Equilibrium shape of isolated precipitates in the α-Mg phase

• The habit plane of a plate-shaped precipitate in the α-Mg phase was calculated.
• The habit-plane orientation depends on the stress-free transformation strain (SFTS).
• We revealed SFTS conditions for prismatic plate precipitation.
• Formation mechanism of plate- and rod-shaped precipitates was explored.

The habit plane of an isolated plate-shaped precipitate in an α-Mg matrix was calculated as a function of the stress-free transformation strain (i.e., the lattice mismatch between the precipitate and α  -Mg matrix) using micromechanics. The results were categorized into 10 cases according to the habit-plane orientation, and the conditions for prismatic plate precipitation (i.e., {011¯0}α or {21¯1¯0}α plates), which is assumed to be the most effective type of precipitation for dispersion strengthening for a given volume fraction and number density of a precipitate, were revealed. Furthermore, it was demonstrated that the equilibrium shape of precipitates (the plate- and rod-shaped precipitates often observed in Mg-based alloys) can be explained in terms of minimization of the strain energy associated with precipitation. The obtained results are believed to be essential for attempting precipitate shape control through the optimization of the lattice parameters of the precipitates and matrix phase.