Pressure Derivative Of Bulk Modulus Research Articles

Study of Nanomaterials Under Second Order Bulk Modulus

In this study, we analyze the variation of pressure under different values of (𝑽𝑽𝟎) for nanomaterials using secondorder pressure derivative of bulk modulus equation of state. Second order pressure derivative of bulk modulus show fine studies of nanomaterials. The Gupta & Gupta EOS is used to calculate the resultant data of ε-Fe (Hexagonal iron), α-Fe2O3 and Ni-filled MWCNT nanomaterials and compared with other equations of state, like Tait EOS, Mie–Gruneisen EOS, Vinet EOS and experimental data available in literature. The resultant data show good agreement with experimental data and other EOSs.

Explore the fascinating realm of comparing metal melting curves by applying the equation of state and Lindemann's law

Our research, which is not just theoretical but also has practical implications, is a comprehensive study that aims to find the equation of state needed to calculate the pressure-dependent melting curves of metals. We have introduced a unique model for the melting curve, utilizing equations of state such as those proposed by Srivastava-Pandey and Kholiya. This model has been compared with Lindemann's model and available experimental data. It establishes the relationship between pressure, bulk modulus, pressure derivative of bulk modulus, and volume compression. Our findings show that a significant increase in melting temperature is directly linked to a substantial rise in bulk modulus and a gradual decrease in the first-order pressure derivative of bulk modulus. This study provides insights into understanding the effect of pressure on melting temperature. The present study finds that the equation of state of Srivastava-Pandey is more suitable for describing the melting temperature of metals, which could have significant implications for material science and engineering.

Attractive and repulsive forces in a crystal of [Rb(18-crown-6)][SbCl6] under high pressure.

The compression behavior of [Rb(18-crown-6)][SbCl6] crystal under pressure up to 2.16 (3) GPa was investigated in a diamond anvil cell (DAC) using a mixture of pentane-isopentane (1:4) as the pressure-transmitting fluid. The compound crystallizes in trigonal space group R3 and no phase transition was observed in the indicated pressure range. The low value of pressure bulk modulus [9.1 (5) GPa] found in this crystal is a characteristic of soft materials with predominant dispersive and electrostatic interaction forces. The nonlinear relationship between unit-cell parameters under high pressure is attributed to the influence of reduced intermolecular H...Cl contacts under pressure over 0.73 GPa. It also explains the high compression efficiency of [Rb(18-crown-6)][SbCl6] crystals at relatively low pressures, resulting in a significant shift of the Rb atom to the center of the crown ether cavity. At pressures above 0.9 GPa, steric repulsion forces begin to play a remarkable role, since an increasing number of interatomic H...Cl and H...H contacts become shorter than the sum of their van der Waals (vdW) radii. Below 0.9 GPa, both unit-cell parameter dependences (P-a and P-c) exhibit hysteresis upon pressure release, demonstrating their influence on the disordered model of Rb atoms. The void reduction under pressure also demonstrates two linear sections with the inflection point at 0.9 GPa. Compression of the crystal is accompanied by a significant decrease in the volume of the voids, leading to the rapid approach of Rb atoms to the center of the crown ether cavity. For the Rb atom to penetrate into the center of the crown ether cavity in [Rb(18-crown-6)][SbCl6], it is necessary to apply a pressure of about 2.5 GPa to disrupt the balance of atomic forces in the crystal. This sample serves as a compression model demonstrating the influence of both attractive and repulsive forces on the change in unit-cell parameters under pressure.

