Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “faces”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,675 records · Page 93
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Materials Data on MgTi2 by Materials Project

MgTi2 is beta-derived structured and crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. there are two inequivalent Mg sites. In the first Mg site, Mg is bonded to four Mg and eight Ti atoms to form MgMg4Ti8 cuboctahedra that share corners with six equivalent TiMg4Ti8 cuboctahedra, corners with twelve MgMg4Ti8 cuboctahedra, edges with three equivalent MgMg4Ti8 cuboctahedra, edges with fifteen TiMg4Ti8 cuboctahedra, faces with six MgMg4Ti8 cuboctahedra, and faces with fourteen TiMg2Ti10 cuboctahedra. There are two shorter (2.88 Å) and two longer (2.98 Å) Mg–Mg bond lengths. There are a spread of Mg–Ti bond distances ranging from 2.90–3.03 Å. In the second Mg site, Mg is bonded to four Mg and eight Ti atoms to form MgMg4Ti8 cuboctahedra that share corners with six equivalent TiMg4Ti8 cuboctahedra, corners with twelve MgMg4Ti8 cuboctahedra, edges with three equivalent MgMg4Ti8 cuboctahedra, edges with fifteen TiMg2Ti10 cuboctahedra, faces with six MgMg4Ti8 cuboctahedra, and faces with fourteen TiMg2Ti10 cuboctahedra. Both Mg–Mg bond lengths are 2.88 Å. There are a spread of Mg–Ti bond distances ranging from 2.99–3.04 Å. There are four inequivalent Ti sites. In the first Ti site, Ti is bonded to two equivalent Mg and ten Ti atoms to form TiMg2Ti10 cuboctahedra that share corners with eighteen TiMg2Ti10 cuboctahedra, edges with eight equivalent MgMg4Ti8 cuboctahedra, edges with ten TiMg4Ti8 cuboctahedra, faces with eight MgMg4Ti8 cuboctahedra, and faces with twelve TiMg2Ti10 cuboctahedra. There are a spread of Ti–Ti bond distances ranging from 2.87–2.98 Å. In the second Ti site, Ti is bonded to four equivalent Mg and eight Ti atoms to form TiMg4Ti8 cuboctahedra that share corners with eighteen TiMg2Ti10 cuboctahedra, edges with six TiMg2Ti10 cuboctahedra, edges with twelve MgMg4Ti8 cuboctahedra, faces with six MgMg4Ti8 cuboctahedra, and faces with fourteen TiMg2Ti10 cuboctahedra. There are a spread of Ti–Ti bond distances ranging from 2.88–3.03 Å. In the third Ti site, Ti is bonded to six Mg and six Ti atoms to form TiMg6Ti6 cuboctahedra that share corners with eighteen TiMg2Ti10 cuboctahedra, edges with four equivalent MgMg4Ti8 cuboctahedra, edges with fourteen TiMg2Ti10 cuboctahedra, faces with ten MgMg4Ti8 cuboctahedra, and faces with ten TiMg2Ti10 cuboctahedra. Both Ti–Ti bond lengths are 2.88 Å. In the fourth Ti site, Ti is bonded to four Mg and eight Ti atoms to form distorted TiMg4Ti8 cuboctahedra that share corners with six equivalent TiMg4Ti8 cuboctahedra, corners with twelve MgMg4Ti8 cuboctahedra, edges with six MgMg4Ti8 cuboctahedra, edges with twelve TiMg2Ti10 cuboctahedra, faces with four MgMg4Ti8 cuboctahedra, and faces with sixteen TiMg2Ti10 cuboctahedra. Both Ti–Ti bond lengths are 2.88 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on BaHfMg6 by Materials Project

BaMg6Hf crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. Ba is bonded to ten Mg and two equivalent Hf atoms to form BaHf2Mg10 cuboctahedra that share corners with four equivalent MgBa2Mg10 cuboctahedra, corners with six equivalent BaHf2Mg10 cuboctahedra, edges with two equivalent MgBa2Mg10 cuboctahedra, edges with four equivalent HfBa2Mg10 cuboctahedra, faces with two equivalent BaHf2Mg10 cuboctahedra, faces with two equivalent HfBa2Mg10 cuboctahedra, and faces with eight MgBa2Mg10 cuboctahedra. There are a spread of Ba–Mg bond distances ranging from 3.30–3.44 Å. Both Ba–Hf bond lengths are 3.40 Å. There are four inequivalent Mg sites. In the first Mg site, Mg is bonded in a 12-coordinate geometry to two equivalent Ba, seven Mg, and two equivalent Hf atoms. There are a spread of Mg–Mg bond distances ranging from 3.16–3.41 Å. Both Mg–Hf bond lengths are 3.22 Å. In the second Mg site, Mg is bonded to two equivalent Ba and ten Mg atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent BaHf2Mg10 cuboctahedra, corners with six equivalent MgBa2Mg10 cuboctahedra, edges with two equivalent BaHf2Mg10 cuboctahedra, edges with four equivalent MgHf2Mg10 cuboctahedra, faces with two equivalent BaHf2Mg10 cuboctahedra, faces with four MgBa2Mg10 cuboctahedra, and faces with six equivalent HfBa2Mg10 cuboctahedra. There are four shorter (3.29 Å) and two longer (3.34 Å) Mg–Mg bond lengths. In the third Mg site, Mg is bonded in a 12-coordinate geometry to two equivalent Ba, eight Mg, and two equivalent Hf atoms. There are a spread of Mg–Mg bond distances ranging from 3.20–3.53 Å. There are one shorter (3.15 Å) and one longer (3.58 Å) Mg–Hf bond lengths. In the fourth Mg site, Mg is bonded to ten Mg and two equivalent Hf atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent HfBa2Mg10 cuboctahedra, corners with six equivalent MgHf2Mg10 cuboctahedra, edges with two equivalent HfBa2Mg10 cuboctahedra, edges with four equivalent MgBa2Mg10 cuboctahedra, faces with two equivalent HfBa2Mg10 cuboctahedra, faces with four MgBa2Mg10 cuboctahedra, and faces with six equivalent BaHf2Mg10 cuboctahedra. Both Mg–Hf bond lengths are 3.37 Å. Hf is bonded to two equivalent Ba and ten Mg atoms to form distorted HfBa2Mg10 cuboctahedra that share corners with four equivalent MgHf2Mg10 cuboctahedra, corners with six equivalent HfBa2Mg10 cuboctahedra, edges with two equivalent MgHf2Mg10 cuboctahedra, edges with four equivalent BaHf2Mg10 cuboctahedra, faces with two equivalent BaHf2Mg10 cuboctahedra, faces with two equivalent HfBa2Mg10 cuboctahedra, and faces with eight MgBa2Mg10 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ba7Ti2Nb4O21 by Materials Project

Ba7Ti2Nb4O21 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. there are four inequivalent Ba2+ sites. In the first Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with nine BaO12 cuboctahedra, faces with three equivalent BaO12 cuboctahedra, faces with three equivalent TiO6 octahedra, and faces with four NbO6 octahedra. There are a spread of Ba–O bond distances ranging from 2.73–3.06 Å. In the second 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 2.81–3.23 Å. In the third Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with nine equivalent BaO12 cuboctahedra, faces with six BaO12 cuboctahedra, faces with three equivalent TiO6 octahedra, and faces with five NbO6 octahedra. There are a spread of Ba–O bond distances ranging from 2.83–2.98 Å. In the fourth Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with twelve BaO12 cuboctahedra, faces with six equivalent BaO12 cuboctahedra, faces with two equivalent TiO6 octahedra, and faces with six equivalent NbO6 octahedra. There are six shorter (2.91 Å) and six longer (2.93 Å) Ba–O bond lengths. Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six NbO6 octahedra and faces with seven BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 8–12°. There are three shorter (1.87 Å) and three longer (2.24 Å) Ti–O bond lengths. There are two inequivalent Nb5+ sites. In the first Nb5+ site, Nb5+ is bonded to six O2- atoms to form distorted NbO6 octahedra that share corners with three equivalent TiO6 octahedra and faces with four BaO12 cuboctahedra. The corner-sharing octahedral tilt angles are 12°. There are three shorter (1.87 Å) and three longer (2.30 Å) Nb–O bond lengths. In the second Nb5+ site, Nb5+ is bonded to six O2- atoms to form NbO6 octahedra that share corners with three equivalent TiO6 octahedra, corners with three equivalent NbO6 octahedra, and faces with eight BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–8°. There are three shorter (1.97 Å) and three longer (2.13 Å) Nb–O bond lengths. There are four inequivalent O2- sites. In the first O2- site, O2- is bonded in a 1-coordinate geometry to four Ba2+, one Ti4+, and one Nb5+ atom. In the second O2- site, O2- is bonded in a 2-coordinate geometry to four Ba2+, one Ti4+, and one Nb5+ atom. In the third O2- site, O2- is bonded in a distorted single-bond geometry to four Ba2+ and one Nb5+ atom. In the fourth O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two equivalent Nb5+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Sc(TiFe3)2 by Materials Project

