Unveiling Cr segregation against precipitation at grain boundaries in Fe-Cr alloys by Ising-machine accelerated Monte Carlo optimization

The segregation of Cr at grain boundaries (GBs) critically influences the mechanical properties of high-strength steels, but it challenges the Monte Carlo (MC) optimization based on density-functional theory calculations due to high computational costs. For the Σ5(310) GB, we have compared the efficiency of MC with the emerging factorization-machine quantum-annealing (FMQA) algorithm using Ising-machines. We find FMQA is more effective in low-concentration scenarios, while MC retains advantages at higher Cr concentrations. By integrating FMQA steps into the MC process, we introduce an FMQA-accelerated MC (FMMC) method, which demonstrates a threefold improvement in predicting low-energy atomic configurations. Utilizing FMMC, we have investigated Σ3(111) and Σ21(541), and find Cr segregates at all GBs, but does not precipitate across them. Analyses suggest that spin polarization acts as a driving force for Cr segregation, while the high GB formation energy of pure Cr inhibits Cr atom precipitation at the GBs within Fe-Cr alloys.