Hydrostatic pressure response of semiconducting GaSb applying a semi-empirical approach

In addition to experimental investigations, semi-empirical approaches prove valuable for replicating experimental results and predicting material behavior under high-pressure conditions. This study investigates the variation of unit cell volume in cubic zinc blende Gallium antimonide (GaSb) up to the phase transition pressure, relying solely on structural parameters from literature measurements at ambient conditions. The research extends to inspect the impact of high pressure on various properties, including mass density, bulk modulus, bulk sound wave velocity, microhardness, first-order pressure derivative of the isothermal bulk modulus, Grüneisen parameter, and Debye temperature for the GaSb compound. The bulk modulus and microhardness show nearly linear increases with pressure, while sound wave velocity and Debye temperature exhibit nonlinear variations. The first-order pressure derivative of the bulk modulus and Grüneisen parameter gradually decreased in the material under study. Similar trends under pressure are found in literature for materials with different crystallographic structures. Additionally, the study predicts and analyzes extra physical parameters of GaSb, comparing them with existing literature data.

Formulation of an appropriate equation of state to predict the melting temperature of metallic solids

The aim of this work is to derive an equation for the melting curve of metals through distinct isothermal equations of state, namely the equations of state proposed by Singh and Kao, Murnaghan, and Kholiya. The developed models define the relation among the pressure, bulk modulus, melting temperature, volume, and pressure derivative of bulk modulus at zero pressure. These models are applied for the metals Pd, Au, Zn, Cu and Pt to determine the melting curves over the wide range of pressure to 30 GPa. The outcome of the Singh and Kao equation of state gives a too large increment in the melting temperature due to the large increment in bulk modulus. The outcome of Kholiya equation of state is the one that best fit experimental results. The results of Murnaghan equation of state tends to underestimate the melting temperature. The study provides insights into the fundamental understanding of quantitative effect of pressure on melting temperature of different solids. The obtained models can be used to extrapolate melting temperatures to higher pressures.

Analysis of pressure derivatives of bulk modulus for materials at high compressions

Pressure derivatives of bulk modulus play a central role in describing thermoelastic behaviour and equation of state for materials at high pressures. It is demonstrated here that the relationships between pressure derivative of bulk modulus and volume compression used by earlier workers are not consistent with the thermodynamic constraints based on the second-, and third order pressure derivatives of bulk modulus, and third order Grüneisen parameter in the limit of infinite pressure. It is pointed out that the compatibility of Keane’s equation and the Stacey reciprocal equation of state as considered by Sinha et al. does not hold at high pressures. The Keane equation does not satisfy the thermodynamic constraint according to which the third order Grüneisen parameter must be less than the pressure derivative of bulk modulus at extreme compression. Values of second-, and third order pressure derivatives of bulk modulus for the Earth lower mantle and outer core determined using the K-primed equations reported by Sinha et al. are found to deviate significantly from the results based on the seismic data at finite pressures obtained by fitting the Stacey reciprocal K-primed EOS.

A Paradigm Shift in High-Pressure Equation of State Modeling: Unveiling the Pressure–Bulk Modulus Relationship

A Paradigm Shift in High-Pressure Equation of State Modeling: Unveiling the Pressure–Bulk Modulus Relationship

Pressure-induced metallization in the absence of a structural transition in the layered transition-metal dichalcogenide ZrSe2.

First-principles calculations were carried out on the ZrSe2 compound, which has been of interest owing to its technologically important physical properties. The structural, electronic and optical properties of this compound were investigated under pressure through the plane wave pseudopotential approach within the framework of density functional theory. A comparison between the computed crystal structure parameters and the corresponding experimental counterparts shows a very good agreement between them. Fitting the pressure-volume data using the third-order Birch-Murnaghan equation of state yielded a bulk modulus B0 = 38.17 GPa and a pressure derivative of bulk modulus B'0 = 8.2 for hexagonal ZrSe2. The relationship between the band structure and pressure is revealed. We calculated the total density of state (TDOS) under different pressures and partial density of state (PDOS) from 0 to 10 GPa. According to our calculations, metallization of hexagonal ZrSe2 is predicted to occur at around 10 GPa and pressure-induced band-gap engineering reveals the transformation of the indirect to direct band gap with increasing pressure. Furthermore, optical properties, such as the complex dielectric function, refractive index and reflectivity spectra of this compound, were studied for incident electromagnetic waves in an energy range up to 45 eV. The contributions to various transition peaks in the optical spectra are analyzed and discussed with the help of the energy-dependent imaginary part of the dielectric function.

