signals, especially for the gasket
material.41 Elimination of RF shielding and eddy currents induced in the metal
components may resolve the B1 inhomogeneity and provide a more uniform field
distribution over the sample volume. With the advent of higher field magnets, the
sensitivity and resolution may be further improved by performing experiments near
proton frequencies of 1 GHz.
61
References
[1] D.J. Wilbur, T. DeFries, and J. Jonas. Self-diffusion in compressed liquidheavy water. Journal of Chemical Physics, 65(5):1783–1786, 1976.
[2] D.J. Wilbur and J. Jonas. Fourier transform NMR in liquids at high pres-sure. iii. spin-lattice relaxation in toluene-d8. Journal of Chemical Physics,62(7):2800–2807, 1975.
[3] D.J. Wilbur and J. Jonas. NMR fourier transform spectroscopy at high pres-sure. Journal of Chemical Physics, 55(12):5840–5841, 1971.
[4] D Vander Velde and J Jonas. A high-pressure probe for NMR studies of ho-mogeneous catalysts. Journal of Magnetic Resonance, 1987.
[5] Shantha Samarasinghe, Douglas M. Campbell, Ana Jonas, and Jiri Jonas.High-resolution NMR study of the pressure-induced unfolding of lysozyme.Biochemistry, 31(34):7773–7778, 1992.
[6] Xiangdong Peng, Ana Jonas, and Jiri Jonas. One and two dimensional 1H-NMR studies of pressure and tetracaine effects on sonicated phospholipidvesicles. Chemistry and Physics of Lipids, 75:59–69, 1995.
[7] Xiangdong Peng, Jiri Jonas, and Jerson L. Silva. Molten-globule conforma-tion of arc repressor monomers determined by high-pressure 1H NMR spec-troscopy. Proceedings of the National Academy of Sciences, 90:1776–1780,1993.
[8] X. Peng and J. Jonas. High-pressure phosphorus-31 NMR study of dipalmi-toylphosphatidylcholine bilayers. Biochemistry, 31(28):6383–6390, 1992.
[9] Bao-Shiang Lee, Stephanie A. Mabry, Ana Jonas, and Jiri Jonas. High-pressure proton NMR study of lateral self-diffusion of phosphatidylcholines insonicated unilamellar vesicles. Chemistry and Physics of Lipids, 78:103–117,1995.
[10] J. Jonas. High-resolution nuclear magnetic resonance studies of proteins.Biochimica et Biophysica Acta, 1595:145–159, 2002.
[11] J. Jonas, L. Ballard, and D. Nash. High-resolution, high-pressure NMR studiesof proteins. Biophysical Journal, 75:445–452, 1998.
[12] J Jonas and A Jonas. High-pressure NMR spectroscopy of proteins and mem-branes. Annual Review of Biophysics and Biomolecular Structure, 23:287–318, 1994.
[13] J. Jonas, P. Kozoil, X. Peng, C. Reiner, and D.M. Campbell. High-resolutionNMR spectroscopy at high pressures. Journal of Magnetic Resonance. SeriesB, 102(3):299–309, 1993.
62
[14] J. Jonas and Y.T. Lee. NMR and laser Raman scattering studies of fluids athigh pressure. Journal of Physics: Condensed Matter, 4(2), 1992.
[15] J. Jonas, C.-L. Xie, A. Jonas, P.J. Grandinetti, D. Campbell, and D. Driscoll.High-resolution 13C NMR study of pressure effects on the main phase transi-tion in l-a-dipalmitoyl phosphatidylcholine vesicles. Proceedings of the Na-tional Academy of Sciences, 85:4115–4117, 1988.
[16] Jiri Jonas. Nuclear magnetic resonance at high pressures. Annual Review ofPhysical Chemistry, 26:167–190, 1975.
[17] J Jonas, TE Bull, and CA Eckert. High pressure sample cell for the NMRrelaxation time measurements in liquids. Review of Scientific Instruments,41:1240, 1970.
[18] S.T. Adamy, P.J. Grandinetti, Y. Masuda, D. Campbell, and J. Jonas. High-pressure nuclear-magnetic-resonance study of carbon-13 relaxation in 2-ethylhexyl benzoate and 2-ethylhexyl cyclohexanecarboxylate. Journal ofChemical Physics, 94(5):3566–3576, 1991.
[19] DA Driscoll, J Jonas, and A Jonas. High pressure 2H nuclear magnetic reso-nance study of the gel phases of dipalmitoylphosphatidylcholine. Chemistryand Physics of Lipids, 58(1-2):97–104, 1991.
[20] T DeFries and J Jonas. Pressure dependence of NMR proton spin-lattice re-laxation times and shear viscosity in liquid water in the temperature range-15-10c. Journal of Chemical Physics, 66(3):896–901, 1977.
[21] L Ballard, A Yu, C Reiner, and J Jonas. A high-pressure, high-resolutionNMR probe for experiments at 500 mhz. Journal of Magnetic Resonance,133:190–193, 1998.
[22] L Ballard and J Jonas. High pressure NMR. Annual Reports on NMR Spec-troscopy, 1997.
[23] L Ballard, C Reiner, and J Jonas. High-resolution NMR probe for experimentsat high pressures. Journal of Magnetic Resonance, Series A, 123(1):81–86,1996.
[24] J.L. Yarger, R.A. Nieman, G.H. Wolf, and R.F. Marzke. High-pressure 1H and13C nuclear magnetic resonance in a diamond anvil cell. Journal of MagneticResonance, Series A, 114(2):255–257, 1995.
[25] Takuo Okuchi, George D. Cody, Ho-Kwang Mao, and Russell J. Hemley. Hy-drogen bonding and dynamics of methanol by high-pressure diamond-anvilcell NMR. Journal of Chemical Physics, 122(24):244509, 2005.
63
[26] R.F. Marzke, D.P. Raffaelle, K.E. Halvorson, and G.H. Wolf. A 1H NMRstudy of glycerol at high pressure. Journal of Non-Crystalline Solids, 172-174:401–407, 1994.
[27] Sam-Hyeon Lee, K Luszczynski, R.E. Norberg, and M.S. Conradi. NMR in adiamond anvil cell. Review of Scientific Instruments, 58(3):415, 1987.
[28] R Bertani, M Mali, J Roos, and D Brinkmann. A diamond anvil cell for high-pressure NMR investigations. Review of Scientific Instruments, 63(6):3303–3306, 1992.
[29] Markus Hakes and Manfred D. Zeidler. High-pressure NMR study of liquidpropanol up to 3 GPa. Physical Chemistry Chemical Physics, 4(20):5119–5122, 2002.
[30] C. Massin, F. Vincent, A. Homsy, K. Ehrmann, G. Boero, P.-A. Besse, A. Dari-don, E. Verpoorte, N.F. de Rooij, and R.S. Popovic. Planar microcoil-basedmicrofluidic NMR probes. Journal of Magnetic Resonance, 164:242–255,2003.
[31] Sam-Hyeon Lee, Mark S. Conradi, and R.E. Norberg. Improved NMR res-onator for diamond anvil cells. Review of Scientific Instruments, 63(7):3674–3676, 1992.
[32] Michael G. Pravica and Isaac F. Silvera. Nuclear magnetic resonance in adiamond anvil cell at very high pressures. Review of Scientific Instruments,69(2):479–484, 1998.
[33] Takuo Okuchi, Russell J. Hemley, and Ho-Kwang Mao. Radio frequencyprobe with improved sensitivity for diamond anvil cell nuclear magnetic res-onance. Review of Scientific Instruments, 76(2):026111, 2005.
[34] Michael G. Pravica and Isaac F. Silvera. NMR study of ortho-para conversionat high pressure in hydrogen. Physical Review Letters, 81(19):4180–4183,1998.
[35] E.L. Hahn. Spin echoes. Physical Review, 80(4):580, 1950.
[36] H.Y Carr and E.M Purcell. Effects of diffusion on free precession in nuclearmagnetic resonance experiments. Physical Review, 94(3):630, 1954.
[37] S Meiboom and D Gill. Modified spin-echo method for measuring nuclearrelaxation times. Review of Scientific Instruments, 29(8):688–691, 1958.
[38] H.K. Mao, J. Xu, and P.M. Bell. Calibration of the ruby pressure gauge to 800kbar under quasi-hydrostatic conditions. Journal of Geophysical Research,91(B5):4673–4676, 1986.
64
[39] J.D. Barnett, S. Block, and G.J. Piermarini. An optical fluorescence systemfor quantitative pressure measurement in the diamond-anvil cell. Review ofScientific Instruments, 44(1):1–9, 1973.
[40] Wilfried B. Holzapfel. Refinement of the ruby luminescence pressure scale.Journal of applied physics, 93(3):1813–1818, 2003.
[41] Daniel Solli and Raymond Jeanloz. Nonmetallic gaskets for ultrahigh pres-sure diamond-cell experiments. Review of Scientific Instruments, 72(4):2110–2113, 2001.
[42] J. Jonas and J.A Akai Transport processes in compressed liquid methanol.Journal of Chemical Physics, 66:4946, 1977.
[43] D. P. Raffaelle. Proton Nuclear Magnetic Resonance of Molecular Liquids atHigh Pressure in the Diamond Anvil Cell. PhD thesis, Arizona State Univer-sity, 1993.
65
Chapter 4
OBSERVING PHASE TRANSITIONS IN SUPERCOOLED TRIPHENYLPHOSPHITE AT HIGH PRESSURES
4.1 Introduction
The existence of multiple liquid phases for a single component system has received
tremendous interest due to its rare behavior. Termed ”polyamorphism,” this first-
order separation between two liquids has been proposed in several materials, yet a
clear example is still missing near ambient conditions. While being commonplace
in solids (polymorphism), the notion that materials can undergo liquid-to-liquid
transitions can restructure the perception of phase transitions and fundamental mod-
els of condensed state interactions. In the past decade, water,1 silica,2 Al2O3-Y2O3
(YAG),3phosphorus,4,5 and silicon6 have all demonstrated the formation of multi-
ple amorphous phases, although the results of many remain ambiguous.
Perhaps the most promising, yet heavily debated polyamorphic system is
triphenyl phosphite (TPP), a fragile glass former that exhibits complex phase evolu-
tion in its supercooled state. Its behavior was first noticed with differential scanning
calorimetry where multiple crystallization endotherms were noticed at slow scan-
ning rates (5-10 K/min), resulting from crystallization of liquid I and a transforma-
tion to an amorphous ”glacial” phase of liquid II.7 Differing in appearance,8 den-
sity,9 viscosity,10 relaxation dynamics,11 and thermal characteristics12 from both
the liquid and normal crystal, the glacial (aII) phase is readily attained by isother-
mal evolution in a range of 210-225 K.
To solve the complex behavior, several methods have been employed to
probe specific aspects of the glacial phase. Differential scanning calorimetry (DSC)
studies8,12 clearly show two exotherms at slow scanning rates, with Tanaka’s results
even showing a glass transition for the glassy phase of liquid II. Various NMR
66
studies9–11,13–17 have also been devoted to measure molecular motion and dynamics
of the glacial phase. Similarly, Raman18,19 and Brillouin15 scattering experiments
have been employed to probe changes in the glacial phase. Diffraction studies20–22
have also been used to deduce partial crystallinity within the glacial phase. Despite
all the data available from these techniques, the nature of the glacial transformation
is yet to be fully understood, and has resulted in various theories about its formation.
