Variation Of Bulk Modulus Research Articles

An in-depth look at the structural, electronic, optical, and thermal properties of the cubic Be x Mg y Zn1−x−y O quaternary alloys

In the present research work, the structural, electrical, optical, and thermodynamic properties of the BexMgyZn1−x-yO quaternary alloy were investigated. Its conventional structure, which is composed of the binary compounds ZnO, BeO, and MgO, and their ordered ternary alloys BexZn1−xO, BexMg1−xO, and MgxZn1−xO are examined. A non-linear variation of lattice constants (a) and bulk modulus (B) as a function of the compositions (x, y) in BexMgyZn1−x-yO alloys is observed due to varying atomic radii of the constituent elements leading to the structural distortion against compositional changes. Both the ternary and quaternary alloys exhibit semiconducting properties, characterized by a direct bandgap ranging from 2–4 eV. This indicates their absorption and emission of light in the visible region of the spectrum, making them promising candidates for optoelectronic applications. The results of optical characteristics display the variation of refractive index and absorption coefficient of these alloys with respect to composition and wavelength. Present results will forecast the possible applications and guidelines for synthesizing such alloys under extreme conditions.

Variation of Bulk Modulus, Its First Pressure Derivative, and Thermal Expansion Coefficient with Applied High Hydrostatic Pressure

Throughout this work, the equations of variation of the isothermal bulk modulus, its first pressure derivative, and the volumetric thermal expansion coefficient as a function of pressure were derived based on the Birch–Murnaghan equation of state (B–M EOS). The bulk modulus and its first derivative at ambient temperature for nine elements were extracted by fitting the published experimental pressure–volume data to B–M EOS, and the results were compared with other published researches, and there was a good agreement. Moreover, those extracted values were used to study the variation of the isothermal bulk modulus, its first pressure derivative, and the isothermal coefficient of thermal expansion as a function of the applied hydrostatic pressure using the equations that were derived from this work.

Effect of V doping on the microstructure and mechanical properties of Mo2FeB2-based cermets and investigation on the enhancement mechanism

In this study, the effect of V doping on the microstructure and mechanical properties of Mo2FeB2-based cermets was explored. The doped V element was mainly dissolved in the Mo2FeB2 particles to substitute the Mo atom inside without generating a new phase. Doping V element increased the volume fraction of borides and the forming temperature of the liquid, thus resulting in the formation of micro pores in Mo2FeB2-based cermets. The appropriate V additions simultaneously enhanced the hardness and transverse rupture strength of Mo2FeB2-based cermets, while the excessive V additions generated negative influences. The nanoindentation results indicated that the intrinsic hardness and Young’s modulus of Mo2FeB2 particle were enhanced monotonously with the increasing V contents. However, the V-containing Mo2FeB2 particles exhibited more brittleness. The first-principles calculation results showed that the enhanced covalent bonds in Mo2FeB2 contributed to the increased hardness. Moreover, V doping decreased the structural stability of Mo2FeB2 by forming the anti-bond. Additionally, the variations of bulk modulus, shear modulus and Poisson’s ratio caused by the V doping were also discussed based on the calculation results.

Mechanical and thermodynamic properties of layered ThB2C

The electronic, mechanical and thermodynamic properties of layered ThB2C are investigated using the first-principles calculations with generalized gradient and local density approximations. The equilibrium geometry and elastic stiffness constants of ThB2C are studied, and various elastic moduli, Poisson’s ratios and velocities are estimated from the elastic stiffness constants. ThB2C exhibits brittle characteristics. The phonon dispersion relationship verifies the thermodynamic stability of ThB2C. Considering the effect of phonon vibration on the thermodynamic properties of ThB2C, the variation of Gibbs free energy, bulk modulus and heat capacity at constant pressure with temperature are calculated using quasi-harmonic approximation in the temperature range of [Formula: see text][Formula: see text]K.

