Phase-field modeling of precipitate evolution dynamics in elastically inhomogeneous low-symmetry systems: Application to hydride precipitation in Zr

A phase-field model was developed within the framework of heterogeneous elasticity theory to study the precipitation of particles with trigonal symmetry in a hexagonal matrix. The model is first calibrated and successfully compared with previous analytical calculations performed to explain the effect of symmetry-breaking transformations on precipitate morphology. Secondly, the model was adapted to study the precipitation of the coherent ζ hydride phase in zirconium. The results are consistent with the well-established experimental observation of the existence of acicular precipitates aligned along the dense directions in the basal plane. Moreover, original kinetic pathways are implied by the presence of a threefold axis of symmetry, leading to the emergence of original morphological bifurcations not previously reported and probably related to the inconsistency between the threefold symmetry and the inversion properties of the B function introduced by Khachaturyan. In spite of its simplicity (only one order parameter is taken into account), the present phase-field model gives rise to very complex morphological sequences.