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DOE OSTI2020

Materials Data on MgTi2 by Materials Project

MgTi2 is beta-derived structured and crystallizes in the monoclinic P2_1/m space group. The structure is three-dimensional. there are four inequivalent Mg sites. In the first Mg site, Mg is bonded to four Mg and eight Ti atoms to form distorted MgMg4Ti8 cuboctahedra that share corners with six MgMg4Ti8 cuboctahedra, corners with twelve TiMg4Ti8 cuboctahedra, edges with seven MgMg4Ti8 cuboctahedra, edges with eleven TiMg4Ti8 cuboctahedra, faces with six MgMg4Ti8 cuboctahedra, and faces with fourteen TiMg4Ti8 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 2.97–3.14 Å. There are a spread of Mg–Ti bond distances ranging from 2.92–3.07 Å. In the second Mg site, Mg is bonded to four Mg and eight Ti atoms to form distorted MgMg4Ti8 cuboctahedra that share corners with four MgMg4Ti8 cuboctahedra, corners with fourteen TiMg4Ti8 cuboctahedra, edges with six MgMg4Ti8 cuboctahedra, edges with twelve TiMg4Ti8 cuboctahedra, faces with six MgMg4Ti8 cuboctahedra, and faces with fourteen TiMg4Ti8 cuboctahedra. There are two shorter (2.97 Å) and one longer (3.14 Å) Mg–Mg bond lengths. There are a spread of Mg–Ti bond distances ranging from 2.93–3.06 Å. In the third Mg site, Mg is bonded to four Mg and eight Ti atoms to form distorted MgMg4Ti8 cuboctahedra that share corners with seven MgMg4Ti8 cuboctahedra, corners with eleven TiMg4Ti8 cuboctahedra, edges with five MgMg4Ti8 cuboctahedra, edges with thirteen TiMg4Ti8 cuboctahedra, faces with six MgMg4Ti8 cuboctahedra, and faces with fourteen TiMg4Ti8 cuboctahedra. Both Mg–Mg bond lengths are 2.96 Å. There are a spread of Mg–Ti bond distances ranging from 2.90–3.00 Å. In the fourth Mg site, Mg is bonded to six Mg and six Ti atoms to form MgMg6Ti6 cuboctahedra that share corners with three MgMg4Ti8 cuboctahedra, corners with fifteen TiMg4Ti8 cuboctahedra, edges with two MgMg4Ti8 cuboctahedra, edges with sixteen TiMg4Ti8 cuboctahedra, faces with eight MgMg4Ti8 cuboctahedra, and faces with twelve TiMg4Ti8 cuboctahedra. There are a spread of Mg–Ti bond distances ranging from 3.06–3.14 Å. There are eight inequivalent Ti sites. In the first Ti site, Ti is bonded to four Mg and eight Ti atoms to form distorted TiMg4Ti8 cuboctahedra that share corners with eight MgMg4Ti8 cuboctahedra, corners with ten TiMg4Ti8 cuboctahedra, edges with seven MgMg4Ti8 cuboctahedra, edges with eleven TiMg4Ti8 cuboctahedra, faces with six MgMg4Ti8 cuboctahedra, and faces with fourteen TiMg4Ti8 cuboctahedra. There are a spread of Ti–Ti bond distances ranging from 2.84–3.12 Å. In the second Ti site, Ti is bonded to four Mg and eight Ti atoms to form distorted TiMg4Ti8 cuboctahedra that share corners with six MgMg4Ti8 cuboctahedra, corners with twelve TiMg4Ti8 cuboctahedra, edges with eight TiMg4Ti8 cuboctahedra, edges with ten MgMg4Ti8 cuboctahedra, faces with six MgMg4Ti8 cuboctahedra, and faces with fourteen TiMg4Ti8 cuboctahedra. There are a spread of Ti–Ti bond distances ranging from 2.81–3.16 Å. In the third Ti site, Ti is bonded to two Mg and ten Ti atoms to form distorted TiMg2Ti10 cuboctahedra that share corners with seven MgMg4Ti8 cuboctahedra, corners with eleven TiMg4Ti8 cuboctahedra, edges with nine MgMg4Ti8 cuboctahedra, edges with nine TiMg4Ti8 cuboctahedra, faces with four MgMg4Ti8 cuboctahedra, and faces with sixteen TiMg4Ti8 cuboctahedra. There are a spread of Ti–Ti bond distances ranging from 2.87–3.08 Å. In the fourth Ti site, Ti is bonded to three Mg and nine Ti atoms to form distorted TiMg3Ti9 cuboctahedra that share corners with seven MgMg4Ti8 cuboctahedra, corners with eleven TiMg4Ti8 cuboctahedra, edges with five MgMg4Ti8 cuboctahedra, edges with thirteen TiMg4Ti8 cuboctahedra, faces with seven MgMg4Ti8 cuboctahedra, and faces with thirteen TiMg4Ti8 cuboctahedra. There are a spread of Ti–Ti bond distances ranging from 2.92–3.04 Å. In the fifth Ti site, Ti is bonded to three Mg and nine Ti atoms to form distorted TiMg3Ti9 cuboctahedra that share corners with three MgMg4Ti8 cuboctahedra, corners with fifteen TiMg4Ti8 cuboctahedra, edges with six MgMg4Ti8 cuboctahedra, edges with twelve TiMg4Ti8 cuboctahedra, faces with seven MgMg4Ti8 cuboctahedra, and faces with thirteen TiMg4Ti8 cuboctahedra. There are one shorter (3.06 Å) and one longer (3.12 Å) Ti–Ti bond lengths. In the sixth Ti site, Ti is bonded to four Mg and eight Ti atoms to form distorted TiMg4Ti8 cuboctahedra that share corners with seven MgMg4Ti8 cuboctahedra, corners with eleven TiMg4Ti8 cuboctahedra, edges with eight MgMg4Ti8 cuboctahedra, edges with ten TiMg4Ti8 cuboctahedra, faces with six MgMg4Ti8 cuboctahedra, and faces with fourteen TiMg4Ti8 cuboctahedra. There are two shorter (2.90 Å) and one longer (3.08 Å) Ti–Ti bond lengths. In the seventh Ti site, Ti is bonded to five Mg and seven Ti atoms to form distorted TiMg5Ti7 cuboctahedra that share corners with seven MgMg4Ti8 cuboctahedra, corners with eleven TiMg4Ti8 cuboctahedra, edges with four MgMg4Ti8 cuboctahedra, edges with fourteen TiMg4Ti8 cuboctahedra, faces with nine MgMg4Ti8 cuboctahedra, and faces with eleven TiMg4Ti8 cuboctahedra. Both Ti–Ti bond lengths are 2.95 Å. In the eighth Ti site, Ti is bonded to five Mg and seven Ti atoms to form distorted TiMg5Ti7 cuboctahedra that share corners with seven MgMg4Ti8 cuboctahedra, corners with eleven TiMg4Ti8 cuboctahedra, edges with three equivalent MgMg4Ti8 cuboctahedra, edges with fifteen TiMg4Ti8 cuboctahedra, faces with nine MgMg4Ti8 cuboctahedra, and faces with eleven TiMg4Ti8 cuboctahedra. Both Ti–Ti bond lengths are 2.91 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ti9O17 by Materials Project

Ti9O17 is zeta iron carbide-like structured and crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are ten inequivalent Ti+3.78+ sites. In the first Ti+3.78+ site, Ti+3.78+ 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 49–50°. There are a spread of Ti–O bond distances ranging from 1.97–2.03 Å. In the second Ti+3.78+ site, Ti+3.78+ 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 47–51°. There are a spread of Ti–O bond distances ranging from 1.99–2.01 Å. In the third Ti+3.78+ site, Ti+3.78+ is bonded to six O2- atoms to form a mixture of distorted face, edge, and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 44–54°. There are a spread of Ti–O bond distances ranging from 1.86–2.19 Å. In the fourth Ti+3.78+ site, Ti+3.78+ is bonded to six O2- atoms to form a mixture of distorted face, edge, and corner-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 44–54°. There are a spread of Ti–O bond distances ranging from 1.84–2.18 Å. In the fifth Ti+3.78+ site, Ti+3.78+ 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 41–61°. There are a spread of Ti–O bond distances ranging from 1.89–2.13 Å. In the sixth Ti+3.78+ site, Ti+3.78+ 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 44–61°. There are a spread of Ti–O bond distances ranging from 1.87–2.16 Å. In the seventh Ti+3.78+ site, Ti+3.78+ 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 41–55°. There are a spread of Ti–O bond distances ranging from 1.87–2.11 Å. In the eighth Ti+3.78+ site, Ti+3.78+ 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 44–55°. There are a spread of Ti–O bond distances ranging from 1.91–2.11 Å. In the ninth Ti+3.78+ site, Ti+3.78+ 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 47–53°. There are a spread of Ti–O bond distances ranging from 1.93–2.07 Å. In the tenth Ti+3.78+ site, Ti+3.78+ 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 44–54°. There are a spread of Ti–O bond distances ranging from 1.92–2.09 Å. There are seventeen inequivalent O2- sites. In the first O2- site, O2- is bonded to four Ti+3.78+ 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 trigonal planar geometry to three Ti+3.78+ atoms. In the third O2- site, O2- is bonded to four Ti+3.78+ atoms to form a mixture of distorted edge and corner-sharing OTi4 trigonal pyramids. In the fourth O2- site, O2- is bonded to four Ti+3.78+ atoms to form distorted edge-sharing OTi4 trigonal pyramids. In the fifth O2- site, O2- is bonded in a 3-coordinate geometry to three Ti+3.78+ atoms. In the sixth O2- site, O2- is bonded in a trigonal planar geometry to three Ti+3.78+ atoms. In the seventh O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.78+ atoms. In the eighth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.78+ atoms. In the ninth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.78+ atoms. In the tenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.78+ atoms. In the eleventh O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.78+ atoms. In the twelfth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.78+ atoms. In the thirteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.78+ atoms. In the fourteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.78+ atoms. In the fifteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.78+ atoms. In the sixteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.78+ atoms. In the seventeenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.78+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ti11O14 by Materials Project

