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Materials Data on Ti20(AlSi3)3 by Materials Project

Ti20(AlSi3)3 crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are sixteen inequivalent Ti sites. In the first Ti site, Ti is bonded in a 8-coordinate geometry to two equivalent Ti, two Al, and four Si atoms. There are one shorter (2.55 Å) and one longer (2.62 Å) Ti–Ti bond lengths. Both Ti–Al bond lengths are 2.69 Å. There are a spread of Ti–Si bond distances ranging from 2.63–2.67 Å. In the second Ti site, Ti is bonded in a 8-coordinate geometry to two equivalent Ti, one Al, and five Si atoms. There are one shorter (2.57 Å) and one longer (2.60 Å) Ti–Ti bond lengths. The Ti–Al bond length is 2.69 Å. There are a spread of Ti–Si bond distances ranging from 2.64–2.68 Å. In the third Ti site, Ti is bonded in a 8-coordinate geometry to two equivalent Ti, two Al, and four Si atoms. There are one shorter (2.55 Å) and one longer (2.62 Å) Ti–Ti bond lengths. There are one shorter (2.68 Å) and one longer (2.69 Å) Ti–Al bond lengths. There are a spread of Ti–Si bond distances ranging from 2.63–2.69 Å. In the fourth Ti site, Ti is bonded in a 8-coordinate geometry to two equivalent Ti, one Al, and five Si atoms. There are one shorter (2.57 Å) and one longer (2.60 Å) Ti–Ti bond lengths. The Ti–Al bond length is 2.69 Å. There are a spread of Ti–Si bond distances ranging from 2.63–2.66 Å. In the fifth Ti site, Ti is bonded in a 5-coordinate geometry to one Al and four Si atoms. The Ti–Al bond length is 2.75 Å. There are a spread of Ti–Si bond distances ranging from 2.57–2.82 Å. In the sixth Ti site, Ti is bonded in a 5-coordinate geometry to two Al and three Si atoms. There are one shorter (2.65 Å) and one longer (2.74 Å) Ti–Al bond lengths. There are one shorter (2.56 Å) and two longer (2.82 Å) Ti–Si bond lengths. In the seventh Ti site, Ti is bonded in a 5-coordinate geometry to two Al and three Si atoms. There are one shorter (2.63 Å) and one longer (2.74 Å) Ti–Al bond lengths. There are one shorter (2.55 Å) and two longer (2.83 Å) Ti–Si bond lengths. In the eighth Ti site, Ti is bonded in a 5-coordinate geometry to one Al and four Si atoms. The Ti–Al bond length is 2.64 Å. There are a spread of Ti–Si bond distances ranging from 2.56–2.79 Å. In the ninth Ti site, Ti is bonded in a 5-coordinate geometry to two Al and three Si atoms. Both Ti–Al bond lengths are 2.62 Å. There are one shorter (2.70 Å) and two longer (2.79 Å) Ti–Si bond lengths. In the tenth Ti site, Ti is bonded in a 5-coordinate geometry to one Al and four Si atoms. The Ti–Al bond length is 2.63 Å. There are a spread of Ti–Si bond distances ranging from 2.56–2.80 Å. In the eleventh Ti site, Ti is bonded in a 5-coordinate geometry to two equivalent Al and three Si atoms. Both Ti–Al bond lengths are 2.81 Å. There are a spread of Ti–Si bond distances ranging from 2.56–2.73 Å. In the twelfth Ti site, Ti is bonded in a 5-coordinate geometry to two equivalent Al and three Si atoms. Both Ti–Al bond lengths are 2.82 Å. There are a spread of Ti–Si bond distances ranging from 2.56–2.73 Å. In the thirteenth Ti site, Ti is bonded in a 3-coordinate geometry to two equivalent Al and three Si atoms. Both Ti–Al bond lengths are 2.83 Å. There are a spread of Ti–Si bond distances ranging from 2.57–2.72 Å. In the fourteenth Ti site, Ti is bonded in a 5-coordinate geometry to five Si atoms. There are a spread of Ti–Si bond distances ranging from 2.59–2.80 Å. In the fifteenth Ti site, Ti is bonded in a 5-coordinate geometry to five Si atoms. There are a spread of Ti–Si bond distances ranging from 2.61–2.80 Å. In the sixteenth Ti site, Ti is bonded in a 5-coordinate geometry to five Si atoms. There are a spread of Ti–Si bond distances ranging from 2.60–2.80 Å. There are three inequivalent Al sites. In the first Al site, Al is bonded in a 9-coordinate geometry to nine Ti atoms. In the second Al site, Al is bonded in a 9-coordinate geometry to nine Ti atoms. In the third Al site, Al is bonded in a 11-coordinate geometry to nine Ti atoms. There are nine inequivalent Si sites. In the first Si site, Si is bonded in a 9-coordinate geometry to nine Ti atoms. In the second Si site, Si is bonded in a 9-coordinate geometry to nine Ti atoms. In the third Si site, Si is bonded in a 9-coordinate geometry to nine Ti atoms. In the fourth Si site, Si is bonded in a 9-coordinate geometry to nine Ti atoms. In the fifth Si site, Si is bonded in a 9-coordinate geometry to nine Ti atoms. In the sixth Si site, Si is bonded in a 9-coordinate geometry to nine Ti atoms. In the seventh Si site, Si is bonded in a 9-coordinate geometry to nine Ti atoms. In the eighth Si site, Si is bonded in a 9-coordinate geometry to nine Ti atoms. In the ninth Si site, Si is bonded in a 9-coordinate geometry to nine Ti atoms.

36 MATERIALS SCIENCE↗

Materials Data on Sr8(TiS3)7 by Materials Project

Sr8(TiS3)7 crystallizes in the trigonal P3 space group. The structure is three-dimensional. there are eight inequivalent Sr2+ sites. In the first Sr2+ site, Sr2+ is bonded in a 8-coordinate geometry to eight S2- atoms. There are a spread of Sr–S bond distances ranging from 2.99–3.48 Å. In the second Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine S2- atoms. There are a spread of Sr–S bond distances ranging from 2.98–3.53 Å. In the third Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine S2- atoms. There are a spread of Sr–S bond distances ranging from 2.96–3.62 Å. In the fourth Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine S2- atoms. There are a spread of Sr–S bond distances ranging from 2.98–3.54 Å. In the fifth Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine S2- atoms. There are a spread of Sr–S bond distances ranging from 2.98–3.52 Å. In the sixth Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine S2- atoms. There are a spread of Sr–S bond distances ranging from 2.95–3.63 Å. In the seventh Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine S2- atoms. There are a spread of Sr–S bond distances ranging from 2.98–3.54 Å. In the eighth Sr2+ site, Sr2+ is bonded in a 8-coordinate geometry to eight S2- atoms. There are a spread of Sr–S bond distances ranging from 2.99–3.49 Å. There are twenty-one inequivalent Ti+3.71+ sites. In the first Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form distorted face-sharing TiS6 octahedra. There are three shorter (2.42 Å) and three longer (2.53 Å) Ti–S bond lengths. In the second Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.36 Å) and three longer (2.54 Å) Ti–S bond lengths. In the third Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.38 Å) and three longer (2.50 Å) Ti–S bond lengths. In the fourth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form distorted face-sharing TiS6 octahedra. There are three shorter (2.37 Å) and three longer (2.57 Å) Ti–S bond lengths. In the fifth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.44 Å) and three longer (2.48 Å) Ti–S bond lengths. In the sixth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.38 Å) and three longer (2.50 Å) Ti–S bond lengths. In the seventh Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.43 Å) and three longer (2.49 Å) Ti–S bond lengths. In the eighth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.38 Å) and three longer (2.51 Å) Ti–S bond lengths. In the ninth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form distorted face-sharing TiS6 octahedra. There are three shorter (2.46 Å) and three longer (2.48 Å) Ti–S bond lengths. In the tenth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.43 Å) and three longer (2.48 Å) Ti–S bond lengths. In the eleventh Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.38 Å) and three longer (2.51 Å) Ti–S bond lengths. In the twelfth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.42 Å) and three longer (2.49 Å) Ti–S bond lengths. In the thirteenth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.38 Å) and three longer (2.53 Å) Ti–S bond lengths. In the fourteenth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.38 Å) and three longer (2.52 Å) Ti–S bond lengths. In the fifteenth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.40 Å) and three longer (2.50 Å) Ti–S bond lengths. In the sixteenth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form distorted face-sharing TiS6 octahedra. There are three shorter (2.39 Å) and three longer (2.54 Å) Ti–S bond lengths. In the seventeenth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.44 Å) and three longer (2.48 Å) Ti–S bond lengths. In the eighteenth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form distorted face-sharing TiS6 octahedra. There are three shorter (2.41 Å) and three longer (2.54 Å) Ti–S bond lengths. In the nineteenth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.37 Å) and three longer (2.51 Å) Ti–S bond lengths. In the twentieth Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form face-sharing TiS6 octahedra. There are three shorter (2.36 Å) and three longer (2.53 Å) Ti–S bond lengths. In the twenty-first Ti+3.71+ site, Ti+3.71+ is bonded to six S2- atoms to form distorted face-sharing TiS6 octahedra. There are three shorter (2.38 Å) and three longer (2.56 Å) Ti–S bond lengths. There are twenty-one inequivalent S2- sites. In the first S2- site, S2- is bonded in a 5-coordinate geometry to three Sr2+ and two Ti+3.71+ atoms. In the second S2- site, S2- is bonded in a 4-coordinate geometry to four Sr2+ and two Ti+3.71+ atoms. In the third S2- site, S2- is bonded in a 6-coordinate geometry to four Sr2+ and two Ti+3.71+ atoms. In the fourth S2- site, S2- is bonded in a 6-coordinate geometry to four Sr2+ and two Ti+3.71+ atoms. In the fifth S2- site, S2- is bonded in a 4-coordinate geometry to four Sr2+ and two Ti+3.71+ atoms. In the sixth S2- site, S2- is bonded in a 4-coordinate geometry to three Sr2+ and two Ti+3.71+ atoms. In the seventh S2- site, S2- is bonded in a 4-coordinate geometry to two Sr2+ and two Ti+3.71+ atoms. In the eighth S2- site, S2- is bonded in a 4-coordinate geometry to two Sr2+ and two Ti+3.71+ atoms. In the ninth S2- site, S2- is bonded in a 6-coordinate geometry to four Sr2+ and two Ti+3.71+ atoms. In the tenth S2- site, S2- is bonded in a 6-coordinate geometry to four Sr2+ and two Ti+3.71+ atoms. In the eleventh S2- site, S2- is bonded in a 4-coordinate geometry to four Sr2+ and two Ti+3.71+ atoms. In the twelfth S2- site, S2- is bonded in a 4-coordinate geometry to three Sr2+ and two Ti+3.71+ atoms. In the thirteenth S2- site, S2- is bonded in a 6-coordinate geometry to four Sr2+ and two Ti+3.71+ atoms. In the fourteenth S2- site, S2- is bonded in a 4-coordinate geometry to two Sr2+ and two Ti+3.71+ atoms. In the fifteenth S2- site, S2- is bonded in a 6-coordinate geometry to four Sr2+ and two Ti+3.71+ atoms. In the sixteenth S2- site, S2- is bonded in a 6-coordinate geometry to four Sr2+ and two Ti+3.71+ atoms. In the seventeenth S2- site, S2- is bonded in a 4-coordinate geometry to two Sr2+ and two Ti+3.71+ atoms. In the eighteenth S2- site, S2- is bonded in a 4-coordinate geometry to two Sr2+ and two Ti+3.71+ atoms. In the nineteenth S2- site, S2- is bonded to four Sr2+ and two Ti+3.71+ atoms to form distorted face-sharing SSr4Ti2 octahedra. In the twentieth S2- site, S2- is bonded in a 4-coordinate geometry to three Sr2+ and two Ti+3.71+ atoms. In the twenty-first S2- site, S2- is bonded in a 4-coordinate geometry to four Sr2+ and two Ti+3.71+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on La7Ti27Al5(CuO4)24 by Materials Project

La7Ti27Al5(CuO4)24 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are seven inequivalent La sites. In the first La site, La is bonded to twelve O atoms to form LaO12 cuboctahedra that share faces with three AlO6 octahedra and faces with five TiO6 octahedra. There are a spread of La–O bond distances ranging from 2.59–2.67 Å. In the second La site, La is bonded to twelve O atoms to form LaO12 cuboctahedra that share faces with three AlO6 octahedra and faces with five TiO6 octahedra. There are a spread of La–O bond distances ranging from 2.58–2.65 Å. In the third La site, La is bonded to twelve O atoms to form LaO12 cuboctahedra that share faces with two equivalent AlO6 octahedra and faces with six TiO6 octahedra. There are a spread of La–O bond distances ranging from 2.58–2.65 Å. In the fourth La site, La is bonded to twelve O atoms to form LaO12 cuboctahedra that share faces with eight TiO6 octahedra. There are a spread of La–O bond distances ranging from 2.59–2.62 Å. In the fifth La site, La is bonded to twelve O atoms to form LaO12 cuboctahedra that share faces with eight TiO6 octahedra. There are five shorter (2.60 Å) and seven longer (2.61 Å) La–O bond lengths. In the sixth La site, La is bonded to twelve O atoms to form LaO12 cuboctahedra that share faces with eight TiO6 octahedra. There are a spread of La–O bond distances ranging from 2.58–2.63 Å. In the seventh La site, La is bonded to twelve O atoms to form LaO12 cuboctahedra that share faces with two equivalent AlO6 octahedra and faces with six TiO6 octahedra. There are a spread of La–O bond distances ranging from 2.53–2.71 Å. There are twenty-seven inequivalent Ti sites. In the first Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share a cornercorner with one AlO6 octahedra, corners with five TiO6 octahedra, and a faceface with one LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 39–44°. There are a spread of Ti–O bond distances ranging from 1.89–2.10 Å. In the second Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with three TiO6 octahedra, corners with three AlO6 octahedra, and faces with two equivalent LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 39–41°. There are a spread of Ti–O bond distances ranging from 1.97–2.02 Å. In the third Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share a cornercorner with one AlO6 octahedra, corners with five TiO6 octahedra, and a faceface with one LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 40–44°. There are a spread of Ti–O bond distances ranging from 1.90–2.10 Å. In the fourth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with three TiO6 octahedra, corners with three AlO6 octahedra, and faces with two equivalent LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 37–41°. There are a spread of Ti–O bond distances ranging from 1.94–2.03 Å. In the fifth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with two TiO6 octahedra, corners with four AlO6 octahedra, and faces with two LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 38–41°. There are a spread of Ti–O bond distances ranging from 1.97–2.01 Å. In the sixth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with two equivalent AlO6 octahedra, corners with four TiO6 octahedra, and faces with two equivalent LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 36–41°. There are a spread of Ti–O bond distances ranging from 1.95–2.02 Å. In the seventh Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with two AlO6 octahedra, corners with four TiO6 octahedra, and faces with two LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 37–40°. There are a spread of Ti–O bond distances ranging from 1.95–2.01 Å. In the eighth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with two AlO6 octahedra, corners with four TiO6 octahedra, and faces with two LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 38–41°. There are a spread of Ti–O bond distances ranging from 1.95–2.02 Å. In the ninth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share a cornercorner with one AlO6 octahedra, corners with five TiO6 octahedra, and faces with two LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 37–40°. There are a spread of Ti–O bond distances ranging from 1.93–2.05 Å. In the tenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and faces with two equivalent LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 37–40°. There are a spread of Ti–O bond distances ranging from 1.96–1.99 Å. In the eleventh Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share a cornercorner with one AlO6 octahedra, corners with five TiO6 octahedra, and faces with two LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 37–41°. There are a spread of Ti–O bond distances ranging from 1.93–2.05 Å. In the twelfth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and faces with two equivalent LaO12 cuboctahedra. The corner-sharing octahedral tilt angles are 38°. There is three shorter (1.97 Å) and three longer (1.98 Å) Ti–O bond length. In the thirteenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and faces with two LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 38–39°. There are a spread of Ti–O bond distances ranging from 1.96–1.98 Å. In the fourteenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and faces with two equivalent LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 37–40°. There are a spread of Ti–O bond distances ranging from 1.95–2.00 Å. In the fifteenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and faces with two LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 38–40°. There are a spread of Ti–O bond distances ranging from 1.96–1.99 Å. In the sixteenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and faces with two LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 38–39°. There are a spread of Ti–O bond distances ranging from 1.96–1.98 Å. In the seventeenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and faces with two equivalent LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 37–41°. There are a spread of Ti–O bond distances ranging from 1.95–2.00 Å. In the eighteenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and faces with two LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 38–39°. There are a spread of Ti–O bond distances ranging from 1.96–1.99 Å. In the nineteenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and faces with two equivalent LaO12 cuboctahedra. The corner-sharing octahedral tilt angles are 38°. There is three shorter (1.97 Å) and three longer (1.98 Å) Ti–O bond length. In the twentieth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with two equivalent AlO6 octahedra, corners with four TiO6 octahedra, and faces with two equivalent LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 34–43°. There are a spread of Ti–O bond distances ranging from 1.92–2.06 Å. In the twenty-first Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share a cornercorner with one AlO6 octahedra, corners with five TiO6 octahedra, and faces with two LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 37–41°. There are a spread of Ti–O bond distances ranging from 1.92–2.06 Å. In the twenty-second Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and faces with two equivalent LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 37–40°. There are a spread of Ti–O bond distances ranging from 1.94–2.02 Å. In the twenty-third Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share a cornercorner with one AlO6 octahedra, corners with five TiO6 octahedra, and faces with two LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 37–43°. There are a spread of Ti–O bond distances ranging from 1.91–2.07 Å. In the twenty-fourth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share a cornercorner with one AlO6 octahedra, corners with five TiO6 octahedra, and a faceface with one LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 37–43°. There are a spread of Ti–O bond distances ranging from 1.89–2.11 Å. In the twenty-fifth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share a cornercorner with one AlO6 octahedra, corners with five TiO6 octahedra, and a faceface with one LaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 38–43°. There are a spread of Ti–O bond distances ranging from 1.88–2.11 Å. In the twenty-sixth Ti site, Ti is bonded to six O atoms to form corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 41–43°. There is two shorter (1.99 Å) and four longer (2.00 Å) Ti–O bond length. In the twenty-seventh Ti site, Ti is bonded to six O atoms to form corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 41–42°. There are a spread of Ti–O bond distances ranging from 1.97–1.99 Å. There are twenty-four inequivalent Cu sites. In the first Cu site, Cu is bonded in a square co-planar geometry to four O atoms. There are a spread of Cu–O bond distances ranging from 1.94–1.97 Å. In the second Cu site, Cu is bonded in a square co-planar geometry to four O atoms. There is one shorter (1.94 Å) and three longer (1.96 Å) Cu–O bond length. In the third Cu site, Cu is bonded in a square co-planar geometry to four O atoms. There are a spread of Cu–O bond distances ranging from 1.95–1.99 Å. In the fourth Cu site, Cu is bonded in a square co-planar geometry to four O atoms. There is two shorter (1.96 Å) and two longer (1.97 Å) Cu–O bond length. In the fifth Cu site, Cu is bonded in a square co-planar geometry to four O atoms. There are a spread of Cu–O bond distances ranging from 1.99–2.01 Å. In the sixth Cu site, Cu is bonded in a square co-planar geometry to four O atoms. There are three shorter (1.99 Å) and one longer (2.03 Å) Cu–O bond lengths. In the seventh Cu site, Cu is bonded in a square co-planar geometry to four O atoms. There are a spread of Cu–O bond distances ranging from 1.99–2.01 Å. In the eighth Cu site, Cu is bonded in a square co-planar geometry to four O atoms. There are three shorter (1.99 Å) and one longer (2.02 Å) Cu–O bond lengths. In the ninth Cu site, Cu is bonded in a square co-planar geometry to four O atoms. There are a spread of Cu–O bond distances ranging from 1.98–2.01 Å. In the tenth Cu site, Cu is bonded in a square co-planar geometry to four O atoms. There are a spread of Cu–O bond distances ranging from 1.98–2.02 Å. In the eleventh Cu site, Cu is bonded in a square co-planar geometry to four O atoms. There are two shorter (2.00 Å) and two longer (2.01 Å) Cu–O bond lengths. In the twelfth Cu site, Cu is bonded in a square co-planar geometry to four O atoms. There are three shorter (2.00 Å) and one longer (2.01 Å) Cu–O bond lengths. In the thirteenth Cu site, Cu

