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Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations
Rb2Ti(GeO3)3 crystallizes in the trigonal P-3c1 space group. The structure is three-dimensional. Rb1+ is bonded in a 7-coordinate geometry to nine O2- atoms. There are a spread of Rb–O bond distances ranging from 2.94–3.48 Å. There are two inequivalent Ti4+ sites. In the first Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six equivalent GeO4 tetrahedra. There is three shorter (1.95 Å) and three longer (2.00 Å) Ti–O bond length. In the second Ti4+ site, Ti4+ is bonded to six equivalent O2- atoms to form TiO6 octahedra that share corners with six equivalent GeO4 tetrahedra. All Ti–O bond lengths are 2.00 Å. There are two inequivalent Ge4+ sites. In the first Ge4+ site, Ge4+ is bonded to four O2- atoms to form GeO4 tetrahedra that share corners with two equivalent TiO6 octahedra and corners with two GeO4 tetrahedra. The corner-sharing octahedra tilt angles range from 40–44°. There are a spread of Ge–O bond distances ranging from 1.74–1.81 Å. In the second Ge4+ site, Ge4+ is bonded to four O2- atoms to form GeO4 tetrahedra that share corners with two equivalent TiO6 octahedra and corners with two equivalent GeO4 tetrahedra. The corner-sharing octahedral tilt angles are 50°. There is two shorter (1.76 Å) and two longer (1.82 Å) Ge–O bond length. There are five inequivalent O2- sites. In the first O2- site, O2- is bonded in a 2-coordinate geometry to two equivalent Rb1+ and two Ge4+ atoms. In the second O2- site, O2- is bonded in a 2-coordinate geometry to two equivalent Rb1+, one Ti4+, and one Ge4+ atom. In the third O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two equivalent Rb1+, one Ti4+, and one Ge4+ atom. In the fourth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two equivalent Rb1+ and two equivalent Ge4+ atoms. In the fifth O2- site, O2- is bonded in a 2-coordinate geometry to two equivalent Rb1+, one Ti4+, and one Ge4+ atom.
TiTl2(GeO3)3 crystallizes in the hexagonal P6_3/m space group. The structure is three-dimensional. Ti4+ is bonded to six equivalent O2- atoms to form TiO6 octahedra that share corners with six equivalent GeO4 tetrahedra. All Ti–O bond lengths are 1.98 Å. Tl1+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Tl–O bond distances ranging from 2.90–3.27 Å. Ge4+ is bonded to four O2- atoms to form GeO4 tetrahedra that share corners with two equivalent TiO6 octahedra and corners with two equivalent GeO4 tetrahedra. The corner-sharing octahedral tilt angles are 41°. There are a spread of Ge–O bond distances ranging from 1.74–1.81 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a 2-coordinate geometry to one Ti4+, two equivalent Tl1+, and one Ge4+ atom. In the second O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two equivalent Tl1+ and two equivalent Ge4+ atoms.
Rb2Ti(GeO3)3 crystallizes in the trigonal P-3c1 space group. The structure is three-dimensional. Rb1+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Rb–O bond distances ranging from 2.71–3.38 Å. There are two inequivalent Ti4+ sites. In the first Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six equivalent GeO4 tetrahedra. There is three shorter (1.96 Å) and three longer (2.02 Å) Ti–O bond length. In the second Ti4+ site, Ti4+ is bonded to six equivalent O2- atoms to form TiO6 octahedra that share corners with six equivalent GeO4 tetrahedra. All Ti–O bond lengths are 1.98 Å. There are two inequivalent Ge4+ sites. In the first Ge4+ site, Ge4+ is bonded to four O2- atoms to form GeO4 tetrahedra that share corners with two equivalent TiO6 octahedra and corners with two GeO4 tetrahedra. The corner-sharing octahedra tilt angles range from 29–38°. There are a spread of Ge–O bond distances ranging from 1.75–1.79 Å. In the second Ge4+ site, Ge4+ is bonded to four O2- atoms to form GeO4 tetrahedra that share corners with two equivalent TiO6 octahedra and corners with two equivalent GeO4 tetrahedra. The corner-sharing octahedral tilt angles are 39°. There is two shorter (1.73 Å) and two longer (1.83 Å) Ge–O bond length. There are five inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted linear geometry to two equivalent Rb1+ and two equivalent Ge4+ atoms. In the second O2- site, O2- is bonded in a 2-coordinate geometry to two equivalent Rb1+ and two Ge4+ atoms. In the third O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one Rb1+, one Ti4+, and one Ge4+ atom. In the fourth O2- site, O2- is bonded in a 2-coordinate geometry to two equivalent Rb1+, one Ti4+, and one Ge4+ atom. In the fifth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two equivalent Rb1+, one Ti4+, and one Ge4+ atom.
