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DOE OSTI2020

Materials Data on KLiMg30O31 by Materials Project

KLiMg30O31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. K1+ is bonded to six O2- atoms to form KO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of K–O bond distances ranging from 2.33–2.38 Å. Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Li–O bond distances ranging from 2.15–2.26 Å. There are sixteen inequivalent Mg2+ sites. In the first Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with two equivalent KO6 octahedra, corners with two equivalent LiO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 8–13°. There are a spread of Mg–O bond distances ranging from 1.94–2.12 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent KO6 octahedra, corners with two equivalent LiO6 octahedra, corners with two equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 1.96–2.21 Å. In the third Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent KO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 1.93–2.24 Å. In the fourth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 8°. There are a spread of Mg–O bond distances ranging from 1.96–2.11 Å. In the fifth Mg2+ site, Mg2+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.09–2.16 Å. In the sixth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent LiO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.06–2.22 Å. In the seventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one KO6 octahedra, an edgeedge with one LiO6 octahedra, edges with seven MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 2–12°. There are a spread of Mg–O bond distances ranging from 2.11–2.22 Å. In the eighth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–5°. There are a spread of Mg–O bond distances ranging from 2.13–2.17 Å. In the ninth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, an edgeedge with one KO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 7–18°. There are a spread of Mg–O bond distances ranging from 1.98–2.13 Å. In the tenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one LiO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–6°. There are a spread of Mg–O bond distances ranging from 2.11–2.20 Å. In the eleventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one KO6 octahedra, edges with nine MgO6 octahedra, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–11°. There are a spread of Mg–O bond distances ranging from 2.13–2.29 Å. In the twelfth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one LiO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. There are a spread of Mg–O bond distances ranging from 2.12–2.19 Å. In the thirteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one KO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–10°. There are a spread of Mg–O bond distances ranging from 2.11–2.22 Å. In the fourteenth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, an edgeedge with one LiO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 9–10°. There are a spread of Mg–O bond distances ranging from 1.95–2.16 Å. In the fifteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one KO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–11°. There are a spread of Mg–O bond distances ranging from 2.13–2.20 Å. In the sixteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one LiO6 octahedra, edges with nine MgO6 octahedra, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 3–7°. There are a spread of Mg–O bond distances ranging from 2.10–2.26 Å. There are seventeen inequivalent O2- sites. In the first O2- site, O2- is bonded to one K1+ and five Mg2+ atoms to form a mixture of edge and corner-sharing OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the second O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the third O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form a mixture of edge and corner-sharing OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the fourth O2- site, O2- is bonded to one K1+ and five Mg2+ atoms to form OKMg5 octahedra that share corners with six OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the fifth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with four OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 5–6°. In the sixth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the seventh O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form OLiMg5 octahedra that share corners with six OLiMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the eighth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–14°. In the ninth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. In the tenth O2- site, O2- is bonded to one K1+ and five Mg2+ atoms to form distorted OKMg5 octahedra that share corners with six OLiMg5 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 5–19°. In the eleventh O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form OLiMg5 octahedra that share corners with six OLiMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. In the twelfth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 3–19°. In the thirteenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OLiMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. In the fourteenth O2- site, O2- is bonded to one K1+ and five Mg2+ atoms to form OKMg5 octahedra that share corners with six OLiMg5 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the fifteenth O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form a mixture of edge and corner-sharing OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–14°. In the sixteenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the seventeenth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 2–14°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on LiHfMg30O31 by Materials Project

LiMg30HfO31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Li is bonded to five O atoms to form LiO5 square pyramids that share corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 2°. There are one shorter (2.12 Å) and four longer (2.20 Å) Li–O bond lengths. There are sixteen inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent LiO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.09–2.15 Å. 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 2.10–2.15 Å. In the third Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one LiO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.09–2.16 Å. In the fourth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.10–2.15 Å. In the fifth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.12–2.14 Å. In the sixth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are three shorter (2.13 Å) and three longer (2.14 Å) Mg–O bond lengths. 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 HfO6 octahedra, edges with eight MgO6 octahedra, an edgeedge with one LiO5 square pyramid, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–7°. There are a spread of Mg–O bond distances ranging from 2.07–2.21 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.12–2.15 Å. In the ninth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one LiO5 square pyramid, corners with four MgO5 square pyramids, an edgeedge with one HfO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–7°. There are a spread of Mg–O bond distances ranging from 2.12–2.21 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are one shorter (2.13 Å) and five longer (2.14 Å) Mg–O bond lengths. In the eleventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one LiO5 square pyramid, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.07–2.20 Å. In the twelfth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.13–2.15 Å. In the thirteenth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one LiO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Mg–O bond distances ranging from 2.13–2.16 Å. In the fourteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.11–2.17 Å. In the fifteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, an edgeedge with one LiO5 square pyramid, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Mg–O bond distances ranging from 2.12–2.16 Å. In the sixteenth 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 octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.11–2.17 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent LiO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.08 Å) and four longer (2.18 Å) Hf–O bond lengths. There are seventeen inequivalent O sites. In the first O site, O is bonded to five Mg and one Hf atom to form a mixture of corner and edge-sharing OHfMg5 octahedra. The corner-sharing octahedral tilt angles are 0°. In the second O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedral tilt angles are 0°. In the third O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedral tilt angles are 0°. In the fourth O site, O is bonded to one Li and five Mg atoms to form OLiMg5 octahedra that share corners with four OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. In the fifth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the sixth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the seventh O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedral tilt angles are 0°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. In the tenth O site, O is bonded to one Li, four Mg, and one Hf atom to form OLiHfMg4 octahedra that share corners with six OMg6 octahedra and edges with eleven OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the eleventh O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the twelfth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the thirteenth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the fourteenth O site, O is bonded to one Li and five Mg atoms to form OLiMg5 octahedra that share corners with six OHfMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form a mixture of corner and edge-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the sixteenth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the seventeenth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedral tilt angles are 0°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on NaLiMg30O31 by Materials Project

NaLiMg30O31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Na1+ is bonded to five O2- atoms to form NaO5 square pyramids that share corners with two equivalent LiO6 octahedra, corners with two equivalent MgO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–4°. There are a spread of Na–O bond distances ranging from 2.17–2.24 Å. Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent NaO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Li–O bond distances ranging from 2.08–2.25 Å. There are sixteen inequivalent Mg2+ sites. In the first Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent LiO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.07–2.16 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent NaO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.05–2.20 Å. In the third Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent LiO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.03–2.21 Å. In the fourth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one NaO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 8–9°. There are a spread of Mg–O bond distances ranging from 1.93–2.11 Å. In the fifth Mg2+ site, Mg2+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.09–2.15 Å. In the sixth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.07–2.19 Å. In the seventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one LiO6 octahedra, edges with eight MgO6 octahedra, an edgeedge with one NaO5 square pyramid, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–8°. There are a spread of Mg–O bond distances ranging from 2.11–2.18 Å. In the eighth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–6°. There are a spread of Mg–O bond distances ranging from 2.12–2.16 Å. In the ninth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one NaO5 square pyramid, corners with four MgO5 square pyramids, an edgeedge with one LiO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–10°. There are a spread of Mg–O bond distances ranging from 1.93–2.12 Å. In the tenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Mg–O bond distances ranging from 2.10–2.19 Å. In the eleventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one LiO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one NaO5 square pyramid, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 3–8°. There are a spread of Mg–O bond distances ranging from 2.10–2.29 Å. In the twelfth Mg2+ site, Mg2+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. There are two shorter (2.13 Å) and four longer (2.15 Å) Mg–O bond lengths. In the thirteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one LiO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–7°. There are a spread of Mg–O bond distances ranging from 2.08–2.19 Å. In the fourteenth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one NaO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–8°. There are a spread of Mg–O bond distances ranging from 1.95–2.10 Å. In the fifteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one LiO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–6°. There are a spread of Mg–O bond distances ranging from 2.11–2.18 Å. In the sixteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, an edgeedge with one NaO5 square pyramid, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 3–5°. There are a spread of Mg–O bond distances ranging from 2.12–2.24 Å. There are seventeen inequivalent O2- sites. In the first O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form a mixture of edge and corner-sharing OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the second O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OLiMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the third O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the fourth O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form OLiMg5 octahedra that share corners with six OLiMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the fifth O2- site, O2- is bonded to one Na1+ and five Mg2+ atoms to form ONaMg5 octahedra that share corners with four OLiMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 5–8°. In the sixth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the seventh O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the eighth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–15°. In the ninth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. In the tenth O2- site, O2- is bonded to one Na1+, one Li1+, and four Mg2+ atoms to form ONaLiMg4 octahedra that share corners with six OMg6 octahedra and edges with eleven OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–12°. In the eleventh O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. In the twelfth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–13°. In the thirteenth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. In the fourteenth O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form OLiMg5 octahedra that share corners with six ONaMg5 octahedra and edges with twelve OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–7°. In the fifteenth O2- site, O2- is bonded to one Na1+ and five Mg2+ atoms to form ONaMg5 octahedra that share corners with six ONaMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 2–9°. In the sixteenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–4°. In the seventeenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six ONaMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 2–12°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on NaHfMg30O31 by Materials Project