The recent studies by Tanaka et al8 support the view of a first-order tran-
sition taking place via two pathways in spinodal decomposition and nucleation
growth, where the paths ultimately lead to slightly different states. Their results
show a complete transformation from liquid I to a glassy amorphous state of liquid
II when aged in the spinodal decomposition temperature range (210-215.5 K), but
also show the transformation to the glacial amorphous phase with small crystallites
embedded in the glassy matrix when aged above 215.5 K. In most studies prior to
Tanaka’s results, the glacial phase was considered to be formed in the entire temper-
ature range above the glass transition to 230 K. Hence, there is great ambiguity in
the debate of various experiments and their implications on the first-order transition
in TPP as a majority of the experiments have been performed in the nucleation-
growth region instead of the more homogeneous spinodal decomposition region.
4.2 Experimental
TPP was purchased from Sigma-Aldrich and further purified by vacuum distilla-
tion. The major impurity being triphenyl phosphate, its amount was determined by
31P liquid state NMR on the distilled product. A series of experiments were also
run with non distilled TPP (97% pure) without any noticeable consequence in the
experimental results.
67
Merrill-Bassett7 design diamond anvil cells were utilized for the pressure
studies. Diamonds with culet diameters of 300-700 µm were used to load large sam-
ples while allowing fine pressure control. Stainless steel gaskets were used for hous-
ing the sample. Pressure was determined using the ruby fluorescence method.10–12
A 2400 grooves/mm grating was used with a 300mm path length Andor Sham-
rock 300i spectrometer to measure small ruby shifts capable of resolving pressures
at 0.25 kBar. Pressures were averaged over 3-4 ruby pieces loaded with the TPP
sample. Annealed ruby pieces were used to obtain consistent ambient wavelength
shifts.
Microscopy and fluorescence studies were performed on an Olympus BH-
2 microscope system using Mitutoyo objectives (20x - 50x). Olympus C5060Z
and Sony DSC-F828 digital cameras were used to record pictures and video of the
sample. A home built circuit was used to take pictures at set intervals over hours
of experimental time. Polarized studies were performed using two linear polarizer
plates rotated 90 degrees with respect to each other. A white LED source was used
for illumination in transmittance mode while a blue LED was used for observing
phase transformations with higher contrast.
Low temperature (205-260 K) studies were performed on a home-built cham-
ber utilizing cold air flow. The temperature of the sample was monitored by a small
thermocouple placed near the diamond face and close to the sample chamber. Tem-
perature gradients across the sample were negligible as the entire cell was cooled
by air flow. A PID equipped heater was used to control the temperature within 1 de-
gree over hours of experimental time. The change in pressure with temperature was
calibrated by observing the wavelength shift of ruby with temperature at ambient
pressure and corrected by using data from previous studies.27
68
4.3 Analysis and Discussion
At ambient pressure conditions, the phase transformation of TPP takes place around
208 K to the higher density glacial phase. While a stark change in color is lacking,
there is an unmistakable change in the topology of the liquid, especially perceived
in thin ( 30-50 µm) samples. Transformations just above the glass transition tem-
perature show a distinct grainy pattern that slowly evolves to a more homogeneous
and clear phase over the course of hours as shown in figure 1. At slightly higher
temperatures for a given pressure, the topology of the new phase changes dramat-
ically, and likely points to the nucleation-growth type mechanism instead of spin-
odal decomposition, in complete agreement with those of Tanaka et al.8 reported at
1 atm.
Although the general morphology of the sample follows that shown by
Tanaka et al,8 its behavior with pressure differs towards the end of the transition.
Specifically, the pressure drop under isothermal conditions leads to a solid phase
that retains some of the grainy characteristics, but appears to be melded much more
in comparison to the mid point of the transition as shown in figure 2. Examination
under crossed polarizers reveals that the melded phase has crystalline components,
although no noticeable grain boundaries exist from the merging of the new domains.
While the size of the domains appears to be much smaller than that seen at higher
temperatures, the end phase appears to be a mixture of liquid and crystalline com-
ponents, suggesting the glacial phase is a liquid with extremely small crystallites
embedded in the matrix, as suggested earlier.28
Upon closer examination, it is noticed that the growth of the glacial phase
and that of the crystallites is not synchronous. In fact, during the first three quarters
of the transition time span, very little crystallinity is observed by way of birefrin-
69
230 minutes 272 minutes 282 minutes 300 minutes 308 minutes0 minutes
Figure 4.1: Microscopy of the glacial phase transition in TPP.
70
25 mins 75 mins 85 mins
Figure 4.2: Change in morphology of the glacial phase of TPP.
71
gence. However, towards the latter part of the transition, an exponential increase
in the amount of transmitted light is noticed. The result of this increase is shown
in figure 3, and suggests that crystallinity closely follows the pressure of the sam-
ple where the crystallites are allowed to nucleate and grow as the viscosity of the
sample decreases.
Further credence to the partial crystalline model is shown by heating a
quenched phase above the glass transition temperature. Starting with a pressure
quenched glass that has undergone the liquid 1 to glacial transformation, heating
inevitably leads to crystallization of the entire sample. It is noticed that the source
of nucleation in each crystallization case appears to be within the boundaries of the
glacial phase, suggesting that growth of nucleation sites is hampered at lower tem-
peratures, suggesting the model8 proposed earlier in which liquid 1 transforms to
glass II.
At higher temperatures, growth of the glacial phase proceeds through nucleation-
growth at room pressure and is noticeably different in appearance from the homoge-
nous grainy morphology of the spinodal phase. Most notably, the newly formed
domains no longer appear to be created homogeneously. Inside the diamond cell
chamber, phase progression is first noticed on the edges where the roughness cre-
ates more nucleation sites. By the time new domains are noticed towards the center
of the sample, the edge phase is further along in the development, which can be
followed by birefringence intensity. Towards the start, the domains appear to be
completely amorphous, and posses a very round shape indicative of immiscible
liquids. However, the new phase does not appear to be spherical, but rather disk
like as shown in figure 1 where overlapping disks can easily be identified due to
their transparency. Hence, a preferential growth direction is noticed even while the
sample appears to be amorphous under orthogonal polarizers.
72
10 20 30 40 50 60 70 80 90 100
0
10
20
30
40
50
Minutes From Start
Bire
frin
ge
nce
Lu
min
osi
ty (
%)
Figure 4.3: Quantification of the birefringence during TPP phase transformation.
73
Interestingly, the amount of measured birefringence is also different in the
nucleation growth region and appears to develop at later stages of phase evolution.
However, it is noticed that transmitted light through crossed polarizers first starts
to appear only in regions where two or more disks cross, suggesting that an unob-
servable amount of crystallinity is still present during early stages of glacial phase
growth. As the disks overlap, the path length of the transmitted light through the
glacial phase increases, and a birefringence effect is noticed only in these regions
of overlap. With further evolution, both the density and size of the crystallites in-
crease and thus transmitted light is noticed more readily across the entire sample.
Hence, the results seem to indicate that some crystallinity is present in the nucle-
ation growth region even during early periods of transformation to the glacial phase.
As pressure is applied to the system, the liquid 1 to glacial transition temper-
ature also increases. By 2.5 kBars of pressure, the required temperature is around
225 K, and further increases to 265 K by 4 kBars. Above 4 kBars of pressure,
the transition is yet to be seen. The behavior clearly proves the dependence of
the transition on a positive Clapeyron slope as shown in figure 4. In contrast, the
liquid-liquid phase transition in polyamorphic systems like water and silicon follow
a negative Clapeyron slope. This agrees with thermal data which shows an exother-
mic transition from liquid I to glass II, and a negative volume change due to the
higher density of the second phase.9 Most transformations above 2 kBar proceed
through a spinodal decomposition type morphology, although nucleation growth
dominates in later stages as the pressure drops due to the density difference. Based
on the observed behavior, a model phase diagram is constructed in figure 4 to fit
around the experimental data points. Its important to note that the lines do not have
any thermodynamic or quantitative significance, although the 1 atm data is based
on previous studies.8 In order for the liquid I to glass II transition to take place, the
74
Figure 4.4: Experimental phase diagram of TPP.
75
majority of the binodal and spinodal regions must be between the Tg/Pg lines since
the second phase cannot grow below Tg I and liquid II would crystallize above Tg II,
both behaviors that are not noticed during initially phase transformation. After fur-
ther isothermal growth, the sample eventually crystallizes, which is also explained
by the the pressure drop in which the stability field of the crystal is entered, and
is likely the global energy basin for the system in which both liquids eventually
crystallize. It can be argued that the heterogeneous nucleation line lies just above
Tg/Pg II, otherwise the transition would stop before entering the stability field of
the crystal. With the crystal being the highest density phase, its growth only pushes
the system further into its crystal region.
4.4 Conclusion
Phase transformation in TPP occurs in a similar manner at high pressure as it does
at ambient pressure, albeit at higher temperatures. Hence, the transition clearly
depends on a positive Clapeyron slope. At higher pressures, both spinodal decom-
position and nucleation growth type of morphology is observed, and the amount of
crystallinity is clearly lower during the former type. During nucleation growth, the
amount of crystallites likely evolve as the size of the domains increase and viscos-
ity of the sample decreases. In contrast, the crystallinity observed during spinodal
decomposition increases exponentially towards the very end of the transition, possi-
bly due to the pressure drop alone. In either case, the transitions occur very closely
above the predicted Tg-Pg line of phase I. It is suggested that the glass transition
line of phase II lies closely below the heterogenous nucleation line.
76
References
[1] O Mishima. Reversible first-order transition between two H2O amorphs at⇠0.2 GPa and 135 K. The Journal of chemical physics, 100:5910, 1994.
[2] Tomoko Sato and Nobumasa Funamori. Sixfold-coordinated amorphous poly-morph of SiO2 under high pressure. Phys. Rev. Lett., 101(25):255502, Dec2008.
[3] S Aasland and PF McMillan. Density-driven liquid-liquid phase separation inthe system Al2O3-Y2O3. Nature, 369(6482):633-636, 1994.
[4] Y Katayama, Y Inamura, T Mizutani, M Yamakata, W Utsumi, and O Shi-momura. Macroscopic separation of dense fluid phase and liquid phase ofphosphorus. Science, 306(5697):848, 2004.
[5] Y Katayama. Macroscopic separation of dense fluid phase and liquid phase ofphosphorus. Science, 306(5697):848-851, Oct 2004.
[6] Tetsuya Morishita. High density amorphous form and polyamorphic transfor-mations of silicon. Phys. Rev. Lett., 93(5):055503, Jul 2004.
[7] A Ha, I Cohen, X Zhao, M Lee, and D Kivelson. Supercooled liquids andpolyamorphism.
[8] Hajime Tanaka, Rei Kurita, and Hiroshi Mataki. Liquid-liquid transition inthe molecular liquid triphenyl phosphite. pages 1-4, Jan 2004.
[9] B.G Demirjian, G Dosseh, A Chauty, M.L Ferrer, D Morineau, C Lawrence,K Takeda, D Kivelson, and S Brown. Metastable solid phase at the crystalline-amorphous border: The glacial phase of triphenyl phosphite. The Journal ofPhysical Chemistry B, 105(11):2107-2116, 2001.