36 MATERIALS SCIENCE↗

Materials Data on Na7Ti16O32 by Materials Project

Na7Ti16O32 is Spinel-like structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are seven inequivalent Na1+ sites. In the first Na1+ site, Na1+ is bonded to four O2- atoms to form NaO4 tetrahedra that share corners with twelve TiO6 octahedra. The corner-sharing octahedra tilt angles range from 60–62°. There are three shorter (2.16 Å) and one longer (2.17 Å) Na–O bond lengths. In the second Na1+ site, Na1+ is bonded to four O2- atoms to form NaO4 tetrahedra that share corners with twelve TiO6 octahedra. The corner-sharing octahedra tilt angles range from 59–63°. There are a spread of Na–O bond distances ranging from 2.15–2.17 Å. In the third Na1+ site, Na1+ is bonded to four O2- atoms to form NaO4 tetrahedra that share corners with twelve TiO6 octahedra. The corner-sharing octahedra tilt angles range from 59–63°. There are a spread of Na–O bond distances ranging from 2.15–2.18 Å. In the fourth Na1+ site, Na1+ is bonded to four O2- atoms to form NaO4 tetrahedra that share corners with twelve TiO6 octahedra. The corner-sharing octahedra tilt angles range from 60–62°. There are a spread of Na–O bond distances ranging from 2.15–2.17 Å. In the fifth Na1+ site, Na1+ is bonded to four O2- atoms to form NaO4 tetrahedra that share corners with twelve TiO6 octahedra. The corner-sharing octahedra tilt angles range from 60–61°. There are a spread of Na–O bond distances ranging from 2.15–2.17 Å. In the sixth Na1+ site, Na1+ is bonded to four O2- atoms to form NaO4 tetrahedra that share corners with twelve TiO6 octahedra. The corner-sharing octahedra tilt angles range from 58–63°. There are three shorter (2.15 Å) and one longer (2.18 Å) Na–O bond lengths. In the seventh Na1+ site, Na1+ is bonded to four O2- atoms to form NaO4 tetrahedra that share corners with twelve TiO6 octahedra. The corner-sharing octahedra tilt angles range from 60–62°. There are a spread of Na–O bond distances ranging from 2.15–2.17 Å. There are sixteen inequivalent Ti+3.56+ sites. In the first Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.99–2.06 Å. In the second Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.99–2.06 Å. In the third Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.98–2.06 Å. In the fourth Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.99–2.05 Å. In the fifth Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 2.00–2.05 Å. In the sixth Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 2.00–2.05 Å. In the seventh Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.98–2.07 Å. In the eighth Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.99–2.06 Å. In the ninth Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 2.00–2.05 Å. In the tenth Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six NaO4 tetrahedra and edges with six TiO6 octahedra. There are three shorter (2.02 Å) and three longer (2.03 Å) Ti–O bond lengths. In the eleventh Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six NaO4 tetrahedra and edges with six TiO6 octahedra. There are two shorter (2.01 Å) and four longer (2.03 Å) Ti–O bond lengths. In the twelfth Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 2.00–2.07 Å. In the thirteenth Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 2.01–2.06 Å. In the fourteenth Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 2.01–2.04 Å. In the fifteenth Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 2.00–2.05 Å. In the sixteenth Ti+3.56+ site, Ti+3.56+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 2.01–2.03 Å. There are thirty-two inequivalent O2- sites. In the first O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the second O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the third O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the fourth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the fifth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the sixth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the seventh O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the eighth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the ninth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the tenth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.56+ atoms. In the eleventh O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.56+ atoms. In the twelfth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the thirteenth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the fourteenth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the fifteenth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the sixteenth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the seventeenth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of edge and corner-sharing ONaTi3 tetrahedra. In the eighteenth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of edge and corner-sharing ONaTi3 tetrahedra. In the nineteenth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the twentieth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the twenty-first O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of edge and corner-sharing ONaTi3 tetrahedra. In the twenty-second O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the twenty-third O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the twenty-fourth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the twenty-fifth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the twenty-sixth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the twenty-seventh O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the twenty-eighth O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the twenty-ninth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.56+ atoms. In the thirtieth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.56+ atoms. In the thirty-first O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra. In the thirty-second O2- site, O2- is bonded to one Na1+ and three Ti+3.56+ atoms to form a mixture of distorted edge and corner-sharing ONaTi3 tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on Na5Ti16O32 by Materials Project

Na5Ti16O32 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are five 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 2.19–2.49 Å. In the second Na1+ site, Na1+ is bonded in a rectangular see-saw-like geometry to four O2- atoms. There are a spread of Na–O bond distances ranging from 2.25–2.48 Å. In the third Na1+ site, Na1+ is bonded in a distorted rectangular see-saw-like geometry to four O2- atoms. There are a spread of Na–O bond distances ranging from 2.24–2.50 Å. In the fourth Na1+ site, Na1+ is bonded in a distorted rectangular see-saw-like geometry to four O2- atoms. There are a spread of Na–O bond distances ranging from 2.23–2.41 Å. In the fifth Na1+ site, Na1+ is bonded in a distorted rectangular see-saw-like geometry to four O2- atoms. There are a spread of Na–O bond distances ranging from 2.24–2.42 Å. There are sixteen inequivalent Ti+3.69+ sites. In the first Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 29–53°. There are a spread of Ti–O bond distances ranging from 1.93–2.12 Å. In the second Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 23–51°. There are a spread of Ti–O bond distances ranging from 1.93–2.10 Å. In the third Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 20–53°. There are a spread of Ti–O bond distances ranging from 1.94–2.15 Å. In the fourth Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 27–52°. There are a spread of Ti–O bond distances ranging from 1.90–2.12 Å. In the fifth Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of distorted edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 29–52°. There are a spread of Ti–O bond distances ranging from 1.85–2.14 Å. In the sixth Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 23–53°. There are a spread of Ti–O bond distances ranging from 1.92–2.14 Å. In the seventh Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 27–53°. There are a spread of Ti–O bond distances ranging from 1.95–2.12 Å. In the eighth Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 20–52°. There are a spread of Ti–O bond distances ranging from 1.92–2.10 Å. In the ninth Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 22–54°. There are a spread of Ti–O bond distances ranging from 1.90–2.11 Å. In the tenth Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 23–53°. There are a spread of Ti–O bond distances ranging from 1.93–2.10 Å. In the eleventh Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 23–54°. There are a spread of Ti–O bond distances ranging from 1.90–2.10 Å. In the twelfth Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of distorted edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 29–52°. There are a spread of Ti–O bond distances ranging from 1.86–2.14 Å. In the thirteenth Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 22–52°. There are a spread of Ti–O bond distances ranging from 1.92–2.13 Å. In the fourteenth Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 23–52°. There are a spread of Ti–O bond distances ranging from 1.93–2.13 Å. In the fifteenth Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 29–52°. There are a spread of Ti–O bond distances ranging from 1.92–2.10 Å. In the sixteenth Ti+3.69+ site, Ti+3.69+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 23–51°. There are a spread of Ti–O bond distances ranging from 1.89–2.08 Å. There are thirty-two inequivalent O2- sites. In the first O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+3.69+ atoms. In the second O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+3.69+ atoms. In the third O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.69+ atoms. In the fourth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.69+ atoms. In the fifth O2- site, O2- is bonded to one Na1+ and three Ti+3.69+ atoms to form distorted corner-sharing ONaTi3 tetrahedra. In the sixth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.69+ atoms. In the seventh O2- site, O2- is bonded in a distorted see-saw-like geometry to two Na1+ and two Ti+3.69+ atoms. In the eighth O2- site, O2- is bonded in a distorted see-saw-like geometry to two Na1+ and two Ti+3.69+ atoms. In the ninth O2- site, O2- is bonded in a distorted T-shaped geometry to one Na1+ and two Ti+3.69+ atoms. In the tenth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+ and two Ti+3.69+ atoms. In the eleventh O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.69+ atoms. In the twelfth O2- site, O2- is bonded in a distorted tetrahedral geometry to one Na1+ and three Ti+3.69+ atoms. In the thirteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.69+ atoms. In the fourteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.69+ atoms. In the fifteenth O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to four Ti+3.69+ atoms. In the sixteenth O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+3.69+ atoms. In the seventeenth O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+3.69+ atoms. In the eighteenth O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+3.69+ atoms. In the nineteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.69+ atoms. In the twentieth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.69+ atoms. In the twenty-first O2- site, O2- is bonded in a trigonal non-coplanar geometry to three Ti+3.69+ atoms. In the twenty-second O2- site, O2- is bonded in a distorted tetrahedral geometry to one Na1+ and three Ti+3.69+ atoms. In the twenty-third O2- site, O2- is bonded in a distorted T-shaped geometry to one Na1+ and two Ti+3.69+ atoms. In the twenty-fourth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+ and two Ti+3.69+ atoms. In the twenty-fifth O2- site, O2- is bonded in a 5-coordinate geometry to three Na1+ and two Ti+3.69+ atoms. In the twenty-sixth O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to two Na1+ and two Ti+3.69+ atoms. In the twenty-seventh O2- site, O2- is bonded to one Na1+ and three Ti+3.69+ atoms to form distorted ONaTi3 tetrahedra that share corners with two equivalent ONaTi3 tetrahedra and an edgeedge with one OTi4 trigonal pyramid. In the twenty-eighth O2- site, O2- is bonded to one Na1+ and three Ti+3.69+ atoms to form distorted ONaTi3 tetrahedra that share corners with two equivalent ONaTi3 tetrahedra and an edgeedge with one OTi4 trigonal pyramid. In the twenty-ninth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.69+ atoms. In the thirtieth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.69+ atoms. In the thirty-first O2- site, O2- is bonded to four Ti+3.69+ atoms to form a mixture of distorted edge and corner-sharing OTi4 trigonal pyramids. In the thirty-second O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+3.69+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Y16Ti16O35 by Materials Project