Sc(TiFe3)2 is Hexagonal Laves-derived structured and crystallizes in the trigonal P3m1 space group. The structure is three-dimensional. there are four inequivalent Sc sites. In the first Sc site, Sc is bonded in a 12-coordinate geometry to three equivalent Sc, one Ti, and twelve Fe atoms. All Sc–Sc bond lengths are 2.98 Å. The Sc–Ti bond length is 2.97 Å. There are a spread of Sc–Fe bond distances ranging from 2.84–2.93 Å. In the second Sc site, Sc is bonded in a 12-coordinate geometry to four Ti and twelve Fe atoms. There are three shorter (2.98 Å) and one longer (3.00 Å) Sc–Ti bond lengths. There are a spread of Sc–Fe bond distances ranging from 2.84–2.87 Å. In the third Sc site, Sc is bonded in a 12-coordinate geometry to four Ti and twelve Fe atoms. There are three shorter (2.98 Å) and one longer (2.99 Å) Sc–Ti bond lengths. There are a spread of Sc–Fe bond distances ranging from 2.84–2.86 Å. In the fourth Sc site, Sc is bonded in a 12-coordinate geometry to three equivalent Sc, one Ti, and twelve Fe atoms. The Sc–Ti bond length is 2.99 Å. There are a spread of Sc–Fe bond distances ranging from 2.84–2.91 Å. There are eight inequivalent Ti sites. In the first Ti site, Ti is bonded in a 12-coordinate geometry to three equivalent Sc, one Ti, and twelve Fe atoms. The Ti–Ti bond length is 2.93 Å. There are a spread of Ti–Fe bond distances ranging from 2.83–2.91 Å. In the second Ti site, Ti is bonded in a 12-coordinate geometry to three equivalent Sc, one Ti, and twelve Fe atoms. The Ti–Ti bond length is 2.93 Å. There are a spread of Ti–Fe bond distances ranging from 2.83–2.90 Å. In the third Ti site, Ti is bonded in a 12-coordinate geometry to one Sc, three equivalent Ti, and twelve Fe atoms. All Ti–Ti bond lengths are 2.95 Å. There are a spread of Ti–Fe bond distances ranging from 2.78–2.83 Å. In the fourth Ti site, Ti is bonded in a 12-coordinate geometry to four Ti and twelve Fe atoms. All Ti–Ti bond lengths are 2.94 Å. There are three shorter (2.76 Å) and nine longer (2.83 Å) Ti–Fe bond lengths. In the fifth Ti site, Ti is bonded in a 12-coordinate geometry to four Ti and twelve Fe atoms. All Ti–Ti bond lengths are 2.94 Å. There are three shorter (2.78 Å) and nine longer (2.83 Å) Ti–Fe bond lengths. In the sixth Ti site, Ti is bonded in a 12-coordinate geometry to one Sc, three equivalent Ti, and twelve Fe atoms. There are a spread of Ti–Fe bond distances ranging from 2.76–2.83 Å. In the seventh Ti site, Ti is bonded in a 12-coordinate geometry to one Sc, three equivalent Ti, and twelve Fe atoms. There are a spread of Ti–Fe bond distances ranging from 2.76–2.84 Å. In the eighth Ti site, Ti is bonded in a 12-coordinate geometry to one Sc, three equivalent Ti, and twelve Fe atoms. There are three shorter (2.77 Å) and nine longer (2.83 Å) Ti–Fe bond lengths. There are twelve inequivalent Fe sites. In the first Fe site, Fe is bonded to six Sc and six Fe atoms to form FeSc6Fe6 cuboctahedra that share corners with twelve FeSc3Ti3Fe6 cuboctahedra, edges with six equivalent FeSc6Fe6 cuboctahedra, and faces with twenty FeTi6Fe6 cuboctahedra. There are three shorter (2.49 Å) and three longer (2.50 Å) Fe–Fe bond lengths. In the second Fe site, Fe is bonded to three equivalent Sc, three equivalent Ti, and six Fe atoms to form FeSc3Ti3Fe6 cuboctahedra that share corners with twelve FeSc2Ti4Fe6 cuboctahedra, edges with six equivalent FeSc3Ti3Fe6 cuboctahedra, and faces with twenty FeTi6Fe6 cuboctahedra. There are three shorter (2.46 Å) and three longer (2.48 Å) Fe–Fe bond lengths. In the third Fe site, Fe is bonded to three equivalent Sc, three equivalent Ti, and six Fe atoms to form FeSc3Ti3Fe6 cuboctahedra that share corners with twelve FeSc2Ti4Fe6 cuboctahedra, edges with six equivalent FeSc3Ti3Fe6 cuboctahedra, and faces with twenty FeTi6Fe6 cuboctahedra. All Fe–Fe bond lengths are 2.46 Å. In the fourth Fe site, Fe is bonded to six Ti and six Fe atoms to form FeTi6Fe6 cuboctahedra that share corners with twelve FeSc2Ti4Fe6 cuboctahedra, edges with six equivalent FeTi6Fe6 cuboctahedra, and faces with twenty FeSc6Fe6 cuboctahedra. There are three shorter (2.39 Å) and three longer (2.40 Å) Fe–Fe bond lengths. In the fifth Fe site, Fe is bonded to six Ti and six Fe atoms to form FeTi6Fe6 cuboctahedra that share corners with twelve FeSc3Ti3Fe6 cuboctahedra, edges with six equivalent FeTi6Fe6 cuboctahedra, and faces with twenty FeSc6Fe6 cuboctahedra. There are three shorter (2.39 Å) and three longer (2.40 Å) Fe–Fe bond lengths. In the sixth Fe site, Fe is bonded to six Ti and six Fe atoms to form FeTi6Fe6 cuboctahedra that share corners with twelve FeSc2Ti4Fe6 cuboctahedra, edges with six equivalent FeTi6Fe6 cuboctahedra, and faces with twenty FeSc3Ti3Fe6 cuboctahedra. All Fe–Fe bond lengths are 2.41 Å. In the seventh Fe site, Fe is bonded to three Sc, three Ti, and six Fe atoms to form FeSc3Ti3Fe6 cuboctahedra that share corners with eighteen FeSc6Fe6 cuboctahedra, edges with six FeSc3Ti3Fe6 cuboctahedra, and faces with eighteen FeSc6Fe6 cuboctahedra. There are two shorter (2.38 Å) and two longer (2.46 Å) Fe–Fe bond lengths. In the eighth Fe site, Fe is bonded to two equivalent Sc, four Ti, and six Fe atoms to form FeSc2Ti4Fe6 cuboctahedra that share corners with eighteen FeSc3Ti3Fe6 cuboctahedra, edges with six FeSc2Ti4Fe6 cuboctahedra, and faces with eighteen FeSc3Ti3Fe6 cuboctahedra. There are two shorter (2.36 Å) and two longer (2.47 Å) Fe–Fe bond lengths. In the ninth Fe site, Fe is bonded to two equivalent Sc, four Ti, and six Fe atoms to form a mixture of corner, edge, and face-sharing FeSc2Ti4Fe6 cuboctahedra. There are two shorter (2.37 Å) and two longer (2.46 Å) Fe–Fe bond lengths. In the tenth Fe site, Fe is bonded to three Sc, three Ti, and six Fe atoms to form FeSc3Ti3Fe6 cuboctahedra that share corners with eighteen FeSc6Fe6 cuboctahedra, edges with six FeSc3Ti3Fe6 cuboctahedra, and faces with eighteen FeSc6Fe6 cuboctahedra. There are two shorter (2.38 Å) and two longer (2.45 Å) Fe–Fe bond lengths. In the eleventh Fe site, Fe is bonded to one Sc, five Ti, and six Fe atoms to form a mixture of corner, edge, and face-sharing FeScTi5Fe6 cuboctahedra. There are two shorter (2.38 Å) and two longer (2.46 Å) Fe–Fe bond lengths. In the twelfth Fe site, Fe is bonded to one Sc, five Ti, and six Fe atoms to form FeScTi5Fe6 cuboctahedra that share corners with eighteen FeSc3Ti3Fe6 cuboctahedra, edges with six FeSc2Ti4Fe6 cuboctahedra, and faces with eighteen FeSc3Ti3Fe6 cuboctahedra. There are two shorter (2.38 Å) and two longer (2.46 Å) Fe–Fe bond lengths.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on MgCd2 by Materials Project

