The Thermodynamic and Lattice Vibrational Properties of CuPd Alloy Under Hydrostatic Pressure

Litov and Anderson after various considerations suggested a four constant potential function for a-Se as well as a-As2S3. Hence we also used a four constant potential function with the sole purpose of applying this potential function to obtain several acoustic, thermodynamic and other properties. We calculated several acoustic properties of a-Se like second order elastic constants (SOECs), their pressure derivatives, the longitudinal and transverse Gruneisen constant by two different methods, phonon frequencies, absorption band position through the use of Nath-Smith-Delaunay’s equation, and the thermodynamic properties like heat capacity, bulk modulus, thermal Gruneisen constant, the pressure derivative of the bulk modulus (dK T/dP=C 1), the pressure derivative ofC 1 which is related to Anderson-Gruneisen parameter, pressure derivative of Gruneisen constant namelyγ′ g which is related to second Gruneisen constant, characteristics of phonon frequencies, potential energy function through the use of fitted parameters and third order elastic constants. Finally we calculatedK T at the reduced density ofρ/ρ 0=1.1.K T is obtained from the potential function with the fitted parameters. In all the above cases the calculated values are found to be in good agreement with experiment wherever available. In this connection it is important to point out that we eliminated ‘C’ a constant in the potential function using the equilibrium condition as was done by Litovet al in a-Se and Gerlichet al in the case of a-As2S3 as all amorphous substances are isotropic as mentioned by several authors. We contemplate to calculate several other properties for a-Se and a-As2S3 and present them at a later stage.

Iron is the main constituent in Earth’s core, along with ~5 to 10 wt% Ni and some light elements (e.g., H, C, O, Si, S). This thesis explores the vibrational thermodynamic and thermoelastic properties of pure hexagonal close-packed iron (e-Fe), in an effort to improve our understanding of the properties of a significant fraction of this remote region of the deep Earth and in turn, better constrain its composition. In order to access the vibrational properties of pure e-Fe, we directly probed its total phonon density of states (DOS) by performing nuclear resonant inelastic x-ray scattering (NRIXS) and in situ x-ray diffraction (XRD) experiments at Sector 3-ID-B of the Advanced Photon Source (APS) at Argonne National Laboratory. NRIXS and in situ XRD were collected over the course of ~14 days at eleven compression points between 30 and 171 GPa, and at 300 K. Our in situ XRD measurements probed the sample volume at each compression point, and our long NRIXS data-collection times and high-energy resolution resulted in the highest statistical quality dataset of this type for e-Fe to outer core pressures. Hydrostatic conditions were achieved in the sample chamber for our experiments at smaller compressions (P ≤ 69 GPa) via the loading of a neon pressure transmitting medium at the GeoSoilEnviroCARS (GSECARS) sector of the APS. For measurements made at P > 69 GPa, the sample was fully embedded in boron epoxy, which served as the pressure transmitting medium. From each measured phonon DOS and thermodynamic definitions, we determined a wide range of vibrational thermodynamic and thermoelastic parameters, including the Lamb-Mossbauer factor; vibrational components of the specific heat capacity, free energy, entropy, internal energy, and kinetic energy; and the Debye sound velocity. Together with our in situ measured volumes, the shape of the total phonon DOS and these parameters gave rise to a number of important properties for e-Fe at Earth’s core conditions. For example, we determined the Debye sound velocity (vD) at each of our compression points from the low-energy region of the phonon DOS and our in situ measured volumes. In turn, vD is related to the compressional and shear sound velocities via our determined densities and the adiabatic bulk modulus. Our high-statistical quality dataset places a new tight constraint on the density dependence of e-Fe’s sound velocities to outer core pressures. Via comparison with existing data for iron alloys, we investigate how nickel and candidate light elements for the core affect the thermoelastic properties of iron. In addition, we explore the effects of temperature on e-Fe’s sound velocities by applying pressure- and temperature-dependent elastic moduli from theoretical calculations to a finite-strain model. Such models allow for direct comparisons with one-dimensional seismic models of Earth’s solid inner core (e.g., the Preliminary Reference Earth Model). Next, the volume dependence of the vibrational free energy is directly related to the vibrational thermal pressure, which we combine with previously reported theoretical values for the electronic and anharmonic thermal pressures to find the total thermal pressure of e-Fe. In addition, we found a steady increase in the Lamb-Mossbauer factor with compression, which suggests restricted thermal atomic motions at outer core pressures. This behavior is related to the high-pressure melting behavior of e-Fe via Gilvarry’s reformulation of Lindemann’s melting criterion, which we used to obtain the shape of e-Fe’s melting curve up to 171 GPa. By anchoring our melting curve shape with experimentally determined melting points and considering thermal pressure and anharmonic effects, we investigated e-Fe’s melting temperature at the pressure of the inner–core boundary (ICB, P = 330 GPa), where Earth’s solid inner core and liquid outer core are in contact. Then, combining this temperature constraint with our thermal pressure, we determined the density of e-Fe under ICB conditions, which offers information about the composition of Earth’s core via the seismically inferred density at the ICB. In addition, the shape of the phonon DOS remained similar at all compression points, while the maximum (cutoff) energy increased regularly with decreasing volume. As a result, we were able to describe the volume dependence of e-Fe’s total phonon DOS with a generalized scaling law and, in turn, constrain the ambient temperature vibrational Gruneisen parameter. We also used the volume dependence of our previously mentioned vD to determine the commonly discussed Debye Gruneisen parameter (γD), which we found to be ~10% smaller than our vibrational Gruneisen parameter at any given volume. Finally, applying our determined vibrational Gruneisen parameter to a Mie-Gruneisen type relationship and an approximate form of the empirical Lindemann melting criterion, we predict the vibrational thermal pressure and estimate the high-pressure melting behavior of e-Fe at Earth’s core pressures, which can be directly compared with our previous results. Finally, we use our measured vibrational kinetic energy and entropy to approximate e-Fe’s vibrational thermodynamic properties to outer core pressures. In particular, the vibrational kinetic energy is related to the pressure- and temperature-dependent reduced isotopic partition function ratios (β-factors) of e-Fe and in turn, provide information about the partitioning behavior of solid iron in equilibrium processes. In addition, the volume dependence of vibrational entropy is directly related to the product of e-Fe’s vibrational component of the thermal expansion coefficient and the isothermal bulk modulus, which we find to be independent of pressure (volume) at 300 K. In turn, this product gives rise to the volume-dependent thermal expansion coefficient of e-Fe at 300 K via established EOS parameters, and the vibrational Gruneisen parameter and temperature dependence of the vibrational thermal pressure via thermodynamic definition.

