Pressure Derivative Of Bulk Modulus Research Articles

Intrinsic material constants of poroelasticity

Biot and Willis (1957) performed micromechanical analysis on isotropic poroelastic materials and presented three material constants, the jacketed compressibility, the unjacketed compressibility, and the coefficient of fluid content, to characterize the volumetric deformation. Brown and Korringa (1975) and Rice and Cleary (1976) recast them into a drained bulk modulus K, an unjacketed bulk modulus Ks′, and an unjacketed pore modulus Ks′′. The constant Ks′′ is tied to the storage capacity of porous medium; hence is highly important in petroleum and geosequestration applications. It is, however, difficult to measure in the laboratory due to the lack of a direct way to observe pore volume deformation.In this work, a physics based approach is used to explore these micromechanical constants. Three intrinsic material constants that isolate the physical mechanisms, an unjacketed solid bulk modulus Ks, a drained pore modulus Kp, and a micro inhomogeneity and anisotropy modulus Kψ, are presented to characterize the porous material. Bounds on material constants are developed based on thermodynamics and elastic stability requirements. Past attempts in measuring Ks′′ using direct or indirect approaches are compiled. Most of the efforts failed to satisfy the theoretical bounds. Only those attempted to measure the change in pore volume passed the test. The intrinsic constants are used to interpret the bulk material constants, such as the drained and undrained bulk modulus, and the storage and Skempton pore pressure coefficient. The total volume change and the storage capacity can be partitioned into those attributed to solid, pore, fluid, and the microinhomogeneity compressibilities. A published data set on stress dependent Skempton pore pressure coefficient and bulk modulus is reanalyzed. The data are matched by the calibration of a single of Kψ value.

Thermodynamic properties of fcc metals using reparameterized MEAM potentials

The modified embedded atom method (MEAM) potentials of Jin et al. (Appl Phys A 120:189, 2015) are reparameterized through fitting the available experimental data and ab initio results of several physical properties better for seven face-centered cubic metals, Ag, Al, Au, Cu, Ni, Pd, and Pt. Results for the structure stabilities, point defects, and phonon dispersion properties are in better agreement with the measured values than those from the original MEAM potentials, showing the reliability of the reparameterized potentials. Also, the thermodynamic properties for these metals are studied within the quasi-harmonic approximation. Calculation results for the temperature dependence of lattice constants, thermal expansion coefficients, molar heat capacities at constant volume and/or constant pressure, isothermal and adiabatic bulk moduli, Gruneisen parameters, and Debye temperatures are compared to those from the earlier embedded atom methods and ab initio method calculations as well as the experimental data.

Pressure-induced octahedral tilting distortion and structural phase transition in columbite structured NiNb2O6

High-pressure behavior of the technologically important compound NiNb2O6 adopting a columbite-type orthorhombic structure at ambient pressure and temperature conditions was investigated using synchrotron x-ray powder diffraction, Raman spectroscopic measurements, and first-principles calculations. The x-ray diffraction data indicate the occurrence of irreversible pressure-induced structural phase transition in the studied compound beyond 9 GPa. The high-pressure phase is found to be monoclinic with space group P2/m. The large volume collapse (∼4.4%) at the transition indicates the nature of the transition to be of the first order. There is a change in oxygen anion coordination number around Nb from 6 to 8; however, the coordination number around Ni remains 6. The experimental pressure–volume data when fitted to the Birch−Murnaghan equation of states yield the value of ambient pressure bulk modulus (B0) as 178.7 (17) GPa for the orthorhombic phase and 244 (6) for the high-pressure monoclinic phase. The changes in Raman spectra indicate the distortion of NbO6 octahedra resulting in structural phase transitions. The logarithmic variation of unit cell volume (V) with optical lattice mode frequency (ν) helped us to calculate their respective Grüneisen parameters (γ) and it also supports the instability of the orthorhombic columbite structure of NiNb2O6 beyond 9 GPa, originated due to strong octahedral deformation of NbO6 octahedra. The variation of structural, electronic, and optical properties with pressure has also been discussed through first-principles calculations based on density functional theory using the revised Perdew–Burke–Ernzerh of generalized gradient approximation. The theoretical bandgap collapses and the distortion of NbO6 octahedra through the O chains with pressure are emphasized from the density of states data.

