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DOE OSTI2020

Materials Data on KNaAl6Si6(HO6)4 by Materials Project

KNaAl6Si6(HO6)4 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are four inequivalent K1+ sites. In the first K1+ site, K1+ is bonded to six O2- atoms to form distorted KO6 octahedra that share corners with two AlO4 tetrahedra and corners with ten SiO4 tetrahedra. There are a spread of K–O bond distances ranging from 2.68–2.87 Å. In the second K1+ site, K1+ is bonded to six O2- atoms to form distorted KO6 octahedra that share corners with four AlO4 tetrahedra and corners with eight SiO4 tetrahedra. There are a spread of K–O bond distances ranging from 2.76–2.88 Å. In the third K1+ site, K1+ is bonded to six O2- atoms to form distorted KO6 octahedra that share corners with four AlO4 tetrahedra and corners with eight SiO4 tetrahedra. There are a spread of K–O bond distances ranging from 2.74–2.91 Å. In the fourth K1+ site, K1+ is bonded to six O2- atoms to form distorted KO6 octahedra that share corners with four AlO4 tetrahedra and corners with eight SiO4 tetrahedra. There are a spread of K–O bond distances ranging from 2.76–2.88 Å. There are four inequivalent Na1+ sites. In the first Na1+ site, Na1+ is bonded to six O2- atoms to form NaO6 octahedra that share corners with two AlO4 tetrahedra and corners with ten SiO4 tetrahedra. There are a spread of Na–O bond distances ranging from 2.46–2.99 Å. In the second Na1+ site, Na1+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Na–O bond distances ranging from 2.57–3.09 Å. In the third Na1+ site, Na1+ is bonded to six O2- atoms to form distorted NaO6 octahedra that share corners with two AlO4 tetrahedra and corners with ten SiO4 tetrahedra. There are a spread of Na–O bond distances ranging from 2.46–3.04 Å. In the fourth Na1+ site, Na1+ is bonded to six O2- atoms to form NaO6 octahedra that share corners with two AlO4 tetrahedra and corners with ten SiO4 tetrahedra. There are a spread of Na–O bond distances ranging from 2.46–2.99 Å. There are twenty-four inequivalent Al3+ sites. In the first Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.99 Å. In the second Al3+ site, Al3+ is bonded to four O2- atoms to form AlO4 tetrahedra that share corners with two KO6 octahedra, corners with two AlO6 octahedra, and corners with three SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 52–71°. There is three shorter (1.75 Å) and one longer (1.77 Å) Al–O bond length. In the third Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.99 Å. In the fourth Al3+ site, Al3+ is bonded to four O2- atoms to form AlO4 tetrahedra that share corners with two KO6 octahedra, corners with two AlO6 octahedra, and corners with three SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 53–71°. There is one shorter (1.75 Å) and three longer (1.76 Å) Al–O bond length. In the fifth Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.99 Å. In the sixth Al3+ site, Al3+ is bonded to four O2- atoms to form AlO4 tetrahedra that share a cornercorner with one NaO6 octahedra, corners with two KO6 octahedra, corners with two AlO6 octahedra, and corners with three SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 52–72°. There is two shorter (1.75 Å) and two longer (1.76 Å) Al–O bond length. In the seventh Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.87–1.98 Å. In the eighth Al3+ site, Al3+ is bonded to four O2- atoms to form AlO4 tetrahedra that share a cornercorner with one NaO6 octahedra, corners with two KO6 octahedra, corners with two AlO6 octahedra, and corners with three SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 52–71°. There is two shorter (1.75 Å) and two longer (1.76 Å) Al–O bond length. In the ninth Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.99 Å. In the tenth Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.99 Å. In the eleventh Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.99 Å. In the twelfth Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.99 Å. In the thirteenth Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.99 Å. In the fourteenth Al3+ site, Al3+ is bonded to four O2- atoms to form AlO4 tetrahedra that share a cornercorner with one KO6 octahedra, a cornercorner with one NaO6 octahedra, corners with two AlO6 octahedra, and corners with three SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 53–69°. There is one shorter (1.75 Å) and three longer (1.76 Å) Al–O bond length. In the fifteenth Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.87–1.99 Å. In the sixteenth Al3+ site, Al3+ is bonded to four O2- atoms to form AlO4 tetrahedra that share a cornercorner with one KO6 octahedra, a cornercorner with one NaO6 octahedra, corners with two AlO6 octahedra, and corners with three SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 53–70°. There are a spread of Al–O bond distances ranging from 1.74–1.77 Å. In the seventeenth Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.99 Å. In the eighteenth Al3+ site, Al3+ is bonded to four O2- atoms to form AlO4 tetrahedra that share a cornercorner with one NaO6 octahedra, corners with two KO6 octahedra, corners with two AlO6 octahedra, and corners with three SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 52–71°. There is two shorter (1.75 Å) and two longer (1.76 Å) Al–O bond length. In the nineteenth Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–2.00 Å. In the twentieth Al3+ site, Al3+ is bonded to four O2- atoms to form AlO4 tetrahedra that share a cornercorner with one NaO6 octahedra, corners with two KO6 octahedra, corners with two AlO6 octahedra, and corners with three SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 52–72°. There is two shorter (1.75 Å) and two longer (1.76 Å) Al–O bond length. In the twenty-first Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.98 Å. In the twenty-second Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.99 Å. In the twenty-third Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.98 Å. In the twenty-fourth Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share a cornercorner with one AlO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with three AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.99 Å. There are twenty-four inequivalent Si4+ sites. In the first Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with two KO6 octahedra, corners with two AlO6 octahedra, a cornercorner with one AlO4 tetrahedra, and corners with two SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 50–72°. There are a spread of Si–O bond distances ranging from 1.61–1.67 Å. In the second Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with two KO6 octahedra, corners with two AlO6 octahedra, a cornercorner with one AlO4 tetrahedra, and corners with two SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 50–72°. There are a spread of Si–O bond distances ranging from 1.61–1.66 Å. In the third Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share a cornercorner with one NaO6 octahedra, corners with two KO6 octahedra, corners with two AlO6 octahedra, a cornercorner with one AlO4 tetrahedra, and corners with two SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 51–72°. There are a spread of Si–O bond distances ranging from 1.61–1.66 Å. In the fourth Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share a cornercorner with one NaO6 octahedra, corners with two KO6 octahedra, corners with two AlO6 octahedra, a cornercorner with one AlO4 tetrahedra, and corners with two SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 50–72°. There are a spread of Si–O bond distances ranging from 1.61–1.66 Å. In the fifth Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share a cornercorner with one NaO6 octahedra, corners with two KO6 octahedra, corners with two AlO6 octahedra, a cornercorner with one SiO4 tetrahedra, and corners with two AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 53–65°. There are a spread of Si–O bond distances ranging from 1.62–1.66 Å. In the sixth Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share a cornercorner with one NaO6 octahedra, corners with two KO6 octahedra, corners with two AlO6 octahedra, and corners with three SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 53–72°. There are a spread of Si–O bond distances ranging from 1.62–1.65 Å. In the seventh Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share a cornercorner with one KO6 octahedra, a cornercorner with one NaO6 octahedra, corners with two AlO6 octahedra, a cornercorner with one SiO4 tetrahedra, and corners with tw

