Bulk Modulus Data Research Articles

Mechanical, magneto-electronic and thermoelectric properties of Ba2MgReO6 and Ba2YMoO6 based cubic double perovskites: an ab initio study

We report an analysis of the structural, electronic, mechanical, and thermoelectric properties of oxide double perovskite structures, specifically the compounds Ba2MgReO6 and Ba2YMoO6. Our study employs first-principles density functional theory (DFT) as the investigative methodology. The electronic attributes of the examined compounds are explained by investigating their energy bands, as well as the total and partial density of states. The computational evaluation of the electronic band structure reveals that both compounds exhibit an indirect band gap semiconductor behavior in the spin-down channel, while demonstrating metallic properties in the spin-up channel. The magnetic attributes indicate a ferromagnetic nature, thus categorizing some double perovskite compounds as materials displaying half-metallic ferromagnetism (HM-FM) in addition to some other properties such as metallic and semiconductor in paramagnetic or antiferromagnetic states. The outcomes derived from the analysis of elastic constants confirm the mechanical robustness of the studied double perovskite compounds. Notably, the computed data for bulk modulus (B), shear modulus (G), and Young’s modulus (E) for Ba2MgReO6 surpass those of Ba2YMoO6. The calculated ratio of Bulk to shear modulus (B/G) indicates that both compounds possess ductile characteristics, rendering them suitable for device fabrication. Furthermore, both compounds display outstanding electronic and elastic properties, positioning them as promising contenders for integration within mechanical and spintronic devices. Finally, we investigate into the thermoelectric potential by evaluating parameters such as the Seebeck coefficient, electrical conductivity, thermal conductivity, figure of merit, and power factor. This assessment is conducted using the semiclassical Boltzmann theory and the constant relaxation time approximation, implemented through the BoltzTraP code. The results indicate that the investigated double perovskite oxides hold promise for utilization in thermoelectric applications.

The effect of Cu doping on the thermoelectric properties of Cs2CuxAg1-xBiBr6 perovskites

This study focuses on examining the thermoelectric properties of Cs2CuxAg1-xBiBr6 perovskites and investigates the influence of lattice thermal conductivity on their thermoelectric performance. To achieve this, the study utilizes a combination of first-principles calculations and Boltzmann transport theory. The calculated structural properties, obtained through the generalized Perdew-Burke-Ernzerhof approximation (GGA-PBE), closely align with both experimental and theoretical data for lattice constants and bulk modulus. The electronic properties were assessed using the TB-mBJ (Tran-Blaha-modified Becke-Johnson) method, indicating relatively small band gaps within the range of 1.146 eV for Cs2CuBiBr6 and 2.072 eV for Cs2AgBiBr6. The materials exhibit significant Seebeck coefficients and controllable lattice thermal conductivity between 0.067 and 0.662 W/mK at room temperature, with the relaxation time being determined using the Drude model. The study revealed that the most significant zT values, approximately 0.80, were observed when x = 0.5 in the Cs2CuxAg1-xBiBr6 perovskite material. This indicates that these perovskites possess the ability to efficiently and inexpensively convert heat into electrical energy. Consequently, these findings propose the potential of Cs2CuxAg1-xBiBr6 perovskites as a favorable option for real-world thermoelectric applications. The study further highlights the importance of utilizing lattice thermal conductivity to enhance the overall thermoelectric performance of such materials.