NaMg30HfO31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Na is bonded to six O atoms to form NaO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Na–O bond distances ranging from 2.25–2.27 Å. There are sixteen inequivalent Mg sites. In the first Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with two equivalent NaO6 octahedra, corners with two equivalent HfO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.03–2.15 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent NaO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 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 2.03–2.19 Å. In the third Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent NaO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.04–2.18 Å. In the fourth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.12–2.17 Å. In the fifth 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 a spread of Mg–O bond distances ranging from 2.12–2.15 Å. In the sixth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.12–2.14 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 NaO6 octahedra, an edgeedge with one HfO6 octahedra, edges with seven MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 4–11°. There are a spread of Mg–O bond distances ranging from 2.08–2.23 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Mg–O bond distances ranging from 2.13–2.17 Å. In the ninth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, an edgeedge with one NaO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–7°. There are a spread of Mg–O bond distances ranging from 2.11–2.17 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Mg–O bond distances ranging from 2.09–2.21 Å. In the eleventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one NaO6 octahedra, edges with nine MgO6 octahedra, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–6°. There are a spread of Mg–O bond distances ranging from 2.12–2.16 Å. In the twelfth 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 octahedra tilt angles range from 1–5°. There are a spread of Mg–O bond distances ranging from 2.09–2.21 Å. In the thirteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one NaO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–8°. There are a spread of Mg–O bond distances ranging from 2.14–2.17 Å. In the fourteenth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, an edgeedge with one HfO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–3°. There are a spread of Mg–O bond distances ranging from 2.12–2.19 Å. In the fifteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one NaO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–8°. There are a spread of Mg–O bond distances ranging from 2.13–2.17 Å. In the sixteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.11–2.19 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Hf–O bond distances ranging from 2.09–2.18 Å. There are seventeen inequivalent O sites. In the first O site, O is bonded to one Na and five Mg atoms to form a mixture of edge and corner-sharing ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six ONaMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the third O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the fourth O site, O is bonded to one Na and five Mg atoms to form ONaMg5 octahedra that share corners with six ONaMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fifth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four ONaMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the sixth 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 seventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–6°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–6°. In the tenth O site, O is bonded to one Na and five Mg atoms to form ONaMg5 octahedra that share corners with six OHfMg5 octahedra and edges with eleven ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the eleventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the twelfth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the thirteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fourteenth O site, O is bonded to one Na and five Mg atoms to form ONaMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the sixteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the seventeenth 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°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KHfMg30O31 by Materials Project

KMg30HfO31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. K is bonded to five O atoms to form KO5 square pyramids that share corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–3°. There are a spread of K–O bond distances ranging from 2.35–2.45 Å. There are sixteen inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent KO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 1.96–2.23 Å. 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 2.13–2.19 Å. In the third Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one KO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 2°. There are a spread of Mg–O bond distances ranging from 2.02–2.25 Å. In the fourth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.11–2.17 Å. In the fifth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.10–2.20 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 octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.15–2.17 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 HfO6 octahedra, edges with eight MgO6 octahedra, an edgeedge with one KO5 square pyramid, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 4–12°. There are a spread of Mg–O bond distances ranging from 2.10–2.26 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Mg–O bond distances ranging from 2.16–2.19 Å. In the ninth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one KO5 square pyramid, corners with four MgO5 square pyramids, an edgeedge with one HfO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–11°. There are a spread of Mg–O bond distances ranging from 2.08–2.25 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Mg–O bond distances ranging from 2.14–2.18 Å. In the eleventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one KO5 square pyramid, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 4–7°. There are a spread of Mg–O bond distances ranging from 2.08–2.25 Å. In the twelfth 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 1–4°. There are a spread of Mg–O bond distances ranging from 2.14–2.19 Å. In the thirteenth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one KO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. There are a spread of Mg–O bond distances ranging from 2.10–2.20 Å. In the fourteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 3–4°. There are a spread of Mg–O bond distances ranging from 2.10–2.23 Å. In the fifteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, an edgeedge with one KO5 square pyramid, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 1–9°. There are a spread of Mg–O bond distances ranging from 2.12–2.19 Å. In the sixteenth 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 octahedra tilt angles range from 3–4°. There are a spread of Mg–O bond distances ranging from 2.10–2.22 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent KO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Hf–O bond distances ranging from 2.01–2.15 Å. There are seventeen inequivalent O sites. In the first O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the second O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedral tilt angles are 0°. In the third O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fourth O site, O is bonded to one K and five Mg atoms to form OKMg5 octahedra that share corners with four OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. In the fifth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the sixth 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 0–5°. In the seventh 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 eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–6°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–6°. In the tenth O site, O is bonded to one K, four Mg, and one Hf atom to form OKHfMg4 octahedra that share corners with six OMg6 octahedra and edges with eleven OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–10°. In the eleventh 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 0–9°. In the twelfth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–10°. In the thirteenth 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 fourteenth O site, O is bonded to one K and five Mg atoms to form OKMg5 octahedra that share corners with six OHfMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–6°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the sixteenth 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 0–6°. In the seventeenth 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 0–4°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KLiMg30O31 by Materials Project

