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DOE OSTI2020

Materials Data on KRbMg30O31 by Materials Project

RbKMg30O31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Rb1+ is bonded in a 4-coordinate geometry to four O2- atoms. There are two shorter (2.33 Å) and two longer (2.57 Å) Rb–O bond lengths. K1+ is bonded to six O2- atoms to form KO6 octahedra that share corners with four MgO6 octahedra, 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 2.28–2.40 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 1.97–2.23 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, 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 Mg–O bond distances ranging from 2.00–2.29 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 0–2°. There are a spread of Mg–O bond distances ranging from 1.90–2.30 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 four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 10°. There are a spread of Mg–O bond distances ranging from 1.93–2.14 Å. In the fifth Mg2+ site, Mg2+ is bonded to six O2- 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 2.07–2.21 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 0–3°. There are a spread of Mg–O bond distances ranging from 2.04–2.23 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, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–10°. There are a spread of Mg–O bond distances ranging from 2.13–2.20 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 0–7°. There are a spread of Mg–O bond distances ranging from 2.12–2.20 Å. In the ninth Mg2+ site, Mg2+ is bonded to five O2- atoms to form distorted MgO5 square pyramids that share corners with four MgO6 octahedra, 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 11–12°. There are a spread of Mg–O bond distances ranging from 1.92–2.17 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 2–5°. There are a spread of Mg–O bond distances ranging from 2.12–2.23 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 an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 3–15°. There are a spread of Mg–O bond distances ranging from 2.07–2.31 Å. In the twelfth Mg2+ site, Mg2+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–3°. There are a spread of Mg–O bond distances ranging from 2.15–2.19 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 0–11°. There are a spread of Mg–O bond distances ranging from 2.10–2.26 Å. In the fourteenth Mg2+ site, Mg2+ is bonded to five O2- atoms to form distorted MgO5 square pyramids that share corners with four MgO6 octahedra, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 4–11°. There are a spread of Mg–O bond distances ranging from 1.90–2.17 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 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 2.14–2.20 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, edges with ten MgO6 octahedra, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 3–7°. There are a spread of Mg–O bond distances ranging from 2.10–2.30 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 corner and edge-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 corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fourth O2- site, O2- is bonded to one K1+ and five Mg2+ atoms to form OKMg5 octahedra that share corners with four OKMg5 octahedra, corners with two equivalent OMg5 square pyramids, 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 five Mg2+ atoms to form OMg5 square pyramids that share corners with eight ORbMg5 octahedra and edges with eight OMg6 octahedra. The corner-sharing octahedra tilt angles range from 7–88°. In the sixth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the seventh O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5 square pyramids, and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. 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 1–17°. In the ninth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra, edges with eleven OKMg5 octahedra, and an edgeedge with one OMg5 square pyramid. The corner-sharing octahedra tilt angles range from 0–6°. In the tenth O2- site, O2- is bonded to one Rb1+, one K1+, and four Mg2+ atoms to form OKRbMg4 octahedra that share corners with six OMg6 octahedra, a cornercorner with one OMg5 square pyramid, and edges with ten OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–53°. In the eleventh O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of corner and edge-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, edges with ten OKMg5 octahedra, and an edgeedge with one OMg5 square pyramid. The corner-sharing octahedra tilt angles range from 2–21°. In the thirteenth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of corner and edge-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 ORbMg5 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 3–10°. In the fifteenth O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form distorted ORbMg5 octahedra that share corners with six ORbMg5 octahedra, a cornercorner with one OMg5 square pyramid, and edges with ten OMg6 octahedra. The corner-sharing octahedra tilt angles range from 7–46°. 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 2–7°. In the seventeenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six ORbMg5 octahedra, edges with ten OMg6 octahedra, and an edgeedge with one OMg5 square pyramid. The corner-sharing octahedra tilt angles range from 3–13°.

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 in a 4-coordinate geometry to four O2- atoms. There are two shorter (2.40 Å) and two longer (2.50 Å) Rb–O bond lengths. Na1+ is bonded to six O2- atoms to form NaO6 octahedra that share corners with four MgO6 octahedra, 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 Na–O bond distances ranging from 2.11–2.31 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 NaO6 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 2.03–2.19 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, 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 Mg–O bond distances ranging from 1.98–2.26 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 octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 1.96–2.27 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 four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 10°. There are a spread of Mg–O bond distances ranging from 1.94–2.13 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 0–3°. There are a spread of Mg–O bond distances ranging from 2.06–2.19 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 0–3°. There are a spread of Mg–O bond distances ranging from 2.03–2.23 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 NaO6 octahedra, edges with eight 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 2.12–2.21 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 1–7°. There are a spread of Mg–O bond distances ranging from 2.11–2.19 Å. In the ninth Mg2+ site, Mg2+ is bonded to five O2- atoms to form distorted MgO5 square pyramids that share corners with four MgO6 octahedra, corners with four MgO5 square pyramids, an edgeedge with one NaO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 4–12°. There are a spread of Mg–O bond distances ranging from 1.90–2.15 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 1–4°. There are a spread of Mg–O bond distances ranging from 2.10–2.22 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, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 3–12°. There are a spread of Mg–O bond distances ranging from 2.05–2.30 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 NaO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–8°. There are a spread of Mg–O bond distances ranging from 2.09–2.22 Å. In the fourteenth Mg2+ site, Mg2+ is bonded to five O2- atoms to form distorted MgO5 square pyramids that share corners with four MgO6 octahedra, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 5–10°. There are a spread of Mg–O bond distances ranging from 1.91–2.14 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 NaO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. There are a spread of Mg–O bond distances ranging from 2.14–2.19 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, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 3–6°. There are a spread of Mg–O bond distances ranging from 2.08–2.27 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 0–6°. 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 Na1+ and five Mg2+ atoms to form ONaMg5 octahedra that share corners with four ONaMg5 octahedra, corners with two equivalent OMg5 square pyramids, and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the fifth O2- site, O2- is bonded to five Mg2+ atoms to form distorted OMg5 square pyramids that share corners with eight ORbMg5 octahedra and edges with eight OMg6 octahedra. The corner-sharing octahedra tilt angles range from 5–85°. 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 OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5 square pyramids, and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. 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 1–18°. In the ninth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra, edges with eleven ONaMg5 octahedra, and an edgeedge with one OMg5 square pyramid. The corner-sharing octahedra tilt angles range from 1–6°. In the tenth O2- site, O2- is bonded to one Rb1+, one Na1+, and four Mg2+ atoms to form ORbNaMg4 octahedra that share corners with six OMg6 octahedra, a cornercorner with one OMg5 square pyramid, and edges with ten ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–42°. 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, edges with ten ONaMg5 octahedra, and an edgeedge with one OMg5 square pyramid. The corner-sharing octahedra tilt angles range from 0–16°. 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 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 2–9°. In the fifteenth O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form distorted ORbMg5 octahedra that share corners with six ORbMg5 octahedra, a cornercorner with one OMg5 square pyramid, and edges with ten OMg6 octahedra. The corner-sharing octahedra tilt angles range from 6–39°. 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 2–5°. In the seventeenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six ORbMg5 octahedra, edges with ten OMg6 octahedra, and an edgeedge with one OMg5 square pyramid. The corner-sharing octahedra tilt angles range from 2–13°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Li9Mn2Co5O16 by Materials Project

Li9Mn2Co5O16 is Caswellsilverite-derived structured and crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are nine inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent MnO6 octahedra, corners with three equivalent CoO6 octahedra, an edgeedge with one CoO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 2–10°. There are a spread of Li–O bond distances ranging from 2.15–2.39 Å. In the second Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CoO6 octahedra, edges with four CoO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 1–10°. There are a spread of Li–O bond distances ranging from 2.08–2.44 Å. In the third Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CoO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 3–8°. There are a spread of Li–O bond distances ranging from 2.11–2.24 Å. In the fourth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent MnO6 octahedra, corners with three equivalent CoO6 octahedra, edges with three MnO6 octahedra, edges with three CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–7°. There are a spread of Li–O bond distances ranging from 2.09–2.20 Å. In the fifth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent LiO6 octahedra, corners with three equivalent MnO6 octahedra, edges with two equivalent CoO6 octahedra, edges with three MnO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–16°. There are a spread of Li–O bond distances ranging from 2.02–2.22 Å. In the sixth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent LiO6 octahedra, corners with three equivalent CoO6 octahedra, edges with five CoO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–18°. There are a spread of Li–O bond distances ranging from 2.02–2.23 Å. In the seventh Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CoO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 2–8°. There are a spread of Li–O bond distances ranging from 2.10–2.21 Å. In the eighth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent MnO6 octahedra, corners with three equivalent CoO6 octahedra, edges with three MnO6 octahedra, edges with three CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 2–9°. There are a spread of Li–O bond distances ranging from 2.10–2.18 Å. In the ninth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with four equivalent CoO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–18°. There are a spread of Li–O bond distances ranging from 2.09–2.15 Å. There are two inequivalent Mn+4.50+ sites. In the first Mn+4.50+ site, Mn+4.50+ is bonded to six O2- atoms to form MnO6 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 6–9°. There are a spread of Mn–O bond distances ranging from 1.96–2.24 Å. In the second Mn+4.50+ site, Mn+4.50+ is bonded to six O2- atoms to form MnO6 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 6–10°. There are a spread of Mn–O bond distances ranging from 1.97–2.23 Å. There are five inequivalent Co+2.80+ sites. In the first Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 3–9°. There are a spread of Co–O bond distances ranging from 1.94–2.20 Å. In the second Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. There are four shorter (2.00 Å) and two longer (2.10 Å) Co–O bond lengths. In the third Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent CoO6 octahedra, and edges with ten LiO6 octahedra. The corner-sharing octahedra tilt angles range from 1–7°. There is two shorter (1.80 Å) and four longer (1.94 Å) Co–O bond length. In the fourth Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 2–10°. There are a spread of Co–O bond distances ranging from 2.01–2.10 Å. In the fifth Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 3–6°. There are a spread of Co–O bond distances ranging from 2.02–2.09 Å. There are sixteen inequivalent O2- sites. In the first O2- site, O2- is bonded to three Li1+ and three Mn+4.50+ atoms to form OLi3Mn3 octahedra that share corners with six OLi5Co octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the second O2- site, O2- is bonded to five Li1+ and one Co+2.80+ atom to form a mixture of distorted corner and edge-sharing OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the third O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of corner and edge-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fourth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of corner and edge-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fifth O2- site, O2- is bonded to three Li1+ and three Mn+4.50+ atoms to form OLi3Mn3 octahedra that share corners with six OLi4Co2 octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. In the sixth O2- site, O2- is bonded to four Li1+ and two equivalent Co+2.80+ atoms to form OLi4Co2 octahedra that share corners with six OLi4Co2 octahedra and edges with twelve OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the seventh O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of corner and edge-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the eighth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of corner and edge-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the ninth O2- site, O2- is bonded to five Li1+ and one Co+2.80+ atom to form a mixture of distorted corner and edge-sharing OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the tenth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of corner and edge-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the eleventh O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of corner and edge-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the twelfth O2- site, O2- is bonded to three Li1+ and three Mn+4.50+ atoms to form a mixture of corner and edge-sharing OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the thirteenth O2- site, O2- is bonded to four Li1+ and two equivalent Co+2.80+ atoms to form a mixture of corner and edge-sharing OLi4Co2 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the fourteenth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form OLi3Co3 octahedra that share corners with six OLi4Co2 octahedra and edges with twelve OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fifteenth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of corner and edge-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the sixteenth O2- site, O2- is bonded to three Li1+ and three Mn+4.50+ atoms to form a mixture of corner and edge-sharing OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 1–4°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Li9Mn2Co5O16 by Materials Project