[10] I Cohen, A Ha, X Zhao, M Lee, T Fischer, M.J Strouse, and D Kivelson. Alow-temperature amorphous phase in a fragile glass-forming substance. TheJournal of Physical Chemistry, 100(20):8518-8526, 1996.
[11] S Dvinskikh, G Benini, J Senker, M Vogel, J Wiedersich, A Kudlik, andE Rossler. Molecular motion in the two amorphous phases of triphenyl phos-phite. The Journal of Physical Chemistry B, 103(10):1727-1737, 1999.
[12] GP Johari and C Ferrari. Calorimetric and dielectric investigations of thephase transformations and glass transition of triphenyl phosphite. The Journalof Physical Chemistry B, 101(49):10191-10197, 1997.
[13] J Senker, J Sehnert, and S Correll. Microscopic description of the polyamor-phic phases of triphenyl phosphite by means of multidimensional solid-stateNMR spectroscopy. Journal of the American Chemical Society, 127(1):337-349, 2005.
77
[14] J Senker and E Rossler. Determination of the local disorder in the polyamor-phic phases of triphenyl phosphite. The Journal of Physical Chemistry B,106(31):7592-7595, 2002.
[15] J Senker and E Rossler. Triphenyl phosphite: a candidate for liquid polyamor-phism. Chemical Geology, 174(1-3):143-156, 2001.
[16] J Senker and J Ludecke. Structure determination for the crystalline phase oftriphenyl phosphite by means of multi-dimensional solid-state NMR and x-raydiffraction. Zeitschrift fur Naturforschung B, 56(11):1089-1099, 2001.
[17] R Lefort, A Hedoux, Y Guinet, E Cochin, and M Descamps. Fast intramolec-ular dynamics of triphenyl phosphite investigated by 2H NMR. The EuropeanPhysical Journal B-Condensed Matter and Complex Systems, 30(4):519-525,2002.
[18] A Hedoux, Y Guinet, M Descamps, and A Benabou. Raman scattering in-vestigation of the glaciation process in triphenyl phosphite. The Journal ofPhysical Chemistry B, 104(49):11774-11780, 2000.
[19] A Hedoux, Y Guinet, and M Descamps. Raman signature of polyamorphismin triphenyl phosphite. Physical Review B, 58(1):31-34, 1998.
[20] P Derollez, O Hernandez, A Hedoux, Y Guinet, O Masson, J Lefebvre, andM Descamps. Structural and microstructural description of the glacial state intriphenyl phosphite from powder synchrotron x-ray diffraction data and ramanscattering investigations. Journal of molecular structure, 694(1-3):131-138,2004.
[21] A Hedoux, Y Guinet, M Descamps, and J Lefebvre. Raman scattering and x-ray diffraction investigations about the polyamorphism in triphenyl phosphite.Phase Transitions: A Multinational Journal, 76(9-10):831-836, 2003.
[22] A Hedoux, O Hernandez, J Lefebvre, Y Guinet, and M Descamps. Meso-scopic description of the glacial state in triphenyl phosphite from an x-raydiffraction experiment. Physical Review B, 60(13):9390, 1999.
[23] L Merrill and W.A Bassett. Miniature diamond anvil pressure cell for singlecrystal x-ray diffraction studies. Review of Scientific Instruments, 45(2):290-294, 1974.
[24] H Mao and J Xu. . . . Calibration of the ruby pressure gauge to 800 kbar underquasi-hydrostatic conditions. J. Geophys. Res, Jan 1986.
[25] J Barnett, S Block, and G Piermarini. An optical fluorescence system for quan-titative pressure measurement in the diamond anvil cell. Review of ScientificInstruments, Jan 1973.
78
[26] W.B Holzapfel. Refinement of the ruby luminescence pressure scale. Journalof applied physics, 93:1813, 2003.
[27] J Yen and M Nicol. Temperature dependence of the ruby lumines-cence method for measuring high pressures. Journal of applied physics,72(12):5535, 1992.
[28] A Hedoux, Y Guinet, P Derollez,O Hernandez,R Lefort, and M Descamps. Acontribution to the understanding of the polyamorphism situation in triphenylphosphite. Phys. Chem. Chem. Phys. , 6:3192-3199, 2004.
79
REFERENCES
Chapter 1 References:
[1] S.A Brawer. Theory of relaxation in viscous liquids and glasses. The Journalof Chemical Physics, 81(2):954, 1984.
[2] Jonathan F. Stebbins. NMR evidence for five-coordinated silicon in a silicateglass at atmospheric pressure. Nature, 351:638–639, 1991.
[3] Michael Toplis, Donald B. Dingwell, and Tommaso Lenci. Peraluminous vis-cosity maxima in Na2O-Al2O3-SiO2 liquids: The role of triclusters in tectosil-icate melts. Geochimica et Cosmochimica Acta, 61(13):2605–2612, 1997.
[4] Harve S. Waff. Pressure-induced coordination changes in magmatic liquids.Geophysical Research Letters, 2(5):193–196, 1975.
[5] S Chakraborty, R Knoche, H Schulze, D.C Rubie, D Dobson, N.L Ross, andR.J Angel. Enhancement of cation diffusion rates across the 410-kilometerdiscontinuity in earth’s mantle. Science, 283:362–365, 1999.
[6] I Kushiro. Changes in viscosity and structure of melt of NaAlSi2O6 composi-tion at high pressures. Journal of Geophysical Research, 81(35):6347–6350,1976.
[7] I Kushiro, H.S Yoder, and B.O Mysen. Viscosities of basalt and andesite meltsat high pressures. Journal of Geophysical Research, 81(35):6351–6356, 1976.
[8] Jeffrey R. Allwardt, Brent T. Poe, and Jonathan F. Stebbins. The effect offictive temperature on al coordination in high-pressure (10 GPa) sodium alu-minosilicate glasses. American Mineralogist, 90(8-9):1453–1457, 2005.
[9] Dominique Massiot, Dominique Trumeau, Bruno Touzo, Ian Farnan, Jean-Claude Rifflet, Andre Douy, and Jean-Pierre Coutures. Structure and dynam-ics of CaAl2O4 from liquid to glass: A high-temperature 27Al NMR time-resolved study. The Journal of Physical Chemistry, 99(44):16455–16459,1995.
[10] Qiang Mei, Chris J. Benmore, J.K. Richard Weber, Martin Wilding, J Kim,and J Rix. Diffraction study of calcium aluminate glasses and melts: Ii. highenergy x-ray diffraction on melts. Journal of Physics: Condensed Matter,20(24):245107, 2008.
[11] Daniel R. Neuville, Laurent Cormier, D. De Ligny, J Roux, A-M Flank, andP Lagarde. Environments around Al, Si, and Ca in aluminate and aluminosil-icate melts by x-ray absorption spectroscopy at high temperature. AmericanMineralogist, 93:228–234, 2008.
80
[12] Brent T. Poe, Paul F. McMillan, Bertrand Cote, Dominique Massiot, and Jean-Pierre Coutures. Magnesium and calcium aluminate liquids: in situ high-temperature 27Al NMR spectroscopy. Science, 259(5096):786, 1993.
[13] Brent T. Poe, Paul F. McMillan, David C. Rubie, Sumit Chakraborty, JeffYarger, and Jason Diefenbacher. Silicon and oxygen self-diffusivities in sili-cate liquids measured to 15 gigapascals and 2800 kelvin. Science, 276:1245–1248, 1997.
[14] Brent T. Poe, Paul F. McMillan, Bertrand Cote, Dominique Massiot, and Jean-Pierre Coutures. Structure and dynamics in calcium aluminate liquids: High-temperature 27Al NMR and Raman spectroscopy. Journal of the AmericanCeramic Society, 77(7):1832–1838, 1994.
[15] Jeffery L. Yarger, K.H Smith, Ronald A. Nieman, J Diefenbacher, George H.Wolf, Brent T. Poe, and Paul F. McMillan. Al coordination changes in high-pressure aluminosilicate liquids. Science, 270(5244):1964–1967, 1995.
[16] Eugenie V. Uhlmann, Michael C. Weinberg, Norbert J. Kreidl, Lori L.Burgner, Raymond Zanoni, and Kenneth H. Church. Spectroscopic proper-ties of rare-earth-doped calcium-aluminate-based glasses. Journal of Non-Crystalline Solids, 178:15–22, 1994.
[17] Kimberly E. Kelsey, Jonathan F. Stebbins, Jed L. Mosenfelder, and Paul D.Asimow. Simultaneous aluminum, silicon, and sodium coordination changesin 6 GPa sodium aluminosilicate glasses. American Mineralogist, 94:1205–1215, 2009.
[18] Sung Keun Lee, George D. Cody, Yingwei Fei, and Bjorn O. Mysen. Natureof polymerization and properties of silicate melts and glasses at high pressure.Geochimica et Cosmochimica Acta, 68(20):4189–4200, 2004.
[19] Sung Keun Lee, George D. Cody, Yingwei Fei, and Bjorn O. Mysen. Theeffect of Na/Si on the structure of sodium silicate and aluminosilicate glassesquenched from melts at high pressure: A multi-nuclear (Al-27, Na-23, O-17)1D and 2D solid-state NMR study. Chemical Geology, 229:162–172, 2006.
[20] Sung Keun Lee, George D. Cody, Yingwei Fei, and Bjorn O. Mysen. Oxygen-17 nuclear magnetic resonance study of the structure of mixed cation calcium-sodium silicate glasses at high pressure: Implications for molecular link toelement partitioning between silicate liquids and crystals. Journal of PhysicalChemistry B, 112:11756–11761, 2008.
[21] Sung Keun Lee. Effect of pressure on structure of oxide glasses at high pres-sure: Insights from solid-state NMR of quadrupolar nuclides. Solid StateNuclear Magnetic Resonance, 38(45-57), 2010.
81
[22] Jonathan F. Stebbins, Scott Kroeker, Sung Keun Lee, and T.J. Kiczenski.Quantification of five-and six-coordinated aluminum ions in aluminosilicateand fluoride-containing glasses by high-field, high-resolution 27Al NMR.Journal of Non-Crystalline Solids, 275:1–6, 2000.
[23] Sung Keun Lee, Michael Deschamps, Julien Hiet, Dominique Massiot, andSun Young Park. Connectivity and proximity between quadrupolar nuclidesin oxide glasses: Insights from through-bond and through-space correlationsin solid-state NMR. Journal of Physical Chemistry B, 113(15):5162–5167,2009.
[24] Sung Keun Lee and Jonathan F. Stebbins. The degree of aluminum avoidancein aluminosilicate glasses. American Mineralogist, 84:937–945, 1999.
[25] Chris J. Benmore, J.K.Richard Weber, Sujatha Sampath, Joan Siewenie,J Urquidi, and J.A Tangeman. A neutron and x-ray diffraction study of cal-cium aluminate glasses. Journal of Physics: Condensed Matter, 15:S2413,2003.
[26] Paul F. McMillan, William T. Petuskey, Bertrand Cote, Dominique Massiot,Claude Landron, and Jean-Pierre Coutures. A structural investigation ofCaO-Al2O4 glasses via 27Al MAS-NMR. Journal of Non-Crystalline Solids,195:261–271, 1996.
[27] Qiang Mei, Chris J. Benmore, Joan Siewenie, J.K. Richard Weber, and MartinWilding. Diffraction study of calcium aluminate glasses and melts: I. high en-ergy x-ray and neutron diffraction on glasses around the eutectic composition.Journal of Physics: Condensed Matter, 20(24):245106, 2008.
