Modeling grain growth kinetics of binary substitutional alloys by the thermodynamic extremal principle

The thermodynamics and kinetics fundaments of grain growth in binary substitutional alloys were analyzed using the thermodynamic extremal principle. Applying the regular solution approximation, a new equation for solute segregation at steady-state diffusion is proposed, which suggests reduced solute segregation as the grain boundary (GB) solute concentration increases, differently from previous models [Acta Mater 2009;57(5):1466, Acta Mater 2012;60:4833, Scripta Mater 2010;63:989] that adopt constant segregation enthalpy. Furthermore, a self-consistent consideration has been carried out to account for the coupled changes in GB energy and GB mobility as a result of solute segregation. On this basis, the quantitative relation is evaluated between the thermodynamic and kinetic effects of solute segregation to determine the dominant role in retarding and even suppressing grain growth, by comparison of the dimensionless GB energy (i.e., the GB energy of alloy over that of pure solvent) and the dimensionless effective GB mobility (i.e., the effective GB mobility over that of pure solvent): the kinetic effect prevails if the dimensionless effective GB mobility is smaller than the dimensionless GB energy, and vice versa. The present model is adopted to describe well the experimental results for Fe–P alloys, and nanocrystalline Ni–P and Pd–Zr alloys.