Non-hydrostatic Conditions Research Articles

Phase transitions of silicon under dynamic and non-hydrostatic conditions

Phase transitions of silicon under dynamic and non-hydrostatic conditions

Semi-analytical solution for time-dependent deformations in swelling rocks around circular tunnels

Underground structures in swelling rocks bear time-dependent swelling effects. Upon excavation of underground spaces, the state of stresses and displacements change compared with the initial state. The stress and displacement variations depend on tunnel advance and the rheological behavior of surrounding rock mass. The swelling behaviour of rocks is known as a complicated phenomenon and very important task in tunnel design process. The paper aim is to predict the time-dependent displacement of the tunnel after the excavation has stopped or after installing the support system. The assumption is made that the medium around tunnel is both isotropic and homogenous. The section of tunnel is also assumed circular which in view of stress field, is excavated in Hydrostatic and non-hydrostatic conditions. A semi-analytical model on the basis of experimental results is adopted to evaluate the ground swelling strains as a function of time and stress. Given the current assumptions and conditions, a semi-analytical solution is derived to predict the time-dependent displacements and lining pressure for a circular shaped tunnel section in a swelling ground. Eventually, the model is loaded by an axisymmetric far-field pressure and the effect of the tunnel face on the lining pressure is also considered. On the whole, the comparison between modeling results and actual data, proved an accordance between them. As the results indicate, such parameters as, time dependent modulus of swelling and swelling strain coefficient as well as the initial aspect ratio, play a prominent role in controlling the swelling deformations. The set up time of lining is also considered as an impressing factor controlling the swelling pressure. In mediums of high swelling potential, the temporary support system installation has to be made to allow some ground deformations prior to the permanent support (lining) gets installed which causes the swelling deformation to get relieved.

Study of the compressibility of FeSi, MnSi, and CoS2 transition-metal compounds at high pressures

Silicides and sulfides of transition metals attract great attention of researchers because of a wide spectrum of interesting magnetic, electronic, and optical properties. The crystal structure of FeSi, MnSi, and CoSi silicides is P213(B20), whereas FeS2, CoS2, and MnS2 sulfides have a structure of pyrite Pa3. Despite the great interest in these systems and the cubic symmetry of crystals, the structure and compressibility of these compounds at high pressures are still insufficiently studied. There is a significant spread (more than a factor of two!) in the bulk modulus and its pressure derivative for a single compound. Most studies were performed under nonhydrostatic conditions. In this work, the compressibility of FeSi and MnSi silicides (at pressures up to 35 GPa) and CoS2 sulfide (up to 22 GPa) has been studied by the X-ray diffraction method in a diamond anvil cell with the use of helium as the softest pressure-transmitting medium. The values obtained for the bulk modulus and its derivative—B = 178 ±3 GPa and Bp = 5.6 ± 0.5 for FeSi, B = 167 ± 3 GPa and Bp' = 4.6 ± 0.5 for MnSi, and B = 94 ± 2 GPa and Bp' = 6.9 ± 0.5 for CoS2—can be considered as the most reliable and can be used to test numerous theoretical models. The results for the compressibility of FeSi are important for the verification of models of the Earth’s core.

Crystal structure and transporting properties of Bi2S3 under high pressure: Experimental and theoretical studies

The high-pressure crystal structure and transporting properties of bismuthinite (Bi2S3) have been studied with a combination of experimental and theoretical methods. The present experimental results show that the structure of orthorhombic Bi2S3 stably exists in the experimental pressure range up to around 55 GPa. Upon compression, the X-Ray diffraction (XRD) patterns are dominated by broad Bragg features and seemingly pressure-induced structural amorphization or disorder occurs. However, by analyzing the XRD data obtained during the decompression cycle we suggest that the broad Bragg diffraction peaks under high pressure could be due to the nonhydrostatic conditions or crystal structural defects. To construct the correlation between the structural variation and the physical properties of Bi2S3, the transporting properties of Bi2S3 were investigated under high pressure. With increasing pressure, the resistance value decreases sharply below 5 GPa and then decreases gently as the pressure further increasing. There is an obvious inflection point at about 5 GPa in the relationships of log (R) versus pressure. We speculate that the observed electrical variation is resulted from the pressure-induced second-order isostructural phase transition according to the reported literature. Temperature dependence of the resistance indicated that a pressure-induced semiconductor → metal transition in Bi2S3 happens at around 20 GPa. The present high pressure resistance measurement indicated that high pressure could help to improve the thermoelectric properties.

