**Deviatoric Stress, a Nuisance or a Gold Mine?**

**William A. Bassett**

**Department of Earth and Atmospheric Sciences**

**Cornell University, Ithaca, NY 14853**

**Both synchrotron radiation and deviatoric stress were once considered
to be nuisances. Now synchrotron radiation is one of the most important
tools available to scientists of all disciplines and deviatoric stress
is one of the most useful aspects of X-ray diffraction at extreme
conditions. Samples in high-pressure devices are under true hydrostatic
pressure only when surrounded by a fluid thus limiting true hydrostatic
pressure studies at ambient temperatures to pressures below about 14
GPa. Elevated temperature is able to extend this limit but has rarely
been used for that purpose. Instead, noble gases have been used as
pressure media as their solids are especially soft. Deviatoric stress
and resultant anisotropic elastic strain in solid samples and solid
media have led to many subtle errors in determinations of elastic
properties and crystal structures, especially in the days before it was
realized that they could be measured and were potentially a valuable
source of information. In recent years measuring anisotropic elastic
strain by X-ray diffraction has provided new insights into materials
strength, elastic properties, crystal structures, mechanisms of phase
transitions, and, of course, ways to make corrections when deviatoric
stress is indeed a nuisance.**

**Radial X-Ray Diffraction in Diamond Anvil Cell**

**Ho-kwang Mao**

**Geophysical Laboratory, Carnegie Institution of Washington**

**5251 Broad Branch Rd. NW, Washington, DC 20015-1305**

**With radial x-ray diffraction in DAC, the uniaxial strain inevitable
in high-pressure experiment has become a blessing; it provides rich
information on the development of preferred orientation under stress,
the yield strength, the single-crystal elasticity, and even the
hydrostatic P-V equation of state. Remaining technical challenges
include the followings: How to optimize the DAC and x-ray probe? How to
eliminate the gasket diffraction while maximize the support? How to
study time-dependent rheology? How to conduct simultaneous high *P-T*
experiment? How to determine stress independently?**

**Radial diffraction in the DAC: Practical and theoretical
considerations**

**S. Merkel**

**Dept. Earth and Planetary Science, U.C. Berkeley**

**In the last few years, radial diffraction has evolved considerably
from a technique designed to study elasticity and stress towards a more
general approach to investigate rheology at very high pressure where
more conventional apparatus can not be used. The technology has also
seen major advances with the introduction of angle dispersive
diffraction, amorphous or composite confining gaskets, and more
appropriate data reduction. However, there are limitations of the radial
diffraction techniques for the study of stress, elasticity, lattice
preferred orientations, or more generally rheology measurements. The
latest experimental developments will be presented, along with important
details to keep mind when designing an experiment. We will also discuss
the current state of the art in data processing, such as the analysis of
stress and texture that do not assume cylindrical symmetry and point out
future directions. Finally, we will try to present a review on the
results obtained from radial diffraction and their applicability to
Earth science.**

![](media/image1.png){width="5.995833333333334in"
height="4.021527777777778in"}

**Recent approach in application of rotational diamond anvil cell**

**Yanzhang Ma**

**Texas Tech University, Department of Mechanical Engineering**

**Lubbock, Texas 79409**

**We have recently performed synchrotron x-ray diffraction in a
rotational diamond anvil cell to study the properties of a material
under high pressure and shear stress and strain. By controlling the
pressure distribution in the sample chamber, including generating a
quasi-homogenous pressure distribution, we explored the shear induced
disorder and their effects on phase transformations. The shear induced
stacking fault, the phase transition induced plasticity, and the shear
resulted formation of bonding with diamond of hexagonal boron nitride
has been studied. The high pressure transformation of iron and zirconium
has also been investigated.**