Y16Ti16O35 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are sixteen inequivalent Y sites. In the first Y site, Y is bonded to five O atoms to form a mixture of corner and edge-sharing YO5 trigonal bipyramids. There are a spread of Y–O bond distances ranging from 2.14–2.38 Å. In the second Y site, Y is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Y–O bond distances ranging from 2.13–2.52 Å. In the third Y site, Y is bonded to four O atoms to form YO4 trigonal pyramids that share corners with two equivalent YO5 trigonal bipyramids and corners with two equivalent YO4 trigonal pyramids. There are a spread of Y–O bond distances ranging from 2.18–2.36 Å. In the fourth Y site, Y is bonded to four O atoms to form YO4 trigonal pyramids that share corners with two equivalent YO5 trigonal bipyramids and corners with two equivalent YO4 trigonal pyramids. There are a spread of Y–O bond distances ranging from 2.19–2.37 Å. In the fifth Y site, Y is bonded in a 5-coordinate geometry to five O atoms. There are a spread of Y–O bond distances ranging from 2.37–2.53 Å. In the sixth Y site, Y is bonded to five O atoms to form distorted corner-sharing YO5 trigonal bipyramids. There are a spread of Y–O bond distances ranging from 2.24–2.38 Å. In the seventh Y site, Y is bonded in a trigonal planar geometry to three O atoms. There are a spread of Y–O bond distances ranging from 2.23–2.32 Å. In the eighth Y site, Y is bonded to five O atoms to form distorted YO5 trigonal bipyramids that share a cornercorner with one YO5 trigonal bipyramid and a cornercorner with one YO4 trigonal pyramid. There are a spread of Y–O bond distances ranging from 2.22–2.36 Å. In the ninth Y site, Y is bonded in a 5-coordinate geometry to five O atoms. There are a spread of Y–O bond distances ranging from 2.24–2.43 Å. In the tenth Y site, Y is bonded in a 5-coordinate geometry to five O atoms. There are a spread of Y–O bond distances ranging from 2.24–2.44 Å. In the eleventh Y site, Y is bonded to four O atoms to form corner-sharing YO4 trigonal pyramids. There are a spread of Y–O bond distances ranging from 2.16–2.36 Å. In the twelfth Y site, Y is bonded to five O atoms to form distorted YO5 trigonal bipyramids that share corners with two YO5 trigonal bipyramids and corners with two equivalent YO4 trigonal pyramids. There are a spread of Y–O bond distances ranging from 2.21–2.36 Å. In the thirteenth Y site, Y is bonded to five O atoms to form distorted YO5 trigonal bipyramids that share corners with three YO5 trigonal bipyramids and a cornercorner with one YO4 trigonal pyramid. There are a spread of Y–O bond distances ranging from 2.20–2.37 Å. In the fourteenth Y site, Y is bonded in a distorted hexagonal planar geometry to six O atoms. There are a spread of Y–O bond distances ranging from 2.27–2.47 Å. In the fifteenth Y site, Y is bonded to five O atoms to form a mixture of distorted corner and edge-sharing YO5 trigonal bipyramids. There are a spread of Y–O bond distances ranging from 2.14–2.37 Å. In the sixteenth Y site, Y is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Y–O bond distances ranging from 2.14–2.57 Å. There are sixteen inequivalent Ti sites. In the first Ti site, Ti is bonded in a distorted trigonal non-coplanar geometry to three O atoms. There are a spread of Ti–O bond distances ranging from 1.91–1.98 Å. In the second Ti site, Ti is bonded in a rectangular see-saw-like geometry to four O atoms. There are a spread of Ti–O bond distances ranging from 1.97–2.14 Å. In the third Ti site, Ti is bonded in a rectangular see-saw-like geometry to four O atoms. There are a spread of Ti–O bond distances ranging from 2.00–2.20 Å. In the fourth Ti site, Ti is bonded in a 3-coordinate geometry to three O atoms. There are a spread of Ti–O bond distances ranging from 1.95–2.05 Å. In the fifth Ti site, Ti is bonded in a rectangular see-saw-like geometry to four O atoms. There are a spread of Ti–O bond distances ranging from 1.96–2.27 Å. In the sixth Ti site, Ti is bonded in a distorted rectangular see-saw-like geometry to four O atoms. There are a spread of Ti–O bond distances ranging from 2.00–2.10 Å. In the seventh Ti site, Ti is bonded in a trigonal non-coplanar geometry to three O atoms. There are a spread of Ti–O bond distances ranging from 1.84–2.04 Å. In the eighth Ti site, Ti is bonded in a see-saw-like geometry to four O atoms. There are a spread of Ti–O bond distances ranging from 1.86–2.04 Å. In the ninth Ti site, Ti is bonded in a see-saw-like geometry to four O atoms. There are a spread of Ti–O bond distances ranging from 1.97–2.11 Å. In the tenth Ti site, Ti is bonded in a distorted rectangular see-saw-like geometry to four O atoms. There are a spread of Ti–O bond distances ranging from 1.95–2.20 Å. In the eleventh Ti site, Ti is bonded in a trigonal non-coplanar geometry to three O atoms. There are a spread of Ti–O bond distances ranging from 1.86–1.99 Å. In the twelfth Ti site, Ti is bonded in a distorted see-saw-like geometry to four O atoms. There are a spread of Ti–O bond distances ranging from 1.98–2.15 Å. In the thirteenth Ti site, Ti is bonded in a see-saw-like geometry to four O atoms. There are a spread of Ti–O bond distances ranging from 1.90–2.02 Å. In the fourteenth Ti site, Ti is bonded in a 4-coordinate geometry to four O atoms. There are a spread of Ti–O bond distances ranging from 1.95–2.17 Å. In the fifteenth Ti site, Ti is bonded in a distorted trigonal non-coplanar geometry to three O atoms. There are a spread of Ti–O bond distances ranging from 1.89–1.99 Å. In the sixteenth Ti site, Ti is bonded in a rectangular see-saw-like geometry to four O atoms. There are a spread of Ti–O bond distances ranging from 1.99–2.26 Å. There are thirty-five inequivalent O sites. In the first O site, O is bonded to four Y atoms to form a mixture of corner and edge-sharing OY4 tetrahedra. In the second O site, O is bonded to two Y and two Ti atoms to form OY2Ti2 tetrahedra that share a cornercorner with one OY4 tetrahedra, corners with three equivalent OY2Ti2 trigonal pyramids, edges with four OY2Ti2 tetrahedra, and an edgeedge with one OY2Ti2 trigonal pyramid. In the third O site, O is bonded to two Y and two Ti atoms to form a mixture of distorted corner and edge-sharing OY2Ti2 tetrahedra. In the fourth O site, O is bonded to two Y and two Ti atoms to form distorted OY2Ti2 trigonal pyramids that share corners with twelve OY2Ti2 tetrahedra, a cornercorner with one OY2Ti2 trigonal pyramid, and an edgeedge with one OY4 tetrahedra. In the fifth O site, O is bonded to two Y and two Ti atoms to form a mixture of distorted corner and edge-sharing OY2Ti2 trigonal pyramids. In the sixth O site, O is bonded to two Y and two Ti atoms to form distorted OY2Ti2 tetrahedra that share corners with seven OY2Ti2 tetrahedra, corners with two equivalent OY2Ti2 trigonal pyramids, and edges with two OY4 tetrahedra. In the seventh O site, O is bonded to two Y and two Ti atoms to form a mixture of corner and edge-sharing OY2Ti2 tetrahedra. In the eighth O site, O is bonded to two Y and two Ti atoms to form distorted corner-sharing OY2Ti2 tetrahedra. In the ninth O site, O is bonded to two Y and two Ti atoms to form distorted OY2Ti2 tetrahedra that share corners with seven OY2Ti2 tetrahedra, corners with three OY2Ti2 trigonal pyramids, and edges with two OY4 tetrahedra. In the tenth O site, O is bonded to two Y and two Ti atoms to form a mixture of corner and edge-sharing OY2Ti2 tetrahedra. In the eleventh O site, O is bonded in a distorted trigonal planar geometry to two Y and one Ti atom. In the twelfth O site, O is bonded in a distorted rectangular see-saw-like geometry to two Y and two Ti atoms. In the thirteenth O site, O is bonded to two Y and two Ti atoms to form a mixture of distorted corner and edge-sharing OY2Ti2 trigonal pyramids. In the fourteenth O site, O is bonded to four Y atoms to form OY4 tetrahedra that share corners with seven OY4 tetrahedra, corners with five OY2Ti2 trigonal pyramids, and an edgeedge with one OY2Ti2 tetrahedra. In the fifteenth O site, O is bonded to two Y and two Ti atoms to form a mixture of distorted corner and edge-sharing OY2Ti2 trigonal pyramids. In the sixteenth O site, O is bonded to two Y and two Ti atoms to form a mixture of distorted corner and edge-sharing OY2Ti2 trigonal pyramids. In the seventeenth O site, O is bonded to two Y and two Ti atoms to form a mixture of corner and edge-sharing OY2Ti2 tetrahedra. In the eighteenth O site, O is bonded to two Y and two Ti atoms to form a mixture of distorted corner and edge-sharing OY2Ti2 trigonal pyramids. In the nineteenth O site, O is bonded to two Y and two Ti atoms to form OY2Ti2 tetrahedra that share corners with two OY2Ti2 tetrahedra, an edgeedge with one OY4 tetrahedra, and edges with two OY2Ti2 trigonal pyramids. In the twentieth O site, O is bonded in a distorted rectangular see-saw-like geometry to two Y and two Ti atoms. In the twenty-first O site, O is bonded in a rectangular see-saw-like geometry to two Y and two Ti atoms. In the twenty-second O site, O is bonded to two Y and two Ti atoms to form distorted OY2Ti2 trigonal pyramids that share corners with two equivalent OY4 tetrahedra, corners with four OY2Ti2 trigonal pyramids, and edges with two OY2Ti2 tetrahedra. In the twenty-third O site, O is bonded in a distorted trigonal planar geometry to two Y and one Ti atom. In the twenty-fourth O site, O is bonded to two Y and two Ti atoms to form distorted OY2Ti2 trigonal pyramids that share corners with two equivalent OY4 tetrahedra, corners with four OY2Ti2 trigonal pyramids, and an edgeedge with one OY2Ti2 tetrahedra. In the twenty-fifth O site, O is bonded to two Y and two Ti atoms to form OY2Ti2 trigonal pyramids that share a cornercorner with one OY4 tetrahedra, corners with four OY2Ti2 trigonal pyramids, and an edgeedge with one OY2Ti2 tetrahedra. In the twenty-sixth O site, O is bonded to two Y and two Ti atoms to form OY2Ti2 tetrahedra that share corners with two OY2Ti2 tetrahedra, an edgeedge with one OY4 tetrahedra, and edges with two OY2Ti2 trigonal pyramids. In the twenty-seventh O site, O is bonded to two Y and two Ti atoms to form OY2Ti2 tetrahedra that share corners with two OY4 tetrahedra, a cornercorner with one OY2Ti2 trigonal pyramid, edges with two OY4 tetrahedra, and an edgeedge with one OY2Ti2 trigonal pyramid. In the twenty-eighth O site, O is bonded in a distorted rectangular see-saw-like geometry to two Y and two Ti atoms. In the twenty-ninth O site, O is bonded in a rectangular see-saw-like geometry to two Y and two Ti atoms. In the thirtieth O site, O is bonded to two Y and two Ti atoms to form distorted OY2Ti2 tetrahedra that share corners with five OY2Ti2 tetrahedra, corners with two OY2Ti2 trigonal pyramids, and edges with two OY4 tetrahedra. In the thirty-first O site, O is bonded in a distorted trigonal planar geometry to two Y and one Ti atom. In the thirty-second O site, O is bonded to four Y atoms to form a mixture of corner and edge-sharing OY4 tetrahedra. In the thirty-third O site, O is bonded to two Y and two Ti atoms to form distorted OY2Ti2 tetrahedra that share corners with six OY4 tetrahedra, a cornercorner with one OY2Ti2 trigonal pyramid, and an edgeedge with one OY4 tetrahedra. In the thirty-fourth O site, O is bonded to two Y and two Ti atoms to form a mixture of distorted corner and edge-sharing OY2Ti2 trigonal pyramids. In the thirty-fifth O site, O is bonded to four Y atoms to form OY4 tetrahedra that share corners with nine OY4 tetrahedra, corners with two OY2Ti2 trigonal pyramids, and an edgeedge with one OY2Ti2 tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on Na11Ti20O40 by Materials Project

Na11Ti20O40 crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are eleven inequivalent Na1+ sites. In the first 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 2.43–2.45 Å. In the second Na1+ site, Na1+ is bonded in a 6-coordinate geometry to six O2- atoms. There are five shorter (2.44 Å) and one longer (2.45 Å) Na–O bond lengths. In the third Na1+ site, Na1+ is bonded to six O2- atoms to form distorted NaO6 octahedra that share corners with six TiO6 octahedra, edges with four NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–21°. There are a spread of Na–O bond distances ranging from 2.30–2.53 Å. In the fourth Na1+ site, Na1+ is bonded to six O2- atoms to form distorted NaO6 octahedra that share corners with six TiO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 9–10°. There are a spread of Na–O bond distances ranging from 2.36–2.40 Å. In the fifth Na1+ site, Na1+ is bonded to six O2- atoms to form distorted NaO6 octahedra that share corners with six TiO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 9–10°. There are a spread of Na–O bond distances ranging from 2.37–2.41 Å. In the sixth Na1+ site, Na1+ is bonded to six O2- atoms to form distorted NaO6 octahedra that share corners with six TiO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 9–10°. There are two shorter (2.37 Å) and four longer (2.39 Å) Na–O bond lengths. In the seventh Na1+ site, Na1+ is bonded to six O2- atoms to form distorted NaO6 octahedra that share corners with six TiO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 9–11°. There are two shorter (2.37 Å) and four longer (2.39 Å) Na–O bond lengths. In the eighth Na1+ site, Na1+ is bonded to six O2- atoms to form distorted NaO6 octahedra that share corners with six TiO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedral tilt angles are 10°. There are two shorter (2.37 Å) and four longer (2.40 Å) Na–O bond lengths. In the ninth Na1+ site, Na1+ is bonded to six O2- atoms to form distorted NaO6 octahedra that share corners with six TiO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 9–10°. There are a spread of Na–O bond distances ranging from 2.36–2.39 Å. In the tenth Na1+ site, Na1+ is bonded to six O2- atoms to form distorted NaO6 octahedra that share corners with six TiO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 9–10°. There are a spread of Na–O bond distances ranging from 2.37–2.41 Å. In the eleventh Na1+ site, Na1+ is bonded to six O2- atoms to form distorted NaO6 octahedra that share corners with six TiO6 octahedra, edges with four NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–21°. There are a spread of Na–O bond distances ranging from 2.29–2.53 Å. There are twenty inequivalent Ti+3.45+ sites. In the first Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one NaO6 octahedra and edges with six TiO6 octahedra. The corner-sharing octahedral tilt angles are 21°. There are a spread of Ti–O bond distances ranging from 1.98–2.06 Å. In the second Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form edge-sharing TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.90–2.05 Å. In the third Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form edge-sharing TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.91–2.09 Å. In the fourth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form edge-sharing TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.93–2.04 Å. In the fifth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form edge-sharing TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.97–2.00 Å. In the sixth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form edge-sharing TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.96–2.00 Å. In the seventh Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form edge-sharing TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.93–2.04 Å. In the eighth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form edge-sharing TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.91–2.09 Å. In the ninth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form edge-sharing TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.90–2.06 Å. In the tenth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one NaO6 octahedra and edges with six TiO6 octahedra. The corner-sharing octahedral tilt angles are 21°. There are a spread of Ti–O bond distances ranging from 1.97–2.06 Å. In the eleventh Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with three NaO6 octahedra, edges with three equivalent NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 10–16°. There are a spread of Ti–O bond distances ranging from 2.02–2.09 Å. In the twelfth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five NaO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedral tilt angles are 10°. There are a spread of Ti–O bond distances ranging from 2.04–2.08 Å. In the thirteenth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six NaO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are a spread of Ti–O bond distances ranging from 2.06–2.10 Å. In the fourteenth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six NaO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 9–10°. There are one shorter (2.08 Å) and five longer (2.09 Å) Ti–O bond lengths. In the fifteenth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six NaO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 9–10°. There are a spread of Ti–O bond distances ranging from 2.07–2.09 Å. In the sixteenth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six NaO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 9–10°. There are a spread of Ti–O bond distances ranging from 2.06–2.09 Å. In the seventeenth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six NaO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 9–10°. There are one shorter (2.08 Å) and five longer (2.09 Å) Ti–O bond lengths. In the eighteenth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six NaO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 8–10°. There are a spread of Ti–O bond distances ranging from 2.06–2.10 Å. In the nineteenth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with five NaO6 octahedra, edges with six NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 10–11°. There are a spread of Ti–O bond distances ranging from 2.02–2.08 Å. In the twentieth Ti+3.45+ site, Ti+3.45+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with three NaO6 octahedra, edges with three equivalent NaO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 10–17°. There are a spread of Ti–O bond distances ranging from 2.02–2.10 Å. There are forty inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to one Na1+ and three Ti+3.45+ atoms. In the second O2- site, O2- is bonded to two equivalent Na1+ and three Ti+3.45+ atoms to form ONa2Ti3 square pyramids that share corners with two equivalent ONa2Ti3 square pyramids, corners with four equivalent ONaTi3 trigonal pyramids, edges with five ONa2Ti3 square pyramids, and an edgeedge with one ONaTi3 trigonal pyramid. In the third O2- site, O2- is bonded to two equivalent Na1+ and three Ti+3.45+ atoms to form ONa2Ti3 square pyramids that share corners with two equivalent ONa2Ti3 square pyramids, edges with five ONa2Ti3 square pyramids, and edges with two equivalent ONaTi3 trigonal pyramids. In the fourth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.45+ atoms. In the fifth O2- site, O2- is bonded to one Na1+ and three Ti+3.45+ atoms to form distorted ONaTi3 trigonal pyramids that share corners with four equivalent ONa2Ti3 square pyramids, corners with two equivalent ONaTi3 trigonal pyramids, and edges with three ONa2Ti3 square pyramids. In the sixth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.45+ atoms. In the seventh O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.45+ atoms. In the eighth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.45+ atoms. In the ninth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.45+ atoms. In the tenth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.45+ atoms. In the eleventh O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.45+ atoms. In the twelfth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.45+ atoms. In the thirteenth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.45+ atoms. In the fourteenth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.45+ atoms. In the fifteenth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.45+ atoms. In the sixteenth O2- site, O2- is bonded to one Na1+ and three Ti+3.45+ atoms to form distorted ONaTi3 trigonal pyramids that share corners with four equivalent ONa2Ti3 square pyramids, corners with two equivalent ONaTi3 trigonal pyramids, and edges with three ONa2Ti3 square pyramids. In the seventeenth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.45+ atoms. In the eighteenth O2- site, O2- is bonded to two equivalent Na1+ and three Ti+3.45+ atoms to form ONa2Ti3 square pyramids that share corners with two equivalent ONa2Ti3 square pyramids, edges with five ONa2Ti3 square pyramids, and edges with two equivalent ONaTi3 trigonal pyramids. In the nineteenth O2- site, O2- is bonded to two equivalent Na1+ and three Ti+3.45+ atoms to form ONa2Ti3 square pyramids that share corners with two equivalent ONa2Ti3 square pyramids, corners with four equivalent ONaTi3 trigonal pyramids, edges with five ONa2Ti3 square pyramids, and an edgeedge with one ONaTi3 trigonal pyramid. In t