A theoretical and experimental investigation of gas adsorption-dependent bulk modulus of fractured coal

Changes in the bulk modulus of coal induced by sorbing gases occur during gas production and CO2 sequestration processes in coal seams. Understanding these changes, however, remains a challenge due to the complexity of coupled sorptive poromechanical processes. Some studies report that the bulk modulus of fractured coal reduces with gas adsorption, others state otherwise. In this study, we perform a set of triaxial experiments to investigate the bulk modulus variation in fractured coals with non-sorbing (helium) and sorbing (carbon dioxide) gases. We then present a theoretical model developed based on energy conservation and poroelasticity to predict the bulk modulus of fractured coal and its variation with sorbing gases. The model performance in predicting the bulk modulus is then assessed using the experimental results where a good performance is observed. A parametric study is further conducted to investigate the effect of key model parameters on the bulk modulus. The experimental results demonstrate that bulk modulus variations are predominantly caused by two counteracting effects: a hydromechanical effect resulting from a decrease in the effective stress due to pore pressure buildup and a sorptive-mechanical effect due to adsorption-induced matrix swelling. The experimental and theoretical results also show that these effects can lead to an increase or decrease in the bulk modulus of fractured coal. The parametric study using the theoretical model reveals that the initial fracture porosity and the adsorbed gas content are important factors controlling the variations in bulk modulus.

Experimental study on bulk modulus and dissipation of dry and wet granular samples under vertical vibration

Dry granular materials are composed of a dense random packing of macroscopic grains. As a small amount of liquid is added to granular samples, the liquid bridge forces, i.e. the forces between liquid and the grains, have an influence on the mechanical properties of wet granular material, and some of these properties are quite different from those of dry granular materials. In this work, by measuring the acceleration of the sample chamber and the force exerted on it by the shaker, the variations of bulk modulus and energy dissipation of both dry and wet glass bead samples with pressure and viscosity under vertical vibration are studied. The results are shown below. 1) Under low saturation, the bulk modulus of dry and wet glass bead sample are both described by a power law scaling law with pressure, which is close to the power law relationship predicted by the efficient medium theory on the basis of Hertz contact potential. A small amount of liquid can increase the bulk modulus of glass bead sample. At the same pressure and liquid content, the bulk modulus of wet glass bead sample increases with liquid viscosity increasing. Based on Hertzian contact mechanics, an efficient elastic network model is proposed to illustrate the mechanism of increasing bulk modulus of wet glass bead samples. 2) The energy dissipation of dry and wet glass bead sample decrease following the power law of pressure, and the energy dissipation of wet glass bead samples is proportional to the kinematic viscosity of liquid. 3) With the increase of strain amplitude, the softening behavior of the wet glass bead sample is similar to that of the dry glass bead sample, when the strain amplitude is higher than the strain threshold value. The kinematic viscosity of liquid inhibits the softening behavior of glass bead sample.

Geomechanical and flow implications with continued bioconversion of coal to methane: Experiments and modeling

Microbial conversion of coal to methane is a promising technology during transition of coal-based energy from conventional coal mining to natural gas recovery from coal. Significant research advances have been made towards engineering ideal microbial communities and nutrients for bio-stimulation of coal. However, actual field applications require geomechanical and flow behavior characterization of coal during the bioconversion process as well as gas production over the life of the created “biogenic gas reservoirs”. This study presents the results of an experimental investigation to estimate gas/methane production using bioconversion of coal and analyses of variations in bulk modulus, strain and permeability. Bulk modulus of coal demonstrated time-dependent behavior with continued bioconversion of solid coal. The phenomenon was modeled using mass balancing in a closed environment and the logistic equation based biogenic gas production with time. The modeled gas production and changes in modulus of coal showed excellent agreement with the corresponding experimental results. Next, numerical simulation of biogenic conversion of coal in a constant stress in-situ condition, replicating the Huff ‘n Puff method under field conditions, was carried out. The results showed that bioconversion can lead to decrease in effective stress, increase in permeability and decrease in the modulus of coal with time. Repeated recharge of coal with nutrients and recovering the produced gas, that is, sequential cycles of Huff n’ Puff, showed further increase in permeability and decrease in coal strength, potentially leading to coal failure in-situ, further increasing the permeability, thus enhancing the prospect of field application of the technology.

