Generalized Universal Equation of States for Magnetic Materials. Part II: Interatomic Potential development for Fe, validation and its predictability
The development of quantitative models for understanding physical properties of alloys requires a proper treatment of magnetic interactions, which is of paramount importance for the microstructural stability, especially in steels and high-entropy alloys containing magnetic elements. These magnetic interactions also control the defects behavior which affects the mechanical properties and the response under irradiation. Current interatomic potentials for molecular dynamics (MD) simulations still lack an adequate formulation to include magnetism into the simulations. In this paper, the universal equation of states (UES) is revisited and generalized by including ferromagnetic (FM) and antiferromagnetic (AFM) configurations with the aim of proposing a new formulation to develop interatomic potentials with magnetic contribution. For the case of Fe, given a fixed magnetic configuration and magnitude of the magnetic moment, the energy of the system is calculated by means of three parameters, namely, the energy, volume, and corresponding scaling volume (directly related to the bulk modulus) at the local ground state of the corresponding lattice. These parameters depend on three terms: firstly, a distance-dependent function, which gathers the nonmagnetic influence of the surrounding atoms; secondly, a magnetically dependent function, contributing to the energy by means of the magnetic nature of the atom, irrespective of the magnetic moment magnitudes of its surrounding atoms; and finally, a term which is magnetically and distance dependent simultaneously, which describes the influence of the magnetic state of the surrounding atoms on the energy considering their interatomic distance. This latter term is built via two functions which cannot be disconnected: one dependent on the distance between two atoms (a decreasing function with the distance in absolute value) multiplied by another function which is dependent on the magnetic moment of these two atoms. In this way, the magnetic influence of a distant atom scales with its distance.