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.