Li9Mn2Co5O16 is Caswellsilverite-derived structured and crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are nine inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent MnO6 octahedra, corners with three equivalent CoO6 octahedra, an edgeedge with one CoO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 2–11°. There are a spread of Li–O bond distances ranging from 2.15–2.30 Å. In the second Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CoO6 octahedra, edges with four CoO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. There are a spread of Li–O bond distances ranging from 2.09–2.38 Å. In the third Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CoO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 3–6°. There are four shorter (2.13 Å) and two longer (2.18 Å) Li–O bond lengths. In the fourth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent MnO6 octahedra, corners with three equivalent CoO6 octahedra, edges with three MnO6 octahedra, edges with three CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 2–10°. There are a spread of Li–O bond distances ranging from 2.09–2.21 Å. In the fifth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent LiO6 octahedra, corners with three equivalent MnO6 octahedra, edges with two equivalent CoO6 octahedra, edges with three MnO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–14°. There are a spread of Li–O bond distances ranging from 2.02–2.24 Å. In the sixth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent LiO6 octahedra, corners with three equivalent CoO6 octahedra, edges with five CoO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–16°. There are a spread of Li–O bond distances ranging from 2.05–2.21 Å. In the seventh Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CoO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 4–5°. There are a spread of Li–O bond distances ranging from 2.12–2.18 Å. In the eighth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent MnO6 octahedra, corners with three equivalent CoO6 octahedra, edges with three MnO6 octahedra, edges with three CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–8°. There are a spread of Li–O bond distances ranging from 2.11–2.23 Å. In the ninth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with four equivalent CoO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–16°. There are a spread of Li–O bond distances ranging from 2.09–2.12 Å. There are two inequivalent Mn+4.50+ sites. In the first Mn+4.50+ site, Mn+4.50+ is bonded to six O2- atoms to form MnO6 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 7–10°. There are a spread of Mn–O bond distances ranging from 1.96–2.22 Å. In the second Mn+4.50+ site, Mn+4.50+ is bonded to six O2- atoms to form MnO6 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 6–11°. There are a spread of Mn–O bond distances ranging from 1.97–2.21 Å. There are five inequivalent Co+2.80+ sites. In the first Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 3–5°. There are a spread of Co–O bond distances ranging from 2.01–2.10 Å. In the second Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 3–5°. There are a spread of Co–O bond distances ranging from 2.00–2.08 Å. In the third Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent CoO6 octahedra, and edges with ten LiO6 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. There are a spread of Co–O bond distances ranging from 1.80–1.95 Å. In the fourth Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 3–5°. There are a spread of Co–O bond distances ranging from 2.02–2.08 Å. In the fifth Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 2–6°. There are a spread of Co–O bond distances ranging from 2.02–2.08 Å. There are sixteen inequivalent O2- sites. In the first O2- site, O2- is bonded to three Li1+ and three Mn+4.50+ atoms to form OLi3Mn3 octahedra that share corners with six OLi5Co octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the second O2- site, O2- is bonded to five Li1+ and one Co+2.80+ atom to form a mixture of distorted edge and corner-sharing OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the third O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the fourth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the fifth O2- site, O2- is bonded to three Li1+ and three Mn+4.50+ atoms to form a mixture of edge and corner-sharing OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the sixth O2- site, O2- is bonded to four Li1+ and two equivalent Co+2.80+ atoms to form OLi4Co2 octahedra that share corners with six OLi4Co2 octahedra and edges with twelve OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the seventh O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the eighth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the ninth O2- site, O2- is bonded to five Li1+ and one Co+2.80+ atom to form a mixture of edge and corner-sharing OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the tenth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the eleventh O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3Co3 octahedra. The corner-sharing octahedral tilt angles are 1°. In the twelfth O2- site, O2- is bonded to three Li1+ and three Mn+4.50+ atoms to form OLi3Mn3 octahedra that share corners with six OLi3Co3 octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the thirteenth O2- site, O2- is bonded to four Li1+ and two equivalent Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi4Co2 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fourteenth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form OLi3Co3 octahedra that share corners with six OLi4Co2 octahedra and edges with twelve OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fifteenth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the sixteenth O2- site, O2- is bonded to three Li1+ and three Mn+4.50+ atoms to form a mixture of edge and corner-sharing OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 0–4°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ca17(Y7S19)2 by Materials Project