The structural response of gadolinium phosphate to pressure

Accurate elastic constants for gadolinium phosphate (GdPO4) have been measured by single-crystal high-pressure diffraction methods. The bulk modulus of GdPO4 determined under hydrostatic conditions, 128.1(8) GPa (Kʹ=5.8(2)), is markedly different from that obtained with GdPO4 under non-hydrostatic conditions (160(2) GPa), which indicates the importance of shear stresses on the elastic response of this phosphate. High pressure Raman and diffraction analysis indicate that the PO4 tetrahedra behave as rigid units in response to pressure and that contraction of the GdPO4 structure is facilitated by bending/twisting of the Gd–O–P links that result in increased distortion in the GdO9 polyhedra.

High pressure structural study of samarium doped CeO2 oxygen vacancy conductor — Insight into the dopant concentration relationship to the strain effect in thin film ionic conductors

The bulk modulus of nanocrystalline, fluorite-structured samarium doped ceria, Sm0.2Ce0.8O1.9, has been investigated using synchrotron-based high-pressure X-ray diffraction technique. Experiments were carried out under both quasi-hydrostatic condition with silicon oil pressure transmitting medium (PTM) and nonhydrostatic conditions without PTM. The high pressure structural results indicate that the highly defected ionic conductor is stable up to 20GPa and has a lower bulk modulus than what has been reported for undoped-CeO2. The isothermal bulk modulus of Sm0.2Ce0.8O1.9 is ~150–190GPa compared to ~210–220GPa for CeO2. The collected data experimentally verifies the effect of Sm3+ dopant and oxygen vacancy defect formation on bulk modulus in doped CeO2. The effect of modulus on misfit dislocation formation and dopant ion segregation is discussed in relation to a fundamental understanding of the strain effect in this important family of fast ionic conductors, with potential application as oxygen vacancy conducting solid state electrolytes.

Guest dependent Brillouin and Raman scattering studies of zeolitic imidazolate framework-8 (ZIF-8) under external pressure.

We have investigated the pressure dependence of the acoustic modes of zeolitic imidazolate framework (ZIF-8) in different pressure transmitting mediums and also under non-hydrostatic conditions using high pressure Brillouin spectroscopy. Our study shows the pressure induced flexibility and dynamics of ZIF-8 framework as well as a huge increase in the acoustic velocities on applying external pressure, illustrating the role of guest in enhancing the elastic properties of the framework. In fact, the elastic constant C11 of the guest incorporated ZIF-8 increases by ∼183% on applying a pressure of only 1.47 GPa. The pressure transmitting medium also plays an important role in controlling the gate opening behaviour of ZIF-8. Pressure dependent Raman study shows significant changes in the modes of ZIF-8 as well as that of that of the pressure transmitting medium which is entrapped within the framework, indicating that the interaction between the framework and guest is responsible for the medium dependent changes observed in the Brillouin spectra.

Shear-Induced Isostructural Phase Transition and Metallization of Layered Tungsten Disulfide under Nonhydrostatic Compression

Pressure-induced structural and electronic transformations of tungsten disulfide (WS2) have been studied to 60 GPa, in both hydrostatic and nonhydrostatic conditions, using four-probe electrical resistance measurements, micro-Raman spectroscopy, and synchrotron X-ray diffraction. The results show the evidence for an isostructural phase transition from hexagonal 2Hc phase to hexagonal 2Ha phase, which accompanies the metallization at ∼37 GPa. This isostructural transition occurs displacively over a large pressure range between 15 and 45 GPa and is driven by the presence of strong shear stress developed in the layer structure of WS2 under nonhydrostatic compression. Interestingly, this transition is absent in hydrostatic conditions using He pressure medium, underscoring its strong dependence on the state of stress. We attribute the absence to the incorporation of He atoms between the layers, mitigating the development of shear stress. We also conjecture a possibility of magnetic ordering in WS2 that may occ...

In situ spectroscopic study of the plastic deformation of amorphous silicon under non-hydrostatic conditions induced by indentation.

