The departure from the equilibrium solid concentration at the solid-liquid interface was often observed during rapid solidification. The energetic associated non-equilibrium solute partitioning has been treated in detail, providing possible ranges of interface concentrations for a given growth condition. For analytical description of specific single-phase dendritic and cellular operating point selection, analytical models for solute partitioning under a given set of growth conditions have been developed and widely utilized in most of the theoretical investigations of rapid solidification. However, these solute trapping models are not rigorously verified due to the difficulty in experimentally measuring under rapid growth conditions. Moreover, since these solute trapping models include kinetic parameters which are difficult to directly measure from experiments, application of the solute trapping models or the associated analytic rapid solidification model is limited. These theoretical models for steady state rapid solidification which incorporate the solute trapping models do not describe the interdependency of solute diffusion, interface kinetics, and alloy thermodynamics.

This research program is focused on critical issues that represent conspicuous gaps in current understanding of rapid solidification, limiting our ability to predict and control microstructural evolution at high undercooling, where conditions depart significantly from local equilibrium. Through careful application of phase-field modeling, using appropriate thin-interface and anti-trapping corrections and addressing important details such as transient effects and a velocity-dependent numerics, the current analysis provides a reasonable simulation-based picture of non-equilibrium solute partitioning and the corresponding oscillatory dynamics associated with single-phase rapid solidification and show that this method is a suitable means for a self-consistent simulation of transient behavior and operating point selection under rapid growth conditions. Moving beyond the limitations of conventional theoretical/analytical treatments of non-equilibrium solute partitioning, these results serve to substantiate recent experimental findings and analytical treatments for single-phase rapid solidification. In addition, the simulations carried out here predict, for the first time, the full scope of behavior, from the initial transient to the steady-state conditions, where departure from equilibrium partitioning may lead to oscillations in composition, velocity, and interface temperature or may lead to a far-from-equilibrium steady-state. Such predictive capability is a necessary prerequisite to more comprehensive modeling of morphological evolution and, therefore, of significant importance.