A Multi-Component Phase Field Crystal Model for Structural   Transformations in Metal Alloys
  We present a new phase field crystal model for structural transformations in multi-component alloys. The formalism builds upon the two-point correlation kernel developed in Greenwood et al. for describing structural transformations in pure materials [Phys. Rev. Lett. 105, 045702 (2010)]. We introduce an effective twopoint correlation function for multi-component 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 threecomponent (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 solidification and solid-state precipitation. 
Nana Ofori-Opoku and Vahid Fallah and Michael Greenwood and Shahrzad   Esmaeili and Nikolas Provatas
cond-mat.mtrl-sci