36 MATERIALS SCIENCE↗

Materials Data on Li13Ti22O48 by Materials Project

Li13Ti22O48 is Spinel-like structured and crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are thirteen inequivalent Li sites. In the first Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with two equivalent LiO6 octahedra and corners with ten TiO6 octahedra. The corner-sharing octahedra tilt angles range from 55–63°. There are a spread of Li–O bond distances ranging from 1.98–2.02 Å. In the second Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with twelve TiO6 octahedra. The corner-sharing octahedra tilt angles range from 59–62°. There are a spread of Li–O bond distances ranging from 2.01–2.04 Å. In the third Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with two equivalent LiO6 octahedra and corners with ten TiO6 octahedra. The corner-sharing octahedra tilt angles range from 56–64°. There are a spread of Li–O bond distances ranging from 1.99–2.03 Å. In the fourth Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with two equivalent LiO6 octahedra and corners with ten TiO6 octahedra. The corner-sharing octahedra tilt angles range from 56–64°. There are a spread of Li–O bond distances ranging from 1.99–2.03 Å. In the fifth Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share a cornercorner with one LiO6 octahedra and corners with eleven TiO6 octahedra. The corner-sharing octahedra tilt angles range from 56–63°. There are a spread of Li–O bond distances ranging from 2.00–2.04 Å. In the sixth Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share a cornercorner with one LiO6 octahedra and corners with eleven TiO6 octahedra. The corner-sharing octahedra tilt angles range from 55–63°. There are a spread of Li–O bond distances ranging from 1.98–2.03 Å. In the seventh Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share a cornercorner with one LiO6 octahedra and corners with eleven TiO6 octahedra. The corner-sharing octahedra tilt angles range from 56–64°. There are a spread of Li–O bond distances ranging from 1.98–2.02 Å. In the eighth Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with twelve TiO6 octahedra. The corner-sharing octahedra tilt angles range from 55–61°. There are three shorter (2.01 Å) and one longer (2.04 Å) Li–O bond lengths. In the ninth Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share a cornercorner with one LiO6 octahedra and corners with eleven TiO6 octahedra. The corner-sharing octahedra tilt angles range from 56–64°. There are one shorter (1.98 Å) and three longer (2.02 Å) Li–O bond lengths. In the tenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO4 tetrahedra and edges with six TiO6 octahedra. There are four shorter (2.12 Å) and two longer (2.13 Å) Li–O bond lengths. In the eleventh Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with two equivalent LiO6 octahedra and corners with ten TiO6 octahedra. The corner-sharing octahedra tilt angles range from 55–64°. There are a spread of Li–O bond distances ranging from 1.98–2.04 Å. In the twelfth Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with twelve TiO6 octahedra. The corner-sharing octahedra tilt angles range from 57–61°. There are one shorter (2.01 Å) and three longer (2.04 Å) Li–O bond lengths. In the thirteenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Li–O bond distances ranging from 2.12–2.14 Å. There are sixteen inequivalent Ti sites. In the first Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.91–2.07 Å. In the second Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with five LiO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.95–2.09 Å. In the third Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with five LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.92–2.07 Å. In the fourth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with five LiO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.97–2.04 Å. In the fifth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.91–2.07 Å. In the sixth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.93–2.05 Å. In the seventh Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.94–2.03 Å. In the eighth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with four LiO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.96–2.06 Å. In the ninth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.98–2.02 Å. In the tenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with five LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.92–2.07 Å. In the eleventh Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.99–2.05 Å. In the twelfth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with four LiO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.96–2.03 Å. In the thirteenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.96–2.04 Å. In the fourteenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra and edges with six TiO6 octahedra. There are five shorter (2.01 Å) and one longer (2.02 Å) Ti–O bond lengths. In the fifteenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with five LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.92–2.07 Å. In the sixteenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.90–2.07 Å. There are thirty-six inequivalent O sites. In the first O site, O is bonded to one Li and three Ti atoms to form distorted OLiTi3 tetrahedra that share corners with two OLiTi3 tetrahedra, corners with four OLi2Ti2 trigonal pyramids, edges with two OLiTi3 tetrahedra, and an edgeedge with one OLiTi3 trigonal pyramid. In the second O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the third O site, O is bonded to one Li and three Ti atoms to form distorted OLiTi3 tetrahedra that share corners with four OLi2Ti2 trigonal pyramids, edges with two equivalent OLiTi3 tetrahedra, and an edgeedge with one OLiTi3 trigonal pyramid. In the fourth O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the fifth O site, O is bonded to two Li and two Ti atoms to form distorted OLi2Ti2 trigonal pyramids that share corners with three OLiTi3 tetrahedra, corners with six OLiTi3 trigonal pyramids, and an edgeedge with one OLi2Ti2 trigonal pyramid. In the sixth O site, O is bonded in a distorted rectangular see-saw-like geometry to two Li and two Ti atoms. In the seventh O site, O is bonded in a distorted rectangular see-saw-like geometry to one Li and three Ti atoms. In the eighth O site, O is bonded in a rectangular see-saw-like geometry to two Li and two equivalent Ti atoms. In the ninth O site, O is bonded to one Li and three Ti atoms to form distorted OLiTi3 trigonal pyramids that share corners with eight OLi2Ti2 trigonal pyramids and edges with three OLiTi3 trigonal pyramids. In the tenth O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the eleventh O site, O is bonded in a distorted rectangular see-saw-like geometry to one Li and three Ti atoms. In the twelfth O site, O is bonded in a rectangular see-saw-like geometry to two Li and two equivalent Ti atoms. In the thirteenth O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted corner and edge-sharing OLiTi3 tetrahedra. In the fourteenth O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the fifteenth O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the sixteenth O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the seventeenth O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the eighteenth O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the nineteenth O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted corner and edge-sharing OLiTi3 tetrahedra. In the twentieth O site, O is bonded in a distorted trigonal non-coplanar geometry to three Ti atoms. In the twenty-first O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted corner and edge-sharing OLiTi3 tetrahedra. In the twenty-second O site, O is bonded to one Li and three Ti atoms to form distorted OLiTi3 tetrahedra that share corners with six OLi2Ti2 trigonal pyramids, an edgeedge with one OLiTi3 tetrahedra, and edges with two equivalent OLiTi3 trigonal pyramids. In the twenty-third O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted corner and edge-sharing OLiTi3 tetrahedra. In the twenty-fourth O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the twenty-fifth O site, O is bonded in a rectangular see-saw-like geometry to two Li and two Ti atoms. In the twenty-sixth O site, O is bonded in a rectangular see-saw-like geometry to two Li and two Ti atoms. In the twenty-seventh O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted corner and edge-sharing OLiTi3 tetrahedra. In the twenty-eighth O site, O is bonded in a distorted T-shaped geometry to three Ti atoms. In the twenty-ninth O site, O is

36 MATERIALS SCIENCE↗

Materials Data on Ti20(Ge3Sb)3 by Materials Project

Ti20(Ge3Sb)3 crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are sixteen inequivalent Ti sites. In the first Ti site, Ti is bonded in a 6-coordinate geometry to four Ge and two Sb atoms. There are a spread of Ti–Ge bond distances ranging from 2.67–2.74 Å. Both Ti–Sb bond lengths are 2.77 Å. In the second Ti site, Ti is bonded in a 6-coordinate geometry to five Ge and one Sb atom. There are a spread of Ti–Ge bond distances ranging from 2.68–2.76 Å. The Ti–Sb bond length is 2.76 Å. In the third Ti site, Ti is bonded in a 6-coordinate geometry to two equivalent Ti, four Ge, and two Sb atoms. There are one shorter (2.56 Å) and one longer (2.69 Å) Ti–Ti bond lengths. There are a spread of Ti–Ge bond distances ranging from 2.66–2.77 Å. There are one shorter (2.74 Å) and one longer (2.78 Å) Ti–Sb bond lengths. In the fourth Ti site, Ti is bonded in a 6-coordinate geometry to five Ge and one Sb atom. There are a spread of Ti–Ge bond distances ranging from 2.68–2.75 Å. The Ti–Sb bond length is 2.77 Å. In the fifth Ti site, Ti is bonded in a 5-coordinate geometry to four Ge and one Sb atom. There are two shorter (2.63 Å) and two longer (2.86 Å) Ti–Ge bond lengths. The Ti–Sb bond length is 2.86 Å. In the sixth Ti site, Ti is bonded in a 5-coordinate geometry to three Ge and two Sb atoms. There are one shorter (2.58 Å) and two longer (2.86 Å) Ti–Ge bond lengths. There are one shorter (2.72 Å) and one longer (2.83 Å) Ti–Sb bond lengths. In the seventh Ti site, Ti is bonded in a 5-coordinate geometry to three Ge and two Sb atoms. There are one shorter (2.55 Å) and two longer (2.85 Å) Ti–Ge bond lengths. There are one shorter (2.71 Å) and one longer (2.82 Å) Ti–Sb bond lengths. In the eighth Ti site, Ti is bonded in a 5-coordinate geometry to four Ge and one Sb atom. There are a spread of Ti–Ge bond distances ranging from 2.57–2.81 Å. The Ti–Sb bond length is 2.72 Å. In the ninth Ti site, Ti is bonded in a 5-coordinate geometry to three Ge and two Sb atoms. There are one shorter (2.71 Å) and two longer (2.80 Å) Ti–Ge bond lengths. There are one shorter (2.66 Å) and one longer (2.68 Å) Ti–Sb bond lengths. In the tenth Ti site, Ti is bonded in a 5-coordinate geometry to four Ge and one Sb atom. There are a spread of Ti–Ge bond distances ranging from 2.56–2.82 Å. The Ti–Sb bond length is 2.71 Å. In the eleventh Ti site, Ti is bonded in a 5-coordinate geometry to three Ge and two equivalent Sb atoms. There are two shorter (2.62 Å) and one longer (2.84 Å) Ti–Ge bond lengths. Both Ti–Sb bond lengths are 2.85 Å. In the twelfth Ti site, Ti is bonded in a 5-coordinate geometry to three Ge and two equivalent Sb atoms. There are two shorter (2.62 Å) and one longer (2.83 Å) Ti–Ge bond lengths. Both Ti–Sb bond lengths are 2.86 Å. In the thirteenth Ti site, Ti is bonded in a 5-coordinate geometry to three Ge and two equivalent Sb atoms. There are a spread of Ti–Ge bond distances ranging from 2.61–2.81 Å. Both Ti–Sb bond lengths are 2.84 Å. In the fourteenth Ti site, Ti is bonded in a 5-coordinate geometry to five Ge atoms. There are a spread of Ti–Ge bond distances ranging from 2.61–2.82 Å. In the fifteenth Ti site, Ti is bonded in a 5-coordinate geometry to five Ge atoms. There are a spread of Ti–Ge bond distances ranging from 2.62–2.82 Å. In the sixteenth Ti site, Ti is bonded in a 5-coordinate geometry to five Ge atoms. There are a spread of Ti–Ge bond distances ranging from 2.62–2.83 Å. There are nine inequivalent Ge sites. In the first Ge site, Ge is bonded in a 9-coordinate geometry to nine Ti atoms. In the second Ge site, Ge is bonded in a 9-coordinate geometry to nine Ti atoms. In the third Ge site, Ge is bonded in a 9-coordinate geometry to nine Ti atoms. In the fourth Ge site, Ge is bonded in a 9-coordinate geometry to nine Ti atoms. In the fifth Ge site, Ge is bonded in a 9-coordinate geometry to nine Ti atoms. In the sixth Ge site, Ge is bonded in a 9-coordinate geometry to nine Ti atoms. In the seventh Ge site, Ge is bonded in a 9-coordinate geometry to nine Ti atoms. In the eighth Ge site, Ge is bonded in a 9-coordinate geometry to nine Ti atoms. In the ninth Ge site, Ge is bonded in a 9-coordinate geometry to nine Ti atoms. There are three inequivalent Sb sites. In the first Sb site, Sb is bonded in a 9-coordinate geometry to nine Ti atoms. In the second Sb site, Sb is bonded in a 9-coordinate geometry to nine Ti atoms. In the third Sb site, Sb is bonded in a 9-coordinate geometry to nine Ti atoms.