Structural, electronic, elastic, magnetic and thermodynamic properties of Mn2LuZ (Z = B, Al, Ga and In) Heusler compounds: A first‐principle study

AbstractThe study of the structural, electronic, thermodynamic, elastic and magnetic properties of rare‐earth based full Heusler alloys Mn2LuZ (Z = B, Al, Ga and In) have been carried out using the full‐potential linearized muffin‐tin orbital method (FP‐LMTO), within density functional theory (DFT) and generalized gradient approximation (GGA) for exchange and correlation energy. The electronic properties studied have shown that the compounds have a metallic behavior. We have also computed the mechanical properties where we found these full Heusler compounds are mechanically stable. Using the quasi‐harmonic Debye model, the variations of bulk modulus, thermal expansion coefficient, heat capacities, Debye temperature and Gibbs free energy with pressures covering the 0–40 GPa interval and temperatures ranging from 0 to 1500 K were also investigated and in‐depth discussed. The calculated properties represent a solid prediction for the Mn2LuZ (Z = B, Al, Ga and In) Heusler compounds and are awaiting for experimental concretization.

An advection-diffusion-mechanical deformation integral model to predict coal matrix methane permeability combining digital rock physics with laboratory measurements

This study proposed an advection-diffusion-mechanical deformation integral model to predict coal matrix methane permeability combining digital rock physics with laboratory measurements. The coal matrix pore network was first extracted from the segmented 3D digital coal image. Organic pore-controlled methane transport pathways and mineral-associated pore methane transport pathways were identified from the coal matrix pore network. Advection and Knudsen diffusion processes were considered for methane transport in the mineral associate pores and bulk methane transport in organic pores. To determine the adsorbed methane surface diffusion ability in organic pores, laboratory adsorption and desorption experiments were conducted to determine the desorption curve and critical desorption pressure. Pore shrinkage was considered for organic pores and mineral-associated pores whereas sorption-induced volumetric strain was also modeled for the organic pore system. The coal matrix methane permeability was calculated over a wide range of production pressures and the influences of reservoir and methane transport properties on coal matrix methane permeability were analyzed in detail. Results revealed that gas slippage and initial formation pressure dominate the coal matrix methane permeability more than other influencing factors. Coal matrix methane permeability was underestimated by at least 40% by using Darcy flow to describe methane flow in the coal matrix and the influence of organic matter bulk modulus variation on coal matrix methane permeability can be neglected at initial formation pressures less than 10 MPa.

Equation of State and Thermo Dynamic Behaviour of C<sub>60</sub> under High Pressure

In the present study, four equations of state (EOSs) were used, namely Birch-Murnaghan, Dodson, Bardeen and modified Lenard Jones for evaluating relative compression volume Vp/Vo, isothermal bulk modulus B and spinodal pressure Psp for C60 under high pressure. Required constant parameters in the EOSs were taken from literature data. Starting from the definition of spinodal pressure, as the pressure at which bulk modulus of a material vanishes (i.e. B=0), A new approach for the evaluation of spinodal pressure have been established, in present work, by extrapolating variation of bulk modulus under high pressure data to the point where B=0, and formulate a new mathematical expression for spinodal pressure. With the aim of finding validity of these equations of state of applying on C60, the calculated results from the entire equations of state are compared with themselves and with other available experimental and theoretical published data. The results for Vp/Vo, B, and Psp are found to be in agreement with each other for whole pressure ranges. Some other theoretical and empirical data are brought in this study and give good agreements with our results. The new spinodal pressure approach and high pressure studies might represent a promising entrance to the formalism of universal equation of state for solids.

