Simulated equation of state of CaF2 with fluorite-type structure at high temperature and high pressure

The pressure-volume-temperature (P-V-T) equation of state (EOS), isothermal bulk modulus, and thermal expansivity of CaF₂ with cubic fluorite-type structure are investigated using the constant temperature and pressure shell model molecular dynamics (MD) method with effective pair potentials which consist of the Coulomb, dispersion, and repulsion interaction. It was shown that MD simulation is very successful in accurately reproducing the measured volumes of the CaF₂ over a wide range of pressures. The simulated P-V data matched X-ray diffraction experimental results up to 9.5 GPa at 300 K. In addition, volume thermal-expansion coefficient and isothermal bulk modulus were also calculated and compared with available experimental data and the latest theoretical results at ambient condition. At extended temperature and pressure ranges, The P-V EOS under different isotherms at selected temperatures, T-V EOS under different isobars at selected pressures, thermal expansivity, and isothermal bulk modulus were predicted up to 1500 K and 10 GPa. The detailed knowledge of thermodynamic behavior and EOS at extreme conditions are of fundamental importance to the understanding of the physical properties of CaF₂.     

Molecular dynamics simulation of P-V-T relationship of ZnO with rock-salt structure using pair-wise interactions

Molecular dynamics (MD) method is used to investigate the behavior of the pressure-volume-temperature (P-V-T) relationship, lattice constant and thermal expansivity for ZnO with rock-salt structure at high pressures and temperatures. The interionic potential is taken to be the sum of pair-wise additive Coulomb, van der Waals attraction, and repulsive interactions. The isothermal and isobaric properties are discussed from the corresponding P-V-T relationship, and it is shown that the MD simulation is successful in reproducing the measured volumes of ZnO over a wide range of temperature and pressure. Meanwhile, the equations of state parameters including lattice constant, linear thermal expansion coefficient, and isothermal bulk modulus are calculated and compared with the available experimental data and the latest theoretical results. At an extended pressure and temperature range, P-V-T relationship, lattice constant, and linear thermal expansion coefficient have been predicted. The structural and thermodynamic properties of ZnO with rock-salt structure are summarized in the pressure 0-100 GPa ranges and the temperature up to 3100 K.     

Elastic, thermal and structural properties of platinum

The thermal equation of state (EOS) for platinum has been calculated to 300 GPa and 3000 K using ab initio molecular dynamics employing the local density approximation (LDA) and the projector augmented-wave methods (PAW). Direct ab initio molecular dynamics avoids the simplifying assumptions inherent in empirical treatments of thermoelasticity. A third-order Birch-Murnaghan equation EOS fitted to the 300 K data yielded an isothermal bulk modulus of B_T0=290.8 GPa and a pressure derivative of B_T′=5.11, which are in better agreement with the measured values than those obtained by previous calculations. The high-temperature data were fitted to a thermal pressure EOS and a Mie-Grüneisen-Debye EOS. The resulting calculated thermal expansion coefficient, α₀, temperature derivative of the isothermal bulk modulus, (∂B_T/∂T)_V, and second temperature derivative of the pressure, (∂²P/∂T²)_V, were 1.94×10⁻⁵ K⁻¹, −0.0038 GPa K⁻¹, and 1.7×10⁻⁷ GPa² K⁻², respectively. A fit to the Mie-Grüneisen-Debye EOS yielded values for the Grüneisen parameter, γ₀, and its volume dependence parameter, q, of 2.18 and 1.75, respectively. An analysis of our data revealed a strong volume dependence of the thermal pressure of platinum. We also present a qualitative analysis of the effects of intrinsic anharmonicity from the calculated Grüneisen parameter at high temperatures.     

Analysis of P-V-T relationships and thermodynamic properties for some alkali halides

In this paper, Pandey approximation for the volume dependence of Anderson-Grüneisen parameter at fixed pressure, Anderson approximation for the temperature dependence of thermal expansivity, the equations of thermal expansivity along isobars derived by Shanker et al., and the presented approximation for the volume dependence of Anderson-Grüneisen parameter along isobars, have been used to study and predict the pressure-volume-temperature (P-V-T) data and the variations of the volume expansion coefficient and isothermal bulk modulus with temperature and pressure for NaCl, CsCl, LiF, NaF crystals, up to 30 GPa and in the temperature range 298-1073 K. The calculated values are compared with each other. It is found that these equations-of-state are valid and present good agreement with the available experimental data.     