[28] Laurent Cormier, Daniel R. Neuville, and Georges Calas. Structure andproperties of low-silica calcium aluminosilicate glasses. Journal of Non-Crystalline Solids, 274(1-3):110–114, 2000.
[29] Eun-Tae Kang, Seong-Joo Lee, and Alex C. Hannon. Molecular dynamicssimulations of calcium aluminate glasses. Journal of Non-Crystalline Solids,352(8):725–736, 2006.
[30] H Morikawa, F Marumo, T Koyama, M Yamane, and A Oyobe. Structuralanalysis of 12CaO.7Al2O3 glass. Journal of Non-Crystalline Solids, 56:355–360, 1983.
[31] Daniel R. Neuville, Laurent Cormier, and Dominique Massiot. Al coordina-tion and speciation in calcium aluminosilicate glasses: Effects of compositiondetermined by 27Al MQ-MAS NMR and Raman spectroscopy. Chemical Ge-ology, 229(1-3):173–185, 2006.
[32] S Ito, K Suzuki, M Inagaki, and S Naka. High-pressure modifications ofCaAl2O4 and CaGa2O4. Materials Research Bulletin, 15:925–932, 1980.
82
[33] B Lazic, V Kahlenberg, J Konzett, and R Kaindl. On the polymorphism ofCaAl2O4-structural investigations of two high pressure modifications. SolidState Sciences, 8:589–597, 2006.
[34] Qiang Mei, Chris J. Benmore, Sujatha Sampath, J.K. Richard Weber, KurtLeinenweber, Samrat A. Amin, Paul Johnston, and Jeffery L Yarger. Thestructure of permanently densified CaAl2O4 glass. Journal of Physics andChemistry of Solids, 67(9-10):2106–2110, 2006.
[35] Isabelle Daniel, Paul F. McMillan, Philippe Gillet, and Brent T. Poe. Ramanspectroscopic study of structural changes in calcium aluminate (CaAl2O4)glass at high pressure and high temperature. Chemical Geology, 128(1-4):5–15, 1996.
[36] J.K. Richard Weber, J.J Felten, and Paul C. Nordine. Laser hearth melt pro-cessing of ceramic materials. Review of Scientific Instruments, 67(2):522–524,1996.
[37] D Massiot, C Bessada, J.P Coutures, and F Taulelle. A quantitative study of27Al MAS NMR in crystalline YAG. Journal of Magnetic Resonance, 90:231–242, 1990.
[38] Lucio Frydman and John S. Harwood. Isotropic spectra of half-integerquadrupolar spins from bidimensional magic-angle spinning NMR. Journalof the American Chemical Society, 117(19):5367–5368, 1995.
[39] Ales Medek, John S. Harwood, and Lucio Frydman. Multiple-quantummagic-angle spinning NMR: a new method for the study of quadrupolar nu-clei in solids. Journal of the American Chemical Society, 117:12779–12787,1995.
[40] Jean-Paul Amoureux, Christian Fernandez, and Stefan Steuernagel. Z filter-ing in MQMAS NMR. Journal of magnetic resonance. Series A, 123(1):116,1996.
[41] E Lippmaa, A Samoson, and M Magi. High-resolution 27Al NMR of alumi-nosilicates. Journal of the American Chemical Society, 108(8):1730–1735,1986.
[42] A Samoson. Satellite transition high-resolution NMR of quadrupolar nucleiin powders. Chemical Physics Letters, 119(1):29–32, 1985.
[43] Jorgen Skibsted, Eric Henderson, and Hans J. Jakobsen. Characterization ofcalcium aluminate phases in cements by 27Al MAS NMR spectroscopy. Inor-ganic chemistry, 32:1013–1027, 1993.
[44] G Czjzek, J Fink, F Gotz, H Schmidt, J Coey, J-P Rebouillat, and A Lienard.Atomic coordination and the distribution of electric field gradients in amor-phous solids. Physical Review B, 23(6):2513–2530, 1981.
83
[45] G Le Caer and R. A. Brand. General models for the distributions of electricfield gradients in disordered solids. Journal of Physics: Condensed Matter,10:10715–10774, 1998.
[46] Jean Baptiste d’Espinose de Lacaillerie, Christian Fretigny, and DominiqueMassiot. Mas NMR spectra of quadrupolar nuclei in disordered solids: TheCzjzek model. Journal of Magnetic Resonance, 192(2):244–251, 2008.
[47] Dominique Massiot, Franck Fayon, Mickael Capron, Ian King, Stephanie LeCalve, Bruno Alonso, Jean-Olivier Durand, Bruno Bujoli, Zhehong Gan, andGina Hoatson. Modelling one-and two-dimensional solid-state NMR spectra.Magnetic Resonance in Chemistry, 40:70–76, 2002.
[48] Christian Jager. How to get more from 27Al MAS NMR by high-speedsatellite-transition spectroscopy. Journal of Magnetic Resonance, 99(2):353–362, 1992.
[49] Jonathan F. Stebbins, Sung Keun Lee, and Jane V. Oglesby. Al-O-Al oxy-gen sites in crystalline aluminates and aluminosilicate glasses; high-resolutionoxygen-17 NMR results. American Mineralogist, 84(5-6):983, 1999.
[50] Daniel R. Neuville, Grant S. Henderson, Laurent Cormier, and DominiqueMassiot. The structure of crystals, glasses, and melts along the CaO-Al2O3join: Results from Raman, Al l- and k-edge x-ray absorption, and 27Al NMRspectroscopy. American Mineralogist, 95:1580–1589, 2010.
[51] Dinu Iuga, Claudia Morais, Zhehong Gan, Daniel R. Neuville, LaurentCormier, and Dominique Massiot. NMR heteronuclear correlation betweenquadrupolar nuclei in solids. Journal of the American Chemical Society,127:11540–11541, 2005.
[52] Volker Kahlenberg, Reinhard X. Fischer, and Cliff S.J. Shaw. High-pressureCa4Al6O13: An example of a calcium aluminate with three different types ofcoordination polyhedra for aluminum. American Mineralogist, 85(10):1492–1496, 2000.
[53] Jeffrey R. Allwardt, Jonathan F. Stebbins, Burkhard C. Schmidt, Daniel J.Frost, Anthony C. Withers, and Marc M. Hirschmann. Aluminum coordina-tion and the densification of high-pressure aluminosilicate glasses. AmericanMineralogist, 90:1218–1222, 2005.
[54] George H. Wolf, Dan J. Durben, and Paul F. McMillan. High-pressure Ramanspectroscopic study of sodium tetrasilicate (Na2Si4O9) glass. The Journal ofChemical Physics, 93(4):2280–2288, 1990.
84
[55] L-S Du, J.R Allwardt, B.C Schmidt, and J.F Stebbins. Pressure-induced struc-tural changes in a borosilicate glass-forming liquid: boron coordination, non-bridging oxygens, and network ordering. Journal of Non-Crystalline Solids,337:196–200, 2004.
[56] Sung Keun Lee. Simplicity in melt densification in multicomponent mag-matic reservoirs in earth’s interior revealed by multinuclear magnetic reso-nance. Proceedings of the National Academy of Sciences, 108(17):6847–6852,2011.
[57] P. Florian, N. Sadiki, D. Massiot, and J.P. Coutures. 27Al NMR study of thestructure of lanthanum- and yttrium-based aluminosilicate glasses and melts.Journal of Physical Chemistry B, 111:9747–9757, 2007.
85
Chapter 2 References:
[1] Francis Birch. Finite elastic strain of cubic crystals. Physical Review,71(11):809–824, 1947.
[2] F.D. Murnaghan. The compressibility of media under extreme pressures. Pro-ceedings of the National Academy of Sciences, 30(9):244–247, 1944.
[3] P.W. Bridgman. The compression of twenty-one halogen compounds andeleven other simple substances to 100,000 kg/cm2. Proceedings of the Amer-ican Academy of Arts and Sciences, 76(1):1–7, 1945.
[4] P.W. Bridgman. The compression of sixty-one solid substances to 25,000kg/cm2, determined by a new rapid method. Proceedings of the AmericanAcademy of Arts and Sciences, 76(1):9–24, 1945.
[5] J. Dyson. Precise measurement by image-splitting. Journal of the OpticalSociety of America, 50(8):754–757, 1960.
[6] Charles Meade and Raymond Jeanloz. Frequency-dependent equation of stateof fused silica to 10 GPa. Physical Review B, 35(1):236–244, 1987.
[7] Cassie Scott and Raymond Jeanloz. Optical length determinations in thediamond-anvil cell. Review of Scientific Instruments, 55(4):558–562, 1984.
[8] K.H. Smith, E. Shero, A. Chizmeshya, and G.H. Wolf. The equation of stateof polyamorphic germania glass: A two-domain description of the viscoelasticresponse. Journal of Chemical Physics, 102(17):6851–6857, 1995.
[9] Joop van Straaten and Isaac F. Silvera. Equation of state of solid molecular h2and d2 at 5 k. Physical Review B, 37(4):1989–2000, 1988.
[10] Yoshinori Katayama, Kazuhiko Tsuji, Osamu Shimomura, Takumi Kikegawa,Mohamed Mezouar, Domingo Martinez-Garcia, Jean Michel Besson, DanielHausermann, and Michael Hanfland. Density measurements of liquid un-der high pressure and high temperature. Journal of Synchrotron Radiation,5:1023–1025, 1998.
[11] Y. Katayama, K. Tsuji, J.-Q. Chen, N. Koyama, T. Kikegawa, K. Yaoita, andO. Shimomura. Density of liquid tellurium under high pressure. Journal ofNon-Crystalline Solids, 156-158:687–690, 1993.
[12] Y. Katayama, K. Tsuji, H. Kanda, H. Nosaka, K. Yaoita, T. Kikegawa, andO. Shimomura. Density of liquid tellurium under pressure. Journal of Non-Crystalline Solids, 205-207:451–454, 1996.
[13] Xinguo Hong, Guoyin Shen, Vitali B. Prakapenka, Mark L. Rivers, andStephen R. Sutton. Density measurements of noncrystalline materials at
86
high pressure with diamond anvil cell. Review of Scientific Instruments,78(10):103905, 2007.
[14] Yanbin Wang, Takeyuki Uchida, Frank Westferro, Mark L. Rivers, NorimasaNishiyama, Jeff Gebhardt, Charles E. Lesher, and Steve R. Sutton. High-pressure x-ray tomography microscope: Synchrotron computed microtomog-raphy at high pressure and temperature. Review of Scientific Instruments,76:073709, 2005.
[15] Leo Merrill and William A. Bassett. Miniature diamond anvil pressure cellfor single crystal x-ray diffraction studies. Review of Scientific Instruments,45(2):290–294, 1974.
[16] Ross J. Angel, Maciej Bujak, Jing Zhao, G. Diego Gatta, and Steven D. Ja-cobsen. Effective hydrostatic limits of pressure media for high-pressure crys-tallographic studies. Journal of Applied Crystallography, 40:26–32, 2007.
[17] H.K. Mao, J. Xu, and P.M. Bell. Calibration of the ruby pressure gauge to 800kbar under quasi-hydrostatic conditions. Journal of Geophysical Research,91(B5):4673–4676, 1986.