Ti11O14 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are eleven inequivalent Ti+2.55+ sites. In the first Ti+2.55+ site, Ti+2.55+ 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 2–9°. There are a spread of Ti–O bond distances ranging from 2.08–2.15 Å. In the second Ti+2.55+ site, Ti+2.55+ 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 2–7°. There are a spread of Ti–O bond distances ranging from 2.07–2.11 Å. In the third Ti+2.55+ site, Ti+2.55+ 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 2–5°. There are a spread of Ti–O bond distances ranging from 2.05–2.10 Å. In the fourth Ti+2.55+ site, Ti+2.55+ 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 2–9°. There are a spread of Ti–O bond distances ranging from 2.01–2.18 Å. In the fifth Ti+2.55+ site, Ti+2.55+ 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 3–7°. There are a spread of Ti–O bond distances ranging from 2.05–2.14 Å. In the sixth Ti+2.55+ site, Ti+2.55+ 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 2–6°. There are a spread of Ti–O bond distances ranging from 2.01–2.16 Å. In the seventh Ti+2.55+ site, Ti+2.55+ 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 2–4°. There are a spread of Ti–O bond distances ranging from 2.05–2.11 Å. In the eighth Ti+2.55+ site, Ti+2.55+ 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 4–6°. There are a spread of Ti–O bond distances ranging from 2.06–2.13 Å. In the ninth Ti+2.55+ site, Ti+2.55+ 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 2–7°. There are a spread of Ti–O bond distances ranging from 2.07–2.11 Å. In the tenth Ti+2.55+ site, Ti+2.55+ 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 2–6°. There are a spread of Ti–O bond distances ranging from 2.06–2.12 Å. In the eleventh Ti+2.55+ site, Ti+2.55+ 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 3–5°. There are a spread of Ti–O bond distances ranging from 2.05–2.15 Å. There are fourteen inequivalent O2- sites. In the first O2- site, O2- is bonded to five Ti+2.55+ atoms to form a mixture of edge and corner-sharing OTi5 square pyramids. In the second O2- site, O2- is bonded to five Ti+2.55+ atoms to form a mixture of edge and corner-sharing OTi5 square pyramids. In the third O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+2.55+ atoms. In the fourth O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+2.55+ atoms. In the fifth O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+2.55+ atoms. In the sixth O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti+2.55+ atoms. In the seventh O2- site, O2- is bonded to five Ti+2.55+ atoms to form a mixture of edge and corner-sharing OTi5 square pyramids. In the eighth O2- site, O2- is bonded to five Ti+2.55+ atoms to form a mixture of edge and corner-sharing OTi5 square pyramids. In the ninth O2- site, O2- is bonded to five Ti+2.55+ atoms to form a mixture of edge and corner-sharing OTi5 square pyramids. In the tenth O2- site, O2- is bonded to five Ti+2.55+ atoms to form a mixture of edge and corner-sharing OTi5 square pyramids. In the eleventh O2- site, O2- is bonded to five Ti+2.55+ atoms to form a mixture of edge and corner-sharing OTi5 square pyramids. In the twelfth O2- site, O2- is bonded to five Ti+2.55+ atoms to form a mixture of edge and corner-sharing OTi5 square pyramids. In the thirteenth O2- site, O2- is bonded to five Ti+2.55+ atoms to form a mixture of edge and corner-sharing OTi5 square pyramids. In the fourteenth O2- site, O2- is bonded to five Ti+2.55+ atoms to form a mixture of edge and corner-sharing OTi5 square pyramids.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Mg3Ti9O20 by Materials Project

Mg3Ti9O20 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are three inequivalent Mg2+ sites. In the first Mg2+ site, Mg2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Mg–O bond distances ranging from 2.02–2.21 Å. In the second Mg2+ site, Mg2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Mg–O bond distances ranging from 2.02–2.22 Å. In the third Mg2+ site, Mg2+ is bonded to six O2- atoms to form distorted MgO6 octahedra that share corners with two TiO6 octahedra and edges with six TiO6 octahedra. The corner-sharing octahedra tilt angles range from 27–28°. There are a spread of Mg–O bond distances ranging from 2.01–2.17 Å. There are nine inequivalent Ti+3.78+ sites. In the first Ti+3.78+ site, Ti+3.78+ is bonded to six O2- atoms to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 30–48°. There are a spread of Ti–O bond distances ranging from 1.84–2.19 Å. In the second Ti+3.78+ site, Ti+3.78+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share a cornercorner with one MgO6 octahedra, corners with three TiO6 octahedra, an edgeedge with one MgO6 octahedra, and edges with three TiO6 octahedra. The corner-sharing octahedra tilt angles range from 28–53°. There are a spread of Ti–O bond distances ranging from 1.82–2.19 Å. In the third Ti+3.78+ site, Ti+3.78+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share a cornercorner with one MgO6 octahedra, corners with three TiO6 octahedra, an edgeedge with one MgO6 octahedra, and edges with three TiO6 octahedra. The corner-sharing octahedra tilt angles range from 27–53°. There are a spread of Ti–O bond distances ranging from 1.82–2.19 Å. In the fourth Ti+3.78+ site, Ti+3.78+ 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 three TiO6 octahedra. The corner-sharing octahedra tilt angles range from 31–50°. There are a spread of Ti–O bond distances ranging from 1.91–2.13 Å. In the fifth Ti+3.78+ site, Ti+3.78+ 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 three TiO6 octahedra. The corner-sharing octahedra tilt angles range from 30–48°. There are a spread of Ti–O bond distances ranging from 1.83–2.24 Å. In the sixth Ti+3.78+ site, Ti+3.78+ is bonded to six O2- atoms to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 30–48°. There are a spread of Ti–O bond distances ranging from 1.83–2.20 Å. In the seventh Ti+3.78+ site, Ti+3.78+ 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 three TiO6 octahedra. The corner-sharing octahedra tilt angles range from 30–48°. There are a spread of Ti–O bond distances ranging from 1.83–2.23 Å. In the eighth Ti+3.78+ site, Ti+3.78+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ti–O bond distances ranging from 1.93–2.18 Å. In the ninth Ti+3.78+ site, Ti+3.78+ 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 three TiO6 octahedra. The corner-sharing octahedra tilt angles range from 31–50°. There are a spread of Ti–O bond distances ranging from 1.91–2.13 Å. There are twenty inequivalent O2- sites. In the first O2- site, O2- is bonded to one Mg2+ and three Ti+3.78+ atoms to form distorted OMgTi3 trigonal pyramids that share corners with four OMgTi3 trigonal pyramids and edges with four OMg2Ti2 trigonal pyramids. In the second O2- site, O2- is bonded to two Mg2+ and two Ti+3.78+ atoms to form a mixture of distorted corner and edge-sharing OMg2Ti2 trigonal pyramids. In the third O2- site, O2- is bonded to one Mg2+ and three Ti+3.78+ atoms to form a mixture of distorted corner and edge-sharing OMgTi3 trigonal pyramids. In the fourth O2- site, O2- is bonded to one Mg2+ and three Ti+3.78+ atoms to form a mixture of distorted corner and edge-sharing OMgTi3 trigonal pyramids. In the fifth O2- site, O2- is bonded to one Mg2+ and three Ti+3.78+ atoms to form distorted OMgTi3 trigonal pyramids that share corners with four OMg2Ti2 trigonal pyramids and edges with four OMgTi3 trigonal pyramids. In the sixth O2- site, O2- is bonded to four Ti+3.78+ atoms to form distorted OTi4 trigonal pyramids that share corners with four OMg2Ti2 trigonal pyramids and edges with four OMgTi3 trigonal pyramids. In the seventh O2- site, O2- is bonded in a distorted T-shaped geometry to one Mg2+ and two Ti+3.78+ atoms. In the eighth O2- site, O2- is bonded in a 3-coordinate geometry to one Mg2+ and two Ti+3.78+ atoms. In the ninth O2- site, O2- is bonded in a distorted T-shaped geometry to one Mg2+ and two Ti+3.78+ atoms. In the tenth O2- site, O2- is bonded in a 3-coordinate geometry to one Mg2+ and two Ti+3.78+ atoms. In the eleventh O2- site, O2- is bonded in a distorted T-shaped geometry to one Mg2+ and two Ti+3.78+ atoms. In the twelfth O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.78+ atoms. In the thirteenth O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.78+ atoms. In the fourteenth O2- site, O2- is bonded in a distorted T-shaped geometry to one Mg2+ and two Ti+3.78+ atoms. In the fifteenth O2- site, O2- is bonded to one Mg2+ and three Ti+3.78+ atoms to form distorted OMgTi3 trigonal pyramids that share corners with four OMgTi3 trigonal pyramids and edges with four OMg2Ti2 trigonal pyramids. In the sixteenth O2- site, O2- is bonded to one Mg2+ and three Ti+3.78+ atoms to form distorted OMgTi3 trigonal pyramids that share corners with four OMgTi3 trigonal pyramids and edges with four OMg2Ti2 trigonal pyramids. In the seventeenth O2- site, O2- is bonded to one Mg2+ and three Ti+3.78+ atoms to form distorted OMgTi3 trigonal pyramids that share corners with four OMgTi3 trigonal pyramids and edges with four OMg2Ti2 trigonal pyramids. In the eighteenth O2- site, O2- is bonded to two Mg2+ and two Ti+3.78+ atoms to form distorted OMg2Ti2 trigonal pyramids that share corners with four OMg2Ti2 trigonal pyramids and edges with four OMgTi3 trigonal pyramids. In the nineteenth O2- site, O2- is bonded to one Mg2+ and three Ti+3.78+ atoms to form a mixture of distorted corner and edge-sharing OMgTi3 trigonal pyramids. In the twentieth O2- site, O2- is bonded to four Ti+3.78+ atoms to form a mixture of distorted corner and edge-sharing OTi4 trigonal pyramids.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ba4Ti12O27 by Materials Project

Ba4Ti12O27 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. there are three inequivalent Ba2+ sites. In the first 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 2.81–3.21 Å. In the second Ba2+ site, Ba2+ is bonded in a 12-coordinate geometry to eleven O2- atoms. There are a spread of Ba–O bond distances ranging from 2.78–2.95 Å. In the third Ba2+ site, Ba2+ is bonded in a 11-coordinate geometry to eleven O2- atoms. There are a spread of Ba–O bond distances ranging from 2.73–3.20 Å. There are ten inequivalent Ti+3.83+ sites. In the first Ti+3.83+ site, Ti+3.83+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four equivalent TiO6 octahedra and corners with two equivalent TiO5 square pyramids. The corner-sharing octahedral tilt angles are 6°. There are two shorter (2.03 Å) and four longer (2.05 Å) Ti–O bond lengths. In the second Ti+3.83+ site, Ti+3.83+ is bonded to six O2- atoms to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles are 16°. There is two shorter (1.97 Å) and four longer (2.00 Å) Ti–O bond length. In the third Ti+3.83+ site, Ti+3.83+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two equivalent TiO6 octahedra, corners with two equivalent TiO5 square pyramids, and edges with four TiO6 octahedra. The corner-sharing octahedral tilt angles are 50°. There are four shorter (1.99 Å) and two longer (2.01 Å) Ti–O bond lengths. In the fourth Ti+3.83+ site, Ti+3.83+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two equivalent TiO6 octahedra, corners with two equivalent TiO5 square pyramids, and edges with three TiO6 octahedra. The corner-sharing octahedral tilt angles are 12°. There are a spread of Ti–O bond distances ranging from 1.92–2.08 Å. In the fifth Ti+3.83+ site, Ti+3.83+ 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 16–52°. There are a spread of Ti–O bond distances ranging from 1.86–2.17 Å. In the sixth Ti+3.83+ site, Ti+3.83+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two equivalent TiO6 octahedra, edges with four TiO6 octahedra, and an edgeedge with one TiO5 square pyramid. The corner-sharing octahedral tilt angles are 55°. There are a spread of Ti–O bond distances ranging from 1.94–2.09 Å. In the seventh Ti+3.83+ site, Ti+3.83+ is bonded to five O2- atoms to form a mixture of distorted edge and corner-sharing TiO5 square pyramids. The corner-sharing octahedra tilt angles range from 3–30°. There are a spread of Ti–O bond distances ranging from 1.82–2.04 Å. In the eighth Ti+3.83+ site, Ti+3.83+ 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 6–47°. There are a spread of Ti–O bond distances ranging from 1.89–2.16 Å. In the ninth Ti+3.83+ site, Ti+3.83+ 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 50–55°. There are a spread of Ti–O bond distances ranging from 1.89–2.15 Å. In the tenth Ti+3.83+ site, Ti+3.83+ 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 40–53°. There are a spread of Ti–O bond distances ranging from 1.84–2.18 Å. There are sixteen inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted see-saw-like geometry to four Ti+3.83+ atoms. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.83+ atoms. In the third O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.83+ atoms. In the fourth O2- site, O2- is bonded in a 3-coordinate geometry to one Ba2+ and three Ti+3.83+ atoms. In the fifth O2- site, O2- is bonded in a distorted linear geometry to three Ba2+ and two Ti+3.83+ atoms. In the sixth O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two Ti+3.83+ atoms. In the seventh O2- site, O2- is bonded in a 3-coordinate geometry to two Ba2+ and three Ti+3.83+ atoms. In the eighth O2- site, O2- is bonded in a distorted water-like geometry to two equivalent Ba2+ and two Ti+3.83+ atoms. In the ninth O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.83+ atoms. In the tenth O2- site, O2- is bonded in a 2-coordinate geometry to two Ba2+ and two Ti+3.83+ atoms. In the eleventh O2- site, O2- is bonded in a distorted trigonal planar geometry to three Ti+3.83+ atoms. In the twelfth O2- site, O2- is bonded in a distorted linear geometry to three Ba2+ and two Ti+3.83+ atoms. In the thirteenth O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.83+ atoms. In the fourteenth O2- site, O2- is bonded in a 2-coordinate geometry to two Ba2+ and two Ti+3.83+ atoms. In the fifteenth O2- site, O2- is bonded in a distorted T-shaped geometry to two Ba2+ and three Ti+3.83+ atoms. In the sixteenth O2- site, O2- is bonded in a 4-coordinate geometry to one Ba2+ and three Ti+3.83+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Gd7Ti8O26 by Materials Project