**Current status and future plan for radial XRD with in-situ laser
heating**

**Yue Meng^1,2^, Guoyin Shen^1,2^, Ho-kwang Mao^2,1^**

**^1^HPCAT, Advanced Photon Source, Argonne National Laboratory**

**^2^Geophysical Laboratory, Carnegie Institution of Washington**

**After more than 30 years since the invention of the laser heating in
diamond anvil cell, the technique has been developing into a powerful
and routine tool for synchrotron x-ray diffraction research under
simultaneous high PT conditions. One of the key challenges of
integrating the laser heating of diamond anvil cell with in-situ
synchrotron x-ray diffraction is the system stability including both
mechanical and optical aspects. At HPCAT, we have established the
capability of double-side laser heating with in-situ x-ray diffraction
with considerable efforts on system's stability. Our laser heating
system has been used for x-ray diffraction studies of a wide range of
materials to over 150 GPa and above 3000 K.**

**High-pressure radial x-ray diffraction has been used for rheology and
elasticity studies, it is also a useful method to study the samples that
develop strong preferred orientation or evolve into a single crystal
form at high pressure. This type of research under simultaneous high PT
conditions is not feasible due to the conflicting geometries of the
radial diffraction and the available heating optics. To overcome the
technical difficulty, we have developed an initial design of a rotating
laser heating system. With this system, laser heating can be conducted
at any angle relative to the x-ray direction, allowing for radial
diffraction studies carried out at high pressures with in-situ laser
heating. The design concept will be discussed.**

**Rheological Studies in the Diamond Anvil Cell: Opportunities and
Difficulties**

**Harry W. Green, II**

**University of California, Riverside**

**The project to develop the ability to perform controlled deformation
experiments in the Diamond Anvil Cell (DAC) is an exciting one with many
potentially important implications for understanding the rheology of
Earth's deep mantle and inner core, as well as for understanding the
interior of the giant planets. Among the exciting applications of such
work will be an ability to probe more effectively the complexities of
the D'' layer at the bottom of the mantle and to develop a true
rheological model for convection in the entire mantle. The very high
pressures, very high temperatures and very small sample sizes involved
in this endeavor create formidable barriers that must be overcome in
order to collect meaningful data that can be applied to flow in Earth.**

**Technical considerations involve developing ways to establish an
underformed specimen composed of the stable mineral (or assemblage of
minerals) before deformation begins and the ability to measure stress
accurately (in the sense of the conventional macroscopic stress that can
be used in continuum calculations) at reasonably homogeneous
temperatures in excess of 0.5 of the melting temperature. Most
importantly, significant permanent strains (\>10% minimum) will need to
be achieved over at least 3 orders of magnitude in strain rate. Such
strains may only be possible via rotation of one of the diamonds.**

**Ideally, specimen materials should eventually be polycrystalline,
polyphase aggregates but until much larger diamonds are available, the
grain size of polycrystalline material will be limited to those under
which only diffusion creep is attainable and one will need to guard
against crystal sizes so small that nanocrystalline behavior sets in
(material heavily dominated by grain boundaries) that will radically
change many physical properties and greatly complicate extrapolation to
nature. To achieve dislocation creep, oriented single crystals can be
employed but careful attention to avoidance of end effects will be
necessary, with subsequent calculation of polycrystalline behavior
(although uncertainties still exist in such calculations). For phases
that cannot be quenched to room T and P, the problem of generating
single crystals *in situ* at very high pressure in the DAC will be
challenging.**

**To determine deformation mechanisms, interrogation of specimens that
can be quenched to room conditions can be accomplished in the same ways
as currently done for lower-pressure experiments (SEM with EBSD, TEM
with associated tilting and diffraction techniques). Decompression
artifacts (cracks, dislocations, twinning, inversion to metastable
phases, vitrification, etc.) will be complications but can be overcome.
Materials that cannot be quenched will require *in situ* techniques such
as X-ray measurement of pole figures to measure lattice preferred
orientation (LPO), but significant strains will be necessary to develop
such LPOs and interpretation of flow mechanisms from LPOs is not
necessarily unique.**

**A stroke of good luck is that MgO is stable under all conditions in
Earth's mantle, hence it becomes an ideal material with which to begin
and to develop appropriate techniques. However, the rheology of MgO is
particularly sensitive to specimen preparation procedures (especially
surface preparation), hence reproducibility may initially be a problem.
The good news in that is that once such problems are solved for MgO,
they will be easier to address in other phases. Also, comparison of DAC
experiments with germanate, titanate, or other silicate analogues
deformed in the multianvil will be helpful. Collaboration with members
of the deformation community who already have or are currently
experiencing similar problems at lower pressures can avoid many blind
alleys.**