Ca17(Y7S19)2 crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are seventeen inequivalent Ca2+ sites. In the first Ca2+ site, Ca2+ is bonded to six S2- atoms to form CaS6 octahedra that share corners with three CaS6 octahedra, edges with two equivalent YS6 octahedra, and edges with seven CaS6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Ca–S bond distances ranging from 2.79–2.88 Å. In the second Ca2+ site, Ca2+ is bonded to six S2- atoms to form CaS6 octahedra that share corners with five YS6 octahedra, edges with four CaS6 octahedra, and edges with eight YS6 octahedra. The corner-sharing octahedra tilt angles range from 1–6°. There are a spread of Ca–S bond distances ranging from 2.75–2.87 Å. In the third Ca2+ site, Ca2+ is bonded to six S2- atoms to form CaS6 octahedra that share a cornercorner with one CaS6 octahedra, corners with five YS6 octahedra, edges with four CaS6 octahedra, and edges with eight YS6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Ca–S bond distances ranging from 2.82–2.88 Å. In the fourth Ca2+ site, Ca2+ is bonded to six S2- atoms to form CaS6 octahedra that share a cornercorner with one CaS6 octahedra, corners with five YS6 octahedra, edges with four CaS6 octahedra, and edges with eight YS6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Ca–S bond distances ranging from 2.82–2.86 Å. In the fifth Ca2+ site, Ca2+ is bonded to six S2- atoms to form CaS6 octahedra that share corners with six YS6 octahedra, edges with six CaS6 octahedra, and edges with six YS6 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. There are a spread of Ca–S bond distances ranging from 2.84–2.87 Å. In the sixth Ca2+ site, Ca2+ is bonded to six S2- atoms to form CaS6 octahedra that share a cornercorner with one CaS6 octahedra, corners with five YS6 octahedra, edges with six CaS6 octahedra, and edges with six YS6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Ca–S bond distances ranging from 2.83–2.85 Å. In the seventh Ca2+ site, Ca2+ is bonded to six S2- atoms to form CaS6 octahedra that share corners with six CaS6 octahedra, edges with two equivalent YS6 octahedra, and edges with ten CaS6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. There are a spread of Ca–S bond distances ranging from 2.74–2.89 Å. In the eighth Ca2+ site, Ca2+ is bonded to six S2- atoms to form CaS6 octahedra that share corners with three CaS6 octahedra, corners with three YS6 octahedra, edges with three equivalent YS6 octahedra, and edges with nine CaS6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Ca–S bond distances ranging from 2.76–2.87 Å. In the ninth Ca2+ site, Ca2+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing CaS6 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Ca–S bond distances ranging from 2.73–2.93 Å. In the tenth Ca2+ site, Ca2+ is bonded to six S2- atoms to form CaS6 octahedra that share a cornercorner with one YS6 octahedra, corners with five CaS6 octahedra, and edges with twelve CaS6 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Ca–S bond distances ranging from 2.73–2.97 Å. In the eleventh Ca2+ site, Ca2+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing CaS6 octahedra. The corner-sharing octahedra tilt angles range from 2–4°. There are a spread of Ca–S bond distances ranging from 2.74–2.93 Å. In the twelfth Ca2+ site, Ca2+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing CaS6 octahedra. The corner-sharing octahedra tilt angles range from 2–4°. There are a spread of Ca–S bond distances ranging from 2.73–2.93 Å. In the thirteenth Ca2+ site, Ca2+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing CaS6 octahedra. The corner-sharing octahedra tilt angles range from 2–4°. There are a spread of Ca–S bond distances ranging from 2.76–2.93 Å. In the fourteenth Ca2+ site, Ca2+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing CaS6 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Ca–S bond distances ranging from 2.74–2.93 Å. In the fifteenth Ca2+ site, Ca2+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing CaS6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Ca–S bond distances ranging from 2.74–2.91 Å. In the sixteenth Ca2+ site, Ca2+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing CaS6 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Ca–S bond distances ranging from 2.77–2.92 Å. In the seventeenth Ca2+ site, Ca2+ is bonded to six S2- atoms to form CaS6 octahedra that share a cornercorner with one YS6 octahedra, corners with five CaS6 octahedra, and edges with ten CaS6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. There are a spread of Ca–S bond distances ranging from 2.79–2.95 Å. There are fourteen inequivalent Y3+ sites. In the first Y3+ site, Y3+ is bonded to six S2- atoms to form YS6 octahedra that share a cornercorner with one CaS6 octahedra, edges with two equivalent CaS6 octahedra, and edges with four YS6 octahedra. The corner-sharing octahedral tilt angles are 4°. There are a spread of Y–S bond distances ranging from 2.70–2.75 Å. In the second Y3+ site, Y3+ is bonded to six S2- atoms to form edge-sharing YS6 octahedra. There are a spread of Y–S bond distances ranging from 2.71–2.73 Å. In the third Y3+ site, Y3+ is bonded to six S2- atoms to form edge-sharing YS6 octahedra. There are a spread of Y–S bond distances ranging from 2.71–2.73 Å. In the fourth Y3+ site, Y3+ is bonded to six S2- atoms to form edge-sharing YS6 octahedra. There are five shorter (2.72 Å) and one longer (2.73 Å) Y–S bond lengths. In the fifth Y3+ site, Y3+ is bonded to six S2- atoms to form edge-sharing YS6 octahedra. There are a spread of Y–S bond distances ranging from 2.72–2.74 Å. In the sixth Y3+ site, Y3+ is bonded to six S2- atoms to form distorted YS6 octahedra that share corners with three YS6 octahedra, edges with two equivalent CaS6 octahedra, and edges with seven YS6 octahedra. The corner-sharing octahedra tilt angles range from 1–11°. There are a spread of Y–S bond distances ranging from 2.43–3.15 Å. In the seventh Y3+ site, Y3+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing YS6 octahedra. The corner-sharing octahedral tilt angles are 9°. There are a spread of Y–S bond distances ranging from 2.61–3.12 Å. In the eighth Y3+ site, Y3+ is bonded to six S2- atoms to form YS6 octahedra that share corners with three CaS6 octahedra, corners with three YS6 octahedra, edges with three equivalent CaS6 octahedra, and edges with seven YS6 octahedra. The corner-sharing octahedra tilt angles range from 3–11°. There are a spread of Y–S bond distances ranging from 2.58–2.92 Å. In the ninth Y3+ site, Y3+ is bonded to six S2- atoms to form YS6 octahedra that share corners with two YS6 octahedra, corners with four CaS6 octahedra, edges with six CaS6 octahedra, and edges with six YS6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Y–S bond distances ranging from 2.76–2.82 Å. In the tenth Y3+ site, Y3+ is bonded to six S2- atoms to form YS6 octahedra that share corners with three CaS6 octahedra, corners with three YS6 octahedra, edges with five CaS6 octahedra, and edges with seven YS6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Y–S bond distances ranging from 2.79–2.84 Å. In the eleventh Y3+ site, Y3+ is bonded to six S2- atoms to form YS6 octahedra that share corners with three CaS6 octahedra, corners with three YS6 octahedra, edges with five CaS6 octahedra, and edges with seven YS6 octahedra. The corner-sharing octahedral tilt angles are 1°. There are two shorter (2.82 Å) and four longer (2.83 Å) Y–S bond lengths. In the twelfth Y3+ site, Y3+ is bonded to six S2- atoms to form YS6 octahedra that share a cornercorner with one YS6 octahedra, corners with five CaS6 octahedra, edges with six CaS6 octahedra, and edges with six YS6 octahedra. The corner-sharing octahedral tilt angles are 1°. There are a spread of Y–S bond distances ranging from 2.80–2.82 Å. In the thirteenth Y3+ site, Y3+ is bonded to six S2- atoms to form YS6 octahedra that share corners with six CaS6 octahedra, edges with four YS6 octahedra, and edges with eight CaS6 octahedra. The corner-sharing octahedral tilt angles are 1°. There are a spread of Y–S bond distances ranging from 2.77–2.81 Å. In the fourteenth Y3+ site, Y3+ is bonded to six S2- atoms to form YS6 octahedra that share corners with six CaS6 octahedra, edges with six CaS6 octahedra, and edges with six YS6 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. There are three shorter (2.81 Å) and three longer (2.82 Å) Y–S bond lengths. There are thirty-eight inequivalent S2- sites. In the first S2- site, S2- is bonded in a rectangular see-saw-like geometry to three Ca2+ and one Y3+ atom. In the second S2- site, S2- is bonded in a distorted T-shaped geometry to three Y3+ atoms. In the third S2- site, S2- is bonded in a distorted T-shaped geometry to one Ca2+ and two equivalent Y3+ atoms. In the fourth S2- site, S2- is bonded in a distorted T-shaped geometry to three Y3+ atoms. In the fifth S2- site, S2- is bonded in a distorted T-shaped geometry to three Y3+ atoms. In the sixth S2- site, S2- is bonded in a distorted T-shaped geometry to three Y3+ atoms. In the seventh S2- site, S2- is bonded in a distorted T-shaped geometry to three Y3+ atoms. In the eighth S2- site, S2- is bonded in a distorted T-shaped geometry to three Y3+ atoms. In the ninth S2- site, S2- is bonded in a distorted T-shaped geometry to three Y3+ atoms. In the tenth S2- site, S2- is bonded in a distorted T-shaped geometry to three Y3+ atoms. In the eleventh S2- site, S2- is bonded in a distorted T-shaped geometry to three Y3+ atoms. In the twelfth S2- site, S2- is bonded in a 3-coordinate geometry to three Y3+ atoms. In the thirteenth S2- site, S2- is bonded in a distorted T-shaped geometry to three Y3+ atoms. In the fourteenth S2- site, S2- is bonded to one Ca2+ and four Y3+ atoms to form SCaY4 square pyramids that share corners with three SCa3Y3 octahedra, edges with five SCa3Y3 octahedra, and edges with two equivalent SCaY4 square pyramids. The corner-sharing octahedra tilt angles range from 1–9°. In the fifteenth S2- site, S2- is bonded in a distorted see-saw-like geometry to four Y3+ atoms. In the sixteenth S2- site, S2- is bonded to three Ca2+ and three Y3+ atoms to form SCa3Y3 octahedra that share corners with five SCa3Y3 octahedra, edges with ten SCa3Y3 octahedra, and edges with two equivalent SCaY4 square pyramids. The corner-sharing octahedra tilt angles range from 1–3°. In the seventeenth S2- site, S2- is bonded to two equivalent Ca2+ and four Y3+ atoms to form SCa2Y4 octahedra that share corners with three SCa3Y3 octahedra, corners with two equivalent SCaY4 square pyramids, edges with seven SCa3Y3 octahedra, and edges with three equivalent SCaY4 square pyramids. The corner-sharing octahedral tilt angles are 1°. In the eighteenth S2- site, S2- is bonded to two equivalent Ca2+ and four Y3+ atoms to form a mixture of edge and corner-sharing SCa2Y4 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the nineteenth S2- site, S2- is bonded to three Ca2+ and three Y3+ atoms to form SCa3Y3 octahedra that share corners with five SCa2Y4 octahedra, a cornercorner with one SCaY4 square pyramid, and edges with twelve SCa3Y3 octahedra. The corner-sharing octahedra tilt angles range from 0–3°.

