Mean field theory of ionic free energy using scaled binding energies

Abstract

A mean field model for ionic free energy is developed using the scaled binding energy formula. The model is evaluated using experimental data on Hugoniot, phase diagrams, melting curves, and other thermodynamic parameters of several solids. Predictions of the model are also compared with the Debye–Gruneisen theory, which is also based on the same binding energy formula. The binding energy formulation employs just four parameters, all corresponding to ambient condition—density, bulk modulus, its pressure derivative, and cohesive energy. These are obtained either from experiments or electronic structure theory. The Debye–Gruneisen theory compares better with available data for the phase diagrams of iron, zirconium, and titanium. However, the Hugoniot and melting curves obtained using both models yield similar results.

High-Temperature Vibrational Properties and Melting Curve of Aluminum

“…Recently, Bhattacharya and Menon [14] have demonstrated that λ in Eq. 1 may be treated as an adjustable parameter, and for the case of aluminum, its value is −2.…”

“…These studies clearly reveal that the parameter t or λ, which in turn determines the Grüneisen parameter, should be treated as a free parameter as long as its choice gives a better thermal description for a given material. Illustrating this fact, Bhattacharya and Menon [14] have examined this point within the MFP formalism, and have proposed that for the case of fcc-Al, either λ = −2 or t = −1 value gives correct thermophysical properties at high temperatures. While for other metals, they retain the value of λ as either −1 or +1.…”

“…As noted earlier, different authors have used different means to construct the MFP [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], but we follow the one due to Wang and co-workers in conjunction with the local pseudopotential due to Fiolhais et al [22,23]. Assuming the vibration of the lattice ion is symmetrical with respect to its equilibrium position, Wang and Li [9] have proposed an analytical form for the MFP, as given by…”

“…This was applied to obtain the thermodynamics of low symmetry or complex structure crystals, taking beryllium as a prototype. Bhattacharya and Menon [14] have calculated the ionic free energy using the scaled binding energy. They suggested an improvement over the MFP calculated by Wang and Li [9] and Bhatt et al [21], if the parameter λ is treated as a free parameter.…”

“…In the past, different philosophies were used to compute the mean-field potential (MFP): free volume theory [2][3][4][5][6], Debye-Grüneisen theory [7], classical cell-model [8], and 0 K isotherm-based MFP [9,[11][12][13][14][15][16][17][18][19][20][21]. Wang and his coworkers [9,10,[18][19][20], and others [11][12][13][14][15][16][17]21] have proposed a method of modeling the vibrational free energy in terms of the 0 K total energy from the concept of the MFP approach. The concept of the MFP due to Wang and co-workers does not require detailed electronic band structure calculations over the complete density range of interest.…”