MgCd2 crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are two inequivalent Mg sites. In the first Mg site, Mg is bonded to eight Cd atoms to form distorted MgCd8 cuboctahedra that share corners with ten MgCd8 cuboctahedra, corners with sixteen CdMg3Cd9 cuboctahedra, edges with three equivalent MgCd8 cuboctahedra, edges with eight CdMg3Cd9 cuboctahedra, faces with three MgCd8 cuboctahedra, and faces with nine CdMg3Cd9 cuboctahedra. There are a spread of Mg–Cd bond distances ranging from 3.02–3.17 Å. In the second Mg site, Mg is bonded to eight Cd atoms to form distorted MgCd8 cuboctahedra that share corners with ten MgCd8 cuboctahedra, corners with fourteen CdMg3Cd9 cuboctahedra, edges with three equivalent MgCd8 cuboctahedra, edges with ten CdMg3Cd9 cuboctahedra, faces with three MgCd8 cuboctahedra, and faces with seven CdMg3Cd9 cuboctahedra. There are a spread of Mg–Cd bond distances ranging from 3.05–3.20 Å. There are four inequivalent Cd sites. In the first Cd site, Cd is bonded to three Mg and nine Cd atoms to form distorted CdMg3Cd9 cuboctahedra that share corners with six MgCd8 cuboctahedra, corners with twenty CdMg3Cd9 cuboctahedra, edges with five MgCd8 cuboctahedra, edges with six CdMg5Cd7 cuboctahedra, faces with six MgCd8 cuboctahedra, and faces with thirteen CdMg3Cd9 cuboctahedra. There are a spread of Cd–Cd bond distances ranging from 3.06–3.30 Å. In the second Cd site, Cd is bonded to five Mg and seven Cd atoms to form distorted CdMg5Cd7 cuboctahedra that share corners with six MgCd8 cuboctahedra, corners with twenty CdMg3Cd9 cuboctahedra, edges with eight MgCd8 cuboctahedra, edges with eight CdMg3Cd9 cuboctahedra, faces with two equivalent MgCd8 cuboctahedra, and faces with twelve CdMg3Cd9 cuboctahedra. There are a spread of Cd–Cd bond distances ranging from 3.09–3.30 Å. In the third Cd site, Cd is bonded to four Mg and six Cd atoms to form distorted CdMg4Cd6 cuboctahedra that share corners with six MgCd8 cuboctahedra, corners with twenty-two CdMg3Cd9 cuboctahedra, edges with five MgCd8 cuboctahedra, edges with six CdMg3Cd9 cuboctahedra, faces with two MgCd8 cuboctahedra, and faces with eleven CdMg3Cd9 cuboctahedra. Both Cd–Cd bond lengths are 3.14 Å. In the fourth Cd site, Cd is bonded to four Mg and eight Cd atoms to form distorted CdMg4Cd8 cuboctahedra that share corners with eight CdMg4Cd6 cuboctahedra, corners with twelve MgCd8 cuboctahedra, edges with ten CdMg3Cd9 cuboctahedra, faces with six MgCd8 cuboctahedra, and faces with fourteen CdMg3Cd9 cuboctahedra. Both Cd–Cd bond lengths are 3.30 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Tb2HfAl9 by Materials Project

Tb2HfAl9 is Uranium Silicide-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. Tb is bonded to twelve Al atoms to form TbAl12 cuboctahedra that share corners with four equivalent HfAl12 cuboctahedra, corners with eight equivalent TbAl12 cuboctahedra, edges with twenty AlHf4Al8 cuboctahedra, a faceface with one HfAl12 cuboctahedra, faces with five equivalent TbAl12 cuboctahedra, and faces with eight AlTb2Hf2Al8 cuboctahedra. There are a spread of Tb–Al bond distances ranging from 2.98–3.02 Å. Hf is bonded to twelve Al atoms to form HfAl12 cuboctahedra that share corners with four equivalent HfAl12 cuboctahedra, corners with eight equivalent TbAl12 cuboctahedra, edges with sixteen equivalent AlTb2Hf2Al8 cuboctahedra, faces with two equivalent TbAl12 cuboctahedra, faces with four equivalent HfAl12 cuboctahedra, and faces with twelve AlHf4Al8 cuboctahedra. There are eight shorter (2.90 Å) and four longer (2.98 Å) Hf–Al bond lengths. There are four inequivalent Al sites. In the first Al site, Al is bonded to four equivalent Hf and eight equivalent Al atoms to form AlHf4Al8 cuboctahedra that share corners with four equivalent AlHf4Al8 cuboctahedra, edges with eight equivalent TbAl12 cuboctahedra, edges with sixteen equivalent AlTb2Hf2Al8 cuboctahedra, faces with four equivalent HfAl12 cuboctahedra, and faces with twelve AlHf4Al8 cuboctahedra. All Al–Al bond lengths are 2.90 Å. In the second Al site, Al is bonded in a distorted rectangular see-saw-like geometry to four equivalent Tb and eight Al atoms. There are four shorter (2.99 Å) and four longer (3.05 Å) Al–Al bond lengths. In the third Al site, Al is bonded to two equivalent Tb, two equivalent Hf, and eight Al atoms to form distorted AlTb2Hf2Al8 cuboctahedra that share corners with twelve AlTb2Hf2Al8 cuboctahedra, edges with four equivalent TbAl12 cuboctahedra, edges with four equivalent HfAl12 cuboctahedra, edges with twelve AlHf4Al8 cuboctahedra, faces with two equivalent TbAl12 cuboctahedra, faces with two equivalent HfAl12 cuboctahedra, and faces with twelve AlHf4Al8 cuboctahedra. All Al–Al bond lengths are 2.98 Å. In the fourth Al site, Al is bonded to four equivalent Tb and eight Al atoms to form distorted AlTb4Al8 cuboctahedra that share corners with twelve AlTb2Hf2Al8 cuboctahedra, edges with eight equivalent TbAl12 cuboctahedra, edges with eight equivalent AlTb2Hf2Al8 cuboctahedra, faces with four equivalent TbAl12 cuboctahedra, and faces with ten AlTb2Hf2Al8 cuboctahedra. All Al–Al bond lengths are 2.98 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Dy2(GaNi)5 by Materials Project