36 MATERIALS SCIENCE↗

Materials Data on Li14Ti21O48 by Materials Project

Li14Ti21O48 is Spinel-like structured and crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are fourteen inequivalent Li sites. In the first Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with three equivalent LiO6 octahedra and corners with nine TiO6 octahedra. The corner-sharing octahedra tilt angles range from 56–62°. There are three shorter (1.98 Å) and one longer (2.04 Å) Li–O bond lengths. In the second Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with twelve TiO6 octahedra. The corner-sharing octahedra tilt angles range from 58–61°. There are one shorter (2.02 Å) and three longer (2.03 Å) Li–O bond lengths. In the third Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with twelve TiO6 octahedra. The corner-sharing octahedra tilt angles range from 57–61°. There are three shorter (2.03 Å) and one longer (2.04 Å) Li–O bond lengths. In the fourth Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with three equivalent LiO6 octahedra and corners with nine TiO6 octahedra. The corner-sharing octahedra tilt angles range from 56–64°. There are three shorter (2.00 Å) and one longer (2.01 Å) Li–O bond lengths. In the fifth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO4 tetrahedra and edges with six TiO6 octahedra. There are three shorter (2.12 Å) and three longer (2.13 Å) Li–O bond lengths. In the sixth Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with twelve TiO6 octahedra. The corner-sharing octahedra tilt angles range from 57–61°. There are three shorter (2.03 Å) and one longer (2.04 Å) Li–O bond lengths. In the seventh Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with three equivalent LiO6 octahedra and corners with nine TiO6 octahedra. The corner-sharing octahedra tilt angles range from 56–64°. There is one shorter (1.99 Å) and three longer (2.00 Å) Li–O bond length. In the eighth Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share a cornercorner with one LiO6 octahedra and corners with eleven TiO6 octahedra. The corner-sharing octahedra tilt angles range from 58–64°. There are a spread of Li–O bond distances ranging from 2.01–2.07 Å. In the ninth Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with three equivalent LiO6 octahedra and corners with nine TiO6 octahedra. The corner-sharing octahedra tilt angles range from 57–63°. There are three shorter (1.99 Å) and one longer (2.05 Å) Li–O bond lengths. In the tenth Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with two equivalent LiO6 octahedra and corners with ten TiO6 octahedra. The corner-sharing octahedra tilt angles range from 53–64°. There are a spread of Li–O bond distances ranging from 1.99–2.05 Å. In the eleventh Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Li–O bond distances ranging from 2.11–2.14 Å. In the twelfth Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share corners with two equivalent LiO6 octahedra and corners with ten TiO6 octahedra. The corner-sharing octahedra tilt angles range from 52–64°. There are a spread of Li–O bond distances ranging from 1.98–2.04 Å. In the thirteenth Li site, Li is bonded to four O atoms to form LiO4 tetrahedra that share a cornercorner with one LiO6 octahedra and corners with eleven TiO6 octahedra. The corner-sharing octahedra tilt angles range from 57–65°. There are a spread of Li–O bond distances ranging from 2.00–2.06 Å. In the fourteenth Li site, Li is bonded to six O atoms to form LiO6 octahedra that share corners with six LiO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Li–O bond distances ranging from 2.10–2.12 Å. There are fifteen inequivalent Ti sites. In the first Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with five LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.92–2.06 Å. In the second Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with three equivalent LiO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.97–2.02 Å. In the third Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with five LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.93–2.05 Å. In the fourth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.92–2.06 Å. In the fifth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.92–2.06 Å. In the sixth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.92–2.06 Å. In the seventh Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra and edges with six TiO6 octahedra. All Ti–O bond lengths are 1.99 Å. In the eighth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.91–2.07 Å. In the ninth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.92–2.06 Å. In the tenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.95–2.05 Å. In the eleventh Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra, edges with two equivalent LiO6 octahedra, and edges with four TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.95–2.04 Å. In the twelfth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.86–2.11 Å. In the thirteenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with four LiO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.96–2.04 Å. In the fourteenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with six LiO4 tetrahedra, an edgeedge with one LiO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.84–2.16 Å. In the fifteenth Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with four LiO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.97–2.03 Å. There are thirty-six inequivalent O sites. In the first O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted edge and corner-sharing OLiTi3 tetrahedra. In the second O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted edge and corner-sharing OLiTi3 tetrahedra. In the third O site, O is bonded to one Li and three Ti atoms to form distorted edge-sharing OLiTi3 tetrahedra. In the fourth O site, O is bonded in a rectangular see-saw-like geometry to two Li and two equivalent Ti atoms. In the fifth O site, O is bonded in a rectangular see-saw-like geometry to two Li and two Ti atoms. In the sixth O site, O is bonded in a distorted rectangular see-saw-like geometry to one Li and three Ti atoms. In the seventh O site, O is bonded in a rectangular see-saw-like geometry to two Li and two Ti atoms. In the eighth O site, O is bonded in a distorted T-shaped geometry to three Ti atoms. In the ninth O site, O is bonded in a rectangular see-saw-like geometry to two Li and two equivalent Ti atoms. In the tenth O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted edge and corner-sharing OLiTi3 tetrahedra. In the eleventh O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted edge and corner-sharing OLiTi3 tetrahedra. In the twelfth O site, O is bonded to one Li and three Ti atoms to form distorted edge-sharing OLiTi3 tetrahedra. In the thirteenth O site, O is bonded to one Li and three Ti atoms to form distorted edge-sharing OLiTi3 tetrahedra. In the fourteenth O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted edge and corner-sharing OLiTi3 tetrahedra. In the fifteenth O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted edge and corner-sharing OLiTi3 tetrahedra. In the sixteenth O site, O is bonded in a rectangular see-saw-like geometry to two Li and two equivalent Ti atoms. In the seventeenth O site, O is bonded in a rectangular see-saw-like geometry to two Li and two Ti atoms. In the eighteenth O site, O is bonded in a distorted rectangular see-saw-like geometry to one Li and three Ti atoms. In the nineteenth O site, O is bonded in a rectangular see-saw-like geometry to two Li and two Ti atoms. In the twentieth O site, O is bonded to one Li and three Ti atoms to form distorted OLiTi3 trigonal pyramids that share corners with nine OLiTi3 tetrahedra and corners with two equivalent OLi2Ti2 trigonal pyramids. In the twenty-first O site, O is bonded in a rectangular see-saw-like geometry to two Li and two equivalent Ti atoms. In the twenty-second O site, O is bonded in a rectangular see-saw-like geometry to one Li and three Ti atoms. In the twenty-third O site, O is bonded to one Li and three Ti atoms to form distorted OLiTi3 tetrahedra that share corners with two OLiTi3 tetrahedra, corners with five OLi2Ti2 trigonal pyramids, and edges with three OLiTi3 tetrahedra. In the twenty-fourth O site, O is bonded to two Li and two equivalent Ti atoms to form distorted OLi2Ti2 trigonal pyramids that share corners with three OLiTi3 tetrahedra, corners with three equivalent OLi2Ti2 trigonal pyramids, and edges with two equivalent OLi2Ti2 trigonal pyramids. In the twenty-fifth O site, O is bonded to two Li and two Ti atoms to form distorted OLi2Ti2 trigonal pyramids that share corners with three OLiTi3 tetrahedra, corners with four OLi2Ti2 trigonal pyramids, and edges with two OLi2Ti2 trigonal pyramids. In the twenty-sixth O site, O is bonded to one Li and three Ti atoms to form a mixture of distorted edge and corner-sharing OLiTi3 tetrahedra. In the twenty-seventh O site, O is bonded to one Li and three Ti atoms to form OLiTi3 tetrahedra that share corners with two equivalent OLiTi3 tetrahedra, corners with five OLi2Ti2 trigonal pyramids, and edges with three OLiTi3 tetrahedra. In the twenty-eighth O site, O is bonded in a distorted rectangular see-saw-like geometry to two Li and two Ti atoms. In the twenty-ninth O site, O is bonded to one Li and three Ti atoms to form OLiTi3 tetrahedra that share corners with two equivalent OLiTi3 tetrahedra, corners with three OLi2Ti2 trig

36 MATERIALS SCIENCE↗

Materials Data on Ba3Sr5Ti7MnO20 by Materials Project

Ba3Sr5Ti7MnO20 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are twelve inequivalent Ba2+ sites. In the first Ba2+ site, Ba2+ is bonded in a distorted q6 geometry to ten O2- atoms. There are a spread of Ba–O bond distances ranging from 2.80–2.96 Å. In the second Ba2+ site, Ba2+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Ba–O bond distances ranging from 2.78–3.14 Å. In the third Ba2+ site, Ba2+ is bonded in a distorted q6 geometry to ten O2- atoms. There are a spread of Ba–O bond distances ranging from 2.77–3.07 Å. In the fourth Ba2+ site, Ba2+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Ba–O bond distances ranging from 2.77–3.17 Å. In the fifth Ba2+ site, Ba2+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Ba–O bond distances ranging from 2.71–3.14 Å. In the sixth Ba2+ site, Ba2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Ba–O bond distances ranging from 2.67–3.21 Å. In the seventh Ba2+ site, Ba2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Ba–O bond distances ranging from 2.67–3.13 Å. In the eighth Ba2+ site, Ba2+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Ba–O bond distances ranging from 2.76–3.13 Å. In the ninth Ba2+ site, Ba2+ is bonded in a distorted q6 geometry to ten O2- atoms. There are a spread of Ba–O bond distances ranging from 2.79–3.10 Å. In the tenth Ba2+ site, Ba2+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Ba–O bond distances ranging from 2.78–3.11 Å. In the eleventh Ba2+ site, Ba2+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Ba–O bond distances ranging from 2.77–3.14 Å. In the twelfth Ba2+ site, Ba2+ is bonded in a 9-coordinate geometry to eight O2- atoms. There are a spread of Ba–O bond distances ranging from 2.66–2.98 Å. There are twenty inequivalent Sr2+ sites. In the first Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to eight O2- atoms. There are a spread of Sr–O bond distances ranging from 2.48–2.95 Å. In the second Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sr–O bond distances ranging from 2.42–3.19 Å. In the third Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sr–O bond distances ranging from 2.48–3.07 Å. In the fourth Sr2+ site, Sr2+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Sr–O bond distances ranging from 2.46–3.05 Å. In the fifth Sr2+ site, Sr2+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Sr–O bond distances ranging from 2.59–3.09 Å. In the sixth Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sr–O bond distances ranging from 2.42–3.03 Å. In the seventh Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sr–O bond distances ranging from 2.61–2.97 Å. In the eighth Sr2+ site, Sr2+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Sr–O bond distances ranging from 2.60–3.06 Å. In the ninth Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sr–O bond distances ranging from 2.58–2.89 Å. In the tenth Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sr–O bond distances ranging from 2.38–3.20 Å. In the eleventh Sr2+ site, Sr2+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Sr–O bond distances ranging from 2.49–2.98 Å. In the twelfth Sr2+ site, Sr2+ is bonded in a 7-coordinate geometry to eight O2- atoms. There are a spread of Sr–O bond distances ranging from 2.51–3.08 Å. In the thirteenth Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sr–O bond distances ranging from 2.51–3.08 Å. In the fourteenth Sr2+ site, Sr2+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Sr–O bond distances ranging from 2.59–3.07 Å. In the fifteenth Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sr–O bond distances ranging from 2.52–3.06 Å. In the sixteenth Sr2+ site, Sr2+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Sr–O bond distances ranging from 2.65–3.17 Å. In the seventeenth Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sr–O bond distances ranging from 2.45–3.12 Å. In the eighteenth Sr2+ site, Sr2+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Sr–O bond distances ranging from 2.61–3.16 Å. In the nineteenth Sr2+ site, Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sr–O bond distances ranging from 2.59–3.02 Å. In the twentieth Sr2+ site, Sr2+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Sr–O bond distances ranging from 2.63–3.10 Å. There are twenty-eight inequivalent Ti+3.14+ sites. In the first Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 1–9°. There are a spread of Ti–O bond distances ranging from 2.00–2.23 Å. In the second Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four TiO6 octahedra, a cornercorner with one TiO4 tetrahedra, and a cornercorner with one TiO4 trigonal pyramid. The corner-sharing octahedra tilt angles range from 4–12°. There are a spread of Ti–O bond distances ranging from 2.00–2.27 Å. In the third Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share corners with four TiO6 octahedra and a cornercorner with one TiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 5–7°. There are a spread of Ti–O bond distances ranging from 1.97–2.61 Å. In the fourth Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four TiO6 octahedra, a cornercorner with one TiO4 trigonal pyramid, and a cornercorner with one MnO4 trigonal pyramid. The corner-sharing octahedra tilt angles range from 4–9°. There are a spread of Ti–O bond distances ranging from 2.01–2.07 Å. In the fifth Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four TiO6 octahedra and a cornercorner with one MnO4 trigonal pyramid. The corner-sharing octahedra tilt angles range from 3–7°. There are a spread of Ti–O bond distances ranging from 2.00–2.15 Å. In the sixth Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four TiO6 octahedra and a cornercorner with one TiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 1–7°. There are a spread of Ti–O bond distances ranging from 1.99–2.20 Å. In the seventh Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four TiO6 octahedra and a cornercorner with one MnO4 tetrahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Ti–O bond distances ranging from 1.93–2.27 Å. In the eighth Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four TiO6 octahedra and a cornercorner with one MnO4 tetrahedra. The corner-sharing octahedra tilt angles range from 5–11°. There are a spread of Ti–O bond distances ranging from 1.99–2.06 Å. In the ninth Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four TiO6 octahedra and a cornercorner with one TiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 2–9°. There are a spread of Ti–O bond distances ranging from 2.00–2.46 Å. In the tenth Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four TiO6 octahedra and a cornercorner with one MnO4 tetrahedra. The corner-sharing octahedra tilt angles range from 4–6°. There are a spread of Ti–O bond distances ranging from 1.96–2.09 Å. In the eleventh Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four TiO6 octahedra and a cornercorner with one MnO4 trigonal pyramid. The corner-sharing octahedra tilt angles range from 0–7°. There are a spread of Ti–O bond distances ranging from 2.02–2.14 Å. In the twelfth Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four TiO6 octahedra and a cornercorner with one MnO4 trigonal pyramid. The corner-sharing octahedra tilt angles range from 5–11°. There are a spread of Ti–O bond distances ranging from 2.01–2.04 Å. In the thirteenth Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four TiO6 octahedra, a cornercorner with one TiO4 tetrahedra, and a cornercorner with one TiO4 trigonal pyramid. The corner-sharing octahedra tilt angles range from 3–5°. There are a spread of Ti–O bond distances ranging from 1.99–2.18 Å. In the fourteenth Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four TiO6 octahedra and a cornercorner with one TiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 1–11°. There are a spread of Ti–O bond distances ranging from 1.95–2.33 Å. In the fifteenth Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four TiO6 octahedra, a cornercorner with one MnO4 tetrahedra, and a cornercorner with one TiO4 trigonal pyramid. The corner-sharing octahedra tilt angles range from 1–6°. There are a spread of Ti–O bond distances ranging from 1.99–2.19 Å. In the sixteenth Ti+3.14+ site, Ti+3.14+ is bonded to six O2- atoms to form corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 4–12°. There are a spread of Ti–O bond distances ranging from 2.00–2.22 Å. In the seventeenth Ti+3.14+ site, Ti+3.14+ is bonded in a see-saw-like geometry to four O2- atoms. There are a spread of Ti–O bond distances ranging from 1.92–1.97 Å. In the eighteenth Ti+3.14+ site, Ti+3.14+ is bonded to four O2- atoms to form TiO4 tetrahedra that share corners with two TiO6 octahedra and a cornercorner with one MnO4 trigonal pyramid. The corner-sharing octahedra tilt angles range from 27–32°. There are a spread of Ti–O bond distances ranging from 1.83–1.89 Å. In the nineteenth Ti+3.14+ site, Ti+3.14+ is bonded in a see-saw-like geometry to four O2- atoms. There are a spread of Ti–O bond distances ranging from 1.89–2.01 Å. In the twentieth Ti+3.14+ site, Ti+3.14+ is bonded in a rectangular see-saw-like geometry to four O2- atoms. There are a spread of Ti–O bond distances ranging from 1.87–1.97 Å. In the twenty-first Ti+3.14+ site, Ti+3.14+ is bonded to four O2- atoms to form TiO4 tetrahedra that share corners with two TiO6 octahedra and a cornercorner with one MnO4 trigonal pyramid. The corner-sharing octahedra tilt angles range from 14–21°. There are a spread of Ti–O bond distances ranging from 1.85–1.97 Å. In the twenty-second Ti+3.14+ site, Ti+3.14+ is bonded in a rectangular see-saw-like geometry to four O2- atoms. There are a spread of Ti–O bond distances ranging from 1.92–1.94 Å. In the twenty-third Ti+3.14+ site, Ti+3.14+ is bonded in a rectangular see-saw-like geometry to four O2- atoms. There are a spread of Ti–O bond distances ranging from 1.90–2.02 Å. In the twenty-fourth Ti+3.14+ site, Ti+3.14+ is bonded in a rectangular see-saw-like geometry to four O2- atoms. There is one shorter (1.91 Å) and three longer (1.96 Å) Ti–O bond length. In the twenty-fifth Ti+3.14+ site, Ti+3.14+ is bonded to four O2- atoms to form corner-sharing TiO4 trigonal pyramids. The corner-sharing octahedra tilt a