First-principles calculations of vibrational and optical properties of half-Heusler NaScSi

Ab initio calculation of the structural, mechanical, dynamic, thermodynamic, electronic, and optical properties of cubic half-Heusler compound NaScSi have been reported using density functional theory. Generalized gradient approximation has been used as the exchange and correlation potential for investigating these properties. The lattice constant, bulk modulus, the first pressure derivative of bulk modulus, and band gap of NaScSi have been calculated and compared to the previous XScSi (X = Na, Li, Ag, K) studies. The band structure and corresponding density of states have also been determined and analyzed. The elastic properties of the compound, calculated by the strain–stress method, satisfy the mechanical stability conditions for a cubic structure. According to the data obtained from the vibration properties, the compound is also stable dynamically. Additionally, heat capacity, entropy, and free energy of NaScSi have been calculated by using the phonon frequencies. The optical investigation of the compound shows high reflectivity in the UV region of the photon energy.

On the Applicability of Lindemann’s Law for the Melting of Alkali Metals

The experimental melting data for alkali metals reported in the literature reveal that the melting temperature becomes maximum at a particular value of high pressure and then decreases with the increase in pressure. We demonstrate in the present communication that the Lindemann law does not yield negative values for the melting slopes of solids at high pressures as far as the bulk modulus increases and the Gruneisen parameter decreases with the increase in pressure such that the pressure derivative of bulk modulus and the Gruneisen parameter remain positive finite. Arafin and Singh have produced an agreement with the experimental melting data for alkali metals with the help of the Lindemann law using quadratic equations in powers of pressure for the Gruneisen parameter and bulk modulus. These quadratic equations are shown here to be inadequate and invalid at high pressures. For explaining the negative slopes of the melting curves, we need a theory of melting which should take into account the structural and electronic changes at melting. We present a discussion of some very important and highly relevant studies (Martinez-Canales and Bergara; Deng and Lee) based on fundamental considerations and ab initio calculations used recently for explaining the turnover in the melting curves of alkali metals and ferropericlase, an important Earth lower mantle mineral. The structural and electronic changes are responsible for the anomalous thermoelastic behavior yielding negative values of elastic moduli and Gruneisen parameter both, thus making the Lindemann law applicable to materials under study.

Thermal Expansion and Response to Pressure of Double-ReO3-Type Fluorides NaMVF6 (M = Nb, Ta).

Several II-IV double-ReO3-type (DROT) fluorides are known to exhibit strong negative thermal expansion (NTE) over a wide temperature range while retaining a cubic structure down to 120 K or lower. CaZrF6, CaNbF6, CaTiF6, and MgZrF6, embody these properties. In contrast to the behavior of these II-IV materials, the I-V DROT material, NaSbF6, has been reported to display a phase transition from rhombohedral to cubic above 300 K and positive thermal expansion both above and below the transition. In this work, NaNbF6 and NaTaF6 are shown to undergo first-order cubic-to-rhombohedral transitions on cooling to ∼130 K. Above this transition, NaNbF6 shows modest NTE between 160 and 250 K, whereas NaTaF6 exhibits near-zero thermal expansion over the range 210-270 K. These I-V systems are elastically softer than their II-IV counterparts, with a zero pressure bulk modulus, K0, of 14.6(8) GPa and first derivative of the bulk modulus with respect to pressure, K0', of -18(3) for cubic NaNbF6, and K0 = 14.47(3) GPa and K0'= -21.56(7) for cubic NaTaF6. When subject to ∼0.3 GPa at 300 K, both compounds exhibit a phase transition from Fm3̅m to R3̅. The R3̅ phases exhibit negative linear compressibility over a limited pressure range. A further transition with phase coexistence occurs at ∼2.5-3.0 GPa for NaNbF6 and ∼4.5 GPa for NaTaF6. Compression of NaNbF6 in helium at room temperature and below provides no evidence for helium penetration into the structure to form a perovskite with helium on the A-site, as was previously reported for CaZrF6.