Analysis of the volume dependence of Grüneisen parameter for γ-Fe2O3 nanomaterial

The volume dependence of Grüneisen parameter of γ-Fe2O3 nanomaterial has been investigated using the results obtained from the Barton-Stacey formula and three different equations of state viz. the Birch-Murnaghan equation, Brennan-Stacey equation and the Vinet-Rydberg equation of state. Values of the ratio of Grüneisen parameter and volume compression have been determined using the results for pressure, bulk modulus and pressure derivative of bulk modulus for γ-Fe2O3 at different volumes. The Brennan-Stacey equation of state is based on the assumption that the ratio of the Grüneisen parameter to volume compression remains constant. It has been found that the ratio of Grüneisen parameter and volume does not remain constant with the change in volume compression for the Birch-Murnaghan and the Vinet- Rydberg equations of state.

Crystallographic structural variations in nano-crystalline Sc2O3 under pressure

The present manuscript reports high-pressure investigations on nano-crystalline Scandium Oxide (Sc2O3) through synchrotron angle dispersive x-ray diffraction technique (ADXRD) up to a pressure of ∼35.4 GPa using a diamond-anvil cell (DAC). The sample, having a cubic bixbyite structure at ambient conditions, underwent substantial changes in crystallographic parameters under the application of external pressure, while exhibiting phase stability i.e. does not undergo any structural phase transition up to 35.4 GPa. The lattice parameters and the unit cell volume decrease significantly with an increase in pressure, revealing the compressible nature of the crystal structure. The pressure-volume data is fitted using the third-order Birch-Murnaghan equation of state to calculate the bulk modulus and its first derivative, which yields zero pressure bulk modulus of 217(35) GPa, with = 12(4) and the corresponding ambient volume per unit molecule comes out to be 59.18(18) Å3.

Theoretical prediction of Grüneisen Parameter for γ-Fe2O3

The application of nanomaterials in modern technologies requires the study of its Grüneisen parameter. For this purpose, we have theoretically calculated the pressure, bulk modulus, and first order pressure derivative of bulk modulus at different compression ratios (V/V0). Further, we have tried to predict the variation of Grüneisen parameter with respect to compression ratio (V/V0) for ɣ-Fe2O3 nanomaterial. The Grüneisen parameter was calculated using the Borton and Stacey model at compressions up to V/V0 = 0.64. We have used three different equations of state: Birch- Murnaghan EOS, Brennan-Stacey EOS, and Vinet-Rydberg.

Exploration of the structural, vibrational, electronic, mechanical and thermal properties of Ru4Al3B2 and Ru9Al3B8: a DFT study.

The structural, dynamical, electro-optical, mechanical, and thermal characteristics of the newly synthesized intermetallic compounds Ru4Al3B2 and Ru9Al3B8 have been studied under ambient and elevated pressure through density functional theory (DFT). The obtained lattice parameters of the compounds are consistent with the experimental values. The metallic character of these compounds is established by the band structure and density of states (DOS). The electronic charge density distribution and bond analysis imply that Ru4Al3B2 and Ru9Al3B8 have mainly both ionic and covalent bonding. The non-negative phonon dispersion frequency of the compounds reaffirms their dynamical stability. Both compounds are tough as well as have high melting points, and hence, can be applied in harsh conditions. Mechanical properties are significantly improved under pressure. Thermal barrier coating (TBC) is a possible field of application for both compounds. The different thermal properties such as the Debye temperature (ΘD), Grüneisen parameter (γ), melting temperature (Tm), minimum thermal conductivity (Kmin) and lattice thermal conductivity (κph) of these compounds have been studied to figure out the suitable application areas in thermally demanding situations. The pressure and temperature dependent bulk modulus (B) and other thermodynamic properties have also been analyzed, which suggested that the present compounds are strong candidates for device applications at high temperature and pressure. Owing to their high optical absorptivity and reflectivity in the UV region, they are also candidates for UV-based applications. Furthermore, they also have applicability in the fields of electronics, aviation, energy storage, and supercapacitor devices for their superior electronic, thermal and mechanical properties.