36 MATERIALS SCIENCE↗

Materials Data on Na11Ti8(PO4)12 by Materials Project

Na11Ti8(PO4)12 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are eleven 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 2.23–2.40 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 2.24–2.39 Å. In the third Na1+ site, Na1+ is bonded in a 5-coordinate geometry to six O2- atoms. There are a spread of Na–O bond distances ranging from 2.24–2.80 Å. In the fourth Na1+ site, Na1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Na–O bond distances ranging from 2.17–2.70 Å. In the fifth 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 2.25–2.35 Å. In the sixth 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 2.25–2.40 Å. In the seventh Na1+ site, Na1+ is bonded in a 4-coordinate geometry to seven O2- atoms. There are a spread of Na–O bond distances ranging from 2.18–2.99 Å. In the eighth Na1+ site, Na1+ is bonded in a 5-coordinate geometry to six O2- atoms. There are a spread of Na–O bond distances ranging from 2.22–2.80 Å. In the ninth Na1+ site, Na1+ is bonded in a 5-coordinate geometry to six O2- atoms. There are a spread of Na–O bond distances ranging from 2.22–2.81 Å. In the tenth 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 2.25–2.40 Å. In the eleventh Na1+ site, Na1+ is bonded in a 4-coordinate geometry to five O2- atoms. There are a spread of Na–O bond distances ranging from 2.17–2.77 Å. There are eight inequivalent Ti+3.12+ sites. In the first Ti+3.12+ site, Ti+3.12+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six PO4 tetrahedra. There are a spread of Ti–O bond distances ranging from 1.94–2.15 Å. In the second Ti+3.12+ site, Ti+3.12+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six PO4 tetrahedra. There are a spread of Ti–O bond distances ranging from 1.97–2.09 Å. In the third Ti+3.12+ site, Ti+3.12+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six PO4 tetrahedra. There are a spread of Ti–O bond distances ranging from 1.96–2.18 Å. In the fourth Ti+3.12+ site, Ti+3.12+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six PO4 tetrahedra. There are a spread of Ti–O bond distances ranging from 1.98–2.10 Å. In the fifth Ti+3.12+ site, Ti+3.12+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six PO4 tetrahedra. There are a spread of Ti–O bond distances ranging from 1.93–2.16 Å. In the sixth Ti+3.12+ site, Ti+3.12+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six PO4 tetrahedra. There are a spread of Ti–O bond distances ranging from 1.94–2.17 Å. In the seventh Ti+3.12+ site, Ti+3.12+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six PO4 tetrahedra. There are a spread of Ti–O bond distances ranging from 1.91–2.20 Å. In the eighth Ti+3.12+ site, Ti+3.12+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six PO4 tetrahedra. There are a spread of Ti–O bond distances ranging from 1.94–2.15 Å. There are twelve inequivalent P5+ sites. In the first P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four TiO6 octahedra. The corner-sharing octahedra tilt angles range from 22–33°. There is one shorter (1.54 Å) and three longer (1.55 Å) P–O bond length. In the second P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four TiO6 octahedra. The corner-sharing octahedra tilt angles range from 20–34°. There are a spread of P–O bond distances ranging from 1.54–1.56 Å. In the third P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four TiO6 octahedra. The corner-sharing octahedra tilt angles range from 16–34°. There are a spread of P–O bond distances ranging from 1.54–1.56 Å. In the fourth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four TiO6 octahedra. The corner-sharing octahedra tilt angles range from 16–36°. There are a spread of P–O bond distances ranging from 1.54–1.56 Å. In the fifth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four TiO6 octahedra. The corner-sharing octahedra tilt angles range from 18–34°. There is two shorter (1.54 Å) and two longer (1.56 Å) P–O bond length. In the sixth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four TiO6 octahedra. The corner-sharing octahedra tilt angles range from 15–36°. There are a spread of P–O bond distances ranging from 1.54–1.57 Å. In the seventh P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four TiO6 octahedra. The corner-sharing octahedra tilt angles range from 22–34°. There are a spread of P–O bond distances ranging from 1.54–1.56 Å. In the eighth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four TiO6 octahedra. The corner-sharing octahedra tilt angles range from 22–32°. There are a spread of P–O bond distances ranging from 1.54–1.56 Å. In the ninth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four TiO6 octahedra. The corner-sharing octahedra tilt angles range from 17–36°. There is one shorter (1.53 Å) and three longer (1.56 Å) P–O bond length. In the tenth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four TiO6 octahedra. The corner-sharing octahedra tilt angles range from 16–37°. There is one shorter (1.55 Å) and three longer (1.56 Å) P–O bond length. In the eleventh P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four TiO6 octahedra. The corner-sharing octahedra tilt angles range from 15–37°. There are a spread of P–O bond distances ranging from 1.53–1.56 Å. In the twelfth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four TiO6 octahedra. The corner-sharing octahedra tilt angles range from 13–39°. There is two shorter (1.55 Å) and two longer (1.56 Å) P–O bond length. There are forty-eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted linear geometry to one Ti+3.12+ and one P5+ atom. In the second O2- site, O2- is bonded in a distorted linear geometry to one Ti+3.12+ and one P5+ atom. In the third O2- site, O2- is bonded in a distorted T-shaped geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the fourth O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the fifth O2- site, O2- is bonded in a bent 150 degrees geometry to one Ti+3.12+ and one P5+ atom. In the sixth O2- site, O2- is bonded in a bent 150 degrees geometry to one Ti+3.12+ and one P5+ atom. In the seventh O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the eighth O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the ninth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the tenth O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the eleventh O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the twelfth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the thirteenth O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the fourteenth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the fifteenth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the sixteenth O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the seventeenth O2- site, O2- is bonded in a distorted T-shaped geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the eighteenth O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the nineteenth O2- site, O2- is bonded in a distorted T-shaped geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the twentieth O2- site, O2- is bonded in a bent 150 degrees geometry to one Ti+3.12+ and one P5+ atom. In the twenty-first O2- site, O2- is bonded in a 3-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the twenty-second O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the twenty-third O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one Ti+3.12+ and one P5+ atom. In the twenty-fourth O2- site, O2- is bonded in a distorted linear geometry to one Ti+3.12+ and one P5+ atom. In the twenty-fifth O2- site, O2- is bonded in a 2-coordinate geometry to one Ti+3.12+ and one P5+ atom. In the twenty-sixth O2- site, O2- is bonded in a distorted linear geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the twenty-seventh O2- site, O2- is bonded in a 3-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the twenty-eighth O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the twenty-ninth O2- site, O2- is bonded in a distorted T-shaped geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the thirtieth O2- site, O2- is bonded in a bent 150 degrees geometry to one Ti+3.12+ and one P5+ atom. In the thirty-first O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the thirty-second O2- site, O2- is bonded in a distorted trigonal pyramidal geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the thirty-third O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the thirty-fourth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the thirty-fifth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the thirty-sixth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the thirty-seventh O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the thirty-eighth O2- site, O2- is bonded in a 4-coordinate geometry to three Na1+, one Ti+3.12+, and one P5+ atom. In the thirty-ninth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the fortieth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the forty-first O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the forty-second O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the forty-third O2- site, O2- is bonded in a distorted T-shaped geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the forty-fourth O2- site, O2- is bonded in a bent 150 degrees geometry to one Ti+3.12+ and one P5+ atom. In the forty-fifth O2- site, O2- is bonded in a 3-coordinate geometry to two Na1+, one Ti+3.12+, and one P5+ atom. In the forty-sixth O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one Ti+3.12+, and one P5+ atom. In the forty-seventh O2- site, O2- is bonded in a distorted linear geometry to one Ti+3.12+ and one P5+ atom. In the forty-eighth O2- site, O2- is bonded in a distorted linear

36 MATERIALS SCIENCE↗

Materials Data on BaTi7O14 by Materials Project

BaTi7O14 is zeta iron carbide-derived structured and crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are two inequivalent Ba2+ sites. In the first Ba2+ site, Ba2+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Ba–O bond distances ranging from 2.90–3.07 Å. In the second Ba2+ site, Ba2+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Ba–O bond distances ranging from 2.75–3.27 Å. There are fourteen inequivalent Ti+3.71+ sites. In the first Ti+3.71+ site, Ti+3.71+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 48–51°. There are a spread of Ti–O bond distances ranging from 1.97–2.05 Å. In the second Ti+3.71+ site, Ti+3.71+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 47–51°. There are a spread of Ti–O bond distances ranging from 1.96–2.04 Å. In the third Ti+3.71+ site, Ti+3.71+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 48–50°. There are a spread of Ti–O bond distances ranging from 1.94–2.03 Å. In the fourth Ti+3.71+ site, Ti+3.71+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 48–51°. There are a spread of Ti–O bond distances ranging from 1.97–2.03 Å. In the fifth Ti+3.71+ site, Ti+3.71+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 48–51°. There are a spread of Ti–O bond distances ranging from 1.96–2.04 Å. In the sixth Ti+3.71+ site, Ti+3.71+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 48–52°. There are a spread of Ti–O bond distances ranging from 1.97–2.04 Å. In the seventh Ti+3.71+ site, Ti+3.71+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 46–50°. There are a spread of Ti–O bond distances ranging from 1.92–2.05 Å. In the eighth Ti+3.71+ site, Ti+3.71+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 47–51°. There are a spread of Ti–O bond distances ranging from 1.95–2.02 Å. In the ninth Ti+3.71+ site, Ti+3.71+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 48–51°. There are a spread of Ti–O bond distances ranging from 1.94–2.05 Å. In the tenth Ti+3.71+ site, Ti+3.71+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 48–51°. There are a spread of Ti–O bond distances ranging from 1.97–2.03 Å. In the eleventh Ti+3.71+ site, Ti+3.71+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 46–52°. There are a spread of Ti–O bond distances ranging from 1.93–2.03 Å. In the twelfth Ti+3.71+ site, Ti+3.71+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 47–51°. There are a spread of Ti–O bond distances ranging from 1.96–2.04 Å. In the thirteenth Ti+3.71+ site, Ti+3.71+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 47–51°. There are a spread of Ti–O bond distances ranging from 1.93–2.03 Å. In the fourteenth Ti+3.71+ site, Ti+3.71+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 47–51°. There are a spread of Ti–O bond distances ranging from 1.93–2.03 Å. There are twenty-eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.71+ atoms. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.71+ atoms. In the third O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.71+ atoms. In the fourth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.71+ atoms. In the fifth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.71+ atoms. In the sixth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.71+ atoms. In the seventh O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.71+ atoms. In the eighth O2- site, O2- is bonded in a 3-coordinate geometry to two equivalent Ba2+ and three Ti+3.71+ atoms. In the ninth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.71+ atoms. In the tenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.71+ atoms. In the eleventh O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.71+ atoms. In the twelfth O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.71+ atoms. In the thirteenth O2- site, O2- is bonded in a 3-coordinate geometry to two equivalent Ba2+ and three Ti+3.71+ atoms. In the fourteenth O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.71+ atoms. In the fifteenth O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.71+ atoms. In the sixteenth O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.71+ atoms. In the seventeenth O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.71+ atoms. In the eighteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.71+ atoms. In the nineteenth O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.71+ atoms. In the twentieth O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.71+ atoms. In the twenty-first O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.71+ atoms. In the twenty-second O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.71+ atoms. In the twenty-third O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.71+ atoms. In the twenty-fourth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.71+ atoms. In the twenty-fifth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.71+ atoms. In the twenty-sixth O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.71+ atoms. In the twenty-seventh O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.71+ atoms. In the twenty-eighth O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.71+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on LiTi2O4 by Materials Project

LiTi2O4 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are seven inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded in a rectangular see-saw-like geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.90–2.12 Å. In the second Li1+ site, Li1+ is bonded in a rectangular see-saw-like geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.89–2.13 Å. In the third Li1+ site, Li1+ is bonded in a rectangular see-saw-like geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.89–2.08 Å. In the fourth Li1+ site, Li1+ is bonded to six O2- atoms to form distorted LiO6 octahedra that share corners with nine TiO6 octahedra, edges with three TiO6 octahedra, and a faceface with one TiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–58°. There are a spread of Li–O bond distances ranging from 2.07–2.62 Å. In the fifth Li1+ site, Li1+ is bonded in a rectangular see-saw-like geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.89–2.14 Å. In the sixth Li1+ site, Li1+ is bonded to six O2- atoms to form distorted LiO6 octahedra that share corners with nine TiO6 octahedra, edges with three TiO6 octahedra, and a faceface with one TiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–54°. There are a spread of Li–O bond distances ranging from 2.10–2.55 Å. In the seventh Li1+ site, Li1+ is bonded in a rectangular see-saw-like geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.89–2.13 Å. There are fourteen inequivalent Ti+3.50+ sites. In the first Ti+3.50+ site, Ti+3.50+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two LiO6 octahedra and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 5–13°. There are a spread of Ti–O bond distances ranging from 1.96–2.10 Å. In the second Ti+3.50+ site, Ti+3.50+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two LiO6 octahedra and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 9–15°. There are a spread of Ti–O bond distances ranging from 1.96–2.12 Å. In the third Ti+3.50+ site, Ti+3.50+ is bonded to six O2- atoms to form TiO6 octahedra that share an edgeedge with one LiO6 octahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.93–2.07 Å. In the fourth Ti+3.50+ site, Ti+3.50+ is bonded to six O2- atoms to form TiO6 octahedra that share edges with two LiO6 octahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 2.00–2.03 Å. In the fifth Ti+3.50+ site, Ti+3.50+ is bonded to six O2- atoms to form TiO6 octahedra that share an edgeedge with one LiO6 octahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.98–2.05 Å. In the sixth Ti+3.50+ site, Ti+3.50+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one LiO6 octahedra, an edgeedge with one LiO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedral tilt angles are 7°. There are a spread of Ti–O bond distances ranging from 1.98–2.04 Å. In the seventh Ti+3.50+ site, Ti+3.50+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one LiO6 octahedra, an edgeedge with one LiO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedral tilt angles are 14°. There are a spread of Ti–O bond distances ranging from 1.99–2.07 Å. In the eighth Ti+3.50+ site, Ti+3.50+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two LiO6 octahedra and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 46–54°. There are a spread of Ti–O bond distances ranging from 2.03–2.07 Å. In the ninth Ti+3.50+ site, Ti+3.50+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two LiO6 octahedra and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 44–50°. There are a spread of Ti–O bond distances ranging from 2.00–2.08 Å. In the tenth Ti+3.50+ site, Ti+3.50+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one LiO6 octahedra, edges with six TiO6 octahedra, and a faceface with one LiO6 octahedra. The corner-sharing octahedral tilt angles are 46°. There are a spread of Ti–O bond distances ranging from 1.99–2.07 Å. In the eleventh Ti+3.50+ site, Ti+3.50+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two LiO6 octahedra and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 39–43°. There are a spread of Ti–O bond distances ranging from 1.96–2.08 Å. In the twelfth Ti+3.50+ site, Ti+3.50+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one LiO6 octahedra, edges with six TiO6 octahedra, and a faceface with one LiO6 octahedra. The corner-sharing octahedral tilt angles are 58°. There are a spread of Ti–O bond distances ranging from 2.01–2.08 Å. In the thirteenth Ti+3.50+ site, Ti+3.50+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two LiO6 octahedra and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 49–54°. There are a spread of Ti–O bond distances ranging from 1.96–2.11 Å. In the fourteenth Ti+3.50+ site, Ti+3.50+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two LiO6 octahedra and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 49–53°. There are a spread of Ti–O bond distances ranging from 1.98–2.07 Å. There are twenty-eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.50+ atoms. In the second O2- site, O2- is bonded to two Li1+ and three Ti+3.50+ atoms to form OLi2Ti3 square pyramids that share a cornercorner with one OLi2Ti3 square pyramid, a cornercorner with one OLi2Ti3 trigonal bipyramid, corners with three OLiTi3 trigonal pyramids, edges with two OLi2Ti3 square pyramids, an edgeedge with one OLi2Ti3 trigonal bipyramid, and an edgeedge with one OLiTi3 trigonal pyramid. In the third O2- site, O2- is bonded to two Li1+ and three Ti+3.50+ atoms to form OLi2Ti3 square pyramids that share a cornercorner with one OLi2Ti3 trigonal bipyramid, corners with three OLiTi3 trigonal pyramids, edges with three OLi2Ti3 square pyramids, edges with two OLi2Ti3 trigonal bipyramids, and edges with two OLiTi3 trigonal pyramids. In the fourth O2- site, O2- is bonded to two Li1+ and three Ti+3.50+ atoms to form distorted OLi2Ti3 trigonal bipyramids that share corners with two OLi2Ti3 square pyramids, a cornercorner with one OLi2Ti3 trigonal bipyramid, a cornercorner with one OLiTi3 trigonal pyramid, edges with two OLi2Ti3 square pyramids, an edgeedge with one OLi2Ti3 trigonal bipyramid, and edges with two OLiTi3 trigonal pyramids. In the fifth O2- site, O2- is bonded to one Li1+ and three Ti+3.50+ atoms to form OLiTi3 trigonal pyramids that share corners with three OLi2Ti3 square pyramids, a cornercorner with one OLiTi3 trigonal pyramid, an edgeedge with one OLi2Ti3 square pyramid, and edges with three OLi2Ti3 trigonal bipyramids. In the sixth O2- site, O2- is bonded to two Li1+ and three Ti+3.50+ atoms to form distorted OLi2Ti3 trigonal bipyramids that share a cornercorner with one OLi2Ti3 square pyramid, corners with two OLiTi3 trigonal pyramids, edges with two OLi2Ti3 square pyramids, edges with two OLi2Ti3 trigonal bipyramids, and edges with two OLiTi3 trigonal pyramids. In the seventh O2- site, O2- is bonded to two Li1+ and three Ti+3.50+ atoms to form OLi2Ti3 square pyramids that share a cornercorner with one OLi2Ti3 square pyramid, a cornercorner with one OLi2Ti3 trigonal bipyramid, corners with three OLiTi3 trigonal pyramids, edges with two OLi2Ti3 square pyramids, edges with two OLi2Ti3 trigonal bipyramids, and an edgeedge with one OLiTi3 trigonal pyramid. In the eighth O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.50+ atoms. In the ninth O2- site, O2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.50+ atoms. In the tenth O2- site, O2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.50+ atoms. In the eleventh O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to one Li1+ and three Ti+3.50+ atoms. In the twelfth O2- site, O2- is bonded to one Li1+ and three Ti+3.50+ atoms to form distorted OLiTi3 trigonal pyramids that share corners with two OLi2Ti3 square pyramids, a cornercorner with one OLi2Ti3 trigonal bipyramid, a cornercorner with one OLiTi3 trigonal pyramid, and an edgeedge with one OLiTi3 trigonal pyramid. In the thirteenth O2- site, O2- is bonded to one Li1+ and three Ti+3.50+ atoms to form distorted OLiTi3 trigonal pyramids that share corners with two OLi2Ti3 square pyramids, a cornercorner with one OLi2Ti3 trigonal bipyramid, and a cornercorner with one OLiTi3 trigonal pyramid. In the fourteenth O2- site, O2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.50+ atoms. In the fifteenth O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.50+ atoms. In the sixteenth O2- site, O2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.50+ atoms. In the seventeenth O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.50+ atoms. In the eighteenth O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to one Li1+ and three Ti+3.50+ atoms. In the nineteenth O2- site, O2- is bonded to one Li1+ and three Ti+3.50+ atoms to form distorted OLiTi3 trigonal pyramids that share a cornercorner with one OLi2Ti3 square pyramid and an edgeedge with one OLiTi3 trigonal pyramid. In the twentieth O2- site, O2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.50+ atoms. In the twenty-first O2- site, O2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.50+ atoms. In the twenty-second O2- site, O2- is bonded to two Li1+ and three Ti+3.50+ atoms to form OLi2Ti3 square pyramids that share corners with two OLi2Ti3 square pyramids, a cornercorner with one OLi2Ti3 trigonal bipyramid, corners with three OLiTi3 trigonal pyramids, an edgeedge with one OLi2Ti3 square pyramid, an edgeedge with one OLi2Ti3 trigonal bipyramid, and an edgeedge with one OLiTi3 trigonal pyramid. In the twenty-third O2- site, O2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.50+ atoms. In the twenty-fourth O2- site, O2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.50+ atoms. In the twenty-fifth O2- site, O2- is bonded to one Li1+ and three Ti+3.50+ atoms to form distorted OLiTi3 trigonal pyramids that share corners with two OLi2Ti3 square pyramids, a cornercorner with one OLiTi3 trigonal pyramid, edges with two OLi2Ti3 square pyramids, edges with two OLi2Ti3 trigonal bipyramids, and an edgeedge with one OLiTi3 trigonal pyramid. In the twenty-sixth O2- site, O2- is bonded to one Li1+ and three Ti+3.50+ atoms to form OLiTi3 trigonal pyramids that share corners with two OLi2Ti3 square pyramids, a cornercorner with one OLi2Ti3 trigonal bipyramid, edges with two OLi2Ti3 square pyramids, edges with two OLi2Ti3 trigonal bipyramids, and an edgeedge with one OLiTi3 trigonal pyramid. In the twenty-seventh O2- site, O2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.50+ atoms. In the twenty-eighth O2- site, O2- is bonded to two Li1+ and three Ti+3.50+ atoms to form distorted OLi2Ti3 trigonal bipyramids that share a cornercorner with one OLi2Ti3 square pyramid, a cornercorner with one OLi2Ti3 trigonal bipyramid, edges w

