First-principles modeling and machine learning of the Gibbs free energy of the Fe-C system in a magnetic field

Modeling the thermodynamics and kinetics of steels for designing processes in high magnetic fields requires knowledge of the magnetic Gibbs free energy. Monte Carlo and thermodynamic perturbation or integration methods require integrals over configuration space involving millions of accurate potential energy evaluations. Density-functional theory (DFT) calculations provide sufficient accuracy to describe the Fe-C phases. However, the high computational cost of DFT hinders the direct application to thermodynamic and kinetic modeling.

To address this challenge, the ultra-fast force field (UF³) model [1], an ultra-fast machine-learning potential that combines effective two- and three-body potentials in a cubic B-spline basis with regularized linear regression, can be used to approximate the potential energy landscape. In this work, we use the Vienna Ab initio Simulation Package (VASP) to assemble a DFT database of structural configurations of Fe-C systems with various magnetic states. These configurations focus on BCC and FCC phases, and C concentrations up to 20 at. %. We train and validate a UF³ model for the Fe-C energy landscape on the energies and forces. We will discuss the machine learning approach and the resulting accuracy of the UF³ model for predicting thermodynamic properties.

[1] S. R. Xie, M. Rupp, R. G. Hennig, arXiv:2110.00624 (2021).