Binary Ti–Fe system. Part II: Modelling of pressure-dependent phase stabilities

Based on the experimental and calculated data from literature, the thermodynamic assessment of the binary Ti–Fe system under hydrostatic pressure was performed. The pressure-independent part of the Gibbs energy was modelled using the heat capacity data. The description of the pressure-dependent part of the Gibbs energy was based on the molar volume, thermal expansion and bulk modulus data, and on their pressure derivatives. Using the Murnaghan equation of state, the binary phase stabilities in the Ti–Fe system were assessed to reproduce the experimental results in the pressure range between 2.3 and 2.7 GPa. The thermodynamic functions were converted into the parameters of a phenomenological pressure model, which is implemented in the Thermo-Calc software. The reliability of the assessment is illustrated on the unary systems Ti and Fe containing high-temperature and high-pressure phases, and on the binary Ti–Fe system containing intermetallic phases TiFe and TiFe2 in addition to the terminal solid solutions. It is shown that the calculation of the T0 lines can help in understanding the formation of α′-Ti(Fe) martensite and the high-pressure phase ω-Ti and its metastability at atmospheric pressure.

Coherent thermodynamic model for ice Ih-A model case for complex behavior.

New data on the variation of the thermal expansion of ice Ih with temperature at ambient pressure together with new evaluations of the bulk modulus and earlier data for the heat capacity provide the basis for a coherent thermodynamic modeling of the main thermophysical properties of ice Ih over its whole range of stability. The quasi-harmonic approximation with one Debye term and seven Einstein terms, together with explicit anharmonicity, represents the dominant contribution next to minor "anomalies" from hydrogen ordering and lattice defects. The model accurately fits the main features of all experimental data and provides a basis for the comparison with earlier determinations of the phonon density of states and the Grüneisen parameters.

Reinvestigation of the Bulk Modulus for fcc Al using a Helmholtz Energy Approach

While extensive studies on the bulk modulus of fcc Al have been conducted, there still exist controversies regarding to the experimental values. In the present work, we adopted a Helmholtz energy approach based on the Morse function, the free electron Fermi gas model, as well as a modified Debye–Gruneisen model ensuring intrinsic thermodynamic relationship satisfied. To identify consistent bulk modulus data, all the model parameters for fcc Al were evaluated by using comprehensively available experimental data on heat capacity, elastic modulus, thermal expansivity, molar volume, etc., over wide temperature and pressure ranges. Reasonable agreements have been achieved in this work without inconsistency among various thermodynamic and thermophysical properties. Our calculated bulk modulus of fcc Al agrees well with the data reported by Kamm and Alers, Gerlich and Fisher, Ho and Ruoff and the assessment done by Wang and Reeber. However, it is impossible to reconcile the parameters to fit the recent data from Raju et al., as well as the results from Tallon and Wolfenden due to the intrinsic thermodynamic constraints.

Simultaneous prediction of rock matrix modulus and critical porosity

The matrix modulus and critical porosity in rocks are two critical parameters to seismic rock physics models; however, the critical porosity is difficult to obtain. Based on the linear relation between the effective bulk modulus and porosity, we propose a fast method for calculating the matrix modulus and critical porosity by least square fitting of effective bulk modulus and porosity data measured in laboratory or field. The proposed method is well suited for samples with wide porosity range. The calculation results accurately reflect the differences in clay content, pressure, and saturation state. Samples with high clay content have low matrix modulus and critical porosity. The matrix modulus is independent of pressure, whereas the critical porosity increases with increasing pressure. The calculated matrix modulus for water-saturated samples is higher than that for dry rock samples.

40 years of mineral elasticity: a critical review and a new parameterisation of equations of state for mantle olivines and diamond inclusions

