Characterizing solute segregation and grain boundary energy in binary alloy phase field crystal models

This paper studies how solute segregation and its relationship to grain boundary energy in binary alloys are captured in the phase field crystal (PFC) formalism, a continuum method that incorporates atomic scale elasto-plastic effects on diffusional time scales. Grain boundaries are simulated using two binary alloy PFC models – the original binary model by Elder et al. [18] and the XPFC model by Greenwood et al. [25]. In both cases, grain boundary energy versus misorientation data is shown to be well described by Read–Shockley theory. The Gibbs adsorption theorem is then used to derive a semi-analytic function describing solute segregation to grain boundaries. This is used to characterize grain boundary energy versus average alloy concentration and undercooling below the solidus. We also investigate how size mismatch between different species and their interaction strength affects segregation to the grain boundary. Finally, we interpret the implications of our simulations on material properties related to interface segregation.