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 CsO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent LiO5 trigonal bipyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 0–6°. There are a spread of Cs–O bond distances ranging from 2.43–2.57 Å. Li1+ is bonded to five O2- atoms to form distorted LiO5 trigonal bipyramids that share corners with two equivalent CsO6 octahedra, corners with two equivalent MgO6 octahedra, corners with three MgO5 square pyramids, corners with two equivalent MgO5 trigonal bipyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 8–25°. There are a spread of Li–O bond distances ranging from 1.81–2.36 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 four MgO6 octahedra, corners with two equivalent LiO5 trigonal bipyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.03–2.28 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 four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. There are a spread of Mg–O bond distances ranging from 1.89–2.27 Å. In the third 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, a cornercorner with one LiO5 trigonal bipyramid, corners with two equivalent MgO5 trigonal bipyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 8°. There are a spread of Mg–O bond distances ranging from 1.97–2.16 Å. In the fourth 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 ten MgO6 octahedra, and edges with two equivalent MgO5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 1.84–2.26 Å. In the fifth 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 octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.10–2.23 Å. In the sixth Mg2+ site, Mg2+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.10–2.17 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 CsO6 octahedra, edges with eight MgO6 octahedra, an edgeedge with one MgO5 square pyramid, an edgeedge with one LiO5 trigonal bipyramid, and an edgeedge with one MgO5 trigonal bipyramid. The corner-sharing octahedra tilt angles range from 1–20°. There are a spread of Mg–O bond distances ranging from 2.07–2.24 Å. In the eighth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, edges with two MgO5 square pyramids, and an edgeedge with one MgO5 trigonal bipyramid. The corner-sharing octahedra tilt angles range from 1–7°. There are a spread of Mg–O bond distances ranging from 2.13–2.20 Å. In the ninth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 trigonal bipyramids that share corners with four MgO6 octahedra, corners with three MgO5 square pyramids, a cornercorner with one LiO5 trigonal bipyramid, a cornercorner with one MgO5 trigonal bipyramid, an edgeedge with one CsO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 6–24°. There are a spread of Mg–O bond distances ranging from 2.00–2.19 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 trigonal bipyramids, 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 2.12–2.19 Å. In the eleventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form distorted MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 trigonal bipyramids, an edgeedge with one CsO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one LiO5 trigonal bipyramid. The corner-sharing octahedra tilt angles range from 0–17°. There are a spread of Mg–O bond distances ranging from 2.10–2.51 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 2–4°. There are a spread of Mg–O bond distances ranging from 2.14–2.24 Å. In the thirteenth 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, a cornercorner with one LiO5 trigonal bipyramid, corners with two equivalent MgO5 trigonal bipyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 4–8°. There are a spread of Mg–O bond distances ranging from 2.00–2.18 Å. In the fourteenth 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 1–12°. There are a spread of Mg–O bond distances ranging from 2.11–2.28 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, edges with ten MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one LiO5 trigonal bipyramid. The corner-sharing octahedra tilt angles range from 4–6°. There are a spread of Mg–O bond distances ranging from 2.13–2.29 Å. In the sixteenth 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, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–17°. There are a spread of Mg–O bond distances ranging from 2.14–2.30 Å. There are seventeen inequivalent O2- sites. In the first 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 second 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 0–4°. In the third 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 0–8°. In the fourth O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form OLiMg5 octahedra that share corners with four OCsMg5 octahedra and edges with ten OMg6 octahedra. The corner-sharing octahedra tilt angles range from 6–9°. In the fifth 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 0–9°. In the sixth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the seventh O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. 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 OCsMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–11°. 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 0–6°. In the tenth O2- site, O2- is bonded in a 6-coordinate geometry to one Cs1+, one Li1+, and four Mg2+ atoms. In the eleventh O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. In the twelfth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with four OMg6 octahedra and edges with eleven OCsMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–14°. In the thirteenth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fourteenth O2- site, O2- is bonded to one Li1+ and five Mg2+ atoms to form OLiMg5 octahedra that share corners with six OCsMg5 octahedra and edges with nine OMg6 octahedra. The corner-sharing octahedra tilt angles range from 3–12°. In the fifteenth 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 4–11°. In the sixteenth 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 1–12°. In the seventeenth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–6°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Na3Mg2Mn4Be6Si9(SnO13)3 by Materials Project

