Effects of Alloying on Nanoscale Grain Growth in Substitutional Binary Alloy System: Thermodynamics and Kinetics

Applying the regular solution model, the Gibbs free energy of mixing for substitutional binary alloy system was constructed. Then, thermodynamic and kinetic parameters, e.g., driving force and solute drag force, controlling nanoscale grain growth of substitutional binary alloy systems were derived and compared to their generally accepted definitions and interpretations. It is suggested that for an actual grain growth process, the classical driving force P = γ/D (γ the grain boundary (GB) energy, D the grain size) should be replaced by a new expression, i.e.,$$ P^{\prime} = \gamma /D - \Delta P $$^P′=γ/D-ΔP. ΔP represents the energy required to adjust nonequilibrium solute distribution to equilibrium solute distribution, which is equivalent to the generally accepted solute drag force impeding GB migration. By incorporating the derived new driving force for grain growth into the classical grain growth model, the reported grain growth behaviors of nanocrystalline Fe-4at. pct Zr and Pd-19at. pct Zr alloys were analyzed. On this basis, the effect of thermodynamic and kinetic parameters (i.e.,P, ΔP and the GB mobility (M^GB)) on nanoscale grain growth, were investigated. Upon grain growth, the decrease of P is caused by the reduction of γ as a result of solute segregation in GBs; the decrease of ΔP is, however, due to the decrease of grain growth velocity; whereas the decrease of M^GB is attributed to the enhanced difference of solute molar fractions between the bulk and the GBs as well as the increased activation energy for GB diffusion.