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 ΔH_mix using an appropriately scaled linear superposition. The total Gibbs mixing free energy ΔG_mix 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.

This work presents a model for evaluating thermodynamic stabilization of ternary nanocrystalline alloys. It is applicable to alloy systems containing strongly segregating size-misfit solutes with a significant enthalpy of elastic strain and/or immiscible solutes with a positive mixing enthalpy. On the basis of a regular solution model, the chemical and elastic strain energy contributions are incorporated into the mixing enthalpy ΔH_mix, and the mixing entropy ΔS_mix is obtained using the ideal solution approximation. The Gibbs mixing free energy ΔG_mix is minimized with respect to simultaneous variations in grain size and solute segregation parameters. The Lagrange multiplier method is used to obtain numerical solutions for the minimum ΔG_mix corresponding to an equilibrium grain size for given alloy compositions. The numerical solutions will serve as a guideline for choosing solutes and assessing the possibility of thermodynamic stabilization. The temperature dependence of the nanocrystalline grain size and interfacial solute excess can be evaluated for selected ternary systems. Model predictions are presented using available input data for a wide range of solvent-solute combinations. The model predictions are compared to experimental results for Cu-Zn-Zr, Fe-Cr-Zr, and Fe-Ni-Zr alloys where thermodynamic stabilization might be effective.