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 in a 4-coordinate geometry to four Mg2+ and five O2- atoms. There are two shorter (2.75 Å) and two longer (2.76 Å) Rb–Mg bond lengths. There are four shorter (2.47 Å) and one longer (2.88 Å) Rb–O bond lengths. Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with four MgO6 octahedra, edges with ten MgO6 octahedra, and edges with two equivalent MgRbO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Li–O bond distances ranging from 1.97–2.35 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 0–4°. There are a spread of Mg–O bond distances ranging from 2.06–2.17 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, edges with ten MgO6 octahedra, and edges with two equivalent MgRbO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 1.98–2.25 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 MgRbO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 1.99–2.24 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 four MgRbO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 10–11°. 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 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 2.07–2.17 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 MgRbO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.03–2.22 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 LiO6 octahedra, edges with eight MgO6 octahedra, and edges with two MgRbO5 square pyramids. The corner-sharing octahedra tilt angles range from 2–10°. There are a spread of Mg–O bond distances ranging from 2.10–2.22 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 1–6°. There are a spread of Mg–O bond distances ranging from 2.11–2.19 Å. In the ninth Mg2+ site, Mg2+ is bonded to one Rb1+ and five O2- atoms to form distorted MgRbO5 square pyramids that share corners with four MgO6 octahedra, corners with four ORbLiMg4 octahedra, a cornercorner with one ORbMg5 square pyramid, corners with three MgO5 square pyramids, an edgeedge with one LiO6 octahedra, edges with seven MgO6 octahedra, and edges with two equivalent MgRbO5 square pyramids. The corner-sharing octahedra tilt angles range from 2–134°. There are a spread of Mg–O bond distances ranging from 1.89–2.14 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 MgRbO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgRbO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Mg–O bond distances ranging from 2.10–2.22 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 MgRbO5 square pyramids, an edgeedge with one LiO6 octahedra, edges with nine MgO6 octahedra, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 4–10°. There are a spread of Mg–O bond distances ranging from 2.04–2.30 Å. In the twelfth Mg2+ site, Mg2+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Mg–O bond distances ranging from 2.13–2.17 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 MgRbO5 square pyramids, an edgeedge with one LiO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgRbO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–8°. There are a spread of Mg–O bond distances ranging from 2.08–2.22 Å. In the fourteenth Mg2+ site, Mg2+ is bonded to one Rb1+ and five O2- atoms to form distorted MgRbO5 square pyramids that share corners with four MgO6 octahedra, corners with four ORbLiMg4 octahedra, a cornercorner with one ORbMg5 square pyramid, corners with three MgO5 square pyramids, edges with eight MgO6 octahedra, and edges with two equivalent MgRbO5 square pyramids. The corner-sharing octahedra tilt angles range from 4–133°. There are a spread of Mg–O bond distances ranging from 1.91–2.12 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 2.12–2.20 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 MgRbO5 square pyramids, edges with ten MgO6 octahedra, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 3–6°. There are a spread of Mg–O bond distances ranging from 2.07–2.26 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 corner and edge-sharing OLiMg5 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 OLiMg5 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 corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fourth O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form OLiMg5 octahedra that share corners with four OLiMg5 octahedra, corners with two equivalent ORbMg5 square pyramids, and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fifth O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form distorted ORbMg5 square pyramids that share corners with four OLiMg5 octahedra, corners with four MgRbO5 square pyramids, and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 4–7°. In the sixth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the seventh O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent ORbMg5 square pyramids, and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. 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 1–18°. In the ninth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra, edges with eleven OLiMg5 octahedra, and an edgeedge with one ORbMg5 square pyramid. The corner-sharing octahedra tilt angles range from 1–6°. In the tenth O2- site, O2- is bonded to one Rb1+, one Li1+, and four Mg2+ atoms to form distorted ORbLiMg4 octahedra that share corners with six ORbLiMg4 octahedra, corners with four MgRbO5 square pyramids, edges with ten OLiMg5 octahedra, and an edgeedge with one ORbMg5 square pyramid. The corner-sharing octahedra tilt angles range from 2–37°. In the eleventh O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of corner and edge-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, edges with ten OLiMg5 octahedra, and an edgeedge with one ORbMg5 square pyramid. The corner-sharing octahedra tilt angles range from 2–15°. In the thirteenth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. 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 2–8°. In the fifteenth O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form distorted ORbMg5 octahedra that share corners with six OLiMg5 octahedra, corners with four MgRbO5 square pyramids, edges with ten OMg6 octahedra, and an edgeedge with one ORbMg5 square pyramid. The corner-sharing octahedra tilt angles range from 5–36°. 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 2–5°. In the seventeenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six ORbMg5 octahedra, edges with ten OMg6 octahedra, and an edgeedge with one ORbMg5 square pyramid. The corner-sharing octahedra tilt angles range from 2–14°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Li2MnCrO4 by Materials Project

Li2CrMnO4 is Caswellsilverite-derived structured and crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are eight inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CrO6 octahedra, an edgeedge with one CrO6 octahedra, edges with five MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–8°. There are a spread of Li–O bond distances ranging from 2.08–2.40 Å. In the second Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with five MnO6 octahedra, edges with three CrO6 octahedra, edges with three MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–10°. There are a spread of Li–O bond distances ranging from 2.12–2.23 Å. In the third Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one MnO6 octahedra, corners with five CrO6 octahedra, edges with three CrO6 octahedra, edges with three MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–9°. There are a spread of Li–O bond distances ranging from 2.10–2.34 Å. In the fourth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with two equivalent MnO6 octahedra, corners with four CrO6 octahedra, edges with two CrO6 octahedra, edges with four MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–10°. There are a spread of Li–O bond distances ranging from 2.08–2.38 Å. In the fifth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six MnO6 octahedra, edges with two MnO6 octahedra, edges with four CrO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–10°. There are a spread of Li–O bond distances ranging from 2.12–2.21 Å. In the sixth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with two equivalent CrO6 octahedra, corners with four MnO6 octahedra, edges with two MnO6 octahedra, edges with four CrO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–10°. There are a spread of Li–O bond distances ranging from 2.02–2.34 Å. In the seventh Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six MnO6 octahedra, edges with two MnO6 octahedra, edges with four CrO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–10°. There are a spread of Li–O bond distances ranging from 2.13–2.20 Å. In the eighth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CrO6 octahedra, edges with three CrO6 octahedra, edges with three MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–7°. There are a spread of Li–O bond distances ranging from 2.10–2.37 Å. There are six inequivalent Cr4+ sites. In the first Cr4+ site, Cr4+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent CrO6 octahedra, edges with four MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–8°. There are a spread of Cr–O bond distances ranging from 2.01–2.05 Å. In the second Cr4+ site, Cr4+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with six LiO6 octahedra, edges with two CrO6 octahedra, edges with four MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–7°. There are a spread of Cr–O bond distances ranging from 2.02–2.05 Å. In the third Cr4+ site, Cr4+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with four CrO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–10°. There are a spread of Cr–O bond distances ranging from 2.03–2.05 Å. In the fourth Cr4+ site, Cr4+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with four CrO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–9°. There are a spread of Cr–O bond distances ranging from 2.02–2.06 Å. In the fifth Cr4+ site, Cr4+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent CrO6 octahedra, edges with four MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–7°. There are a spread of Cr–O bond distances ranging from 2.02–2.05 Å. In the sixth Cr4+ site, Cr4+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with six LiO6 octahedra, edges with two CrO6 octahedra, edges with four MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–8°. There are a spread of Cr–O bond distances ranging from 2.01–2.06 Å. There are six inequivalent Mn2+ sites. In the first Mn2+ site, Mn2+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent CrO6 octahedra, edges with four MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–10°. There are a spread of Mn–O bond distances ranging from 1.97–2.26 Å. In the second Mn2+ site, Mn2+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with four CrO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–10°. There are a spread of Mn–O bond distances ranging from 1.97–2.18 Å. In the third Mn2+ site, Mn2+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with three CrO6 octahedra, edges with three MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–10°. There are a spread of Mn–O bond distances ranging from 1.94–2.26 Å. In the fourth Mn2+ site, Mn2+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent CrO6 octahedra, edges with four MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–10°. There are a spread of Mn–O bond distances ranging from 1.96–2.24 Å. In the fifth Mn2+ site, Mn2+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, an edgeedge with one MnO6 octahedra, edges with five CrO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–10°. There are a spread of Mn–O bond distances ranging from 1.98–2.23 Å. In the sixth Mn2+ site, Mn2+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with four CrO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–10°. There are a spread of Mn–O bond distances ranging from 1.98–2.22 Å. There are sixteen inequivalent O2- sites. In the first O2- site, O2- is bonded to three Li1+ and three Mn2+ atoms to form OLi3Mn3 octahedra that share corners with six OLi3Mn3 octahedra and edges with twelve OLi3Mn2Cr octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the second O2- site, O2- is bonded to three Li1+, one Cr4+, and two Mn2+ atoms to form OLi3Mn2Cr octahedra that share corners with six OLi3Mn2Cr octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the third O2- site, O2- is bonded to three Li1+, two Cr4+, and one Mn2+ atom to form OLi3MnCr2 octahedra that share corners with six OLi3Cr3 octahedra and edges with twelve OLi3Mn2Cr octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fourth O2- site, O2- is bonded to three Li1+, one Cr4+, and two Mn2+ atoms to form OLi3Mn2Cr octahedra that share corners with six OLi3Cr3 octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fifth O2- site, O2- is bonded to three Li1+, two Cr4+, and one Mn2+ atom to form OLi3MnCr2 octahedra that share corners with six OLi3MnCr2 octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the sixth O2- site, O2- is bonded to three Li1+, one Cr4+, and two Mn2+ atoms to form OLi3Mn2Cr octahedra that share corners with six OLi3Mn3 octahedra and edges with twelve OLi3Mn2Cr octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the seventh O2- site, O2- is bonded to three Li1+, one Cr4+, and two Mn2+ atoms to form OLi3Mn2Cr octahedra that share corners with six OLi3MnCr2 octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the eighth O2- site, O2- is bonded to three Li1+, one Cr4+, and two Mn2+ atoms to form OLi3Mn2Cr octahedra that share corners with six OLi3MnCr2 octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the ninth O2- site, O2- is bonded to three Li1+ and three Cr4+ atoms to form OLi3Cr3 octahedra that share corners with six OLi3Cr3 octahedra and edges with twelve OLi3Mn2Cr octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the tenth O2- site, O2- is bonded to three Li1+, two Cr4+, and one Mn2+ atom to form a mixture of corner and edge-sharing OLi3MnCr2 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the eleventh O2- site, O2- is bonded to three Li1+, two Cr4+, and one Mn2+ atom to form OLi3MnCr2 octahedra that share corners with six OLi3Mn2Cr octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the twelfth O2- site, O2- is bonded to three Li1+, two Cr4+, and one Mn2+ atom to form OLi3MnCr2 octahedra that share corners with six OLi3MnCr2 octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the thirteenth O2- site, O2- is bonded to three Li1+, one Cr4+, and two Mn2+ atoms to form a mixture of corner and edge-sharing OLi3Mn2Cr octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the fourteenth O2- site, O2- is bonded to three Li1+, one Cr4+, and two Mn2+ atoms to form OLi3Mn2Cr octahedra that share corners with six OLi3Mn3 octahedra and edges with twelve OLi3Mn2Cr octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the fifteenth O2- site, O2- is bonded to three Li1+, two Cr4+, and one Mn2+ atom to form OLi3MnCr2 octahedra that share corners with six OLi3Mn3 octahedra and edges with twelve OLi3Mn2Cr octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the sixteenth O2- site, O2- is bonded to three Li1+, two Cr4+, and one Mn2+ atom to form OLi3MnCr2 octahedra that share corners with six OLi3Cr3 octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 0–4°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Li6Cr5O12 by Materials Project