Na3Mg2Be6Mn4Si9(SnO13)3 is Esseneite-derived structured and crystallizes in the monoclinic C2 space group. The structure is three-dimensional. there are three inequivalent Na1+ sites. In the first Na1+ site, Na1+ is bonded in a 4-coordinate geometry to four O2- atoms. There are a spread of Na–O bond distances ranging from 2.47–2.50 Å. In the second Na1+ site, Na1+ is bonded in a 4-coordinate geometry to four O2- atoms. There are a spread of Na–O bond distances ranging from 2.47–2.49 Å. In the third Na1+ site, Na1+ is bonded in a 4-coordinate geometry to four O2- atoms. There are a spread of Na–O bond distances ranging from 2.47–2.49 Å. There are three 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 SnO6 octahedra, corners with four SiO4 tetrahedra, an edgeedge with one MnO6 octahedra, an edgeedge with one SiO4 tetrahedra, and edges with two equivalent BeO4 tetrahedra. The corner-sharing octahedral tilt angles are 61°. There are a spread of Mg–O bond distances ranging from 2.10–2.16 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two SnO6 octahedra, corners with four SiO4 tetrahedra, an edgeedge with one MnO6 octahedra, an edgeedge with one SiO4 tetrahedra, and edges with two BeO4 tetrahedra. The corner-sharing octahedral tilt angles are 60°. There are a spread of Mg–O bond distances ranging from 2.09–2.16 Å. In the third Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent SnO6 octahedra, corners with four SiO4 tetrahedra, an edgeedge with one MnO6 octahedra, an edgeedge with one SiO4 tetrahedra, and edges with two equivalent BeO4 tetrahedra. The corner-sharing octahedral tilt angles are 61°. There are a spread of Mg–O bond distances ranging from 2.09–2.17 Å. There are six inequivalent Be2+ sites. In the first Be2+ site, Be2+ is bonded to four O2- atoms to form BeO4 tetrahedra that share a cornercorner with one BeO4 tetrahedra, corners with three SiO4 tetrahedra, an edgeedge with one MgO6 octahedra, and an edgeedge with one MnO6 octahedra. There are a spread of Be–O bond distances ranging from 1.55–1.73 Å. In the second Be2+ site, Be2+ is bonded to four O2- atoms to form BeO4 tetrahedra that share a cornercorner with one BeO4 tetrahedra, corners with three SiO4 tetrahedra, an edgeedge with one MgO6 octahedra, and an edgeedge with one MnO6 octahedra. There are a spread of Be–O bond distances ranging from 1.55–1.75 Å. In the third Be2+ site, Be2+ is bonded to four O2- atoms to form BeO4 tetrahedra that share a cornercorner with one BeO4 tetrahedra, corners with three SiO4 tetrahedra, an edgeedge with one MgO6 octahedra, and an edgeedge with one MnO6 octahedra. There are a spread of Be–O bond distances ranging from 1.55–1.73 Å. In the fourth Be2+ site, Be2+ is bonded to four O2- atoms to form BeO4 tetrahedra that share a cornercorner with one BeO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with two MnO6 octahedra. There are a spread of Be–O bond distances ranging from 1.54–1.74 Å. In the fifth Be2+ site, Be2+ is bonded to four O2- atoms to form BeO4 tetrahedra that share a cornercorner with one BeO4 tetrahedra, corners with three SiO4 tetrahedra, an edgeedge with one MgO6 octahedra, and an edgeedge with one MnO6 octahedra. There are a spread of Be–O bond distances ranging from 1.55–1.73 Å. In the sixth Be2+ site, Be2+ is bonded to four O2- atoms to form BeO4 tetrahedra that share a cornercorner with one BeO4 tetrahedra, corners with three SiO4 tetrahedra, and edges with two MnO6 octahedra. There are a spread of Be–O bond distances ranging from 1.54–1.74 Å. There are five inequivalent Mn+3.25+ sites. In the first Mn+3.25+ site, Mn+3.25+ is bonded to six O2- atoms to form distorted MnO6 octahedra that share corners with two SnO6 octahedra, corners with four SiO4 tetrahedra, an edgeedge with one MnO6 octahedra, an edgeedge with one SiO4 tetrahedra, and edges with two BeO4 tetrahedra. The corner-sharing octahedral tilt angles are 62°. There are a spread of Mn–O bond distances ranging from 2.13–2.19 Å. In the second Mn+3.25+ site, Mn+3.25+ is bonded to six O2- atoms to form distorted MnO6 octahedra that share corners with two SnO6 octahedra, corners with four SiO4 tetrahedra, an edgeedge with one MnO6 octahedra, an edgeedge with one SiO4 tetrahedra, and edges with two BeO4 tetrahedra. The corner-sharing octahedral tilt angles are 62°. There are a spread of Mn–O bond distances ranging from 2.16–2.19 Å. In the third Mn+3.25+ site, Mn+3.25+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with two equivalent SnO6 octahedra, corners with four SiO4 tetrahedra, an edgeedge with one MgO6 octahedra, an edgeedge with one SiO4 tetrahedra, and edges with two equivalent BeO4 tetrahedra. The corner-sharing octahedral tilt angles are 62°. There are a spread of Mn–O bond distances ranging from 2.15–2.20 Å. In the fourth Mn+3.25+ site, Mn+3.25+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with two SnO6 octahedra, corners with four SiO4 tetrahedra, an edgeedge with one MgO6 octahedra, an edgeedge with one SiO4 tetrahedra, and edges with two BeO4 tetrahedra. The corner-sharing octahedra tilt angles range from 61–62°. There are a spread of Mn–O bond distances ranging from 2.13–2.19 Å. In the fifth Mn+3.25+ site, Mn+3.25+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with two equivalent SnO6 octahedra, corners with four SiO4 tetrahedra, an edgeedge with one MgO6 octahedra, an edgeedge with one SiO4 tetrahedra, and edges with two equivalent BeO4 tetrahedra. The corner-sharing octahedral tilt angles are 62°. There are a spread of Mn–O bond distances ranging from 2.13–2.19 Å. There are three inequivalent Sn+3.33+ sites. In the first Sn+3.33+ site, Sn+3.33+ is bonded to six O2- atoms to form SnO6 octahedra that share corners with two MgO6 octahedra, corners with two MnO6 octahedra, and corners with six SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 61–62°. There are a spread of Sn–O bond distances ranging from 2.01–2.11 Å. In the second Sn+3.33+ site, Sn+3.33+ is bonded to six O2- atoms to form SnO6 octahedra that share a cornercorner with one MgO6 octahedra, corners with three MnO6 octahedra, and corners with six SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 60–62°. There are a spread of Sn–O bond distances ranging from 2.00–2.11 Å. In the third Sn+3.33+ site, Sn+3.33+ is bonded to six O2- atoms to form SnO6 octahedra that share a cornercorner with one MgO6 octahedra, corners with three MnO6 octahedra, and corners with six SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 60–62°. There are a spread of Sn–O bond distances ranging from 2.00–2.11 Å. There are eleven inequivalent Si4+ sites. In the first Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with two equivalent MnO6 octahedra, corners with two SnO6 octahedra, corners with two BeO4 tetrahedra, and an edgeedge with one MnO6 octahedra. The corner-sharing octahedra tilt angles range from 47–51°. There are a spread of Si–O bond distances ranging from 1.63–1.69 Å. In the second Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with two equivalent MnO6 octahedra, corners with two equivalent SnO6 octahedra, corners with two equivalent BeO4 tetrahedra, and an edgeedge with one MnO6 octahedra. The corner-sharing octahedra tilt angles range from 46–51°. There is two shorter (1.63 Å) and two longer (1.68 Å) Si–O bond length. In the third Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with two equivalent MnO6 octahedra, corners with two SnO6 octahedra, corners with two BeO4 tetrahedra, and an edgeedge with one MnO6 octahedra. The corner-sharing octahedra tilt angles range from 46–50°. There is two shorter (1.63 Å) and two longer (1.68 Å) Si–O bond length. In the fourth Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with two equivalent MnO6 octahedra, corners with two equivalent SnO6 octahedra, corners with two equivalent BeO4 tetrahedra, and an edgeedge with one MnO6 octahedra. The corner-sharing octahedra tilt angles range from 47–50°. There is two shorter (1.63 Å) and two longer (1.68 Å) Si–O bond length. In the fifth Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with two equivalent MgO6 octahedra, corners with two equivalent SnO6 octahedra, corners with two equivalent BeO4 tetrahedra, and an edgeedge with one MgO6 octahedra. The corner-sharing octahedra tilt angles range from 45–52°. There is two shorter (1.63 Å) and two longer (1.68 Å) Si–O bond length. In the sixth Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with two equivalent MgO6 octahedra, corners with two SnO6 octahedra, corners with two BeO4 tetrahedra, and an edgeedge with one MnO6 octahedra. The corner-sharing octahedra tilt angles range from 44–51°. There is two shorter (1.62 Å) and two longer (1.69 Å) Si–O bond length. In the seventh Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with two equivalent MgO6 octahedra, corners with two equivalent SnO6 octahedra, corners with two equivalent BeO4 tetrahedra, and an edgeedge with one MgO6 octahedra. The corner-sharing octahedra tilt angles range from 45–52°. There is two shorter (1.63 Å) and two longer (1.68 Å) Si–O bond length. In the eighth Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with two equivalent MnO6 octahedra, corners with two SnO6 octahedra, corners with two BeO4 tetrahedra, and an edgeedge with one MgO6 octahedra. The corner-sharing octahedra tilt angles range from 47–51°. There is two shorter (1.63 Å) and two longer (1.68 Å) Si–O bond length. In the ninth Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share a cornercorner with one MgO6 octahedra, corners with two SnO6 octahedra, corners with three MnO6 octahedra, and corners with two BeO4 tetrahedra. The corner-sharing octahedra tilt angles range from 31–63°. There are a spread of Si–O bond distances ranging from 1.61–1.67 Å. In the tenth Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with two MgO6 octahedra, corners with two MnO6 octahedra, corners with two SnO6 octahedra, and corners with two BeO4 tetrahedra. The corner-sharing octahedra tilt angles range from 31–63°. There are a spread of Si–O bond distances ranging from 1.61–1.67 Å. In the eleventh Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share a cornercorner with one MgO6 octahedra, corners with two equivalent SnO6 octahedra, corners with three MnO6 octahedra, and corners with two BeO4 tetrahedra. The corner-sharing octahedra tilt angles range from 31–63°. There are a spread of Si–O bond distances ranging from 1.61–1.67 Å. There are thirty-nine inequivalent O2- sites. In the first O2- site, O2- is bonded in a bent 150 degrees geometry to one Sn+3.33+ and one Si4+ atom. In the second O2- site, O2- is bonded in a bent 150 degrees geometry to one Sn+3.33+ and one Si4+ atom. In the third O2- site, O2- is bonded in a bent 150 degrees geometry to one Sn+3.33+ and one Si4+ atom. In the fourth O2- site, O2- is bonded in a bent 150 degrees geometry to one Sn+3.33+ and one Si4+ atom. In the fifth O2- site, O2- is bonded in a bent 150 degrees geometry to one Sn+3.33+ and one Si4+ atom. In the sixth O2- site, O2- is bonded in a bent 150 degrees geometry to one Sn+3.33+ and one Si4+ atom. In the seventh O2- site, O2- is bonded to one Na1+, one Mg2+, one Sn+3.33+, and one Si4+ atom to form a mixture of distorted corner and edge-sharing ONaMgSiSn