Structural, Electronic and Optical Properties of Titanium Based Fluoro-Perovskites MTiF3 (M = Rb and Cs) via Density Functional Theory Computation.

This study reports the theoretical investigations on the structural, electronic, and optical properties of titanium-based fluoro-perovskites MTiF3 (M = Cs and Rb) using density functional theory. The impact of on-site Coulomb interactions is considered, and calculations are performed in generalized gradient approximation with the Hubbard U term (GGA + U). The ground state parameters, such as lattice constants, bulk modulus, and pressure derivatives of bulk modulus, were found. These compounds are found stable in cubic perovskite structures having lattice constants of 4.30 and 4.38 Å for RbTiF3 and CsTiF3, respectively. Analysis of elastic properties shows that both of the compounds are ductile in nature. According to the band structure profile, the examined compounds have a half-metallic character, exhibiting conducting behavior in the spin-up configuration and nonconducting behavior in the spin-down configuration. The ferromagnetic nature is conformed from the study of its magnetic moments. The optical behaviors such as reflectivity, absorption, refraction, and conductivity of the cubic phase of MTiF3 (M = Rb and Cs) are studied in the energy range of 0-40 eV.

Compressibilities along the magnetite–magnesioferrite solid solution

To calculate the thermodynamic properties of recently discovered high-pressure mixed valence iron oxides in the system Fe–Mg–O, information on the equation of state of precursor inverse spinel phases along the magnetite–magnesioferrite join is needed. The existing equation of state data, particularly for magnesioferrite, are in poor agreement and no data exist for intermediate compositions. In this study, the compressibility of nearly pure magnesioferrite as well as of an intermediate {{mathrm{Mg}}_{0.5}}^{vphantom{2+}}mathrm{Fe}_{0.5}^{2+}{mathrm{Fe}}_{2}^{3+}{mathrm{O}}_{4}^{vphantom{2+}} sample have been investigated for the first time up to approximately 19 and 13 GPa, respectively, using single-crystal X-ray diffraction in a diamond anvil cell. Samples were produced in high-pressure synthesis experiments to promote a high level of cation ordering, with the obtained inversion parameters larger than 0.83. The room pressure unit cell volumes, V0, and bulk moduli, KT0, could be adequately constrained using a second-order Birch–Murnaghan equation of state, which yields V0 = 588.97 (8) Å3 and KT0 = 178.4 (5) GPa for magnesioferrite and V0 = 590.21 (5) Å3 and KT0 = 188.0 (6) GPa for the intermediate composition. As magnetite has KT0 = 180 (1) GPa (Gatta et al. in Phys Chem Min 34:627–635, 2007. https://doi.org/10.1007/s00269-007-0177-3), this means the variation in KT0 across the magnetite–magnesioferrite solid solution is significantly non-linear, in contrast to several other Fe–Mg spinels. The larger incompressibility of the intermediate composition compared to the two end-members may be a peculiarity of the magnetite–magnesioferrite solid solution caused by an interruption of Fe2+–Fe3+ electron hopping by Mg cations substituting in the octahedral site.