Li6Cr5O12 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are twelve inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five CrO6 octahedra, edges with five CrO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–13°. There are a spread of Li–O bond distances ranging from 2.02–2.31 Å. In the second Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five CrO6 octahedra, edges with five CrO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–16°. There are a spread of Li–O bond distances ranging from 2.07–2.31 Å. In the third Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five CrO6 octahedra, edges with five CrO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–15°. There are a spread of Li–O bond distances ranging from 2.09–2.30 Å. In the fourth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five CrO6 octahedra, edges with five CrO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–13°. There are a spread of Li–O bond distances ranging from 2.03–2.32 Å. In the fifth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five CrO6 octahedra, edges with five CrO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–11°. There are a spread of Li–O bond distances ranging from 2.03–2.25 Å. In the sixth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five CrO6 octahedra, edges with five LiO6 octahedra, and edges with five CrO6 octahedra. The corner-sharing octahedra tilt angles range from 6–15°. There are a spread of Li–O bond distances ranging from 2.05–2.29 Å. In the seventh Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with five LiO6 octahedra, edges with five LiO6 octahedra, and edges with six CrO6 octahedra. The corner-sharing octahedra tilt angles range from 6–15°. There are a spread of Li–O bond distances ranging from 2.09–2.22 Å. In the eighth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five CrO6 octahedra, edges with five LiO6 octahedra, and edges with five CrO6 octahedra. The corner-sharing octahedra tilt angles range from 6–13°. There are a spread of Li–O bond distances ranging from 2.00–2.28 Å. In the ninth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five CrO6 octahedra, edges with five LiO6 octahedra, and edges with five CrO6 octahedra. The corner-sharing octahedra tilt angles range from 6–14°. There are a spread of Li–O bond distances ranging from 2.05–2.33 Å. In the tenth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five CrO6 octahedra, edges with five CrO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are a spread of Li–O bond distances ranging from 2.03–2.26 Å. In the eleventh Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five CrO6 octahedra, edges with five LiO6 octahedra, and edges with five CrO6 octahedra. The corner-sharing octahedra tilt angles range from 5–12°. There are a spread of Li–O bond distances ranging from 2.01–2.27 Å. In the twelfth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with five LiO6 octahedra, edges with five LiO6 octahedra, and edges with six CrO6 octahedra. The corner-sharing octahedra tilt angles range from 5–14°. There are a spread of Li–O bond distances ranging from 2.09–2.18 Å. There are ten inequivalent Cr+3.60+ sites. In the first Cr+3.60+ site, Cr+3.60+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with five LiO6 octahedra, edges with five LiO6 octahedra, and edges with six CrO6 octahedra. The corner-sharing octahedra tilt angles range from 6–11°. There are a spread of Cr–O bond distances ranging from 1.99–2.02 Å. In the second Cr+3.60+ site, Cr+3.60+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with five LiO6 octahedra, edges with five LiO6 octahedra, and edges with six CrO6 octahedra. The corner-sharing octahedra tilt angles range from 6–12°. There are a spread of Cr–O bond distances ranging from 1.98–2.02 Å. In the third Cr+3.60+ site, Cr+3.60+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with five LiO6 octahedra, edges with five LiO6 octahedra, and edges with six CrO6 octahedra. The corner-sharing octahedra tilt angles range from 6–13°. There are a spread of Cr–O bond distances ranging from 1.97–2.04 Å. In the fourth Cr+3.60+ site, Cr+3.60+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with five LiO6 octahedra, edges with five LiO6 octahedra, and edges with six CrO6 octahedra. The corner-sharing octahedra tilt angles range from 6–12°. There are a spread of Cr–O bond distances ranging from 1.97–2.05 Å. In the fifth Cr+3.60+ site, Cr+3.60+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with five LiO6 octahedra, edges with five LiO6 octahedra, and edges with six CrO6 octahedra. The corner-sharing octahedra tilt angles range from 6–13°. There are a spread of Cr–O bond distances ranging from 1.98–2.05 Å. In the sixth Cr+3.60+ site, Cr+3.60+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with five LiO6 octahedra, edges with five LiO6 octahedra, and edges with six CrO6 octahedra. The corner-sharing octahedra tilt angles range from 6–13°. There are a spread of Cr–O bond distances ranging from 1.97–2.04 Å. In the seventh Cr+3.60+ site, Cr+3.60+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with five LiO6 octahedra, edges with three CrO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–16°. There are a spread of Cr–O bond distances ranging from 1.85–2.06 Å. In the eighth Cr+3.60+ site, Cr+3.60+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with five LiO6 octahedra, edges with three CrO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–15°. There are a spread of Cr–O bond distances ranging from 1.86–2.02 Å. In the ninth Cr+3.60+ site, Cr+3.60+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with five LiO6 octahedra, edges with three CrO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are a spread of Cr–O bond distances ranging from 1.86–2.00 Å. In the tenth Cr+3.60+ site, Cr+3.60+ is bonded to six O2- atoms to form CrO6 octahedra that share corners with five LiO6 octahedra, edges with three CrO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–14°. There are a spread of Cr–O bond distances ranging from 1.91–2.01 Å. There are twenty-four inequivalent O2- sites. In the first O2- site, O2- is bonded to two Li1+ and three Cr+3.60+ atoms to form OLi2Cr3 square pyramids that share corners with three OLi3Cr3 octahedra, corners with six OLi3Cr2 square pyramids, edges with six OLi3Cr3 octahedra, and edges with two OLi2Cr3 square pyramids. The corner-sharing octahedra tilt angles range from 3–11°. In the second O2- site, O2- is bonded to two Li1+ and three Cr+3.60+ atoms to form OLi2Cr3 square pyramids that share corners with three OLi3Cr3 octahedra, corners with six OLi3Cr2 square pyramids, edges with six OLi3Cr3 octahedra, and edges with two OLi2Cr3 square pyramids. The corner-sharing octahedra tilt angles range from 3–5°. In the third O2- site, O2- is bonded to three Li1+ and three Cr+3.60+ atoms to form OLi3Cr3 octahedra that share corners with three OLi3Cr3 octahedra, corners with three OLi3Cr2 square pyramids, edges with seven OLi3Cr3 octahedra, and edges with five OLi2Cr3 square pyramids. The corner-sharing octahedra tilt angles range from 0–6°. In the fourth O2- site, O2- is bonded to three Li1+ and two Cr+3.60+ atoms to form OLi3Cr2 square pyramids that share corners with three OLi4Cr2 octahedra, corners with six OLi2Cr3 square pyramids, edges with six OLi3Cr3 octahedra, and edges with two OLi3Cr2 square pyramids. The corner-sharing octahedra tilt angles range from 6–14°. In the fifth O2- site, O2- is bonded to three Li1+ and two Cr+3.60+ atoms to form OLi3Cr2 square pyramids that share corners with three OLi4Cr2 octahedra, corners with six OLi2Cr3 square pyramids, edges with six OLi4Cr2 octahedra, and edges with two OLi3Cr2 square pyramids. The corner-sharing octahedra tilt angles range from 2–6°. In the sixth O2- site, O2- is bonded to three Li1+ and three Cr+3.60+ atoms to form OLi3Cr3 octahedra that share corners with three OLi3Cr3 octahedra, corners with three OLi2Cr3 square pyramids, edges with seven OLi4Cr2 octahedra, and edges with five OLi2Cr3 square pyramids. The corner-sharing octahedra tilt angles range from 1–7°. In the seventh O2- site, O2- is bonded to two Li1+ and three Cr+3.60+ atoms to form OLi2Cr3 square pyramids that share corners with three OLi3Cr3 octahedra, corners with six OLi2Cr3 square pyramids, edges with six OLi3Cr3 octahedra, and edges with two OLi2Cr3 square pyramids. The corner-sharing octahedra tilt angles range from 3–6°. In the eighth O2- site, O2- is bonded to two Li1+ and three Cr+3.60+ atoms to form OLi2Cr3 square pyramids that share corners with three OLi3Cr3 octahedra, corners with six OLi2Cr3 square pyramids, edges with six OLi3Cr3 octahedra, and edges with two OLi2Cr3 square pyramids. The corner-sharing octahedra tilt angles range from 3–11°. In the ninth O2- site, O2- is bonded to four Li1+ and two Cr+3.60+ atoms to form OLi4Cr2 octahedra that share corners with three OLi4Cr2 octahedra, corners with three OLi3Cr2 square pyramids, edges with seven OLi4Cr2 octahedra, and edges with five OLi3Cr2 square pyramids. The corner-sharing octahedra tilt angles range from 5–10°. In the tenth O2- site, O2- is bonded to four Li1+ and two Cr+3.60+ atoms to form OLi4Cr2 octahedra that share corners with three OLi4Cr2 octahedra, corners with three OLi3Cr2 square pyramids, edges with seven OLi3Cr3 octahedra, and edges with five OLi3Cr2 square pyramids. The corner-sharing octahedra tilt angles range from 5–11°. In the eleventh O2- site, O2- is bonded to three Li1+ and two Cr+3.60+ atoms to form OLi3Cr2 square pyramids that share corners with three OLi4Cr2 octahedra, corners with six OLi3Cr2 square pyramids, edges with six OLi3Cr3 octahedra, and edges with two OLi3Cr2 square pyramids. The corner-sharing octahedra tilt angles range from 3–8°. In the twelfth O2- site, O2- is bonded to three Li1+ and two Cr+3.60+ atoms to form OLi3Cr2 square pyramids that share corners with three OLi4Cr2 octahedra, corners with six OLi3Cr2 square pyramids, edges with six OLi3Cr3 octahedra, and edges with two OLi3Cr2 square pyramids. The corner-sharing octahedra tilt angles range from 7–13°. In the thirteenth O2- site, O2- is bonded to three Li1+ and three Cr+3.60+ atoms to form OLi3Cr3 octahedra that share corners with three OLi4Cr2 octahedra, corners with three OLi3Cr2 square pyramids, edges with six OLi3Cr3 octahedra, and edges wi