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Li7Fe5O12 by Materials Project

Li7Fe5O12 is Caswellsilverite-like structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are fourteen inequivalent Li sites. In the first Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five FeO6 octahedra, edges with five FeO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–10°. There are a spread of Li–O bond distances ranging from 2.08–2.25 Å. In the second Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five FeO6 octahedra, edges with five FeO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–9°. There are a spread of Li–O bond distances ranging from 2.06–2.28 Å. In the third Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six FeO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are four shorter (2.14 Å) and two longer (2.15 Å) Li–O bond lengths. In the fourth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five FeO6 octahedra, edges with five FeO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–10°. There are a spread of Li–O bond distances ranging from 2.07–2.25 Å. In the fifth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five FeO6 octahedra, edges with five FeO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–9°. There are a spread of Li–O bond distances ranging from 2.05–2.33 Å. In the sixth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five FeO6 octahedra, edges with five FeO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–10°. There are a spread of Li–O bond distances ranging from 2.07–2.27 Å. In the seventh Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five FeO6 octahedra, edges with five FeO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–9°. There are a spread of Li–O bond distances ranging from 2.05–2.35 Å. In the eighth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five FeO6 octahedra, edges with five FeO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–11°. There are a spread of Li–O bond distances ranging from 2.08–2.24 Å. In the ninth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five FeO6 octahedra, edges with five FeO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–9°. There are a spread of Li–O bond distances ranging from 2.06–2.35 Å. In the tenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five FeO6 octahedra, edges with five FeO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–10°. There are a spread of Li–O bond distances ranging from 2.05–2.29 Å. In the eleventh Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six FeO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are five shorter (2.14 Å) and one longer (2.15 Å) Li–O bond lengths. In the twelfth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five FeO6 octahedra, edges with five FeO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–10°. There are a spread of Li–O bond distances ranging from 2.05–2.29 Å. In the thirteenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five FeO6 octahedra, edges with five FeO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–10°. There are a spread of Li–O bond distances ranging from 2.05–2.29 Å. In the fourteenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with five FeO6 octahedra, edges with five FeO6 octahedra, and edges with seven LiO6 octahedra. The corner-sharing octahedra tilt angles range from 3–9°. There are a spread of Li–O bond distances ranging from 2.05–2.32 Å. There are ten inequivalent Fe sites. In the first Fe site, Fe is bonded to six O atoms to form FeO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six FeO6 octahedra. The corner-sharing octahedra tilt angles range from 4–6°. There are a spread of Fe–O bond distances ranging from 2.04–2.06 Å. In the second Fe site, Fe is bonded to six O atoms to form FeO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six FeO6 octahedra. The corner-sharing octahedra tilt angles range from 3–7°. There are a spread of Fe–O bond distances ranging from 2.04–2.06 Å. In the third Fe site, Fe is bonded to six O atoms to form FeO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six FeO6 octahedra. The corner-sharing octahedra tilt angles range from 3–7°. There are a spread of Fe–O bond distances ranging from 2.04–2.06 Å. In the fourth Fe site, Fe is bonded to six O atoms to form FeO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six FeO6 octahedra. The corner-sharing octahedra tilt angles range from 3–7°. There are a spread of Fe–O bond distances ranging from 2.04–2.06 Å. In the fifth Fe site, Fe is bonded to six O atoms to form FeO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six FeO6 octahedra. The corner-sharing octahedra tilt angles range from 4–6°. There are a spread of Fe–O bond distances ranging from 2.04–2.06 Å. In the sixth Fe site, Fe is bonded to six O atoms to form FeO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six FeO6 octahedra. The corner-sharing octahedra tilt angles range from 3–6°. There are a spread of Fe–O bond distances ranging from 2.04–2.06 Å. In the seventh Fe site, Fe is bonded to six O atoms to form FeO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent FeO6 octahedra, and edges with nine LiO6 octahedra. The corner-sharing octahedra tilt angles range from 9–11°. There are two shorter (2.03 Å) and four longer (2.04 Å) Fe–O bond lengths. In the eighth Fe site, Fe is bonded to six O atoms to form FeO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent FeO6 octahedra, and edges with nine LiO6 octahedra. The corner-sharing octahedra tilt angles range from 9–10°. All Fe–O bond lengths are 2.04 Å. In the ninth Fe site, Fe is bonded to six O atoms to form FeO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent FeO6 octahedra, and edges with nine LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–6°. There is one shorter (1.92 Å) and five longer (1.93 Å) Fe–O bond length. In the tenth Fe site, Fe is bonded to six O atoms to form FeO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent FeO6 octahedra, and edges with nine LiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–6°. There is two shorter (1.92 Å) and four longer (1.93 Å) Fe–O bond length. There are twenty-four inequivalent O sites. In the first O site, O is bonded to four Li and two Fe atoms to form a mixture of edge and corner-sharing OLi4Fe2 octahedra. The corner-sharing octahedra tilt angles range from 2–8°. In the second O site, O is bonded to four Li and two Fe atoms to form OLi4Fe2 octahedra that share corners with six OLi3Fe3 octahedra and edges with twelve OLi4Fe2 octahedra. The corner-sharing octahedra tilt angles range from 2–8°. In the third O site, O is bonded to four Li and two Fe atoms to form a mixture of edge and corner-sharing OLi4Fe2 octahedra. The corner-sharing octahedra tilt angles range from 3–8°. In the fourth O site, O is bonded to three Li and three Fe atoms to form a mixture of edge and corner-sharing OLi3Fe3 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the fifth O site, O is bonded to three Li and three Fe atoms to form a mixture of edge and corner-sharing OLi3Fe3 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the sixth O site, O is bonded to four Li and two Fe atoms to form a mixture of edge and corner-sharing OLi4Fe2 octahedra. The corner-sharing octahedra tilt angles range from 3–8°. In the seventh O site, O is bonded to three Li and three Fe atoms to form a mixture of edge and corner-sharing OLi3Fe3 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the eighth O site, O is bonded to three Li and three Fe atoms to form a mixture of edge and corner-sharing OLi3Fe3 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the ninth O site, O is bonded to four Li and two Fe atoms to form a mixture of edge and corner-sharing OLi4Fe2 octahedra. The corner-sharing octahedra tilt angles range from 3–8°. In the tenth O site, O is bonded to four Li and two Fe atoms to form a mixture of edge and corner-sharing OLi4Fe2 octahedra. The corner-sharing octahedra tilt angles range from 3–8°. In the eleventh O site, O is bonded to three Li and three Fe atoms to form OLi3Fe3 octahedra that share corners with six OLi4Fe2 octahedra and edges with twelve OLi3Fe3 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the twelfth O site, O is bonded to three Li and three Fe atoms to form OLi3Fe3 octahedra that share corners with six OLi4Fe2 octahedra and edges with twelve OLi3Fe3 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the thirteenth O site, O is bonded to four Li and two Fe atoms to form a mixture of edge and corner-sharing OLi4Fe2 octahedra. The corner-sharing octahedra tilt angles range from 1–9°. In the fourteenth O site, O is bonded to three Li and three Fe atoms to form a mixture of edge and corner-sharing OLi3Fe3 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fifteenth O site, O is bonded to three Li and three Fe atoms to form a mixture of edge and corner-sharing OLi3Fe3 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the sixteenth O site, O is bonded to three Li and three Fe atoms to form a mixture of edge and corner-sharing OLi3Fe3 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the seventeenth O site, O is bonded to four Li and two Fe atoms to form a mixture of edge and corner-sharing OLi4Fe2 octahedra. The corner-sharing octahedra tilt angles range from 2–8°. In the eighteenth O site, O is bonded to four Li and two Fe atoms to form a mixture of edge and corner-sharing OLi4Fe2 octahedra. The corner-sharing octahedra tilt angles range from 3–8°. In the nineteenth O site, O is bonded to three Li and three Fe atoms to form a mixture of edge and corner-sharing OLi3Fe3 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In