KLiMg30O31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. K1+ is bonded to six O2- atoms to form KO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent LiO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of K–O bond distances ranging from 2.32–2.41 Å. Li1+ is bonded to five O2- atoms to form LiO5 square pyramids that share corners with two equivalent KO6 octahedra, corners with two equivalent MgO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 8–13°. There are a spread of Li–O bond distances ranging from 1.90–2.28 Å. There are sixteen inequivalent Mg2+ sites. In the first Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent KO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 1.96–2.20 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent LiO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.06–2.22 Å. In the third Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent KO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 1.93–2.24 Å. In the fourth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one LiO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 9°. There are a spread of Mg–O bond distances ranging from 1.95–2.13 Å. In the fifth Mg2+ site, Mg2+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.09–2.16 Å. In the sixth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.09–2.21 Å. In the seventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one KO6 octahedra, edges with eight MgO6 octahedra, an edgeedge with one LiO5 square pyramid, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–13°. There are a spread of Mg–O bond distances ranging from 2.09–2.20 Å. In the eighth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–6°. There are a spread of Mg–O bond distances ranging from 2.13–2.17 Å. In the ninth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one LiO5 square pyramid, corners with four MgO5 square pyramids, an edgeedge with one KO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 7–18°. There are a spread of Mg–O bond distances ranging from 1.99–2.14 Å. In the tenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 2–3°. There are a spread of Mg–O bond distances ranging from 2.11–2.19 Å. In the eleventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one KO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one LiO5 square pyramid, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 1–14°. There are a spread of Mg–O bond distances ranging from 2.11–2.27 Å. In the twelfth Mg2+ site, Mg2+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Mg–O bond distances ranging from 2.13–2.18 Å. In the thirteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one KO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–10°. There are a spread of Mg–O bond distances ranging from 2.12–2.21 Å. In the fourteenth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one LiO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–8°. There are a spread of Mg–O bond distances ranging from 1.98–2.14 Å. In the fifteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one KO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–11°. There are a spread of Mg–O bond distances ranging from 2.15–2.18 Å. In the sixteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, an edgeedge with one LiO5 square pyramid, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 2–5°. There are a spread of Mg–O bond distances ranging from 2.11–2.27 Å. There are seventeen inequivalent O2- sites. In the first O2- site, O2- is bonded to one K1+ and five Mg2+ atoms to form a mixture of edge and corner-sharing OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the second O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the third O2- site, O2- is bonded to six Mg2+ 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 O2- site, O2- is bonded to one K1+ and five Mg2+ atoms to form OKMg5 octahedra that share corners with six OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the fifth O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form OLiMg5 octahedra that share corners with four OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. In the sixth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the seventh O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the eighth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–12°. In the ninth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. In the tenth O2- site, O2- is bonded to one K1+, one Li1+, and four Mg2+ atoms to form distorted OKLiMg4 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 6–19°. In the eleventh O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–6°. In the twelfth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 4–19°. In the thirteenth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the fourteenth O2- site, O2- is bonded to one K1+ and five Mg2+ atoms to form OKMg5 octahedra that share corners with six OLiMg5 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–9°. In the fifteenth O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form OLiMg5 octahedra that share corners with six OLiMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 3–12°. In the sixteenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. In the seventeenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OLiMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 2–13°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on RbLiMg30O31 by Materials Project

RbLiMg30O31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Rb1+ is bonded to six O2- atoms to form RbO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 trigonal bipyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Rb–O bond distances ranging from 2.38–2.46 Å. Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 trigonal bipyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Li–O bond distances ranging from 2.14–2.30 Å. There are sixteen inequivalent Mg2+ sites. In the first Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 trigonal bipyramids that share corners with two equivalent RbO6 octahedra, corners with two equivalent LiO6 octahedra, corners with three MgO5 square pyramids, corners with two equivalent MgO5 trigonal bipyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 7–18°. There are a spread of Mg–O bond distances ranging from 1.90–2.15 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent RbO6 octahedra, corners with two equivalent LiO6 octahedra, corners with two equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Mg–O bond distances ranging from 1.93–2.24 Å. In the third Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent LiO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.06–2.23 Å. In the fourth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, corners with three MgO5 trigonal bipyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 8°. There are a spread of Mg–O bond distances ranging from 1.97–2.12 Å. In the fifth Mg2+ site, Mg2+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.10–2.16 Å. In the sixth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent RbO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 1.89–2.25 Å. In the seventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one RbO6 octahedra, an edgeedge with one LiO6 octahedra, edges with seven MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and edges with two MgO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 2–15°. There are a spread of Mg–O bond distances ranging from 2.10–2.25 Å. In the eighth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, edges with two MgO5 square pyramids, and an edgeedge with one MgO5 trigonal bipyramid. The corner-sharing octahedra tilt angles range from 1–6°. There are a spread of Mg–O bond distances ranging from 2.13–2.19 Å. In the ninth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with two MgO5 square pyramids, corners with three MgO5 trigonal bipyramids, an edgeedge with one LiO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 9–10°. There are a spread of Mg–O bond distances ranging from 1.96–2.18 Å. In the tenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one RbO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 1–11°. There are a spread of Mg–O bond distances ranging from 2.10–2.25 Å. In the eleventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one LiO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one MgO5 trigonal bipyramid. The corner-sharing octahedra tilt angles range from 4–7°. There are a spread of Mg–O bond distances ranging from 2.11–2.27 Å. In the twelfth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one RbO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–14°. There are a spread of Mg–O bond distances ranging from 2.12–2.23 Å. In the thirteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 trigonal bipyramids, an edgeedge with one LiO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–6°. There are a spread of Mg–O bond distances ranging from 2.13–2.19 Å. In the fourteenth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 trigonal bipyramids that share corners with four MgO6 octahedra, corners with three MgO5 square pyramids, corners with two MgO5 trigonal bipyramids, an edgeedge with one RbO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 7–20°. There are a spread of Mg–O bond distances ranging from 1.99–2.16 Å. In the fifteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one LiO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. There are a spread of Mg–O bond distances ranging from 2.13–2.21 Å. In the sixteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 trigonal bipyramids, an edgeedge with one RbO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one MgO5 trigonal bipyramid. The corner-sharing octahedra tilt angles range from 1–12°. There are a spread of Mg–O bond distances ranging from 2.13–2.45 Å. There are seventeen inequivalent O2- sites. In the first O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form a mixture of edge and corner-sharing OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the second O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OLiMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the third O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form a mixture of distorted edge and corner-sharing ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the fourth O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form OLiMg5 octahedra that share corners with six OLiMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the fifth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with four OLiMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedral tilt angles are 5°. In the sixth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the seventh O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form ORbMg5 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the eighth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–13°. In the ninth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–6°. In the tenth O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form OLiMg5 octahedra that share corners with six ORbMg5 octahedra and edges with eleven OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–14°. In the eleventh O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form ORbMg5 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. In the twelfth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–14°. In the thirteenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the fourteenth O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form OLiMg5 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the fifteenth O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form a mixture of distorted edge and corner-sharing ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 6–24°. In the sixteenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the seventeenth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 2–21°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on RbHfMg30O31 by Materials Project

RbMg30HfO31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Rb is bonded to six O atoms to form RbO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are one shorter (2.42 Å) and five longer (2.43 Å) Rb–O bond lengths. There are sixteen inequivalent Mg sites. In the first Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with two equivalent RbO6 octahedra, corners with two equivalent HfO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 1.92–2.26 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent RbO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 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 1.92–2.25 Å. In the third Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent RbO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 1.92–2.23 Å. In the fourth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are three shorter (2.13 Å) and two longer (2.21 Å) Mg–O bond lengths. In the fifth 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 a spread of Mg–O bond distances ranging from 2.12–2.20 Å. In the sixth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.14–2.23 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 RbO6 octahedra, an edgeedge with one HfO6 octahedra, edges with seven MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 3–16°. There are a spread of Mg–O bond distances ranging from 2.15–2.22 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 2–4°. There are two shorter (2.16 Å) and four longer (2.19 Å) Mg–O bond lengths. In the ninth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, an edgeedge with one RbO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–13°. There are a spread of Mg–O bond distances ranging from 2.15–2.23 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–7°. There are a spread of Mg–O bond distances ranging from 2.11–2.24 Å. In the eleventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one RbO6 octahedra, edges with nine MgO6 octahedra, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–11°. There are a spread of Mg–O bond distances ranging from 2.13–2.23 Å. In the twelfth 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 octahedra tilt angles range from 1–7°. There are a spread of Mg–O bond distances ranging from 2.11–2.24 Å. In the thirteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one RbO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–13°. There are a spread of Mg–O bond distances ranging from 2.14–2.22 Å. In the fourteenth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, an edgeedge with one HfO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 4–7°. There are a spread of Mg–O bond distances ranging from 2.13–2.25 Å. In the fifteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one RbO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–13°. There are a spread of Mg–O bond distances ranging from 2.14–2.23 Å. In the sixteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Mg–O bond distances ranging from 2.11–2.23 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.09 Å) and two longer (2.13 Å) Hf–O bond lengths. There are seventeen inequivalent O sites. In the first O site, O is bonded to one Rb and five Mg atoms to form a mixture of edge and corner-sharing ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the third O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fourth O site, O is bonded to one Rb and five Mg atoms to form ORbMg5 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the fifth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 3–6°. In the sixth 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 0–6°. In the seventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. In the tenth O site, O is bonded to one Rb and five Mg atoms to form distorted ORbMg5 octahedra that share corners with six OHfMg5 octahedra and edges with eleven ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–11°. In the eleventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–11°. In the twelfth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the thirteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the fourteenth O site, O is bonded to one Rb and five Mg atoms to form distorted ORbMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–11°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–11°. In the sixteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the seventeenth 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 0–6°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMg30BO31 by Materials Project