[18] J.D. Barnett, S. Block, and G.J. Piermarini. An optical fluorescence systemfor quantitative pressure measurement in the diamond anvil cell. Review ofScientific Instruments, 44(1):1–8, 1973.
[19] Wilfried B. Holzapfel. Refinement of the ruby luminescence pressure scale.Journal of Applied Physics, 93(3):1813–1818, 2003.
[20] John Canny. A computational approach to edge detection. IEEE Transac-tions on Pattern Analysis and Machine Intelligence, PAMI-8(6):679–698, Apr1986.
[21] Jon H. Eggert, Liwen Xu, Rongzheng Che, Liangchen Chen, and Jifang Wang.High pressure refractive index measurements of 4:1 methanol:ethanol. Jour-nal of applied physics, 72(6):2453–2461, 1992.
[22] D.W. Piston. Choosing objective lenses: The importance of numerical aper-ture and magnification in digital optical microscopy. The Biological Bulletin,195(1):1–4, 1998.
[23] C.J. Benmore, E. Soignard, M. Guthrie, S.A. Amin, J.K.R. Weber, K. McKier-nan, M.C. Wilding, and J.L. Yarger. High pressure x-ray diffraction measure-ments on Mg2SiO4 glass. Journal of Non-Crystalline Solids, 357(14):2632–2636, Jan 2011.
[24] E. Soignard, S.A. Amin, Q. Mei, C.J. Benmore, and J.L. Yarger. High-pressure behavior of As2O3: Amorphous-amorphous and crystalline-amorphous transitions. Physical Review B, 77(14):144113, Apr 2008.
87
[25] Q Mei, C.J. Benmore, R.T. Hart, E. Bychkov, P.S. Salmon, C.D. Martin,F.M. Michel, S.M. Antao, P.J. Chupas, P.L. Lee, S.D. Shastri, J.B. Parise,K. Leinenweber, S. Amin, and J.L. Yarger. Topological changes in glassyGeSe2 at pressures up to 9.3 GPa determined by high-energy x-ray and neu-tron diffraction measurements. Physical Review B, 74(1):014203, 2006.
[26] L. Cartz, S.R. Srinivasa, R.J. Riedner, J.D. Jorgensen, and T.G. Worlton. Ef-fect of pressure on bonding in black phosphorus. The Journal of ChemicalPhysics, 71(4):1718–1721, 1979.
[27] Takumi Kikegawa and Hiroshi Iwasaki. An x-ray diffraction study of latticecompression and phase transition of crystalline phosphorus. Acta Crystallo-graphica Section B: Structural Science, B39:158–164, 1983.
[28] Erin N. Oelker, Emmanuel Soignard, Keri A. McKiernan, Chris J. Benmore,and Jeffery L. Yarger. Pressure-induced crystallization of amorphous redphosphorus. Solid State Communications, in press, 2011.
[29] Joseph M. Zaug, Alan K. Soper, and Simon M. Clark. Pressure-dependentstructures of amorphous red phosphorus and the origin of the first sharpdiffraction peaks. Nature Materials, 7(11):890–899, 2008.
88
Chapter 3 References:
[1] D.J. Wilbur, T. DeFries, and J. Jonas. Self-diffusion in compressed liquidheavy water. Journal of Chemical Physics, 65(5):1783–1786, 1976.
[2] D.J. Wilbur and J. Jonas. Fourier transform NMR in liquids at high pres-sure. iii. spin-lattice relaxation in toluene-d8. Journal of Chemical Physics,62(7):2800–2807, 1975.
[3] D.J. Wilbur and J. Jonas. NMR fourier transform spectroscopy at high pres-sure. Journal of Chemical Physics, 55(12):5840–5841, 1971.
[4] D Vander Velde and J JONAS. A high-pressure probe for NMR studies ofhomogeneous catalysts. Journal of Magnetic Resonance, 1987.
[5] Shantha Samarasinghe, Douglas M. Campbell, Ana Jonas, and Jiri Jonas.High-resolution NMR study of the pressure-induced unfolding of lysozyme.Biochemistry, 31(34):7773–7778, 1992.
[6] Xiangdong Peng, Ana Jonas, and Jiri Jonas. One and two dimensional 1H-NMR studies of pressure and tetracaine effects on sonicated phospholipidvesicles. Chemistry and Physics of Lipids, 75:59–69, 1995.
[7] Xiangdong Peng, Jiri Jonas, and Jerson L. Silva. Molten-globule conforma-tion of arc repressor monomers determined by high-pressure 1H NMR spec-troscopy. Proceedings of the National Academy of Sciences, 90:1776–1780,1993.
[8] X. Peng and J. Jonas. High-pressure phosphorus-31 NMR study of dipalmi-toylphosphatidylcholine bilayers. Biochemistry, 31(28):6383–6390, 1992.
[9] Bao-Shiang Lee, Stephanie A. Mabry, Ana Jonas, and Jiri Jonas. High-pressure proton NMR study of lateral self-diffusion of phosphatidylcholines insonicated unilamellar vesicles. Chemistry and Physics of Lipids, 78:103–117,1995.
[10] J. Jonas. High-resolution nuclear magnetic resonance studies of proteins.Biochimica et Biophysica Acta, 1595:145–159, 2002.
[11] J. Jonas, L. Ballard, and D. Nash. High-resolution, high-pressure NMR studiesof proteins. Biophysical Journal, 75:445–452, 1998.
[12] J Jonas and A Jonas. High-pressure NMR spectroscopy of proteins and mem-branes. Annual Review of Biophysics and Biomolecular Structure, 23:287–318, 1994.
[13] J. Jonas, P. Kozoil, X. Peng, C. Reiner, and D.M. Campbell. High-resolutionNMR spectroscopy at high pressures. Journal of Magnetic Resonance. SeriesB, 102(3):299–309, 1993.
89
[14] J. Jonas and Y.T. Lee. NMR and laser Raman scattering studies of fluids athigh pressure. Journal of Physics: Condensed Matter, 4(2), 1992.
[15] J. Jonas, C.-L. Xie, A. Jonas, P.J. Grandinetti, D. Campbell, and D. Driscoll.High-resolution 13C NMR study of pressure effects on the main phase transi-tion in l-a-dipalmitoyl phosphatidylcholine vesicles. Proceedings of the Na-tional Academy of Sciences, 85:4115–4117, 1988.
[16] Jiri Jonas. Nuclear magnetic resonance at high pressures. Annual Review ofPhysical Chemistry, 26:167–190, 1975.
[17] J Jonas, TE Bull, and CA Eckert. High pressure sample cell for the NMRrelaxation time measurements in liquids. Review of Scientific Instruments,41:1240, 1970.
[18] S.T. Adamy, P.J. Grandinetti, Y. Masuda, D. Campbell, and J. Jonas. High-pressure nuclear-magnetic-resonance study of carbon-13 relaxation in 2-ethylhexyl benzoate and 2-ethylhexyl cyclohexanecarboxylate. Journal ofChemical Physics, 94(5):3566–3576, 1991.
[19] DA Driscoll, J Jonas, and A Jonas. High pressure 2H nuclear magnetic reso-nance study of the gel phases of dipalmitoylphosphatidylcholine. Chemistryand Physics of Lipids, 58(1-2):97–104, 1991.
[20] T DeFries and J Jonas. Pressure dependence of NMR proton spin-lattice re-laxation times and shear viscosity in liquid water in the temperature range-15-10c. Journal of Chemical Physics, 66(3):896–901, 1977.
[21] L Ballard, A Yu, C Reiner, and J Jonas. A high-pressure, high-resolutionNMR probe for experiments at 500 mhz. Journal of Magnetic Resonance,133:190–193, 1998.
[22] L Ballard and J Jonas. High pressure NMR. Annual Reports on NMR Spec-troscopy, 1997.
[23] L Ballard, C Reiner, and J Jonas. High-resolution NMR probe for experimentsat high pressures. Journal of Magnetic Resonance, Series A, 123(1):81–86,1996.
[24] J.L. Yarger, R.A. Nieman, G.H. Wolf, and R.F. Marzke. High-pressure 1H and13C nuclear magnetic resonance in a diamond anvil cell. Journal of MagneticResonance, Series A, 114(2):255–257, 1995.
[25] Takuo Okuchi, George D. Cody, Ho-Kwang Mao, and Russell J. Hemley. Hy-drogen bonding and dynamics of methanol by high-pressure diamond-anvilcell NMR. Journal of Chemical Physics, 122(24):244509, 2005.
90
[26] R.F. Marzke, D.P. Raffaelle, K.E. Halvorson, and G.H. Wolf. A 1H NMRstudy of glycerol at high pressure. Journal of Non-Crystalline Solids, 172-174:401–407, 1994.
[27] Sam-Hyeon Lee, K Luszczynski, R.E. Norberg, and M.S. Conradi. NMR in adiamond anvil cell. Review of Scientific Instruments, 58(3):415, 1987.
[28] R Bertani, M Mali, J Roos, and D Brinkmann. A diamond anvil cell for high-pressure NMR investigations. Review of Scientific Instruments, 63(6):3303–3306, 1992.
[29] Markus Hakes and Manfred D. Zeidler. High-pressure NMR study of liquidpropanol up to 3 GPa. Physical Chemistry Chemical Physics, 4(20):5119–5122, 2002.
[30] C. Massin, F. Vincent, A. Homsy, K. Ehrmann, G. Boero, P.-A. Besse, A. Dari-don, E. Verpoorte, N.F. de Rooij, and R.S. Popovic. Planar microcoil-basedmicrofluidic NMR probes. Journal of Magnetic Resonance, 164:242–255,2003.
[31] Sam-Hyeon Lee, Mark S. Conradi, and R.E. Norberg. Improved NMR res-onator for diamond anvil cells. Review of Scientific Instruments, 63(7):3674–3676, 1992.
[32] Michael G. Pravica and Isaac F. Silvera. Nuclear magnetic resonance in adiamond anvil cell at very high pressures. Review of Scientific Instruments,69(2):479–484, 1998.
[33] Takuo Okuchi, Russell J. Hemley, and Ho-Kwang Mao. Radio frequencyprobe with improved sensitivity for diamond anvil cell nuclear magnetic res-onance. Review of Scientific Instruments, 76(2):026111, 2005.
[34] Michael G. Pravica and Isaac F. Silvera. NMR study of ortho-para conversionat high pressure in hydrogen. Physical Review Letters, 81(19):4180–4183,1998.
[35] E.L. Hahn. Spin echoes. Physical Review, 80(4):580, 1950.
[36] H.Y Carr and E.M Purcell. Effects of diffusion on free precession in nuclearmagnetic resonance experiments. Physical Review, 94(3):630, 1954.
[37] S Meiboom and D Gill. Modified spin-echo method for measuring nuclearrelaxation times. Review of Scientific Instruments, 29(8):688–691, 1958.
[38] H.K. Mao, J. Xu, and P.M. Bell. Calibration of the ruby pressure gauge to 800kbar under quasi-hydrostatic conditions. Journal of Geophysical Research,91(B5):4673–4676, 1986.
91
[39] J.D. Barnett, S. Block, and G.J. Piermarini. An optical fluorescence systemfor quantitative pressure measurement in the diamond-anvil cell. Review ofScientific Instruments, 44(1):1–9, 1973.
[40] Wilfried B. Holzapfel. Refinement of the ruby luminescence pressure scale.Journal of applied physics, 93(3):1813–1818, 2003.