Dy2(NiGa)5 crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are six inequivalent Dy sites. In the first Dy site, Dy is bonded in a 10-coordinate geometry to eight Ni and ten Ga atoms. There are a spread of Dy–Ni bond distances ranging from 3.03–3.11 Å. There are a spread of Dy–Ga bond distances ranging from 3.10–3.32 Å. In the second Dy site, Dy is bonded in a 11-coordinate geometry to seven Ni and eleven Ga atoms. There are a spread of Dy–Ni bond distances ranging from 3.03–3.10 Å. There are a spread of Dy–Ga bond distances ranging from 3.10–3.34 Å. In the third Dy site, Dy is bonded in a 11-coordinate geometry to eight Ni and ten Ga atoms. There are a spread of Dy–Ni bond distances ranging from 3.03–3.11 Å. There are a spread of Dy–Ga bond distances ranging from 3.08–3.29 Å. In the fourth Dy site, Dy is bonded in a 7-coordinate geometry to seven Ni and eleven Ga atoms. There are a spread of Dy–Ni bond distances ranging from 3.04–3.09 Å. There are a spread of Dy–Ga bond distances ranging from 3.11–3.33 Å. In the fifth Dy site, Dy is bonded in a distorted hexagonal planar geometry to eight Ni and ten Ga atoms. There are a spread of Dy–Ni bond distances ranging from 2.77–3.29 Å. There are a spread of Dy–Ga bond distances ranging from 3.21–3.37 Å. In the sixth Dy site, Dy is bonded in a 6-coordinate geometry to ten Ni and eight Ga atoms. There are a spread of Dy–Ni bond distances ranging from 2.79–3.33 Å. There are a spread of Dy–Ga bond distances ranging from 3.14–3.36 Å. There are fifteen inequivalent Ni sites. In the first Ni site, Ni is bonded in a 9-coordinate geometry to three Dy and six Ga atoms. There are a spread of Ni–Ga bond distances ranging from 2.45–2.51 Å. In the second Ni site, Ni is bonded in a 9-coordinate geometry to three Dy and six Ga atoms. There are a spread of Ni–Ga bond distances ranging from 2.42–2.52 Å. In the third Ni site, Ni is bonded in a 9-coordinate geometry to three Dy, two equivalent Ni, and four Ga atoms. Both Ni–Ni bond lengths are 2.51 Å. There are a spread of Ni–Ga bond distances ranging from 2.41–2.46 Å. In the fourth Ni site, Ni is bonded in a 9-coordinate geometry to three Dy, two equivalent Ni, and four Ga atoms. Both Ni–Ni bond lengths are 2.51 Å. There are a spread of Ni–Ga bond distances ranging from 2.41–2.46 Å. In the fifth Ni site, Ni is bonded in a 9-coordinate geometry to three Dy, two equivalent Ni, and four Ga atoms. Both Ni–Ni bond lengths are 2.52 Å. There are a spread of Ni–Ga bond distances ranging from 2.40–2.48 Å. In the sixth Ni site, Ni is bonded in a 9-coordinate geometry to three Dy and six Ga atoms. There are a spread of Ni–Ga bond distances ranging from 2.45–2.50 Å. In the seventh Ni site, Ni is bonded in a 9-coordinate geometry to three Dy, two equivalent Ni, and four Ga atoms. Both Ni–Ni bond lengths are 2.51 Å. There are a spread of Ni–Ga bond distances ranging from 2.41–2.46 Å. In the eighth Ni site, Ni is bonded in a 9-coordinate geometry to three Dy and six Ga atoms. There are a spread of Ni–Ga bond distances ranging from 2.42–2.52 Å. In the ninth Ni site, Ni is bonded in a 9-coordinate geometry to three Dy, two equivalent Ni, and four Ga atoms. Both Ni–Ni bond lengths are 2.51 Å. There are a spread of Ni–Ga bond distances ranging from 2.41–2.50 Å. In the tenth Ni site, Ni is bonded in a 9-coordinate geometry to three Dy, two equivalent Ni, and four Ga atoms. Both Ni–Ni bond lengths are 2.51 Å. There are a spread of Ni–Ga bond distances ranging from 2.40–2.45 Å. In the eleventh Ni site, Ni is bonded in a 9-coordinate geometry to three Dy and six Ga atoms. There are a spread of Ni–Ga bond distances ranging from 2.43–2.50 Å. In the twelfth Ni site, Ni is bonded in a 9-coordinate geometry to three Dy and six Ga atoms. There are a spread of Ni–Ga bond distances ranging from 2.45–2.51 Å. In the thirteenth Ni site, Ni is bonded to four Dy, four Ni, and four Ga atoms to form distorted NiDy4Ga4Ni4 cuboctahedra that share corners with three equivalent NiDy4Ga4Ni4 cuboctahedra, corners with three GaDy4Ga4Ni4 cuboctahedra, faces with two equivalent GaDy4Ga4Ni4 cuboctahedra, and faces with three NiDy4Ga4Ni4 cuboctahedra. There are a spread of Ni–Ga bond distances ranging from 2.53–2.64 Å. In the fourteenth Ni site, Ni is bonded to four Dy, four Ni, and four Ga atoms to form distorted NiDy4Ga4Ni4 cuboctahedra that share a cornercorner with one NiDy4Ga4Ni4 cuboctahedra, corners with five GaDy4Ga4Ni4 cuboctahedra, faces with two equivalent NiDy4Ga4Ni4 cuboctahedra, and faces with five GaDy4Ga2Ni6 cuboctahedra. There are a spread of Ni–Ga bond distances ranging from 2.52–2.65 Å. In the fifteenth Ni site, Ni is bonded to four Dy, four Ni, and four Ga atoms to form distorted NiDy4Ga4Ni4 cuboctahedra that share corners with two equivalent GaDy4Ga2Ni6 cuboctahedra, corners with four NiDy4Ga4Ni4 cuboctahedra, and faces with three NiDy4Ga4Ni4 cuboctahedra. There are a spread of Ni–Ga bond distances ranging from 2.52–2.64 Å. There are fifteen inequivalent Ga sites. In the first Ga site, Ga is bonded in a 12-coordinate geometry to four Dy, six Ni, and two equivalent Ga atoms. Both Ga–Ga bond lengths are 2.87 Å. In the second Ga site, Ga is bonded to four Dy, six Ni, and two equivalent Ga atoms to form distorted GaDy4Ga2Ni6 cuboctahedra that share corners with two equivalent NiDy4Ga4Ni4 cuboctahedra, corners with four GaDy4Ga4Ni4 cuboctahedra, faces with two equivalent NiDy4Ga4Ni4 cuboctahedra, and faces with six GaDy4Ga2Ni6 cuboctahedra. Both Ga–Ga bond lengths are 2.77 Å. In the third Ga site, Ga is bonded in a 12-coordinate geometry to four Dy, six Ni, and two equivalent Ga atoms. Both Ga–Ga bond lengths are 2.85 Å. In the fourth Ga site, Ga is bonded to four Dy, four Ni, and four Ga atoms to form distorted GaDy4Ga4Ni4 cuboctahedra that share corners with two equivalent NiDy4Ga4Ni4 cuboctahedra, corners with six GaDy4Ga2Ni6 cuboctahedra, faces with two equivalent NiDy4Ga4Ni4 cuboctahedra, and faces with seven GaDy4Ga2Ni6 cuboctahedra. There are two shorter (2.74 Å) and two longer (2.83 Å) Ga–Ga bond lengths. In the fifth Ga site, Ga is bonded in a 12-coordinate geometry to four Dy, four Ni, and four Ga atoms. There are two shorter (2.72 Å) and two longer (2.87 Å) Ga–Ga bond lengths. In the sixth Ga site, Ga is bonded to four Dy, four Ni, and four Ga atoms to form distorted GaDy4Ga4Ni4 cuboctahedra that share corners with two equivalent NiDy4Ga4Ni4 cuboctahedra, corners with eight GaDy4Ga2Ni6 cuboctahedra, faces with two equivalent NiDy4Ga4Ni4 cuboctahedra, and faces with seven GaDy4Ga2Ni6 cuboctahedra. There are two shorter (2.73 Å) and two longer (2.83 Å) Ga–Ga bond lengths. In the seventh Ga site, Ga is bonded to four Dy, four Ni, and four Ga atoms to form distorted GaDy4Ga4Ni4 cuboctahedra that share corners with two equivalent GaDy4Ga4Ni4 cuboctahedra, corners with four NiDy4Ga4Ni4 cuboctahedra, a faceface with one NiDy4Ga4Ni4 cuboctahedra, and faces with eight GaDy4Ga2Ni6 cuboctahedra. There are one shorter (2.61 Å) and one longer (2.63 Å) Ga–Ga bond lengths. In the eighth Ga site, Ga is bonded in a 12-coordinate geometry to four Dy, four Ni, and four Ga atoms. Both Ga–Ga bond lengths are 2.62 Å. In the ninth Ga site, Ga is bonded in a 12-coordinate geometry to four Dy, four Ni, and four Ga atoms. There are one shorter (2.62 Å) and one longer (2.63 Å) Ga–Ga bond lengths. In the tenth Ga site, Ga is bonded in a 12-coordinate geometry to four Dy, five Ni, and three Ga atoms. In the eleventh Ga site, Ga is bonded in a 12-coordinate geometry to four Dy, four Ni, and four Ga atoms. In the twelfth Ga site, Ga is bonded in a 12-coordinate geometry to four Dy, five Ni, and three Ga atoms. In the thirteenth Ga site, Ga is bonded in a 12-coordinate geometry to four Dy, five Ni, and three Ga atoms. In the fourteenth Ga site, Ga is bonded in a 12-coordinate geometry to four Dy, six Ni, and two equivalent Ga atoms. In the fifteenth Ga site, Ga is bonded in a 12-coordinate geometry to four Dy, five Ni, and three Ga atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on MgTi by Materials Project

MgTi is beta-derived structured and crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are three inequivalent Mg sites. In the first Mg site, Mg is bonded to five Mg and seven Ti atoms to form MgMg5Ti7 cuboctahedra that share corners with six equivalent TiMg6Ti6 cuboctahedra, corners with twelve MgMg5Ti7 cuboctahedra, edges with seven MgMg6Ti6 cuboctahedra, edges with eleven TiMg5Ti7 cuboctahedra, faces with nine MgMg5Ti7 cuboctahedra, and faces with eleven TiMg5Ti7 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 2.97–3.12 Å. There are a spread of Mg–Ti bond distances ranging from 3.01–3.05 Å. In the second Mg site, Mg is bonded to six Mg and six Ti atoms to form MgMg6Ti6 cuboctahedra that share corners with six equivalent MgMg6Ti6 cuboctahedra, corners with twelve TiMg7Ti5 cuboctahedra, edges with six MgMg5Ti7 cuboctahedra, edges with twelve TiMg5Ti7 cuboctahedra, faces with nine TiMg5Ti7 cuboctahedra, and faces with eleven MgMg5Ti7 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 2.97–3.12 Å. There are a spread of Mg–Ti bond distances ranging from 3.10–3.18 Å. In the third Mg site, Mg is bonded to seven Mg and five Ti atoms to form distorted MgMg7Ti5 cuboctahedra that share corners with six equivalent TiMg6Ti6 cuboctahedra, corners with twelve MgMg5Ti7 cuboctahedra, edges with five MgMg5Ti7 cuboctahedra, edges with thirteen TiMg5Ti7 cuboctahedra, faces with ten MgMg5Ti7 cuboctahedra, and faces with ten TiMg5Ti7 cuboctahedra. Both Mg–Mg bond lengths are 2.97 Å. There are a spread of Mg–Ti bond distances ranging from 2.97–3.13 Å. There are three inequivalent Ti sites. In the first Ti site, Ti is bonded to five Mg and seven Ti atoms to form distorted TiMg5Ti7 cuboctahedra that share corners with six equivalent MgMg6Ti6 cuboctahedra, corners with twelve TiMg7Ti5 cuboctahedra, edges with five TiMg6Ti6 cuboctahedra, edges with thirteen MgMg5Ti7 cuboctahedra, faces with ten MgMg5Ti7 cuboctahedra, and faces with ten TiMg5Ti7 cuboctahedra. There are a spread of Ti–Ti bond distances ranging from 2.78–3.34 Å. In the second Ti site, Ti is bonded to six Mg and six Ti atoms to form distorted TiMg6Ti6 cuboctahedra that share corners with six equivalent TiMg6Ti6 cuboctahedra, corners with twelve MgMg5Ti7 cuboctahedra, edges with six TiMg5Ti7 cuboctahedra, edges with twelve MgMg5Ti7 cuboctahedra, faces with nine MgMg5Ti7 cuboctahedra, and faces with eleven TiMg5Ti7 cuboctahedra. There are one shorter (2.75 Å) and two longer (2.97 Å) Ti–Ti bond lengths. In the third Ti site, Ti is bonded to seven Mg and five Ti atoms to form TiMg7Ti5 cuboctahedra that share corners with six equivalent MgMg6Ti6 cuboctahedra, corners with twelve TiMg7Ti5 cuboctahedra, edges with seven TiMg5Ti7 cuboctahedra, edges with eleven MgMg5Ti7 cuboctahedra, faces with nine TiMg5Ti7 cuboctahedra, and faces with eleven MgMg5Ti7 cuboctahedra. Both Ti–Ti bond lengths are 2.97 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Lu5B4Rh15 by Materials Project