Gd7Ti8O26 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are seven inequivalent Gd3+ sites. In the first Gd3+ site, Gd3+ is bonded to eight O2- atoms to form distorted GdO8 hexagonal bipyramids that share an edgeedge with one GdO7 hexagonal pyramid, edges with three TiO6 octahedra, and edges with three TiO5 trigonal bipyramids. There are a spread of Gd–O bond distances ranging from 2.16–2.71 Å. In the second Gd3+ site, Gd3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Gd–O bond distances ranging from 2.23–2.60 Å. In the third Gd3+ site, Gd3+ is bonded to seven O2- atoms to form distorted GdO7 hexagonal pyramids that share corners with two TiO5 trigonal bipyramids, an edgeedge with one GdO8 hexagonal bipyramid, edges with three TiO6 octahedra, and an edgeedge with one TiO5 trigonal bipyramid. There are a spread of Gd–O bond distances ranging from 2.19–2.65 Å. In the fourth Gd3+ site, Gd3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Gd–O bond distances ranging from 2.21–2.80 Å. In the fifth Gd3+ site, Gd3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Gd–O bond distances ranging from 2.25–2.88 Å. In the sixth Gd3+ site, Gd3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Gd–O bond distances ranging from 2.16–2.79 Å. In the seventh Gd3+ site, Gd3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Gd–O bond distances ranging from 2.14–2.74 Å. There are eight inequivalent Ti+3.88+ sites. In the first Ti+3.88+ site, Ti+3.88+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with three TiO6 octahedra, corners with three TiO5 trigonal bipyramids, and an edgeedge with one GdO8 hexagonal bipyramid. The corner-sharing octahedra tilt angles range from 33–55°. There are a spread of Ti–O bond distances ranging from 1.88–2.10 Å. In the second Ti+3.88+ site, Ti+3.88+ is bonded to five O2- atoms to form TiO5 trigonal bipyramids that share a cornercorner with one GdO7 hexagonal pyramid, corners with three TiO6 octahedra, corners with two TiO5 trigonal bipyramids, and edges with two equivalent GdO8 hexagonal bipyramids. The corner-sharing octahedra tilt angles range from 34–60°. There are a spread of Ti–O bond distances ranging from 1.89–2.02 Å. In the third Ti+3.88+ site, Ti+3.88+ is bonded to five O2- atoms to form TiO5 trigonal bipyramids that share corners with three TiO6 octahedra, corners with two TiO5 trigonal bipyramids, and an edgeedge with one GdO8 hexagonal bipyramid. The corner-sharing octahedra tilt angles range from 28–56°. There are a spread of Ti–O bond distances ranging from 1.81–2.01 Å. In the fourth Ti+3.88+ site, Ti+3.88+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with three TiO6 octahedra, corners with three TiO5 trigonal bipyramids, and an edgeedge with one GdO7 hexagonal pyramid. The corner-sharing octahedra tilt angles range from 42–48°. There are a spread of Ti–O bond distances ranging from 1.93–2.03 Å. In the fifth Ti+3.88+ site, Ti+3.88+ is bonded to five O2- atoms to form TiO5 trigonal bipyramids that share corners with five TiO6 octahedra and an edgeedge with one GdO7 hexagonal pyramid. The corner-sharing octahedra tilt angles range from 31–62°. There are a spread of Ti–O bond distances ranging from 1.83–1.99 Å. In the sixth Ti+3.88+ site, Ti+3.88+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one TiO6 octahedra, corners with five TiO5 trigonal bipyramids, an edgeedge with one GdO8 hexagonal bipyramid, and edges with two equivalent GdO7 hexagonal pyramids. The corner-sharing octahedral tilt angles are 42°. There are a spread of Ti–O bond distances ranging from 1.96–2.06 Å. In the seventh Ti+3.88+ site, Ti+3.88+ is bonded to five O2- atoms to form TiO5 trigonal bipyramids that share a cornercorner with one GdO7 hexagonal pyramid, corners with three TiO6 octahedra, and corners with two TiO5 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 37–60°. There are a spread of Ti–O bond distances ranging from 1.88–2.00 Å. In the eighth Ti+3.88+ site, Ti+3.88+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with three TiO6 octahedra, corners with three TiO5 trigonal bipyramids, and an edgeedge with one GdO8 hexagonal bipyramid. The corner-sharing octahedra tilt angles range from 33–55°. There are a spread of Ti–O bond distances ranging from 1.88–2.30 Å. There are twenty-six inequivalent O2- sites. In the first O2- site, O2- is bonded in a 2-coordinate geometry to one Gd3+ and two Ti+3.88+ atoms. In the second O2- site, O2- is bonded to four Gd3+ atoms to form OGd4 tetrahedra that share corners with four OGd4 tetrahedra and edges with two OGd2Ti2 tetrahedra. In the third O2- site, O2- is bonded in a 4-coordinate geometry to two Gd3+ and two Ti+3.88+ atoms. In the fourth O2- site, O2- is bonded to two Gd3+ and two Ti+3.88+ atoms to form a mixture of distorted edge and corner-sharing OGd2Ti2 tetrahedra. In the fifth O2- site, O2- is bonded in a 3-coordinate geometry to one Gd3+ and two Ti+3.88+ atoms. In the sixth O2- site, O2- is bonded to two Gd3+ and two Ti+3.88+ atoms to form a mixture of distorted edge and corner-sharing OGd2Ti2 tetrahedra. In the seventh O2- site, O2- is bonded in a 4-coordinate geometry to two Gd3+ and two Ti+3.88+ atoms. In the eighth O2- site, O2- is bonded in a trigonal planar geometry to three Gd3+ atoms. In the ninth O2- site, O2- is bonded in a 2-coordinate geometry to two Gd3+ and two Ti+3.88+ atoms. In the tenth O2- site, O2- is bonded in a 4-coordinate geometry to two Gd3+ and two Ti+3.88+ atoms. In the eleventh O2- site, O2- is bonded in a 4-coordinate geometry to two Gd3+ and two Ti+3.88+ atoms. In the twelfth O2- site, O2- is bonded in a 2-coordinate geometry to two Gd3+ and two Ti+3.88+ atoms. In the thirteenth O2- site, O2- is bonded in a 4-coordinate geometry to two Gd3+ and two Ti+3.88+ atoms. In the fourteenth O2- site, O2- is bonded in a 2-coordinate geometry to two Gd3+ and two Ti+3.88+ atoms. In the fifteenth O2- site, O2- is bonded in a 4-coordinate geometry to two Gd3+ and two Ti+3.88+ atoms. In the sixteenth O2- site, O2- is bonded to two Gd3+ and two Ti+3.88+ atoms to form a mixture of distorted edge and corner-sharing OGd2Ti2 tetrahedra. In the seventeenth O2- site, O2- is bonded in a 2-coordinate geometry to two Gd3+ and two Ti+3.88+ atoms. In the eighteenth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Gd3+ and two Ti+3.88+ atoms. In the nineteenth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Gd3+ and two Ti+3.88+ atoms. In the twentieth O2- site, O2- is bonded in a 2-coordinate geometry to two Gd3+ and two Ti+3.88+ atoms. In the twenty-first O2- site, O2- is bonded in a 4-coordinate geometry to two Gd3+ and two Ti+3.88+ atoms. In the twenty-second O2- site, O2- is bonded to four Gd3+ atoms to form OGd4 tetrahedra that share corners with five OGd4 tetrahedra and an edgeedge with one OGd2Ti2 tetrahedra. In the twenty-third O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two Gd3+ and two Ti+3.88+ atoms. In the twenty-fourth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Gd3+ and two Ti+3.88+ atoms. In the twenty-fifth O2- site, O2- is bonded in a 3-coordinate geometry to two Gd3+ and two Ti+3.88+ atoms. In the twenty-sixth O2- site, O2- is bonded in a trigonal non-coplanar geometry to three Gd3+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ti7B8(IrRh2)2 by Materials Project

