Multiscale thermo-kinetic characterization for β′ and β1 precipitation in Mg-Sm alloys

Two types of metastable β-series phases have been reported to exist in aged Mg-Sm alloys. The first type refers to preferentially precipitated β′-series phases (including β′s, β′l and β′h), which are intrinsically different Sm orderings on the hexagonal close-packed (HCP) lattice of α-Mg, while the second type refers to subsequently precipitated β1 phase having a face-centered cubic (FCC) lattice. Up to now, whether β1 forms from the α-Mg matrix or the pre-existing βʹ is still on debate, due to unavailable convincing experimental evidence. Employing the first-principles calculations and a statistical mechanics approach consisting of the cluster expansion (CLEX) model and the Monte Carlo simulation, a multiscale phase-field model is herein constructed to thermo-kinetically characterize the precipitations of β′s, β′l, β′h and β1 in Mg-Sm alloys. Equipped with a newly revised explicit nucleation algorithm developed from so-called thermo-kinetic correlation, the present phase-field model can reproduce multi-particle morphologies upon independent precipitations of β′s, β′l, β′h and β1. And then, correlative precipitations of β′ (referring to β′s, β′l or β′h) and β1 are focused on, where, it has been proved that, any pre-existing βʹ variant can transform to a specific single variant or multi-variant configurations of β1. Notably, the precipitations above should follow a rule determined by so-called strain energy dominated thermo-kinetic connectivity. The newly proposed nucleation algorithm is widely applicable for precipitation modeling, and the revealed thermo-kinetic mechanism for precipitations of β-series phases should be enlightening for the rational design of Mg-rare earth (RE) alloys.