Mg30HfBO31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. there are sixteen inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 1.97–2.22 Å. 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 octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.11–2.20 Å. In the third Mg site, Mg is bonded to one B and five O atoms to form a mixture of distorted corner and edge-sharing MgBO5 octahedra. The corner-sharing octahedral tilt angles are 0°. The Mg–B bond length is 2.35 Å. There are a spread of Mg–O bond distances ranging from 2.00–2.23 Å. In the fourth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four MgBO5 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.10–2.20 Å. In the fifth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.07–2.19 Å. In the sixth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.12–2.16 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 HfO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–15°. There are a spread of Mg–O bond distances ranging from 2.04–2.31 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra and edges with twelve MgBO5 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. There are a spread of Mg–O bond distances ranging from 2.13–2.19 Å. In the ninth Mg site, Mg is bonded to one B and five O atoms to form MgBO5 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with ten MgBO5 octahedra. The corner-sharing octahedra tilt angles range from 2–15°. The Mg–B bond length is 2.23 Å. There are a spread of Mg–O bond distances ranging from 2.10–2.19 Å. In the tenth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.12–2.18 Å. In the eleventh 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 ten MgBO5 octahedra. The corner-sharing octahedra tilt angles range from 1–10°. There are a spread of Mg–O bond distances ranging from 2.03–2.30 Å. In the twelfth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. There are a spread of Mg–O bond distances ranging from 2.12–2.19 Å. In the thirteenth Mg site, Mg is bonded to one B and five O atoms to form a mixture of corner and edge-sharing MgBO5 octahedra. The corner-sharing octahedra tilt angles range from 0–12°. The Mg–B bond length is 2.26 Å. There are a spread of Mg–O bond distances ranging from 2.05–2.22 Å. In the fourteenth 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 octahedra tilt angles range from 2–6°. There are a spread of Mg–O bond distances ranging from 2.08–2.23 Å. In the fifteenth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–10°. There are a spread of Mg–O bond distances ranging from 2.09–2.20 Å. In the sixteenth 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 octahedra tilt angles range from 1–6°. There are a spread of Mg–O bond distances ranging from 2.08–2.21 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with four MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Hf–O bond distances ranging from 2.03–2.14 Å. B is bonded to five Mg atoms to form BMg5 square pyramids that share corners with four OHfMg5 octahedra, corners with five OMg5 square pyramids, and edges with eight OMg6 octahedra. The corner-sharing octahedra tilt angles range from 4–9°. There are seventeen inequivalent O sites. In the first O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with four OMg6 octahedra, corners with two equivalent BMg5 square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OHfMg4 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent BMg5 square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. In the third O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fourth O site, O is bonded to five Mg atoms to form OMg5 square pyramids that share corners with four OHfMg5 octahedra, a cornercorner with one BMg5 square pyramid, corners with four OHfMg4 square pyramids, and edges with eight OMg6 octahedra. The corner-sharing octahedra tilt angles range from 4–7°. In the fifth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with four OHfMg5 octahedra, corners with two equivalent OMg5 square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OHfMg4 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. In the sixth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5 square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. In the seventh O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra, edges with nine OHfMg5 octahedra, an edgeedge with one BMg5 square pyramid, and edges with two OHfMg4 square pyramids. The corner-sharing octahedra tilt angles range from 2–9°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra, edges with nine OHfMg5 octahedra, and edges with three OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 2–9°. In the tenth O site, O is bonded to four Mg and one Hf atom to form OHfMg4 square pyramids that share corners with four OMg6 octahedra, a cornercorner with one BMg5 square pyramid, corners with four OMg5 square pyramids, and edges with eight OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 3–13°. In the eleventh O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OHfMg4 square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 0–4°. In the twelfth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OHfMg4 square pyramids, edges with ten OHfMg5 octahedra, an edgeedge with one BMg5 square pyramid, and an edgeedge with one OMg5 square pyramid. The corner-sharing octahedra tilt angles range from 2–4°. In the thirteenth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fourteenth O site, O is bonded to five Mg atoms to form OMg5 square pyramids that share corners with four OHfMg5 octahedra, a cornercorner with one BMg5 square pyramid, corners with four OMg5 square pyramids, and edges with eight OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with four OHfMg5 octahedra, corners with two equivalent OMg5 square pyramids, edges with ten OHfMg5 octahedra, and edges with two equivalent OHfMg4 square pyramids. The corner-sharing octahedra tilt angles range from 0–5°. In the sixteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5 square pyramids, edges with ten OMg6 octahedra, an edgeedge with one BMg5 square pyramid, and an edgeedge with one OMg5 square pyramid. The corner-sharing octahedra tilt angles range from 1–2°. In the seventeenth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KNaMg30O31 by Materials Project

KNaMg30O31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. K1+ is bonded to six O2- atoms to form KO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent NaO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of K–O bond distances ranging from 2.30–2.39 Å. Na1+ is bonded to five O2- atoms to form NaO5 square pyramids that share corners with two equivalent KO6 octahedra, corners with two equivalent MgO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 4–8°. There are a spread of Na–O bond distances ranging from 2.04–2.29 Å. There are sixteen inequivalent Mg2+ sites. In the first Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent KO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 1.95–2.20 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent NaO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.03–2.23 Å. In the third Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent KO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 1.91–2.26 Å. In the fourth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one NaO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 8°. There are a spread of Mg–O bond distances ranging from 1.93–2.13 Å. In the fifth Mg2+ site, Mg2+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.09–2.19 Å. In the sixth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.08–2.20 Å. In the seventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one KO6 octahedra, edges with eight MgO6 octahedra, an edgeedge with one NaO5 square pyramid, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–11°. There are a spread of Mg–O bond distances ranging from 2.14–2.20 Å. In the eighth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–6°. There are a spread of Mg–O bond distances ranging from 2.13–2.17 Å. In the ninth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one NaO5 square pyramid, corners with four MgO5 square pyramids, an edgeedge with one KO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 8–12°. There are a spread of Mg–O bond distances ranging from 1.98–2.15 Å. In the tenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 2–3°. There are a spread of Mg–O bond distances ranging from 2.12–2.19 Å. In the eleventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one KO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one NaO5 square pyramid, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 1–13°. There are a spread of Mg–O bond distances ranging from 2.14–2.25 Å. In the twelfth Mg2+ site, Mg2+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Mg–O bond distances ranging from 2.14–2.18 Å. In the thirteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one KO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–11°. There are a spread of Mg–O bond distances ranging from 2.12–2.21 Å. In the fourteenth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one NaO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–8°. There are a spread of Mg–O bond distances ranging from 1.97–2.13 Å. In the fifteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one KO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–12°. There are two shorter (2.15 Å) and four longer (2.18 Å) Mg–O bond lengths. In the sixteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, an edgeedge with one NaO5 square pyramid, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 1–6°. There are a spread of Mg–O bond distances ranging from 2.14–2.26 Å. There are seventeen inequivalent O2- sites. In the first O2- site, O2- is bonded to one K1+ and five Mg2+ atoms to form a mixture of edge and corner-sharing OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the second O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the third O2- site, O2- is bonded to six Mg2+ 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 O2- site, O2- is bonded to one K1+ and five Mg2+ atoms to form OKMg5 octahedra that share corners with six OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the fifth O2- site, O2- is bonded to one Na1+ and five Mg2+ atoms to form ONaMg5 octahedra that share corners with four OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. In the sixth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the seventh O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the eighth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–13°. In the ninth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. In the tenth O2- site, O2- is bonded to one K1+, one Na1+, and four Mg2+ atoms to form OKNaMg4 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 4–17°. In the eleventh O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the twelfth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 4–17°. In the thirteenth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the fourteenth O2- site, O2- is bonded to one K1+ and five Mg2+ atoms to form OKMg5 octahedra that share corners with six ONaMg5 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–9°. In the fifteenth O2- site, O2- is bonded to one Na1+ and five Mg2+ atoms to form ONaMg5 octahedra that share corners with six ONaMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 3–9°. In the sixteenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–6°. In the seventeenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six ONaMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 2–11°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KHfMg30O31 by Materials Project