Indentation-induced plastic deformation of amorphous silicon (a-Si) thin films was studied by in situ Raman imaging of the deformed contact region of an indented sample, employing a Raman spectroscopy-enhanced instrumented indentation technique. Quantitative analyses of the generated in situ Raman maps provide unique, new insight into the phase behavior of as-implanted a-Si. In particular, the occurrence and evolving spatial distribution of changes in the a-Si structure caused by processes, such as polyamorphization and crystallization, induced by indentation loading were measured. The experimental results are linked with previously published work on the plastic deformation of a-Si under hydrostatic compression and shear deformation to establish a sequence for the development of deformation of a-Si under indentation loading. The sequence involves three distinct deformation mechanisms of a-Si: (1) reversible deformation, (2) increase in coordination defects (onset of plastic deformation), and (3) phase transformation. Estimated conditions for the occurrence of these mechanisms are given with respect to relevant intrinsic and extrinsic parameters, such as indentation stress, volumetric strain, and bond angle distribution (a measure for the structural order of the amorphous network). The induced volumetric strains are accommodated solely by reversible deformation of the tetrahedral network when exposed to small indentation stresses. At greater indentation stresses, the increased volumetric strains in the tetrahedral network lead to the formation of predominately five-fold coordination defects, which seems to mark the onset of irreversible or plastic deformation of the a-Si thin film. Further increase in the indentation stress appears to initiate the formation of six-fold coordinated atomic arrangements. These six-fold coordinated arrangements may maintain their amorphous tetrahedral structure with a high density of coordination defects or nucleate as a new crystalline β-tin phase within the a-Si network.

Yield strength of Ni–Al–Cr superalloy under pressure

Abstract Ni based superalloy Ni–Al–Cr with γ and γ′ phase was studied under high pressure up to 30 GPa using diamond anvil cell technique. In-situ X-ray diffraction data was collected on these alloys under hydrostatic and non-hydrostatic conditions. Cubic phase remains stable up to the highest pressure of about 30 GPa. Bulk modulus and its pressure derivative obtained from the volume compression of pressure data are K = 166.6 ± 5.8 GPa with K′ set to 4 under hydrostatic conditions and K = 211.3 ± 4.7 GPa with K′ set to 4 for non-hydrostatic conditions. Using lattice strain theory, maximum shear stress ‘t’ was determined from the difference between the axial and radial stress components in the sample. The magnitude of shear stress suggests that the lower limit of compressive strength increases with pressure and shows maximum yield strength of 1.8 ± 0.3 GPa at 20 GPa. Further, we have also determined yield strength using pressure gradient method. In both the methods, yield strength increases linearly with applied pressure. The results are found to be in good agreement with each other and the literature values at ambient conditions.

Cobalt ferrite nanoparticles under high pressure

We report by the first time a high pressure X-ray diffraction and Raman spectroscopy study of cobalt ferrite (CoFe2O4) nanoparticles carried out at room temperature up to 17 GPa. In contrast with previous studies of nanoparticles, which proposed the transition pressure to be reduced from 20–27 GPa to 7.5–12.5 GPa (depending on particle size), we found that cobalt ferrite nanoparticles remain in the spinel structure up to the highest pressure covered by our experiments. In addition, we report the pressure dependence of the unit-cell parameter and Raman modes of the studied sample. We found that under quasi-hydrostatic conditions, the bulk modulus of the nanoparticles (B0 = 204 GPa) is considerably larger than the value previously reported for bulk CoFe2O4 (B0 = 172 GPa). In addition, when the pressure medium becomes non-hydrostatic and deviatoric stresses affect the experiments, there is a noticeable decrease of the compressibility of the studied sample (B0 = 284 GPa). After decompression, the cobalt ferrite lattice parameter does not revert to its initial value, evidencing a unit cell contraction after pressure was removed. Finally, Raman spectroscopy provides information on the pressure dependence of all Raman-active modes and evidences that cation inversion is enhanced by pressure under non-hydrostatic conditions, being this effect not fully reversible.

Coexistence pressure for a martensitic transformation from theory and experiment: Revisiting the bcc-hcp transition of iron under pressure

The coexistence pressure of two phases is a well-defined point at fixed temperature. In experiment, however, due to non-hydrostatic stresses and a stress-dependent potential energy barrier, different measurements yield different ranges of pressure with a hysteresis. Accounting for these effects, we propose an inequality for comparison of the theoretical value to a plurality of measured intervals. We revisit decades of pressure experiments on the bcc - hcp transformations in iron, which are sensitive to non-hydrostatic conditions and sample size. From electronic-structure calculations, we find a bcc - hcp coexistence pressure of 8.4 GPa. We construct the equation of state for competing phases under hydrostatic pressure, compare to experiments and other calculations, and address the observed pressure hysteresis and range of onset pressures of the nucleating phase.