Lu5Rh15B4 crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are three inequivalent Lu sites. In the first Lu site, Lu is bonded to twelve Rh atoms to form LuRh12 cuboctahedra that share corners with twelve LuRh12 cuboctahedra, faces with six LuRh12 cuboctahedra, and faces with four equivalent BRh6 octahedra. There are a spread of Lu–Rh bond distances ranging from 2.89–2.96 Å. In the second Lu site, Lu is bonded to twelve Rh atoms to form LuRh12 cuboctahedra that share corners with twelve LuRh12 cuboctahedra, faces with six LuRh12 cuboctahedra, and faces with eight BRh6 octahedra. There are a spread of Lu–Rh bond distances ranging from 2.93–2.96 Å. In the third Lu site, Lu is bonded to twelve Rh atoms to form LuRh12 cuboctahedra that share corners with twelve LuRh12 cuboctahedra, faces with six LuRh12 cuboctahedra, and faces with eight equivalent BRh6 octahedra. There are eight shorter (2.93 Å) and four longer (2.96 Å) Lu–Rh bond lengths. There are six inequivalent Rh sites. In the first Rh site, Rh is bonded in a distorted single-bond geometry to four equivalent Lu and one B atom. The Rh–B bond length is 2.04 Å. In the second Rh site, Rh is bonded to four equivalent Lu and two B atoms to form a mixture of distorted face, edge, and corner-sharing RhLu4B2 octahedra. The corner-sharing octahedra tilt angles range from 0–61°. There are one shorter (2.07 Å) and one longer (2.17 Å) Rh–B bond lengths. In the third Rh site, Rh is bonded to four equivalent Lu and two equivalent B atoms to form a mixture of distorted face, edge, and corner-sharing RhLu4B2 octahedra. The corner-sharing octahedra tilt angles range from 0–60°. Both Rh–B bond lengths are 2.09 Å. In the fourth Rh site, Rh is bonded in a distorted square co-planar geometry to four equivalent Lu atoms. In the fifth Rh site, Rh is bonded to four Lu and two equivalent B atoms to form a mixture of distorted face, edge, and corner-sharing RhLu4B2 octahedra. The corner-sharing octahedra tilt angles range from 0–61°. Both Rh–B bond lengths are 2.10 Å. In the sixth Rh site, Rh is bonded to four Lu and two equivalent B atoms to form a mixture of distorted face, edge, and corner-sharing RhLu4B2 octahedra. The corner-sharing octahedra tilt angles range from 0–61°. Both Rh–B bond lengths are 2.09 Å. There are two inequivalent B sites. In the first B site, B is bonded to six Rh atoms to form BRh6 octahedra that share corners with five BRh6 octahedra and faces with eight LuRh12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the second B site, B is bonded to six Rh atoms to form BRh6 octahedra that share corners with six BRh6 octahedra and faces with eight LuRh12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–2°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on YMg2 by Materials Project

Mg2Y is beta-derived structured and crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. there are four inequivalent Mg sites. In the first Mg site, Mg is bonded to ten Mg and two equivalent Y atoms to form MgY2Mg10 cuboctahedra that share corners with eighteen MgY2Mg10 cuboctahedra, edges with eight equivalent YY4Mg8 cuboctahedra, edges with ten MgY4Mg8 cuboctahedra, faces with eight YY4Mg8 cuboctahedra, and faces with twelve MgY2Mg10 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.33–3.44 Å. Both Mg–Y bond lengths are 3.34 Å. In the second Mg site, Mg is bonded to eight Mg and four equivalent Y atoms to form MgY4Mg8 cuboctahedra that share corners with eighteen MgY2Mg10 cuboctahedra, edges with six MgY2Mg10 cuboctahedra, edges with twelve YY4Mg8 cuboctahedra, faces with six YY4Mg8 cuboctahedra, and faces with fourteen MgY2Mg10 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.33–3.38 Å. All Mg–Y bond lengths are 3.33 Å. In the third Mg site, Mg is bonded to six Mg and six Y atoms to form MgY6Mg6 cuboctahedra that share corners with eighteen MgY2Mg10 cuboctahedra, edges with four equivalent YY4Mg8 cuboctahedra, edges with fourteen MgY2Mg10 cuboctahedra, faces with ten MgY2Mg10 cuboctahedra, and faces with ten YY4Mg8 cuboctahedra. Both Mg–Mg bond lengths are 3.38 Å. All Mg–Y bond lengths are 3.38 Å. In the fourth Mg site, Mg is bonded to eight Mg and four Y atoms to form MgY4Mg8 cuboctahedra that share corners with six equivalent MgY4Mg8 cuboctahedra, corners with twelve YY4Mg8 cuboctahedra, edges with six YY4Mg8 cuboctahedra, edges with twelve MgY2Mg10 cuboctahedra, faces with four YY4Mg8 cuboctahedra, and faces with sixteen MgY2Mg10 cuboctahedra. Both Mg–Mg bond lengths are 3.38 Å. There are two shorter (3.28 Å) and two longer (3.33 Å) Mg–Y bond lengths. There are two inequivalent Y sites. In the first Y site, Y is bonded to eight Mg and four Y atoms to form YY4Mg8 cuboctahedra that share corners with six equivalent MgY4Mg8 cuboctahedra, corners with twelve YY4Mg8 cuboctahedra, edges with three equivalent YY4Mg8 cuboctahedra, edges with fifteen MgY2Mg10 cuboctahedra, faces with six YY4Mg8 cuboctahedra, and faces with fourteen MgY2Mg10 cuboctahedra. There are two shorter (3.38 Å) and two longer (3.50 Å) Y–Y bond lengths. In the second Y site, Y is bonded to eight Mg and four Y atoms to form YY4Mg8 cuboctahedra that share corners with six equivalent MgY4Mg8 cuboctahedra, corners with twelve YY4Mg8 cuboctahedra, edges with three equivalent YY4Mg8 cuboctahedra, edges with fifteen MgY4Mg8 cuboctahedra, faces with six YY4Mg8 cuboctahedra, and faces with fourteen MgY2Mg10 cuboctahedra. Both Y–Y bond lengths are 3.38 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on YMg by Materials Project

MgY crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. there are three inequivalent Mg sites. In the first Mg site, Mg is bonded to six Mg and six Y atoms to form MgY6Mg6 cuboctahedra that share corners with six equivalent MgY6Mg6 cuboctahedra, corners with twelve YY8Mg4 cuboctahedra, edges with six YY8Mg4 cuboctahedra, edges with twelve MgY4Mg8 cuboctahedra, faces with ten MgY6Mg6 cuboctahedra, and faces with ten YY8Mg4 cuboctahedra. There are four shorter (3.42 Å) and two longer (3.45 Å) Mg–Mg bond lengths. All Mg–Y bond lengths are 3.41 Å. In the second Mg site, Mg is bonded to four Mg and eight Y atoms to form MgY8Mg4 cuboctahedra that share corners with six equivalent YY6Mg6 cuboctahedra, corners with twelve MgY4Mg8 cuboctahedra, edges with seven YY4Mg8 cuboctahedra, edges with eleven MgY4Mg8 cuboctahedra, faces with eight MgY6Mg6 cuboctahedra, and faces with twelve YY8Mg4 cuboctahedra. There are two shorter (3.40 Å) and two longer (3.45 Å) Mg–Mg bond lengths. All Mg–Y bond lengths are 3.42 Å. In the third Mg site, Mg is bonded to eight Mg and four Y atoms to form MgY4Mg8 cuboctahedra that share corners with six equivalent YY6Mg6 cuboctahedra, corners with twelve MgY4Mg8 cuboctahedra, edges with seven MgY6Mg6 cuboctahedra, edges with eleven YY8Mg4 cuboctahedra, faces with ten MgY6Mg6 cuboctahedra, and faces with ten YY8Mg4 cuboctahedra. Both Mg–Mg bond lengths are 3.45 Å. There are two shorter (3.39 Å) and two longer (3.44 Å) Mg–Y bond lengths. There are three inequivalent Y sites. In the first Y site, Y is bonded to four Mg and eight Y atoms to form YY8Mg4 cuboctahedra that share corners with six equivalent MgY6Mg6 cuboctahedra, corners with twelve YY8Mg4 cuboctahedra, edges with seven YY4Mg8 cuboctahedra, edges with eleven MgY4Mg8 cuboctahedra, faces with ten MgY6Mg6 cuboctahedra, and faces with ten YY8Mg4 cuboctahedra. There are four shorter (3.41 Å) and four longer (3.45 Å) Y–Y bond lengths. In the second Y site, Y is bonded to eight Mg and four Y atoms to form YY4Mg8 cuboctahedra that share corners with six equivalent MgY6Mg6 cuboctahedra, corners with twelve YY8Mg4 cuboctahedra, edges with seven MgY6Mg6 cuboctahedra, edges with eleven YY8Mg4 cuboctahedra, faces with eight YY8Mg4 cuboctahedra, and faces with twelve MgY6Mg6 cuboctahedra. Both Y–Y bond lengths are 3.45 Å. In the third Y site, Y is bonded to six Mg and six Y atoms to form YY6Mg6 cuboctahedra that share corners with six equivalent YY6Mg6 cuboctahedra, corners with twelve MgY4Mg8 cuboctahedra, edges with six MgY4Mg8 cuboctahedra, edges with twelve YY8Mg4 cuboctahedra, faces with ten MgY6Mg6 cuboctahedra, and faces with ten YY8Mg4 cuboctahedra. Both Y–Y bond lengths are 3.45 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on ErMg5 by Materials Project

