A novel computational framework to calculate Gibbs energy and phase transitions under external magnetic fields applied to the Bi–Mn system

Applying an external magnetic field can obtain unique microstructure and thus enhanced properties, which are unattainable without such a field. The thermodynamic description is essential for focused development of such materials under magnetic field. Based on the molecular field theory of Weiss in the mean field approximation using the Heisenberg model, a predictive computational framework for materials under external magnetic field is developed for the first time. Only three magnetic material parameters, atomic magnetic moment ( gJµ _B ), total angular momentum ( J ), and Curie temperature ( T _C ) are used to generate explicit functions of normalized dimensionless quantities, establishing basic equations for quantitative thermodynamic calculations of the Gibbs energy, phase transitions and phase diagrams in multicomponent and multiphase systems under external magnetic field with established and potent software packages. The approach is demonstrated for the Bi–Mn system, where strong interactions of the compounds with magnetic field are known. The four-phase equilibrium existing in this system is proven to be a true peritectic-type formation reaction, Liquid + Mn + BiMn = BiMn _1.08, at the predicted state point T ₄ = 719.6 K, B ₄ = 48.56 T, and µ _{Mn, 4} = -29.288 kJ/mol. Manipulation of phase transition and microstructure under external magnetic field guided by thermodynamic considerations is also discussed. The present work provides a fundament for quantitative calculations of phase equilibria and thermodynamics in multicomponent and multiphase systems under external magnetic field.