Ti7B8(IrRh2)2 crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are seven inequivalent Ti sites. In the first Ti site, Ti is bonded to twelve B atoms to form face-sharing TiB12 cuboctahedra. All Ti–B bond lengths are 2.40 Å. In the second Ti site, Ti is bonded in a 11-coordinate geometry to four Ir, two equivalent Rh, and five B atoms. There are two shorter (2.69 Å) and two longer (2.89 Å) Ti–Ir bond lengths. Both Ti–Rh bond lengths are 2.72 Å. There are a spread of Ti–B bond distances ranging from 2.34–2.61 Å. In the third Ti site, Ti is bonded in a 11-coordinate geometry to two equivalent Ir, four Rh, and five B atoms. Both Ti–Ir bond lengths are 2.68 Å. There are two shorter (2.72 Å) and two longer (2.89 Å) Ti–Rh bond lengths. There are a spread of Ti–B bond distances ranging from 2.34–2.61 Å. In the fourth Ti site, Ti is bonded in a 11-coordinate geometry to two equivalent Ir, four Rh, and five B atoms. Both Ti–Ir bond lengths are 2.88 Å. There are two shorter (2.68 Å) and two longer (2.72 Å) Ti–Rh bond lengths. There are a spread of Ti–B bond distances ranging from 2.35–2.61 Å. In the fifth Ti site, Ti is bonded in a 11-coordinate geometry to two equivalent Ir, four Rh, and five B atoms. Both Ti–Ir bond lengths are 2.72 Å. There are two shorter (2.68 Å) and two longer (2.87 Å) Ti–Rh bond lengths. There are a spread of Ti–B bond distances ranging from 2.35–2.60 Å. In the sixth Ti site, Ti is bonded in a 11-coordinate geometry to six Rh and five B atoms. There are a spread of Ti–Rh bond distances ranging from 2.68–2.87 Å. There are a spread of Ti–B bond distances ranging from 2.35–2.60 Å. In the seventh Ti site, Ti is bonded in a 11-coordinate geometry to two equivalent Ir, four Rh, and five B atoms. Both Ti–Ir bond lengths are 2.72 Å. There are two shorter (2.68 Å) and two longer (2.87 Å) Ti–Rh bond lengths. There are a spread of Ti–B bond distances ranging from 2.35–2.60 Å. There are two inequivalent Ir sites. In the first Ir site, Ir is bonded in a 2-coordinate geometry to six Ti, one Rh, and three B atoms. The Ir–Rh bond length is 2.80 Å. There are two shorter (2.24 Å) and one longer (2.39 Å) Ir–B bond lengths. In the second Ir site, Ir is bonded in a 12-coordinate geometry to six Ti, one Rh, and three B atoms. The Ir–Rh bond length is 2.81 Å. There are two shorter (2.24 Å) and one longer (2.38 Å) Ir–B bond lengths. There are four inequivalent Rh sites. In the first Rh site, Rh is bonded in a 12-coordinate geometry to six Ti and three B atoms. There are two shorter (2.25 Å) and one longer (2.39 Å) Rh–B bond lengths. In the second Rh site, Rh is bonded in a 10-coordinate geometry to six Ti, one Ir, and three B atoms. There are two shorter (2.24 Å) and one longer (2.40 Å) Rh–B bond lengths. In the third Rh site, Rh is bonded in a 10-coordinate geometry to six Ti, one Ir, and three B atoms. There are two shorter (2.24 Å) and one longer (2.40 Å) Rh–B bond lengths. In the fourth Rh site, Rh is bonded in a 9-coordinate geometry to six Ti and three B atoms. There are two shorter (2.24 Å) and one longer (2.40 Å) Rh–B bond lengths. There are eight inequivalent B sites. In the first B site, B is bonded in a 9-coordinate geometry to six Ti, one Rh, and two B atoms. Both B–B bond lengths are 1.79 Å. In the second B site, B is bonded in a 9-coordinate geometry to six Ti, one Rh, and two B atoms. Both B–B bond lengths are 1.79 Å. In the third B site, B is bonded in a 9-coordinate geometry to six Ti, one Rh, and two B atoms. Both B–B bond lengths are 1.79 Å. In the fourth B site, B is bonded in a 9-coordinate geometry to six Ti, one Ir, and two B atoms. In the fifth B site, B is bonded in a 9-coordinate geometry to six Ti, one Rh, and two B atoms. In the sixth B site, B is bonded in a 9-coordinate geometry to six Ti, one Ir, and two B atoms. In the seventh B site, B is bonded in a 9-coordinate geometry to three Ti, four Ir, and two equivalent Rh atoms. In the eighth B site, B is bonded in a 9-coordinate geometry to three Ti and six Rh atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ti9Co2(B4Ru9)2 by Materials Project

Ti9Co2(Ru9B4)2 crystallizes in the tetragonal P4/mbm space group. The structure is three-dimensional. there are seven inequivalent Ti sites. In the first Ti site, Ti is bonded in a 12-coordinate geometry to eight Ru and four B atoms. There are four shorter (2.67 Å) and four longer (2.83 Å) Ti–Ru bond lengths. There are two shorter (2.70 Å) and two longer (2.86 Å) Ti–B bond lengths. In the second Ti site, Ti is bonded in a body-centered cubic geometry to eight equivalent Ru atoms. All Ti–Ru bond lengths are 2.59 Å. In the third Ti site, Ti is bonded in a 12-coordinate geometry to two equivalent Ti, ten Ru, and three B atoms. Both Ti–Ti bond lengths are 2.99 Å. There are a spread of Ti–Ru bond distances ranging from 2.77–2.99 Å. There are a spread of Ti–B bond distances ranging from 2.64–2.94 Å. In the fourth Ti site, Ti is bonded in a 12-coordinate geometry to two equivalent Ti, ten Ru, and three B atoms. Both Ti–Ti bond lengths are 2.99 Å. There are a spread of Ti–Ru bond distances ranging from 2.77–2.99 Å. There are a spread of Ti–B bond distances ranging from 2.64–2.94 Å. In the fifth Ti site, Ti is bonded in a 12-coordinate geometry to two equivalent Ti, ten Ru, and three B atoms. Both Ti–Ti bond lengths are 2.99 Å. There are a spread of Ti–Ru bond distances ranging from 2.77–2.99 Å. There are a spread of Ti–B bond distances ranging from 2.64–2.94 Å. In the sixth Ti site, Ti is bonded in a 12-coordinate geometry to two equivalent Ti, ten Ru, and three B atoms. Both Ti–Ti bond lengths are 2.99 Å. There are a spread of Ti–Ru bond distances ranging from 2.77–2.99 Å. There are a spread of Ti–B bond distances ranging from 2.64–2.94 Å. In the seventh Ti site, Ti is bonded in a body-centered cubic geometry to eight Ru atoms. There are four shorter (2.55 Å) and four longer (2.60 Å) Ti–Ru bond lengths. There are five inequivalent Ru sites. In the first Ru site, Ru is bonded in a 8-coordinate geometry to six Ti and two equivalent B atoms. Both Ru–B bond lengths are 2.16 Å. In the second Ru site, Ru is bonded in a 8-coordinate geometry to four Ti and four B atoms. There are two shorter (2.21 Å) and two longer (2.23 Å) Ru–B bond lengths. In the third Ru site, Ru is bonded in a 4-coordinate geometry to four equivalent Co and four equivalent B atoms. All Ru–Co bond lengths are 2.80 Å. All Ru–B bond lengths are 2.22 Å. In the fourth Ru site, Ru is bonded in a 8-coordinate geometry to four Ti, two equivalent Co, and two equivalent B atoms. Both Ru–Co bond lengths are 2.57 Å. Both Ru–B bond lengths are 2.16 Å. In the fifth Ru site, Ru is bonded in a 8-coordinate geometry to six Ti and two equivalent B atoms. Both Ru–B bond lengths are 2.18 Å. Co is bonded in a 11-coordinate geometry to eight Ru, one Co, and two equivalent B atoms. The Co–Co bond length is 2.44 Å. Both Co–B bond lengths are 2.52 Å. There are three inequivalent B sites. In the first B site, B is bonded in a 9-coordinate geometry to three Ti and six Ru atoms. In the second B site, B is bonded in a 9-coordinate geometry to three Ti and six Ru atoms. The B–Ti bond length is 2.70 Å. There are a spread of B–Ru bond distances ranging from 2.16–2.23 Å. In the third B site, B is bonded in a 6-coordinate geometry to two Ti, six Ru, and one Co atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ti12Se16O3 by Materials Project

Ti12Se16O3 crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are nine inequivalent Ti+3.17+ sites. In the first Ti+3.17+ site, Ti+3.17+ is bonded to six Se2- atoms to form a mixture of edge, corner, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 37–51°. There are a spread of Ti–Se bond distances ranging from 2.55–2.70 Å. In the second Ti+3.17+ site, Ti+3.17+ is bonded in a distorted single-bond geometry to three Se2- and one O2- atom. There are two shorter (2.59 Å) and one longer (2.61 Å) Ti–Se bond lengths. The Ti–O bond length is 1.64 Å. In the third Ti+3.17+ site, Ti+3.17+ is bonded to six Se2- atoms to form a mixture of edge, corner, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 41–49°. There are a spread of Ti–Se bond distances ranging from 2.56–2.73 Å. In the fourth Ti+3.17+ site, Ti+3.17+ is bonded in a distorted single-bond geometry to four Se2- and one O2- atom. There are a spread of Ti–Se bond distances ranging from 2.51–2.96 Å. The Ti–O bond length is 1.64 Å. In the fifth Ti+3.17+ site, Ti+3.17+ is bonded in a distorted single-bond geometry to four Se2- and one O2- atom. There are a spread of Ti–Se bond distances ranging from 2.59–3.12 Å. The Ti–O bond length is 1.66 Å. In the sixth Ti+3.17+ site, Ti+3.17+ is bonded to six Se2- atoms to form a mixture of edge and corner-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 37–46°. There are a spread of Ti–Se bond distances ranging from 2.52–2.72 Å. In the seventh Ti+3.17+ site, Ti+3.17+ is bonded to six Se2- atoms to form a mixture of edge, corner, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 36–46°. There are a spread of Ti–Se bond distances ranging from 2.53–2.75 Å. In the eighth Ti+3.17+ site, Ti+3.17+ is bonded to six Se2- atoms to form a mixture of edge, corner, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 36–51°. There are a spread of Ti–Se bond distances ranging from 2.56–2.73 Å. In the ninth Ti+3.17+ site, Ti+3.17+ is bonded to six Se2- atoms to form a mixture of edge, corner, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 39–49°. There are a spread of Ti–Se bond distances ranging from 2.55–2.75 Å. There are twelve inequivalent Se2- sites. In the first Se2- site, Se2- is bonded in a 6-coordinate geometry to six Ti+3.17+ atoms. In the second Se2- site, Se2- is bonded in a 6-coordinate geometry to six Ti+3.17+ atoms. In the third Se2- site, Se2- is bonded in a 4-coordinate geometry to three Ti+3.17+ atoms. In the fourth Se2- site, Se2- is bonded to four Ti+3.17+ and one O2- atom to form distorted corner-sharing SeTi4O square pyramids. The Se–O bond length is 3.19 Å. In the fifth Se2- site, Se2- is bonded in a 5-coordinate geometry to four Ti+3.17+ and one O2- atom. The Se–O bond length is 2.96 Å. In the sixth Se2- site, Se2- is bonded to four Ti+3.17+ atoms to form distorted corner-sharing SeTi4 trigonal pyramids. In the seventh Se2- site, Se2- is bonded in a 4-coordinate geometry to four Ti+3.17+ atoms. In the eighth Se2- site, Se2- is bonded in a 6-coordinate geometry to four Ti+3.17+ and two O2- atoms. There are one shorter (2.85 Å) and one longer (3.03 Å) Se–O bond lengths. In the ninth Se2- site, Se2- is bonded in a 3-coordinate geometry to three Ti+3.17+ atoms. In the tenth Se2- site, Se2- is bonded in a 4-coordinate geometry to four Ti+3.17+ atoms. In the eleventh Se2- site, Se2- is bonded in a 5-coordinate geometry to four Ti+3.17+ and one O2- atom. The Se–O bond length is 2.74 Å. In the twelfth Se2- site, Se2- is bonded in a 4-coordinate geometry to four Ti+3.17+ atoms. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded in a single-bond geometry to one Ti+3.17+ and one Se2- atom. In the second O2- site, O2- is bonded in a single-bond geometry to one Ti+3.17+ and four Se2- atoms. In the third O2- site, O2- is bonded in a single-bond geometry to one Ti+3.17+ and one Se2- atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ti2Mn3V by Materials Project