Optical response functions and thermodynamic stability of BSb1-xNx ternary alloys in zinc blende structure

Optical properties and thermodynamic stability of BSb1-xNx ternary alloys in zinc blende structure are investigated by employing the first-principles calculations based on the density functional theory. We have evaluated BSb1-xNx ternary alloys for 0 ≤ x ≤ 1 using special quasi-random structures with 16 atoms. The generalized gradient approximation of Perdew et al. (PBEsol-GGA) was used as the exchange correlation potential to calculate the structural properties at different nitrogen concentrations x (0 ≤ x ≤ 1). The lattice parameter (a), bulk modulus (B) and pressure derivative of bulk modulus (B′) have been evaluated and analyzed for ternary alloys. Our obtained results show that the lattice parameter of BSb1-xNx decreases with nitrogen concentration (x) while its bulk modulus increases.The enthalpy of mixing (ΔHm) is calculated in the whole composition range. The obtained phase diagrams indicate a significant phase miscibility gap. The calculated critical temperature is found to be 246.6 K. The electronic properties of these ternary alloys were predicted using the Tran–Blaha-modified Becke–Johnson (TB-mBJ) scheme. The band gap of BSb1-xNx positively deviate from Vegard's law. The optical response functions such as dielectric function and, complex refractive index are determined for BSb1-xNx in the zinc-blende structure. In general, our results are in agreement with the available experimental and theoretical data reported in the literature. The investigation of the optical response functions for BSb1-xNx ternary alloys is reported for the first time. The calculation endorses that the BSb1-xNx ternary is a promising candidate for optoelectronics.

FP-LAPW calculations on electronic and thermoelectric properties of Mn2CoCr Heusler compound

Heusler compounds have been remarkable among the materials due to their fascinating properties. These materials are also important in terms of applications in thermoelectric device formation. The Mn2CoCr is one of the Heusler compounds investigated in reference to its band structure and thermo-electric properties by using density functional theory. Mn2CoCr crystallizes in Fm-3m (space group 225) phase and ferromagnetically stable under ambient conditions. We have calculated its bulk modulus, first order pressure derivative of bulk modulus, band structure, density of states, Seebeck coefficient and power factor.

Electronic, Elastic, Vibrational and Thermodynamic Properties of HfIrX (X = As, Sb and Bi) Compounds: Insights from DFT-Based Computer Simulation

Ab-initio calculations were performed to reveal and thoroughly understand the structural, electronic, elastic, thermodynamic and vibrational properties of HfIrX (X = As, Sb and Bi) compounds in the C1b phase. Basic physical characteristics, such as bulk modulus, pressure derivative of bulk modulus, anisotropy factor, shear modulus, Poisson’s ratio, Cauchy pressure, elastic constants and Young’s modulus were obtained and some of them were compared with those in the literature. Electronic band structure, the density of states and phonon dispersion curves were obtained and compared with current theoretical calculations. It was concluded according to current band structure calculations that the HfIrAs and HfIrBi compounds showed semimetal characteristics, while the HfIrSb compound behaves as a semiconductor. It was determined based on phonon calculations that all three compounds were dynamically stable. Various thermodynamic properties, such as heat capacity, thermal expansion coefficient values and Gruneisen parameter were calculated under constant volume and constant pressure by using Gibbs2 code within the Quasi-harmonic approach, and these results are discussed.

BAND STRUCTURE, METALLIZATION AND STRUCTURAL PHASE TRANSITION OF NABR UNDER HIGHPRESSURE

The metallization and the phase transition of the alkali bromide sodium bromide (NaBr) is investigated through its band structure. The equilibrium lattice constant, bulk modulus, pressure derivative of bulk modulus and the phase transition pressure at which the compound undergo structural phase transition from NaCl (B1) to the CsCl (B2) structure is predicted from the total energy calculations. The ground state properties and band gap values are compared with the experimental and other theoretical results. At normal pressure NaBr is a direct band gap insulator. When the pressure is increased there is enhanced overlapping between the wave functions of the neighboring atoms. As a result the widths of the valence and empty conduction bands increase. These changes lead to the narrowing and indirect closing of band gap in NaBr (metallization). It is also confirmed that the metallization and structural phase transition do not occur simultaneously in ionic compounds.