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 distorted 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 4–20°. There are a spread of Li–O bond distances ranging from 2.00–2.29 Å. In the second Li1+ site, Li1+ is bonded to six O2- atoms to form distorted LiO6 octahedra that share a cornercorner with one CoO6 octahedra, corners with five NiO6 octahedra, edges with four LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 2–21°. There are a spread of Li–O bond distances ranging from 1.95–2.43 Å. In the third 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 1.98–2.33 Å. In the fourth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with two equivalent CoO6 octahedra, corners with four NiO6 octahedra, an edgeedge with one CoO6 octahedra, edges with five NiO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 2–10°. There are a spread of Li–O bond distances ranging from 2.07–2.18 Å. In the fifth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with two equivalent CoO6 octahedra, corners with four NiO6 octahedra, an edgeedge with one CoO6 octahedra, edges with five NiO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–6°. There are a spread of Li–O bond distances ranging from 2.12–2.15 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 four LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–18°. There are a spread of Li–O bond distances ranging from 2.01–2.19 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 1–10°. There are a spread of Li–O bond distances ranging from 2.07–2.18 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 3–15°. There are a spread of Li–O bond distances ranging from 1.95–2.49 Å. In the ninth Li1+ site, Li1+ is bonded to six O2- atoms to form distorted 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 1.98–2.26 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 two equivalent CoO6 octahedra, edges with four NiO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. There are a spread of Li–O bond distances ranging from 2.07–2.35 Å. In the eleventh 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 4–8°. There are a spread of Li–O bond distances ranging from 2.09–2.33 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 3–8°. There are a spread of Li–O bond distances ranging from 2.08–2.29 Å. In the thirteenth 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 8–16°. There are a spread of Li–O bond distances ranging from 2.00–2.24 Å. In the fourteenth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with two equivalent CoO6 octahedra, corners with four NiO6 octahedra, an edgeedge with one CoO6 octahedra, edges with five NiO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 2–9°. There are a spread of Li–O bond distances ranging from 2.05–2.30 Å. In the fifteenth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with two equivalent CoO6 octahedra, corners with four NiO6 octahedra, an edgeedge with one CoO6 octahedra, edges with five NiO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–9°. There are a spread of Li–O bond distances ranging from 2.08–2.30 Å. In the sixteenth Li1+ site, Li1+ is bonded to six O2- atoms to form distorted 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 5–19°. There are a spread of Li–O bond distances ranging from 1.98–2.40 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 corners with five LiO6 octahedra, edges with two equivalent CoO6 octahedra, edges with four NiO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 2–7°. There are a spread of Co–O bond distances ranging from 1.89–1.94 Å. In the second Co4+ site, Co4+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with four LiO6 octahedra, edges with two equivalent CoO6 octahedra, edges with four NiO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–7°. There are a spread of Co–O bond distances ranging from 1.86–1.93 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 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 1.91–2.17 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 4–18°. There are a spread of Ni–O bond distances ranging from 1.99–2.13 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 six LiO6 octahedra, edges with four LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 2–21°. There are a spread of Ni–O bond distances ranging from 1.98–2.16 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 six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–10°. There are a spread of Ni–O bond distances ranging from 1.93–2.11 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 four LiO6 octahedra, edges with five LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–9°. There are a spread of Ni–O bond distances ranging from 1.90–2.10 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 five LiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–11°. There are a spread of Ni–O bond distances ranging from 1.90–1.92 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 six LiO6 octahedra, edges with four LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 1–19°. There are a spread of Ni–O bond distances ranging from 1.92–2.16 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 four LiO6 octahedra, edges with three LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–18°. There are a spread of Ni–O bond distances ranging from 1.90–2.15 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 two equivalent CoO6 octahedra, edges with four LiO6 octahedra, and edges with four NiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–20°. There are a spread of Ni–O bond distances ranging from 1.99–2.14 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 two equivalent CoO6 octahedra, edges with four LiO6 octahedra, and edges with four NiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–19°. There are a spread of Ni–O bond distances ranging from 1.97–2.12 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 three LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 9–18°. There are a spread of Ni–O bond distances ranging from 1.90–2.14 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 two LiO6 octahedra, edges with four LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–5°. There are a spread of Ni–O bond distances ranging from 1.88–1.91 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 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 1.94–2.11 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 five LiO6 octahedra, edges with six LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–10°. There are a spread of Ni–O bond distances ranging from 1.91–1.95 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 five LiO6 octahedra, and edges with six NiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–10°. There are a spread of Ni–O bond distances ranging from 1.88–1.93 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 2–9°. There are a spread of Ni–O bond distances ranging from 1.98–2.11 Å. In the seven

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Li9Mn2Co5O16 by Materials Project

Li9Mn2Co5O16 is Caswellsilverite-derived structured and crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are nine inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one MnO6 octahedra, corners with five CoO6 octahedra, edges with two equivalent MnO6 octahedra, edges with four CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–8°. There are a spread of Li–O bond distances ranging from 2.10–2.41 Å. In the second Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CoO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 3–6°. There are a spread of Li–O bond distances ranging from 2.10–2.36 Å. In the third Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one MnO6 octahedra, corners with five CoO6 octahedra, edges with four CoO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. There are a spread of Li–O bond distances ranging from 2.10–2.21 Å. In the fourth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one MnO6 octahedra, corners with five CoO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Li–O bond distances ranging from 2.11–2.19 Å. In the fifth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five CoO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 3–10°. There are a spread of Li–O bond distances ranging from 2.03–2.17 Å. In the sixth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one MnO6 octahedra, a cornercorner with one CoO6 octahedra, corners with four equivalent LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with two equivalent CoO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–11°. There are a spread of Li–O bond distances ranging from 2.04–2.13 Å. In the seventh Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with two CoO6 octahedra, corners with four equivalent MnO6 octahedra, edges with four MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–10°. There are a spread of Li–O bond distances ranging from 2.15–2.28 Å. In the eighth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, a cornercorner with one CoO6 octahedra, corners with four equivalent MnO6 octahedra, edges with two equivalent CoO6 octahedra, edges with four MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–10°. There are a spread of Li–O bond distances ranging from 2.12–2.20 Å. In the ninth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with two equivalent CoO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–11°. There are a spread of Li–O bond distances ranging from 2.01–2.17 Å. There are two inequivalent Mn+4.50+ sites. In the first Mn+4.50+ site, Mn+4.50+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent CoO6 octahedra, edges with four MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–10°. There are a spread of Mn–O bond distances ranging from 1.98–2.21 Å. In the second Mn+4.50+ site, Mn+4.50+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with four MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 0–10°. There are a spread of Mn–O bond distances ranging from 1.82–2.12 Å. There are five inequivalent Co+2.80+ sites. In the first Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 3–6°. There are a spread of Co–O bond distances ranging from 2.02–2.12 Å. In the second Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 1–10°. There are a spread of Co–O bond distances ranging from 2.00–2.05 Å. In the third Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 3–6°. There are a spread of Co–O bond distances ranging from 2.03–2.07 Å. In the fourth Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with four CoO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–8°. There are a spread of Co–O bond distances ranging from 1.73–2.03 Å. In the fifth Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with four CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–7°. There are a spread of Co–O bond distances ranging from 1.99–2.20 Å. There are sixteen inequivalent O2- sites. In the first O2- site, O2- is bonded to three Li1+ and three Mn+4.50+ atoms to form OLi3Mn3 octahedra that share corners with six OLi3Co3 octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 2–4°. In the second O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the third O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fourth O2- site, O2- is bonded to three Li1+, one Mn+4.50+, and two equivalent Co+2.80+ atoms to form OLi3MnCo2 octahedra that share corners with six OLi3Co3 octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 2–4°. In the fifth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the sixth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 3–8°. In the seventh O2- site, O2- is bonded to five Li1+ and one Co+2.80+ atom to form a mixture of edge and corner-sharing OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 3–6°. In the eighth O2- site, O2- is bonded to four Li1+ and two equivalent Mn+4.50+ atoms to form OLi4Mn2 octahedra that share corners with six OLi4Co2 octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 2–6°. In the ninth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form OLi3Co3 octahedra that share corners with six OLi3Mn3 octahedra and edges with twelve OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the tenth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the eleventh O2- site, O2- is bonded to five Li1+ and one Mn+4.50+ atom to form OLi5Mn octahedra that share corners with six OLi3Mn3 octahedra and edges with twelve OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 3–4°. In the twelfth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form OLi3Co3 octahedra that share corners with six OLi3MnCo2 octahedra and edges with twelve OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the thirteenth O2- site, O2- is bonded to four Li1+ and two equivalent Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi4Co2 octahedra. The corner-sharing octahedra tilt angles range from 2–8°. In the fourteenth O2- site, O2- is bonded to three Li1+ and three Mn+4.50+ atoms to form OLi3Mn3 octahedra that share corners with six OLi3MnCo2 octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 2–6°. In the fifteenth O2- site, O2- is bonded to three Li1+, two equivalent Mn+4.50+, and one Co+2.80+ atom to form a mixture of edge and corner-sharing OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the sixteenth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form OLi3Co3 octahedra that share corners with six OLi3MnCo2 octahedra and edges with twelve OLi3Mn3 octahedra. The corner-sharing octahedra tilt angles range from 2–4°.

