First-Principles and Experimental Insights into the Phase Stability and Invar Effect of a Co–Fe–Cr–Ni Stainless Invar Alloy

The Co–Fe–Cr–Ni stainless invar alloy exhibits face-centered cubic (fcc) phase stability and low thermal expansion characteristics at cryogenic temperatures. However, this fcc phase stability has proven difficult to explain using existing CALPHAD approaches. Experimentally, increasing Cr content enhances hexagonal close-packed (hcp) phase stability while increasing Fe content favors body-centered cubic (bcc) phase, and the base fcc phase is itself metastable, readily transforming into strain-induced bcc martensite under plastic deformation that subsequently precipitates hcp upon annealing, revealing an intricate thermodynamic competition among the three phases. In this study, we systematically evaluated the free energies of the bcc, fcc, and hcp phases in the metastable 51Co–38Fe–9Cr–2Ni (mass%) stainless invar alloy at 0 K and finite temperatures, integrating density functional theory (DFT) with three magnetic thermodynamic models, the Bragg–Williams (BW) approximation, the Inden–Hillert–Jarl (IHJ) model, and the optimized Inden–Hillert–Xiong (IHX) model, to quantitatively resolve the origin of this competition. The DFT + IHX framework achieves the best agreement with experiment, correctly accounting for the transformation-induced plasticity (TRIP) effect near room temperature and the hcp stability window near 773 K. Extending the 0 K free energy analysis to nearby compositions and incorporating a modified Masumoto empirical rule, we further demonstrate that the stainless invar composition offers a particularly favorable balance of fcc metastability and low thermal expansion.