K2TiGe3O9 is Esseneite-like structured and crystallizes in the monoclinic C2 space group. The structure is three-dimensional. there are six inequivalent K1+ sites. In the first K1+ site, K1+ is bonded in a 4-coordinate geometry to eight O2- atoms. There are a spread of K–O bond distances ranging from 2.52–3.31 Å. In the second K1+ site, K1+ is bonded in a 4-coordinate geometry to eight O2- atoms. There are a spread of K–O bond distances ranging from 2.52–3.29 Å. In the third K1+ site, K1+ is bonded in a 4-coordinate geometry to eight O2- atoms. There are a spread of K–O bond distances ranging from 2.52–3.30 Å. In the fourth K1+ site, K1+ is bonded in a 4-coordinate geometry to eight O2- atoms. There are a spread of K–O bond distances ranging from 2.52–3.31 Å. In the fifth K1+ site, K1+ is bonded in a 4-coordinate geometry to eight O2- atoms. There are a spread of K–O bond distances ranging from 2.52–3.31 Å. In the sixth K1+ site, K1+ is bonded in a 4-coordinate geometry to eight O2- atoms. There are a spread of K–O bond distances ranging from 2.52–3.31 Å. There are three inequivalent Ti4+ sites. In the first Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six GeO4 tetrahedra. There is three shorter (1.97 Å) and three longer (1.99 Å) Ti–O bond length. In the second Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six GeO4 tetrahedra. All Ti–O bond lengths are 1.99 Å. In the third Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six GeO4 tetrahedra. There is three shorter (1.97 Å) and three longer (1.99 Å) Ti–O bond length. There are eight inequivalent Ge4+ sites. In the first Ge4+ site, Ge4+ is bonded to four O2- atoms to form GeO4 tetrahedra that share corners with two equivalent TiO6 octahedra and corners with two GeO4 tetrahedra. The corner-sharing octahedral tilt angles are 49°. There are a spread of Ge–O bond distances ranging from 1.75–1.81 Å. In the second Ge4+ site, Ge4+ is bonded to four O2- atoms to form GeO4 tetrahedra that share corners with two TiO6 octahedra and corners with two GeO4 tetrahedra. The corner-sharing octahedra tilt angles range from 33–41°. There are a spread of Ge–O bond distances ranging from 1.74–1.79 Å. In the third Ge4+ site, Ge4+ is bonded to four O2- atoms to form GeO4 tetrahedra that share corners with two TiO6 octahedra and corners with two GeO4 tetrahedra. The corner-sharing octahedra tilt angles range from 33–41°. There are a spread of Ge–O bond distances ranging from 1.74–1.79 Å. In the fourth Ge4+ site, Ge4+ is bonded to four O2- atoms to form GeO4 tetrahedra that share corners with two TiO6 octahedra and corners with two GeO4 tetrahedra. The corner-sharing octahedra tilt angles range from 34–41°. There are a spread of Ge–O bond distances ranging from 1.75–1.79 Å. In the fifth Ge4+ site, Ge4+ is bonded to four O2- atoms to form GeO4 tetrahedra that share corners with two TiO6 octahedra and corners with two GeO4 tetrahedra. The corner-sharing octahedra tilt angles range from 33–41°. There are a spread of Ge–O bond distances ranging from 1.75–1.79 Å. In the sixth Ge4+ site, Ge4+ is bonded to four O2- atoms to form GeO4 tetrahedra that share corners with two equivalent TiO6 octahedra and corners with two GeO4 tetrahedra. The corner-sharing octahedral tilt angles are 49°. There are a spread of Ge–O bond distances ranging from 1.75–1.81 Å. In the seventh Ge4+ site, Ge4+ is bonded to four O2- atoms to form GeO4 tetrahedra that share corners with two equivalent TiO6 octahedra and corners with two equivalent GeO4 tetrahedra. The corner-sharing octahedral tilt angles are 49°. There is two shorter (1.75 