New automated shear cell with diamond anvils for in situ studies of materials using X-ray diffraction

A new design of an automated shear cell with diamond anvils for X-ray in situ studies has been developed and manufactured. As compared with a previous design, the dimensions and weight of the new cell have been reduced almost by one half on retention of the pressure range up to 100 GPa. To demonstrate the efficiency of the apparatus, the investigations of the possibility to use polycrystalline NaCl as a sensor of pressure at diffraction studies of samples in nonhydrostatic compression conditions have been carried out.

Deviatoric stress-induced phase transitions in diamantane.

The high-pressure behavior of diamantane was investigated using angle-dispersive synchrotron x-ray diffraction (XRD) and Raman spectroscopy in diamond anvil cells. Our experiments revealed that the structural transitions in diamantane were extremely sensitive to deviatoric stress. Under non-hydrostatic conditions, diamantane underwent a cubic (space group Pa3) to a monoclinic phase transition at below 0.15 GPa, the lowest pressure we were able to measure. Upon further compression to 3.5 GPa, this monoclinic phase transformed into another high-pressure monoclinic phase which persisted to 32 GPa, the highest pressure studied in our experiments. However, under more hydrostatic conditions using silicone oil as a pressure medium, the transition pressure to the first high-pressure monoclinic phase was elevated to 7-10 GPa, which coincided with the hydrostatic limit of silicone oil. In another experiment using helium as a pressure medium, no phase transitions were observed to the highest pressure we reached (13 GPa). In addition, large hysteresis and sluggish transition kinetics were observed upon decompression. Over the pressure range where phase transitions were confirmed by XRD, only continuous changes in the Raman spectra were observed. This suggests that these phase transitions are associated with unit cell distortions and modifications in molecular packing rather than the formation of new carbon-carbon bonds under pressure.

Structural stability and compressive behavior of ZrH2under hydrostatic pressure and nonhydrostatic pressure

The important transition metal dihydride ZrH2 has been characterized using in situ synchrotron X-ray diffraction combined with diamond anvil cell techniques and ab initio calculations. The effect of a pressure-transmitting medium on the structural stability and compressive behavior was investigated under both hydrostatic pressure and nonhydrostatic pressure conditions. The ambient I4/mmm structure is stable under both nonhydrostatic and hydrostatic compressions. The supplementary theoretical calculations have proposed that the I4/mmm structure transformed into the P4/nmm structure above 100 GPa confirming the stability of the I4/mmm structure during the experimental runs. The difference in the volume reduction between the two compressions becomes larger with increasing pressure. Up to about 50 GPa, the volume collapse of nonhydrostatic compression is 6% relative to the hydrostatic compression. The present study offers a new approach with nonhydrostatic compression or shear stress for finding higher volumetric density hydrogen structures in metal hydrides.

Dilation and Post-peak Behaviour Inputs for Practical Engineering Analysis

Numerical models used by engineers to simulate rockmass behaviour are often limited by poor or incomplete representations of post-yield behaviour. Although conventional plasticity theory is often capable of predicting stress distributions around excavations, it is more difficult to fully capture the complex displacement patterns that are observed in situ. This is largely because conventional material models fail to capture the confinement and damage accumulation dependencies of post-yield dilatancy. Even with these mechanistic limitations in mind, simple constitutive models can be used for practical applications, although no reliable methodology for parameter selection exists. This study aims to remedy this deficiency. In this work, existing models for dilatancy based on laboratory testing data are considered and their limitations are discussed. The most accurate of these models add complexity to the analyses and also require additional input parameters beyond those which are typically obtained from laboratory testing. While the concept of a constant dilation angle during yield is not physically valid, it may be, in some cases, a sufficient model for ground response prediction. It is of interest, for practical engineering analyses, to understand the conditions where this additional complexity is required and where simplified models may be adequate. For the case of circular excavations in a uniform stress field, plastic zone displacements for mobilized and constant dilation angle models are compared and parametric sensitivities are discussed. Many material parameter combinations representative of relatively ductile rockmasses are tested, and it is shown that for most of these cases, the results obtained using a mobilized dilation angle can be well approximated through the use of an appropriate best-fit constant dilation angle. Through a statistical analysis of the data, a practical methodology for the selection of a constant dilation angle for use in simpler continuum numerical models is proposed. Further analysis under more general conditions performed using finite-difference models shows that the methodology can be applied to non-circular excavation geometries (errors are only significant near corners), general strain softening behaviour, and non-hydrostatic stress conditions where the stress anisotropy is moderate. An example of the methodology is presented in the context of extensometer data from a deep mine shaft, and the success of the methodology in providing a reasonable dilation angle estimate is demonstrated.