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 Li32Mn11Cr5O48 by Materials Project

Li32Cr5Mn11O48 is beta Polonium-derived structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are thirty-two inequivalent Li sites. In the first Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with two LiO6 octahedra, corners with two CrO6 octahedra, corners with two MnO6 octahedra, edges with two CrO6 octahedra, edges with two MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–10°. There are a spread of Li–O bond distances ranging from 2.06–2.23 Å. In the second Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–9°. There are a spread of Li–O bond distances ranging from 2.03–2.20 Å. In the third Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent CrO6 octahedra, edges with three equivalent MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are a spread of Li–O bond distances ranging from 2.07–2.12 Å. In the fourth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–10°. There are a spread of Li–O bond distances ranging from 2.02–2.19 Å. In the fifth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent CrO6 octahedra, edges with three equivalent MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are a spread of Li–O bond distances ranging from 2.07–2.13 Å. In the sixth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–9°. There are a spread of Li–O bond distances ranging from 2.03–2.19 Å. In the seventh Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six MnO6 octahedra. The corner-sharing octahedral tilt angles are 9°. There are a spread of Li–O bond distances ranging from 2.08–2.10 Å. In the eighth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with two LiO6 octahedra, corners with two CrO6 octahedra, corners with two MnO6 octahedra, edges with two CrO6 octahedra, edges with two MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–9°. There are a spread of Li–O bond distances ranging from 2.06–2.22 Å. In the ninth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with two LiO6 octahedra, corners with two CrO6 octahedra, corners with two MnO6 octahedra, edges with two CrO6 octahedra, edges with two MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. There are a spread of Li–O bond distances ranging from 2.03–2.20 Å. In the tenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are a spread of Li–O bond distances ranging from 2.07–2.20 Å. In the eleventh Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–9°. There are a spread of Li–O bond distances ranging from 2.07–2.20 Å. In the twelfth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent CrO6 octahedra, edges with three equivalent MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are a spread of Li–O bond distances ranging from 2.07–2.12 Å. In the thirteenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–8°. There are a spread of Li–O bond distances ranging from 2.03–2.21 Å. In the fourteenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with two LiO6 octahedra, corners with two CrO6 octahedra, corners with two MnO6 octahedra, edges with two CrO6 octahedra, edges with two MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are a spread of Li–O bond distances ranging from 2.07–2.21 Å. In the fifteenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–9°. There are a spread of Li–O bond distances ranging from 2.06–2.20 Å. In the sixteenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–9°. There are a spread of Li–O bond distances ranging from 2.05–2.19 Å. In the seventeenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–9°. There are a spread of Li–O bond distances ranging from 2.06–2.20 Å. In the eighteenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–9°. There are a spread of Li–O bond distances ranging from 2.06–2.20 Å. In the nineteenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–9°. There are a spread of Li–O bond distances ranging from 2.06–2.20 Å. In the twentieth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–9°. There are a spread of Li–O bond distances ranging from 2.06–2.19 Å. In the twenty-first Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–9°. There are a spread of Li–O bond distances ranging from 2.06–2.19 Å. In the twenty-second Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six MnO6 octahedra. The corner-sharing octahedral tilt angles are 9°. There are a spread of Li–O bond distances ranging from 2.08–2.10 Å. In the twenty-third Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with two LiO6 octahedra, corners with two CrO6 octahedra, corners with two MnO6 octahedra, edges with two CrO6 octahedra, edges with two MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–10°. There are a spread of Li–O bond distances ranging from 2.06–2.22 Å. In the twenty-fourth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–10°. There are a spread of Li–O bond distances ranging from 2.06–2.23 Å. In the twenty-fifth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–9°. There are a spread of Li–O bond distances ranging from 2.03–2.20 Å. In the twenty-sixth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share a cornercorner with one CrO6 octahedra, corners with two LiO6 octahedra, corners with three MnO6 octahedra, an edgeedge with one CrO6 octahedra, edges with three MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–9°. There are a spread of Li–O bond distances ranging from 2.06–2.19 Å. In the twenty-seventh Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with three equivalent CrO6 octahedra, edges with three equivalent MnO6 octahedra, and edges with six LiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are a spread of Li–O bond distances ranging from 2.07–2.12 Å. In the twenty-eighth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with two LiO6 octahedra, corners with two CrO6 octahedra, corners with two MnO6 octahedra, edges with two CrO6 octahedra, edges with two MnO6 octahedra, and edges with eight LiO6 octahedra. The corner-sharing octahedra tilt angles range from 6–9°. There are a spread of Li–O bond distances ranging from 2.03–2.19 Å. In the twenty-ninth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO6 octahedra, edges with six LiO6 octahedra, and edges with six MnO6 octahedra. The corner-sharing octahedra tilt angles range from 8–9°. There are a spread of Li–O bond distances ranging from 2.08–2.10 Å. In the thirtieth Li site, Li is bonded