The High-Pressure Structural Evolution of Olivine along the Forsterite–Fayalite Join

Structural refinements from single-crystal X-ray diffraction data are reported for olivine with a composition of Fo100 (forsterite Mg2SiO4, synthetic), Fo80 and Fo62 (~Mg1.6Fe0.4SiO4 and ~Mg1.24Fe0.76SiO4, both natural) at room temperature and high pressure to ~8 GPa. The new results, along with data from the literature on Fo0 (fayalite Fe2SiO4), were used to investigate the previously reported structural mechanisms which caused small variations of olivine bulk modulus with increasing Fe content. For all the investigated compositions, the M2 crystallographic site, with its bonding configuration and its larger polyhedral volume, was observed to control the compression mechanisms in olivine. From Fo100 to Fo0, the compression rates for M2–O and M1–O bond lengths were observed to control the relative polyhedral volumes, resulting in a less-compressible M1O6 polyhedral volume, likely causing the slight increase in bulk modulus with increasing Fe content.

First principles study of thermodynamic properties of Cd-substituted Zn Chalcogenides by employing quasi harmonic Debye model

First Principles study of thermodynamic properties of Cd-substituted Zn Chalcogenides have been performed by using quasi harmonic Debye Model. A non linear variation in bulk modulus of is found in Chalcogen’s group (X = O, S, Se, Te). Slack equation is used to calculate the thermal conductivity of materials and it is found that Cd-rich Zn Chalcogenides have less thermal conductivity. The anharmonicity and thermal expansion coefficient of increase linearly from X = O to X = Se but then interestingly a crossover is appeared in their values at X = Te. Several other thermodynamic parameters like Debye temperature, molar heat capacities, internal energy and entropy are also determined and compared to available theoretical and experimental results.

Theoretical Study of Mechanical, Elastic and Phonon Frequency Spectrum Properties for GaAs at High Pressure

The calculations for variations of bulk modulus (B), compression volume (Vp Vo ); lattice constant and phonon frequency spectrum (pfs) under high pressure up to 17 GPa at room temperature has been carried out. Three equations of state (EOSs) including (Birch- Murnaghan, Vinet and modified Lennard-Jouns) are used in the calculations. The variations of these properties under such high pressure for GaAs are obtained and we got suitable EOS for it.

Insight into the Structural, Electronic, Elastic, Mechanical, and Thermodynamic Properties of XReO3 (X = Rb, Cs, Tl) Perovskite Oxides: A DFT Study

Abstract In the present work, perovskite oxides XReO3 (X = Rb, Cs, Tl) have been reported using density functional theory (DFT) for structural, electronic, mechanical, elastic, and thermodynamic properties. Structural optimization has been carried out using local density approximation (LDA) and generalized gradient approximation (GGA) in the scheme of Perdew, Burke, and Ernzerhof. Electronic properties have been calculated using GGA, and all the three materials were found to have metallic nature. From the elastic constants, all the three compounds were found mechanically stable in cubic structure. Poisson’s ratio (ν), Cauchy’s pressure (C 12–C 44) and Pugh ratio (B/G) present the ductile nature of RbReO3 and TlReO3, whereas CsReO3 was found to establish a brittle nature. These compounds were found to have an elastically anisotropic nature. The calculated melting temperatures were found to be 2851 ± 300, 2814 ± 300, and 2924 ± 300 K, respectively, for XReO3 (X = Rb, Cs, Tl). Using quasi-harmonic Debye approximation, we have calculated the pressure- and temperature-dependent variation in cell volume, bulk modulus, Debye temperature, and specific heat capacity.

A Thermodynamic Perspective of the Composition Dependence of Bulk Modulus in Terms of Electron Density and Molar Volume