Mn3Ti2V is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. there are six inequivalent Ti sites. In the first Ti site, Ti is bonded in a 12-coordinate geometry to four Ti, four equivalent V, and eight Mn atoms. There are a spread of Ti–Ti bond distances ranging from 2.92–3.11 Å. There are two shorter (2.84 Å) and two longer (2.87 Å) Ti–V bond lengths. There are a spread of Ti–Mn bond distances ranging from 2.74–2.88 Å. In the second Ti site, Ti is bonded in a 12-coordinate geometry to four Ti, two equivalent V, and ten Mn atoms. There are one shorter (2.89 Å) and two longer (2.94 Å) Ti–Ti bond lengths. Both Ti–V bond lengths are 2.86 Å. There are a spread of Ti–Mn bond distances ranging from 2.77–2.84 Å. In the third Ti site, Ti is bonded in a 12-coordinate geometry to four Ti, two equivalent V, and ten Mn atoms. There are one shorter (2.92 Å) and two longer (2.94 Å) Ti–Ti bond lengths. Both Ti–V bond lengths are 2.86 Å. There are a spread of Ti–Mn bond distances ranging from 2.77–2.84 Å. In the fourth Ti site, Ti is bonded in a 12-coordinate geometry to four Ti, four equivalent V, and eight Mn atoms. There are two shorter (2.84 Å) and two longer (2.87 Å) Ti–V bond lengths. There are a spread of Ti–Mn bond distances ranging from 2.74–2.88 Å. In the fifth Ti site, Ti is bonded in a 12-coordinate geometry to four Ti, two equivalent V, and ten Mn atoms. There are one shorter (2.89 Å) and one longer (2.92 Å) Ti–Ti bond lengths. Both Ti–V bond lengths are 2.86 Å. There are a spread of Ti–Mn bond distances ranging from 2.77–2.84 Å. In the sixth Ti site, Ti is bonded in a 12-coordinate geometry to four Ti, four equivalent V, and eight Mn atoms. The Ti–Ti bond length is 3.11 Å. There are two shorter (2.84 Å) and two longer (2.87 Å) Ti–V bond lengths. There are a spread of Ti–Mn bond distances ranging from 2.74–2.88 Å. V is bonded to six Ti, two equivalent V, and four Mn atoms to form distorted VTi6Mn4V2 cuboctahedra that share corners with four equivalent VTi6Mn4V2 cuboctahedra, corners with fourteen MnTi6Mn6 cuboctahedra, edges with two equivalent VTi6Mn4V2 cuboctahedra, edges with four equivalent MnTi6Mn6 cuboctahedra, faces with four equivalent VTi6Mn4V2 cuboctahedra, and faces with fourteen MnTi6Mn2V4 cuboctahedra. There are one shorter (2.40 Å) and one longer (2.44 Å) V–V bond lengths. There are a spread of V–Mn bond distances ranging from 2.35–2.49 Å. There are four inequivalent Mn sites. In the first Mn site, Mn is bonded to six Ti, four equivalent V, and two equivalent Mn atoms to form distorted MnTi6Mn2V4 cuboctahedra that share corners with eighteen MnTi6Mn2V4 cuboctahedra, edges with six MnTi6Mn2V4 cuboctahedra, faces with eight equivalent VTi6Mn4V2 cuboctahedra, and faces with ten MnTi6Mn6 cuboctahedra. Both Mn–Mn bond lengths are 2.47 Å. In the second Mn site, Mn is bonded to six Ti and six Mn atoms to form MnTi6Mn6 cuboctahedra that share corners with six equivalent VTi6Mn4V2 cuboctahedra, corners with twelve MnTi6Mn2V4 cuboctahedra, edges with two equivalent MnTi6Mn6 cuboctahedra, edges with four equivalent VTi6Mn4V2 cuboctahedra, faces with two equivalent VTi6Mn4V2 cuboctahedra, and faces with sixteen MnTi6Mn2V4 cuboctahedra. There are a spread of Mn–Mn bond distances ranging from 2.32–2.49 Å. In the third Mn site, Mn is bonded to six Ti and six Mn atoms to form MnTi6Mn6 cuboctahedra that share corners with eight equivalent VTi6Mn4V2 cuboctahedra, corners with ten MnTi6Mn2V4 cuboctahedra, edges with six MnTi6Mn2V4 cuboctahedra, faces with four equivalent VTi6Mn4V2 cuboctahedra, and faces with fourteen MnTi6Mn6 cuboctahedra. Both Mn–Mn bond lengths are 2.39 Å. In the fourth Mn site, Mn is bonded to six Ti, two equivalent V, and four Mn atoms to form distorted MnTi6Mn4V2 cuboctahedra that share corners with four equivalent VTi6Mn4V2 cuboctahedra, corners with eight MnTi6Mn2V4 cuboctahedra, edges with six equivalent MnTi6Mn4V2 cuboctahedra, faces with six equivalent VTi6Mn4V2 cuboctahedra, and faces with fourteen MnTi6Mn2V4 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ti20H2N17 by Materials Project

Ti20N17H2 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. there are ten inequivalent Ti+2.45+ sites. In the first Ti+2.45+ site, Ti+2.45+ is bonded to six N3- atoms to form TiN6 octahedra that share corners with two TiH2N4 octahedra, corners with two equivalent TiN5 square pyramids, edges with eight TiN6 octahedra, and an edgeedge with one TiN5 square pyramid. The corner-sharing octahedra tilt angles range from 1–2°. There are a spread of Ti–N bond distances ranging from 2.11–2.15 Å. In the second Ti+2.45+ site, Ti+2.45+ is bonded in a rectangular see-saw-like geometry to four N3- atoms. There are two shorter (2.06 Å) and two longer (2.10 Å) Ti–N bond lengths. In the third Ti+2.45+ site, Ti+2.45+ is bonded to five N3- atoms to form TiN5 square pyramids that share corners with five TiN6 octahedra, edges with six TiN6 octahedra, and edges with two equivalent TiN5 square pyramids. The corner-sharing octahedra tilt angles range from 2–4°. There are a spread of Ti–N bond distances ranging from 2.06–2.12 Å. In the fourth Ti+2.45+ site, Ti+2.45+ is bonded to five N3- and one H1+ atom to form TiHN5 octahedra that share corners with five TiN6 octahedra, edges with ten TiN6 octahedra, and edges with two equivalent TiN5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Ti–N bond distances ranging from 2.07–2.13 Å. The Ti–H bond length is 2.18 Å. In the fifth Ti+2.45+ site, Ti+2.45+ is bonded to four N3- and two equivalent H1+ atoms to form TiH2N4 octahedra that share corners with six TiN6 octahedra and edges with twelve TiHN5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Ti–N bond distances ranging from 2.08–2.11 Å. Both Ti–H bond lengths are 2.16 Å. In the sixth Ti+2.45+ site, Ti+2.45+ is bonded to four N3- and two equivalent H1+ atoms to form TiH2N4 octahedra that share corners with five TiH2N4 octahedra, a cornercorner with one TiN5 square pyramid, and edges with twelve TiHN5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are two shorter (2.08 Å) and two longer (2.11 Å) Ti–N bond lengths. Both Ti–H bond lengths are 2.17 Å. In the seventh Ti+2.45+ site, Ti+2.45+ is bonded to five N3- and one H1+ atom to form TiHN5 octahedra that share corners with six TiHN5 octahedra and edges with twelve TiH2N4 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Ti–N bond distances ranging from 2.09–2.13 Å. The Ti–H bond length is 2.14 Å. In the eighth Ti+2.45+ site, Ti+2.45+ is bonded to six N3- atoms to form a mixture of corner and edge-sharing TiN6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Ti–N bond distances ranging from 2.10–2.15 Å. In the ninth Ti+2.45+ site, Ti+2.45+ is bonded to six N3- atoms to form TiN6 octahedra that share corners with five TiHN5 octahedra, edges with ten TiHN5 octahedra, and edges with two equivalent TiN5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Ti–N bond distances ranging from 2.11–2.14 Å. In the tenth Ti+2.45+ site, Ti+2.45+ is bonded to six N3- atoms to form TiN6 octahedra that share corners with four TiN6 octahedra, corners with two equivalent TiN5 square pyramids, edges with nine TiN6 octahedra, and an edgeedge with one TiN5 square pyramid. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Ti–N bond distances ranging from 2.12–2.14 Å. There are nine inequivalent N3- sites. In the first N3- site, N3- is bonded to six Ti+2.45+ atoms to form NTi6 octahedra that share corners with three NTi6 octahedra, corners with three equivalent HTi6 octahedra, an edgeedge with one HTi6 octahedra, and edges with eleven NTi6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the second N3- site, N3- is bonded to six Ti+2.45+ atoms to form NTi6 octahedra that share corners with two equivalent HTi6 octahedra, corners with four NTi6 octahedra, an edgeedge with one HTi6 octahedra, and edges with eleven NTi6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the third N3- site, N3- is bonded to six Ti+2.45+ atoms to form NTi6 octahedra that share corners with six NTi6 octahedra, edges with two equivalent HTi6 octahedra, and edges with ten NTi6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fourth N3- site, N3- is bonded to six Ti+2.45+ atoms to form NTi6 octahedra that share a cornercorner with one HTi6 octahedra, corners with five NTi6 octahedra, and edges with ten NTi6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. In the fifth N3- site, N3- is bonded to six Ti+2.45+ atoms to form a mixture of corner and edge-sharing NTi6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the sixth N3- site, N3- is bonded to six Ti+2.45+ atoms to form NTi6 octahedra that share corners with five NTi6 octahedra, edges with two equivalent HTi6 octahedra, and edges with ten NTi6 octahedra. The corner-sharing octahedra tilt angles range from 2–4°. In the seventh N3- site, N3- is bonded to six Ti+2.45+ atoms to form NTi6 octahedra that share corners with six NTi6 octahedra, edges with two equivalent HTi6 octahedra, and edges with ten NTi6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. In the eighth N3- site, N3- is bonded to six Ti+2.45+ atoms to form NTi6 octahedra that share corners with six NTi6 octahedra, edges with four equivalent HTi6 octahedra, and edges with eight NTi6 octahedra. The corner-sharing octahedra tilt angles range from 2–3°. In the ninth N3- site, N3- is bonded to six Ti+2.45+ atoms to form a mixture of corner and edge-sharing NTi6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. H1+ is bonded to six Ti+2.45+ atoms to form HTi6 octahedra that share corners with six NTi6 octahedra, edges with two equivalent HTi6 octahedra, and edges with ten NTi6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ti10O11 by Materials Project

