Equation of state for inert gas solids

The equation of state is a fundamental relation to analyse the thermophysical properties of different class of solids and it plays a key role in basic and applied condensed matter physics research. A lot of work has been done in the field of ionic solids, minerals and metals but a very little work is done in the field of inert gas solids. Most of the equations of state failed to explain the properties of inert gas solid because of their abnormal behavior in the low temperature range. In the present paper, Singh-Gupta equation of state has been used to study the properties of these solids. The results obtained using these equations have shown a good agreement with available experimental results. Thus it is shown that these equations of states successfully explain the behavior of inert gas solids.      

Isothermal bulk modulus and its first pressure derivative of NaCl at high pressure and high temperature

The isothermal bulk modulus and its first pressure derivative of NaCl are investigated using the classical molecular dynamics method and the quasi-harmonic Debye model.To ensure faithful molecular dynamics simulations,two types of potentials,the shell-model(SM) potential and the two-body rigid-ion Born-Mayer-Huggins-Fumi-Tosi(BMHFT) potential,are fully tested.Compared with the SM potential based simulation,the molecular dynamics simulation with the BMHFT potential is very successful in reproducing accurately the measured bulk modulus of NaCl.Particular attention is paid to the prediction of the isothermal bulk modulus and its first pressure derivative using the reliable potential and to the comparison of the SM and the BMHFT potentials based molecular dynamics simulations with the quasi-harmonic Debye model.The properties of NaCl in the pressure range of 0-30 GPa at temperatures up to the melting temperature of 1050 K are investigated.     

New isothermal equation of state of solids applied to high pressures

In the present paper, a new two-parameter inverted equation of state (EOS) is developed which is found to be working very well in the high-pressure region. To check its success and validity, this EOS has been applied in a number of solids. The computed volume compression is found to be in very good agreement with the experimental data in the whole range of pressure in all the solids. The minimum and the maximum pressure range used in the present study is 0–320 kbar and 0–3000 kbar, respectively.     

On the limitations of the equation of state based on the Lennard-Jones potential

It is emphasized that any equation of state (EOS) based on the generalized Lennard-Jones potential or the Mie potential, suffers from two main shortcomings as pointed out by Stacey and Davis [2]. One of the shortcomings viz. the problem related to imaginary numbers for the exponents in the potential function, has been removed recently by Jiuxun [11] by using a relationship between the exponents. However, the modified EOS obtained by Jiuxun suffers from the second shortcoming viz. it gives lower values for −B ₀ B″₀, an important equation of state parameter related to the second pressure derivative of the bulk modulus. Values of B ₀ B″₀ obtained by Jiuxun are not consistent with those reported by Stacey and Davis.      

Total energy, equation of state and bulk modulus of AlP, AlAs and AlSb semiconductors

Recently proposed model potential which combines both linear and quadratic types of interactions is employed for the investigation of some properties like the total energy, equation of state and bulk modulus of AlP, AlAs and AlSb semiconductor compounds using higher-order perturbation theory. The model potential parameter is determined using zero pressure condition. The ratio of the covalent bonding termE _cov to the secondorder termE ₂ is 6.77% to 11.85% which shows that contribution from higher order terms are important for zinc-blende-type crystals. The calculated numerical results of the total energy, energy band gap at Jones-zone face and bulk modulus of these compounds are in good agreement with the experimental data and found much better than other such theoretical findings. We have also studied pressure-volume relations of these compounds. The present study is carried out using six different screening functions along with latest screening function proposed by Sarkaret al. It is found from the present study that effect of exchange and correlation is clearly distinguishable.     

