An Equation of State for Metals at High Temperature and Pressure in Compressed and Expanded Volume Regions

Menon, Suresh; Nayak, B.K.

doi:10.3390/condmat4030071

Cited by 10 publications

(8 citation statements)

References 36 publications

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“…Thermodynamic models of fluid properties, particularly in the two-phase region, are essential in applications involving equations of state of liquid metals [19,20], which are important in high pressure physics. It is expected that CPE will find good use in generating the equations of state data [21] in the fluid domain.…”

Section: Introductionmentioning

confidence: 99%

Convergence of Coupling-Parameter Expansion-Based Solutions to Ornstein–Zernike Equation in Liquid State Theory

Menon¹

2021

Condensed Matter

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The objective of this paper is to investigate the convergence of coupling-parameter expansion-based solutions to the Ornstein–Zernike equation in liquid state theory. The analytically solved Baxter’s adhesive hard sphere model is analyzed first by using coupling-parameter expansion. It was found that the expansion provides accurate approximations to solutions—including the liquid-vapor phase diagram—in most parts of the phase plane. However, it fails to converge in the region where the model has only complex solutions. Similar analysis and results are obtained using analytical solutions within the mean spherical approximation for the hardcore Yukawa potential. However, numerical results indicate that the expansion converges in all regions in this model. Next, the convergence of the expansion is analyzed for the Lennard-Jones potential by using an accurate density-dependent bridge function in the closure relation. Numerical results are presented which show convergence of correlation functions, compressibility versus density profiles, etc., in the single as well as two-phase regions. Computed liquid-vapor phase diagrams, using two independent schemes employing the converged profiles, compare excellently with simulation data. The results obtained for the generalized Lennard-Jones potential, with varying repulsive exponent, also compare well with the simulation data. Solution-spaces and the bifurcation of the solutions of the Ornstein–Zernike equation that are relevant to coupling-parameter expansion are also briefly discussed. All of these results taken together establish the coupling-parameter expansion as a practical tool for studying single component fluid phases modeled via general pair-potentials.

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Section: Introductionmentioning

confidence: 99%

Convergence of Coupling-Parameter Expansion-Based Solutions to Ornstein–Zernike Equation in Liquid State Theory

Menon¹

2021

Condensed Matter

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“…The overall conclusion emerging from this analysis is that CPE is a practical approach for obtaining thermodynamic properties of one-component fluids, interacting via general potentials. It is hoped that CPE would find good use in generating equation of state data [17] in the fluid domain, which have important applications in high pressure physics.…”

Section: Introductionmentioning

confidence: 99%

Convergence of coupling-parameter expansion-based solutions to Ornstein-Zernike equation in liquid state theory

Menon¹

2021

Preprint

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The objective of this paper is to investigate the convergence of coupling-parameter expansion-based solutions to Ornstein-Zernike equation in liquid state theory. The analytically solved Baxter's adhesive hard sphere model is analyzed first using coupling-parameter expansion. It is found that the expansion provides accurate approximations to solutions - including the liquid-vapor phase diagram - in most parts of the phase plane. However, it fails to converge in the region where the model has only complex solutions. Similar analysis and results are, then, obtained using analytical solutions within the mean spherical approximation for the hard-core Yukawa potential. Next, convergence of the expansion is analyzed for the Lennard-Jonnes potential using an accurate density-dependent bridge function in the closure relation. Numerical results are presented which show convergence of correlation functions, compressibility versus density profiles, etc., in the single as well as two phase regions. Computed liquid-vapor phase diagrams, using two independent schemes employing the converged profiles, compare excellently with simulation data. Results obtained for the generalized Lennard-Jonnes potential, with varying repulsive exponent, also compare well with simulation data. All these results together establish the coupling-parameter expansion as a practical tool for studying single component fluid phases modeled via general pair-potentials.

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“…Solutions of the critical conditions ∂ v P = 0 and ∂ 2 v P = 0 provide the critical point parameters and Maxwell's construction the phase diagram. Using thermodynamic relations to obtain other quantities, like energy and entropy, equation of state tables [32] can be generated in the expanded volume regions.…”

Section: Thermodynamic Functionsmentioning

confidence: 99%

Scaling of Phase Diagram and Critical Point Parameters in Liquid-Vapour Phase Transition of Metallic Fluids

Menon¹

2021

Condensed Matter

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The first objective of this paper is to investigate the scaling behavior of liquid-vapor phase transition in FCC and BCCmetals starting from the zero-temperature four-parameter formula for cohesive energy. The effective potentials between the atoms in the solid are determined while using lattice inversion techniques as a function of scaling variables in the four-parameter formula. These potentials are split into repulsive and attractive parts, as per the Weeks–Chandler–Anderson prescription, and used in the coupling-parameter expansion for solving the Ornstein–Zernike equation that was supplemented with an accurate closure. Thermodynamic quantities obtained via the correlation functions are used in order to obtain critical point parameters and liquid-vapor phase diagrams. Their dependence on the scaling variables in the cohesive energy formula are also determined. An equally important second objective of the paper is to revisit coupling parameter expansion for solving the Ornstein–Zernike equation. The Newton–Armijo non-linear solver and Krylov-space based linear solvers are employed in this regard. These methods generate a robust algorithm that can be used to span the entire fluid region, except very low temperatures. The accuracy of the method is established by comparing the phase diagrams with those that were obtained via computer simulation. The avoidance of the ’no-solution-region’ of the Ornstein-Zernike equation in coupling-parameter expansion is also discussed. Details of the method and complete algorithm provided here would make this technique more accessible to researchers investigating the thermodynamic properties of one component fluids.

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An Equation of State for Metals at High Temperature and Pressure in Compressed and Expanded Volume Regions

Cited by 10 publications

References 36 publications

Convergence of Coupling-Parameter Expansion-Based Solutions to Ornstein–Zernike Equation in Liquid State Theory

Convergence of Coupling-Parameter Expansion-Based Solutions to Ornstein–Zernike Equation in Liquid State Theory

Convergence of coupling-parameter expansion-based solutions to Ornstein-Zernike equation in liquid state theory

Scaling of Phase Diagram and Critical Point Parameters in Liquid-Vapour Phase Transition of Metallic Fluids

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