Magnetic, Electronic, Mechanic, Anisotropic Elastic and Vibrational Properties of Antiferromagnetic Ru2TGa (T = Cr, Mn, and Co) Heusler Alloys

A theoretical study of magnetic, electronic, mechanic, anisotropic elastic, and vibrational properties of $$ {\hbox{Ru}}_{2} $$ TGa (T = Cr, Mn, and Co) Heusler alloys has been extensively investigated by the first-principles method using the generalized gradient approximation. Structural parameters such as lattice constant ( $$ a_{0} $$ ), bulk modulus (B) and first pressure derivative of bulk modulus (B′) were obtained by using the Murnaghan equation. The calculated formation enthalpies ( $$ \Delta H_{f} $$ ) showed that these alloys are thermodynamically stable. The total spin magnetic moments per unit cell of $$ {\hbox{Ru}}_{2} $$ TGa (T = Cr, Mn, and Co) alloys were found to be 1.16 $$ \mu_{B} $$ , 2.16 $$ \mu_{B} $$ and 0.29 $$ \mu_{B} $$ , respectively. In addition to electronic band structures along the high symmetry directions, corresponding total and partial density of states were also plotted. It was found that the spin-up states have a metallic character for all alloys, but the spin-down states of the other alloys except for $$ {\hbox{Ru}}_{2} $$ CoGa have a pseudo-gap at the Fermi level. The bulk modulus (B), shear modulus ( $$ G $$ ), ratio of B/ $$ G $$ , Young’s modulus (E), Poisson’s ratios (ν), Vickers hardness ( $$ H_{V} $$ ), sound velocities ( $$ v_{l} $$ , $$ v_{t} $$ , and $$ v_{m} $$ ), Debye temperatures ( $$ \varTheta_{D} $$ ) and melting temperatures ( $$ T_{\rm{melt}} $$ ) were obtained from elastic constants ( $$ C_{ij} $$ ) in accordance with the Voigt–Reuss–Hill approximation. The calculated elastic constants showed that these alloys are mechanically stable and they have anisotropic character. The elastic anisotropy of the considered alloys was analyzed and pictured in great detail with 2D and 3D figures of directional dependence of Young’s modulus, linear compressibility, shear modulus, and Poisson’s ratio.These alloys are dynamically stable because there are no negative modes in their phonon dispersion curves.

Structural, magnetic, electronic and elastic properties of half-metallic ferromagnetism full-Heusler alloys: Normal-Co2TiSn and inverse- Zr2RhGa using FP-LAPW method

The equilibrium structural parameters, electronic, magnetic and elastic properties of the inverse Zr2RhGa and normal Co2TiSn Full-Heusler compounds have been studied using density-functional theory (DFT) and full-potential linearized augmented plane-wave (FP-LAPW) method as implemented in the WIEN2k package. The Generalized Gradient Approximation (GGA) has been used for the exchange-correlation potential (Vxc) to compute the equilibrium structural parameters; lattice constant (a), bulk modulus (B) and bulk modulus pressure derivative (B′). In addition to the GGA approach, the modified Becke Johnson (mBJ) scheme has been used to calculate the band gap energies. The normal Heusler Co2TiSn compound and the inverse Heusler Zr2RhGa compound within GGA and mBJ approaches are found to have a half-metallic behavior, with an indirect energy gap in the spin down configuration. The calculated total magnetic moments for both compounds are to some extent compatible with the available experimental and theoretical results. Elastic constants and their related properties were obtained by using the IRelast package. These compounds are mechanically stable. The elastic constants satisfy the Born mechanical stability criteria. B/S ratio shows that the normal Co2TiSn has a brittle nature, while the inverse Zr2RhGa has a ductile nature; Poisson's ratio (ν) values show that both compounds have an ionic bond nature.

Structural stability of scandium monochalcogeides ScS and ScSe under pressure and superconductivity: A first principles study

The structural phase transition, electronic, phonon and superconducting properties of scandium monochalcogenides ScS and ScSe which are looked as potential materials for heterogeneous catalysts, high temperature coating and superconducting applications have been studied by using a first principles scheme. Local density approximation (LDA) of Perdew-Wang has been used. Lattice constants, bulk modulus, pressure derivative of bulk modulus and structural phase transitions of ScS and ScSe are reported and compared with available experimental and other theoretical results. Electronic and bonding properties have been analyzed from electronic band structures, density of states, Fermi surfaces and charge density plots. The phonon dispersion curves for these compounds are calculated in B1 and B2 phases at zero as well as high pressure for the first time. The superconductivity is discussed in terms of Eliashberg spectral function, electron phonon coupling constants and superconducting transition temperature (TC). The calculated value of TC for ScS is 4.52 K and for ScSe is 3.88 K in B1 phase and 2.35 K for ScS and 1.09 K for ScSe in B2 phase, The calculated Tc in B1 phase for both the compounds agree well with the experimental value (TC = 4.5 K (ScS) and 3.7 K (ScSe)).