Interatomic force constants have been determined, acoustic and optical phonon frequencies have been calculated, phonon dispersion curves have been constructed, and the density of states in the phonon spectrum has been obtained for Hg2Br2 model ferroelastic crystals. The effect of hydrostatic pressure on the acoustic and optical phonon frequencies and their dispersion has been theoretically analyzed. It is established that an increase in the pressure leads to significant softening of the slowest acoustic TA branch (soft mode) at the X point of the Brillouin zone, which agrees with the phenomenological Landau theory of phase transitions and is consistent with the available experimental data.

The present research is a systematic computational study focused on structural, mechanical, electronic, vibrational, optical and thermo-dynamical properties of zinc-blende (B3) structured beryllium chalcogenides BeZ (Z=S, Se, Te) compounds using ATK-DFT method using PZ and PBEsol exchange and correlation potentials within the local density approximation (LDA) and the generalized gradient approximation (GGA) respectively and their comparison. The k-point and energy cut-off values were tested and provided convergence in self-consistent calculations. The structural parameters such as lattice constant, bulk modulus, second order elastic constants (C11, C12, C44) and material properties (B, G, Y and σ) for these crystals are computed and discussed. To explain the electronic properties, electronic energy band structure, complex band structures, phonon band structure, phonon density of state and electron density distribution are plotted. The effect of pressure on elastic constant, material properties and phase transitions are also studied, including phase transition from ZB structure to NiAs appearing at 53 GPa, 49 GPa and 33 GPa for BeS, BeSe, and BeTe respectively.

Dispersion relations of the acoustic and optical phonon frequencies have been calculated and plotted, and the density of states of the phonon spectrum of Hg2Cl2 and Hg2Br2 crystals has been derived. The effect of hydrostatic pressure on the frequencies of acoustic and optical phonons and their dispersion has been theoretically analyzed. It has been found that an increase in the pressure leads to a strong softening of the slowest acoustic TA branch (the soft mode) at the X point of the Brillouin zone boundary, which is consistent with the phenomenological Landau theory and correlates with experiment.

The effects of temperature and hydrostatic pressure have been measured on the velocities of longitudinal and shear ultrasonic waves propagated in ceramic specimens of a composite comprising YBa2Cu3O7-x together with 15 vol.% metallic silver. At room temperature and atmospheric pressure the bulk modulus B0 of the composite is 1.8 times larger than that of the pure YBa2Cu3O7-x ceramic of similar porosity. The ultrasonic wave velocities increase smoothly with decreasing temperature from 300 to 10 K and do not show the anomalous step-like changes including the hysteresis effects in the temperature range 190-235 K, which characterize the elastic behaviour of pure YBa2Cu3O7-x ceramic. The ultrasonic attenuation shows peaks resembling those observed in YBa2Cu3O7-x itself, which result from low-activation-energy anelastic relaxation processes. The effects of hydrostatic pressure on the velocities of ultrasonic waves propagated in the composite and hence the hydrostatic pressure derivatives ( delta CL/ delta P)P=0 and ( delta mu / delta P)P=0 of the elastic stiffnesses and ( delta B/ delta P)P=0 of the bulk modulus are substantially smaller than those found previously for pure YBa2Cu3O7-x ceramics.

