DOE OSTI2020
Mg(Hf) is Copper-derived structured and crystallizes in the trigonal R-3m space group. The structure is three-dimensional. there are two inequivalent Mg sites. In the first Mg site, Mg is bonded to six equivalent Mg and six Hf atoms to form MgHf6Mg6 cuboctahedra that share corners with twelve MgHf6Mg6 cuboctahedra, edges with twelve MgHf6Mg6 cuboctahedra, edges with twelve HfHf6Mg6 cuboctahedra, faces with six equivalent MgHf6Mg6 cuboctahedra, and faces with twelve HfHf6Mg6 cuboctahedra. All Mg–Mg bond lengths are 3.05 Å. All Mg–Hf bond lengths are 3.26 Å. In the second Mg site, Mg is bonded to ten equivalent Mg and six Hf atoms to form MgHf6Mg10 cuboctahedra that share corners with ten HfHf6Mg6 cuboctahedra, corners with twelve MgHf6Mg6 cuboctahedra, edges with eight HfHf6Mg6 cuboctahedra, edges with sixteen MgHf6Mg6 cuboctahedra, faces with sixteen equivalent MgHf6Mg10 cuboctahedra, and faces with eighteen HfHf6Mg6 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.05–6.09 Å. All Mg–Hf bond lengths are 3.26 Å. There are three inequivalent Hf sites. In the first Hf site, Hf is bonded to six equivalent Mg and six equivalent Hf atoms to form HfHf6Mg6 cuboctahedra that share corners with twelve HfHf6Mg6 cuboctahedra, edges with twelve equivalent MgHf6Mg6 cuboctahedra, edges with twelve HfHf6Mg6 cuboctahedra, faces with six equivalent HfHf6Mg6 cuboctahedra, and faces with twelve equivalent MgHf6Mg6 cuboctahedra. All Hf–Hf bond lengths are 3.05 Å. In the second Hf site, Hf is bonded to six Mg and six equivalent Hf atoms to form HfHf6Mg6 cuboctahedra that share corners with five equivalent MgHf6Mg10 cuboctahedra, corners with twelve HfHf6Mg6 cuboctahedra, edges with ten MgHf6Mg6 cuboctahedra, edges with twelve HfHf6Mg6 cuboctahedra, faces with six equivalent HfHf6Mg6 cuboctahedra, and faces with fifteen MgHf6Mg6 cuboctahedra. All Hf–Hf bond lengths are 3.05 Å. In the third Hf site, Hf is bonded to six Mg and six equivalent Hf atoms to form HfHf6Mg6 cuboctahedra that share corners with five equivalent MgHf6Mg10 cuboctahedra, corners with twelve HfHf6Mg6 cuboctahedra, edges with ten MgHf6Mg6 cuboctahedra, edges with twelve HfHf6Mg6 cuboctahedra, faces with six equivalent HfHf6Mg6 cuboctahedra, and faces with fifteen MgHf6Mg6 cuboctahedra. All Hf–Mg bond lengths are 3.26 Å. All Hf–Hf bond lengths are 3.05 Å.