Non-hydrostatic Stress Research Articles

Effects of deviatoric stresses in the diamond-anvil pressure cell on single-crystal samples

The nonhydrostatic stress states that are developed in the pressure media within diamond-anvil pressure cells have been investigated by single-crystal X-ray diffraction. Measurements of unit-cell parameters of small single crystals under nonhydrostatic conditions are used to calculate the deviatoric strains and, through knowledge of the elastic tensors of the crystals, the stress state of the media. The results confirm that the stress state is effectively cylindrically symmetrical with the stress parallel to the load axis being greater than the radial stresses. The stress state in a given medium can be predicted and can be used to design a specific response of the lattice parameters of small single crystals to pressure beyond the hydrostatic pressure limit of the pressure medium.

Morphological instabilities of stressed and reactive geological interfaces

Interfaces between contacting rocks of the Earth's crust are shown to be unstable and corrugating and develop roughness at various scales when submitted to nonhydrostatic stress. This instability may occur in various geological settings as long as a coherent deformation of the interface is allowed and the bodies that the interface separates have different material properties (i.e., viscosity, density, or elastic moduli). Relevant examples include fault planes, dissolution interfaces, or grain boundaries. Performing a two‐dimensional linear stability analysis, we consider two cases: one solid in contact with a viscous layer and two solids separated by a thin viscous layer. In both cases either shear and/or normal loads are imposed on the interface and thermodynamical conditions for the initiation of roughening are established. Applied on several geological systems such as grain contacts and fault planes, we propose that our analysis can explain how complex patterns may emerge at rock‐rock interfaces. Finally, we provide an analysis of the evolution of the static friction coefficient along sheared interfaces. The evolution is shown to depend solely on Poisson's ratio of the solid and the ratio of the shear and compressional stresses along the interface.

Role of the plate margin curvature in the plateau buildup: Consequences for the central Andes

The influence of convergent plate boundary curvature on the stress distribution in an overriding plate is explored using analytical and numerical modeling techniques. Trench‐parallel compression can be produced near the symmetry axis of a seaward‐concave plate boundary if the interplate friction is high and/or if the subducting lithosphere has a low flexural rigidity, which produces little nonhydrostatic normal stress on the plate boundary. This situation favors the formation of trench‐parallel thrusts with minor trench‐parallel component of slip. Trench‐parallel compression is reduced along the most oblique parts of the plate boundary, which favors the formation of strike slip faults with major trench‐parallel slip. Both the stress conditions on the interplate zone and the 3‐D geometry of this zone control whether the trench‐parallel stress in the center of a seaward‐concave curvature is a tension or compression. Low dip angle and high convergence obliquity angle favor trench‐parallel compression. In the central Andes, N‐S minor shortening in the center of the Arica bend and strike slip systems north and south of the symmetry axis suggest that the effect of shear traction dominated during Cenozoic time when the curvature of the plate boundary was forming. This result suggests that the processes responsible for the formation of the plate boundary curvature were assisted by enhanced interplate friction and/or reduced compressive nonhydrostatic normal stress. For a geometry resembling the present‐day South American plate margin, estimations of normal and shear stresses on the plate boundary suggest that the trench‐parallel stress in the center of the curvature is compressive.

Inelastic Deformation Mechanisms and Damage in Structural Ceramics Subjected to High‐Velocity Impact

The inelastic deformation mechanisms and damage features observed in structural ceramics subjected to nonpenetrating, high‐velocity impacts are similar to those seen in quasistatic Hertzian indentation, albeit more severe. For impacts on large ceramic bodies (relative to impactor diameter), cone cracking is the primary mechanism in regions of high tensile stresses. In regions of nonhydrostatic compressive stresses, depending on the material characteristics, elasticity, grain‐boundary microcracking, or plasticity are the primary mechanisms, and depending on their associated energetics, may be able to compete with the initiation and growth of cone cracks. In this regard, a new model is presented that examines the effect of grain‐boundary microcracking on cone cracking through shear‐induced dilatancy (i.e., bulking) within the quasiplastic zone that forms just underneath the impact site. Depending on the size of the quasiplastic zone and bulking pressure, it is shown that the bulking phenomenon has the potential to suppress cone cracking. Lastly, examples of other shear‐driven inelastic deformation mechanisms are presented.