Structural, Mechanical and Thermodynamic properties of Manganese Monocarbide (MnC) in ZnS phase under High Pressure: a DFT Study

The structural, elastic and thermodynamic properties of the manganese monocarbide in ZnS (B3) phase were investigated using the DFT calculation with the PBE functional. The ground state properties of this materials such as lattice constant, bulk modulus, pressure derivatives of bulk modulus and Young’s modulus are calculated and the obtained results show a good agreement with the experimental data. Moreover, the estimated values of elastic constants indicate that the studied material is found to be mechanically stable. The results show also that the heat capacity of this materials as a function of the temperature is close to the Dulong-Petit limit (49.6 J/mol.K)at higher temperatures. The thermal expansion( α) and Debye parameter were also calculated at the different temperatures. The pressure effects on the above parameters were computed and their values are compared with the experimental results.

First-principles study of the structural, electronic, optical, and thermoelectric properties of the RhVZ (Z= Si, Ge, Sn)

In this work, we have explored half-Heusler RhVZ (Z ​= ​Si, Ge, Sn) with 18 valence electrons per unit cell within the Density Functional Theory (DFT). The structural, electronic, optical, thermoelectric, and phonon properties have been investigated. The structural properties such as lattice constant, bulk modulus, and pressure derivative of bulk modulus have been reported. All materials are semiconductors with a narrow bandgap as it is concluded from the electronic band structure, and the phonon dispersion approve the dynamical stability, meanwhile, the absorption coefficient is found to be around 104 ​cm−1 in the visible region indicating that these materials can be used in Photovoltaic applications. The semi-classical Boltzmann transport equation used to calculate the thermoelectric characteristics and all materials under investigation show high performance in the p-type region due to the valence band degeneracy. The thermoelectric analysis provided show that the power factor of the materials lies on 3.12 ​× ​10−3, 3.26 ​× ​10−3, and 6.52 ​× ​10−3 ​W/msK2 for RhVSi, RhVGe, and RhVSn respectively, the figure of merit ZT reaches the maximum value of 0.8 ​at room temperature indicating that those materials are suitable for thermo-generation application at near room temperature. However, we found that RhVSn is more suitable for thermoelectric applications with its high ZT values more than RhVSi, and RhVGe compounds.

Examining computationally the structural, elastic, optical, and electronic properties of CaQCl3 (Q = Li and K) chloroperovskites using DFT framework.

This study presents the investigations of structural, elastic, optical, and electronic properties of CaQCl3 (Q = Li and K) chloroperovskites for the first time using the DFT framework. The WIEN2K and IRelast packages are used in which the exchange-correlation potential of the modified Becke-Johnson potential (TB-mBJ) is used for obtaining better results. The optimized crystal structural parameters comprising the lattice constant, optimum volume, ground state energy, bulk modulus, and the pressure derivative of bulk modulus are computed by fitting the primitive unit cell energy versus primitive unit cell volume using the Birch-Murnaghan equation of state. The elastic properties which consist of cubic elastic constants, Poisson's ratio, elastic moduli, anisotropy factor, and the Pugh ratio are computed using the very precise IRelast package incorporated inside WIEN2K. The electronic properties are analyzed from the computation of electronic bands structure and density of states (DOS), and it is concluded that an indirect band gap of 4.6 eV exists for CaLiCl3 and a direct band gap of 3.3 eV for CaKCl3 which confirms that CaLiCl3 is an insulator while CaKCl3 is a wide band gap semiconductor. The analysis of DOS shows that the greater contribution to the conduction band (CB) occurs because of the "Ca" element whereas in the valence band the major contribution is from the "Cl" element. The spectral curves of various parameters of optical properties from 0 eV up to 42 eV incident photon energies are observed and it is found that the CaQCl3 (Q = Li and K) chloroperovskites are optically active having a high absorption coefficient, optical conductivity, optical reflectivity, and energy loss function from 25 eV to 35 eV incident photon energies. The applications of these materials can be deemed to alter or control electromagnetic radiation in the ultraviolet (UV) spectral regions. In summary, the results for selected CaQCl3 (Q = Li and K) chloroperovskites depict that these are important compounds and can be used as scintillators, and energy storage devices, and in many modern electronic gadgets.

