A validated phase-field model for spinodal decomposition in the ternary Fe–Cr–Co system under an external magnetic field

Abstract

Magnetic-assisted manufacturing is a processing technique that enables controlled microstructure evolution through the application of external magnetic fields. This approach holds promise for producing rare-earth-free permanent magnets with tailored properties from common alloy systems such as Fe-Cr-Co. In this work, we develop and validate a thermodynamically consistent phase-field model to simulate spinodal decomposition in the Fe-Cr-Co system under combined thermal and magnetic driving forces. The model incorporates CALPHAD-based Gibbs energy functions and magnetic contributions including Zeeman and demagnetization energies. The governing Cahn–Hilliard equations are solved using a finite-element framework, enabling simulation of microstructure evolution in both two and three dimensions. Model predictions are validated against experimental transmission electron microscopy (TEM) data, demonstrating good agreement in phase morphology, feature size, and compositional distribution. The simulations capture key features of field-assisted processing, including anisotropic domain growth and magnetic biasing effects. Three-dimensional simulations further illustrate the elongation and alignment of magnetic phases along the field direction, providing mechanistic insight into morphology control during thermomagnetic treatment. This validated modeling framework offers a predictive tool for designing magnetically processed alloys and optimizing the microstructural basis of their functional properties.