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

Abstract

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.

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

“…In CPE, the Newton-Armijo solver is employed only for determining correlation functions of reference-part. Starting with an initial guess y 0 (and hence c 0 ,c 0 andȳ 0 ), a correction ∆y is obtained by solving the linear system [16]:…”

“…Derivations of these expressions are given in detail in the recent formulation of CPE mentioned earlier [16]. Concise algorithms for implementing the complete CPE method are also discussed there.…”

“…The first step in introducing the general CPE [16] is to divide the inter-particle potential U(r) into a reference (purely repulsive) and perturbation (purely attractive) components employing the the WCA prescription [15]. These components are given by:…”

“…One of the most appropriate divisions of molecular potentials to reference and perturbing parts is based on the Weeks-Chandler-Anderson (WCA) prescription [15]. Recently, the CPE employing this division, and also incorporating density-dependent bridge functions, is developed as a general method, making use of efficient Newton-Armijo and Krylov space-based solvers [16]. It has been also applied to compute phase diagrams of metallic fluids using effective pair-potentials derived from cohesive energy curves.…”

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

“…One of the most appropriate divisions of molecular potentials to reference and perturbing parts is based on the Weeks-Chandler-Andersen (WCA) prescription [17]. Recently, the CPE that employs this division and also incorporating density-dependent bridge functions is developed as a general method, making use of efficient Newton-Armijo and Krylov space-based solvers [18]. It has also been applied to compute phase diagrams of metallic fluids using effective pair-potentials derived from cohesive energy curves.…”