Phase stability in irradiated alloys by constrained equilibrium thermodynamics

A set of equilibrium thermodynamics relationships are developed to account for the effects of fixed levels of interstitials and vacancies on phase free energy in binary alloys. Such defects would typically be found in alloys under irradiation, and could account for shifts in phase solubility limits and stable temperature ranges. While the total defect concentrations are fixed, no external constraints are placed on the distribution in types of interstitials. These distributions and the alloy phase compositions are allowed to adjust to minimize the system free energy and predict the constrained thermodynamic equilibrium phase structures. Calculational results are presented for three binary alloy systems, iron-chromium, titanium-zirconium, and manganese-silicon, where substantial shifts particularly in stable phase temperature range, and also in the phase solubility limits, are found when large defect concentrations (one defect per one thousand lattice sites) are present in one phase or the other. This imbalance in defect concentrations between coexisting phases is necessary; similar defect concentrations in each phase shift both phase free energies and result in only small changes in phase equilibria. The required imbalance of defect concentrations is thought to be significant during irradiation of single-phase systems with normal subsaturation levels of solute. Large defect concentrations in this phase would provide the driving energy, or shift in solubility limit, to form small precipitates of the second phase. Due to their small size, these precipitates would maintain a relatively low defect concentration, and thus remain stable