Equation of state of aluminum carbide Al4C3

Quasi-hydrostatic compression of aluminum carbide, Al₄C₃ has been studied to 6 GPa at room temperature using energy-dispersive X-ray powder diffraction with synchrotron radiation. A fit of the experimental p-V data to the Birch equation of state yields the values of the bulk modulus, B₀, of 130(5) GPa and the first pressure derivative of the bulk modulus, B′₀, of 4.6(9). The compression is found to be anisotropic, with the a-axis being more compressible than the c-axis.     

The thermodynamics of elastic deformation—I: Equation of state for solids

The isobaric and isothermal volume derivatives of In B, In μ and In μ' are investigated, where B, μ and μ' are the isothermal bulk modulus and the two shear moduli, respectively, of a cubic crystal. In the case of the bulk modulus, the temperature independence of αB (where α is the volume thermal expansion) for a large number of materials, ensures that the derivatives are constant and approximately equal, while for the shear moduli, evidence is advanced that the isothermal derivatives are constant along an isotherm, but not along an isobar except at high temperatures near the melting point. The relationships satisfied by the bulk modulus enable the explicit temperature and pressure dependence of the molar volume, V, thermal expansion, and bulk modulus to be determined. The most adequate representation of the volume dependence of the Grüneisen parameter, γ, appears to be that γ/V is independent of volume between the Debye and melting temperatures.     

High pressure X-ray diffraction and electrical resistance study of the quasi-one-dimensional sulfide InV6S8

The ambient structural details and the results of room temperature high pressure angle dispersive X-ray diffraction and electrical resistance measurements on the quasi-one-dimensional sulfide, InV₆S₈, to a pressure of 25 GPa are reported. The material does not undergo a phase transition in this pressure range, though an anomaly in the c/a ratio has been observed around 10 Gpa. A fit of the Murnaghan equation of state to the V/V₀ versus pressure data, with the value of the derivative of B₀ with respect to pressure, B′₀, fixed at 4 has yielded a value of the bulk modulus, B₀, of 110 GPa. We also present data of the pressure dependence of the lattice constants, a and c, the ratio c/a, and the resistance at room temperature.     

Pressure dependence of the Grüneisen parameter of sodium and potassium

Temperature changes associated with adiabatic pressure changes (?T/?P)_s have been measured for sodium and potassium at room temperature (297 K) under hydrostatic pressures up to 32 kbar. For both metals a large decrease in the value of (?T/?P)_s is observed as the pressure increases. The Grüneisen parameter γ is related to (?T/?P)_s by γ = B_s(?T/?T)_s/T where B_s is the adiabatic bulk modulus. Available data for the pressure dependence of B_s and the isothermal bulk modulus B_T are used to predict the pressure and volume dependence of γ.     

Elastic and thermodynamic properties of CaB6 under pressure from first principles

The elastic and thermodynamic properties of CsCl-type structure CaB₆ under high pressure are investigated by first-principles calculations based on plane-wave pseudopotential density functional theory method within the generalized gradient approximation (GGA). The calculated lattice parameters of CaB₆ under zero pressure and zero temperature are in good agreement with the existing experimental data and other theoretical data. The pressure dependences of the elastic constants, bulk modulus B (GPa), and its pressure derivative B′, shear modulus G, Young's modulus E, elastic Debye temperature Θ_B, Zener's anisotropy parameter A, Poisson ratios σ, and Kleinmann parameter ζ are also presented. An analysis for the calculated elastic constants has been made to reveal the mechanical stability of CaB₆ up to 100 GPa. The thermodynamic properties of the CsCl-type structure CaB₆ are predicted using the quasi-harmonic Debye model. The pressure-volume-temperature (P-V-T) relationship, the variations of the heat capacity C_V, Debye temperature Θ_D, and the thermal expansion α with pressure P and temperature T, as well as the Grüneisen parameters γ are obtained systematically in the ranges of 0-100 GPa and 0-2000 K.     

Comparative investigations of the P-V-T relationship of NaCl at high pressure and temperature

Two different potential models of molecular dynamics (MD) simulations have been applied to investigate the pressure-volume-temperature (P-V-T) relationship and lattice parameter of NaCl under high pressure and temperature. The first one is the shell model (SM) potentials in which due to the short-range interaction pairs of ions are moved together as is the case in polarization of a crystal due to the motion of the positive and negative ions, and the second one is the two-body rigid-ion Born-Mayer-Huggins-Fumi-Tosi (BMHFT) potentials with full treatment of long-range Coulomb forces. The P-V relationship at 300 K, T-V relationship at zero pressure, and lattice parameter a, have been obtained and compared with the available experimental data and other theoretical results. Compared with SM potentials, the MD simulation with BMHFT potentials is very successful in reproducing accurately the measured volumes of NaCl. At an extended pressure and temperature ranges, P-V relationship under different isotherms at selected temperatures, T-V relationship under different pressures, and lattice parameter a have also been predicted. The properties of NaCl are summarized in the pressure range 0-30 GPa and the temperature up to 2000 K.     

