A first-principles study of [formula omitted] phase in magnesium-rare earth binary systems

Abstract

The formation energies, elastic constants, moduli and electronic structures of the coherent βF′ phase in eight different binary Mg-RE (RE = La, Ce, Pr, Nd, Pm, Sm, Eu and Gd) systems are calculated systematically by a first-principles method, and the interfacial energies between the βF′ phases and α-Mg matrix are also predicted. The results of these calculations indicate that for the alloys considered the βF′ phase has a higher moduli than the α-Mg phase. In terms of electronic structure, charge density plots show that the electrons concentrate among the RE atoms and their neighboring Mg atoms, and the density of states reveal the overlapping of the p-orbitals of Mg atoms and d-orbitals of RE atoms. These observations suggest that strong intermetallic bonds formed between RE atoms and neighboring Mg atoms inside the βF′ phases, which explains the shrinkage of the βF′ phases in 11¯00α and 〈0001〉α directions and the higher stiffness of the βF′ phases. The results also show that the rare earth systems in which βF′ has been observed (RE = Nd, Sm and Gd) have lower interface formation energies than the other Mg-RE systems. A comparison of the βF′ and β′ phases in the Mg-Gd system is also carried out to interpret experimental observations that, whilst these two phases can form simultaneously, the βF′ phase is less frequently observed.