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Sn2N2O by Materials Project

Sn2N2O is Ilmenite-like structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are sixteen inequivalent Sn4+ sites. In the first Sn4+ site, Sn4+ is bonded to two N3- and four O2- atoms to form SnN2O4 octahedra that share corners with five SnN3O3 octahedra and edges with five SnN4O2 octahedra. The corner-sharing octahedra tilt angles range from 48–57°. There are one shorter (2.13 Å) and one longer (2.14 Å) Sn–N bond lengths. There are a spread of Sn–O bond distances ranging from 2.15–2.18 Å. In the second Sn4+ site, Sn4+ is bonded in a 6-coordinate geometry to three N3- and three O2- atoms. There are one shorter (2.16 Å) and two longer (2.17 Å) Sn–N bond lengths. There are a spread of Sn–O bond distances ranging from 2.12–2.35 Å. In the third Sn4+ site, Sn4+ is bonded to three N3- and three O2- atoms to form distorted SnN3O3 octahedra that share corners with five SnN2O4 octahedra and edges with six SnN6 octahedra. The corner-sharing octahedra tilt angles range from 49–57°. There are a spread of Sn–N bond distances ranging from 2.18–2.23 Å. There are a spread of Sn–O bond distances ranging from 2.09–2.25 Å. In the fourth Sn4+ site, Sn4+ is bonded in a 6-coordinate geometry to four N3- and two O2- atoms. There are a spread of Sn–N bond distances ranging from 2.09–2.16 Å. There are one shorter (2.38 Å) and one longer (2.48 Å) Sn–O bond lengths. In the fifth Sn4+ site, Sn4+ is bonded to four N3- and two O2- atoms to form distorted SnN4O2 octahedra that share corners with six SnN3O3 octahedra and edges with five SnN2O4 octahedra. The corner-sharing octahedra tilt angles range from 50–57°. There are a spread of Sn–N bond distances ranging from 2.13–2.21 Å. There are one shorter (2.17 Å) and one longer (2.28 Å) Sn–O bond lengths. In the sixth Sn4+ site, Sn4+ is bonded to three N3- and three O2- atoms to form distorted SnN3O3 octahedra that share corners with five SnN2O4 octahedra and edges with five SnN4O2 octahedra. The corner-sharing octahedra tilt angles range from 48–58°. There are a spread of Sn–N bond distances ranging from 2.11–2.18 Å. There are a spread of Sn–O bond distances ranging from 2.15–2.26 Å. In the seventh Sn4+ site, Sn4+ is bonded to six N3- atoms to form SnN6 octahedra that share corners with five SnN4O2 octahedra and edges with five SnN3O3 octahedra. The corner-sharing octahedra tilt angles range from 53–59°. There are a spread of Sn–N bond distances ranging from 2.22–2.27 Å. In the eighth Sn4+ site, Sn4+ is bonded to four N3- and two O2- atoms to form distorted SnN4O2 octahedra that share corners with five SnN3O3 octahedra and edges with five SnN2O4 octahedra. The corner-sharing octahedra tilt angles range from 50–58°. There are a spread of Sn–N bond distances ranging from 2.10–2.21 Å. There are one shorter (2.32 Å) and one longer (2.34 Å) Sn–O bond lengths. In the ninth Sn4+ site, Sn4+ is bonded to four N3- and two O2- atoms to form a mixture of corner and edge-sharing SnN4O2 octahedra. The corner-sharing octahedra tilt angles range from 49–61°. There are a spread of Sn–N bond distances ranging from 2.13–2.19 Å. There are one shorter (2.26 Å) and one longer (2.30 Å) Sn–O bond lengths. In the tenth Sn4+ site, Sn4+ is bonded to four N3- and two O2- atoms to form distorted SnN4O2 octahedra that share corners with five SnN2O4 octahedra and edges with five SnN3O3 octahedra. The corner-sharing octahedra tilt angles range from 51–59°. There are a spread of Sn–N bond distances ranging from 2.11–2.21 Å. There are one shorter (2.29 Å) and one longer (2.33 Å) Sn–O bond lengths. In the eleventh Sn4+ site, Sn4+ is bonded to four N3- and two O2- atoms to form SnN4O2 octahedra that share corners with four SnN4O2 octahedra and edges with six SnN3O3 octahedra. The corner-sharing octahedra tilt angles range from 54–55°. There are a spread of Sn–N bond distances ranging from 2.16–2.23 Å. Both Sn–O bond lengths are 2.20 Å. In the twelfth Sn4+ site, Sn4+ is bonded to five N3- and one O2- atom to form distorted SnN5O octahedra that share corners with five SnN4O2 octahedra and edges with five SnN2O4 octahedra. The corner-sharing octahedra tilt angles range from 53–61°. There are a spread of Sn–N bond distances ranging from 2.13–2.23 Å. The Sn–O bond length is 2.51 Å. In the thirteenth Sn4+ site, Sn4+ is bonded to four N3- and two O2- atoms to form distorted SnN4O2 octahedra that share corners with five SnN6 octahedra and edges with six SnN2O4 octahedra. The corner-sharing octahedra tilt angles range from 53–58°. There are a spread of Sn–N bond distances ranging from 2.10–2.19 Å. There are one shorter (2.28 Å) and one longer (2.35 Å) Sn–O bond lengths. In the fourteenth Sn4+ site, Sn4+ is bonded to five N3- and one O2- atom to form distorted SnN5O octahedra that share corners with five SnN4O2 octahedra and edges with six SnN2O4 octahedra. The corner-sharing octahedra tilt angles range from 53–58°. There are a spread of Sn–N bond distances ranging from 2.12–2.25 Å. The Sn–O bond length is 2.41 Å. In the fifteenth Sn4+ site, Sn4+ is bonded to four N3- and two O2- atoms to form distorted SnN4O2 octahedra that share corners with six SnN2O4 octahedra and edges with five SnN4O2 octahedra. The corner-sharing octahedra tilt angles range from 51–58°. There are a spread of Sn–N bond distances ranging from 2.09–2.27 Å. There are one shorter (2.17 Å) and one longer (2.29 Å) Sn–O bond lengths. In the sixteenth Sn4+ site, Sn4+ is bonded to five N3- and one O2- atom to form distorted SnN5O octahedra that share corners with five SnN2O4 octahedra and edges with six SnN3O3 octahedra. The corner-sharing octahedra tilt angles range from 54–58°. There are a spread of Sn–N bond distances ranging from 2.15–2.27 Å. The Sn–O bond length is 2.18 Å. There are sixteen inequivalent N3- sites. In the first N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 tetrahedra that share corners with six NSn4 tetrahedra, corners with two NSn4 trigonal pyramids, corners with three OSn4 trigonal pyramids, an edgeedge with one NSn4 tetrahedra, and edges with three OSn4 trigonal pyramids. In the second N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 tetrahedra that share corners with seven NSn4 tetrahedra, corners with two NSn4 trigonal pyramids, corners with three OSn4 trigonal pyramids, an edgeedge with one NSn4 tetrahedra, and edges with three OSn4 trigonal pyramids. In the third N3- site, N3- is bonded to four Sn4+ atoms to form NSn4 tetrahedra that share corners with seven NSn4 tetrahedra, corners with two OSn4 trigonal pyramids, corners with three NSn4 trigonal pyramids, an edgeedge with one NSn4 trigonal pyramid, and edges with two OSn4 trigonal pyramids. In the fourth N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 tetrahedra that share corners with seven NSn4 tetrahedra, corners with two NSn4 trigonal pyramids, corners with three OSn4 trigonal pyramids, an edgeedge with one NSn4 tetrahedra, an edgeedge with one NSn4 trigonal pyramid, and an edgeedge with one OSn4 trigonal pyramid. In the fifth N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 tetrahedra that share corners with four NSn4 tetrahedra, corners with three NSn4 trigonal pyramids, corners with four OSn4 trigonal pyramids, edges with two NSn4 tetrahedra, and edges with two OSn4 trigonal pyramids. In the sixth N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 tetrahedra that share corners with five NSn4 tetrahedra, corners with three NSn4 trigonal pyramids, corners with four OSn4 trigonal pyramids, edges with two NSn4 tetrahedra, an edgeedge with one NSn4 trigonal pyramid, and an edgeedge with one OSn4 trigonal pyramid. In the seventh N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 tetrahedra that share corners with six NSn4 tetrahedra, corners with two NSn4 trigonal pyramids, corners with three OSn4 trigonal pyramids, an edgeedge with one NSn4 tetrahedra, an edgeedge with one OSn4 trigonal pyramid, and edges with two NSn4 trigonal pyramids. In the eighth N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 trigonal pyramids that share corners with four NSn4 tetrahedra, corners with three NSn4 trigonal pyramids, corners with four OSn4 trigonal pyramids, edges with three NSn4 tetrahedra, and an edgeedge with one OSn4 trigonal pyramid. In the ninth N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 trigonal pyramids that share corners with four NSn4 tetrahedra, corners with two NSn4 trigonal pyramids, corners with five OSn4 trigonal pyramids, edges with three NSn4 tetrahedra, and an edgeedge with one NSn4 trigonal pyramid. In the tenth N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 tetrahedra that share corners with six NSn4 tetrahedra, corners with two NSn4 trigonal pyramids, corners with three OSn4 trigonal pyramids, edges with two NSn4 trigonal pyramids, and edges with two OSn4 trigonal pyramids. In the eleventh N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 tetrahedra that share corners with seven NSn4 tetrahedra, corners with two NSn4 trigonal pyramids, corners with three OSn4 trigonal pyramids, an edgeedge with one NSn4 tetrahedra, an edgeedge with one NSn4 trigonal pyramid, and an edgeedge with one OSn4 trigonal pyramid. In the twelfth N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 trigonal pyramids that share corners with seven NSn4 tetrahedra, corners with two NSn4 trigonal pyramids, corners with three OSn4 trigonal pyramids, edges with two NSn4 tetrahedra, and edges with two OSn4 trigonal pyramids. In the thirteenth N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 tetrahedra that share corners with four NSn4 tetrahedra, corners with three NSn4 trigonal pyramids, corners with four OSn4 trigonal pyramids, edges with two NSn4 tetrahedra, an edgeedge with one NSn4 trigonal pyramid, and an edgeedge with one OSn4 trigonal pyramid. In the fourteenth N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 tetrahedra that share corners with seven NSn4 tetrahedra, corners with two NSn4 trigonal pyramids, corners with three OSn4 trigonal pyramids, an edgeedge with one NSn4 tetrahedra, an edgeedge with one OSn4 trigonal pyramid, and edges with two NSn4 trigonal pyramids. In the fifteenth N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 trigonal pyramids that share corners with four NSn4 tetrahedra, corners with three NSn4 trigonal pyramids, corners with four OSn4 trigonal pyramids, edges with three NSn4 tetrahedra, and an edgeedge with one NSn4 trigonal pyramid. In the sixteenth N3- site, N3- is bonded to four Sn4+ atoms to form distorted NSn4 trigonal pyramids that share corners with seven NSn4 tetrahedra, corners with two NSn4 trigonal pyramids, corners with three OSn4 trigonal pyramids, edges with two NSn4 trigonal pyramids, and edges with two OSn4 trigonal pyramids. There are eight inequivalent O2- sites. In the first O2- site, O2- is bonded to four Sn4+ atoms to form distorted OSn4 trigonal pyramids that share corners with seven NSn4 tetrahedra, corners with two OSn4 trigonal pyramids, corners with three NSn4 trigonal pyramids, edges with two NSn4 tetrahedra, and edges with two OSn4 trigonal pyramids. In the second O2- site, O2- is bonded to four Sn4+ atoms to form distorted OSn4 trigonal pyramids that share corners with four NSn4 tetrahedra, corners with two NSn4 trigonal pyramids, corners with five OSn4 trigonal pyramids, edges with three NSn4 tetrahedra, and an edgeedge with one NSn4 trigonal pyramid. In the third O2- site, O2- is bonded to four Sn4+ atoms to form distorted OSn4 trigonal pyramids that share corners with four NSn4 tetrahedra, corners with two NSn4 trigonal pyramids, corners with five OSn4 trigonal pyramids, edges with two NSn4 tetrahedra, and edges with two NSn4 trigonal pyramids. In the fourth O2- site, O2- is bonded to four Sn4+ atoms to fo