[41] Daniel Solli and Raymond Jeanloz. Nonmetallic gaskets for ultrahigh pres-sure diamond-cell experiments. Review of Scientific Instruments, 72(4):2110–2113, 2001.
[42] J. Jonas and J.A Akai Transport processes in compressed liquid methanol.Journal of Chemical Physics, 66:4946, 1977.
[43] D. P. Raffaelle. Proton Nuclear Magnetic Resonance of Molecular Liquids atHigh Pressure in the Diamond Anvil Cell. PhD thesis, Arizona State Univer-sity, 1993.
92
Chapter 4 References:
[1] O Mishima. Reversible first-order transition between two H2O amorphs at⇠0.2 GPa and 135 K. The Journal of chemical physics, 100:5910, 1994.
[2] Tomoko Sato and Nobumasa Funamori. Sixfold-coordinated amorphous poly-morph of SiO2 under high pressure. Phys. Rev. Lett., 101(25):255502, Dec2008.
[3] S Aasland and PF McMillan. Density-driven liquid-liquid phase separation inthe system Al2O3-Y2O3. Nature, 369(6482):633-636, 1994.
[4] Y Katayama, Y Inamura, T Mizutani, M Yamakata, W Utsumi, and O Shi-momura. Macroscopic separation of dense fluid phase and liquid phase ofphosphorus. Science, 306(5697):848, 2004.
[5] Y Katayama. Macroscopic separation of dense fluid phase and liquid phase ofphosphorus. Science, 306(5697):848-851, Oct 2004.
[6] Tetsuya Morishita. High density amorphous form and polyamorphic transfor-mations of silicon. Phys. Rev. Lett., 93(5):055503, Jul 2004.
[7] A Ha, I Cohen, X Zhao, M Lee, and D Kivelson. Supercooled liquids andpolyamorphism.
[8] Hajime Tanaka, Rei Kurita, and Hiroshi Mataki. Liquid-liquid transition inthe molecular liquid triphenyl phosphite. pages 1-4, Jan 2004.
[9] B.G Demirjian, G Dosseh, A Chauty, M.L Ferrer, D Morineau, C Lawrence,K Takeda, D Kivelson, and S Brown. Metastable solid phase at the crystalline-amorphous border: The glacial phase of triphenyl phosphite. The Journal ofPhysical Chemistry B, 105(11):2107-2116, 2001.
[10] I Cohen, A Ha, X Zhao, M Lee, T Fischer, M.J Strouse, and D Kivelson. Alow-temperature amorphous phase in a fragile glass-forming substance. TheJournal of Physical Chemistry, 100(20):8518-8526, 1996.
[11] S Dvinskikh, G Benini, J Senker, M Vogel, J Wiedersich, A Kudlik, andE Rossler. Molecular motion in the two amorphous phases of triphenyl phos-phite. The Journal of Physical Chemistry B, 103(10):1727-1737, 1999.
[12] GP Johari and C Ferrari. Calorimetric and dielectric investigations of thephase transformations and glass transition of triphenyl phosphite. The Journalof Physical Chemistry B, 101(49):10191-10197, 1997.
[13] J Senker, J Sehnert, and S Correll. Microscopic description of the polyamor-phic phases of triphenyl phosphite by means of multidimensional solid-stateNMR spectroscopy. Journal of the American Chemical Society, 127(1):337-349, 2005.
93
[14] J Senker and E Rossler. Determination of the local disorder in the polyamor-phic phases of triphenyl phosphite. The Journal of Physical Chemistry B,106(31):7592-7595, 2002.
[15] J Senker and E Rossler. Triphenyl phosphite: a candidate for liquid polyamor-phism. Chemical Geology, 174(1-3):143-156, 2001.
[16] J Senker and J Ludecke. Structure determination for the crystalline phase oftriphenyl phosphite by means of multi-dimensional solid-state NMR and x-raydiffraction. Zeitschrift fur Naturforschung B, 56(11):1089-1099, 2001.
[17] R Lefort, A Hedoux, Y Guinet, E Cochin, and M Descamps. Fast intramolec-ular dynamics of triphenyl phosphite investigated by 2H NMR. The EuropeanPhysical Journal B-Condensed Matter and Complex Systems, 30(4):519-525,2002.
[18] A Hedoux, Y Guinet, M Descamps, and A Benabou. Raman scattering in-vestigation of the glaciation process in triphenyl phosphite. The Journal ofPhysical Chemistry B, 104(49):11774-11780, 2000.
[19] A Hedoux, Y Guinet, and M Descamps. Raman signature of polyamorphismin triphenyl phosphite. Physical Review B, 58(1):31-34, 1998.
[20] P Derollez, O Hernandez, A Hedoux, Y Guinet, O Masson, J Lefebvre, andM Descamps. Structural and microstructural description of the glacial state intriphenyl phosphite from powder synchrotron x-ray diffraction data and ramanscattering investigations. Journal of molecular structure, 694(1-3):131-138,2004.
[21] A Hedoux, Y Guinet, M Descamps, and J Lefebvre. Raman scattering and x-ray diffraction investigations about the polyamorphism in triphenyl phosphite.Phase Transitions: A Multinational Journal, 76(9-10):831-836, 2003.
[22] A Hedoux, O Hernandez, J Lefebvre, Y Guinet, and M Descamps. Meso-scopic description of the glacial state in triphenyl phosphite from an x-raydiffraction experiment. Physical Review B, 60(13):9390, 1999.
[23] L Merrill and W.A Bassett. Miniature diamond anvil pressure cell for singlecrystal x-ray diffraction studies. Review of Scientific Instruments, 45(2):290-294, 1974.
[24] H Mao and J Xu. . . . Calibration of the ruby pressure gauge to 800 kbar underquasi-hydrostatic conditions. J. Geophys. Res, Jan 1986.
[25] J Barnett, S Block, and G Piermarini. An optical fluorescence system for quan-titative pressure measurement in the diamond anvil cell. Review of ScientificInstruments, Jan 1973.
94
[26] W.B Holzapfel. Refinement of the ruby luminescence pressure scale. Journalof applied physics, 93:1813, 2003.
[27] J Yen and M Nicol. Temperature dependence of the ruby lumines-cence method for measuring high pressures. Journal of applied physics,72(12):5535, 1992.
[28] A Hedoux, Y Guinet, P Derollez,O Hernandez,R Lefort, and M Descamps. Acontribution to the understanding of the polyamorphism situation in triphenylphosphite. Phys. Chem. Chem. Phys. , 6:3192-3199, 2004.
95
Appendix A References:
[1] A Jayaraman. Diamond anvil cell and high-pressure physical investigations.Reviews of Modern Physics, Jan 1983.
[2] Richard B. Kaner, John J. Gilman, and Sarah H. Tolbert. Designing superhardmaterials. Science, 308:1268, 2005.
[3] D.J. Twitchen, C.S.J. Pickles, S.E. Coe, R.S. Sussmann, and C.E. Hall. Ther-mal conductivity measurements on CVD diamond. Diamond and related . . . ,10(731-735), 2001.
[4] Y. Yamamoto, T. Imai, K. Tanabe, T. Tsuno, Y. Kumazawa, and N. Fijumori.The measurement of thermal properties of diamond. Diamond and RelatedMaterials, 6:1057–1061, 1997.
[5] D Adams, S Payne, and K Martin. The fluorescence of diamond and Ramanspectroscopy at high pressures using a new design of diamond anvil cell. Ap-plied Spectroscopy, 27(5):377, 1973.
[6] J Eggert, K Goettel, and I.F. Silvera. Elimination of pressure-induced fluores-cence in diamond anvils. Applied Physics Letters, 53:2489, 1988.
[7] L Merrill and W.A Bassett. Miniature diamond anvil pressure cell for singlecrystal x-ray diffraction studies. Review of Scientific Instruments, 45(2):290–294, 1974.
[8] D. J. Dunstan. Theory of the gasket in diamond anvil high-pressure cells.Review of scientific instruments, 60:3789, 1989.
[9] Ross J. Angel, Maciej Bujak, Jing Zhao, G. Diego Gatta, and Steven D. Ja-cobsen. Effective hydrostatic limits of pressure media for high-pressure crys-tallographic studies. Journal of Applied Crystallography, 40:26–32, 2007.
[10] J.D. Barnett, S. Block, and G.J. Piermarini. An optical fluorescence systemfor quantitative pressure measurement in the diamond anvil cell. Review ofScientific Instruments, 44(1):1–9, 1973.
[11] W.B Holzapfel. Refinement of the ruby luminescence pressure scale. Journalof applied physics, 93:1813, 2003.
[12] H.K. Mao, J. Xu, and P.M. Bell. Calibration of the ruby pressure gauge to 800kbar under quasi-hydrostatic conditions. Journal of Geophysical Research,91(B5):4673–4676, 1986.
[13] Yuichi Nakamura, Ikuya Fijishiro, and Kazunori Taniguchi. Hysteresis of rubyfluorescent line by pressure and annealing effect. High Pressure Research,6:301–307, 1991.
96
[14] Melinda J. Duer. Introduction to Solid-State NMR Spectroscopy. Blackwell,2004.
[15] Malcolm H. Levitt. Spin Dynamics. Wiley, 2008.
[16] Christian Jager. How to get more from 27Al MAS NMR by high-speedsatellite-transition spectroscopy. Jornal of Magnetic Resonance, 99(2):353–362, 1992.
[17] Ales Medek, John S. Harwood, and Lucio Frydman. Multiple-quantummagic-angle spinning NMR: a new method for the study of quadrupolar nu-clei in solids. Journal of the American Chemical Society, 117:12779–12787,1995.
[18] E.L Hahn. Spin echoes. Physical Review, 80(4):580, 1950.
[19] H.Y Carr and E.M Purcell. Effects of diffusion on free precession in nuclearmagnetic resonance experiments. Physical Review, 94(3):630, 1954.
[20] S Meiboom and D Gill. Modified spin-echo method for measuring nuclearrelaxation times. Review of Scientific Instruments, 29(8):688–691, 1958.
[21] Charles P. Slichter. Principles of Magnetic Resonance. Springer-Verlag, 1978.
97
Appendix A
EXPERIMENTAL METHODS
98
A.1 Diamond Anvil Cell
Diamond anvil cells (DAC) have become standard equipment for generating static
pressures in the gigapascal to megabar range.1 Utilizing a pair of opposed diamond
anvils, a metal gasket and a supporting body as shown in figure 1, pressures in
the megabar range can be achieved without complex machinery. The underlying
mechanism behind pressure generation relies on a volume collapse within the sam-
ple chamber as the diamond anvils are forced closer together. Aside from being
the hardest known material,2 diamond also offers excellent thermal conductivity,3,4
shock resistance (thermal and mechanical), and optical windows for most of the
electromagnetic spectrum, including the entire visible range. This diversity makes
diamond suitable for various types of spectroscopy (Raman, IR, NMR), laser heat-
ing, and diffraction studies (Xray and Neutron).