KMg30HfO31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. K is bonded to six O atoms to form KO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of K–O bond distances ranging from 2.36–2.38 Å. There are sixteen inequivalent Mg sites. In the first Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with two equivalent KO6 octahedra, corners with two equivalent HfO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 1.95–2.19 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent KO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 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 1.95–2.23 Å. In the third Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent KO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 1.96–2.21 Å. In the fourth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are three shorter (2.12 Å) and two longer (2.19 Å) Mg–O bond lengths. In the fifth 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 a spread of Mg–O bond distances ranging from 2.12–2.17 Å. In the sixth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.14–2.16 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 KO6 octahedra, an edgeedge with one HfO6 octahedra, edges with seven MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 3–14°. There are a spread of Mg–O bond distances ranging from 2.13–2.22 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Mg–O bond distances ranging from 2.15–2.18 Å. In the ninth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, an edgeedge with one KO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–11°. There are a spread of Mg–O bond distances ranging from 2.15–2.20 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 2–6°. There are a spread of Mg–O bond distances ranging from 2.10–2.22 Å. In the eleventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one KO6 octahedra, edges with nine MgO6 octahedra, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–10°. There are a spread of Mg–O bond distances ranging from 2.14–2.19 Å. In the twelfth 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 octahedra tilt angles range from 2–6°. There are a spread of Mg–O bond distances ranging from 2.11–2.22 Å. In the thirteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one KO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–11°. There are a spread of Mg–O bond distances ranging from 2.15–2.19 Å. In the fourteenth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, an edgeedge with one HfO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedral tilt angles are 3°. There are a spread of Mg–O bond distances ranging from 2.13–2.22 Å. In the fifteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one KO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–11°. There are a spread of Mg–O bond distances ranging from 2.15–2.19 Å. In the sixteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.12–2.21 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Hf–O bond distances ranging from 2.09–2.17 Å. There are seventeen inequivalent O sites. In the first O site, O is bonded to one K and five Mg atoms to form a mixture of edge and corner-sharing OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the third O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the fourth O site, O is bonded to one K and five Mg atoms to form OKMg5 octahedra that share corners with six OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the fifth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. In the sixth 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 0–5°. In the seventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. In the tenth O site, O is bonded to one K and five Mg atoms to form OKMg5 octahedra that share corners with six OHfMg5 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the eleventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the twelfth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the thirteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the fourteenth O site, O is bonded to one K and five Mg atoms to form OKMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the sixteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the seventeenth 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 0–4°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Li8CoNi9O20 by Materials Project

Li8CoNi9O20 crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are sixteen inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six NiO6 octahedra, edges with two equivalent CoO6 octahedra, edges with four LiO6 octahedra, and edges with four NiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–18°. There are a spread of Li–O bond distances ranging from 1.98–2.23 Å. In the second Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six NiO6 octahedra, edges with two equivalent LiO6 octahedra, edges with two equivalent CoO6 octahedra, and edges with four NiO6 octahedra. The corner-sharing octahedra tilt angles range from 12–16°. There are three shorter (2.10 Å) and three longer (2.12 Å) Li–O bond lengths. In the third Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one CoO6 octahedra, corners with five NiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–8°. There are a spread of Li–O bond distances ranging from 2.11–2.27 Å. In the fourth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six NiO6 octahedra, edges with four LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–18°. There are a spread of Li–O bond distances ranging from 2.00–2.24 Å. In the fifth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six NiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–9°. There are a spread of Li–O bond distances ranging from 2.06–2.13 Å. In the sixth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six NiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–8°. There are a spread of Li–O bond distances ranging from 2.04–2.40 Å. In the seventh Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six NiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–10°. There are a spread of Li–O bond distances ranging from 2.05–2.37 Å. In the eighth Li1+ site, Li1+ is bonded to six O2- atoms to form distorted LiO6 octahedra that share corners with six NiO6 octahedra, edges with four LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–17°. There are a spread of Li–O bond distances ranging from 1.98–2.42 Å. In the ninth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six NiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–6°. There are a spread of Li–O bond distances ranging from 2.10–2.15 Å. In the tenth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six NiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–8°. There are a spread of Li–O bond distances ranging from 2.09–2.14 Å. In the eleventh Li1+ site, Li1+ is bonded to six O2- atoms to form distorted LiO6 octahedra that share corners with six NiO6 octahedra, edges with four LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–18°. There are a spread of Li–O bond distances ranging from 1.98–2.30 Å. In the twelfth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six NiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–7°. There are a spread of Li–O bond distances ranging from 2.08–2.15 Å. In the thirteenth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one CoO6 octahedra, corners with five NiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–11°. There are a spread of Li–O bond distances ranging from 2.07–2.31 Å. In the fourteenth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one CoO6 octahedra, corners with five NiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–8°. There are a spread of Li–O bond distances ranging from 2.10–2.35 Å. In the fifteenth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six NiO6 octahedra, edges with two equivalent CoO6 octahedra, edges with four LiO6 octahedra, and edges with four NiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–19°. There are a spread of Li–O bond distances ranging from 2.01–2.22 Å. In the sixteenth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six NiO6 octahedra, edges with two equivalent CoO6 octahedra, edges with four LiO6 octahedra, and edges with four NiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–15°. There are a spread of Li–O bond distances ranging from 1.98–2.30 Å. There are two inequivalent Co4+ sites. In the first Co4+ site, Co4+ is bonded to six O2- atoms to form CoO6 octahedra that share a cornercorner with one LiO6 octahedra, edges with two equivalent CoO6 octahedra, edges with four LiO6 octahedra, and edges with four NiO6 octahedra. The corner-sharing octahedral tilt angles are 8°. There are a spread of Co–O bond distances ranging from 1.88–1.96 Å. In the second Co4+ site, Co4+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with two LiO6 octahedra, edges with two equivalent CoO6 octahedra, edges with four LiO6 octahedra, and edges with four NiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–5°. There are a spread of Co–O bond distances ranging from 1.89–1.92 Å. There are eighteen inequivalent Ni+3.11+ sites. In the first Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with six LiO6 octahedra, edges with two LiO6 octahedra, edges with two equivalent CoO6 octahedra, and edges with four NiO6 octahedra. The corner-sharing octahedra tilt angles range from 14–18°. There are a spread of Ni–O bond distances ranging from 1.96–2.14 Å. In the second Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent CoO6 octahedra, edges with four LiO6 octahedra, and edges with four NiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–16°. There are a spread of Ni–O bond distances ranging from 1.97–2.19 Å. In the third Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with three LiO6 octahedra, edges with five LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–7°. There are a spread of Ni–O bond distances ranging from 1.86–1.94 Å. In the fourth Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with three LiO6 octahedra, edges with five LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–8°. There are a spread of Ni–O bond distances ranging from 1.86–1.94 Å. In the fifth Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–10°. There are a spread of Ni–O bond distances ranging from 1.92–2.11 Å. In the sixth Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with six LiO6 octahedra, edges with four LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–15°. There are a spread of Ni–O bond distances ranging from 1.90–2.17 Å. In the seventh Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with five LiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–8°. There are a spread of Ni–O bond distances ranging from 1.92–2.14 Å. In the eighth Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with five LiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–8°. There are a spread of Ni–O bond distances ranging from 1.92–2.11 Å. In the ninth Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–11°. There are a spread of Ni–O bond distances ranging from 1.91–2.16 Å. In the tenth Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with six LiO6 octahedra, edges with four LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–17°. There are a spread of Ni–O bond distances ranging from 1.91–2.21 Å. In the eleventh Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with four LiO6 octahedra, edges with five LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–11°. There are a spread of Ni–O bond distances ranging from 1.89–2.14 Å. In the twelfth Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with four LiO6 octahedra, edges with five LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–10°. There are a spread of Ni–O bond distances ranging from 1.89–2.14 Å. In the thirteenth Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with six LiO6 octahedra, edges with four LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–18°. There are a spread of Ni–O bond distances ranging from 1.92–2.16 Å. In the fourteenth Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. There are a spread of Ni–O bond distances ranging from 1.91–2.13 Å. In the fifteenth Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with four LiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedral tilt angles are 8°. There are a spread of Ni–O bond distances ranging from 1.87–1.93 Å. In the sixteenth Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with five LiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–8°. There are a spread of Ni–O bond distances ranging from 1.93–2.12 Å. In the seventeenth Ni+3.11+ site, Ni+3.11+ is bonded to six O2- atoms to form NiO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent CoO6 octahedra, edges with four LiO6 octahedra, and edges with four NiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–19°. There are a spread of Ni–