Elasticity is a key property of materials, not only for predicting volumes and densities of minerals at the pressures and temperatures in the interior of the Earth, but also because it is a major factor in the energetics of structural phase transitions, surface energies, and defects within minerals. Over the 40 years of publication of Physics and Chemistry of Minerals, great progress has been made in the accuracy and precision of the measurements of both volumes and elastic tensors of minerals and in the pressures and temperatures at which the measurements are made. As an illustration of the state of the art, all available single-crystal data that constrain the elastic properties and pressure–volume–temperature equation of state (EoS) of mantle-composition olivine are reviewed. Single-crystal elasticity measurements clearly distinguish the Reuss and Voigt bulk moduli of olivine at all conditions. The consistency of volume and bulk modulus data is tested by fitting them simultaneously. Data collected at ambient pressure and data collected at ambient temperature up to 15 GPa are consistent with a Mie–Grunesien–Debye thermal-pressure EoS in combination with a third-order Birch–Murnaghan (BM) compressional EoS, the parameter V 0 = 43.89 cm3 mol−1, isothermal Reuss bulk modulus $$K_{\text{TR,0}} = 126.3(2){\text{ GPa}}$$ , $$K^{\prime}_{\text{TR,0}} = 4.54(6)$$ , a Debye temperature $$\theta_{\text{D}} = 644(9)\;{\text{K}}$$ , and a Gruneisen parameter γ 0 = 1.044(4), whose volume dependence is described by q = 1.9(2). High-pressure softening of the bulk modulus at room temperature, relative to this EoS, can be fit with a fourth-order BM EoS. However, recent high-P, T Brillouin measurements are incompatible with these EoS and the intrinsic physics implied by it, especially that $$\left( {\frac{{\partial K^{\prime}_{\text{TR}} }}{\partial T}} \right)_{P} > 0$$ . We introduce a new parameterisation for isothermal-type EoS that scales both the Reuss isothermal bulk modulus and its pressure derivative at temperature by the volume, $$K_{\text{TR}} (T,P = 0) = K_{\text{TR,0}} \left[ {\frac{{V_{0} }}{V(T)}} \right]^{{\delta_{\text{T}} }}$$ and $$K^{\prime}_{\text{TR}} (T,P = 0) = K^{\prime}_{\text{TR,0}} \left[ {\frac{V(T)}{{V_{0} }}} \right]^{{\delta^{\prime}}}$$ , to ensure thermodynamic correctness at low temperatures. This allows the elastic softening implied by the high-P, T Brillouin data for mantle olivine to be fit simultaneously and consistently with the same bulk moduli and pressure derivatives (at room temperature) as the MGD EoS, and with the additional parameters of α V0 = 2.666(9) × 10−5 K−1, $$\theta_{\text{E}} = 484(6)$$ , $$\delta_{\text{T}}$$ = 5.77(8), and $$\delta^{\prime}$$ = −3.5(1.1). The effects of the differences between the two EoS on the calculated density, volume, and elastic properties of olivine at mantle conditions and on the calculation of entrapment conditions of olivine inclusions in diamonds are discussed, and approaches to resolve the current uncertainties are proposed.

Technetium incorporation in scheelite: insights from first-principles.

Atomistic investigations of crystalline scheelite, CaWO4, and 99Tc-bearing scheelite, CaWO4:Tc, have been carried out using density functional theory. The lattice constants, bulk modulus, and volume compression data of CaWO4 have been calculated and compared with experimental data, with a focus on predictive understanding of 99Tc incorporation in CaWO4. Defect formation energies have been computed for several possible interstitial (I) and substitutional (S) sites of 99Tc in CaWO4. Both I(Oh) and S(W) sites were found to be energetically favourable for Tc doping. X-ray diffraction (XRD) spectra for each 99Tc defect type have been simulated to help interpret the complex experimental XRD patterns. This work on CaWO4:Tc provides insights into materials generated during nuclear weapons testing and useful spectral signatures for nuclear forensics.

The dynamic bulk modulus of three glass-forming liquids.

We present dynamic adiabatic bulk modulus data for three organic glass-forming liquids: two van der Waal's liquids, trimethyl-pentaphenyl-trisiloxane (DC705) and dibuthyl phtalate (DBP), and one hydrogen-bonded liquid, 1,2-propanediol (PD). All three liquids are found to obey time-temperature superposition within the uncertainty of the measurement in the adiabatic bulk modulus. The bulk modulus spectra are compared to the shear modulus spectra. The time scales of the two responses were found to be similar. The shapes of the shear and bulk modulus alpha loss peak are nearly identical for DBP and DC705, while the bulk modulus spectrum for PD is significantly broader than that of the shear modulus. The data further suggest that a "bulk modulus version of the shoving model" for the temperature dependence of the activation energy using the bulk modulus relaxation strength, ΔK(T), works well for DC705 and DBP, but not PD, while a formulation of the model using the high-frequency plateau value, K∞(T), gave a poor result for all three liquids.