Mg5Er is Magnesium-derived structured and crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. there are five inequivalent Mg sites. In the first Mg site, Mg is bonded to twelve Mg atoms to form MgMg12 cuboctahedra that share corners with eighteen MgMg12 cuboctahedra, edges with eight equivalent ErEr2Mg10 cuboctahedra, edges with ten MgEr4Mg8 cuboctahedra, faces with two equivalent ErEr2Mg10 cuboctahedra, and faces with eighteen MgMg12 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.20–3.27 Å. In the second Mg site, Mg is bonded to eight Mg and four equivalent Er atoms to form MgEr4Mg8 cuboctahedra that share corners with eighteen MgMg12 cuboctahedra, edges with four equivalent ErEr2Mg10 cuboctahedra, edges with fourteen MgMg12 cuboctahedra, faces with four equivalent ErEr2Mg10 cuboctahedra, and faces with sixteen MgMg12 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.22–3.35 Å. All Mg–Er bond lengths are 3.28 Å. In the third Mg site, Mg is bonded to ten Mg and two equivalent Er atoms to form MgEr2Mg10 cuboctahedra that share corners with eighteen MgMg12 cuboctahedra, edges with eighteen MgMg12 cuboctahedra, faces with six equivalent ErEr2Mg10 cuboctahedra, and faces with fourteen MgMg12 cuboctahedra. There are two shorter (3.22 Å) and four longer (3.27 Å) Mg–Mg bond lengths. Both Mg–Er bond lengths are 3.33 Å. In the fourth Mg site, Mg is bonded to ten Mg and two equivalent Er atoms to form MgEr2Mg10 cuboctahedra that share corners with six equivalent ErEr2Mg10 cuboctahedra, corners with twelve MgEr2Mg10 cuboctahedra, edges with three equivalent ErEr2Mg10 cuboctahedra, edges with fifteen MgMg12 cuboctahedra, faces with two equivalent ErEr2Mg10 cuboctahedra, and faces with eighteen MgMg12 cuboctahedra. There are two shorter (3.17 Å) and two longer (3.22 Å) Mg–Mg bond lengths. Both Mg–Er bond lengths are 3.29 Å. In the fifth Mg site, Mg is bonded to ten Mg and two equivalent Er atoms to form MgEr2Mg10 cuboctahedra that share corners with six equivalent ErEr2Mg10 cuboctahedra, corners with twelve MgEr2Mg10 cuboctahedra, edges with three equivalent ErEr2Mg10 cuboctahedra, edges with fifteen MgEr4Mg8 cuboctahedra, faces with two equivalent ErEr2Mg10 cuboctahedra, and faces with eighteen MgMg12 cuboctahedra. Both Mg–Mg bond lengths are 3.22 Å. Both Mg–Er bond lengths are 3.34 Å. Er is bonded to ten Mg and two equivalent Er atoms to form ErEr2Mg10 cuboctahedra that share corners with six equivalent ErEr2Mg10 cuboctahedra, corners with twelve MgEr2Mg10 cuboctahedra, edges with eighteen MgMg12 cuboctahedra, faces with four equivalent ErEr2Mg10 cuboctahedra, and faces with sixteen MgMg12 cuboctahedra. Both Er–Er bond lengths are 3.22 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on MgTi by Materials Project

MgTi is beta-derived structured and crystallizes in the monoclinic C2 space group. The structure is three-dimensional. there are two inequivalent Mg sites. In the first Mg site, Mg is bonded to four equivalent Mg and eight Ti atoms to form MgMg4Ti8 cuboctahedra that share corners with six equivalent MgMg4Ti8 cuboctahedra, corners with twelve TiMg7Ti5 cuboctahedra, edges with four equivalent TiMg8Ti4 cuboctahedra, edges with fourteen MgMg5Ti7 cuboctahedra, faces with eight equivalent MgMg5Ti7 cuboctahedra, and faces with twelve TiMg7Ti5 cuboctahedra. There are two shorter (2.94 Å) and two longer (2.99 Å) Mg–Mg bond lengths. There are a spread of Mg–Ti bond distances ranging from 3.01–3.08 Å. In the second Mg site, Mg is bonded to five Mg and seven Ti atoms to form distorted MgMg5Ti7 cuboctahedra that share corners with six equivalent TiMg8Ti4 cuboctahedra, corners with twelve equivalent MgMg5Ti7 cuboctahedra, edges with eight TiMg7Ti5 cuboctahedra, edges with ten MgMg4Ti8 cuboctahedra, faces with eight MgMg4Ti8 cuboctahedra, and faces with twelve TiMg7Ti5 cuboctahedra. There are one shorter (3.01 Å) and two longer (3.04 Å) Mg–Mg bond lengths. There are a spread of Mg–Ti bond distances ranging from 2.94–3.09 Å. There are four inequivalent Ti sites. In the first Ti site, Ti is bonded to seven Mg and five Ti atoms to form distorted TiMg7Ti5 cuboctahedra that share corners with six equivalent MgMg4Ti8 cuboctahedra, corners with twelve TiMg7Ti5 cuboctahedra, edges with eight equivalent MgMg5Ti7 cuboctahedra, edges with ten TiMg8Ti4 cuboctahedra, faces with eight TiMg7Ti5 cuboctahedra, and faces with twelve MgMg4Ti8 cuboctahedra. There are a spread of Ti–Ti bond distances ranging from 2.88–3.12 Å. In the second Ti site, Ti is bonded to seven Mg and five Ti atoms to form distorted TiMg7Ti5 cuboctahedra that share corners with six equivalent MgMg4Ti8 cuboctahedra, corners with twelve TiMg7Ti5 cuboctahedra, edges with eight equivalent MgMg5Ti7 cuboctahedra, edges with ten TiMg8Ti4 cuboctahedra, faces with eight TiMg7Ti5 cuboctahedra, and faces with twelve MgMg4Ti8 cuboctahedra. There are a spread of Ti–Mg bond distances ranging from 2.94–3.09 Å. There are a spread of Ti–Ti bond distances ranging from 2.88–3.01 Å. In the third Ti site, Ti is bonded to eight Mg and four Ti atoms to form TiMg8Ti4 cuboctahedra that share corners with six equivalent TiMg8Ti4 cuboctahedra, corners with twelve equivalent MgMg5Ti7 cuboctahedra, edges with four equivalent MgMg4Ti8 cuboctahedra, edges with fourteen TiMg7Ti5 cuboctahedra, faces with eight TiMg7Ti5 cuboctahedra, and faces with twelve MgMg4Ti8 cuboctahedra. The Ti–Ti bond length is 3.01 Å. In the fourth Ti site, Ti is bonded to seven Mg and five Ti atoms to form distorted TiMg7Ti5 cuboctahedra that share corners with six equivalent MgMg4Ti8 cuboctahedra, corners with twelve TiMg7Ti5 cuboctahedra, edges with eight equivalent MgMg5Ti7 cuboctahedra, edges with ten TiMg8Ti4 cuboctahedra, faces with eight TiMg7Ti5 cuboctahedra, and faces with twelve MgMg4Ti8 cuboctahedra. The Ti–Ti bond length is 3.12 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ba4Nb2WO12 by Materials Project