Equation of state and thermal stability of Al3BC

The lattice parameters of Al₃BC have been measured up to 5 GPa at ambient temperature using energy-dispersive X-ray powder diffraction with synchrotron radiation. A fit to the experimental p-V data using Birch-Murnaghan equation of state gives values of the Al₃BC bulk modulus 116(4) GPa and its first pressure derivative 9(2). In the 1.6-4.8 GPa range at temperatures above 1700 K Al₃BC undergoes incongruent melting that results in the formation of Al₃BC₃, AlB₂ and liquid aluminum.     

Compression behavior of nanocrystalline anatase TiO2

We present a synchrotron X-ray diffraction study of pressure-induced changes in nanocrystalline anatase (with a crystallite size of 30-40 nm) to 35 GPa. The nanoanatase was observed to a pressure above 20 GPa. Direct transformation to the baddeleyite-TiO₂ polymorph was seen at 18 GPa. A fit of the pressure versus volume data to a Birch-Murnaghan equation yielded the following parameters: zero-pressure volume, V₀=136.15 Å³, bulk modulus, K_T=243(3) GPa, and the pressure derivative of bulk modulus, K′=4 (fixed). The bulk modulus value obtained for the nanocrystalline anatase is about 35% larger than that of the macrocrystalline counterpart.     

Thermal equation-of-state of osmium: a synchrotron X-ray diffraction study

The pressure-volume-temperature behavior of osmium was studied at pressures and temperatures up to 15 GPa and 1273 K. In situ measurements were conducted using energy-dispersive synchrotron X-ray diffraction in a T-cup 6-8 high pressure apparatus. A fit of room-temperature data by the third-order Birch-Murnaghan equation-of-state yielded isothermal bulk modulus K₀=435(19) GPa and its pressure derivative K′₀=3.5(0.8) GPa. High-temperature data were analyzed using Birch-Murnaghan equation of state and thermal pressure approach. The temperature derivative of bulk modulus was found to be −0.061(9) GPa K⁻¹. Significant anisotropy of osmium compressibility was observed.     

Volume and structural study of Fe64Mn36 anti-ferromagnetic Invar alloy under high pressure

We have investigated the pressure variation of the volume and structure of an FCC Fe₆₄Mn₃₆ anti-ferromagnetic Invar alloy. The inclination of the pressure-volume (P-V) curve of the FCC structure becomes discontinuous at a pressure of 4 GPa. According to the bulk modulus at zero pressure estimated by the Birch-Murnaghan equation of state, the pressure between 4 and 10 GPa is 33 GPa larger than that at a pressure below 4 GPa. Considering previous experiments on magnetism at high pressure the Neel temperature at 4 GPa almost decreases to room temperature. These results suggest that the increase in the bulk modulus by 33 GPa can be attributed to the pressure-induced magnetic phase transition from anti-ferromagnetism to paramagnetism. Volume at zero pressure was estimated using the Birch-Murnaghan equation of state. The volume of FCC structure in the anti-ferromagnetic state was 1.17% larger than the volume in the paramagnetic state, namely, the spontaneous magnetostriction was 1.17%. Pressure-induced structural transition from FCC to HCP occurs with an increase in the pressure, especially at up to 5 GPa. The value of c/a is 1.62; this value almost corresponds to that of an ideal HCP structure. The bulk modulus of the HCP structure estimated by the Birch-Murnaghan equation of state is larger than that of the FCC structure, and the volume/atom ratio is smaller than that of the FCC structure.     

Elasticity and thermodynamic properties of RuB2 under pressure

First-principles calculations of the crystal structure and the elastic properties of RuB₂ have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The elastic constants c_ij, the aggregate elastic moduli (B, G, E), Poisson's ratio, and the elastic anisotropy with pressure have been investigated. Through the quasi-harmonic Debye model considering the phonon effects, the isothermal bulk modulus, the thermal expansions, Grüneisen parameters, and Debye temperatures depending on the temperature and pressure are obtained in the whole pressure range from 0 to 60 GPa and temperature range from 0 to 1100 K as well as compared to available data.     