36 MATERIALS SCIENCE↗

Materials Data on Ti5O8 by Materials Project

Ti5O8 is beta indium sulfide-like structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are fifteen inequivalent Ti+3.20+ sites. In the first Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 38–61°. There are a spread of Ti–O bond distances ranging from 1.94–2.16 Å. In the second Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 36–61°. There are a spread of Ti–O bond distances ranging from 1.93–2.17 Å. In the third Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 48–55°. There are a spread of Ti–O bond distances ranging from 2.01–2.11 Å. In the fourth Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 47–61°. There are a spread of Ti–O bond distances ranging from 1.96–2.09 Å. In the fifth Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 47–59°. There are a spread of Ti–O bond distances ranging from 2.01–2.09 Å. In the sixth Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 35–61°. There are a spread of Ti–O bond distances ranging from 1.93–2.13 Å. In the seventh Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 36–59°. There are a spread of Ti–O bond distances ranging from 1.88–2.14 Å. In the eighth Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 43–58°. There are a spread of Ti–O bond distances ranging from 1.99–2.10 Å. In the ninth Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 46–61°. There are a spread of Ti–O bond distances ranging from 1.96–2.10 Å. In the tenth Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 38–59°. There are a spread of Ti–O bond distances ranging from 1.89–2.15 Å. In the eleventh Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 46–61°. There are a spread of Ti–O bond distances ranging from 1.93–2.10 Å. In the twelfth Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 46–58°. There are a spread of Ti–O bond distances ranging from 2.01–2.09 Å. In the thirteenth Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 45–57°. There are a spread of Ti–O bond distances ranging from 2.01–2.10 Å. In the fourteenth Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 35–58°. There are a spread of Ti–O bond distances ranging from 1.90–2.08 Å. In the fifteenth Ti+3.20+ site, Ti+3.20+ is bonded to six O2- atoms to form a mixture of corner, edge, and face-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 46–59°. There are a spread of Ti–O bond distances ranging from 2.01–2.09 Å. There are twenty-four inequivalent O2- sites. In the first O2- site, O2- is bonded to four Ti+3.20+ atoms to form a mixture of distorted corner and edge-sharing OTi4 trigonal pyramids. In the second O2- site, O2- is bonded to four Ti+3.20+ atoms to form a mixture of distorted corner and edge-sharing OTi4 trigonal pyramids. In the third O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+3.20+ atoms. In the fourth O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.20+ atoms. In the fifth O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+3.20+ atoms. In the sixth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.20+ atoms. In the seventh O2- site, O2- is bonded to four Ti+3.20+ atoms to form a mixture of distorted corner and edge-sharing OTi4 trigonal pyramids. In the eighth O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+3.20+ atoms. In the ninth O2- site, O2- is bonded to four Ti+3.20+ atoms to form a mixture of distorted corner and edge-sharing OTi4 trigonal pyramids. In the tenth O2- site, O2- is bonded to four Ti+3.20+ atoms to form a mixture of distorted corner and edge-sharing OTi4 trigonal pyramids. In the eleventh O2- site, O2- is bonded to four Ti+3.20+ atoms to form a mixture of distorted corner and edge-sharing OTi4 trigonal pyramids. In the twelfth O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+3.20+ atoms. In the thirteenth O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+3.20+ atoms. In the fourteenth O2- site, O2- is bonded to four Ti+3.20+ atoms to form a mixture of distorted corner and edge-sharing OTi4 trigonal pyramids. In the fifteenth O2- site, O2- is bonded to four Ti+3.20+ atoms to form a mixture of distorted corner and edge-sharing OTi4 trigonal pyramids. In the sixteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.20+ atoms. In the seventeenth O2- site, O2- is bonded to four Ti+3.20+ atoms to form a mixture of distorted corner and edge-sharing OTi4 trigonal pyramids. In the eighteenth O2- site, O2- is bonded to four Ti+3.20+ atoms to form a mixture of distorted corner and edge-sharing OTi4 trigonal pyramids. In the nineteenth O2- site, O2- is bonded to four Ti+3.20+ atoms to form a mixture of distorted corner and edge-sharing OTi4 trigonal pyramids. In the twentieth O2- site, O2- is bonded in a T-shaped geometry to three Ti+3.20+ atoms. In the twenty-first O2- site, O2- is bonded in a T-shaped geometry to three Ti+3.20+ atoms. In the twenty-second O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.20+ atoms. In the twenty-third O2- site, O2- is bonded to four Ti+3.20+ atoms to form a mixture of distorted corner and edge-sharing OTi4 trigonal pyramids. In the twenty-fourth O2- site, O2- is bonded to four Ti+3.20+ atoms to form a mixture of distorted corner and edge-sharing OTi4 trigonal pyramids.

36 MATERIALS SCIENCE↗

Materials Data on Ba4Li6Ti19O44 by Materials Project

Li6Ba4Ti19O44 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are six inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Li–O bond distances ranging from 1.93–2.40 Å. In the second Li1+ site, Li1+ is bonded to six O2- atoms to form distorted LiO6 octahedra that share corners with five TiO6 octahedra, edges with three TiO6 octahedra, a faceface with one BaO12 cuboctahedra, and a faceface with one TiO6 octahedra. The corner-sharing octahedra tilt angles range from 7–49°. There are a spread of Li–O bond distances ranging from 2.04–2.40 Å. In the third Li1+ site, Li1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Li–O bond distances ranging from 1.94–2.19 Å. In the fourth Li1+ site, Li1+ is bonded to four O2- atoms to form LiO4 tetrahedra that share corners with ten TiO6 octahedra and an edgeedge with one BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 55–61°. There are a spread of Li–O bond distances ranging from 1.97–2.05 Å. In the fifth Li1+ site, Li1+ is bonded in a 4-coordinate geometry to four O2- atoms. There are a spread of Li–O bond distances ranging from 1.85–2.29 Å. In the sixth Li1+ site, Li1+ is bonded to four O2- atoms to form LiO4 tetrahedra that share corners with ten TiO6 octahedra. The corner-sharing octahedra tilt angles range from 54–63°. There are a spread of Li–O bond distances ranging from 1.95–2.06 Å. There are four inequivalent Ba2+ sites. In the first Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with two equivalent BaO12 cuboctahedra, corners with six TiO6 octahedra, edges with three TiO6 octahedra, faces with two equivalent BaO12 cuboctahedra, a faceface with one LiO6 octahedra, and faces with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 23–48°. There are a spread of Ba–O bond distances ranging from 2.77–3.04 Å. In the second Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with two equivalent BaO12 cuboctahedra, corners with seven TiO6 octahedra, edges with three TiO6 octahedra, an edgeedge with one LiO4 tetrahedra, and faces with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 28–49°. There are a spread of Ba–O bond distances ranging from 2.79–3.11 Å. In the third Ba2+ site, Ba2+ is bonded in a 12-coordinate geometry to twelve O2- atoms. There are a spread of Ba–O bond distances ranging from 2.73–3.25 Å. In the fourth Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with two equivalent BaO12 cuboctahedra, corners with six TiO6 octahedra, edges with three TiO6 octahedra, faces with two equivalent BaO12 cuboctahedra, and faces with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 27–53°. There are a spread of Ba–O bond distances ranging from 2.81–3.08 Å. There are nineteen inequivalent Ti+3.89+ sites. In the first Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one BaO12 cuboctahedra, corners with two TiO6 octahedra, corners with two LiO4 tetrahedra, an edgeedge with one BaO12 cuboctahedra, and edges with five TiO6 octahedra. The corner-sharing octahedra tilt angles range from 49–53°. There are a spread of Ti–O bond distances ranging from 1.98–2.03 Å. In the second Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one BaO12 cuboctahedra, a cornercorner with one LiO6 octahedra, corners with two TiO6 octahedra, corners with two LiO4 tetrahedra, an edgeedge with one BaO12 cuboctahedra, and edges with five TiO6 octahedra. The corner-sharing octahedra tilt angles range from 44–52°. There are a spread of Ti–O bond distances ranging from 1.94–2.13 Å. In the third Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two BaO12 cuboctahedra, corners with two TiO6 octahedra, an edgeedge with one BaO12 cuboctahedra, and edges with five TiO6 octahedra. The corner-sharing octahedra tilt angles range from 49–50°. There are a spread of Ti–O bond distances ranging from 1.93–2.09 Å. In the fourth Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share corners with three TiO6 octahedra, corners with three LiO4 tetrahedra, an edgeedge with one BaO12 cuboctahedra, and edges with three TiO6 octahedra. The corner-sharing octahedra tilt angles range from 42–59°. There are a spread of Ti–O bond distances ranging from 1.79–2.18 Å. In the fifth Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one BaO12 cuboctahedra, corners with seven TiO6 octahedra, edges with two TiO6 octahedra, and faces with three BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 11–53°. There are a spread of Ti–O bond distances ranging from 1.84–2.16 Å. In the sixth Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one BaO12 cuboctahedra, corners with six TiO6 octahedra, edges with two TiO6 octahedra, a faceface with one BaO12 cuboctahedra, and a faceface with one LiO6 octahedra. The corner-sharing octahedra tilt angles range from 11–51°. There are a spread of Ti–O bond distances ranging from 1.87–2.15 Å. In the seventh Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with three TiO6 octahedra, corners with three LiO4 tetrahedra, edges with three TiO6 octahedra, and a faceface with one BaO12 cuboctahedra. The corner-sharing octahedral tilt angles are 11°. There are a spread of Ti–O bond distances ranging from 1.93–2.06 Å. In the eighth Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one LiO6 octahedra, corners with three TiO6 octahedra, edges with two TiO6 octahedra, and faces with three BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 2–13°. There are a spread of Ti–O bond distances ranging from 1.91–2.17 Å. In the ninth Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two equivalent BaO12 cuboctahedra, corners with four TiO6 octahedra, an edgeedge with one BaO12 cuboctahedra, and edges with three TiO6 octahedra. The corner-sharing octahedra tilt angles range from 49–52°. There are a spread of Ti–O bond distances ranging from 1.87–2.17 Å. In the tenth Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two BaO12 cuboctahedra, corners with two TiO6 octahedra, an edgeedge with one BaO12 cuboctahedra, and edges with five TiO6 octahedra. The corner-sharing octahedra tilt angles range from 49–52°. There are a spread of Ti–O bond distances ranging from 1.95–2.04 Å. In the eleventh Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one BaO12 cuboctahedra, a cornercorner with one LiO6 octahedra, corners with two TiO6 octahedra, corners with two LiO4 tetrahedra, an edgeedge with one BaO12 cuboctahedra, and edges with five TiO6 octahedra. The corner-sharing octahedra tilt angles range from 48–49°. There are a spread of Ti–O bond distances ranging from 1.87–2.19 Å. In the twelfth Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one BaO12 cuboctahedra, corners with two TiO6 octahedra, corners with two LiO4 tetrahedra, an edgeedge with one BaO12 cuboctahedra, and edges with five TiO6 octahedra. The corner-sharing octahedra tilt angles range from 50–53°. There are a spread of Ti–O bond distances ranging from 1.97–2.01 Å. In the thirteenth Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two BaO12 cuboctahedra, corners with two TiO6 octahedra, an edgeedge with one LiO6 octahedra, and edges with three TiO6 octahedra. The corner-sharing octahedra tilt angles range from 42–51°. There are a spread of Ti–O bond distances ranging from 1.89–2.09 Å. In the fourteenth Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share corners with two equivalent LiO6 octahedra, corners with three TiO6 octahedra, edges with three TiO6 octahedra, and faces with three BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 9–17°. There are a spread of Ti–O bond distances ranging from 1.82–2.20 Å. In the fifteenth Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two equivalent BaO12 cuboctahedra, corners with four TiO6 octahedra, edges with two equivalent LiO6 octahedra, and edges with two TiO6 octahedra. The corner-sharing octahedra tilt angles range from 33–52°. There are a spread of Ti–O bond distances ranging from 1.90–2.12 Å. In the sixteenth Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one BaO12 cuboctahedra, corners with seven TiO6 octahedra, edges with two TiO6 octahedra, and faces with two equivalent BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 11–52°. There are a spread of Ti–O bond distances ranging from 1.97–2.13 Å. In the seventeenth Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two equivalent BaO12 cuboctahedra, corners with four TiO6 octahedra, corners with three LiO4 tetrahedra, an edgeedge with one BaO12 cuboctahedra, and edges with three TiO6 octahedra. The corner-sharing octahedral tilt angles are 49°. There are a spread of Ti–O bond distances ranging from 1.85–2.22 Å. In the eighteenth Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with three TiO6 octahedra, corners with three LiO4 tetrahedra, edges with three TiO6 octahedra, and faces with two equivalent BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 15–17°. There are a spread of Ti–O bond distances ranging from 1.90–2.12 Å. In the nineteenth Ti+3.89+ site, Ti+3.89+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with seven TiO6 octahedra, an edgeedge with one TiO6 octahedra, and faces with three BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 2–59°. There are a spread of Ti–O bond distances ranging from 1.81–2.23 Å. There are forty-four inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to one Li1+, one Ba2+, and two Ti+3.89+ atoms. In the second O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.89+ atoms. In the third O2- site, O2- is bonded in a distorted T-shaped geometry to two Ba2+ and three Ti+3.89+ atoms. In the fourth O2- site, O2- is bonded in a 3-coordinate geometry to two Ba2+ and three Ti+3.89+ atoms. In the fifth O2- site, O2- is bonded in a 4-coordinate geometry to one Li1+, one Ba2+, and two Ti+3.89+ atoms. In the sixth O2- site, O2- is bonded in a 5-coordinate geometry to two Li1+, one Ba2+, and two Ti+3.89+ atoms. In the seventh O2- site, O2- is bonded to one Li1+ and three Ti+3.89+ atoms to form distorted corner-sharing OLiTi3 tetrahedra. In the eighth O2- site, O2- is bonded to two Li1+ and three Ti+3.89+ atoms to form distorted edge-sharing OLi2Ti3 square pyramids. In the ninth O2- site, O2- is bonded in a 4-coordinate geometry to one Li1+, one Ba2+, and three Ti+3.89+ atoms. In the tenth O2- site, O2- is bonded in a distorted linear geometry to three Ba2+ and two Ti+3.89+ atoms. In the eleventh O2- site, O2- is bonded in a bent 150 degrees geometry to two Ti+3.89+ atoms. In the twelfth O2- site, O2- is bonded in a 2-coordinate geometry to three Ba2+ and two Ti+3.89+ atoms. In the thirteenth O2- site, O2- is bonded to one Li1+ and three

