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

2021 ◽  
Vol 6 (1) ◽  
pp. 6
Author(s):  
S.V.G. Menon

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.

Author(s):  
S.V.G. Menon

The first objective of this paper is to investigate the scaling behavior of liquid-vapor phase transition in FCC and BCC metals starting from the zero-temperature four-parameter formula for cohesive energy. The effective potentials between the atoms in the solid are determined using lattice inversion techniques as a function of scaling variables in the above 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 supplemented with an accurate closure. Thermodynamic quantities obtained via the correlation functions are used to obtain critical point parameters and liquid-vapor phase diagrams. Their dependence on the scaling variables in the cohesive energy formula are also determined. 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. Accuracy of the method is established by comparing the phase diagrams with those obtained via computer simulation. Avoidance of the 'no-solution-region' of Ornstein-Zernike equation in coupling-parameter expansion is also discussed. Details of the method and the complete algorithm provided here would make this technique more accessible to researchers investigating thermodynamic properties of one component fluids.


Author(s):  
S. V. G. MENON

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.


2021 ◽  
Vol 3 (1) ◽  
pp. 2170013
Author(s):  
Jie Han ◽  
Weitao Jiang ◽  
Hongjian Zhang ◽  
Biao Lei ◽  
Lanlan Wang ◽  
...  

2011 ◽  
Vol 85 (7) ◽  
pp. 1285-1287
Author(s):  
V. N. Volodin ◽  
V. E. Khrapunov ◽  
I. A. Marki

2008 ◽  
Vol 403 (2-3) ◽  
pp. 505-508 ◽  
Author(s):  
I. Jancskar ◽  
Z. Sari ◽  
L. Szakonyi ◽  
A. Ivanyi

2021 ◽  
Vol 29 (1) ◽  
pp. 5-14
Author(s):  
D. Anchishkin ◽  
V. Gnatovskyy ◽  
D. Zhuravel ◽  
V. Karpenko

A system of interacting relativistic bosons at finite temperatures and isospin densities is studied within the framework of the Skyrme­like mean­field model. The mean field contains both attractive and repulsive terms. The consideration is taken within the framework of the Canonical Ensemble and the isospin­density dependencies of thermodynamic quantities is obtained, in particular as the phase diagrams. It is shown that in such a system, in addition to the formation of a Bose­Einstein condensate, a liquid­gas phase transition is possible. We prove that the multi­boson system develops the Bose condensate for particles of high­density component only.


2000 ◽  
Vol 39 (4) ◽  
pp. 481-489 ◽  
Author(s):  
Zeng-Yuan Guo ◽  
Da-Xi Xiong ◽  
Chun Yang ◽  
Min Chen ◽  
Zhi-Xin Li

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