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on RbHfMg30O31 by Materials Project

RbMg30HfO31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Rb is bonded to five O atoms to form RbO5 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 4–5°. There are a spread of Rb–O bond distances ranging from 2.40–2.55 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 RbO5 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 1.93–2.26 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent 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 2.13–2.21 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 RbO5 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 2.01–2.28 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 octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.11–2.18 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 octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.10–2.21 Å. In the sixth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.15–2.18 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 RbO5 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 2.10–2.28 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Mg–O bond distances ranging from 2.16–2.21 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 RbO5 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 4–12°. There are a spread of Mg–O bond distances ranging from 2.06–2.28 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Mg–O bond distances ranging from 2.14–2.19 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 RbO5 square pyramid, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 4–8°. There are a spread of Mg–O bond distances ranging from 2.07–2.26 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 2.14–2.21 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 RbO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–10°. There are a spread of Mg–O bond distances ranging from 2.09–2.22 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 3–5°. There are a spread of Mg–O bond distances ranging from 2.10–2.24 Å. In the fifteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, an edgeedge with one RbO5 square pyramid, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 1–11°. There are a spread of Mg–O bond distances ranging from 2.11–2.21 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 3–5°. There are a spread of Mg–O bond distances ranging from 2.10–2.23 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent RbO5 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 2.00–2.15 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 octahedra tilt angles range from 0–1°. In the third O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fourth O site, O is bonded to one Rb and five Mg atoms to form ORbMg5 octahedra that share corners with four OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 2–6°. 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 0–6°. In the seventh O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. 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 ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–6°. In the tenth O site, O is bonded to one Rb, four Mg, and one Hf atom to form ORbHfMg4 octahedra that share corners with six OMg6 octahedra and edges with eleven OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–11°. 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 0–11°. 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 0–4°. In the fourteenth O site, O is bonded to one Rb and five Mg atoms to form ORbMg5 octahedra that share corners with six OHfMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. 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 0–7°. In the seventeenth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on 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 HfO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.25 Å) and two longer (2.26 Å) Na–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 two equivalent NaO6 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 2.04–2.17 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent HfO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.10–2.15 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 2.03–2.17 Å. In the fourth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one HfO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.12–2.15 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 2.12–2.16 Å. In the sixth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are one shorter (2.12 Å) and five 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 NaO6 octahedra, edges with eight MgO6 octahedra, an edgeedge with one HfO5 square pyramid, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–8°. There are a spread of Mg–O bond distances ranging from 2.09–2.20 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 2.13–2.16 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, a cornercorner with one HfO5 square pyramid, 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 2–8°. There are a spread of Mg–O bond distances ranging from 2.08–2.19 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.13–2.16 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, an edgeedge with one MgO5 square pyramid, and an edgeedge with one HfO5 square pyramid. The corner-sharing octahedra tilt angles range from 2–4°. There are a spread of Mg–O bond distances ranging from 2.10–2.19 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 1–2°. There are a spread of Mg–O bond distances ranging from 2.13–2.16 Å. In the thirteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one NaO6 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 2.13–2.15 Å. In the fourteenth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one HfO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. There are a spread of Mg–O bond distances ranging from 2.11–2.21 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 1–6°. There are a spread of Mg–O bond distances ranging from 2.14–2.16 Å. In the sixteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one HfO5 square pyramid. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.11–2.17 Å. Hf is bonded to five O atoms to form HfO5 square pyramids that share corners with two equivalent NaO6 octahedra, corners with two equivalent MgO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–6°. There are a spread of Hf–O bond distances ranging from 2.05–2.26 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 0–4°. 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 0–4°. In the third O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedral tilt angles are 0°. 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 five Mg and one Hf atom to form OHfMg5 octahedra that share corners with four ONaMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedral tilt angles are 1°. 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 0–4°. In the seventh O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the tenth O site, O is bonded to one Na, four Mg, and one Hf atom to form ONaHfMg4 octahedra that share corners with six OMg6 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 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 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 0–7°. 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 0–2°. 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 0–4°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the sixteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve ONaMg5 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 OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on RbNaMg30O31 by Materials Project