An isothermal equation of state for solids

An isothermal equation of state (EOS) for solids, recently suggested by the authors in the realistic form, V/V₀=f(P), with relative volume as the dependent and the pressure as the independent variable, was shown to have an advantage for some close-packed materials in that it allows B′_∞=(∂B_s/∂P)_s(P→∞) to be fitted, and this is where the usual standard equations fail. In the present study, our EOS is applied to a number of inorganic as well as organic solids, including alloys, glasses, rubbers and plastics; varying widely in their bonding and structural characteristics, as well as in their bulk modulus values. A very good agreement is observed between the data and fits. The results obtained are compared with those from two well-known equations, expressible in the realistic form, proposed by Murnaghan and Luban. Further, the results are also compared with those from the widely used two- and three-parameter EOSs, expressible in the unrealistic form only, P=f(V/V₀), proposed by Birch—and also with those from the EOS model of Keane in which B′_∞ is explicitly expressed as an equation of state parameter. The results obtained from our model compare well to these EOSs. Our EOS, in general, yields the smallest mean-squared deviations between data and fits. The values of B′_∞calculated from our EOS are compared with those from Keane's model. Further, we have studied the variation of B′_∞with temperature using the experimental isotherms of Mo and W at 10 different temperatures ranging from 100 to 1000 K, and observed that the values of B′_∞ yielded by our model and that of Keane vary, as expected, within a narrow range. Furthermore, our EOS is applied to study the stability of the fit parameters with variation in the pressure ranges with reference to the isothermal compression data on Mo and W—and also to study the variation of isothermal bulk modulus with pressure, with reference to the ultrasonic data on NaCl and noted a very good agreement with experiment. In addition, our model is applied, with B₀ and B′₀ constrained to the theoretical values, to the five theoretical isotherms of MgO at 300, 500, 1000, 1500 and 2000 K obtained on the basis of a first principles approach—a good agreement is observed with the predictions, and the values of B′_∞ inferred at different temperatures tend to converge to a constant value.     

Effects of pressure and temperature on the isothermal bulk modulus of CaO

Molecular dynamics (MD) simulations have been performed to investigate the effects of pressure and temperature on the isothermal bulk modulus of CaO using pair-wise interactions that include polarization effects through the shell model (SM). The dependence of isothermal bulk modulus B_T of CaO on the compression ratio V/V₀ and pressure P have been obtained from MD runs at T=300 K, and compared with the available experimental data and other theoretical results. A good agreement between theory and experiment is obtained. Meanwhile, B_T dependence on temperature T at zero pressure is investigated. At extended pressure and temperature ranges, SM-MD method has also been carried out for predicting the P-V-T equation of state and isothermal bulk modulus at different temperatures along the isotherms 0, 1000, 2000, 3000, and 4000 K, and at different pressures along the isobars 5, 15, 30, 40, and 50 GPa for CaO, respectively.     

Lattice energy and phase transition of alkaline earth chalcogenide

In this study, we have investigated the high-pressure structural phase transition of alkaline earth's chalcogenides within the framework of three-body potentials. We are considering short-range repulsive interactions up to the second nearest neighbors. The structural phase transition from the low-pressure NaCl (B1) to the high-pressure CsCl (B2) structure is estimated by Gibbs free energy calculations. The results are satisfactory and in agreement with the available experimental and other theoretical results.     

Equation of state for the Universe from similarity symmetries

In this paper we proposed to use the group of analysis of symmetries of the dynamical system to describe the evolution of the Universe. This method is used in searching for the unknown equation of state. It is shown that group of symmetries enforce the form of the equation of state for noninteracting scaling multifluids. We showed that symmetries give rise to the equation of state in the form p =-Λ + w ₁ρ(a) + w ₂ a ^β + 0 and energy density ρ = Λ+ρ₀₁ a ^-3(1+w) +ρ₀₂ a ^α +ρ₀₃ a ^-3, which is commonly used in cosmology. The FRW model filled with scaling fluid (called homological) is confronted with the observations of distant type Ia supernovae. We found the class of model parameters admissible by the statistical analysis of SNIa data.We showed that the model with scaling fluid fits well to supernovae data. We found that Ω_m,0 ≃ 0.4 and n ≃ -1 (β = -3n), which can correspond to (hyper) phantom fluid, and to a high density universe. However if we assume prior that Ω_m,0 = 0.3 then the favoured model is close to concordance ΛCDM model. Our results predict that in the considered model with scaling fluids distant type Ia supernovae should be brighter than in the ΛCDM model, while intermediate distant SNIa should be fainter than in the ΛCDM model. We also investigate whether the model with scaling fluid is actually preferred by data over ΛCDM model. As a result we find from the Akaike model selection criterion: it prefers the model with noninteracting scaling fluid.     

Equation of state of Al for compressed and expanded states from first-principles calculations

Results of theoretical calculations of equation of state and critical temperature of Al are presented using a three-term EOS model. In this model cold (0 K) term is calculated from first-principles method near normal conditions. Cold curve is extrapolated to ultrahigh pressures using Thomas– Fermi–Dirac model and to expanded states using a soft sphere function. Electron thermal term is calculated using Thomas–Fermi statistical model. Ion-thermal term is calculated using the modified Cowan model. In expanded state, the adjustable parameters of the modified Cowan model are tuned using quantum molecular dynamics (QMD) results. In compressed state, P−ρ$P-\rho$ and U_s−U_p$U_{\mathrm{s}}-U_{\mathrm{p}}$ Hugoniots derived using our results show good agreement with the reported experimental results. In expanded state, the estimated critical temperature shows good agreement with the reported results and pressure versus internal energy along isochores show reasonably good agreement with the reported experimental results.     