A First Principle Study of Structural, Electronic, and Vibrational Properties of LuPdBi Half‐Heusler Alloy

Half‐Heusler alloys offer a variety of applications in the field of electronics and superconductors. They are suitable for the formation of thermoelectric materials and superconductors. Their stupendous applications arouse curiosity among many researchers. Therefore, in this paper, a systematic study of structural, electronic, and vibrational properties has been done using density functional theory and density functional perturbation theory. The structural properties such as lattice constant, bulk modulus, and pressure derivative of bulk modulus have been calculated. Electronic and bonding properties have been examined from electronic band structure, charge density contours, and Fermi surfaces. The phonon dispersion spectra and phonon density of states for LuPdBi are reported and discussed for the first time. Moreover, the eigenvector displacements for optical phonons at the zone center are also described to support the reliability of phonon calculations. The computation of phonon spectra disclosed the fact that the resulted phonons are real. Real frequencies of phonons are witness of alloy stability in the cubic phase. The superconducting properties have also been evaluated by employing electron–phonon interaction and Eliashberg theory. The Coulomb pseudopotential variable µ* is selected to be 0.11 and the computed value of transition temperature is found to be Tc = 1.802 K. This value of Tc is in agreement with the experimental value of Tc = 1.80 K.

Probing the Structural, Electronic, Mechanical Strength and Thermodynamic Properties of Tungsten-Based Oxide Perovskites RbWO3 and CsWO3: First-Principles Investigation

In the present paper we have investigated tungsten-based cubic perovskite oxides RbWO3 and CsWO3 for structural, electronic and elastic-mechanical results using first-principles density functional theory. Generalized gradient approximation (GGA) and local density approximation (LDA) have been used for structural optimization. The calculated results like lattice constant, volume, bulk modulus, pressure derivative of bulk modulus and energy have been obtained from both GGA and LDA. Results of band structure calculations along high-symmetry directions of the Brillouin zone and the density of states showed the metallic nature for both the materials. The d-states of tungsten and p-states of oxygen are found to be present at the Fermi level and are responsible for the metallic nature of these compounds. The elastic constants (C11, C12 and C44) have been computed in order to understand the mechanical stability of these materials. Using the value of these elastic constants, some important mechanical properties of these materials like Young’s modulus, shear modulus and bulk modulus have been predicted. Both the materials were found to have a large bulk modulus, Young’s modulus and shear modulus, and hence may serve as important candidates in fuel cells as electrode materials. The calculated melting temperature from elastic constants for both the materials was found to be large enough, equal to 3215 ± 300 K and 3016 ± 300 K, respectively, for RbWO3 and CsWO3. Cauchy’s pressure (C12–C44), Poisson’s ratio (υ) and the Pugh ratio (B/G) predict both the materials as brittle. Thermodynamic parameters like specific heat capacity, Debye temperature and thermal expansion have been calculated as a function of temperature (0 K to 1400 K) and pressure (0 GPa to 32 GPa).

High-Pressure Phase Transitions of Cubic Y2O3 under High Pressures by In-situ Synchrotron X-Ray Diffraction**Supported by the National Natural Science Foundation of China under Grant Nos 11775292, 11104307 and U1530134, the Natural Science Foundation of Shanghai under Grant No 18ZR1448100, and the Shanghai Sailing Program under Grant No 17YF1423600.

High-pressure phase transitions of cubic Y2O3 are investigated using in situ synchrotron x-ray diffraction in a diamond anvil cell up to 36.3 GPa. The pressure-induced phase transitions of cubic Y2O3, which display apparent inconsistencies in previous studies, are verified to be from a cubic phase to a monoclinic phase and further to a hexagonal phase at 11.7 and 21.6 GPa, respectively. The hexagonal Y2O3 displays noticeable anisotropic compressibility due to its layered structure and it is stable up to the highest pressure in the present study. A third-order Birch–Murnaghan fit based on the observed pressure-volume data yields zero pressure bulk moduli of 180(3), 196(7) and 177(7) GPa for cubic, monoclinic and hexagonal phases, respectively.