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on RbHfMg30O31 by Materials Project

RbMg30HfO31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Rb is bonded to six O atoms to form RbO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent HfO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Rb–O bond distances ranging from 2.39–2.43 Å. There are sixteen 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 RbO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 1.91–2.23 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent HfO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.11–2.20 Å. In the third Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent RbO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 1.90–2.23 Å. In the fourth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one HfO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 1°. There are a spread of Mg–O bond distances ranging from 2.11–2.19 Å. In the fifth 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 0–1°. There are a spread of Mg–O bond distances ranging from 2.10–2.19 Å. In the sixth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.13–2.17 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 RbO6 octahedra, edges with eight MgO6 octahedra, an edgeedge with one HfO5 square pyramid, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 2–13°. There are a spread of Mg–O bond distances ranging from 2.08–2.28 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Mg–O bond distances ranging from 2.15–2.19 Å. In the ninth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one HfO5 square pyramid, corners with four MgO5 square pyramids, an edgeedge with one RbO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 4–13°. There are a spread of Mg–O bond distances ranging from 2.06–2.36 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–4°. There are four shorter (2.15 Å) and two longer (2.19 Å) Mg–O bond lengths. In the eleventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one RbO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one HfO5 square pyramid. The corner-sharing octahedra tilt angles range from 2–9°. There are one shorter (2.10 Å) and five longer (2.17 Å) Mg–O bond lengths. In the twelfth 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 0–4°. There are a spread of Mg–O bond distances ranging from 2.14–2.18 Å. In the thirteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one RbO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–12°. There are a spread of Mg–O bond distances ranging from 2.11–2.24 Å. In the fourteenth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one HfO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Mg–O bond distances ranging from 2.10–2.25 Å. In the fifteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one RbO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–11°. There are a spread of Mg–O bond distances ranging from 2.12–2.21 Å. In the sixteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one HfO5 square pyramid. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.14–2.18 Å. Hf is bonded to five O atoms to form distorted HfO5 square pyramids that share corners with two equivalent RbO6 octahedra, corners with two equivalent MgO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 7–10°. There are a spread of Hf–O bond distances ranging from 1.97–2.37 Å. There are seventeen inequivalent O sites. In the first O site, O is bonded to one Rb and five Mg atoms to form a mixture of edge and corner-sharing ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. 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 0–1°. In the fourth O site, O is bonded to one Rb and five Mg atoms to form ORbMg5 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the fifth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with four ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the sixth 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 0–6°. In the seventh 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 0–1°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–6°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the tenth O site, O is bonded to one Rb, four Mg, and one Hf atom to form ORbHfMg4 octahedra that share corners with six OMg6 octahedra and edges with eleven ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 4–15°. In the eleventh 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 0–9°. In the twelfth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–10°. In the thirteenth 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 fourteenth O site, O is bonded to one Rb and five Mg atoms to form ORbMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–12°. In the sixteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the seventeenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KHfMg30O31 by Materials Project

KMg30HfO31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. K is bonded to six O atoms to form KO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent HfO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of K–O bond distances ranging from 2.33–2.37 Å. There are sixteen 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 KO6 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 1.95–2.21 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent HfO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.11–2.18 Å. In the third Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent KO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 1.94–2.21 Å. In the fourth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one HfO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.11–2.17 Å. In the fifth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.11–2.18 Å. In the sixth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.12–2.16 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 KO6 octahedra, edges with eight MgO6 octahedra, an edgeedge with one HfO5 square pyramid, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–11°. There are a spread of Mg–O bond distances ranging from 2.09–2.25 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.15–2.18 Å. In the ninth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one HfO5 square pyramid, corners with four MgO5 square pyramids, an edgeedge with one KO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–11°. There are a spread of Mg–O bond distances ranging from 2.08–2.26 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Mg–O bond distances ranging from 2.14–2.18 Å. In the eleventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one KO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one HfO5 square pyramid. The corner-sharing octahedra tilt angles range from 2–8°. There are a spread of Mg–O bond distances ranging from 2.10–2.21 Å. In the twelfth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.14–2.17 Å. In the thirteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one KO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–10°. There are a spread of Mg–O bond distances ranging from 2.13–2.20 Å. In the fourteenth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one HfO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. There are a spread of Mg–O bond distances ranging from 2.10–2.24 Å. In the fifteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one KO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–10°. There are a spread of Mg–O bond distances ranging from 2.13–2.19 Å. In the sixteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one HfO5 square pyramid. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.12–2.18 Å. Hf is bonded to five O atoms to form HfO5 square pyramids that share corners with two equivalent KO6 octahedra, corners with two equivalent MgO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 5–6°. There are a spread of Hf–O bond distances ranging from 2.00–2.31 Å. There are seventeen inequivalent O sites. In the first O site, O is bonded to one K and five Mg atoms to form a mixture of corner and edge-sharing OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the third O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedral tilt angles are 0°. In the fourth O site, O is bonded to one K and five Mg atoms to form OKMg5 octahedra that share corners with six OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the fifth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with four OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the sixth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the seventh O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the tenth O site, O is bonded to one K, four Mg, and one Hf atom to form OKHfMg4 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–9°. In the eleventh O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the twelfth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the thirteenth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fourteenth O site, O is bonded to one K and five Mg atoms to form OKMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–11°. In the sixteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the seventeenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on LiHfMg30O31 by Materials Project

LiMg30HfO31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Li is bonded to six O atoms to form LiO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Li–O bond distances ranging from 2.19–2.22 Å. There are sixteen inequivalent Mg sites. In the first Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with two equivalent LiO6 octahedra, corners with two equivalent HfO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.09–2.14 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent LiO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 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 2.07–2.17 Å. In the third Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent LiO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.09–2.16 Å. In the fourth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.12–2.16 Å. In the fifth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.13 Å) and four longer (2.14 Å) Mg–O bond lengths. In the sixth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.09–2.13 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 LiO6 octahedra, an edgeedge with one HfO6 octahedra, edges with seven MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 3–9°. There are a spread of Mg–O bond distances ranging from 2.06–2.23 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Mg–O bond distances ranging from 2.13–2.16 Å. In the ninth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, an edgeedge with one LiO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. There are a spread of Mg–O bond distances ranging from 2.09–2.17 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Mg–O bond distances ranging from 2.09–2.20 Å. In the eleventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one LiO6 octahedra, edges with nine MgO6 octahedra, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 2–4°. There are a spread of Mg–O bond distances ranging from 2.10–2.17 Å. In the twelfth 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 octahedra tilt angles range from 0–4°. There are a spread of Mg–O bond distances ranging from 2.09–2.20 Å. In the thirteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one LiO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–6°. There are a spread of Mg–O bond distances ranging from 2.11–2.17 Å. In the fourteenth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, an edgeedge with one HfO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.12–2.18 Å. In the fifteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one LiO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–6°. There are a spread of Mg–O bond distances ranging from 2.11–2.18 Å. In the sixteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Mg–O bond distances ranging from 2.11–2.18 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Hf–O bond distances ranging from 2.10–2.19 Å. There are seventeen inequivalent O sites. In the first O site, O is bonded to one Li and five Mg atoms to form a mixture of corner and edge-sharing OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OLiMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the third O site, O is bonded to five Mg and one Hf atom to form a mixture of corner and edge-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the fourth O site, O is bonded to one Li and five Mg atoms to form OLiMg5 octahedra that share corners with six OLiMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fifth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OLiMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the sixth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the seventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–7°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–7°. In the tenth O site, O is bonded to one Li and five Mg atoms to form OLiMg5 octahedra that share corners with six OHfMg5 octahedra and edges with eleven OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the eleventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the twelfth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the thirteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fourteenth O site, O is bonded to one Li and five Mg atoms to form OLiMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form a mixture of corner and edge-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the sixteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the seventeenth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMg30BO31 by Materials Project

