Multicomponent phase-field crystal model for structural transformations in metal alloys

We present a phase-field crystal model for structural transformations in multicomponent alloys. The presented formalism builds upon the two-point correlation kernel developed in Greenwood et al. for describing structural transformations in pure materials [Greenwood, Provatas, and Rottler, Phys. Rev. Lett. 105, 045702 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.045702]. We introduce an effective two-point correlation function for multicomponent alloys that uses the local species concentrations to interpolate between different crystal structures. A simplified version of the model is derived for the particular case of three-component (ternary) alloys, and its equilibrium properties are demonstrated. Dynamical equations of motion for the density and multiple species concentration fields are derived, and the robustness of the model is illustrated with examples of complex microstructure evolution in dendritic and eutectic solidification and solid-state precipitation.