Thermodynamic regularities for non-polar and polar fluids from the modified SAFT-BACK equation of state

We have used the modified SAFT-BACK EOS for its ability to predict three important thermodynamic regularities for several fluids composed of molecules with different geometries and interactions. The studied regularities included: (i) the common bulk-modulus point on the isotherms of the reduced bulk modulus versus reduced density, (ii) near linearity of the reduced isothermal bulk-modulus as a function of reduced pressure, and (iii) Zeno line regularity which describes near linearity of a contour in the temperature-density plane along which the compressibility factor equals unity. In this work, we also reported the influence of the molecular size and shape on the displacement of intersection point of isothermal bulk-modulus curves versus density.     

Applicability of equation of state in extreme compression region and study of diatomic solids under pressure

In the present study, the expression of first pressure derivative of bulk modulus B′?earlier derived by Goyal and Gupta EoS [7] is corrected and the validity of the EoS is then verified in extreme compression region. The expressions of second and third order pressure derivative $(B^{{}^{″}},B^{″\prime })$of bulk modulus are obtained. The values of B′, B²B? to BB″,?Grunesien parameters?λ_∞,?γ_∞,?q_∞ at infinite pressure (P?→?∞)?are calculated using the identities [11–13] to check the validity of the equation in extreme compression region. The Goyal and Gupta EoS is then used to study the volume compression in diatomic solids, LiH and MgO. The values of pressure, bulk modulus and its first order pressure derivative at different compressions are calculated and compared with the results obtained from Hama–Suito EoS. The results justify the validity of the present EoS in high pressure region and the results for diatomic solids are also found in good consistency with the compared results.     

Equation of state of matter at high pressures and temperatures by the modified hartree-fock-slater model

Abstract

The equation of state of matter at extremely high pressures P～ 10–100 Mbars and temperatures T～ 5–50 eV has been very intensively investigated^1,2. The experimental determination of the matter properties in this region of parameters is very expensive, while the theory meets with grave difficulties because the matter under these conditions represents a strongly coupled multicomponent nonideal plasma. In practice, for calculations of the equation of state quasiclassical models are used, as those by Thomas-Fermi (TF) and Thomas-Fenni with corrections3. However, they do not include the shell effects. Most consistently these effects can be taken into account by quantomechanical self-consistent models^4–7     

Equation of state in hybrid stars and the stability window of quark matter

Properties of hybrid stars with a mixed phase composed of asymmetric nuclear matter and strange quark matter are studied. The quark phase is investigated by the quark quasiparticle model with a self-consistent thermodynamic and statistical treatment. We present the stability windows of the strange quark matter with respect to the interaction coupling constant versus the bag constant. We find that the appearance of the quark–hadron mixed phases is associated with the meta-stable or unstable regions of the pure quark matter parameters. The mass–radius relation of the hybrid star is dominated by the equation of state of quark matter rather than nuclear matter. The contour plots of the maximum mass of the hybrid star are shown in the plane of the coupling constant and the bag constant.     

Equation of state for solids considering cohesive energy and anharmonic effect and its application to MgO

A simple equation of state(EOS) in wide ranges of pressure and temperature is constructed within the MieGrneisen-Debye framework.Instead of the popular Birch-Murnaghan and Vinet EOS,we employ a five-parameter cold energy expression to represent the static EOS term,which can correctly produce cohesive energy without any spurious oscillations in the extreme compression and expansion regions.We developed a Pad’e approximation-based analytic Debye quasiharmonic model with high accuracy which improves the performance of EOS in the low temperature region.The anharmonic effect is taken into account by using a semi-empirical approach.Its reasonability is verified by the fact that the total thermal pressure tends to the lowest-order anharmonic expansion in the literature at low temperature,and tends to ideal-gas limitation at high temperature,which is physically correct.Besides,based on this approach,the anharmonic thermal pressure can be expressed in the Gru¨neisen form,which is convenient for applications.The proposed EOS is used to study the thermodynamic properties of MgO including static and shock compression conditions,and the results are very satisfactory as compared with the experimental data.     

