Nana Ofori-Opoku

Multicomponent 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.

Complex order parameter phase-field models derived from structural phase-field-crystal models

The phase-field-crystal (PFC) modeling paradigm is rapidly emerging as the model of choice when investigating materials phenomena with atomistic scale effects over diffusive time scales. Recent variants of the PFC model, so-called structural PFC (XPFC) models introduced by Greenwood et al., have further increased the capability of the method by allowing for easy access to various structural transformations in pure materials [Phys. Rev. Lett. 105, 045702 (2010)] and binary alloys [Phys. Rev. B. 84, 064104, (2011)]. We present an amplitude expansion of these XPFC models, leading to a mesoscale complex order-parameter (amplitude), i.e., phase-field representation, model for two dimensional square-triangular structures. Amplitude models retain the salient atomic scale features of the underlying PFC models, while resolving microstructures on mesoscales as in traditional phase-field models. The applicability and capability of this complex amplitude model is demonstrated with simulations of peritectic solidification and grain growth exhibiting the emergence of secondary phase structures.

Calculating the role of composition in the anisotropy of solid-liquid interface energy using phase-field-crystal theory.

This work uses Ginzburg-Landau theory derived from a recent structural phase-field-crystal model of binary alloys developed by the authors to study the roles of concentration, temperature, and pressure on the interfacial energy anisotropy of a solid-liquid front. It is found that the main contribution to the change in anisotropy with concentration arises from a change in preferred crystallographic orientation controlled by solute-dependent changes in the two-point density correlation function of a binary alloy, a mechanism that leads to such phenomena as solute-induced elastic strain and dislocation-assisted solute clustering. Our results are consistent with experimental observations in recent studies by Rappaz et al. [J. Fife, P. Di Napoli, and M. Rappaz, Metall. Mater. Trans. A 44, 5522 (2013)]. This is the first PFC work, to our knowledge, to incorporate temperature, pressure, and density into the thermodynamic description of alloys.