On the structure and role of β F ′ in β1 precipitation in Mg–Nd alloys

The crystal structure and atomic coordinates of β F ′ in aged samples of a Mg–3wt.%Nd alloy are examined using high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and the first-principles density functional theory (DFT). It is found that the lattice parameters and the atomic positions in the orthorhombic β F ′ unit cell deviate from the atomic model that has been generally accepted. The newly proposed β F ′ structure is similar to that of β ₁ which also forms in the alloy, and a simple atomic replacement and structural relaxation can transform the structure of β F ′ to that of β ₁. A specific variant of the β F ′ phase is often observed to be attached to the end of a β ₁ precipitate after ageing for longer time. The stress field analysis and interaction energy calculations indicate that this attachment can reduce the stress field around the end facet of the β ₁ precipitate and may influence β ₁ lengthening. DFT computation results suggest that the β F ′ phase is more stable than β′, but less stable than β ₁, in the Mg–Nd system, and this finding is extendable to other Mg–RE (where RE represents rare earth elements) systems such as Mg–La, Mg–Ce, Mg–Pr, Mg–Pm, Mg–Sm and Mg–Eu alloys.