Equation of state and P-V-T properties of polymer melts based on glass transition data

This paper addresses a method for predicting the participating constants in equation of state (EOS) for compressed polymeric fluids using two scaling constants. The theoretical EOS undertaken is Ihm-Song-Mason (ISM), which is based on the Weeks-Chandler-Anderson (WCA), and the two constants are the surface tension γ_g and the molar density ρ_g, both at the glass transition point. There are three temperature-dependent quantities that are required to use the EOS: the second virial coefficients B₂(T), an effective van der Waals co-volume, b(T) and a correction factor, α(T). The second virial coefficients are calculated from a two-parameter corresponding states correlation, which is constructed with two constants as scaling parameters, i.e., the surface tension γ_g and molar density ρ_g. This new correlation has been applied to the ISM EOS to predict the volumetric behavior of polymer melts including polypropylene (PP), poly(ethylene oxide) (PEO), polystyrene (PS), poly(vinyl methyl ether) (PVME), and polycarbonate bisphenol-A (PC) at compressed states. The operating temperature range is from 311.5 to 603.4 K and pressures up to 200.0 MPa. Other two-temperature-dependent parameters α(T) and b(T) appearing in the ISM EOS, are calculated by scaling rules. It was found that the calculated volumes agree well with the experimental values. A collection of 421 data points has been examined for the aforementioned polymers. The average absolute deviation between the calculated densities and the experimental densities is of the order of 0.6%. The newly obtained correlation has been further assessed through a detailed comparison against previous correlations proposed by other researchers.     

Application of the Englert-Schwinger model to the equation of state and the fullerene molecule

The Englert-Schwinger model (ESM) is applied to two problems. One is the calculation of zero-temperature equation of state (EOS) of elements within the spherically symmetric Wigner-Sietz cell approximation. The other is to obtain the equilibrium radius of fullerene molecule using March’s approach [N. H. March, Proc. Camb. Philos. Soc. 48, 665 (1952)]. In each case, the results of the ESM are compared with those of Thomas-Fermi-Dirac (TFD) and Thomas-Fermi-Dirac-Weizsacker (TFDW) models. Zero-temperature equation of state calculations are done for Al and Cu. The results of the ESM show an enormous improvement over those of the TFD model. Also, the ESM is in good agreement with the TFDW model for compressions greater than 2. In the regime of validity of TFDW theory, i.e., compressions greater than 20 and 10 for Al and Cu, respectively, the deviations between the results of the two models are negligible. Hence, the ESM may be used in lieu of the TFDW model for EOS calculations. In the fullerene case, we have obtained the cohesive energy using the models assuming the radius obtained from accurate calculations of the fullerene molecule. We have also obtained the equilibrium radius predicted by each model. The results obtained show that the ESM results are not much of an improvement over the TFD results. This shows that the ESM cannot always improve the results of the TFD model and be a replacement for the TFDW model. However, as in the EOS case, it would give results in good agreement with TFDW results for properties that are dependent on the electron density at the outer reaches of the atom.     

Equation of state and elastic properties of ACrO3 (A=Pb,Ca, Sr and Ba) perovskites under high pressure

We employ the spin-polarized generalized gradient approximation within the density functional theory to investigate the equation of state, magnetism and elastic constant of cubic ACrO₃ (A=Pb, Ca, Sr, and Ba) perovskite. The antiferromagnetic phase is the most stable state at zero pressure. Under pressure, the ferromagnetic state will transform to the non-magnetic state. Considering the effect of magnetism, the equilibrium lattice constant, the bulk modulus and the high pressure equations of state agree well with the available experiments. By using the energy-strain method, the predicted elastic properties are satisfactory.     

High-pressure and high-temperature bulk modulus of cubic fluorite-type MgF2 from quasi-harmonic Debye model

A detailed theoretical study of the isothermal and adiabatic bulk moduli of MgF₂ with a fluorite structure under high pressure and temperature has been carried out by means of first-principles density functional theory calculations combined with the quasi-harmonic Debye model in which the phononic effects are considered. Particular attention is paid to the prediction of the isothermal bulk modulus and its first and second pressure derivatives for the first time. The calculated ground state properties agree well with other theoretical values. At extended pressure and temperature ranges, the variation of the bulk modulus which plays a central role in the formulation of approximate equations of state has also been predicted. The properties of MgF₂ with a fluorite structure are summarized in the pressure range of 0–135 GPa and the temperature up to melting temperature 1500 K.