Physical factors controlling the observed high-strength precipitate morphology in Mg–rare earth alloys

In an effort to understand the exceptional precipitation strength in Mg–RE (RE = rare earth) alloys, we use first-principles density functional theory calculations to study the energetic stability, elastic constants and coherency strain energy of Mg3RE-D019Mg3RE-D019 precipitate phases in a Mg matrix and make extensive comparisons with experimental and theoretical work, where available. We find the metastable β′′-D019β′′-D019 phases are energetically competitive with the stable Mg-rich phases for all RE elements. We also investigate the coherency strain energy of Mg–Mg3REMg–Mg3RE binary systems using first-principles methods and harmonic elasticity theory. We find the two approaches to computing coherency strain energy in good agreement, indicating the validity of using harmonic elasticity equations, which we extend to hexagonal systems, to study the direction-dependent coherency strain energy of D019D019 precipitates in Mg–RE binary systems. From our coherency strain calculations, we find the D019D019 precipitates to strongly prefer prismatic, as opposed to basal, habit planes for all Mg–RE systems. This work thus provides an explanation for the observed prismatic plate-shaped morphology of many Mg–RE precipitates, which is ultimately responsible for their strengthening response.