Development of a ReaxFF Reactive Force Field for Titanium Dioxide/Water Systems

A new ReaxFF reactive force field has been developed to describe reactions in the Ti-O-H system. The ReaxFF force field parameters have been fitted to a quantum mechanical (QM) training set containing structures and energies related to bond dissociation energies, angle and dihedral distortions, and reactions between water and titanium dioxide, as well as experimental crystal structures, heats of formation, and bulk modulus data. Model configurations for the training set were based on DFT calculations on molecular clusters and periodic systems (both bulk crystals and surfaces). ReaxFF reproduces accurately the QM training set for structures and energetics of small clusters. ReaxFF also describes the relative energetics for rutile, brookite, and anatase. The results of ReaxFF match reasonably well with those of QM for water binding energies, surface energies, and H2O dissociation energy barriers. To validate this ReaxFF description, we have compared its performance against DFT/MD simulations for 1 and 3 monolayers of water interacting with a rutile (110) surface. We found agreement within a 10% error between the DFT/MD and ReaxFF water dissociation levels for both coverages.

Quantum Drude oscillator model of atoms and molecules: Many-body polarization and dispersion interactions for atomistic simulation

Treating both many-body polarization and dispersion interactions is now recognized as a key element in achieving the level of atomistic modeling required to reveal novel physics in complex systems. The quantum Drude oscillator (QDO), a Gaussian-based, coarse grained electronic structure model, captures both many-body polarization and dispersion and has linear scale computational complexity with system size, hence it is a leading candidate next-generation simulation method. Here, we investigate the extent to which the QDO treatment reproduces the desired long-range atomic and molecular properties. We present closed form expressions for leading order polarizabilities and dispersion coefficients and derive invariant (parameter-free) scaling relationships among multipole polarizability and many-body dispersion coefficients that arise due to the Gaussian nature of the model. We show that these ``combining rules'' hold to within a few percent for noble gas atoms, alkali metals, and simple (first-row hydride) molecules such as water; this is consistent with the surprising success that models with underlying Gaussian statistics often exhibit in physics. We present a diagrammatic Jastrow-type perturbation theory tailored to the QDO model that serves to illustrate the rich types of responses that the QDO approach engenders. QDO models for neon, argon, krypton, and xenon, designed to reproduce gas phase properties, are constructed and their condensed phase properties explored via linear scale diffusion Monte Carlo (DMC) and path integral molecular dynamics (PIMD) simulations. Good agreement with experimental data for structure, cohesive energy, and bulk modulus is found, demonstrating a degree of transferability that cannot be achieved using current empirical models or fully ab initio descriptions.

The heat capacity of fayalite at high temperatures

The high-temperature heat capacity of fayalite was reinvestigated using drop and differential scanning calorimetry. The resulting data together with drop calorimetry data taken from the literature were analyzed yielding C P J/(mol·K) = −584.388 + 129 440· T −1 − 3.84956·107· T −2 + 4.10143·109· T −3 + 98.4368·ln( T ). This new C P polynomial is recommended for calculating phase equilibria involving fayalite at mantle conditions. Using thermal expansion coefficient and isothermal bulk modulus data from the literature, the isochoric heat capacity was calculated resulting in C V J/(mol·K) = − 217.137 + 63 023.1· T −1 − 2.15863·107· T −2 + 2.23513·109· T −3 + 51.7620·ln( T ).