Ba4Nb2WO12 crystallizes in the trigonal R3m space group. The structure is three-dimensional. there are four inequivalent Ba2+ sites. In the first Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with nine BaO12 cuboctahedra, faces with seven BaO12 cuboctahedra, faces with three equivalent WO6 octahedra, and faces with four NbO6 octahedra. There are a spread of Ba–O bond distances ranging from 2.79–2.94 Å. In the second Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with nine BaO12 cuboctahedra, faces with seven BaO12 cuboctahedra, a faceface with one WO6 octahedra, and faces with six NbO6 octahedra. There are a spread of Ba–O bond distances ranging from 2.75–3.00 Å. In the third Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form distorted BaO12 cuboctahedra that share corners with nine BaO12 cuboctahedra, corners with three equivalent WO6 octahedra, faces with seven BaO12 cuboctahedra, and faces with four NbO6 octahedra. The corner-sharing octahedral tilt angles are 22°. There are a spread of Ba–O bond distances ranging from 2.87–3.23 Å. In the fourth Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form distorted BaO12 cuboctahedra that share corners with nine BaO12 cuboctahedra, corners with three equivalent NbO6 octahedra, faces with seven BaO12 cuboctahedra, a faceface with one NbO6 octahedra, and faces with three equivalent WO6 octahedra. The corner-sharing octahedral tilt angles are 25°. There are a spread of Ba–O bond distances ranging from 2.83–3.17 Å. There are two inequivalent Nb5+ sites. In the first Nb5+ site, Nb5+ is bonded to six O2- atoms to form NbO6 octahedra that share corners with three equivalent NbO6 octahedra, corners with three equivalent WO6 octahedra, and faces with eight BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 2–8°. There are three shorter (1.97 Å) and three longer (2.12 Å) Nb–O bond lengths. In the second Nb5+ site, Nb5+ is bonded to six O2- atoms to form distorted NbO6 octahedra that share corners with three equivalent BaO12 cuboctahedra, corners with three equivalent NbO6 octahedra, and faces with seven BaO12 cuboctahedra. The corner-sharing octahedral tilt angles are 8°. There are three shorter (1.87 Å) and three longer (2.28 Å) Nb–O bond lengths. W6+ is bonded to six O2- atoms to form WO6 octahedra that share corners with three equivalent BaO12 cuboctahedra, corners with three equivalent NbO6 octahedra, and faces with seven BaO12 cuboctahedra. The corner-sharing octahedral tilt angles are 2°. There is three shorter (1.87 Å) and three longer (2.10 Å) W–O bond length. There are four inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted linear geometry to four Ba2+, one Nb5+, and one W6+ atom. In the second O2- site, O2- is bonded in a 2-coordinate geometry to four Ba2+ and two Nb5+ atoms. In the third O2- site, O2- is bonded in a distorted single-bond geometry to four Ba2+ and one Nb5+ atom. In the fourth O2- site, O2- is bonded in a distorted single-bond geometry to four Ba2+ and one W6+ atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on La5B4Rh15 by Materials Project

La5Rh15B4 crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are three inequivalent La sites. In the first La site, La is bonded to twelve Rh atoms to form LaRh12 cuboctahedra that share corners with twelve LaRh12 cuboctahedra, faces with six LaRh12 cuboctahedra, and faces with four equivalent BRh6 octahedra. There are a spread of La–Rh bond distances ranging from 2.95–3.05 Å. In the second La site, La is bonded to twelve Rh atoms to form LaRh12 cuboctahedra that share corners with twelve LaRh12 cuboctahedra, faces with six LaRh12 cuboctahedra, and faces with eight BRh6 octahedra. There are four shorter (3.01 Å) and eight longer (3.03 Å) La–Rh bond lengths. In the third La site, La is bonded to twelve Rh atoms to form LaRh12 cuboctahedra that share corners with twelve LaRh12 cuboctahedra, faces with six LaRh12 cuboctahedra, and faces with eight equivalent BRh6 octahedra. There are eight shorter (3.02 Å) and four longer (3.03 Å) La–Rh bond lengths. There are six inequivalent Rh sites. In the first Rh site, Rh is bonded in a 1-coordinate geometry to four equivalent La and one B atom. The Rh–B bond length is 2.10 Å. In the second Rh site, Rh is bonded to four equivalent La and two B atoms to form a mixture of distorted edge, face, and corner-sharing RhLa4B2 octahedra. The corner-sharing octahedra tilt angles range from 0–61°. There are one shorter (2.14 Å) and one longer (2.18 Å) Rh–B bond lengths. In the third Rh site, Rh is bonded to four equivalent La and two equivalent B atoms to form a mixture of distorted edge, face, and corner-sharing RhLa4B2 octahedra. The corner-sharing octahedra tilt angles range from 0–60°. Both Rh–B bond lengths are 2.13 Å. In the fourth Rh site, Rh is bonded in a distorted square co-planar geometry to four equivalent La atoms. In the fifth Rh site, Rh is bonded to four La and two equivalent B atoms to form a mixture of distorted edge, face, and corner-sharing RhLa4B2 octahedra. The corner-sharing octahedra tilt angles range from 0–61°. Both Rh–B bond lengths are 2.15 Å. In the sixth Rh site, Rh is bonded to four La and two equivalent B atoms to form a mixture of distorted edge, face, and corner-sharing RhLa4B2 octahedra. The corner-sharing octahedra tilt angles range from 0–60°. Both Rh–B bond lengths are 2.14 Å. There are two inequivalent B sites. In the first B site, B is bonded to six Rh atoms to form BRh6 octahedra that share corners with five BRh6 octahedra and faces with eight LaRh12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the second B site, B is bonded to six Rh atoms to form BRh6 octahedra that share corners with six BRh6 octahedra and faces with eight LaRh12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–1°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ce4Pu by Materials Project

PuCe4 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Pu is bonded to six equivalent Pu and six equivalent Ce atoms to form PuCe6Pu6 cuboctahedra that share corners with six equivalent PuCe6Pu6 cuboctahedra, corners with six CeCe12 cuboctahedra, edges with six equivalent PuCe6Pu6 cuboctahedra, edges with eighteen CeCe9Pu3 cuboctahedra, faces with six equivalent PuCe6Pu6 cuboctahedra, and faces with twelve equivalent CeCe9Pu3 cuboctahedra. All Pu–Pu bond lengths are 3.21 Å. All Pu–Ce bond lengths are 3.14 Å. There are eight inequivalent Ce sites. In the first Ce site, Ce is bonded to three equivalent Pu and nine Ce atoms to form CeCe9Pu3 cuboctahedra that share corners with twelve CeCe9Pu3 cuboctahedra, edges with six equivalent PuCe6Pu6 cuboctahedra, edges with eighteen CeCe9Pu3 cuboctahedra, faces with six equivalent PuCe6Pu6 cuboctahedra, and faces with twelve CeCe9Pu3 cuboctahedra. There are six shorter (3.21 Å) and three longer (3.30 Å) Ce–Ce bond lengths. In the second Ce site, Ce is bonded to twelve Ce atoms to form CeCe12 cuboctahedra that share corners with three equivalent PuCe6Pu6 cuboctahedra, corners with nine CeCe9Pu3 cuboctahedra, edges with three equivalent PuCe6Pu6 cuboctahedra, edges with twenty-one CeCe9Pu3 cuboctahedra, and faces with eighteen CeCe9Pu3 cuboctahedra. There are six shorter (3.21 Å) and three longer (3.29 Å) Ce–Ce bond lengths. In the third Ce site, Ce is bonded to twelve Ce atoms to form CeCe12 cuboctahedra that share corners with three equivalent PuCe6Pu6 cuboctahedra, corners with nine CeCe9Pu3 cuboctahedra, edges with three equivalent PuCe6Pu6 cuboctahedra, edges with twenty-one CeCe9Pu3 cuboctahedra, and faces with eighteen CeCe9Pu3 cuboctahedra. There are six shorter (3.21 Å) and three longer (3.30 Å) Ce–Ce bond lengths. In the fourth Ce site, Ce is bonded to twelve Ce atoms to form CeCe12 cuboctahedra that share corners with three equivalent PuCe6Pu6 cuboctahedra, corners with nine CeCe9Pu3 cuboctahedra, edges with three equivalent PuCe6Pu6 cuboctahedra, edges with twenty-one CeCe9Pu3 cuboctahedra, and faces with eighteen CeCe9Pu3 cuboctahedra. There are a spread of Ce–Ce bond distances ranging from 3.21–3.30 Å. In the fifth Ce site, Ce is bonded to twelve Ce atoms to form CeCe12 cuboctahedra that share corners with three equivalent PuCe6Pu6 cuboctahedra, corners with nine CeCe9Pu3 cuboctahedra, edges with three equivalent PuCe6Pu6 cuboctahedra, edges with twenty-one CeCe9Pu3 cuboctahedra, and faces with eighteen CeCe9Pu3 cuboctahedra. There are six shorter (3.21 Å) and three longer (3.30 Å) Ce–Ce bond lengths. In the sixth Ce site, Ce is bonded to twelve Ce atoms to form CeCe12 cuboctahedra that share corners with three equivalent PuCe6Pu6 cuboctahedra, corners with fourteen CeCe12 cuboctahedra, edges with three equivalent PuCe6Pu6 cuboctahedra, edges with nineteen CeCe9Pu3 cuboctahedra, and faces with twenty-one CeCe9Pu3 cuboctahedra. There are a spread of Ce–Ce bond distances ranging from 3.21–3.30 Å. In the seventh Ce site, Ce is bonded to sixteen Ce atoms to form CeCe16 cuboctahedra that share corners with three equivalent PuCe6Pu6 cuboctahedra, corners with nineteen CeCe9Pu3 cuboctahedra, edges with three equivalent PuCe6Pu6 cuboctahedra, edges with twenty-one CeCe9Pu3 cuboctahedra, and faces with thirty-four CeCe12 cuboctahedra. There are a spread of Ce–Ce bond distances ranging from 3.21–6.42 Å. In the eighth Ce site, Ce is bonded to three equivalent Pu and nine Ce atoms to form CeCe9Pu3 cuboctahedra that share corners with seventeen CeCe9Pu3 cuboctahedra, edges with six equivalent PuCe6Pu6 cuboctahedra, edges with sixteen CeCe9Pu3 cuboctahedra, faces with six equivalent PuCe6Pu6 cuboctahedra, and faces with fifteen CeCe16 cuboctahedra. All Ce–Pu bond lengths are 3.14 Å. All Ce–Ce bond lengths are 3.21 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on U5B4Rh15 by Materials Project