Half-metallic ferromagnetism and thermoelectric properties of vanadium doped Hf1−xVxO2 (x = 0, 0.25, 0.50, 0.75) alloys by first principles perspective

In this work, we have reported the first-principles calculations based on functional theory density on the structural, electronic, magnetic, bonding nature and thermoelectric properties of Hf1-xVxO2 alloys (x = 0, 0.25, 0.50, 0.75). For all the materials, the equilibrium structural parameters like that of lattice constant, bulk modulus and first pressure derivative of bulk modulus have been computed. The band profile and the density of states results demonstrate half-metallic nature for Hf1-xVxO2 alloys (x = 0.25, 0.50, 0.75). The calculated total magnetic moment was 1.0 μB/cell, 2.0 μB/cell, and 3.0 μB/cell, and the partial moment of V or local contribution is 1.08 μB, 1.85 μB, and 2.73 μB, respectively for Hf1-xVxO2 alloys (x = 0.25, 0.50, 0.75). The transport properties such as Seebeck coefficient, thermo power and thermal conductivity are found to have a great variation with V concentration. These alloys may find suitable applications in spintronic materials and in high temperature thermoelectric devices.

Phase transformations of zircon-type DyVO4 at high pressures up to 36.4 GPa: X-ray diffraction measurements

The compression behavior of zircon-type DyVO4 has been investigated in a diamond anvil cell by angle-dispersive X-ray diffraction (ADXRD) at high pressures up to 36.4 GPa. Under quasi-hydrostatic compression with argon as the pressure transmitting medium, DyVO4 underwent a sluggish zircon-to-scheelite phase transformation that started at approximately 8.0 GPa and was completed at 15.3 ± 0.9 GPa. The scheelite-type phase remained stable at pressures up to 25.3 GPa and during the process of decompression to ambient conditions, implying that the zircon-to-scheelite transformation is irreversible. Fitting the pressure-volume data using the third-order Birch-Murnaghan equation of state yielded a bulk modulus B0 = 129 (7) GPa and a pressure derivative of bulk modulus B′ = 3.4 (4) for the zircon-type phase, and B0 = 184 (10) GPa and B′ = 5.3 (8) for the scheelite-type phase. When compressed in a methanol-ethanol (4:1) pressure transmitting medium, DyVO4 was transformed into the scheelite-type phase at a pressure of 8.8 ± 1.1 GPa and then transformed into a fergusonite-type phase at 21.3 ± 1.6 GPa. The scheelite-to-fergusonite transformation was reversible during decompression. Our study indicates that DyVO4 under compression experiences a sequential zircon-scheelite-fergusonite phase transformation and that the scheelite-fergusonite transformation is sensitive to nonhydrostatic conditions.

The structures, phase transition and elastic and thermodynamic properties of ZnS from first-principles calculations

The phase transition of zinc sulfide (ZnS) from Zinc-blende (ZB) to a rocksalt (RS) structure and the elastic, thermodynamic properties of the two structures under high temperature and pressure are investigated by first-principles study based on the pseudo-potential plane-wave density functional theory (DFT) combined with the quasi-harmonic Debye model. The lattice constant [Formula: see text], bulk modulus [Formula: see text] and the pressure derivative of bulk modulus [Formula: see text]’ of the two structures are calculated. The results are in good agreement with experimental results and the other theoretical data. From the energy–volume curve, enthalpy equal principle and mechanical stability criterion, the transition pressures from the ZB to the RS structure are 16.83, 16.96 and 16.61 GPa, respectively. The three results and the experimental values 14.7–18.1, 16 GPa are very close to each other. Then the elastic properties are also calculated under the pressure ranging from 0 to 30 GPa. Finally, through the quasi-harmonic Debye model, the thermodynamic properties dependence of temperature and pressure in the ranges between 0–1600 K and 0–30 GPa are obtained successfully.