Texture information from radial DAC experiments and relevance for deep
earth geophysics, illustrated with examples

**H.-R. Wenk**

**Dept. Earth and Planetary Science, U.C. Berkeley**

**With diamond anvil cells in radial geometry diffraction images reveal
immediately elastic and plastic deformation of polycrystalline samples.
The plastic deformation may result in texture development if the
material deforms by slip or mechanical twinning or if grains have a
non-equiaxed shape. Texture is revealed by intensity differences on
Debye rings between parallel and perpendicular to the compression
direction. Images (CCD or image plate) can be used to extract
quantitative texture information. Currently the most elegent and
powerful method is a modified Rietveld method as implemented in the
software package MAUD. From texture data one can evaluate the
homogeneity of strain in a diamond anvil cell, the strain magnitude and
deformation mechanisms, the latter by comparing observed textures with
results from polycrystal plasticity simulations. Some examples such as
olivine, MgSiO~3~ perovskite and ε-iron will be discussed.**

**Mechanical properties of tantalum under high pressure**

> **Agnès Dewaele and Paul Loubeyre**
>
> **DIF/DPTA, Commissariat à l'Energie Atomique**
>
> **91680 Bruyères-le-Châtel, France**

**We present here an approach that allows to measure the mechanical
properties under pressure in a diamond anvil cell. It is based on the
x-ray diffraction measurement of the stress state of a single crystal
and on the interferometric measurement of its plastic strain. It is
almost the exact transposition in the diamond anvil cell of the geometry
of the mechanical experiments that are usually performed at ambient
pressure. The confrontation of single crystal yield strength
measurements at very high pressure with theoretical predictions has thus
been achieved. The intrinsic effect of pressure on the yield stress is
less dramatic than what has been published before. In fact, the
Steinberg-Cochran-Guinan model is valid with two parameters that fall
within their various experimental determination at ambient pressure. A
better understanding of coupled pressure and plastic strain effects
should be possible by carrying out similar measurements in different
pressure-plastic strain domains.**

**Strength of Hydrous Phase at High Pressures**

**Sean R. Shieh**

**Department of Earth Sciences, University of Western Ontario, Ontario,
N6A 5B7**

**Thomas S. Duffy**

**Department of Geosciences, Princeton University, Princeton, NJ 08544**

**Eiji Ohtani**

**Institute of Mineralogy, Petrology, and Economic Geology, Tohoku
University, Sendai 980-8578, Japan**

**Boris Kiefer**

**Department of Physics, New Mexico State University, Las Cruces, NM
88003**

**High-pressure strength study of hydrous phase will be helpful for
understanding the convection of Earth's interior but, however, limited
data are available. Two hydrous materials, phase D and brucite, were
individually examined using radial x-ray diffraction method, together
with lattice strain theory in a diamond anvil cell. Phase D can be
thermodynamically stable at lower mantle conditions, and brucite serves
as a proto-type of magnesium-bearing hydrous phase. Phase D was
compressed to 58 GPa at room temperature. The ratios of differential
stress to shear modulus are 0.006(5)-0.034(23) for phase D at pressure
from 9 to 58 GPa. Brucite was compressed to 62 GPa at room temperature.
The ratios of differential stress to shear modulus are
0.017(4)-0.053(17) for brucite at pressure from 14 to 62 GPa. Our
results show that brucite has slightly higher ratios of differential
stress to shear modulus values than those of phase D but are still
similar to other six-coordinated silicates such as silica and CaSiO~3~
perovskite. The yield strength for phase D is 0.7(7)-6.3(4.4) GPa in the
pressure of 9-58 GPa and for brucite is 1.3(3)-8.2(2.7) in the pressure
of 14-62 GPa. Our yield strength results suggest that brucite is
slightly stronger than phase D at pressures to 62 GPa.**