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 Li9Mn2Co5O16 by Materials Project

Li9Mn2Co5O16 is Caswellsilverite-derived structured and crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are nine inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CoO6 octahedra, edges with two equivalent MnO6 octahedra, edges with two CoO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–10°. There are a spread of Li–O bond distances ranging from 2.11–2.35 Å. In the second Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CoO6 octahedra, edges with four CoO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 2–7°. There are a spread of Li–O bond distances ranging from 2.13–2.42 Å. In the third Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CoO6 octahedra, edges with two equivalent MnO6 octahedra, edges with four CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–8°. There are a spread of Li–O bond distances ranging from 2.10–2.21 Å. In the fourth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent MnO6 octahedra, corners with three equivalent CoO6 octahedra, edges with three MnO6 octahedra, edges with three CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. There are a spread of Li–O bond distances ranging from 2.10–2.20 Å. In the fifth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent LiO6 octahedra, corners with three equivalent MnO6 octahedra, an edgeedge with one MnO6 octahedra, edges with four CoO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–15°. There are a spread of Li–O bond distances ranging from 2.01–2.21 Å. In the sixth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent LiO6 octahedra, corners with three equivalent CoO6 octahedra, edges with five CoO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–16°. There are a spread of Li–O bond distances ranging from 2.02–2.27 Å. In the seventh Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent MnO6 octahedra, corners with three equivalent CoO6 octahedra, an edgeedge with one MnO6 octahedra, edges with five CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–10°. There are a spread of Li–O bond distances ranging from 2.10–2.19 Å. In the eighth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent MnO6 octahedra, corners with three equivalent CoO6 octahedra, edges with three MnO6 octahedra, edges with three CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–8°. There are a spread of Li–O bond distances ranging from 2.07–2.21 Å. In the ninth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with four equivalent CoO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–16°. There are a spread of Li–O bond distances ranging from 2.09–2.13 Å. There are two inequivalent Mn+4.50+ sites. In the first Mn+4.50+ site, Mn+4.50+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with four equivalent CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. There are a spread of Mn–O bond distances ranging from 1.95–2.19 Å. In the second Mn+4.50+ site, Mn+4.50+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with four equivalent CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–10°. There are a spread of Mn–O bond distances ranging from 1.96–2.21 Å. There are five inequivalent Co+2.80+ sites. In the first Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 4–7°. There are a spread of Co–O bond distances ranging from 1.98–2.10 Å. In the second Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent CoO6 octahedra, edges with four equivalent MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–10°. There are a spread of Co–O bond distances ranging from 1.94–2.20 Å. In the third Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent CoO6 octahedra, and edges with ten LiO6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. There are a spread of Co–O bond distances ranging from 1.80–1.96 Å. In the fourth Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six CoO6 octahedra. The corner-sharing octahedra tilt angles range from 3–7°. There are a spread of Co–O bond distances ranging from 2.00–2.10 Å. In the fifth Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent CoO6 octahedra, edges with four equivalent MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–8°. There are a spread of Co–O bond distances ranging from 1.94–2.19 Å. There are sixteen inequivalent O2- sites. In the first O2- site, O2- is bonded to three Li1+, two equivalent Mn+4.50+, and one Co+2.80+ atom to form OLi3Mn2Co octahedra that share corners with six OLi5Co octahedra and edges with twelve OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 1–8°. In the second O2- site, O2- is bonded to five Li1+ and one Co+2.80+ atom to form a mixture of distorted corner and edge-sharing OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the third O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of corner and edge-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. In the fourth O2- site, O2- is bonded to three Li1+, two equivalent Mn+4.50+, and one Co+2.80+ atom to form a mixture of corner and edge-sharing OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the fifth O2- site, O2- is bonded to three Li1+, one Mn+4.50+, and two equivalent Co+2.80+ atoms to form OLi3MnCo2 octahedra that share corners with six OLi3MnCo2 octahedra and edges with twelve OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 1–5°. In the sixth O2- site, O2- is bonded to four Li1+ and two equivalent Co+2.80+ atoms to form OLi4Co2 octahedra that share corners with six OLi4Co2 octahedra and edges with twelve OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the seventh O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of corner and edge-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the eighth O2- site, O2- is bonded to three Li1+, one Mn+4.50+, and two equivalent Co+2.80+ atoms to form OLi3MnCo2 octahedra that share corners with six OLi3MnCo2 octahedra and edges with twelve OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the ninth O2- site, O2- is bonded to five Li1+ and one Co+2.80+ atom to form a mixture of distorted corner and edge-sharing OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the tenth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of corner and edge-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. In the eleventh O2- site, O2- is bonded to three Li1+, two equivalent Mn+4.50+, and one Co+2.80+ atom to form a mixture of corner and edge-sharing OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the twelfth O2- site, O2- is bonded to three Li1+, one Mn+4.50+, and two equivalent Co+2.80+ atoms to form a mixture of corner and edge-sharing OLi3MnCo2 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the thirteenth O2- site, O2- is bonded to four Li1+ and two equivalent Co+2.80+ atoms to form OLi4Co2 octahedra that share corners with six OLi3MnCo2 octahedra and edges with twelve OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the fourteenth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form OLi3Co3 octahedra that share corners with six OLi4Co2 octahedra and edges with twelve OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fifteenth O2- site, O2- is bonded to three Li1+, one Mn+4.50+, and two equivalent Co+2.80+ atoms to form a mixture of corner and edge-sharing OLi3MnCo2 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the sixteenth O2- site, O2- is bonded to three Li1+, two equivalent Mn+4.50+, and one Co+2.80+ atom to form a mixture of corner and edge-sharing OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 0–2°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Li9Mn2Co5O16 by Materials Project

Li9Mn2Co5O16 is Caswellsilverite-derived structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are nine inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent LiO6 octahedra, corners with three equivalent MnO6 octahedra, an edgeedge with one MnO6 octahedra, edges with four equivalent CoO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–11°. There are a spread of Li–O bond distances ranging from 2.03–2.19 Å. In the second Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CoO6 octahedra, edges with two CoO6 octahedra, and edges with ten LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–9°. There are a spread of Li–O bond distances ranging from 2.17–2.23 Å. In the third Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent LiO6 octahedra, corners with three equivalent CoO6 octahedra, edges with five CoO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–11°. There are a spread of Li–O bond distances ranging from 2.03–2.28 Å. In the fourth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent MnO6 octahedra, corners with three equivalent CoO6 octahedra, an edgeedge with one MnO6 octahedra, edges with five CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–8°. There are a spread of Li–O bond distances ranging from 2.08–2.22 Å. In the fifth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CoO6 octahedra, edges with two CoO6 octahedra, edges with four equivalent MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–7°. There are a spread of Li–O bond distances ranging from 2.11–2.28 Å. In the sixth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent MnO6 octahedra, corners with three equivalent CoO6 octahedra, an edgeedge with one MnO6 octahedra, edges with five CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–8°. There are a spread of Li–O bond distances ranging from 2.10–2.24 Å. In the seventh Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with three equivalent MnO6 octahedra, corners with three equivalent CoO6 octahedra, an edgeedge with one MnO6 octahedra, edges with five CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–7°. There are a spread of Li–O bond distances ranging from 2.11–2.24 Å. In the eighth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six CoO6 octahedra, edges with two CoO6 octahedra, edges with four equivalent MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–7°. There are a spread of Li–O bond distances ranging from 2.09–2.28 Å. In the ninth Li1+ site, Li1+ is bonded to six O2- atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with four CoO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–11°. There are a spread of Li–O bond distances ranging from 2.03–2.20 Å. There are two inequivalent Mn+4.50+ sites. In the first Mn+4.50+ site, Mn+4.50+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with four CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–10°. There are a spread of Mn–O bond distances ranging from 1.93–2.23 Å. In the second Mn+4.50+ site, Mn+4.50+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with four CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–8°. There are a spread of Mn–O bond distances ranging from 1.95–2.25 Å. There are five inequivalent Co+2.80+ sites. In the first Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form distorted CoO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with two equivalent CoO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–9°. There are a spread of Co–O bond distances ranging from 1.73–2.27 Å. In the second Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form distorted CoO6 octahedra that share corners with six LiO6 octahedra, edges with four CoO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–9°. There are a spread of Co–O bond distances ranging from 1.74–2.27 Å. In the third Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with four CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. There are a spread of Co–O bond distances ranging from 1.89–2.12 Å. In the fourth Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with four CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–7°. There are a spread of Co–O bond distances ranging from 1.92–2.11 Å. In the fifth Co+2.80+ site, Co+2.80+ is bonded to six O2- atoms to form CoO6 octahedra that share corners with six LiO6 octahedra, edges with two equivalent MnO6 octahedra, edges with four CoO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–7°. There are a spread of Co–O bond distances ranging from 1.92–2.11 Å. There are sixteen inequivalent O2- sites. In the first O2- site, O2- is bonded to three Li1+, two equivalent Mn+4.50+, and one Co+2.80+ atom to form OLi3Mn2Co octahedra that share corners with six OLi5Co octahedra and edges with twelve OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 1–8°. In the second O2- site, O2- is bonded to four Li1+ and two equivalent Co+2.80+ atoms to form OLi4Co2 octahedra that share corners with six OLi4Co2 octahedra and edges with twelve OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the third O2- site, O2- is bonded to five Li1+ and one Co+2.80+ atom to form OLi5Co octahedra that share corners with six OLi5Co octahedra and edges with twelve OLi4Co2 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the fourth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form OLi3Co3 octahedra that share corners with six OLi4Co2 octahedra and edges with twelve OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 1–8°. In the fifth O2- site, O2- is bonded to three Li1+, one Mn+4.50+, and two equivalent Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3MnCo2 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the sixth O2- site, O2- is bonded to three Li1+, two equivalent Mn+4.50+, and one Co+2.80+ atom to form OLi3Mn2Co octahedra that share corners with six OLi3Mn2Co octahedra and edges with twelve OLi3MnCo2 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the seventh O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form OLi3Co3 octahedra that share corners with six OLi3MnCo2 octahedra and edges with twelve OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the eighth O2- site, O2- is bonded to three Li1+, one Mn+4.50+, and two equivalent Co+2.80+ atoms to form OLi3MnCo2 octahedra that share corners with six OLi3Co3 octahedra and edges with twelve OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the ninth O2- site, O2- is bonded to five Li1+ and one Co+2.80+ atom to form a mixture of edge and corner-sharing OLi5Co octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the tenth O2- site, O2- is bonded to four Li1+ and two equivalent Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi4Co2 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the eleventh O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the twelfth O2- site, O2- is bonded to three Li1+, two equivalent Mn+4.50+, and one Co+2.80+ atom to form a mixture of edge and corner-sharing OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the thirteenth O2- site, O2- is bonded to three Li1+, one Mn+4.50+, and two equivalent Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3MnCo2 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the fourteenth O2- site, O2- is bonded to three Li1+ and three Co+2.80+ atoms to form a mixture of edge and corner-sharing OLi3Co3 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fifteenth O2- site, O2- is bonded to three Li1+, two equivalent Mn+4.50+, and one Co+2.80+ atom to form a mixture of edge and corner-sharing OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 1–3°. In the sixteenth O2- site, O2- is bonded to three Li1+, one Mn+4.50+, and two equivalent Co+2.80+ atoms to form OLi3MnCo2 octahedra that share corners with six OLi4Co2 octahedra and edges with twelve OLi3Mn2Co octahedra. The corner-sharing octahedra tilt angles range from 2–8°.

