Calculation of the critical nucleus size and minimum energy path of T3 phase in Fe-Mn-Ni-Si alloys: An integrated phase-field and constrained string method

Abstract

Manganese-Nickel-Silicon Precipitate (MNSP) phase (T3) significantly influences the properties of Fe-Mn-Ni-Si quaternary alloys, particularly for potential applications in irradiation environments. Understanding the nucleation thermodynamics and kinetics of this specific phase is therefore crucial for predicting microstructure evolution. In this work, a phase-field model coupled with constrained string method was employed to investigate the minimum energy path (MEP) for T3 phase and to characterize the energy barrier, size, and elemental composition of the T3 critical nucleus under the consideration of an irradiation-enhanced diffusion mechanism, as affected by temperature, initial silicon concentration effects. The chemical free energies used in the model were derived from the thermodynamic database of Fe-Mn-Ni-Si system. Simulations reveal that the formation of the T3 phase requires overcoming a distinct nucleation energy barrier, which varies strongly with both temperature and initial alloy composition. Specifically, the nucleation energy barrier increases significantly with increasing temperature but decreases with increasing initial silicon concentration in the alloy. Analysis of the critical nucleus reveals that its size generally expands with rising temperature. Separately, the average concentrations of Mn and Ni within the nucleus also increase with temperature, while showing a complex dependence on the initial alloy composition. The findings highlight the complex interplay of thermodynamic driving forces and kinetic factors governing T3 nucleation in this multi-component system and provide quantitative insights valuable for guiding alloy design and predicting microstructural evolution, especially under irradiation conditions.