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A Predictive Model for Thermodynamic Stability of Grain size in Nanocrystalline Ternary Alloys
Journal of Applied Physics (2013)
  • Mostafa Saber, Portland State University
  • Hasan Kotan, North Carolina State University
  • Carl C. Koch, North Carolina State University
  • Ronald O. Scattergood, North Carolina State University at Raleigh
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 significantenthalpy 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 ΔHmix , and the mixing entropy ΔSmix is obtained using the ideal solution approximation. The Gibbs mixing free energy ΔGmix 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 ΔGmix 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 ofthermodynamic 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 thermodynamicstabilization might be effective.
  • Nanocrystals -- Research
Publication Date
Publisher Statement
Copyright (2013) AIP Publishing

Citation Information
Saber, M., Kotan, H., Koch, C. C., & Scattergood, R. O. (2013). A predictive model for thermodynamic stability of grain size in nanocrystalline ternary alloys. Journal of Applied Physics, 114(10), 103510.