Preferred Mineral Orientation by Recrystallization under non-Hydrostatic Stress and Geotectonic Stress in the Upper Mantle

Significant elastic anisotropy of olivine single crystal is well known. The velocity of P waves has a maximum in the direction of crystallographic a-axis (identical to optical-acoustic Z-axis). It is also known that dunite and peridotite which are found at the central core of an orogenic zone have a strong tendency to preferred orientation of olivine. The preferred orientation of olivine and elastic anisotropy of dunite in the tectonic zone of Japan are measured optically and acoustically. The latter is carried out using the ultrasonic wave at high pressures. The direction dependence of P wave velocity is expressed by V, = a + b cos2 8, where the direction of 8 = 0 is found to be nearly equal to the direction of lineation which coincides statistically with the direction of a-axis concentration. Recently the existence of anisotropy of the uppermoFt mantle came to be convincing by analysing the results of seismic refraction profiles at the ocean bottom. The P wave velocity can be expressed empirically as V, = a + b cos2 8 where 0 is the azimuth to the perpendicular to the ridge direction. Here the observed seismic anisotropy is attributed to the regional preferred orientation of constituent minerals of rocks composing the upper mantle. The mechanism to produce preferred orientation is known to be either a recrystallization due to elastic anisotropy of minerals or a non-elastic effect such as gliding. In olivine the translation gliding in (010) plane is known. However, it does not seem that such a pure translation gliding can give rise to the significant preferred lattice orientation under stress. Let the preferred orientation of olivine aggregates be due to recrystallization. The stable mineral orientation is specified by the minimum condition of a certain thermodynamic function 4. It must be consistent with the stress and strain continuities at the grain boundary. According to our theory (1) and (2) 4 is represented by a sum of: (a) A function dependent upon a grain shape (interface configuration between grains) (first order). It plays a significant role in mineral orientation of tectonite. However, it is insensitive to the elastic anisotropy. (b) A linear function of deviatric stress component (second order). (c) A quadratic function of stress component (second order). Terms (b) and (c) are related to the stored energy and potential due to deformation and are dependent upon the stress-strain relation, while (a) is independent of stressstrain relation. The expression of C#J is shown in Table 1. Under high hydrostatic pressures greater than lOkb, term (b) becomes predominant. In the actual mineral aggregates, the grain boundary is not a plane, and the surface integral expression of 4 is necessary. To find the condition C#J = min the variational problem for the relative angle between the axis of anisotropy and the axis of external

Equation of State of Tantalum up to 133 GPa

The static equation of state (EOS) of tantalum (Ta) is determined by in situ energy-dispersive synchrotron powder x-ray diffraction in a diamond anvil cell (DAC) up to 133 GPa. The body-centered-cubic (bcc) phase of Ta is found to be stable over the entire pressure range investigated. The bulk moduli and its first pressure derivative of Ta are constrained by fitting the determined pressure-volume data to Vinet form EOS: B0 = 192.65 ± (3.08) GPa and B′0 = 3.58 ± (0.11). For the sake of avoiding the affect of non-hydrostatic stress, argon is used as a pressure media. A careful checking of the stress state of the sample is presented simultaneously.

Ultrafast equilibration of excited electrons in dynamical simulations

In our density-functional-based simulations of materials responding to femtosecond-scalelaser pulses, we have observed a potentially useful phenomenon: the excitedelectrons automatically equilibrate to a Fermi–Dirac distribution within∼100 fs, solely because of their coupling to the nuclear motion, even though the resultingelectronic temperature is one to two orders of magnitude higher than the kinetictemperature defined by the nuclear motion. Microscopic simulations like these can thenprovide the separate electronic and kinetic temperatures, chemical potentials, pressures,and nonhydrostatic stresses as input for studies on larger lengths and timescales.

Solid-liquid interface free energy in binary systems: Theory and atomistic calculations for the (110) Cu–Ag interface

We analyze thermodynamics of solid-liquid interfaces in binary systems when the solid is in a nonhydrostatic state of stress. The difficulty lies in the fact that chemical potential of at least one of the chemical components in a nonhydrostatic solid is an undefined quantity. We show, nevertheless, that the interface free energy gamma can be defined as excess of an appropriate thermodynamic potential that depends on the chemical potentials in the liquid phase. We derive different forms of the adsorption equation for solid-liquid interfaces, with differential coefficients representing excesses of extensive properties. This leads, in particular, to the formulation of interface stress tau(ij) as an appropriate excess over nonhydrostatic bulk stresses. The interface stress is not unique unless the solid is in a hydrostatic state of stress. We also derive Gibbs-Helmholtz type equations that can be applied for thermodynamic integration of gamma. All thermodynamic relations derived here are presented in forms suitable for atomistic simulations. In particular, the excess quantities can be computed without constructing interface profiles. As an application, we perform semigrand canonical Monte Carlo simulations of the (110) solid-liquid interface in the Cu-Ag system. We show that gamma computed by thermodynamic integration along a coexistence path decreases with increasing composition difference between the phases. At the same time, tau(ij) remains negative (i.e., the interface is in a state of compression), drastically increases in magnitude, and becomes highly anisotropic. Some of the interface excess properties are computed by different methods and demonstrate accurate agreement with each other, confirming the correctness of our analysis.