**Future development for DAC radial diffraction studies**

**Haozhe Liu**

**HPCAT, Carnegie Institution of Washington, Bldg. 434E, APS, Argonne
National Laboratory, Argonne, IL 60439**

**Understanding the deep earth is dependant on our knowledge of the
crystalline structures and properties of minerals at pressures and
temperatures consistent with the environments of lower mantle and core.
High pressure powder diffraction using diamond anvil cell (DAC)
techniques is a unique way to approach these conditions. The current
state-of-the-art DAC techniques combined with synchrotron x-ray
diffraction (XRD) make powder diffraction studies under high pressure
one of most active, burgeoning fields in the COMPRES community. By
taking advantage of the feature of deviatoric stress in DAC, radial
diffraction measurements add a possibility to simulate the deformation
behavior of minerals during the Earth's long history. We are just
beginning to explore this field where major discoveries are yet to be
made. The elastic anisotropy, strain and stress, yield strength,
preferred orientation etc. information could be obtained by using radial
diffraction techniques in DAC. The future development within one year
frame, mainly from technology point of view, will be focused in this
talk. These will include the motor driven revised panoramic DAC
development, gasket technology continually optimization, development
rotational laser heating system at HPCAT for DAC radial diffraction
studies. Other technical developments include of rotational DAC and
dynamic DAC techniques combined with the *in situ* laser heating under
high pressure, data analysis software improvement will be also
discussed. These future developments will further push the technological
frontier of rheology and elasticity studies in DAC, further broaden
COMPRES community access to the DAC radial diffraction studies.**

**Radial X-ray diffraction in the DAC and Drickamer cell**

# 

# Takehiko Yagi

## Institute for Solid State Physics, University of Tokyo

**Radial X-ray diffraction provides unique information which is
difficult to obtain with a conventional diffraction. In the DAC, it is
possible to observe the full circle of the Debye ring and using proper
analysis, we can get various information on the elastic and plastic
property of materials. Recent improvements of the X-ray transparent
gasket made it possible to obtain very high quality data, and the fine
structures of the deviation form hydrostatic compression are now clearly
observed. Radial diffraction is also a powerful tool to study the
high-pressure behavior of highly anisotropic material. An example of the
graphite-diamond transition at room temperature will be presented. For
the high-temperature experiments, Drickamer-type apparatus has the
advantage because we can heat the sample stably and uniformly using
resistance heater embedded in the sample chamber. Various examples of
this kind of study will be presented.**

**Deformation experiments using RDA under the transition zone conditions
and the challenges in rheological experiments under deep Earth
conditions**

**Shun-ichiro Karato**

**Department of Geology & Geophsyics, Yale University\
**

**One of the important differences between rheological properties and
other static properties such as elastic constants is that there is no
such a thing as "the plastic strength" of a material at a given P-T
conditions. Rheological properties are controlled (usually) by thermally
activated motion of crystalline defects and consequently even at a given
P-T condition, one can see a wide range of rheological properties
depending on (i) the rate of deformation (or stress level), (ii)
chemical environment (i.e., water fugacity), and (iii) microstructures
(i.e., grain-size). This applies both to the measurements of creep
strength (viscosity) and the study of deformation microstructures such
as lattice-preferred orientation (LPO). In addition, in the study of
deformation microstructures such as lattice-preferred orientation, we
need an apparatus by which large strain deformation experiments can be
conducted.**

**An apparatus has been designed and developed in our group to study
both creep strength and lattice-preferred orientation under deep mantle
conditions. This is a RDA (rotational Drickamer apparatus) that has a
rotational actuator attached to a Drickamer-type high-pressure
apparatus. We chose this type of apparatus for two reasons: (i) the
support for anvils in this design is identical between static and
dynamic experiments and there is a good support for anvils due to the
geometry of anvils and gasket, and hence one can go to higher pressure
than other designs, and (ii) because of the geometry of deformation
(torsion tests), large strains can be achieved that is critical to the
study of "steady-state" creep strength as well as the study of
lattice-preferred orientation.**

**The RDA has been operated at synchrotron facility at NSLS (Brookhaven)
to obtain the stress-strain curves for mantle minerals such as olivine
and wadsleyite. I will report some of these results and discuss
challenges in the quantitative rheological experiments.**