While DACs are suited for a range of high pressure studies, there are funda-
mental limitations that impair its ability to be useful in other work. Mainly, the use
of minute sample sizes restricts its use in studies requiring extremely small sam-
ples. For inherently insensitive techniques such as NMR, the DAC severely hinders
the ability to perform experiments in a timely manner as typical NMR samples are
20,000 times the size typically loaded in a DAC. Furthermore, the large thermal
conductivity makes it difficult to accurately heat a sample using laser or resistive
heating as the diamonds readily draw away heat from the sample. In such cases,
the entire cell assembly must be heated to avoid any thermal gradients, hence re-
stricting the temperature space to that limited by the cell material instead. Although
diamonds appear to be optically transparent, impurities and defects also play a large
role in spectral artifacts when performing optical spectroscopy. This is largely due
99
Diamond Anvil
Metal Gasket
Force applied by cell body
Force applied by cell body
Figure A.1: Diagram of a typical diamond anvil cell.
100
to fluorescence which increases with the stress applied on the diamonds, and vari-
ous studies have been dedicated to eliminate it.5,6
The pressure a cell is capable of reaching is dependent on several factors.
First, the type of cell body used for generating the initial force upon the anvils is
responsible for alignment of the anvils, symmetric pressure distribution, and being
able to generate and withstand forces necessary for the study. Various cell types
have been developed,1including Merrill-Bassett7 triangular bodies with 3 equilat-
eral screws, cylindrical type cells which utilize a piston and cylinder to limit travel
along a single axis, and gas membrane cells that use a gas expansion within a disk
like chamber to drive a piston-cylinder setup. A second important factor in deter-
mining the pressure range arises from selection of the diamonds, and more specif-
ically relies on their cut. For a given anvil size, more pressure can be generated
with a smaller culet size because the same amount of force will be concentrated to
a smaller area. However, smaller culet sizes also leads to smaller sample chambers,
thus making it extremely difficult to prepare and perform studies. Finally, the type
of metal used for the sample chamber is also an important factor in pressure gen-
eration. As the diamond culets are forced together, the metal gasket flows outward
radially while collapsing the radius and thickness of the volume directly between
the two culets. This decrease in volume results in an increase in pressure. Hence,
the material holding the sample must be able to withstand the force and pressure
being applied while being able to maintain the ability to flow with pressure. Studies
have been devised to properly setup the gasket for various conditions.8 In general,
rhenium gaskets are used to achieve extremely high pressures while standard stain-
less steel (T301) type materials are typically used for studies below 30 GPa.
Proper setup is required before pressurizing a sample in a DAC. Most im-
portantly, the cell body and diamond anvils must be aligned properly such that the
101
diamond culets are perfectly aligned and parallel when spaced within the thickness
of a typical sample (thinner than 200 µm). This ensures that the force is distributed
symmetrically across and between the two anvils and reduces the chance of break-
age. The gasket material is also pre-indented to a certain hardness before the exper-
iment in order to densify the region in which the sample will be placed, a step that
allows higher pressures to be achieved.8 After an indentation has been made, a hole
is generated in the center of the gasket using an electric discharge machine (EDM)
which erodes the metal away using a high voltage electric charge. The diameter
of the hole is typically around half the diameter of the culet being used, ensuring
enough area is present for the anvils to compress the gasket.
Samples can be loaded in various ways, but typically done in one of three
conditions. Perhaps the easiest is a packed setup in which a solid sample is forced
into the chamber and excess sample is removed. A second method is to place the
sample within a separate matrix, typically a quasi-hydrostatic media that allows
some flow with pressure. Salts such as KBr or NaCl can be used in such studies,
while materials such as Al2O3 or ceramics can be used as hard insulating material.
Finally, the sample can also be loaded in a liquid medium, which can provide hy-
drostatic stress to the sample, making compression completely isotropic. However,
care must be taken to select the right liquid medium, as many reach non-hydrostatic
conditions at fairly low pressures.9
The pressure response of the cell is measured using the well characterized
ruby fluorescence technique.10–12 During a typical experiment, two to three small
pieces of ruby (Cr2+:Al2O3) are loaded along with the sample. Ruby exhibits a
red shift to lower energies as the pressure is increased. When excited with a laser
operating with a wavelength lower than 694 nm, its fluorescence response can then
be collected and used to determine pressure based on a calibrated scale. The size of
102
ruby chips are typically only a few micrometers in diameter, and placed in a trian-
gular array around the sample to judge any pressure gradients that arise when per-
forming non-hydrostatic experiments. Furthermore, pre-strained ruby pieces will
show broadened and shifted fluorescence bands, thus hindering the accuracy of the
technique. To avoid this, it can be annealed just below its melting temperature for
several hours to alleviate the stress.13
A.2 Solid State Nuclear Magnetic Resonance Spectroscopy
Solid state nuclear magnetic resonance (NMR) experiments are typically dominated
by magnetic interactions that make it difficult to obtain useful structural information
from static samples. The primary cause of this is the chemical shift anisotropy and
direct dipolar coupling, both of which exist in powder samples and broaden the
signal considerably. The total hamiltonian of a spin system can be divided into the
sum of a few main terms:
H = H0 +HCS +HD +HQ (A.1)
where H0 is the Zeeman hamiltonian, HCS is for chemical shielding, HD for dipo-
lar interaction, and HQ for the quadrupolar interaction.
The chemical shielding hamiltonian is dependent on the symmetric and
asymmetric parts of the second-rank chemical shielding tensor s and represented
by
HCS = g I ·s ·B0 (A.2)
where B0 is the applied field acting on spin I and g is the gyromagnetic ratio of
the nucleus. Ultimately, the consequence to the frequency shift determined by the
chemical shielding is given by
wCS(q) =�w0IsPAFzz (3cos2q �1)/2 (A.3)
103
where q and f are the polar angles that define the orientation of B0 in the principal
axis frame of the shielding tensor.14 Hence, depending on the molecular orienta-
tion with respect to the static field, wCS will change depending on the effective field
felt by the nuclear spin, I. In the case of a crystalline powder, all possible orienta-
tions contribute to give an inhomogeneous powder pattern made of various spectral
frequencies.
Similarly, the direct dipolar interaction also leads to broadening of spectral
lines, albeit in a homogeneous manner. Looking at a pair of nuclear spins, the
magnitude of the dipolar coupling is represented by
d =µ0
4pgig jhr3
i j(A.4)
where ri j represents the distance between the spins.15 The dipolar hamiltonian is
then shown to be
HD =�d12(3cos2q �1)[3IzSz� I · S] (A.5)
.
Its clear to see that both interactions depend on the (3 cos2 q -1) term, which
can be taken to zero as q approaches 54.74 degrees, which is the so called magic
angle condition. Hence, both interactions can be averaged by spinning the sample
faster than the strength of the interaction using the magic angle spinning (MAS)
technique. In such a case, the entire pattern now collapses into its isotropic parts,
thus increasing the resolution immensely while increasing the signal to noise ratio
at the same time. The interactions can also be recoupled to measure their strength
experimentally. MAS probes are commercially available, and at the time of this
writing, capable of spinning speeds greater than 60 kHz.
Obtaining high resolution spectra for spin-1/2 nuclei is relatively straight-
forward as long as the strength of the CSA and dipolar interactions is moderately104
smaller than the spinning speed available, especially when coupled with high-power
decoupling techniques. Such is not always the case for nuclei possessing spins I >
1/2, termed quadrupoles, which not only contain a magnetic dipole moment, but
also an electric quadrupole moment which couples with the electric field gradients
in non-cubic environments. While CSA and dipolar interactions are typically on the
order of tens of kilohertz, its not uncommon to encounter quadrupolar interactions
ranging in the tens of megahertz. This sometimes approaches within an order of
magnitude to the Zeeman interaction itself. The quadrupole moment of the nucleus
is an intrinsic property and thus does not depend on the chemical makeup.
Because the quadrupolar interaction is so large, even the second order per-
turbations to the Zeeman levels caused by it are large enough to significantly alter
the resultant spectra. The first order quadrupolar interaction is much larger than
the second order, but depends on the same (3 cos2 q -1) term as CSA and dipolar
interactions, and consequently averaged by spinning the sample at the magic an-
gle. For nuclei such as 27Al (I = 5/2), typical quadrupole couplings range from .5
to 10 MHz depending on the site symmetry. Its clear that even the fastest MAS
probes will not come close to completely averaging the first order quadrupole cou-
pling in such a case. However, the interaction is broken into spinning sidebands,
which afford extra resolution, and usually provide adequate spacing to deduce the
central transitions with spinning speeds exceeding 20 kHz. Because the strength of
the first order interaction is much greater than that of the second, it is preferential
to average it by the MAS technique. Unfortunately, the second order interaction
relies instead on two other averaging angles, so it is not affected by MAS. Never-
theless, it does exhibit an inversely proportional relationship with the strength of
B0, hence extra resolution can be obtained by use of high magnetic fields combined
with MAS. Other techniques can also be used to gain resolution in spectra, the sim-
105
Figure A.2: 3QMAS spectrum of rubidium nitrate taken at 9.4T and 20 kHz MAS.
106
plest of which is to use satellite transition spectroscopy (SATRAS).16 Although the
central transition is largely affected by second order broadening, one can use the
satellite transitions (spinning sidebands) of the first order spectra where the effect
of second order broadening is only 1/8 that of the central transition, thus providing
much higher resolution even at lower magnetic fields. Another technique to obtain
higher resolution is to use multiple quantum MAS (MQMAS)17 spectroscopy in
which multiple quantum coherences are utilized to gain resolution in the second di-
mension. Multiple quantum coherences evolve at higher frequencies in addition to
the single quantum dimension, but are always unobservable as detection only takes
place through the -1 coherence pathway. In MQMAS experiments, multiple quan-
tum coherences are excited by a two pulse sequence, converted to single quantum
(observable) coherences and selected exclusively through the use of phase cycling.
The resultant two dimensional plot correlates the single quantum (MAS) dimension
with the multiple quantum dimension which is free of second order broadening, as
shown in figure 2 with RbNO3 as an example.
A.3 High Pressure Liquid State NMR
The magnetic and electric interactions mentioned in the previous section are often
completely averaged in the liquid state, leaving only the Zeeman interaction along
with J-coupling interactions. Hence, the spectra obtained from liquids are typi-
cally of much higher resolution than those of solids. However, in the case of high
pressure studies done in the diamond anvil cell, magnetic susceptibility broaden-
ing often distorts the B0 field enough to cause a frequency spread that is 2 orders
of magnitude larger than those typically found in liquids. Here, one can use two
different pulse sequences to artificially narrow line shapes, as shown in Chapter 3.
The first of these is a simple spin-echo18 pulse sequence, which consists of an ini-
tial 90(x) degree pulse followed by an evolution period, t , where the magnetization
107
dephases and is thereafter refocussed by a 180(y) pulse before acquiring the signal.
A modification of the spin-echo sequence is the CPMG pulse train,19,20 which adds
N 180 degree pulses after the first echo to refocus the magnetization N times until
the signal completely decays. The result of a spin-echo is a free induction decay
(FID) that rephases at a time of 2t instead (and 2nt for CPMG). This alone is a
useful technique for a DAC NMR experiment where homebuilt probes and small
coils are not adequate enough to properly dissipate the RF power before the FID
is collected. During this situation, one can use the spin-echo sequence to shift the
FID by a few milliseconds, thus allowing ring down power to dissipate. However,
the real advantage of using the spin-echo or CPMG type sequences is usually to
measure true T2 relaxation times in heterogenous static fields where the observed
linewidth does not properly reflect the true T2. Measuring the intensity decay as a
function of the t delay, the equation21
M(t) =�M0 exp(�2tT2
)exp(�Dg2G2)2t3
3(A.6)
can be used to measure the magnetization intensity at a time t = t for a given diffu-
sion coefficient (D) and field gradient (G). It can be seen here that if experiments are
performed in a homogenous static field (5 = 0), then the decay of the magnetization
collapses to a form of the normal Bloch equations describing T2 decay.