First Principle Mechanical and Thermodynamic Properties of Some TbX (X = S, Se) Compounds

The mechanical and thermodynamic results of some terbium chalcogenides, TbX (X = S, Se) compounds have been examined using full-potential linear augmented plane wave (FP-LAPW) method based on density functional theory. The local spin density approximation with Hubbard potential (LSDA+U) has been used for proper treatment of 4f-electrons of Tb. The magnetic moment of TbS and TbSe was calculated to be 5.44μB and 5.57μB, respectively. The ground state properties such as lattice parameter, bulk modulus, and pressure derivative of bulk modulus were obtained and found in good agreement with already available theory and experiment results. The mechanical properties such as Young modulus (E), shear modulus (G), Poisson ratio (υ), Cauchy pressure and B/G ratio were also predicted. Further, in thermodynamic properties, Debye temperatures (θD), specific heats at constant volume(CV), thermal expansion co-efficient (α), and entropies (S) and their behavior with high temperature(0–1200 K) and pressure (0–50 GPa) were also predicted.

Thermoelastic properties of solids based on equation of state

Thermoelastic properties of solids at high pressures are studied using various equations of state (EOS) such as Eularian Birch-Murnaghan EOS, Poirier-Tarantola logarithmic EOS and the generalized Vinet-Rydberg EOS. We have determined the pressure derivatives of bulk modulus upto third order which are useful for predicting the Gruneisen parameter and its volume derivatives. Expressions have been obtained for the derivative properties based on different equations of state, and extrapolated to the limit of extreme compression. It is found that all the three equations lead to a common relationship between second and third pressure derivatives of bulk modulus in the limit of extreme compression.

Investigations of structural, electronic, mechanical and lattice dynamic properties of TiRu3 and TiOs3 compounds

Ab initio calculations of structural, electronic, elastic, and phonon properties of TiRu3 and TiOs3 compounds have been studied using the density functional theory (DFT) within the generalized gradient approximation (GGA). The basic structural properties such as lattice constants, bulk modulus and pressure derivative of bulk modulus of these compounds were studied and compared with the previous theoretical data. Electronic band structures and partial densities of states for TiRu3 and TiOs3 compounds were computed and analyzed. The electronic band calculations showed that the TiRu3 and TiOs3 compounds have metallic nature. Phonon spectra, their total and projected densities of states for these compounds were computed by using a linear-response method in the framework of the density functional perturbation theory. The specific heat capacities at a constant volume CV and Debye temperature of TiCr3 and TiOs3 compounds were also calculated and discussed.

Pressure induced structural phase transition in rare earth sesquioxide Tm2O3: Experiment and ab initio calculations

Among the small cation sized rare earth sesquioxides, the reported transition pressure of cubic Tm2O3 is ambiguous. Pressure induced structural phase transition in cubic Tm2O3 has been reinvestigated using the synchrotron X-ray diffraction, Raman spectroscopy, and ab initio density functional theory (DFT) calculations up to a pressure of 25 GPa. Both the X-ray diffraction and Raman spectroscopic measurements revealed an irreversible polymorphic structural phase transition from type-C cubic to type-B monoclinic at around 12 GPa, whereas the same is predicted to be 8 GPa from the density functional theory. The phase transition observed at 12 GPa is in contrast to the literature and the reasoning has been established by other studies, viz., Raman spectroscopy and DFT. A third order Birch-Murnaghan equation of state fit to the experimental compressibility curve yielded a zero pressure bulk modulus of 149(2) GPa with the pressure derivatives 4.8(5) for the parent cubic phase and 169(2) GPa with the pressure derivative 4 for the high pressure monoclinic phase, respectively. These values are in good agreement with the calculated bulk modulus of 146 and 151 GPa for the cubic and monoclinic phases, respectively. Raman modes for the monoclinic phase of Tm2O3 are measured and reported for the first time. The mode Grüneisen parameter of different Raman modes for both cubic and monoclinic phases of Tm2O3 has also been determined. The experimental results are correlated with changes in the density of states near the Fermi level, which are indicative of structural instabilities in the parent cubic structure.