Misfit-driven β′′′ precipitate composition and morphology in Mg-Nd alloys

Abstract We report on a combined computational and experimental examination of coherent precipitation in a Mg-Nd alloy, a prototypical Mg-rare earth alloy. Three-dimensional phase field simulations are conducted to predict the composition and morphology of β ′ ′ ′ precipitates, a unique family of hierarchically ordered phases that are metastable in a wide Nd concentration range. Predictions are compared to experimental high-angle annular dark-field scanning transmission electron microscopy observations. The phase field model thermodynamic description is parameterized entirely from first-principles calculations. The simulations predict an elevated Nd composition in β ′ ′ ′ that is above the stress-free equilibrium value. The elevated Nd concentration in β ′ ′ ′ is in very good agreement with experimental observations and arises from a large misfit strain energy penalty and the low curvature of the β ′ ′ ′ free energy well. The phase field simulations predict that isolated precipitates are lenticular with a (100) habit plane, and are approximately equiaxial when viewed along the [100] direction. The predicted habit plane and precipitate dimensions are shown to be generally consistent with experimental observations, within the uncertainty introduced by density functional theory calculations of the stress-free transformation (misfit) strain and by precipitate interactions not accounted for in the simulations. Contrary to the predictions for isolated precipitates, some experimentally observed precipitates are elongated along the [001] direction relative to the [010] direction. This elongation is frequently correlated with a particular arrangement of two orientation variants of β ′ ′ ′ . A phase field simulation of two precipitates in this arrangement is shown to exhibit similar [001] elongation.