RbNaMg30O31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Rb1+ is bonded to six O2- atoms to form RbO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent NaO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–5°. There are a spread of Rb–O bond distances ranging from 2.36–2.49 Å. Na1+ is bonded to five O2- atoms to form NaO5 square pyramids that share corners with two equivalent RbO6 octahedra, corners with two equivalent MgO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 5–16°. There are a spread of Na–O bond distances ranging from 2.01–2.32 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 four MgO6 octahedra, corners with two equivalent NaO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.03–2.26 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent RbO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. There are a spread of Mg–O bond distances ranging from 1.92–2.25 Å. In the third Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one NaO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 8°. There are a spread of Mg–O bond distances ranging from 1.94–2.14 Å. In the fourth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent RbO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 1.88–2.28 Å. In the fifth 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 octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.09–2.21 Å. In the sixth 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 0–1°. There are a spread of Mg–O bond distances ranging from 2.10–2.19 Å. In the seventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one RbO6 octahedra, edges with eight MgO6 octahedra, an edgeedge with one NaO5 square pyramid, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–13°. 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 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 2.13–2.18 Å. In the ninth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one NaO5 square pyramid, corners with four MgO5 square pyramids, an edgeedge with one RbO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 8–14°. There are a spread of Mg–O bond distances ranging from 1.99–2.18 Å. In the tenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, 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 2.14–2.20 Å. In the eleventh Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one RbO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one NaO5 square pyramid, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 1–15°. There are a spread of Mg–O bond distances ranging from 2.14–2.39 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 1–3°. There are a spread of Mg–O bond distances ranging from 2.15–2.21 Å. In the thirteenth Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one NaO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–8°. There are a spread of Mg–O bond distances ranging from 1.97–2.14 Å. In the fourteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one RbO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–11°. There are a spread of Mg–O bond distances ranging from 2.11–2.25 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, edges with ten MgO6 octahedra, an edgeedge with one NaO5 square pyramid, and an edgeedge with one MgO5 square pyramid. The corner-sharing octahedra tilt angles range from 2–7°. There are a spread of Mg–O bond distances ranging from 2.15–2.27 Å. In the sixteenth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one RbO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–15°. There are a spread of Mg–O bond distances ranging from 2.15–2.24 Å. There are seventeen inequivalent O2- sites. In the first O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form a mixture of distorted corner and edge-sharing ORbMg5 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 a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the third O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the fourth O2- site, O2- is bonded to one Na1+ and five Mg2+ atoms to form ONaMg5 octahedra that share corners with four ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 6–9°. In the fifth O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form distorted ORbMg5 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. 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 a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the eighth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–12°. In the ninth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve ONaMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the tenth O2- site, O2- is bonded to one Rb1+, one Na1+, and four Mg2+ atoms to form distorted ORbNaMg4 octahedra that share corners with six OMg6 octahedra and edges with eleven ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 5–19°. 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 and edges with eleven ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 3–19°. In the thirteenth O2- site, O2- is bonded to six Mg2+ atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fourteenth O2- site, O2- is bonded to one Na1+ and five Mg2+ atoms to form ONaMg5 octahedra that share corners with six ORbMg5 octahedra and edges with eleven OMg6 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 a mixture of corner and edge-sharing ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 3–10°. In the sixteenth 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 2–11°. In the seventeenth 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 1–6°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on CsRbMg30O31 by Materials Project

CsRbMg30O31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Cs1+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Cs–O bond distances ranging from 2.45–2.70 Å. Rb1+ is bonded to six O2- atoms to form RbO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 trigonal bipyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Rb–O bond distances ranging from 2.39–2.53 Å. There are sixteen inequivalent Mg2+ sites. In the first Mg2+ site, Mg2+ is bonded to five O2- atoms to form MgO5 trigonal bipyramids that share corners with two equivalent RbO6 octahedra, corners with five MgO5 square pyramids, corners with two equivalent MgO5 trigonal bipyramids, and edges with six MgO6 octahedra. The corner-sharing octahedral tilt angles are 9°. There are a spread of Mg–O bond distances ranging from 1.95–2.11 Å. In the second Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent RbO6 octahedra, corners with two equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 1.95–2.38 Å. In the third Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent RbO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 1.95–2.29 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, 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 2.02–2.12 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 0–1°. There are a spread of Mg–O bond distances ranging from 2.06–2.16 Å. In the sixth Mg2+ site, Mg2+ is bonded to six O2- atoms to form MgO6 octahedra that share corners with two equivalent 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 octahedral tilt angles are 1°. There are a spread of Mg–O bond distances ranging from 1.86–2.29 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 RbO6 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 2.18–2.32 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 0–8°. There are a spread of Mg–O bond distances ranging from 2.13–2.27 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 RbO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 7–17°. There are a spread of Mg–O bond distances ranging from 2.02–2.21 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 nine MgO6 octahedra, and edges with two equivalent MgO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 2–9°. There are a spread of Mg–O bond distances ranging from 2.07–2.30 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 RbO6 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 2–14°. There are a spread of Mg–O bond distances ranging from 2.19–2.30 Å. In the twelfth Mg2+ site, Mg2+ is bonded to six O2- atoms to form distorted MgO6 octahedra that share corners with six MgO6 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 2.13–2.55 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 RbO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 2–12°. There are a spread of Mg–O bond distances ranging from 2.11–2.26 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, and edges with seven MgO6 octahedra. The corner-sharing octahedral tilt angles are 9°. There are a spread of Mg–O bond distances ranging from 1.96–2.24 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 RbO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–14°. There are a spread of Mg–O bond distances ranging from 2.14–2.27 Å. In the sixteenth 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 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 6–82°. There are a spread of Mg–O bond distances ranging from 2.10–2.21 Å. There are seventeen inequivalent O2- sites. In the first O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form a mixture of distorted corner and edge-sharing ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–10°. In the second O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–10°. In the third O2- site, O2- is bonded to one Cs1+ and five Mg2+ atoms to form a mixture of distorted corner and edge-sharing OCsMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the fourth O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form distorted ORbMg5 octahedra that share corners with six ORbMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–10°. In the fifth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with four ORbMg5 octahedra and edges with ten OMg6 octahedra. The corner-sharing octahedra tilt angles range from 2–8°. 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 0–10°. In the seventh O2- site, O2- is bonded to one Cs1+ and five Mg2+ atoms to form a mixture of distorted corner and edge-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 ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–12°. In the ninth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–13°. In the tenth O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form distorted ORbMg5 octahedra that share corners with six OCsMg5 octahedra and edges with nine ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–19°. 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 2–21°. 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 ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–19°. 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 2–4°. In the fourteenth O2- site, O2- is bonded to one Rb1+ and five Mg2+ atoms to form ORbMg5 octahedra that share corners with four OMg6 octahedra and edges with twelve ORbMg5 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 ORbMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the seventeenth O2- site, O2- is bonded to six Mg2+ atoms to form OMg6 octahedra that share corners with four OMg6 octahedra and edges with eleven OCsMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–15°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on LiHfMg30O31 by Materials Project

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

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on NaLiMg30O31 by Materials Project

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

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KHfMg30O31 by Materials Project

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

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KLiMg30O31 by Materials Project

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

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KNaMg30O31 by Materials Project

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

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on RbHfMg30O31 by Materials Project

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

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KHfMg30O31 by Materials Project

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

36 MATERIALS SCIENCE↗