Ti10O11 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are eleven inequivalent Ti+2.20+ sites. In the first Ti+2.20+ site, Ti+2.20+ 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 2–8°. There are a spread of Ti–O bond distances ranging from 2.05–2.12 Å. In the second Ti+2.20+ site, Ti+2.20+ 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 0–12°. There are a spread of Ti–O bond distances ranging from 2.09–2.15 Å. In the third Ti+2.20+ site, Ti+2.20+ 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 2–18°. There are a spread of Ti–O bond distances ranging from 2.06–2.20 Å. In the fourth Ti+2.20+ site, Ti+2.20+ 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 1–18°. There are a spread of Ti–O bond distances ranging from 2.08–2.30 Å. In the fifth Ti+2.20+ site, Ti+2.20+ is bonded to six O2- atoms to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedra tilt angles range from 0–21°. There are a spread of Ti–O bond distances ranging from 2.07–2.33 Å. In the sixth Ti+2.20+ site, Ti+2.20+ 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 2–21°. There are a spread of Ti–O bond distances ranging from 2.04–2.29 Å. In the seventh Ti+2.20+ site, Ti+2.20+ 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 0–18°. There are a spread of Ti–O bond distances ranging from 2.06–2.24 Å. In the eighth Ti+2.20+ site, Ti+2.20+ 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 0–18°. There are a spread of Ti–O bond distances ranging from 2.07–2.23 Å. In the ninth Ti+2.20+ site, Ti+2.20+ 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 5–23°. There are a spread of Ti–O bond distances ranging from 2.08–2.21 Å. In the tenth Ti+2.20+ site, Ti+2.20+ 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 4–23°. There are a spread of Ti–O bond distances ranging from 2.06–2.17 Å. In the eleventh Ti+2.20+ site, Ti+2.20+ 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 2–18°. There are a spread of Ti–O bond distances ranging from 2.11–2.20 Å. There are eleven inequivalent O2- sites. In the first O2- site, O2- is bonded to six Ti+2.20+ atoms to form distorted OTi6 octahedra that share corners with two OTi6 octahedra, corners with four OTi5 square pyramids, edges with six OTi6 octahedra, and edges with six OTi5 square pyramids. The corner-sharing octahedra tilt angles range from 14–16°. In the second O2- site, O2- is bonded to six Ti+2.20+ atoms to form OTi6 octahedra that share corners with two OTi6 octahedra, corners with four OTi5 square pyramids, edges with five OTi6 octahedra, and edges with seven OTi5 square pyramids. The corner-sharing octahedra tilt angles range from 6–22°. In the third O2- site, O2- is bonded to five Ti+2.20+ atoms to form OTi5 square pyramids that share a cornercorner with one OTi6 octahedra, corners with eight OTi5 square pyramids, edges with six OTi6 octahedra, and edges with two OTi5 square pyramids. The corner-sharing octahedral tilt angles are 17°. In the fourth O2- site, O2- is bonded to five Ti+2.20+ atoms to form OTi5 square pyramids that share corners with two OTi6 octahedra, corners with seven OTi5 square pyramids, edges with six OTi6 octahedra, and edges with two OTi5 square pyramids. The corner-sharing octahedra tilt angles range from 15–16°. In the fifth O2- site, O2- is bonded to six Ti+2.20+ atoms to form OTi6 octahedra that share corners with three OTi6 octahedra, corners with three OTi5 square pyramids, edges with six OTi6 octahedra, and edges with six OTi5 square pyramids. The corner-sharing octahedra tilt angles range from 5–16°. In the sixth O2- site, O2- is bonded to five Ti+2.20+ atoms to form OTi5 square pyramids that share corners with two OTi6 octahedra, corners with seven OTi5 square pyramids, edges with six OTi6 octahedra, and edges with two OTi5 square pyramids. The corner-sharing octahedra tilt angles range from 3–19°. In the seventh O2- site, O2- is bonded to six Ti+2.20+ atoms to form OTi6 octahedra that share corners with four OTi6 octahedra, corners with two OTi5 square pyramids, edges with four OTi6 octahedra, and edges with eight OTi5 square pyramids. The corner-sharing octahedra tilt angles range from 0–22°. In the eighth O2- site, O2- is bonded to five Ti+2.20+ atoms to form OTi5 square pyramids that share corners with three OTi6 octahedra, corners with six OTi5 square pyramids, edges with four OTi6 octahedra, and edges with four OTi5 square pyramids. The corner-sharing octahedra tilt angles range from 6–12°. In the ninth O2- site, O2- is bonded to five Ti+2.20+ atoms to form OTi5 square pyramids that share corners with three OTi6 octahedra, corners with six OTi5 square pyramids, edges with six OTi6 octahedra, and edges with two OTi5 square pyramids. The corner-sharing octahedra tilt angles range from 7–16°. In the tenth O2- site, O2- is bonded to five Ti+2.20+ atoms to form OTi5 square pyramids that share corners with three OTi6 octahedra, corners with six OTi5 square pyramids, edges with six OTi6 octahedra, and edges with two OTi5 square pyramids. The corner-sharing octahedra tilt angles range from 11–16°. In the eleventh O2- site, O2- is bonded to six Ti+2.20+ atoms to form OTi6 octahedra that share corners with five OTi6 octahedra, a cornercorner with one OTi5 square pyramid, edges with five OTi6 octahedra, and edges with seven OTi5 square pyramids. The corner-sharing octahedra tilt angles range from 0–15°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ti2P by Materials Project

Ti2P crystallizes in the hexagonal P-62m space group. The structure is three-dimensional. there are twelve inequivalent Ti sites. In the first Ti site, Ti is bonded to four P atoms to form a mixture of distorted edge and corner-sharing TiP4 tetrahedra. There are two shorter (2.43 Å) and two longer (2.51 Å) Ti–P bond lengths. In the second Ti site, Ti is bonded in a 5-coordinate geometry to five P atoms. There are a spread of Ti–P bond distances ranging from 2.66–2.71 Å. In the third Ti site, Ti is bonded to four P atoms to form a mixture of distorted edge and corner-sharing TiP4 tetrahedra. There are two shorter (2.43 Å) and two longer (2.51 Å) Ti–P bond lengths. In the fourth Ti site, Ti is bonded in a 5-coordinate geometry to five P atoms. There are a spread of Ti–P bond distances ranging from 2.66–2.71 Å. In the fifth Ti site, Ti is bonded in a 5-coordinate geometry to five P atoms. There are four shorter (2.66 Å) and one longer (2.71 Å) Ti–P bond lengths. In the sixth Ti site, Ti is bonded to four P atoms to form a mixture of distorted edge and corner-sharing TiP4 tetrahedra. There are two shorter (2.43 Å) and two longer (2.51 Å) Ti–P bond lengths. In the seventh Ti site, Ti is bonded in a 5-coordinate geometry to five P atoms. There are four shorter (2.66 Å) and one longer (2.70 Å) Ti–P bond lengths. In the eighth Ti site, Ti is bonded to four P atoms to form a mixture of distorted edge and corner-sharing TiP4 tetrahedra. There are two shorter (2.43 Å) and two longer (2.51 Å) Ti–P bond lengths. In the ninth Ti site, Ti is bonded to four P atoms to form a mixture of distorted edge and corner-sharing TiP4 tetrahedra. There are two shorter (2.43 Å) and two longer (2.51 Å) Ti–P bond lengths. In the tenth Ti site, Ti is bonded to four P atoms to form a mixture of distorted edge and corner-sharing TiP4 tetrahedra. There are two shorter (2.43 Å) and two longer (2.51 Å) Ti–P bond lengths. In the eleventh Ti site, Ti is bonded in a 5-coordinate geometry to five P atoms. There are four shorter (2.66 Å) and one longer (2.71 Å) Ti–P bond lengths. In the twelfth Ti site, Ti is bonded in a 5-coordinate geometry to five P atoms. There are four shorter (2.66 Å) and one longer (2.71 Å) Ti–P bond lengths. There are seven inequivalent P sites. In the first P site, P is bonded in a 9-coordinate geometry to nine Ti atoms. In the second P site, P is bonded in a 9-coordinate geometry to nine Ti atoms. In the third P site, P is bonded in a 9-coordinate geometry to nine Ti atoms. In the fourth P site, P is bonded in a 9-coordinate geometry to nine Ti atoms. In the fifth P site, P is bonded in a 9-coordinate geometry to nine Ti atoms. In the sixth P site, P is bonded in a 9-coordinate geometry to nine Ti atoms. In the seventh P site, P is bonded in a 9-coordinate geometry to nine Ti atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ti19Se20 by Materials Project

Ti19Se20 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are eleven inequivalent Ti+2.11+ sites. In the first Ti+2.11+ site, Ti+2.11+ is bonded to six Se2- atoms to form a mixture of corner, edge, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 42–45°. There are a spread of Ti–Se bond distances ranging from 2.57–2.63 Å. In the second Ti+2.11+ site, Ti+2.11+ is bonded to six Se2- atoms to form a mixture of corner, edge, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 42–50°. There are a spread of Ti–Se bond distances ranging from 2.57–2.66 Å. In the third Ti+2.11+ site, Ti+2.11+ is bonded to six Se2- atoms to form a mixture of corner, edge, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 43–47°. There are a spread of Ti–Se bond distances ranging from 2.57–2.64 Å. In the fourth Ti+2.11+ site, Ti+2.11+ is bonded to six Se2- atoms to form a mixture of corner, edge, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 42–50°. There are a spread of Ti–Se bond distances ranging from 2.59–2.67 Å. In the fifth Ti+2.11+ site, Ti+2.11+ is bonded to six Se2- atoms to form a mixture of corner, edge, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 43–48°. There are a spread of Ti–Se bond distances ranging from 2.57–2.65 Å. In the sixth Ti+2.11+ site, Ti+2.11+ is bonded to six Se2- atoms to form a mixture of corner, edge, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 42–50°. There are a spread of Ti–Se bond distances ranging from 2.57–2.66 Å. In the seventh Ti+2.11+ site, Ti+2.11+ is bonded to six Se2- atoms to form a mixture of corner, edge, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 43–48°. There are a spread of Ti–Se bond distances ranging from 2.58–2.64 Å. In the eighth Ti+2.11+ site, Ti+2.11+ is bonded to six Se2- atoms to form a mixture of corner, edge, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 42–47°. There are a spread of Ti–Se bond distances ranging from 2.57–2.63 Å. In the ninth Ti+2.11+ site, Ti+2.11+ is bonded to six Se2- atoms to form a mixture of corner, edge, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 45–48°. There are four shorter (2.60 Å) and two longer (2.62 Å) Ti–Se bond lengths. In the tenth Ti+2.11+ site, Ti+2.11+ is bonded to six Se2- atoms to form a mixture of corner, edge, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 46–48°. There are a spread of Ti–Se bond distances ranging from 2.59–2.62 Å. In the eleventh Ti+2.11+ site, Ti+2.11+ is bonded to six Se2- atoms to form a mixture of corner, edge, and face-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 45–46°. There are four shorter (2.57 Å) and two longer (2.62 Å) Ti–Se bond lengths. There are ten inequivalent Se2- sites. In the first Se2- site, Se2- is bonded to six Ti+2.11+ atoms to form distorted SeTi6 pentagonal pyramids that share corners with six SeTi6 pentagonal pyramids, edges with five SeTi6 pentagonal pyramids, and edges with three equivalent SeTi5 trigonal bipyramids. In the second Se2- site, Se2- is bonded in a 5-coordinate geometry to five Ti+2.11+ atoms. In the third Se2- site, Se2- is bonded to six Ti+2.11+ atoms to form distorted SeTi6 pentagonal pyramids that share corners with three SeTi6 pentagonal pyramids, edges with nine SeTi6 pentagonal pyramids, and edges with two equivalent SeTi5 trigonal bipyramids. In the fourth Se2- site, Se2- is bonded to six Ti+2.11+ atoms to form distorted SeTi6 pentagonal pyramids that share corners with three equivalent SeTi6 pentagonal pyramids, corners with two equivalent SeTi5 trigonal bipyramids, and edges with ten SeTi6 pentagonal pyramids. In the fifth Se2- site, Se2- is bonded to five Ti+2.11+ atoms to form distorted SeTi5 trigonal bipyramids that share corners with three SeTi6 pentagonal pyramids, corners with two equivalent SeTi5 trigonal bipyramids, and edges with eight SeTi6 pentagonal pyramids. In the sixth Se2- site, Se2- is bonded to six Ti+2.11+ atoms to form a mixture of distorted corner and edge-sharing SeTi6 pentagonal pyramids. In the seventh Se2- site, Se2- is bonded in a 5-coordinate geometry to five Ti+2.11+ atoms. In the eighth Se2- site, Se2- is bonded to six Ti+2.11+ atoms to form distorted SeTi6 pentagonal pyramids that share corners with five SeTi6 pentagonal pyramids, a cornercorner with one SeTi5 trigonal bipyramid, and edges with ten SeTi6 pentagonal pyramids. In the ninth Se2- site, Se2- is bonded to six Ti+2.11+ atoms to form distorted SeTi6 pentagonal pyramids that share corners with five SeTi6 pentagonal pyramids, edges with nine SeTi6 pentagonal pyramids, and an edgeedge with one SeTi5 trigonal bipyramid. In the tenth Se2- site, Se2- is bonded to six Ti+2.11+ atoms to form distorted SeTi6 pentagonal pyramids that share corners with three SeTi6 pentagonal pyramids, edges with nine SeTi6 pentagonal pyramids, and edges with two equivalent SeTi5 trigonal bipyramids.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ti9ZnS16 by Materials Project