Mg30HfBO31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. there are sixteen 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 BO6 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 2.02–2.17 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent HfO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.10–2.16 Å. In the third Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent MgO6 octahedra, corners with two equivalent BO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.02–2.17 Å. In the fourth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one HfO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight 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 fifth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.12–2.16 Å. In the sixth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.12–2.15 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 BO6 octahedra, edges with eight MgO6 octahedra, an edgeedge with one HfO5 square pyramid, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–10°. There are a spread of Mg–O bond distances ranging from 2.09–2.22 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.14–2.16 Å. In the ninth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one HfO5 square pyramid, corners with four MgO5 square pyramids, an edgeedge with one BO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–10°. There are a spread of Mg–O bond distances ranging from 2.07–2.19 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.13–2.17 Å. In the eleventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one BO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one HfO5 square pyramid. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Mg–O bond distances ranging from 2.10–2.20 Å. In the twelfth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. There are a spread of Mg–O bond distances ranging from 2.13–2.16 Å. In the thirteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one BO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–8°. There are a spread of Mg–O bond distances ranging from 2.13–2.16 Å. In the fourteenth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one HfO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 1°. There are a spread of Mg–O bond distances ranging from 2.11–2.22 Å. In the fifteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one BO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–7°. There are a spread of Mg–O bond distances ranging from 2.13–2.16 Å. In the sixteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one HfO5 square pyramid. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.11–2.17 Å. Hf is bonded to five O atoms to form HfO5 square pyramids that share corners with two equivalent MgO6 octahedra, corners with two equivalent BO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–6°. There are a spread of Hf–O bond distances ranging from 2.03–2.27 Å. B is bonded to six O atoms to form distorted BO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent HfO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of B–O bond distances ranging from 2.26–2.28 Å. There are seventeen inequivalent O sites. In the first O site, O is bonded to five Mg and one B atom to form distorted OMg5B square pyramids that share corners with two equivalent OMg6 octahedra, corners with two equivalent OMg5B square pyramids, edges with eight OMg6 octahedra, and edges with four OHfMg4B square pyramids. The corner-sharing octahedral tilt angles are 5°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5B square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5B square pyramids. The corner-sharing octahedral tilt angles are 0°. In the third O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedral tilt angles are 0°. In the fourth O site, O is bonded to five Mg and one B atom to form distorted OMg5B square pyramids that share corners with four OHfMg5 octahedra, corners with two equivalent OMg5B square pyramids, edges with eight OMg6 octahedra, and edges with four OHfMg4B square pyramids. The corner-sharing octahedra tilt angles range from 2–4°. In the fifth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with two equivalent OMg6 octahedra, corners with two equivalent OMg5B square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OHfMg4B square pyramids. The corner-sharing octahedral tilt angles are 1°. In the sixth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5B square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5B square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. In the seventh O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra, edges with eight OMg6 octahedra, and edges with three OMg5B square pyramids. 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 OMg6 octahedra, edges with nine OHfMg5 octahedra, and edges with three OMg5B square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. In the tenth O site, O is bonded to four Mg, one Hf, and one B atom to form distorted OHfMg4B square pyramids that share corners with four OMg6 octahedra, corners with two equivalent OHfMg4B square pyramids, edges with seven OHfMg5 octahedra, and edges with four OMg5B square pyramids. The corner-sharing octahedra tilt angles range from 7–8°. In the eleventh O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OHfMg4B square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5B square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. In the twelfth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OHfMg4B square pyramids, edges with nine OHfMg5 octahedra, and edges with two OMg5B square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. In the thirteenth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the fourteenth O site, O is bonded to five Mg and one B atom to form distorted OMg5B square pyramids that share corners with four OHfMg5 octahedra, corners with two equivalent OMg5B square pyramids, edges with eight OMg6 octahedra, and edges with four OMg5B square pyramids. The corner-sharing octahedra tilt angles range from 3–5°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with four OHfMg5 octahedra, corners with two equivalent OMg5B square pyramids, edges with nine OMg6 octahedra, and edges with two equivalent OHfMg4B square pyramids. The corner-sharing octahedra tilt angles range from 0–9°. In the sixteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5B square pyramids, edges with ten OMg6 octahedra, and edges with two OMg5B square pyramids. The corner-sharing octahedral tilt angles are 0°. In the seventeenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on RbNaMg30O31 by Materials Project

RbNaMg30O31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Rb1+ is bonded to six O2- atoms to form RbO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 trigonal bipyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Rb–O bond distances ranging from 2.38–2.46 Å. Na1+ is bonded to six O2- atoms to form NaO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 trigonal bipyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Na–O bond distances ranging from 2.22–2.32 Å. There are sixteen inequivalent Mg2+ sites. In the first Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 trigonal bipyramids that share corners with two equivalent RbO6 octahedra, corners with two equivalent NaO6 octahedra, corners with three MgO5 square pyramids, corners with two equivalent MgO5 trigonal bipyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 8–18°. There are a spread of Mg–O bond distances ranging from 1.92–2.10 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent RbO6 octahedra, corners with two equivalent NaO6 octahedra, corners with two equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Mg–O bond distances ranging from 1.94–2.26 Å. In the third Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent NaO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.02–2.25 Å. In the fourth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, corners with three MgO5 trigonal bipyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 8°. There are a spread of Mg–O bond distances ranging from 1.97–2.12 Å. In the fifth Mg2+ site, Mg2+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.09–2.16 Å. In the sixth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent RbO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 1.89–2.26 Å. In the seventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one RbO6 octahedra, an edgeedge with one NaO6 octahedra, edges with seven MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and edges with two MgO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 3–15°. There are a spread of Mg–O bond distances ranging from 2.13–2.24 Å. In the eighth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, edges with two MgO5 square pyramids, and an edgeedge with one MgO5 trigonal bipyramid. The corner-sharing octahedra tilt angles range from 1–6°. There are a spread of Mg–O bond distances ranging from 2.13–2.19 Å. In the ninth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with two MgO5 square pyramids, corners with three MgO5 trigonal bipyramids, an edgeedge with one NaO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 9–12°. There are a spread of Mg–O bond distances ranging from 1.98–2.16 Å. In the tenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one RbO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 2–11°. There are a spread of Mg–O bond distances ranging from 2.10–2.26 Å. In the eleventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one NaO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one MgO5 trigonal bipyramid. The corner-sharing octahedra tilt angles range from 3–9°. There are a spread of Mg–O bond distances ranging from 2.14–2.26 Å. In the twelfth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one RbO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–14°. There are a spread of Mg–O bond distances ranging from 2.13–2.24 Å. In the thirteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 trigonal bipyramids, an edgeedge with one NaO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–7°. There are a spread of Mg–O bond distances ranging from 2.13–2.20 Å. In the fourteenth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 trigonal bipyramids that share corners with four MgO6 octahedra, corners with three MgO5 square pyramids, corners with two MgO5 trigonal bipyramids, an edgeedge with one RbO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 7–20°. There are a spread of Mg–O bond distances ranging from 1.99–2.17 Å. In the fifteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one NaO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–8°. There are a spread of Mg–O bond distances ranging from 2.15–2.21 Å. In the sixteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 trigonal bipyramids, an edgeedge with one RbO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one MgO5 trigonal bipyramid. The corner-sharing octahedra tilt angles range from 2–12°. There are a spread of Mg–O bond distances ranging from 2.14–2.44 Å. There are seventeen inequivalent O2- sites. In the first O2- site, O2- is bonded to one Na1+ and five Mg2+ atoms to form a mixture of edge and corner-sharing ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the second O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six ONaMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the third O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form a mixture of distorted edge and corner-sharing ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the fourth O2- site, O2- is bonded to one Na1+ and five Mg2+ atoms to form ONaMg5 octahedra that share corners with six ONaMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the fifth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with four ONaMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 5–6°. In the sixth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the seventh O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form ORbMg5 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the eighth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–13°. In the ninth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. In the tenth O2- site, O2- is bonded to one Na1+ and five Mg2+ atoms to form ONaMg5 octahedra that share corners with six ORbMg5 octahedra and edges with eleven ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–15°. In the eleventh O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form ORbMg5 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. In the twelfth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–15°. In the thirteenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fourteenth O2- site, O2- is bonded to one Na1+ and five Mg2+ atoms to form ONaMg5 octahedra that share corners with six ORbMg5 octahedra and edges with twelve ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the fifteenth O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form a mixture of distorted edge and corner-sharing ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 5–23°. In the sixteenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the seventeenth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 3–21°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Li32Mn11Cr5O48 by Materials Project