Å) and two longer (1.81 Å) Ge–O bond length. In the eighth Ge4+ site, Ge4+ is bonded to four O2- atoms to form GeO4 tetrahedra that share corners with two equivalent TiO6 octahedra and corners with two equivalent GeO4 tetrahedra. The corner-sharing octahedral tilt angles are 49°. There is two shorter (1.75 Å) and two longer (1.81 Å) Ge–O bond length. There are twenty-eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two K1+, one Ti4+, and one Ge4+ atom. In the second O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two K1+, one Ti4+, and one Ge4+ atom. In the third O2- site, O2- is bonded in a 2-coordinate geometry to two K1+, one Ti4+, and one Ge4+ atom. In the fourth O2- site, O2- is bonded in a 2-coordinate geometry to two K1+, one Ti4+, and one Ge4+ atom. The O–Ge bond length is 1.76 Å. In the fifth O2- site, O2- is bonded in a 2-coordinate geometry to two K1+, one Ti4+, and one Ge4+ atom. In the sixth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two K1+, one Ti4+, and one Ge4+ atom. In the seventh O2- site, O2- is bonded in a 2-coordinate geometry to two K1+, one Ti4+, and one Ge4+ atom. In the eighth O2- site, O2- is bonded in a 3-coordinate geometry to one K1+ and two Ge4+ atoms. In the ninth O2- site, O2- is bonded in a 2-coordinate geometry to two K1+, one Ti4+, and one Ge4+ atom. The O–Ge bond length is 1.75 Å. In the tenth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two K1+, one Ti4+, and one Ge4+ atom. In the eleventh O2- site, O2- is bonded in a 3-coordinate geometry to one K1+ and two Ge4+ atoms. In the twelfth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two K1+, one Ti4+, and one Ge4+ atom. The O–Ge bond length is 1.75 Å. In the thirteenth O2- site, O2- is bonded in a distorted linear geometry to two K1+ and two Ge4+ atoms. The O–Ge bond length is 1.78 Å. In the fourteenth O2- site, O2- is bonded in a 3-coordinate geometry to one K1+ and two Ge4+ atoms. In the fifteenth O2- site, O2- is bonded in a 3-coordinate geometry to one K1+ and two Ge4+ atoms. The O–Ge bond length is 1.79 Å. In the sixteenth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two K1+, one Ti4+, and one Ge4+ atom. In the seventeenth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two K1+, one Ti4+, and one Ge4+ atom. In the eighteenth O2- site, O2- is bonded in a 3-coordinate geometry to one K1+ and two Ge4+ atoms. The O–Ge bond length is 1.79 Å. In the nineteenth O2- site, O2- is bonded in a distorted linear geometry to two K1+ and two Ge4+ atoms. The O–Ge bond length is 1.78 Å. In the twentieth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two K1+, one Ti4+, and one Ge4+ atom. In the twenty-first O2- site, O2- is bonded in a 2-coordinate geometry to two K1+, one Ti4+, and one Ge4+ atom. In the twenty-second O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two K1+, one Ti4+, and one Ge4+ atom. The O–Ge bond length is 1.74 Å. In the twenty-third O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two K1+, one Ti4+, and one Ge4+ atom. In the twenty-fourth O2- site, O2- is bonded in a distorted linear geometry to two equivalent K1+ and two equivalent Ge4+ atoms. In the twenty-fifth O2- site, O2- is bonded in a 3-coordinate geometry to one K1+ and two Ge4+ atoms. In the twenty-sixth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two K1+, one Ti4+, and one Ge4+ atom. In the twenty-seventh O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two K1+, one Ti4+, and one Ge4+ atom. In the twenty-eighth O2- site, O2- is bonded in a distorted linear geometry to two equivalent K1+ and two equivalent Ge4+ atoms.