36 MATERIALS SCIENCE↗

Materials Data on Li8Ti16CuS32 by Materials Project

Li8Ti16CuS32 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are eight inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded in a 6-coordinate geometry to one Cu1+ and six S2- atoms. The Li–Cu bond length is 2.54 Å. There are a spread of Li–S bond distances ranging from 2.40–2.72 Å. In the second Li1+ site, Li1+ is bonded to six S2- atoms to form LiS6 octahedra that share corners with six TiS6 octahedra, edges with two LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 2–3°. All Li–S bond lengths are 2.53 Å. In the third Li1+ site, Li1+ is bonded to six S2- atoms to form LiS6 octahedra that share corners with six TiS6 octahedra, an edgeedge with one LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. There are four shorter (2.53 Å) and two longer (2.54 Å) Li–S bond lengths. In the fourth Li1+ site, Li1+ is bonded to six S2- atoms to form LiS6 octahedra that share corners with six TiS6 octahedra, edges with three LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 2–3°. There are a spread of Li–S bond distances ranging from 2.52–2.55 Å. In the fifth Li1+ site, Li1+ is bonded to six S2- atoms to form LiS6 octahedra that share corners with six TiS6 octahedra, edges with two LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. There are one shorter (2.52 Å) and five longer (2.53 Å) Li–S bond lengths. In the sixth Li1+ site, Li1+ is bonded to six S2- atoms to form LiS6 octahedra that share corners with six TiS6 octahedra, edges with four LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are four shorter (2.52 Å) and two longer (2.54 Å) Li–S bond lengths. In the seventh Li1+ site, Li1+ is bonded to six S2- atoms to form LiS6 octahedra that share corners with six TiS6 octahedra, edges with two LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Li–S bond distances ranging from 2.50–2.56 Å. In the eighth Li1+ site, Li1+ is bonded to six S2- atoms to form LiS6 octahedra that share corners with six TiS6 octahedra, edges with four LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Li–S bond distances ranging from 2.51–2.54 Å. There are sixteen inequivalent Ti+3.44+ sites. In the first Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with two equivalent CuLiS4 tetrahedra, an edgeedge with one LiS6 octahedra, and edges with six TiS6 octahedra. There are a spread of Ti–S bond distances ranging from 2.42–2.49 Å. In the second Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with six LiS6 octahedra, edges with two equivalent LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 2–3°. There are two shorter (2.44 Å) and four longer (2.46 Å) Ti–S bond lengths. In the third Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with three equivalent LiS6 octahedra, corners with two equivalent CuLiS4 tetrahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. There are a spread of Ti–S bond distances ranging from 2.43–2.47 Å. In the fourth Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with three equivalent LiS6 octahedra, corners with three equivalent CuLiS4 tetrahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Ti–S bond distances ranging from 2.40–2.51 Å. In the fifth Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with three equivalent LiS6 octahedra, edges with two equivalent LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. There are a spread of Ti–S bond distances ranging from 2.41–2.47 Å. In the sixth Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with two equivalent CuLiS4 tetrahedra, an edgeedge with one LiS6 octahedra, and edges with six TiS6 octahedra. There are a spread of Ti–S bond distances ranging from 2.42–2.49 Å. In the seventh Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share edges with four LiS6 octahedra and edges with six TiS6 octahedra. There are a spread of Ti–S bond distances ranging from 2.45–2.47 Å. In the eighth Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share edges with four LiS6 octahedra and edges with six TiS6 octahedra. There are four shorter (2.46 Å) and two longer (2.47 Å) Ti–S bond lengths. In the ninth Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with six LiS6 octahedra, edges with two equivalent LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 2–3°. There are a spread of Ti–S bond distances ranging from 2.43–2.47 Å. In the tenth Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with three equivalent LiS6 octahedra, edges with four LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedral tilt angles are 2°. There are a spread of Ti–S bond distances ranging from 2.44–2.48 Å. In the eleventh Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share edges with five LiS6 octahedra and edges with six TiS6 octahedra. There are a spread of Ti–S bond distances ranging from 2.44–2.48 Å. In the twelfth Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with three equivalent LiS6 octahedra, a cornercorner with one CuLiS4 tetrahedra, edges with three LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Ti–S bond distances ranging from 2.43–2.50 Å. In the thirteenth Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with six LiS6 octahedra, edges with three LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Ti–S bond distances ranging from 2.43–2.48 Å. In the fourteenth Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with three equivalent LiS6 octahedra, a cornercorner with one CuLiS4 tetrahedra, edges with three LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Ti–S bond distances ranging from 2.43–2.50 Å. In the fifteenth Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with six LiS6 octahedra, edges with four LiS6 octahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Ti–S bond distances ranging from 2.44–2.48 Å. In the sixteenth Ti+3.44+ site, Ti+3.44+ is bonded to six S2- atoms to form TiS6 octahedra that share a cornercorner with one CuLiS4 tetrahedra, edges with four LiS6 octahedra, and edges with six TiS6 octahedra. There are a spread of Ti–S bond distances ranging from 2.44–2.48 Å. Cu1+ is bonded to one Li1+ and four S2- atoms to form distorted CuLiS4 tetrahedra that share corners with twelve TiS6 octahedra and corners with five SLiTi3Cu square pyramids. The corner-sharing octahedra tilt angles range from 55–61°. There are a spread of Cu–S bond distances ranging from 2.20–2.27 Å. There are thirty-two inequivalent S2- sites. In the first S2- site, S2- is bonded to one Li1+, three Ti+3.44+, and one Cu1+ atom to form distorted SLiTi3Cu square pyramids that share corners with three equivalent SLi2Ti3 square pyramids, a cornercorner with one CuLiS4 tetrahedra, a cornercorner with one STi3Cu trigonal pyramid, and edges with five SLiTi3Cu square pyramids. In the second S2- site, S2- is bonded to one Li1+, three Ti+3.44+, and one Cu1+ atom to form distorted SLiTi3Cu square pyramids that share a cornercorner with one CuLiS4 tetrahedra, a cornercorner with one STi3Cu trigonal pyramid, and edges with six SLiTi3Cu square pyramids. In the third S2- site, S2- is bonded in a distorted T-shaped geometry to three Ti+3.44+ atoms. In the fourth S2- site, S2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.44+ atoms. In the fifth S2- site, S2- is bonded to two Li1+ and three Ti+3.44+ atoms to form SLi2Ti3 square pyramids that share corners with five SLi2Ti3 square pyramids, a cornercorner with one CuLiS4 tetrahedra, and edges with five SLi2Ti3 square pyramids. In the sixth S2- site, S2- is bonded to two Li1+ and three Ti+3.44+ atoms to form SLi2Ti3 square pyramids that share corners with five SLi2Ti3 square pyramids, a cornercorner with one CuLiS4 tetrahedra, and edges with five SLi2Ti3 square pyramids. In the seventh S2- site, S2- is bonded to one Li1+, three Ti+3.44+, and one Cu1+ atom to form distorted SLiTi3Cu square pyramids that share corners with three equivalent SLi2Ti3 square pyramids, a cornercorner with one CuLiS4 tetrahedra, a cornercorner with one STi3Cu trigonal pyramid, and edges with five SLiTi3Cu square pyramids. In the eighth S2- site, S2- is bonded to two Li1+ and three Ti+3.44+ atoms to form a mixture of edge and corner-sharing SLi2Ti3 square pyramids. In the ninth S2- site, S2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.44+ atoms. In the tenth S2- site, S2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.44+ atoms. In the eleventh S2- site, S2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.44+ atoms. In the twelfth S2- site, S2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.44+ atoms. In the thirteenth S2- site, S2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.44+ atoms. In the fourteenth S2- site, S2- is bonded to two Li1+ and three Ti+3.44+ atoms to form a mixture of edge and corner-sharing SLi2Ti3 square pyramids. In the fifteenth S2- site, S2- is bonded to two Li1+ and three Ti+3.44+ atoms to form a mixture of edge and corner-sharing SLi2Ti3 square pyramids. In the sixteenth S2- site, S2- is bonded to two Li1+ and three Ti+3.44+ atoms to form SLi2Ti3 square pyramids that share corners with nine SLi2Ti3 square pyramids, edges with three SLi3Ti3 octahedra, and edges with three SLi2Ti3 square pyramids. In the seventeenth S2- site, S2- is bonded to two Li1+ and three Ti+3.44+ atoms to form a mixture of edge and corner-sharing SLi2Ti3 square pyramids. In the eighteenth S2- site, S2- is bonded to two Li1+ and three Ti+3.44+ atoms to form SLi2Ti3 square pyramids that share corners with five SLi2Ti3 square pyramids, an edgeedge with one SLi3Ti3 octahedra, and edges with five SLi2Ti3 square pyramids. In the nineteenth S2- site, S2- is bonded to two Li1+ and three Ti+3.44+ atoms to form SLi2Ti3 square pyramids that share corners with three equivalent SLi3Ti3 octahedra, corners with two equivalent SLi2Ti3 square pyramids, and edges with six SLi2Ti3 square pyramids. The corner-sharing octahedral tilt angles are 1°. In the twentieth S2- site, S2- is bonded to two Li1+ and three Ti+3.44+ atoms to form SLi2Ti3 square pyramids that share corners with six SLi2Ti3 square pyramids, edges with three SLi3Ti3 octahedra, and edges with four SLi2Ti3 square pyramids. In the twenty-first S2- site, S2- is bonded in a rectangular see-saw-like geometry to one Li1+ and three Ti+3.44+ atoms. In the

36 MATERIALS SCIENCE↗

Materials Data on MgTi14O25 by Materials Project

MgTi14O25 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. Mg2+ is bonded to six O2- atoms to form distorted MgO6 octahedra that share corners with three TiO6 octahedra and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 23–42°. There are a spread of Mg–O bond distances ranging from 2.01–2.18 Å. There are fourteen inequivalent Ti+3.43+ sites. In the first Ti+3.43+ site, Ti+3.43+ is bonded to six O2- atoms to form a mixture of distorted edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 21–41°. There are a spread of Ti–O bond distances ranging from 1.92–2.17 Å. In the second Ti+3.43+ site, Ti+3.43+ is bonded to six O2- atoms to form a mixture of distorted edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 32–56°. There are a spread of Ti–O bond distances ranging from 1.90–2.21 Å. In the third Ti+3.43+ site, Ti+3.43+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share corners with four TiO6 octahedra, an edgeedge with one MgO6 octahedra, and edges with four TiO6 octahedra. The corner-sharing octahedra tilt angles range from 26–53°. There are a spread of Ti–O bond distances ranging from 1.93–2.15 Å. In the fourth Ti+3.43+ site, Ti+3.43+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share corners with four TiO6 octahedra, an edgeedge with one MgO6 octahedra, and edges with three TiO6 octahedra. The corner-sharing octahedra tilt angles range from 26–52°. There are a spread of Ti–O bond distances ranging from 1.92–2.19 Å. In the fifth Ti+3.43+ site, Ti+3.43+ is bonded to six O2- atoms to form a mixture of distorted edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 20–53°. There are a spread of Ti–O bond distances ranging from 1.92–2.21 Å. In the sixth Ti+3.43+ site, Ti+3.43+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share corners with four TiO6 octahedra, an edgeedge with one MgO6 octahedra, and edges with four TiO6 octahedra. The corner-sharing octahedra tilt angles range from 21–52°. There are a spread of Ti–O bond distances ranging from 1.91–2.23 Å. In the seventh Ti+3.43+ site, Ti+3.43+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share a cornercorner with one MgO6 octahedra, corners with three TiO6 octahedra, and edges with five TiO6 octahedra. The corner-sharing octahedra tilt angles range from 23–55°. There are a spread of Ti–O bond distances ranging from 1.85–2.23 Å. In the eighth Ti+3.43+ site, Ti+3.43+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ti–O bond distances ranging from 1.95–2.18 Å. In the ninth Ti+3.43+ site, Ti+3.43+ is bonded to six O2- atoms to form a mixture of distorted edge and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 20–41°. There are a spread of Ti–O bond distances ranging from 1.93–2.17 Å. In the tenth Ti+3.43+ site, Ti+3.43+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share corners with four TiO6 octahedra, an edgeedge with one MgO6 octahedra, and edges with five TiO6 octahedra. The corner-sharing octahedra tilt angles range from 20–53°. There are a spread of Ti–O bond distances ranging from 1.91–2.22 Å. In the eleventh Ti+3.43+ site, Ti+3.43+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share corners with four TiO6 octahedra, an edgeedge with one MgO6 octahedra, and edges with five TiO6 octahedra. The corner-sharing octahedra tilt angles range from 27–53°. There are a spread of Ti–O bond distances ranging from 1.90–2.21 Å. In the twelfth Ti+3.43+ site, Ti+3.43+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share corners with three TiO6 octahedra, an edgeedge with one MgO6 octahedra, and edges with five TiO6 octahedra. The corner-sharing octahedra tilt angles range from 30–56°. There are a spread of Ti–O bond distances ranging from 1.92–2.19 Å. In the thirteenth Ti+3.43+ site, Ti+3.43+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share a cornercorner with one MgO6 octahedra, corners with three TiO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 20–42°. There are a spread of Ti–O bond distances ranging from 1.93–2.16 Å. In the fourteenth Ti+3.43+ site, Ti+3.43+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share a cornercorner with one MgO6 octahedra, corners with three TiO6 octahedra, and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 28–55°. There are a spread of Ti–O bond distances ranging from 1.84–2.20 Å. There are twenty-five inequivalent O2- sites. In the first O2- site, O2- is bonded to four Ti+3.43+ atoms to form a mixture of distorted edge and corner-sharing OTi4 trigonal pyramids. In the second O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.43+ atoms. In the third O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.43+ atoms. In the fourth O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.43+ atoms. In the fifth O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.43+ atoms. In the sixth O2- site, O2- is bonded in a distorted T-shaped geometry to one Mg2+ and two Ti+3.43+ atoms. In the seventh O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.43+ atoms. In the eighth O2- site, O2- is bonded to four Ti+3.43+ atoms to form a mixture of distorted edge and corner-sharing OTi4 trigonal pyramids. In the ninth O2- site, O2- is bonded to four Ti+3.43+ atoms to form a mixture of distorted edge and corner-sharing OTi4 trigonal pyramids. In the tenth O2- site, O2- is bonded to four Ti+3.43+ atoms to form a mixture of distorted edge and corner-sharing OTi4 trigonal pyramids. In the eleventh O2- site, O2- is bonded to four Ti+3.43+ atoms to form a mixture of distorted edge and corner-sharing OTi4 trigonal pyramids. In the twelfth O2- site, O2- is bonded to four Ti+3.43+ atoms to form a mixture of distorted edge and corner-sharing OTi4 trigonal pyramids. In the thirteenth O2- site, O2- is bonded to four Ti+3.43+ atoms to form a mixture of distorted edge and corner-sharing OTi4 trigonal pyramids. In the fourteenth O2- site, O2- is bonded to one Mg2+ and three Ti+3.43+ atoms to form a mixture of distorted edge and corner-sharing OMgTi3 trigonal pyramids. In the fifteenth O2- site, O2- is bonded to one Mg2+ and three Ti+3.43+ atoms to form a mixture of distorted edge and corner-sharing OMgTi3 trigonal pyramids. In the sixteenth O2- site, O2- is bonded to one Mg2+ and three Ti+3.43+ atoms to form a mixture of distorted edge and corner-sharing OMgTi3 trigonal pyramids. In the seventeenth O2- site, O2- is bonded to four Ti+3.43+ atoms to form a mixture of distorted edge and corner-sharing OTi4 trigonal pyramids. In the eighteenth O2- site, O2- is bonded to one Mg2+ and three Ti+3.43+ atoms to form distorted OMgTi3 trigonal pyramids that share corners with three OTi4 trigonal pyramids and edges with four OMgTi3 trigonal pyramids. In the nineteenth O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.43+ atoms. In the twentieth O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.43+ atoms. In the twenty-first O2- site, O2- is bonded to four Ti+3.43+ atoms to form a mixture of distorted edge and corner-sharing OTi4 trigonal pyramids. In the twenty-second O2- site, O2- is bonded to four Ti+3.43+ atoms to form a mixture of distorted edge and corner-sharing OTi4 trigonal pyramids. In the twenty-third O2- site, O2- is bonded in a distorted see-saw-like geometry to four Ti+3.43+ atoms. In the twenty-fourth O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.43+ atoms. In the twenty-fifth O2- site, O2- is bonded in a distorted T-shaped geometry to one Mg2+ and two Ti+3.43+ atoms.

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