The effect of hydrostatic pressure on the physical properties of magnesium arsenide in cubic and hexagonal phases

The thermal and mechanical properties of Pd, Pt, and Rh pure metals are thoroughly investigated using advanced molecular dynamics (MD) simulations, employing the Sutton-Chen (SC) and quantum Sutton-Chen (Q-SC) potential models. The study aims to analyze the behavior of these metals under increasing temperatures, providing insights into their structural stability and thermodynamic properties. The materials are heated from 0 K to temperatures slightly above their respective melting points in increments of 100 K. Temperature-dependent polynomial and linear functions of the simulation results, derived using both SC and Q-SC models, are obtained to establish a comprehensive understanding of their temperature-dependent properties. Key physical properties, including lattice parameter, density, enthalpy, cohesive energy, elastic constants, bulk modulus, shear modulus, Poisson’s ratio, Young’s modulus, heat capacity, and thermal expansion coefficient, are systematically calculated. The study compares the performance of SC and Q-SC potentials in predicting these properties and evaluates their accuracy against available experimental and theoretical data in the literature. The findings contribute to a better understanding of the thermomechanical behavior of noble metals, aiding in their potential applications in high-temperature environments and advanced material design. The comparative analysis of SC and Q-SC models also highlights their strengths and limitations in simulating metallic systems.

Elastic nonlinearities are particularly relevant for soft materials because of their inherently small linear elasticity. Nonlinear elastic properties may even take over the leading role for the transformation at mechanical instabilities accompanying many phase transitions in soft matter. Because of inherent experimental difficulties, only little is known about third order (nonlinear) elastic constants within liquids, gels and polymers. Here we show that a key concept to access third order elasticity in soft materials is the determination of mode Grüneisen parameters. We report the first direct observation of third order elastic constants across mechanical instabilities accompanying the liquid–liquid demixing transition of semi-dilute aqueous poly(N-isopropylacrylamide) (PNIPAM) solutions. Immense elastic nonlinearities, leading to a strong strain-softening in the phase-separating PNIPAM solutions, are observed. Molecular mechanisms, which may be responsible for these immense elastic nonlinearities, are discussed. The importance of third order elastic constants in comparison to second order (linear) elastic constants in the demixing PNIPAM solutions evidences the need to focus more on the general role played by nonlinear elasticity at phase transitions within synthetic and biological liquids and gels.

Temperature-dependent ultrasonic velocities and ultrasonic Gruneisen parameters have been studied in berkelium monopnictides BkX (X N, P, As, Sb) in the temperature range 100–500K along the \({\langle100\rangle}\), \({\langle110\rangle}\) and \({\langle111\rangle}\) for longitudinal and shear modes of propagation. For the same evaluation we have also computed second and third order elastic constants using Coulomb and Born–Mayer potentials at temperatures 0–500K. The bulk moduli, tetragonal moduli, the ratio of bulk modulus (BT) and isotropic shear modulus (G), i.e., BT/G and Debye temperatures are also evaluated at room temperature using second and third order elastic constants. We found BT/G less than 1.75, so the chosen materials are brittle in nature. Since the Born mechanical stability criterion is satisfied by these compounds, so these are stable at the chosen temperature range. Propagation of ultrasonic wave is found highest in case of BkN due to the high ultrasonic velocity. BkN and BkSb are the best candidates along \({\langle100\rangle}\) for longitudinal mode of propagation and along \({\langle110\rangle}\) for shear mode of propagation, respectively, for thermal uses as their high valued Gruneisen parameters. The results of this investigation are discussed in correlation with other known thermophysical properties.

