First-principles modeling of ordering in Fe-rich Fe-Si alloys
The atomic ordering in Fe-rich Fe-Si alloys strongly influences their magnetic properties and mechanical behavior. While general features of long-range atomic ordering are known from the experimentally established phase diagram in this composition range, detailed atomic configurations and driving forces behind them remain speculative. Here, we address this gap by using effective cluster interactions (ECI) obtained from density functional theory (DFT) calculations and subsequent statistical thermodynamics modeling to unravel the interplay between magnetism, composition, and temperature in body-centered cubic (bcc) Fe-Si alloys up to 20 at% Si. Our analysis reveals that the ordering behavior is governed by a strong coupling between magnetic order, lattice expansion, and Si concentration, with specific ECI shells switching sign or magnitude as the magnetic state changes, which is reflected in the phase equilibria and ordering behavior of Fe-Si alloys. In particular, we demonstrate that D0$_3$ ordering is, in fact, primary in the totally ordered ferromagnetic state, while the B2 type of ordering is promoted in the paramagnetic state at elevated temperatures. The temperature-dependent evolution of these ordering patterns, obtained from Monte Carlo simulations based on the magnetically resolved ECIs, reproduces the experimentally observed phase equilibria and short-range order characteristics. By explicitly linking the magnetic state with the effective interactions and macroscopic phase behavior, this work establishes a predictive framework for an ab initio-based description of ordering in Fe-rich Fe-Si alloys and highlights the decisive role of magnetism in ordering phenomena in this system.