U5Rh15B4 crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are three inequivalent U sites. In the first U site, U is bonded to twelve Rh atoms to form URh12 cuboctahedra that share corners with twelve URh12 cuboctahedra, faces with six URh12 cuboctahedra, and faces with four equivalent BRh6 octahedra. There are a spread of U–Rh bond distances ranging from 2.85–3.02 Å. In the second U site, U is bonded to twelve Rh atoms to form URh12 cuboctahedra that share corners with twelve URh12 cuboctahedra, faces with six URh12 cuboctahedra, and faces with eight BRh6 octahedra. There are a spread of U–Rh bond distances ranging from 2.96–3.00 Å. In the third U site, U is bonded to twelve Rh atoms to form URh12 cuboctahedra that share corners with twelve URh12 cuboctahedra, faces with six URh12 cuboctahedra, and faces with eight equivalent BRh6 octahedra. All U–Rh bond lengths are 2.98 Å. There are six inequivalent Rh sites. In the first Rh site, Rh is bonded in a distorted single-bond geometry to four equivalent U and one B atom. The Rh–B bond length is 2.00 Å. In the second Rh site, Rh is bonded to four equivalent U and two B atoms to form a mixture of distorted corner, edge, and face-sharing RhU4B2 octahedra. The corner-sharing octahedra tilt angles range from 0–60°. There are one shorter (2.11 Å) and one longer (2.22 Å) Rh–B bond lengths. In the third Rh site, Rh is bonded to four equivalent U and two equivalent B atoms to form a mixture of distorted corner, edge, and face-sharing RhU4B2 octahedra. The corner-sharing octahedra tilt angles range from 0–60°. Both Rh–B bond lengths are 2.15 Å. In the fourth Rh site, Rh is bonded in a distorted square co-planar geometry to four equivalent U atoms. In the fifth Rh site, Rh is bonded to four U and two equivalent B atoms to form a mixture of distorted corner, edge, and face-sharing RhU4B2 octahedra. The corner-sharing octahedra tilt angles range from 1–60°. Both Rh–B bond lengths are 2.11 Å. In the sixth Rh site, Rh is bonded to four U and two equivalent B atoms to form a mixture of distorted corner, edge, and face-sharing RhU4B2 octahedra. The corner-sharing octahedra tilt angles range from 0–60°. Both Rh–B bond lengths are 2.11 Å. There are two inequivalent B sites. In the first B site, B is bonded to six Rh atoms to form BRh6 octahedra that share corners with five BRh6 octahedra and faces with eight URh12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the second B site, B is bonded to six Rh atoms to form BRh6 octahedra that share corners with six BRh6 octahedra and faces with eight URh12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–2°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Lu4V5B18 by Materials Project

Lu4V5B18 crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are sixteen inequivalent Lu3+ sites. In the first Lu3+ site, Lu3+ is bonded in a 6-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.62–2.66 Å. In the second Lu3+ site, Lu3+ is bonded in a 12-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.62–2.71 Å. In the third Lu3+ site, Lu3+ is bonded in a 12-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.62–2.71 Å. In the fourth Lu3+ site, Lu3+ is bonded in a 6-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.62–2.66 Å. In the fifth Lu3+ site, Lu3+ is bonded in a 2-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.61–2.72 Å. In the sixth Lu3+ site, Lu3+ is bonded in a 2-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.61–2.72 Å. In the seventh Lu3+ site, Lu3+ is bonded in a 10-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.59–2.71 Å. In the eighth Lu3+ site, Lu3+ is bonded in a 10-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.59–2.71 Å. In the ninth Lu3+ site, Lu3+ is bonded in a 10-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.60–2.71 Å. In the tenth Lu3+ site, Lu3+ is bonded in a 10-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.59–2.71 Å. In the eleventh Lu3+ site, Lu3+ is bonded in a 10-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.60–2.71 Å. In the twelfth Lu3+ site, Lu3+ is bonded in a 10-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.60–2.72 Å. In the thirteenth Lu3+ site, Lu3+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing LuB12 cuboctahedra. There are a spread of Lu–B bond distances ranging from 2.47–2.50 Å. In the fourteenth Lu3+ site, Lu3+ is bonded to twelve B+1.33- atoms to form LuB12 cuboctahedra that share edges with two equivalent VB12 cuboctahedra, a faceface with one VB12 cuboctahedra, and faces with two equivalent LuB12 cuboctahedra. There are a spread of Lu–B bond distances ranging from 2.47–2.51 Å. In the fifteenth Lu3+ site, Lu3+ is bonded to twelve B+1.33- atoms to form LuB12 cuboctahedra that share edges with two equivalent VB12 cuboctahedra, a faceface with one VB12 cuboctahedra, and faces with two equivalent LuB12 cuboctahedra. There are a spread of Lu–B bond distances ranging from 2.46–2.51 Å. In the sixteenth Lu3+ site, Lu3+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing LuB12 cuboctahedra. There are a spread of Lu–B bond distances ranging from 2.47–2.50 Å. There are twenty inequivalent V+2.40+ sites. In the first V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.22–2.30 Å. In the second V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.22–2.29 Å. In the third V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.22–2.29 Å. In the fourth V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.22–2.30 Å. In the fifth V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.25–2.29 Å. In the sixth V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.25–2.29 Å. In the seventh V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.25–2.30 Å. In the eighth V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.24–2.29 Å. In the ninth V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.24–2.29 Å. In the tenth V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.24–2.29 Å. In the eleventh V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.25–2.28 Å. In the twelfth V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.25–2.28 Å. In the thirteenth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form VB12 cuboctahedra that share edges with two equivalent LuB12 cuboctahedra, a faceface with one LuB12 cuboctahedra, and faces with two equivalent VB12 cuboctahedra. There are a spread of V–B bond distances ranging from 2.41–2.44 Å. In the fourteenth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form VB12 cuboctahedra that share edges with two equivalent LuB12 cuboctahedra, a faceface with one LuB12 cuboctahedra, and faces with two equivalent VB12 cuboctahedra. There are two shorter (2.41 Å) and ten longer (2.43 Å) V–B bond lengths. In the fifteenth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing VB12 cuboctahedra. There are a spread of V–B bond distances ranging from 2.39–2.45 Å. In the sixteenth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing VB12 cuboctahedra. There are a spread of V–B bond distances ranging from 2.40–2.45 Å. In the seventeenth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing VB12 cuboctahedra. There are a spread of V–B bond distances ranging from 2.39–2.45 Å. In the eighteenth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing VB12 cuboctahedra. There are a spread of V–B bond distances ranging from 2.39–2.45 Å. In the nineteenth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing VB12 cuboctahedra. There are a spread of V–B bond distances ranging from 2.40–2.44 Å. In the twentieth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing VB12 cuboctahedra. There are a spread of V–B bond distances ranging from 2.40–2.44 Å. There are seventy-two inequivalent B+1.33- sites. In the first B+1.33- site, B+1.33- is bonded in a 3-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There is one shorter (1.75 Å) and two longer (1.76 Å) B–B bond length. In the second B+1.33- site, B+1.33- is bonded in a 3-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.74–1.76 Å. In the third B+1.33- site, B+1.33- is bonded in a 3-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.75–1.77 Å. In the fourth B+1.33- site, B+1.33- is bonded in a 3-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There is one shorter (1.74 Å) and one longer (1.75 Å) B–B bond length. In the fifth B+1.33- site, B+1.33- is bonded in a 3-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There is one shorter (1.74 Å) and one longer (1.75 Å) B–B bond length. In the sixth B+1.33- site, B+1.33- is bonded in a 3-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There is one shorter (1.74 Å) and one longer (1.75 Å) B–B bond length. In the seventh B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to six Lu3+ and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.80–1.97 Å. In the eighth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.72–1.87 Å. In the ninth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.72–1.88 Å. In the tenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to six Lu3+ and three B+1.33- atoms. There is one shorter (1.80 Å) and one longer (1.81 Å) B–B bond length. In the eleventh B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There is one shorter (1.72 Å) and one longer (1.88 Å) B–B bond length. In the twelfth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There is one shorter (1.71 Å) and one longer (1.88 Å) B–B bond length. In the thirteenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.77–1.83 Å. In the fourteenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.77–1.83 Å. In the fifteenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There is two shorter (1.78 Å) and one longer (1.84 Å) B–B bond length. In the sixteenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.77–1.83 Å. In the seventeenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.71–1.80 Å. In the eighteenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.71–1.80 Å. In the nineteenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.68–1.79 Å. In the twentieth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.68–1.79 Å. In the twenty-first B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.68–1.79 Å. In the twenty-second B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.68–1.79 Å. In the twenty-third B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There is one shorter (1.70 Å) and two longer (1.79 Å) B–B bond length. In the twenty-fourth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.70–1.79 Å. In the twenty-fifth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+,

36 MATERIALS SCIENCE↗