**Do Reuss and Voigt bounds really bound in rheology experiments?**

**Jiuhua Chen, Li Li, Tony Yu, Hongbo Long, Donald Weidner**

**Mineral Physics Institute, Stony Brook University**

**X-ray diffraction has become the most powerful tool to assess the
stress experienced by a bulk sample at ultrahigh pressures. However,
x-ray diffraction actually measures lattice strains of individual
crystallographic orientations. To derive the stress externally applied
to the bulk sample, one needs to model the stress/strain propagation
through the grain-to-grain contact in the bulk sample. Most popular
method of the modeling is to use Reuss and Voigt bounds. Reuss bound
describes an extreme condition (iso-stress) under which all the grains
in the bulk sample experience identical stress when forces are applied
to the sample, while Voigt bound describes another extreme (iso-strain)
that all the grains experience the same strain when the bulk sample is
deformed under stress. An intermediate condition is described then
expressed by combining the bounds with a weight parameter k (0\<k\<1,
k=1 and k=0 being the Reuss and Voigt conditions respectively). High
pressure rheology experiments in a multi-anvil press demonstrate that
once plastic deformation occurs in the sample, the Reuss and Voigt
boundary conditions are no longer valid. Data on fayalite sample
indicate that if this model is used to assess that sample stress the
weight parameter k can go beyond the 0\<k\<1 range. A better model needs
to be developed for ultrahigh pressure rheology experiments.**

**Can we determine flow laws under ultrahigh pressures?**

**Yanbin Wang, Norimasa Nishiyama, Takeyuki Uchida, and Mark Rivers**

**Center for Advanced Radiation Sources, the University of Chicago**

**5640 S. Ellis Ave., Chicago, IL 60637**

**Rheology, the science of the deformation and flow of matter, is
concerned with macroscopic strain (ε) and stress (σ) relations of
materials at various conditions of chemical environment (e.g., oxygen
fugacity, f~O2\ ,~ and water content, f~H2~), pressure (P), temperature
(T), and strain rate. In order to establish a flow law, all of the
aforementioned quantities, as well as sample attributes (e.g.,
composition, x, and grain size, d), must be carefully controlled and
accurately measured. A particular challenge in conducting rheological
studies at high P and T has been the difficulty in controlling and
measuring these parameters. Recently developed deformation DIA (D-DIA)
offers an opportunity to push the P-T envelope of rehological studies to
conditions corresponding to the mantle transition zone. In this
presentation, we will use a few examples to illustrate some recent
advances in the D-DIA towards quantitative rheology at high P and T.
Remaining challenges will also be discussed. A possible combination of
LVP and DAC techniques for ultrahigh pressure deformation studies is
proposed.**

## *Poster session*

## 

## Nonhydrostatic compression of gold powder to 60 GPa in a diamond anvil cell: Estimation of compressive strength from x-ray diffraction data

## A. K. Singh^1^[^1], H. P. Liermann^2^, S. K. Saxena^2^, H. K. Mao^3^ and S. Usha Devi^1^

# ^1^ Materials Science Division, National Aerospace Laboratories, Bangalore 560 017, India. 

# ^2^ Center for Study of Matter at Extreme Conditions (CeSMEC), Florida International University, Miami, FL 33199, USA. 

# ^3^ Geophysical Laboratory and Center for High Pressure Research, Carnegie Institution of Washington, Washington DC 20015, USA. 

**Gold powder was compressed without any pressure-transmitting medium in
a diamond anvil cell and the pressure increased in steps of ≈5 GPa.
X-ray diffraction patterns were recorded at each pressure. The
difference between the axial and radial stress components *t* was
estimated from the shifts of the diffraction lines. The grain size
(crystallite size) and maximum micro-stress in the crystallites
*2p~max~* were obtained from the analysis of the line-width data. The
results indicated that *t=2p~max~*~.~ The grain size decreased whereas
*t* and *2p~max~* increased with increasing pressure. The grain size
decrease was much larger than what is expected purely from the
compressibility effect and arises due to the deformation during
nonhydrostatic compression. In many earlier studies, *t* has been taken
as a measure of the compressive strength. However, a comparison of *t*
with the strength derived from an independent method has not been
attempted in the past. In this work we compare *t* with the compressive
strength derived from the hardness versus grain size data at ambient
pressure. This comparison shows that *t* is a good measure of
compressive strength. The grain size dependence of strength is well
known in case of the ambient pressure measurements but has been largely
ignored in the high-pressure studies. The changes in grain size during
nonhydrostatic compression should be taken in to account while
interpreting the strength-pressure data.**