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 CsLiMg30O31 by Materials Project

CsLiMg30O31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Cs1+ is bonded to six O2- atoms to form distorted CsO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, corners with two equivalent MgO5 trigonal bipyramids, edges with eight MgO6 octahedra, and edges with two equivalent MgO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 0–11°. There are a spread of Cs–O bond distances ranging from 2.44–2.62 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 0–3°. There are a spread of Li–O bond distances ranging from 2.12–2.40 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 CsO6 octahedra, corners with two equivalent LiO6 octahedra, corners with five MgO5 square pyramids, corners with two equivalent MgO5 trigonal bipyramids, and edges with six MgO6 octahedra. The corner-sharing octahedra tilt angles range from 7–32°. There are a spread of Mg–O bond distances ranging from 1.88–2.19 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent CsO6 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 0–11°. There are a spread of Mg–O bond distances ranging from 1.90–2.32 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 0–1°. There are a spread of Mg–O bond distances ranging from 2.09–2.24 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 two equivalent MgO5 square pyramids, corners with three MgO5 trigonal bipyramids, edges with six MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 7°. There are a spread of Mg–O bond distances ranging from 2.00–2.14 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 2.09–2.15 Å. In the sixth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent CsO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with eight MgO6 octahedra, edges with two equivalent MgO5 square pyramids, 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 1.85–2.25 Å. In the seventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, a cornercorner with one MgO5 square pyramid, an edgeedge with one CsO6 octahedra, an edgeedge with one LiO6 octahedra, edges with six MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and edges with two MgO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 2–22°. There are a spread of Mg–O bond distances ranging from 2.09–2.29 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 eight MgO6 octahedra, edges with three MgO5 square pyramids, and an edgeedge with one MgO5 trigonal bipyramid. The corner-sharing octahedra tilt angles range from 0–7°. There are a spread of Mg–O bond distances ranging from 2.12–2.24 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 7–10°. There are a spread of Mg–O bond distances ranging from 1.97–2.26 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 CsO6 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 2.09–2.28 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 seven MgO6 octahedra, edges with three MgO5 square pyramids, and an edgeedge with one MgO5 trigonal bipyramid. The corner-sharing octahedra tilt angles range from 5–8°. There are a spread of Mg–O bond distances ranging from 2.13–2.30 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 CsO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–18°. There are a spread of Mg–O bond distances ranging from 2.12–2.42 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 0–8°. There are a spread of Mg–O bond distances ranging from 2.14–2.26 Å. In the fourteenth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 trigonal bipyramids that share corners with two equivalent MgO6 octahedra, corners with four MgO5 square pyramids, corners with two MgO5 trigonal bipyramids, an edgeedge with one CsO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedral tilt angles are 7°. There are a spread of Mg–O bond distances ranging from 1.95–2.21 Å. In the fifteenth 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, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. There are a spread of Mg–O bond distances ranging from 2.12–2.24 Å. In the sixteenth Mg2+ site, Mg2+ is bonded to five O2- atoms to form distorted MgO5 square pyramids that share a cornercorner with one CsO6 octahedra, corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, corners with two MgO5 trigonal bipyramids, edges with seven MgO6 octahedra, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 5–97°. There are a spread of Mg–O bond distances ranging from 2.10–2.17 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 0–8°. 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 0–8°. In the third O2- site, O2- is bonded to one Cs1+ and five Mg2+ atoms to form a mixture of distorted edge and corner-sharing OCsMg5 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 0–7°. 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 ten OMg6 octahedra. The corner-sharing octahedra tilt angles range from 2–6°. 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 Cs1+ and five Mg2+ atoms to form a mixture of distorted edge and corner-sharing OCsMg5 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 ten OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 4–13°. 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 eleven OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 3–12°. In the tenth O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form OLiMg5 octahedra that share corners with six OCsMg5 octahedra and edges with nine OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 4–13°. In the eleventh O2- site, O2- is bonded to one Cs1+ and five Mg2+ atoms to form distorted OCsMg5 octahedra that share corners with six OCsMg5 octahedra and edges with ten OMg6 octahedra. The corner-sharing octahedra tilt angles range from 4–15°. 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 3–13°. In the thirteenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OCsMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. In the fourteenth O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form OLiMg5 octahedra that share corners with four OMg6 octahedra and edges with twelve OLiMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fifteenth O2- site, O2- is bonded in a 5-coordinate geometry to one Cs1+ and four Mg2+ atoms. 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 0–2°. In the seventeenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with four OMg6 octahedra and edges with eleven OCsMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–15°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on CsKMg30O31 by Materials Project

CsKMg30O31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Cs1+ is bonded in a 2-coordinate geometry to four O2- atoms. There are two shorter (2.40 Å) and two longer (2.63 Å) Cs–O bond lengths. K1+ is bonded to six O2- atoms to form KO6 octahedra that share corners with four MgO6 octahedra and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of K–O bond distances ranging from 2.27–2.40 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 1.97–2.22 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, 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 Mg–O bond distances ranging from 1.98–2.30 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, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 1.89–2.29 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, 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 1.93–2.16 Å. In the fifth Mg2+ site, Mg2+ is bonded to six O2- 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 2.07–2.21 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 0–3°. There are a spread of Mg–O bond distances ranging from 2.03–2.23 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, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 0–10°. There are a spread of Mg–O bond distances ranging from 2.13–2.22 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 two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–6°. There are a spread of Mg–O bond distances ranging from 2.12–2.20 Å. In the ninth Mg2+ site, Mg2+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Mg–O bond distances ranging from 1.92–2.24 Å. In the tenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 2–4°. There are a spread of Mg–O bond distances ranging from 2.12–2.25 Å. In the eleventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, an edgeedge with one KO6 octahedra, edges with nine MgO6 octahedra, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 2–13°. There are a spread of Mg–O bond distances ranging from 2.05–2.26 Å. In the twelfth Mg2+ site, Mg2+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–3°. There are a spread of Mg–O bond distances ranging from 2.15–2.20 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, and edges with nine MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–11°. There are a spread of Mg–O bond distances ranging from 2.11–2.28 Å. In the fourteenth Mg2+ site, Mg2+ is bonded to five O2- atoms to form distorted MgO5 square pyramids that share corners with four MgO6 octahedra, corners with two MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 5–11°. There are a spread of Mg–O bond distances ranging from 1.90–2.19 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 1–10°. There are a spread of Mg–O bond distances ranging from 2.14–2.20 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, edges with ten MgO6 octahedra, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 3–7°. There are a spread of Mg–O bond distances ranging from 2.10–2.28 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 corner and edge-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 corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fourth O2- site, O2- is bonded to one K1+ and five Mg2+ atoms to form OKMg5 octahedra that share corners with four OKMg5 octahedra, corners with two equivalent OMg5 square pyramids, 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 five Mg2+ atoms to form OMg5 square pyramids that share corners with eight OCsMg5 octahedra and edges with eight OMg6 octahedra. The corner-sharing octahedra tilt angles range from 6–88°. In the sixth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the seventh O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5 square pyramids, and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. 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 0–16°. In the ninth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra, edges with eleven OKMg5 octahedra, and an edgeedge with one OMg5 square pyramid. The corner-sharing octahedra tilt angles range from 0–6°. In the tenth O2- site, O2- is bonded to one Cs1+, one K1+, and four Mg2+ atoms to form OCsKMg4 octahedra that share corners with six OMg6 octahedra, a cornercorner with one OMg5 square pyramid, and edges with ten OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–57°. In the eleventh O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of corner and edge-sharing 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, edges with ten OKMg5 octahedra, and an edgeedge with one OMg5 square pyramid. The corner-sharing octahedra tilt angles range from 2–20°. In the thirteenth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of corner and edge-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 OCsMg5 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–10°. In the fifteenth O2- site, O2- is bonded to one Cs1+ and five Mg2+ atoms to form distorted OCsMg5 octahedra that share corners with six OCsMg5 octahedra, a cornercorner with one OMg5 square pyramid, and edges with ten OMg6 octahedra. The corner-sharing octahedra tilt angles range from 6–49°. 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 2–6°. In the seventeenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OCsMg5 octahedra, edges with ten OMg6 octahedra, and an edgeedge with one OMg5 square pyramid. 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 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↗