The variation of bulk modulus with composition of alloy phases is a core issue in any thermodynamic theory of alloy formation. Though it emerges from fundamental theory that elastic property, especially the bulk modulus is crucially dependent on interstitial electron density (ρb) distribution and its variation with respect to alloy composition, a coherent thermodynamic treatment connecting bulk modulus with electron density together with its composition dependence, is still lacking. The present study addresses this issue for solid solution alloys. A phenomenological analysis of the composition dependence of bulk modulus (BT) of single phase alloys has been presented in terms of bonding charge density (ρb) and its corresponding change with atomic volume (V). This link is developed using the fundamental interrelationship existing between bulk modulus, electron density, and molar volume. The change in bonding charge density (Δρb) with composition (x) has been modeled using an exponential scaling relation with respect to the corresponding change in atomic volume (ΔV). This scaling relation is based on the concept of the universal binding energy relation, which in turn results in a simple exponential variation of bulk modulus with composition-induced change of atomic volume. It is also shown that a common functional representation namely, BT (V) ≈ Bo exp{C × (ΔV)}, can be obtained for the temperature, pressure, and composition dependence of bulk modulus in terms of corresponding changes in volume (ΔV). The constant C takes context-dependent meaning and values. The applicability of this exponential relation towards representing the effect of composition on bulk modulus has been satisfactorily demonstrated for many substitutional alloy systems.

Constraints on the Equations of State of stiff anisotropic minerals: rutile, and the implications for rutile elastic barometry

AbstractWe present an assessment of the thermo-elastic behaviour of rutile based on X-ray diffraction data and direct elastic measurements available in the literature. The data confirms that the quasi-harmonic approximation is not valid for rutile because rutile exhibits substantial anisotropic thermal pressure, meaning that the unit-cell parameters change significantly along isochors. Simultaneous fitting of both the diffraction and elasticity data yields parameters ofKTR0= 205.14(15) GPa,KSR0= 207.30(14) GPa,$K_{TR0}^{\prime} $= 6.9(4) in a 3rd-order Birch-Murnaghan Equation of State for compression, αV0= 2.526(16) × 10–5K–1, Einstein temperature θE= 328(12) K, Anderson-Grüneisen parameter δT= 7.6(6), with a fixed thermal Grüneisen parameter γ = 1.4 to describe the thermal expansion and variation of bulk modulus with temperature at room pressure. This Equation of State fits all of the available data up to 7.3 GPa at room temperature, and up to 1100 K at room pressure within its uncertainties. We also present a series of formulations and a simple protocol to obtain thermodynamically consistent Equations of State for the volume and the unit-cell parameters for stiff materials, such as rutile. In combination with published data for garnets, the Equation of State for rutile indicates that rutile inclusions trapped inside garnets in metamorphic rocks should exhibit negative residual pressures when measured at room conditions.

Strain effect for the newly discovered spin-gapless diamond-like quaternary-type semiconductor CuMn2InSe4

Spin-gapless semiconductors are considered as promising candidates for spintronic and magnetoelectronic materials. Enormous efforts have been devoted to search for materials in this regard. Recently, a new diamond-like quaternary semiconductor CuMn2InSe4 has been successfully synthesized by experiment and also demonstrated as spin-gapless semiconductor in theory. In this work, we report a theoretical study on the electronic, magnetic and thermodynamic properties of the CuMn2InSe4 under strain conditions by employing the first-principles calculations and quasi-harmonic Debye model. Under uniform strain, the spin-gapless semiconducting nature can only be maintained from 0% to 5% at the stretching side yet immediately destroyed at the compressing side. Although the magnetic moments of all atoms vary continuously with uniform strain, the total magnetic moment shows a good stability against uniform stretching up to 5%. The effect of the tetragonal distortion has also been studied in terms of strains in lattice a and c separately. Results show that strain in a has an important impact and induces larger variation on both the electronic and magnetic properties than in c. CuMn2InSe4 easily loses its spin-gapless semiconducting feature with the variation of strain in a but it can be maintained considerably better by strain in c. In particular, this spin-gapless behavior preserves through the whole studied range of strain in c from −5% to +5% at 100% a. While, the magnetic moments of all atoms under tetragonal distortion show the same variation tendencies under strain in a or c and the changing rate is a slightly larger with strain in a. Additionally, the thermodynamic properties of CuMn2InSe4 are predicted through the quasi-harmonic Debye model. The variation of bulk modulus, lattice constant, heat capacity, thermal expansion coefficient, Grüneisen constant and Debye temperature with pressure and temperature are successfully obtained. To the best of our knowledge, neither experimental nor theoretical reports regarding the electronic, magnetic and thermodynamic properties under strain conditions for CuMn2InSe4 compound are available in the literature and, thus, our results can give a helpful reference or even inspire new studies for this kind of material in the future work.

