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 DH mix , and the mixing entropy DS mix is obtained using the ideal solution approximation. The Gibbs mixing free energy DG 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 DG 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. V C 2013 AIP Publishing LLC. [http://dx.
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