**Synchrotron diffraction study of the pressure-induced transitions in
PbTe- and PbSe- ternary compounds**

[Sergey V. Ovsyannikov]{.underline}^\*^, Andrey Y. Manakov^1^, Alexey I.
Ancharov^2^, Anna Y. Likhacheva^1^, M. A. Sheromov^3^, Ivan F. Berger,
Vladimir V. Shchennikov, Yuri S. Ponosov

*High Pressure Group, Institute of Metal Physics of Russian Academy of
Sciences, Urals Division, GSP-170, 18 S. Kovalevskaya Str.,
Yekaterinburg 620041, Russia, <highpressgroup@mail.ru>, ^1^ A.V.
Nikolaev Institute of Inorganic Chemistry of Russian Academy of
Sciences, Siberian Division, Novosibirsk 630090, Russia, ^2^ Institution
for Solid State and Mechanical Chemistry of Russian Academy of Sciences,
Siberian Division, Novosibirsk 630090, Russia, ^3^ Institute for Nuclear
Physics of Russian Academy of Sciences, Siberian Division, Novosibirsk
630090, Russia*

The structural phase transformations have been investigated both in
ternary Pb~1-x~Sn~x~Te (*x*=0.29), Pb~1-x~Mn~x~Te (*x*=0.05),
Pb~1-x~Sn~x~Se (x=0.125), and in non-stoichiometric compounds
Pb~0.45~Te~0.55~, Pb~0.55~Te~0.45~, at pressures up to 13 GPa with
assistance of short-wave (*λ*=0.3675 Å) synchrotron radiation of the
VEPP-3 accelerator (INP SB RAS, Novosibirsk). The diffraction patterns
were registered by the Image-plate detector MAR-345. A diamond anvils
cell (DAC) with a culet of \~ 1 mm was used for pressure generation in a
liquid medium (ethanol + methanol). A value of pressure was estimated by
the ruby luminescence pressure scale \[1\] as well as by a shift of Ag
diffraction peaks. In the comparative high-pressure Raman measurements
the transition in Pb~1-x~Sn~x~Se (x=0.125) was observed also.

  ---------------------------------------------------- ----------------------------------
  ![](media/image2.jpeg){width="3.216666666666667in"   The crystals taken (Pb~1-x~Sn~x~Te
  height="2.91875in"}                                  (*x*=0.29), Pb~1-x~Mn~x~Te
                                                       (*x*=0.05)) exhibited a difference
                                                       in high-pressure thermoelectric
                                                       power properties measured in the
                                                       synthetic DAC \[2-3\] (Fig. 1)
                                                       that was a motivation for the
                                                       present study. In the
                                                       Pb~1-x~Sn~x~Te (*x*=0.29),
                                                       Pb~1-x~Mn~x~Te (*x*=0.05)
                                                       compounds the phase transformation
                                                       was observed from NaCl to
                                                       distorted NaCl lattice
                                                       (orthorhombic Pnma structure)
                                                       \[4\] above \~ 6 GPa. The lattice
                                                       parameters of both the initial and
                                                       the high-pressure phases were
                                                       estimated by fitting of full
                                                       profile of diffraction spectra.
                                                       Preliminary analysis of a
                                                       transient high-pressure phase in
                                                       the Pb~1-x~Sn~x~Se (x=0.125) did
                                                       not confirm a Pnma lattice, but
                                                       revealed a similarity with GeS
                                                       one. At present the patterns for
                                                       non-stoichiometric compounds are
                                                       deciphered.

  ---------------------------------------------------- ----------------------------------

The work was supported by the Russian Foundation for Basic Research (Gr.
No. 04-02-16178) and by the INTAS (Nr. 03-55-629).