Structural, mechanical and thermal properties of Cu2ZnSiS4 with four structures from the first-principle calculations

In this paper, the structural, mechanical and thermal properties of the four structures of Cu2ZnSiS4 were studied on the basis of density functional theory (DFT). The generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) was used to treat the exchange related energy and potential of total energy calculation. The independent elastic constants of the four structures are calculated, which prove that they are mechanically stable. The bulk modulus, Poisson’s ratios and universal anisotropy indices of Cu2ZnSiS4 can be calculated from the obtained elastic constants. In addition, the variation of the bulk modulus with the pressure (0–25 GPa) and temperature (0–700 K) have been reported. In order to further study the compound, the thermal properties of the compound were analyzed by using the quasi-harmonic Debye model, including specific heat, thermal expansion coefficient and Debye temperature.

Thermodynamic assessment of Mg/Zr unary systems

With consideration of the phase equilibrium dependency upon temperature (T) and pressure (P), the P-T type phase diagrams of Mg and Zr unary systems are constructed. The gaseous phase of the Mg system consists of the species Mg (g) and Mg2 (g), and the condensed phases are liquid, hexagonal close-packed (HCP_A3) and body centered cubic (BCC_A2). Similarly, the gaseous phase of the Zr system consists of the species Zr (g) and Zr2 (g), and the condensed phases are liquid, HCP_A3 (α), BCC_A2 (β) and a more open hexagonal structure (ω). The ω phase has a hexagonal lattice with three atoms per unit cell at (0, 0, 0), (1/3, 2/3, c/2a) and (2/3, 1/3, c/2a), where the c/a ratio is ∼0.62. The real solution model is applied to describe the molar Gibbs free energy of gaseous species by taking the fugacity coefficient into account to ensure the validity of the calculated phase diagrams under high temperature and high pressure. As for the description of the molar Gibbs free energy for condensed phases, the temperature and pressure dependent Murnaghan equation is employed, which is represented by Gpress and is correlated with the molar volume, the variations of voluminal thermal expansivity and compressibility with temperature, and the variation of bulk modulus with pressure. Based on the literature data available, the parameters of the pressure contribution part Gpress for the condensed phases are optimized by use of Pandat Software package. The calculated phase diagrams are well comparable with the experimental and theoretical reports. The favorable consistency between the calculated results for the optimized mechanical and thermophysical properties, such as the variations of the molar volume and the volume ratio with pressure and the molar heat capacity with temperature, and the experimental measurements from literatures further proves the reliability of the present thermodynamic assessment. According to the calculated results, it is indispensable for the contribution of Gpress to the global molar Gibbs free energy to be taken into consideration as the magnitude of pressure exceeds the order of 109 Pa. This CALPHAD method for developing the phase diagrams of Mg/Zr unary systems at high temperature and high pressure can be extended to study other unary systems.

Evaluation of Spinodal Pressure for Gallium nitride in the Zinc-blend and Wurtzite Structures by Using Different Equations of State (EOSs)

According to the definition of spinodal pressure as the negative pressure at which bulk modulus (of a substance) go to zero. Extrapolation of variation of bulk modulus results with pressure has been used to evaluate spinodal pressure for GaN in zinc-blende and wurtzite structures using different equations of state (EOS) (Birch-Murnaghan, Bardeen, Libby and Libby, and Born-Mie). Result obtained in the present work for GaN in the zinc-blende structure using Born-Mie equation of state shows a good agreement with literature. While results for wurtzite structure, obtained by using Birch-Murnaghan and Bardeen EOSs are in a good agreement with literature. Present results and many literature show that (Jiuxun, 2005) approach for evaluation of spinodal pressure yield results in less agreement with other works