Ti9ZnS16 is beta indium sulfide-derived structured and crystallizes in the monoclinic Pc space group. The structure is three-dimensional. there are nine inequivalent Ti+3.33+ sites. In the first Ti+3.33+ site, Ti+3.33+ is bonded to six S2- atoms to form a mixture of edge and corner-sharing TiS6 octahedra. The corner-sharing octahedra tilt angles range from 1–9°. There are a spread of Ti–S bond distances ranging from 2.41–2.56 Å. In the second Ti+3.33+ site, Ti+3.33+ is bonded to six S2- atoms to form edge-sharing TiS6 octahedra. There are a spread of Ti–S bond distances ranging from 2.39–2.50 Å. In the third Ti+3.33+ site, Ti+3.33+ is bonded to six S2- atoms to form TiS6 octahedra that share a cornercorner with one ZnS4 tetrahedra and edges with seven TiS6 octahedra. There are a spread of Ti–S bond distances ranging from 2.42–2.49 Å. In the fourth Ti+3.33+ site, Ti+3.33+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with two equivalent ZnS4 tetrahedra and edges with seven TiS6 octahedra. There are a spread of Ti–S bond distances ranging from 2.37–2.52 Å. In the fifth Ti+3.33+ site, Ti+3.33+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with three equivalent ZnS4 tetrahedra and edges with six TiS6 octahedra. There are a spread of Ti–S bond distances ranging from 2.35–2.53 Å. In the sixth Ti+3.33+ site, Ti+3.33+ is bonded to six S2- atoms to form TiS6 octahedra that share a cornercorner with one ZnS4 tetrahedra and edges with seven TiS6 octahedra. There are a spread of Ti–S bond distances ranging from 2.43–2.50 Å. In the seventh Ti+3.33+ site, Ti+3.33+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with four equivalent TiS6 octahedra, a cornercorner with one ZnS4 tetrahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Ti–S bond distances ranging from 2.41–2.50 Å. In the eighth Ti+3.33+ site, Ti+3.33+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with two equivalent ZnS4 tetrahedra and edges with seven TiS6 octahedra. There are a spread of Ti–S bond distances ranging from 2.39–2.50 Å. In the ninth Ti+3.33+ site, Ti+3.33+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with two equivalent TiS6 octahedra, corners with two equivalent ZnS4 tetrahedra, and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 5–9°. There are a spread of Ti–S bond distances ranging from 2.38–2.52 Å. Zn2+ is bonded to four S2- atoms to form ZnS4 tetrahedra that share corners with twelve TiS6 octahedra. The corner-sharing octahedra tilt angles range from 57–63°. There are three shorter (2.30 Å) and one longer (2.31 Å) Zn–S bond lengths. There are sixteen inequivalent S2- sites. In the first S2- site, S2- is bonded in a rectangular see-saw-like geometry to four Ti+3.33+ atoms. In the second S2- site, S2- is bonded in a rectangular see-saw-like geometry to four Ti+3.33+ atoms. In the third S2- site, S2- is bonded in a distorted T-shaped geometry to three Ti+3.33+ atoms. In the fourth S2- site, S2- is bonded in a distorted T-shaped geometry to three Ti+3.33+ atoms. In the fifth S2- site, S2- is bonded in a rectangular see-saw-like geometry to four Ti+3.33+ atoms. In the sixth S2- site, S2- is bonded in a distorted T-shaped geometry to three Ti+3.33+ atoms. In the seventh S2- site, S2- is bonded in a 3-coordinate geometry to three Ti+3.33+ atoms. In the eighth S2- site, S2- is bonded in a distorted T-shaped geometry to three Ti+3.33+ atoms. In the ninth S2- site, S2- is bonded in a rectangular see-saw-like geometry to three Ti+3.33+ and one Zn2+ atom. In the tenth S2- site, S2- is bonded in a rectangular see-saw-like geometry to four Ti+3.33+ atoms. In the eleventh S2- site, S2- is bonded in a distorted T-shaped geometry to three Ti+3.33+ atoms. In the twelfth S2- site, S2- is bonded in a rectangular see-saw-like geometry to four Ti+3.33+ atoms. In the thirteenth S2- site, S2- is bonded to three Ti+3.33+ and one Zn2+ atom to form a mixture of distorted edge and corner-sharing STi3Zn trigonal pyramids. In the fourteenth S2- site, S2- is bonded to three Ti+3.33+ and one Zn2+ atom to form a mixture of distorted edge and corner-sharing STi3Zn tetrahedra. In the fifteenth S2- site, S2- is bonded in a rectangular see-saw-like geometry to four Ti+3.33+ atoms. In the sixteenth S2- site, S2- is bonded to three Ti+3.33+ and one Zn2+ atom to form a mixture of distorted edge and corner-sharing STi3Zn tetrahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KTi16O32 by Materials Project

KTi16O32 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. K1+ is bonded in a distorted cuboctahedral geometry to two equivalent Ti+3.94+ and ten O2- atoms. Both K–Ti bond lengths are 2.53 Å. There are a spread of K–O bond distances ranging from 2.89–3.16 Å. There are eight inequivalent Ti+3.94+ sites. In the first Ti+3.94+ site, Ti+3.94+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Ti–O bond distances ranging from 1.96–2.54 Å. In the second Ti+3.94+ site, Ti+3.94+ is bonded in a 6-coordinate geometry to one K1+ and five O2- atoms. There are a spread of Ti–O bond distances ranging from 1.96–2.54 Å. In the third Ti+3.94+ site, Ti+3.94+ is bonded in a 2-coordinate geometry to three O2- atoms. There are a spread of Ti–O bond distances ranging from 1.50–2.36 Å. In the fourth Ti+3.94+ site, Ti+3.94+ is bonded in a 2-coordinate geometry to three O2- atoms. There are a spread of Ti–O bond distances ranging from 1.51–2.35 Å. In the fifth Ti+3.94+ site, Ti+3.94+ is bonded in a distorted linear geometry to three O2- atoms. There are a spread of Ti–O bond distances ranging from 1.48–2.41 Å. In the sixth Ti+3.94+ site, Ti+3.94+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Ti–O bond distances ranging from 1.95–2.56 Å. In the seventh Ti+3.94+ site, Ti+3.94+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of Ti–O bond distances ranging from 1.97–2.54 Å. In the eighth Ti+3.94+ site, Ti+3.94+ is bonded in a 2-coordinate geometry to three O2- atoms. There are a spread of Ti–O bond distances ranging from 1.50–2.38 Å. There are sixteen inequivalent O2- sites. In the first O2- site, O2- is bonded in a 1-coordinate geometry to two equivalent Ti+3.94+ and one O2- atom. The O–O bond length is 1.73 Å. In the second O2- site, O2- is bonded in a 2-coordinate geometry to two Ti+3.94+ atoms. In the third O2- site, O2- is bonded in a 2-coordinate geometry to two Ti+3.94+ atoms. In the fourth O2- site, O2- is bonded in a 2-coordinate geometry to one K1+ and two Ti+3.94+ atoms. In the fifth O2- site, O2- is bonded in a 2-coordinate geometry to one K1+ and two Ti+3.94+ atoms. In the sixth O2- site, O2- is bonded in a distorted single-bond geometry to two Ti+3.94+ atoms. In the seventh O2- site, O2- is bonded in a distorted single-bond geometry to two Ti+3.94+ atoms. In the eighth O2- site, O2- is bonded in a distorted single-bond geometry to one K1+ and two Ti+3.94+ atoms. In the ninth O2- site, O2- is bonded in a distorted single-bond geometry to two Ti+3.94+ atoms. In the tenth O2- site, O2- is bonded in a 2-coordinate geometry to two Ti+3.94+ atoms. In the eleventh O2- site, O2- is bonded in a 2-coordinate geometry to two Ti+3.94+ atoms. In the twelfth O2- site, O2- is bonded in a 1-coordinate geometry to two Ti+3.94+ and one O2- atom. The O–O bond length is 1.72 Å. In the thirteenth O2- site, O2- is bonded in a 4-coordinate geometry to one K1+, two equivalent Ti+3.94+, and one O2- atom. In the fourteenth O2- site, O2- is bonded in a 2-coordinate geometry to one K1+, two Ti+3.94+, and one O2- atom. In the fifteenth O2- site, O2- is bonded in a 2-coordinate geometry to two Ti+3.94+ atoms. In the sixteenth O2- site, O2- is bonded in a 2-coordinate geometry to two Ti+3.94+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3Ti8O17 by Materials Project