High-pressure study of the magnetic phase transition in MnSi

Measurements of ac magnetic susceptibility and dc resistivity of a high-quality single-crystal MnSi were carried out at high pressure making use of helium as a pressure medium. The form of the ac magnetic susceptibility curves at the magnetic phase transition suddenly changes upon helium solidification. This implies strong sensitivity of magnetic properties of MnSi to nonhydrostatic stresses and suggests that the early claims on the existence of a tricritical point at the phase-transition line are probably a result of misinterpretation of the experimental data. At the same time resistivity behavior at the phase transition does not show such a significant influence of helium solidification. The sharp peak at the temperature derivative of resistivity, signifying the first-order nature of the phase transition in MnSi successfully survived helium crystallization and continued the same way to the highest pressure.

Mechanics of Randomly Folded Thin Materials

In this work, the mechanical properties of randomly folded thin sheets in the hydrostatic and non-hydrostatic stress states were studied. It is pointed out that under the hydrostatic compression the sheet, rigidity is governed by the volume dependence of its enthalpy, whereas in a non-hydrostatic stress state, the rigidity of folded sheets is controlled by the shape dependence of the Edwards entropy of the network of crumpling creases. Furthermore, the stress relaxation in folded sheets after uni-axial compression was studied. It was found that stress relaxation in folded elasto-plastic sheets differs from this in the folded predominantly plastic sheets and obeys an unusual relaxation law with the universal characteristic exponent.

Phase Transformation of Silicon under Nonhydrostatic Stress State: Formation of Si II Phase under a Round Indenter

Silicon transforms from a diamond cubic structure to a β-Sn structure as induced by mechanical stress, the magnitude of which changes depending on the stress state. In this study, the origin of the transformed silicon is explored with a stress criterion independent of the stress state. As an illustration of a nonhydrostatic stress state, the stress distribution of silicon under a round indenter is analyzed by finite element analysis. As a result, the initial formation of β-Sn structured silicon is successfully explained using the new stress criterion.

Depressurization Amorphization of Single-Crystal Boron Carbide

We report depressurization amorphization of single-crystal boron carbide (B4C) investigated by in situ high-pressure Raman spectroscopy. It was found that localized amorphization of B4C takes place during unloading from high pressures, and nonhydrostatic stresses play a critical role in the high-pressure phase transition. First-principles molecular dynamics simulations reveal that the depressurization amorphization results from pressure-induced irreversible bending of C-B-C atomic chains cross-linking 12 atom icosahedra at the rhombohedral vertices.

Finite-time singularities in surface-diffusion instabilities are cured by plasticity

A free material surface which supports surface diffusion becomes unstable when put under external nonhydrostatic stress. Since the chemical potential on a stressed surface is larger inside an indentation, small shape fluctuations develop because material preferentially diffuses out of indentations. When the bulk of the material is purely elastic one expects this instability to run into a finite-time cusp singularity. It is shown here that this singularity is cured by plastic effects in the material, turning the singular solution to a regular crack.

Fluid–solid interaction finite element modeling of a kinetically driven growth instability in stressed solids

The kinetically driven growth instability in stressed solids has been a subject of recent investigation as there is an increasing interest in the effects of non-hydrostatic stresses on crystal growth processes. Recent experimental and modeling work using advanced numerical methods such as boundary element and level set methods have demonstrated that the effect of stress on the solid phase epitaxy (SPE) growth of crystalline silicon from the amorphous phase is responsible for the roughening of its amorphous-crystalline interface. Although our previous model (Phan et al., in Model Simul Mater Sci Eng, 9:309-325, 2001) has been able to explain the observed interfacial instability during the crystal growth of intrinsic silicon, it has not been very successful when extended to the SPE growth process of doped silicon. In an effort to identify the sources that may improve the accuracy and robustness of the previously proposed model, we present in this paper a new approach for modeling the crystal growth in stressed Si layers. The technique is based upon the coupling of a transition-state-theory-based model, a finite element model of the sequentially weak coupling analysis for fluid-solid interaction, and the marker particle method.

