Multi-scale modeling of solidification phenomena using the phase-field crystal methodology:

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The proposed research will explore and develop a new class of continuum models --coined "phase-field-crystal models"-- for quantitative modeling of solidification phenomena in multi-component alloys. The unique advantage of these models is that they are atomically resolved in space but operate on time scales many orders of magnitudes longer than current molecular dynamics. They contain, on the one hand, an intimate connection to atomic-scale properties of matter, through their connection with classical density functional theory. On the other hand, their dynamics is course-grained in time, which makes it possible to simulate many aspects of elasto-plasticity, grain boundary interactions and topological defects on the same [diffusive] time scales that govern phase transformation kinetics. This work will begin by deriving a suite of phase-field-crystal models for multi-component alloys that are linked to direct correlations functions computed from molecular dynamics and analytical methods. These models will be used, in their own right to study the interplay of thermodynamics, crystal defects and elasticity on several important applications involving nano-microstructure evolution in materials science, which have been typically inaccessible to traditional phase field theory and molecular dynamics. In addition, the proposed research will extend and further develop mathematical and numerical methods to course-grain the new alloy phase-field-crystal models to higher length scales. This will have the advantage of guiding the formation of improved (i.e. quantitative) traditional phase field models for use on higher scales. The research will provide a high level of scientific and applied training in materials science and engineering for two graduate students.