Thermodynamic stabilization of nanocrystalline binary alloys

The work presented here was motivated by the need to develop a predictive model for thermodynamic stabilization of binary alloys that is applicable to strongly segregating size-misfit solutes, and that can use available input data for a wide range of solvent-solute combinations. This will serve as a benchmark for selecting solutes and assessing the possible contribution of thermodynamic stabilization for development of high-temperature nanocrystalline alloys. Following a regular solution model that distinguishes the grain boundary and grain interior volume fractions by a transitional interface in a closed system, we include both the chemical and elastic strain energy contributions to the mixing enthalpy ΔHmix using an appropriately scaled linear superposition. The total Gibbs mixing free energy ΔGmix is minimized with respect to simultaneous variations in the grain-boundary volume fraction and the solute contents in the grain boundary and grain interior. The Lagrange multiplier method was used to obtain numerical solutions with the constraint of fixed total solute content. The model predictions are presented using a parametric variation of the required input parameters. Applications are then given for the dependence of the nanocrystalline grain size on temperature and total solute content for selected binary systems where experimental results suggest that thermodynamic stabilization could be effective.