Estimation of Component Activities and Molar Excess Gibbs Energy of 19 Binary Liquid Alloys from Partial Pair Distribution Functions in Literature

Abstract

This work proposes a new method for estimating the molar excess Gibbs energy and activity of liquid alloy based on recent research. The local composition theory provides a connection between the structures of liquid alloys and the thermodynamic models. The partial pair distribution function (PPDF) was utilized to calculate the parameters of the MIVM, RSM, Wilson, and NRTL. The statistics of the number of molecular pairs of MIVM and RSM were rewritten, which resulted in new forms of the two models. To enhance the NRTL’s estimation performance, the coordination number was incorporated into it (M-NRTL). The aforementioned model and Quasi-chemical model (QCM) were utilized to estimate the excess Gibbs energy and activity of 19 alloys. The alloys contained multiple sets of PPDFs, which enabled the calculation of multiple sets of model parameters. The work examined the impact of expressing the model parameters as first-order linear functions of the components or as constants on the accuracy of the estimation. The parameters were treated as constants. MIVM, RSM, and M-NRTL provided an average relative deviation (ARD) of activity of less than ±20% for 15, 10, and 9 alloys by estimation. When model parameters were expressed as a function of components, QCM showed the best estimation performance, having nine alloys with an ARD of less than ±20%. The number of alloys with an ARD of less than ±20% corresponding to MIVM, RSM, Wilson, NRTL, and M-NRTL was six, five, three, five, and two, respectively. This new method offers simplicity, numerical calculation stability, and excellent reproducibility.

Estimation of Activity and Molar Excess Gibbs Energy of Binary Liquid Alloys Al-Cu, Al-Ni, and Al-Fe from the Partial Radial Distribution Function Simulated by Ab Initio Molecular Dynamics

“…Then, the values of the model parameters were calculated by using the graphical integration method. Obviously, this method is different from the L-PPDF mathematical of Gaussian function fitting adopted by Wang et al [25], which depends on the fitting parameters u and v. Therefore, no fitting parameter was introduced in the calculation process of model parameters in this study.…”

“…εii, εjj, and εij are the molecular mean pair potentials of the molecule for i-i, j-j, and i-j, respectively. Wang et al [25] hypothesized that the equation…”

“…Wang et al [25] hypothesized that the equation ε ii (r) = −kT ln g ii (r) [26], which relates the molecular pair potential of very dilute gases to the radial distribution function, can be approximately applied to binary liquid alloys. Thus, according to the probability density distribution function and the expectation principle, the expressions for the molecular mean pair potentials, ε ii , ε jj , and ε ij of the binary liquid alloy can be obtained as:…”

“…Comparing with similar studies on estimating the activity and molar excess Gibbs energy of binary liquid alloys, Wang et al [25] utilized PRDF obtained from the literature and combined it with thermodynamic models to estimate the activity and molar excess Gibbs energy of 19 binary liquid alloys. The MIVM model achieved an ARD of less than 20% for the activity estimation of 15 alloys, while the RSM model achieved an ARD of less than 20% for 10 alloys.…”

Estimation of Two Component Activities of Binary Liquid Alloys by the Pair Potential Energy Containing a Polynomial of the Partial Radial Distribution Function

“…It is seen formula Equation (17), that there is connection between the RDF and pair potential energy. In the case of ρ 0 = 0, 3 atoms in the pure gas system, labeled 1, 2 and 3, are shown in Figure 3a.…”