Discussion of “Three-dimensional slope stability based on stresses from a stress-deformation analysis”

We have read this paper with interest because of our involvement in slope stability analysis of embankment dams and natural slopes. This discussion is motivated primarily from the results of example problems included in the paper for which the proposed procedure to calculate the factor of safety (FS) shows a large sensitivity to Poisson’s ratio (y). Intuitively, we were expecting to see no or very little change in computed FS results over a commonly used range of y values (say from 0.30 to 0.45). To check our intuitions, we re-analyzed each of the four example problems included in the paper using the continuum-mechanics-based procedure implemented in the Fast Lagrangian Analysis of Continua in 3 Dimensions (FLAC3D) computer program (Itasca Consulting Group 2002). Results of these analyses form the basis of comments included in this discussion. For comparison purposes, the example problems were also analyzed in plane strain mode using the continuum-mechanics-based procedure implemented in the Fast Lagrangian Analysis of Continua (FLAC) computer program (Itasca Consulting Group 2006). Size adequacy of the continuum models was verified by analyzing them via the computer program CLARA-W (O. Hungr Geotechnical Research 2010) and comparing the results with the ones included in the paper. FLAC, FLAC3D, and CLARA-W are commercially available computer programs and their adoption for re-analysis of the example problems was for convenience. Continuum-mechanics-based procedures using the elastoplastic constitutive model with a Mohr–Coulomb yield condition and a flow rule require elastic constants (two for an isotropic material) and plasticity parameters (cohesion c, angle of internal friction 4, and dilation angle j). The elastic constants used in the paper are Young’s modulus (E) and y. FLAC and FLAC3D require data for bulk modulus (K) and

Research on softening of longitudinal mode under high pressure and equation of state of -Ce

Angle dispersive X-ray diffraction measurements of -Ce are performed in a diamond anvil cell under up to 0.74 GPa at room temperature. The accurate high pressure bulk modulus data obtained from ultrasonic measurements are used to calculate the parameters of various equations of states (EOSs). We find that the three order Murnaghan EOS and three order Xu EOS are fitted best to the relationships of the pressure vs. volume and the pressure vs. bulk modulus for -Ce.

Molecular Dynamics Modelling of Liquid Fe-C Alloys

Properties and structure of liquid Fe-C alloys with carbon concentration up to 20 at% at temperatures up to 2500 K were calculated using molecular dynamics modelling. Interaction between Fe-Fe and Fe-C atoms was described using the embedded atom potential (EAM). The Morse potential was chosen for Fe-C pair interaction, while C-C pair interaction was presented in the form of the repul- sive potential. Parameters of potentials were adjusted using experimental data for density, internal energy, bulk modulus and distance between Fe and C atoms in liquid Fe-C alloys near the liquidus temperature. Calculated density and molar volume of Fe-C alloys at 1873 K decreased with increasing carbon concentration; a temperature coefficient of density of liquid alloys was, practically, independent of the carbon concentration. Carbon content of the alloys had a negligible effect on the distance between Fe-Fe and Fe-C atoms and on a sum of coordination numbers Fe-Fe and Fe-C. Distribu- tion of atoms in the first coordination sphere in the Fe-C alloys was close to statistical.

Tuning of the stoichiometry ofFe1−xOwüstite by compression

We report the results of the investigation of the thermoelectric power (Seebeck effect) on quasi-single-crystalline w\ustite (FeO) at a high pressure up to 22 GPa. Using a polaron hopping model, we estimate pressure dependencies of the ${\text{Fe}}^{3+}/{\text{Fe}}^{2+}$ ratio and the stoichiometry. It is found that a typical composition ${\text{Fe}}_{0.935}\text{O}$ is unstable against compression, and gradually and irreversibly ``shifts'' to $\ensuremath{\sim}{\text{Fe}}_{0.89}\text{O}$. Comparative x-ray diffraction and Raman studies confirm, respectively, this change in the stoichiometry and dramatic modification of an incommensurate defect structure. This finding can partly explain discrepant high-pressure properties of ${\text{Fe}}_{1\ensuremath{-}x}\text{O}$, in particular, a strong scattering of bulk modulus data, the high inelasticity, and the differences in the high-pressure phases. This result provides clear evidence of a change in the stoichiometry of FeO under pressure.