In situ high-pressure x-ray diffraction study of H2O ice VII

Ice VII was examined over the entire range of its pressure stability by a suite of x-ray diffraction techniques in order to understand a number of unexplained characteristics of its high-pressure behavior. Axial and radial polycrystalline (diamond anvil cell) x-ray diffraction measurements reveal a splitting of diffraction lines accompanied by changes in sample texture and elastic anisotropy. In situ laser heating of polycrystalline samples resulted in the sharpening of diffraction peaks due to release of nonhydrostatic stresses but did not remove the splitting. Radial diffraction measurements indicate changes in strength of the material at this pressure. Taken together, these observations provide evidence for a transition in ice VII near 14 GPa involving changes in the character of the proton order/disorder. The results are consistent with previous reports of changes in phase boundaries and equation of state at this pressure. The transition can be interpreted as ferroelastic with the appearance of spontaneous strain that vanishes at the hydrogen bond symmetrization transition near 60 GPa.

Instabilities in cubic diamond under non-hydrostatic compressive stress

Diamond is the hardest material with superior mechanical stability. Due to the widespread application in high pressure research, stability limit of diamond at ultrahigh pressure is an importance issue for theoretical and experimental studies, which remains controversy between theoretical prediction and experimental observations. In this paper, we report first-principle calculations on the relative stability of diamond under non-hydrostatic compression and the computational results demonstrate that the cubic diamond would become unstable with respect to the lonsdalite under isotropic stress tensor with mean stress as low as 26 GPa, while agree well with experimental findings under similar non-hydrostatic loading conditions.

Osmium Metal Studied under High Pressure and Nonhydrostatic Stress

Interest in osmium as an ultra-incompressible material and as an analog for the behavior of iron at high pressure has inspired recent studies of its mechanical properties. We have measured elastic and plastic deformation of Os metal at high pressures using in situ high pressure x-ray diffraction in the radial geometry. We show that Os has the highest yield strength observed for any pure metal, supporting up to 10 GPa at a pressure of 26 GPa. Furthermore, our data indicate changes in the nonhydrostatic apparent c/a ratio and clear lattice preferred orientation effects at pressures above 15 GPa.

Pressurizing conditions in helium-pressure-transmitting medium

We present quantitative measurements of the macroscopic non-hydrostatic stress and of the microscopic stress in samples compressed in a diamond anvil cell, using helium as a pressure-transmitting medium. These are based on the analysis of X-ray diffraction line shifts and widths. The macroscopic non-hydrostatic stress reaches 0.3–0.5 GPa at 150 GPa when the sample remains embedded in the pressure medium. The effect of this non-hydrostatic stress on the measured equations of state is estimated in the cases of gold, silver, molybdenum and copper. It is found to be negligible, except in the case of gold. We show that the analysis of the X-ray diffraction line shifts is a more sensitive way of detecting non-hydrostatic compression than the monitoring of the ruby luminescence signal. It can be used to detect when the sample is directly compressed between the diamond anvils. The sample geometry, in particular its thickness, has to be carefully chosen to prevent that situation.

Atomistic Simulation on the Phase Transformation of Silicon under Nonhydrostatic Stress

Silicon transforms from the diamond cubic structure (Si I) to the β-tin structure (Si II) under mechanical stress. The phase transition is affected by the stress state. In this study, we conduct an atomistic simulation to determine the ideal phase transition criterion of silicon under nonhydrostatic stress. We also verify the effects of nonequivalent transverse stress and non-<100>-oriented transverse stress. As a result, we find that the magnitude of transverse stress mainly affects the phase transition, but both transverse differential stress and non<100>-oriented transverse stress have a negligible little effect.

A sequential fluid–solid weak coupling analysis of the SPE in stressed Si layers

The kinetically driven growth instability in stressed solids has been a subject of recent investigation as there is an increasing interest in the effects of non-hydrostatic stresses on crystal growth processes. Recent experimental and modeling work have shown that the effect of stress on the solid phase epitaxy (SPE) growth of crystalline silicon from the amorphous phase is responsible for the roughening of its amorphous–crystalline interface. Although our previous model (Phan, A.-V., Kaplan, T., Gray, L.J., Adalsteinsson, D., Sethian, J.A., Barvosa-Carter, W., Aziz, M.J., 2001. Modelling a growth instability in a stressed solid. Modelling and Simulation in Materials Science and Engineering 9, 309–325.) has been able to explain the observed interfacial instability during the crystal growth of intrinsic silicon, it has not been very successful when extended to the SPE growth process of doped silicon. In an effort to identify the sources that may improve the accuracy and robustness of the previously proposed model, we present in this paper a new approach for modeling the crystal growth in stressed Si layers. The technique is based upon the coupling of finite element analysis, the sequentially weak coupling analysis for fluid–solid interaction, and the marker particle method.