In the case of CPMG, the field gradients can also be used to measure diffu-
sion as a function of pressure. Routine diffusion experiments often employ pulsed
field gradients in combination with echo generating RF pulses. Inside a diamond
anvil cell, the field gradient is inherently generated by the gasket surrounding the
sample, and can be used to measure the diffusivity using one of several techniques
relying on spin-echoes or CPMG pulse sequences. Shown in chapter 3 is the CPMG
108
method, which can be described by the general equation
M(t) = M0 exp�tT2
�exp
�Dg2G2 t3
12n2
�(A.7)
where n is the echo number corresponding to time t.
Echoes are formed at time intervals of t = 2nt , thus the above expression
can be represented by
M(2nt) = M0 exp�2nt
T2
�exp
�Dg2G2 (2nt)3
12n2
�(A.8)
and further simplified to
M(2nt) = M0 exp�2nt
T2+�Dg2G2(2nt)t2
3
�(A.9)
. From here, the equation can be rewritten to get rid of the exponential term,
ln
MM0
�= (2nt)
�1T2
+�Dg2G2t2
3
�(A.10)
and can be fitted to a linear equation where the slope is
1/T2e f f =�1T2
+�Dg2G2t2
3(A.11)
Hence, plotting the log of M/M0 vs 2nt , the effective T2 value can be obtained
for various t values. The resultant 1/T2e f f term can also be described by a linear
equation of its own when the t2 term is used as the independent variable. Thus,
creating a plot of 1/T2e f f versus t2, the diffusion value and true T2 relaxation time
can be obtained as a function of pressure using the CPMG pulse sequence.
In a sample constrained by the DAC chamber, the magnetic susceptibility
differences of the materials surrounding the sample can cause complex gradients in
the static field. Furthermore, the scenario of a linear gradient no longer holds true.
Suppose that a field distribution exists within the sample chamber as discussed in
chapter 3 such that it is no longer linear. In such a case, different regions of the109
sample will now be exposed to differing G values, and thus the decay rates can no
longer be described by the equation above. If the change in this gradient is radial
in nature, then we can expect magnetization from different regions of the sample to
decay at independent rates, thus the signal from larger G values will decay faster
than those of smaller ones. This effect can be used artificially narrow the line widths
of samples exposed to inhomogeneous static fields.
A.4 Equation of State Measurements
Optical microscopy is used to measure the equation of state of amorphous materials,
as shown in chapter 2. An edge detection algorithm is used in MATLAB to deter-
mine the edges of amorphous solids under pressure. Selection of viable areas by the
MATLAB script after scanning a range of threshold values. The selected points are
represented by red circles and the range is used for error calculation while the mean
is returned as the area of the sample. While typical errors are measured by gauging
the range of data from numerous experiments under identical conditions, the script
also provides a range of deviation in calculated areas from the mean value as shown
in figure 3. This range also gives an indication of the quality of the image for edge
detection. In darker and opaque samples, a much larger range of threshold values
yields similar areas, whereas more transparent images produce acceptable areas in
a smaller threshold range due to the lower contrast in defining the edges.
During experimentation, blurring often results from improper focusing, al-
though the quality of the optics can also determine this. In order to quantify the
resultant image and the area calculation, a Gaussian blurring filter is employed in
MATLAB with a range of pixel radii. The pixel radius is kept constant while scan-
ning the areas through a range of threshold values which determines the contrast
of the image, thus producing a contour map to show the relative volume change
110
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
2
4
6
8
10
12
14
16
18
Threshold
Are
a / 1
04
Figure A.3: Selection of viable areas by the MATLAB script after scanning a rangeof threshold values
111
observed in typical calculations. If proper care is taken during most experiments,
the blurring should represent no more than the results simulated with a 5 pixel ra-
dius. Hence, the errors produced by nominal blurring are minimal in the final area
measurement. The result of this analysis is shown in figure 4.
Another error that can frequently arise is that of sample tilting. This can be
easily avoided by selecting the right geometry of the sample and ensuring that a flat
piece of solid with a large surface area is chosen, almost approaching the size of the
sample chamber, which constrains the tilting. Under most experimental conditions,
the tilt is calculated to be less than 5 degrees, resulting in an error less than 1% as
shown in figure 5.
Changes in the refractive index of the pressure medium with pressure can
also cause a perceived magnification in the resultant image. Being path length
dependent, the magnification effect is limited by the finite spacing between the di-
amonds of the sample chamber, and thus becomes inconsequential. To prove this,
a flat piece of copper was placed in methanol and then glycerol to measure the ob-
served area difference as seen in figure 6. In the hydrostatic range of a methanol
and ethanol, the change in refractive index is approximately 0.35 at 10 GPa.21 The
refractive index difference of methanol and glycerol is 0.14 at ambient conditions
and the resultant difference in area is less than the error (6180 pixels) of the mea-
surement. After removal of the top diamond, the measured area is still within this
error. Hence, the assumption that the observed area is independent of the refractive
index change with pressure is valid.
A.5 Low Temperature Assembly
Performing experiments at high pressures and low temperatures requires the use of
special equipment which can house the diamond anvil cell. While these types of
112
0.1
0.15
0.20
0.25 0
5
10
150.96
0.98
1
1.02
1.04
Blurring Pixel W
idth
Threshold
V/V
0
Figure A.4: Relative observed volume change as a result of blurring and thresholdchanges in the image
113
0 2 4 6 8 10 12 14 16 18 200.93
0.94
0.95
0.96
0.97
0.98
0.99
1
Tilt Angle (degrees)
No
rma
lize
d A
rea
(A
/A0 )
Figure A.5: Normalized difference in observed volume as a function of sample tiltangle
114
Copper in Glycerol
Area = 341,490
Copper in Methanol
Area = 341,410
Figure A.6: Change in observed area of a flat copper sample in methanol and glyc-erol to simulate refractive index changes with pressure
115
experiments typically utilize low temperature cryostats, experiments on triphenyl
phosphite require the temperature to be regulated in the range of 205-275K while
allowing optical access to the DAC. Hence, a homebuilt low temperature assembly
was built for this task. An Olympus BH-2 microscope was modified and fitted with
a homebuilt aluminum DAC holder with gas access via a 1/8” brass tube. Figure 7
shows a basic diagram of the entire setup.
To generate low temperature, gas flow was used to cool the entire DAC
chamber, which also ensured that temperature gradients were negligible over the
sample. Starting with dry air, copper coils were used to flow it through a dry ice /
acetone slurry, reaching temperatures below 205 K. Over 30 feet of coil was sub-
merged in the slurry to allow proper heat exchange even with large flow rates. In
order to regulate temperature, a homemade flow heater assembly was made from
nickel chromium wire and glass tubes. Sample temperature was measured by plac-
ing a thermocouple directly in contact with the side of the diamond near the culet,
and the information fed to a local thermocouple reader with a PID control loop. The
heater was controlled with this PID controller, which adjusted the current flow into
the heater to maintain the proper temperature. Data was collected in real time with
a computer. A homemade circuit consisting of a micro controller based timer was
paired with a CCD camera to obtain pictures in specific time intervals.
116
PID Controller
Power Supply
DACAssembly
Thermocouple
Computer
Glass Heater AssemblyCooling Coils
Dry Ice / Acetone Slurry
Needle Valve Dry Filter
Air (25 C)
MicroscopeAssembly
Camera Microprocessor
Spectrometer
Figure A.7: A block diagram of the low temperature microscopy setup used in TPPexperiments
117
References
[1] A Jayaraman. Diamond anvil cell and high-pressure physical investigations.Reviews of Modern Physics, Jan 1983.
[2] Richard B. Kaner, John J. Gilman, and Sarah H. Tolbert. Designing superhardmaterials. Science, 308:1268, 2005.
[3] D.J. Twitchen, C.S.J. Pickles, S.E. Coe, R.S. Sussmann, and C.E. Hall. Ther-mal conductivity measurements on CVD diamond. Diamond and related . . . ,10(731-735), 2001.
[4] Y. Yamamoto, T. Imai, K. Tanabe, T. Tsuno, Y. Kumazawa, and N. Fijumori.The measurement of thermal properties of diamond. Diamond and RelatedMaterials, 6:1057–1061, 1997.
[5] D Adams, S Payne, and K Martin. The fluorescence of diamond and Ramanspectroscopy at high pressures using a new design of diamond anvil cell. Ap-plied Spectroscopy, 27(5):377, 1973.
[6] J Eggert, K Goettel, and I.F. Silvera. Elimination of pressure-induced fluores-cence in diamond anvils. Applied Physics Letters, 53:2489, 1988.
[7] L Merrill and W.A Bassett. Miniature diamond anvil pressure cell for singlecrystal x-ray diffraction studies. Review of Scientific Instruments, 45(2):290–294, 1974.
[8] D. J. Dunstan. Theory of the gasket in diamond anvil high-pressure cells.Review of scientific instruments, 60:3789, 1989.
[9] Ross J. Angel, Maciej Bujak, Jing Zhao, G. Diego Gatta, and Steven D. Ja-cobsen. Effective hydrostatic limits of pressure media for high-pressure crys-tallographic studies. Journal of Applied Crystallography, 40:26–32, 2007.
[10] J.D. Barnett, S. Block, and G.J. Piermarini. An optical fluorescence systemfor quantitative pressure measurement in the diamond anvil cell. Review ofScientific Instruments, 44(1):1–9, 1973.
[11] W.B Holzapfel. Refinement of the ruby luminescence pressure scale. Journalof applied physics, 93:1813, 2003.
[12] H.K. Mao, J. Xu, and P.M. Bell. Calibration of the ruby pressure gauge to 800kbar under quasi-hydrostatic conditions. Journal of Geophysical Research,91(B5):4673–4676, 1986.
[13] Yuichi Nakamura, Ikuya Fijishiro, and Kazunori Taniguchi. Hysteresis of rubyfluorescent line by pressure and annealing effect. High Pressure Research,6:301–307, 1991.
118
[14] Melinda J. Duer. Introduction to Solid-State NMR Spectroscopy. Blackwell,2004.
[15] Malcolm H. Levitt. Spin Dynamics. Wiley, 2008.
[16] Christian Jager. How to get more from 27Al MAS NMR by high-speedsatellite-transition spectroscopy. Jornal of Magnetic Resonance, 99(2):353–362, 1992.
[17] Ales Medek, John S. Harwood, and Lucio Frydman. Multiple-quantummagic-angle spinning NMR: a new method for the study of quadrupolar nu-clei in solids. Journal of the American Chemical Society, 117:12779–12787,1995.
[18] E.L Hahn. Spin echoes. Physical Review, 80(4):580, 1950.
[19] H.Y Carr and E.M Purcell. Effects of diffusion on free precession in nuclearmagnetic resonance experiments. Physical Review, 94(3):630, 1954.
[20] S Meiboom and D Gill. Modified spin-echo method for measuring nuclearrelaxation times. Review of Scientific Instruments, 29(8):688–691, 1958.
[21] Charles P. Slichter. Principles of Magnetic Resonance. Springer-Verlag, 1978.
119