Structural phase stability in nanocrystalline titanium to 161 GPa

Nanocrystalline titanium (nc-Ti) metal was investigated up to 161 GPa at room temperature using a diamond anvil cell. X-ray diffraction and electrical resistance techniques were used to investigate the compressibility and structural phase stability. nc-Ti is observed to undergo three structural phase transitions at high pressures, starting with at 10 GPa and followed by at 127 GPa and at 140 GPa. The observed structural phase transitions, as well as compressibility, are consistent with previously reported values for coarse grained Ti (c-Ti). The high pressure experiments on nc-Ti samples do no show any significant variation of the transition pressure under varying non-hydrostatic conditions. This is in sharp contrast to c-Ti, where a significant decrease in the transition pressure is observed under increasing non-hydrostatic conditions. This would indicate that the decrease in grain size in nano grained titanium makes the phase transition less sensitive to shear stresses as compared to bulk or c-Ti.

Modeling graphite under stress: Equations of state, vibrational modes, and interlayer friction

Extensive two- and three-dimensional periodic first-principles simulations have been carried out to investigate the mechanical response of graphite to hydrostatic and nonhydrostatic stress conditions. Our results show a clear analogy between uniaxial $({\ensuremath{\sigma}}_{z})$ stress and hydrostatic pressure as far as structural changes in the unit cell are concerned. For intralayer C-C distances and in-plane graphite vibrational frequencies, the similarity with hydrostatic conditions is however found under biaxial $({\ensuremath{\sigma}}_{x}={\ensuremath{\sigma}}_{y})$ stresses. The calculated uniaxial equation of state is further used to investigate sliding mechanisms of a graphite layer in graphite at different interlayer separations, thus providing insight at an atomic level on the origin of the low static friction coefficient of graphite.

High-pressure structural behaviour of HoVO4: combined XRD experiments and ab initio calculations

We report a high-pressure experimental and theoretical investigation of the structural properties of zircon-type HoVO4. Angle-dispersive x-ray diffraction measurements were carried out under quasi-hydrostatic and partial non-hydrostatic conditions up to 28 and 23.7 GPa, respectively. In the first case, an irreversible phase transition is found at 8.2 GPa. In the second case, the onset of the transition is detected at 4.5 GPa, a second (reversible) transition is found at 20.4 GPa, and a partial decomposition of HoVO4 was observed. The structures of the different phases have been assigned and their equations of state (EOS) determined. Experimental results have also been compared to theoretical calculations which fully agree with quasi-hydrostatic experiments. Theory also suggests the possibility of another phase transition at 32 GPa; i.e. beyond the pressure limit covered by present experiments. Furthermore, calculations show that deviatoric stresses could trigger the transition found at 20.4 GPa under non-hydrostatic conditions. The reliability of the present experimental and theoretical results is supported by the consistency between the values yielded for transition pressures and EOS parameters by the two methods.

In-situ high-pressure powder X-ray diffraction study of α-zirconium phosphate.

The high-pressure structural chemistry of α-zirconium phosphate, α-Zr(HPO4)2·H2O, was studied using in-situ high-pressure diffraction and synchrotron radiation. The layered phosphate was studied under both hydrostatic and non-hydrostatic conditions and Rietveld refinement carried out on the resulting diffraction patterns. It was found that under hydrostatic conditions no uptake of additional water molecules from the pressure-transmitting medium occurred, contrary to what had previously been observed with some zeolite materials and a layered titanium phosphate. Under hydrostatic conditions the sample remained crystalline up to 10 GPa, but under non-hydrostatic conditions the sample amorphized between 7.3 and 9.5 GPa. The calculated bulk modulus, K0 = 15.2 GPa, showed the material to be very compressible with the weak linkages in the structure of the type Zr-O-P.