Half metallic Co2TiGe—a theoretical and experimental investigation

Using first principle calculations the electronic structure and magnetic properties of the half metallic Co₂TiGe was investigated. The electronic structure calculations were performed using two different parameterization schemes. The band gap obtained in the minority spin state using LDA scheme in TB-LMTO method was smaller than that obtained using GGA scheme in FP-LAPW method. To explore the half metallic property experimentally bulk Co₂TiGe was synthesized by arc melting under argon atmosphere. The magnetic moment per formula unit determined from saturation magnetization at 2 K was 1.9 μ_B, which was close to the theoretically calculated value of 2 μ_B. A detailed analysis of the low temperature transport and magnetotransport properties exhibit characteristic features of half metals such as T^9/2 dependence of low temperature resistivity, negligible temperature dependence of resistivity below 20 K and a cross over from positive to negative MR around 100 K.     

Thermomagnetic transitions and coercivity mechanism in bulk composite Nd60Fe30Al10 alloys

The thermomagnetic behaviour (within the temperature range 553-300 K) for the bulk composite Nd₆₀Fe₃₀Al₁₀ alloy is described in terms of a transition from paramagnetic to superferromagnetic state at T=553 K, followed by a ferromagnetic ordering for T<473 K. For the superferromagnetic regime, the alloy thermomagnetic response was associated to a homogeneous distribution of magnetic clusters with mean magnetic moment and size of 1072 μ_B and 2.5 nm, respectively. For T<473 K, a pinning model of domain walls described properly the alloy coercivity dependence with temperature, from which the domain wall width and the magnetic anisotropy constant were estimated as being of ≈8 nm and ≈10⁵ J/m³, typical values of hard magnetic phases. Results are supported by microstructural and magnetic domain observations.     

The influence of substrate temperature on electrical properties of Cu/CdS/SnO2 Schottky diode

Polycrystalline CdS samples on the SnO₂ coated glass substrate were obtained by vacuum evaporation method at low substrate temperatures (T_S=200 and 300 K) instead of the commonly used vacuum evaporation at high substrate temperatures (T_S>300 K). X-ray diffraction studies showed that the textures of the films are hexagonal with a strong (0 0 2) preferred direction. Circular Cu contacts were deposited on the upper surface of the CdS thin films at 200 K by vacuum evaporation. The effects of low substrate temperature on the current-voltage (I-V) characteristics of the Cu/CdS/SnO₂ structure were investigated in the temperature range 100-300 K. The Cu/CdS (at 300 K)/SnO₂ structure shows exponential current-voltage variations. However, I-V characteristics of the Cu/CdS (at 200 K)/SnO₂ structure deviate from exponential behavior due to high series resistance. The diodes show non-ideal I-V behavior with an ideality factor greater than unity. The results indicate that the current transport mechanism in the Cu/CdS (at 300 K)/SnO₂ structure in the whole temperature range is performed by tunneling with E₀₀=143 meV. However, the current transport mechanism in the Cu/CdS (at 200 K)/SnO₂ structure is tunneling in the range 200-300 K with E₀₀=82 meV.     

Thermal equation of state of goethite (α-FeOOH)

ABSTRACT

The pressure–volume–temperature (P–V–T) equation of state (EoS) of natural goethite (α-FeOOH) has been determined by an X-ray diffraction study using synchrotron radiation. Fitting the volume data to the third-order Birch–Murnaghan EoS yielded an isothermal bulk modulus, B₀ of 85.9(15)?GPa, and a pressure derivative of the bulk modulus, B′, of 12.6(8). The temperature derivative of the bulk modulus, (?B/?T)_P, was –0.022(9)?GPa?K^?1. The thermal expansion coefficient α₀ was determined to be 4.0(5)?×?10^?5?K^?1.     

Analysis of thermoelastic behaviour of MgO at high temperatures and high pressures

The thermoelastic behaviour of MgO has been studied for the temperature range (300-3000 K) under different compressions down to V/V₀=0.3. It has been shown that a comprehensive study of the thermoelastic properties of MgO can be made with the help of the Anderson-Isaak equation for thermal expansivity and the Vinet equation of state taken together. We have estimated the values of thermal expansivity α, isothermal bulk modulus K_T, their variations with pressure and temperature, the Anderson-Gruneisen parameter and the change in entropy with compression for MgO along isotherms at different temperatures. The results have been discussed and compared with the corresponding values reported in the recent literature.