K3Ti8O17 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are three inequivalent K1+ sites. In the first K1+ site, K1+ is bonded in a distorted rectangular see-saw-like geometry to four O2- atoms. There are a spread of K–O bond distances ranging from 2.66–2.68 Å. In the second K1+ site, K1+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of K–O bond distances ranging from 2.73–3.07 Å. In the third K1+ site, K1+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of K–O bond distances ranging from 2.73–3.00 Å. There are eight inequivalent Ti+3.88+ sites. In the first Ti+3.88+ site, Ti+3.88+ 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 0–26°. There are a spread of Ti–O bond distances ranging from 1.89–2.23 Å. In the second Ti+3.88+ site, Ti+3.88+ 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 0–26°. There are a spread of Ti–O bond distances ranging from 1.89–2.24 Å. In the third Ti+3.88+ site, Ti+3.88+ is bonded to six O2- atoms to form a mixture of distorted edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles are 31°. There are a spread of Ti–O bond distances ranging from 1.77–2.26 Å. In the fourth Ti+3.88+ site, Ti+3.88+ is bonded to six O2- atoms to form a mixture of distorted edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles are 31°. There are a spread of Ti–O bond distances ranging from 1.77–2.27 Å. In the fifth Ti+3.88+ site, Ti+3.88+ 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 27–28°. There are a spread of Ti–O bond distances ranging from 1.80–2.25 Å. In the sixth Ti+3.88+ site, Ti+3.88+ 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 27–28°. There are a spread of Ti–O bond distances ranging from 1.81–2.24 Å. In the seventh Ti+3.88+ site, Ti+3.88+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ti–O bond distances ranging from 1.78–2.31 Å. In the eighth Ti+3.88+ site, Ti+3.88+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ti–O bond distances ranging from 1.78–2.31 Å. There are eighteen inequivalent O2- sites. In the first O2- site, O2- is bonded in a linear geometry to four K1+ and two equivalent Ti+3.88+ atoms. In the second O2- site, O2- is bonded in a linear geometry to four K1+ and two equivalent Ti+3.88+ atoms. In the third O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to two K1+ and two Ti+3.88+ atoms. In the fourth O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to two K1+ and two Ti+3.88+ atoms. In the fifth O2- site, O2- is bonded to two equivalent K1+ and two Ti+3.88+ atoms to form distorted OK2Ti2 tetrahedra that share corners with four equivalent OK2Ti2 tetrahedra, corners with six OTi4 trigonal pyramids, an edgeedge with one OK2Ti2 tetrahedra, and an edgeedge with one OTi4 trigonal pyramid. In the sixth O2- site, O2- is bonded to two equivalent K1+ and two Ti+3.88+ atoms to form distorted OK2Ti2 tetrahedra that share corners with four equivalent OK2Ti2 tetrahedra, corners with six OTi4 trigonal pyramids, an edgeedge with one OK2Ti2 tetrahedra, and an edgeedge with one OTi4 trigonal pyramid. In the seventh O2- site, O2- is bonded in a distorted water-like geometry to two K1+ and two Ti+3.88+ atoms. In the eighth O2- site, O2- is bonded in a distorted water-like geometry to two K1+ and two Ti+3.88+ atoms. In the ninth O2- site, O2- is bonded in a distorted linear geometry to two K1+ and two Ti+3.88+ atoms. In the tenth O2- site, O2- is bonded in a distorted linear geometry to two K1+ and two Ti+3.88+ atoms. In the eleventh O2- site, O2- is bonded in a 3-coordinate geometry to three Ti+3.88+ atoms. In the twelfth O2- site, O2- is bonded in a distorted T-shaped geometry to three Ti+3.88+ atoms. In the thirteenth O2- site, O2- is bonded to four Ti+3.88+ atoms to form distorted OTi4 trigonal pyramids that share corners with three OK2Ti2 tetrahedra, corners with three OTi4 trigonal pyramids, and edges with four OTi4 trigonal pyramids. In the fourteenth O2- site, O2- is bonded to four Ti+3.88+ atoms to form distorted OTi4 trigonal pyramids that share corners with three OK2Ti2 tetrahedra, corners with three OTi4 trigonal pyramids, and edges with four OTi4 trigonal pyramids. In the fifteenth O2- site, O2- is bonded to four Ti+3.88+ atoms to form distorted OTi4 trigonal pyramids that share corners with two OK2Ti2 tetrahedra, corners with four OTi4 trigonal pyramids, an edgeedge with one OK2Ti2 tetrahedra, and edges with four OTi4 trigonal pyramids. In the sixteenth O2- site, O2- is bonded to four Ti+3.88+ atoms to form distorted OTi4 trigonal pyramids that share corners with two OK2Ti2 tetrahedra, corners with four OTi4 trigonal pyramids, an edgeedge with one OK2Ti2 tetrahedra, and edges with four OTi4 trigonal pyramids. In the seventeenth O2- site, O2- is bonded to four Ti+3.88+ atoms to form distorted OTi4 trigonal pyramids that share a cornercorner with one OK2Ti2 tetrahedra, corners with three OTi4 trigonal pyramids, and edges with two OTi4 trigonal pyramids. In the eighteenth O2- site, O2- is bonded to four Ti+3.88+ atoms to form distorted OTi4 trigonal pyramids that share a cornercorner with one OK2Ti2 tetrahedra, corners with three OTi4 trigonal pyramids, and edges with two OTi4 trigonal pyramids.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Na6Ti11O24 by Materials Project

Na6Ti11O24 is beta indium sulfide-derived structured and crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are six 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 60–65°. There are a spread of Na–O bond distances ranging from 2.15–2.18 Å. In the second Na1+ site, Na1+ is bonded to four O2- atoms to form NaO4 tetrahedra that share a cornercorner with one NaO6 octahedra and corners with eleven TiO6 octahedra. The corner-sharing octahedra tilt angles range from 57–72°. There are a spread of Na–O bond distances ranging from 2.17–2.25 Å. In the third Na1+ site, Na1+ is bonded to six O2- atoms to form distorted NaO6 octahedra that share corners with six NaO4 tetrahedra and edges with six TiO6 octahedra. There are two shorter (2.20 Å) and four longer (2.30 Å) Na–O bond lengths. In the fourth Na1+ site, Na1+ is bonded to four O2- atoms to form NaO4 tetrahedra that share corners with two equivalent NaO6 octahedra and corners with ten TiO6 octahedra. The corner-sharing octahedra tilt angles range from 52–72°. There are three shorter (2.16 Å) and one longer (2.18 Å) Na–O bond lengths. In the fifth Na1+ site, Na1+ is bonded to four O2- atoms to form NaO4 tetrahedra that share corners with two equivalent NaO6 octahedra and corners with ten TiO6 octahedra. The corner-sharing octahedra tilt angles range from 53–73°. There are three shorter (2.16 Å) and one longer (2.18 Å) Na–O bond lengths. In the sixth Na1+ site, Na1+ is bonded to four O2- atoms to form NaO4 tetrahedra that share a cornercorner with one NaO6 octahedra and corners with eleven TiO6 octahedra. The corner-sharing octahedra tilt angles range from 58–72°. There are a spread of Na–O bond distances ranging from 2.18–2.23 Å. There are eight inequivalent Ti+3.82+ sites. In the first Ti+3.82+ site, Ti+3.82+ 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 second Ti+3.82+ site, Ti+3.82+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with three equivalent 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 third Ti+3.82+ site, Ti+3.82+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six NaO4 tetrahedra, edges with two equivalent NaO6 octahedra, and edges with four TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.93–2.07 Å. In the fourth Ti+3.82+ site, Ti+3.82+ 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 1.98–2.08 Å. In the fifth Ti+3.82+ site, Ti+3.82+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share corners with six NaO4 tetrahedra, an edgeedge with one NaO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.83–2.18 Å. In the sixth Ti+3.82+ site, Ti+3.82+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six NaO4 tetrahedra, an edgeedge with one NaO6 octahedra, and edges with five TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.85–2.13 Å. In the seventh Ti+3.82+ site, Ti+3.82+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.98–2.05 Å. In the eighth Ti+3.82+ site, Ti+3.82+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with four NaO4 tetrahedra and edges with six TiO6 octahedra. There are a spread of Ti–O bond distances ranging from 1.99–2.05 Å. There are eighteen inequivalent O2- sites. In the first O2- site, O2- is bonded to one Na1+ and three Ti+3.82+ atoms to form ONaTi3 tetrahedra that share corners with eight ONaTi3 tetrahedra, corners with four ONa2Ti2 trigonal pyramids, and edges with two equivalent ONaTi3 tetrahedra. In the second O2- site, O2- is bonded to one Na1+ and three Ti+3.82+ atoms to form distorted ONaTi3 tetrahedra that share corners with eight ONaTi3 tetrahedra, corners with four ONa2Ti2 trigonal pyramids, and edges with two ONaTi3 tetrahedra. In the third O2- site, O2- is bonded to one Na1+ and three Ti+3.82+ atoms to form a mixture of corner and edge-sharing ONaTi3 tetrahedra. In the fourth O2- site, O2- is bonded to one Na1+ and three Ti+3.82+ atoms to form a mixture of corner and edge-sharing ONaTi3 tetrahedra. In the fifth O2- site, O2- is bonded to one Na1+ and three Ti+3.82+ atoms to form distorted ONaTi3 tetrahedra that share corners with six ONaTi3 tetrahedra, corners with three ONa2Ti2 trigonal pyramids, and edges with three ONaTi3 tetrahedra. In the sixth O2- site, O2- is bonded to two Na1+ and two Ti+3.82+ atoms to form distorted ONa2Ti2 trigonal pyramids that share corners with four ONaTi3 tetrahedra, corners with eight ONa2Ti2 trigonal pyramids, an edgeedge with one ONa2Ti2 tetrahedra, and edges with two ONa2Ti2 trigonal pyramids. In the seventh O2- site, O2- is bonded to two Na1+ and two Ti+3.82+ atoms to form distorted ONa2Ti2 trigonal pyramids that share corners with six ONaTi3 tetrahedra, corners with six ONa2Ti2 trigonal pyramids, and edges with three ONa2Ti2 trigonal pyramids. In the eighth O2- site, O2- is bonded to two Na1+ and two equivalent Ti+3.82+ atoms to form distorted ONa2Ti2 trigonal pyramids that share corners with six ONaTi3 tetrahedra, corners with six ONa2Ti2 trigonal pyramids, and edges with three ONa2Ti2 trigonal pyramids. In the ninth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.82+ atoms. In the tenth O2- site, O2- is bonded to one Na1+ and three Ti+3.82+ atoms to form distorted ONaTi3 trigonal pyramids that share corners with six ONaTi3 tetrahedra, corners with six ONa2Ti2 trigonal pyramids, and edges with three ONa2Ti2 trigonal pyramids. In the eleventh O2- site, O2- is bonded to one Na1+ and three Ti+3.82+ atoms to form distorted ONaTi3 tetrahedra that share corners with five ONaTi3 tetrahedra, corners with three ONa2Ti2 trigonal pyramids, and edges with three ONaTi3 tetrahedra. In the twelfth O2- site, O2- is bonded to one Na1+ and three Ti+3.82+ atoms to form ONaTi3 tetrahedra that share corners with five ONaTi3 tetrahedra, corners with three ONa2Ti2 trigonal pyramids, and edges with three ONaTi3 tetrahedra. In the thirteenth O2- site, O2- is bonded to one Na1+ and three Ti+3.82+ atoms to form distorted ONaTi3 trigonal pyramids that share corners with four ONaTi3 tetrahedra, corners with eight ONa2Ti2 trigonal pyramids, an edgeedge with one ONa2Ti2 tetrahedra, and edges with two equivalent ONa2Ti2 trigonal pyramids. In the fourteenth O2- site, O2- is bonded to one Na1+ and three Ti+3.82+ atoms to form a mixture of corner and edge-sharing ONaTi3 tetrahedra. In the fifteenth O2- site, O2- is bonded to two Na1+ and two equivalent Ti+3.82+ atoms to form distorted ONa2Ti2 tetrahedra that share corners with three ONaTi3 tetrahedra, corners with nine ONa2Ti2 trigonal pyramids, and edges with three ONa2Ti2 trigonal pyramids. In the sixteenth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.82+ atoms. In the seventeenth O2- site, O2- is bonded to one Na1+ and three Ti+3.82+ atoms to form distorted ONaTi3 tetrahedra that share corners with nine ONaTi3 tetrahedra and corners with three ONa2Ti2 trigonal pyramids. In the eighteenth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Ti+3.82+ atoms.

36 MATERIALS SCIENCE↗