Unified analyses for P‐V‐T equation of state of MgO: A solution for pressure‐scale problems in high P‐T experiments

In order to determine an accurate and reliable high‐pressure and high‐temperature equation of state (EOS) of MgO, unified analyses were carried out for various pressure‐scale‐free experimental data sets measured at 1 atm to 196 GPa and 300–3700 K, which are zero‐pressure thermal expansion data, zero‐pressure and high‐temperature adiabatic bulk modulus (KS) data, room temperature and high‐pressure KS data, and shock compression data. After testing several EOS models based on the Mie‐Grüneisen‐Debye description for the thermal pressures with the Vinet and the third‐order Birch‐Murnaghan equations for the 300‐K isothermal compression, we determined the K′T0 and γ(V) using a new functional form γ = γ0{1 + a[(V/V0)b − 1]} to express the volume dependence of the Grüneisen parameter. Through least squares analyses with prerequisite zero‐pressure and room temperature properties of V0, KS0, α0, and CP0, we simultaneously optimized a set of parameters of K′T0, γ0, a, and b required to represent the P‐V‐T EOS. Determined new EOS models of MgO successfully reproduced all the analyzed P‐V‐T‐KS data up to 196 GPa and 3700 K within the uncertainties, and the total residuals between calculated and observed pressures were found to be 0.8 GPa in root mean squares. These EOS models, even though very simple, are able to reproduce available data quite accurately in the wide pressure‐temperature range and completely independent from other pressure scales. We propose these models for primary pressure calibration standards applicable to quantitative high‐pressure and high‐temperature experiments.

Mechanical properties of bulk and nanoscale TiO 2 phases

The mechanical properties of bulk and nanoscale TiO 2 phases are examined with a view to assess the available bulk modulus and hardness data, and to understand the size-dependent behaviors. The bulk modulus values of thermodynamically stable bulk TiO 2 phases show a general correlation with Ti–O coordination number. As with the cotunnite-structured (OII) phase, it is likely that the seven-coordinated OI and eight-coordinated fluorite forms of TiO 2 are ultrahard substances. Of the nanoscale phases investigated thus far, nanocrystalline anatase displays the strongest size dependence of bulk modulus values, with possible stiffening behavior effected by incipient grain boundary amorphization under pressure. Nanocrystalline rutile and baddeleyite phases do not show appreciable size dependence in their compression behaviors.

Application of a shell model in molecular dynamics simulation to ZnO with zinc-blende cubic structure

The pressure–volume–temperature ( P – V – T ) relationship, lattice constant and isothermal bulk modulus of ZnO with zinc-blende cubic structure are studied using the constant temperature and pressure shell model molecular dynamics method with effective pair potentials which consist of the Coulomb, dispersion, and repulsion interaction. It is shown that the calculated structural and thermodynamic parameters including equilibrium volume, lattice constant, isothermal bulk modulus and its pressure derivative at standard condition are in good agreement with the available experimental data and the latest theoretical results. In addition, the isothermal and isobaric properties are discussed on the basis of the corresponding P – V – T relationship, and the volume compression data and isothermal bulk modulus data are predicted up to 300 kbar at 300 K, 1000 K, and 1500 K. The thermodynamic properties of the zinc-blende phase of ZnO are summarized in the 0–300 kbar pressure range and for temperature up to 2000 K.

The temperature dependence of the isothermal bulk modulus at 1bar pressure

It is well established that the product of the volume coefficient of thermal expansion and the bulk modulus is nearly constant at temperatures higher than the Debye temperature. Using this approximation allows predicting the values of the bulk modulus. The derived analytical solution for the temperature dependence of the isothermal bulk modulus has been applied to ten substances. The good correlations to the experiments indicate that the expression may be useful for substances for which bulk modulus data are lacking.