Pulse-echo overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of ceramic transition-metal carbides TiC and TaC as functions of temperature in the range 135–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. The carbon concentration of each ceramic has been determined using an oxidation method: the carbon-to-metal atomic ratios are both 0.98. In general, the values determined for the adiabatic bulk modulus (B S), shear stiffness (μ), Young's modulus (E), Poisson's ratio (σ) and acoustic Debye temperature (ΘD) for the TiC and TaC ceramics agree well with the experimental values determined previously. The temperature dependences of the longitudinal stiffness (C L) and shear stiffness measured for both ceramics show normal behaviour and can be approximated by a conventional model for vibrational anharmonicity. Both the bulk and Young's moduli of the ceramics increase with decreasing temperature and do not show any unusual effects. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to determine the hydrostatic pressure derivatives of elastic stiffnesses and the acoustic-mode Gruneisen parameters. The values determined at 295 K for the hydrostatic pressure derivatives (∂C L/∂P)P = 0, (∂μ/∂P)P = 0 and (∂B S/∂P)P = 0 for TiC and TaC ceramics are positive and typical for a stiff solid. The adiabatic bulk modulus B S and its hydrostatic pressure derivative (∂B S/∂P)P = 0 of TiC are in good agreement with the results of recent high pressure X-ray diffraction measurements and theoretical calculations. The longitudinal (γL), shear (γS) and mean (γel) acoustic-mode Gruneisen parameters of TiC and TaC ceramics are positive: the zone-centre acoustic phonons stiffen under pressure. The shear γS is much smaller than the longitudinal γL. The relatively larger values estimated for the thermal Gruneisen parameter γth in comparison to γel for the TiC and TaC ceramics indicate that the optical phonons have larger Gruneisen parameters. Hence knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic TiC and TaC.

It has been the object of the present study to elucidate the effect of hydrostatic stress on the mechanical behavior of polycrystalline metals at elevated temperatures. In the studies hitherto made by authors, the effect of hydrostatic stress on metallic tensile creep and torsional creep was investigated through the tests under combined hydrostatic pressure at room temperature. The question concerning the pressure effect under the influence of elevated temperatures has, however, been left still for further inquiry. From (The present) analytical and experimental studies on tensile plastic deformation and tensile creep under hydrostatic pressure at elevated temperatures, the following conclusions have been made.(1) The effect of combined hydrostatic pressure on the plastic flow stress of polycrystalline metals at elevated temperature is observable in the region of large plastic deformation. Therefore, it is necessary to consider the influence of hydrostatic stress in the yielding condition at this region.(2) The effect of concentrated pressure on metallic creep results in decrease in the strain rate of second creep stage at elevated temperature as the same behavior at room temperature. The effect of hydrostatic pressure on metallic creep at elevated temperature may be more intensive than that on the static tensile strength at the same temperature.

An investigation into the influence of hydrostatic pressure on the ultimate capacity of tubular joints is presented. Finite element studies of cross (DT) joints subjected to axial compression and in-plane bending are used to assess the effect that varying amounts of external pressure have on joint capacity. The matrix of geometries evaluated include variations in branch to chord diameter ratio (?), chord radius to thickness ratio (?), and branch to chord thickness ratio (?). Variations in yield strength were also considered, but the same value was always assumed for both the branch and chord. Findings can be divided into two categories. First, longitudinal loads resulting from capped end pressures, as deduced from consideration of isolated members or a frame analysis, may be treated merely as additional axial loads. For deeper water, the magnitude of the branch axial loads from hydrostatic pressure can be substantial and, thus can increase the joint strength utilization ratio. The effect of capped end forces on the chord can be estimated from the normal chord stress effect term, Qf, of the joint capacity equations. However, the impact is expected to be trivial in most instances. The second category of results concerns the effect of hydrostatic radial pressure alone on joint capacity. The analyses show that the capacity can be reduced by as much as 25%, depending on joint parameters and the type of longitudinal load in the branch. Parameter ? is the most important one in relating nondimensionalized branch load and nondimensionalized hydrostatic pressure. Based on a limited number of T-joint cases studied, it appears that the DT-joint interaction equation adjustments, suggested in this study, are a conservative representation T-joint behavior. Also, it seems likely that capacities of other joint configurations will be affected by hydrostatic pressure and should be investigated. INTRODUCTION The offshore oil industry is exploring in progressively deeper water in order to locate economic oil reserves. The deeper waters confront the designers of offshore structures with challenging problems. The member and joint dimensions for shallow water structures are designed according to the expected loading and component capacities, which are provided in various design equations. For deep water structures, an important additional source of loading can be hydrostatic pressure. Overall member behavior in the presence of hydrostatic pressure has received some attention latelyl. In fact, the draft version of API RP2A-LRFD2 reflects these recent studies. However, the effect of hydrostatic pressure on joint capacity has received little or no attention to date. The intent of this analysis has been to provide some design guidance by determining correction factors that can be used to adjust existing joint interaction equations to account for the effect of hydrostatic pressure on joint capacity. The following are interaction equation provided by Hoadley3 and the API2 for tubular joints. Mathematical equation (Available in full paper) The out-of-plane bending terms are not included in Eq. 1 or 2. The results presented below will permit the designer to replace the PU and MU terms in the above equations by new terms that include the effect of hydrostatic pressure.

The Role of Water in the Dissociation of Enolase, a Dimeric Enzyme

Effects of External Hydrostatic Pressure on Orthogonal Cutting Characteristics