DOI: 10.17188/1714968
title: Materials Data on HfMg30TiO32 by Materials Project

description: Mg30HfTiO32 is alpha Po-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are eight inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent TiO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.06 Å) and four longer (2.17 Å) Mg–O bond lengths. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.13–2.16 Å. In the third Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.14 Å) and two longer (2.16 Å) Mg–O bond lengths. In the fourth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.14 Å) and four longer (2.16 Å) Mg–O bond lengths. In the fifth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, an edgeedge with one TiO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–5°. There are a spread of Mg–O bond distances ranging from 2.09–2.21 Å. In the sixth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.13–2.16 Å. In the seventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one TiO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. There are two shorter (2.15 Å) and four longer (2.16 Å) Mg–O bond lengths. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedral tilt angles are 3°. There are a spread of Mg–O bond distances ranging from 2.11–2.21 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with two equivalent TiO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.11 Å) and four longer (2.15 Å) Hf–O bond lengths. Ti is bonded to six O atoms to form TiO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.18 Å) and four longer (2.25 Å) Ti–O bond lengths. There are twelve inequivalent O sites. In the first O site, O is bonded to five Mg and one Ti atom to form a mixture of edge and corner-sharing OMg5Ti octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the second O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OMg5Ti octahedra and edges with twelve OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the third O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fourth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. Both O–Mg bond lengths are 2.16 Å. In the fifth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are two shorter (2.11 Å) and two longer (2.16 Å) O–Mg bond lengths. In the sixth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six equivalent OMg6 octahedra and edges with twelve OMg5Ti octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the seventh O site, O is bonded to four equivalent Mg, one Hf, and one Ti atom to form OHfMg4Ti octahedra that share corners with six OHfMg4Ti octahedra and edges with twelve OMg5Ti octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg4Ti octahedra and edges with twelve OMg5Ti octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg4Ti octahedra and edges with twelve OMg5Ti octahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are two shorter (2.11 Å) and two longer (2.16 Å) O–Mg bond lengths. In the tenth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the eleventh O site, O is bonded to five Mg and one Ti atom to form a mixture of edge and corner-sharing OMg5Ti octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are two shorter (2.09 Å) and two longer (2.16 Å) O–Mg bond lengths. In the twelfth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. The O–Mg bond length is 2.15 Å.