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Embedded-atom method (EAM) has been widely used for the calculation of physical properties of materials from its mathematical simplicity and relative correctness. In EAM, without a direct quantum-mechanical calculation, the energy of an atomic system is treated as the energy to embed an atom into the local electron density distributed from all other atoms of the system, plus a sum of energies of pair interaction between the atoms.
Analytic expressions for the embedding energy and the pair potential energy have been suggested to raise the accuracy of the simulation and the convenience of the application.
The research works for considering the asymmetry of electron density distribution have also been conducted. However, the functions employed in analytic EAM (AEAM) show some serious shortcomings. The electron density function never considers the change of the atomic electron density distribution with respect to the distance between the neighboring atoms in the crystal or the volume occupied by an atom in the crystal. Also, the first order derivative of the embedding energy function diverges when the electron density converges to zero, and an inflection point is appeared in the high electron density domain in the profile of the embedding energy function. These are contradictory to the results from the experimental observation and the quantum-mechanical calculation, and become the principal cause for lowering the correctness of AEAM.
Recently, we have modified the formats of the electron density function and embedding energy function of the previous AEAM in which the nonphysical trends are appeared, and have evaluated many physical properties of widely used body-centered cubic (bcc) Ta by using an extended analytic embedded-atom model (EAEAM) which enables to simulate the materials properties in the extended domain of volume.
Using the model parameters determined, we draw the profiles of the pair potential function, the electron density function, the embedding energy function, and the energy correction function. The results are shown in Fig. The functions vary continuously and smoothly in the whole domain and agree well with the experimental or reliable theoretical results. This means that the model parameters determined here are valid physically and suitable for the simulation of the physical behaviors.
The results of this study were published in Springer's Journal of Thermal Physics (2022) under the title of "Extended Analytic Embedded Atom Model for BCC Tantalum and Its Application to Determination of Gibbs Free Energy and Thermal Equation of State"(https://doi.org/0.1007/s10765-022-03107-9).