Li32Cr5Mn11O48 is beta Polonium-derived structured and crystallizes in the monoclinic C2 space group. The structure is three-dimensional. there are seventeen inequivalent Li sites. In the first Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–10°. There are a spread of Li–O bond distances ranging from 2.06–2.21 Å. In the second Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. There are a spread of Li–O bond distances ranging from 2.04–2.21 Å. In the third Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent CrO6 octahedra, edges with three equivalent MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are a spread of Li–O bond distances ranging from 2.07–2.14 Å. In the fourth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–8°. There are a spread of Li–O bond distances ranging from 2.03–2.20 Å. In the fifth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent CrO6 octahedra, edges with three equivalent MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are a spread of Li–O bond distances ranging from 2.07–2.12 Å. In the sixth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. There are a spread of Li–O bond distances ranging from 2.04–2.20 Å. In the seventh Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six MnO6 octahedra. The corner-sharing octahedra tilt angles range from 8–9°. There are four shorter (2.09 Å) and two longer (2.11 Å) Li–O bond lengths. In the eighth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with two LiO6 octahedra, corners with two CrO6 octahedra, corners with two MnO6 octahedra, edges with two CrO6 octahedra, edges with two MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–9°. There are a spread of Li–O bond distances ranging from 2.05–2.21 Å. In the ninth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with two LiO6 octahedra, corners with two CrO6 octahedra, corners with two MnO6 octahedra, edges with two CrO6 octahedra, edges with two MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. There are a spread of Li–O bond distances ranging from 2.03–2.20 Å. In the tenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–9°. There are a spread of Li–O bond distances ranging from 2.06–2.21 Å. In the eleventh Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six MnO6 octahedra. The corner-sharing octahedra tilt angles range from 8–9°. There are four shorter (2.09 Å) and two longer (2.11 Å) Li–O bond lengths. In the twelfth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–10°. There are a spread of Li–O bond distances ranging from 2.07–2.22 Å. In the thirteenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–9°. There are a spread of Li–O bond distances ranging from 2.06–2.22 Å. In the fourteenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–10°. There are a spread of Li–O bond distances ranging from 2.06–2.21 Å. In the fifteenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–10°. There are a spread of Li–O bond distances ranging from 2.07–2.21 Å. In the sixteenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with two LiO6 octahedra, corners with two CrO6 octahedra, corners with two MnO6 octahedra, edges with two CrO6 octahedra, edges with two MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–10°. There are a spread of Li–O bond distances ranging from 2.06–2.19 Å. In the seventeenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent CrO6 octahedra, edges with three equivalent MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are a spread of Li–O bond distances ranging from 2.07–2.12 Å. There are three inequivalent Cr sites. In the first Cr site, Cr is bonded to six O atoms to form CrO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent MnO6 octahedra, and edges with nine LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–8°. There are a spread of Cr–O bond distances ranging from 1.90–1.98 Å. In the second Cr site, Cr is bonded to six O atoms to form CrO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent MnO6 octahedra, and edges with nine LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–8°. There are a spread of Cr–O bond distances ranging from 1.91–1.99 Å. In the third Cr site, Cr is bonded to six O atoms to form CrO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent MnO6 octahedra, and edges with nine LiO6 octahedra. The corner-sharing octahedral tilt angles are 8°. There are a spread of Cr–O bond distances ranging from 1.90–1.98 Å. There are seven inequivalent Mn sites. In the first Mn site, Mn is bonded to six O atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent MnO6 octahedra, and edges with nine LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–8°. There is four shorter (1.94 Å) and two longer (1.95 Å) Mn–O bond length. In the second Mn site, Mn is bonded to six O atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent MnO6 octahedra, and edges with nine LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–8°. There is four shorter (1.94 Å) and two longer (1.95 Å) Mn–O bond length. In the third Mn site, Mn is bonded to six O atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent CrO6 octahedra, and edges with nine LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. There is two shorter (1.93 Å) and four longer (1.95 Å) Mn–O bond length. In the fourth Mn site, Mn is bonded to six O atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent CrO6 octahedra, and edges with nine LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. There are a spread of Mn–O bond distances ranging from 1.93–1.95 Å. In the fifth Mn site, Mn is bonded to six O atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent CrO6 octahedra, and edges with nine LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. There is two shorter (1.93 Å) and four longer (1.95 Å) Mn–O bond length. In the sixth Mn site, Mn is bonded to six O atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent MnO6 octahedra, and edges with nine LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–8°. There is two shorter (1.94 Å) and four longer (1.95 Å) Mn–O bond length. In the seventh Mn site, Mn is bonded to six O atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent MnO6 octahedra, and edges with nine LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–8°. There is two shorter (1.94 Å) and four longer (1.95 Å) Mn–O bond length. There are twenty-four inequivalent O sites. In the first O site, O is bonded to four Li, one Cr, and one Mn atom to form a mixture of edge and corner-sharing OLi4MnCr octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the second O site, O is bonded to four Li, one Cr, and one Mn atom to form a mixture of edge and corner-sharing OLi4MnCr octahedra. The corner-sharing octahedra tilt angles range from 1–8°. In the third O site, O is bonded to four Li and two Mn atoms to form a mixture of edge and corner-sharing OLi4Mn2 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the fourth O site, O is bonded to four Li and two Mn atoms to form a mixture of edge and corner-sharing OLi4Mn2 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the fifth O site, O is bonded to four Li, one Cr, and one Mn atom to form a mixture of edge and corner-sharing OLi4MnCr octahedra. The corner-sharing octahedra tilt angles range from 1–8°. In the sixth O site, O is bonded to four Li and two Mn atoms to form a mixture of edge and corner-sharing OLi4Mn2 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the seventh O site, O is bonded to four Li and two Mn atoms to form a mixture of edge and corner-sharing OLi4Mn2 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the eighth O site, O is bonded to four Li, one Cr, and one Mn atom to form a mixture of edge and corner-sharing OLi4MnCr octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the ninth O site, O is bonded to four Li, one Cr, and one Mn atom to form a mixture of edge a

36 MATERIALS SCIENCE↗