1.  M.I. Eremets. High Pressure Experimental Methods, Oxford-New
    York-Tokyo, Oxford University Press, 1996.

2.  S.V. Ovsyannikov, V.V. Shchennikov, Y.S. Ponosov, et al -- *J. Phys.
    D: Appl. Phys.* **37** (2004) 1151.

3.  S.V. Ovsyannikov, V.V. Shchennikov. -- *physica status solidi (b)*
    **241** (2004) 3231.

4.  G. Rousse, S. Klotz, A.M. Saitta, J. Rodriguez-Carvajal, M.I.
    McMahon, B. Couzinet, M. Mezouar. -- *Phys. Rev. B* **71** (2005)
    224116-6.

**High pressure behaviour of brucite and serpentine**

**Mainak Mookherjee and Lars Stixrude**

**Department of Geological Sciences,**

**University of Michigan, Ann Arbor, MI 48109**

[**mainak@umich.edu**](mailto:mainak@umich.edu)

**We explore the structure and physical properties of brucite and
serpentine over a wide range of pressures with density functional theory
using the variable cell shape plane wave pseudopotential method in the
local density (LDA) and generalized gradient (GGA) approximations. We
use brucite as a starting model for MgO-SiO~2~-H~2~O ternary system. We
are now extending our study to structurally more complex serpentine,
which is extremely important in subduction zone environments.**

**In brucite, we probe the energetics underlying the structure and
dynamics of the proton sub-lattice by performing a series of constrained
and unconstrained static calculations based on an energetically stable**
$\sqrt{3} \times \sqrt{3} \times 1$ **super-cell wherein proton
locations are related to the *6i* Wyckoff sites as opposed to the ideal
*2d* site. The displacement of the hydrogen from the 3‑fold axis
increases with increasing pressure. This means that even in the absence
of thermal energy, the protons are frustrated and would be expected to
exhibit long-range disorder akin to a spin glass. In order to shed light
on the dynamic nature of the proton hopping between the *6i*-like sites,
we have determined the activation energy barrier for such jumps. We find
that the energy barrier increases with compression, possibly indicating
a transition from dynamic proton disorder at lower pressures to static
disorder at higher pressure. We have also investigated the possibility
of proton jumps across the interlayer, by determining the potential
energy well along the O...O vector. We infer that proton jumps across
the interlayer are either severely limited or highly cooperative since
we do not find any evidence of a double well along the O...O vector. The
absence of a double well along the O...O vector, the evolution of
O-H...O distances with compression and the gradual transition to a
symmetric O-H...O configuration, all argue for weak hydrogen bond.**

**Application of Radial X-ray Diffraction to Determine\
the Hydrostatic Equation of State and Strength\
of TiB~2~ up to 60 GPa**

**George M. Amulele, Murli H. Manghnani\
** \
**Hawaii Institute of Geophysics, University of Hawaii, Honolulu, HI
96822, U. S. A.\
**\
**Maddury Somayazulu, Haozhe Liu\
\
Advanced Photon Source, Argonne National Laboratory, Chicago IL 60637,
U. S. A.**

**Room temperature investigations of the shear strength of hexagonal
TiB~2~ have been performed in order to determine the hydrostatic
equation of state of the material up to 60 GPa using radial x-ray
diffraction in a diamond anvil cell. We have analyzed the deformation
mechanisms under pressure by analyzing the (001) and (100) peaks in the
powder diffraction data, and we have deduced the hydrostatic equation of
state of TiB~2~. The uniaxial stresses in the (100), (001) and (101)
diffraction planes show large pressure dependence indicating a
significantly large anisotropy in the material. The stress in the (001)
plane shows the largest increase with pressure and reaches a maximum
value before the other planes, indicating an initial activation of slip
in the (001) plane at the onset of plastic deformation. Compared to
gold, the averaged uniaxial stress component in TiB~2~ is almost 27
times as large at the maximum loading pressure, 60 GPa, achieved in the
experiment.**

[^1]: ^^ **Corresponding author:**

    A.K. Singh, E-mail address: <aksingh@css.nal.res.in>