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Materials Data on CaHfMg30O32 by Materials Project

CaMg30HfO32 is alpha Po-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. Ca is bonded to six O atoms to form CaO6 octahedra that share corners with six MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. All Ca–O bond lengths are 2.26 Å. There are eight inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent CaO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.06–2.18 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent CaO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.05 Å) and four longer (2.19 Å) Mg–O bond lengths. In the third Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.13–2.18 Å. In the fourth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.15 Å) and two longer (2.19 Å) Mg–O bond lengths. In the fifth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one CaO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. There are two shorter (2.15 Å) and four longer (2.17 Å) Mg–O bond lengths. In the sixth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. There are a spread of Mg–O bond distances ranging from 2.15–2.17 Å. In the seventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one CaO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Mg–O bond distances ranging from 2.13–2.18 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Mg–O bond distances ranging from 2.11–2.22 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with six MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.12 Å) and four longer (2.21 Å) Hf–O bond lengths. There are nine inequivalent O sites. In the first O site, O is bonded to one Ca and five Mg atoms to form OCaMg5 octahedra that share corners with six OCaMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OCaMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the third O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the fourth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six equivalent OMg6 octahedra and edges with twelve OCaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the fifth O site, O is bonded to one Ca and five Mg atoms to form a mixture of edge and corner-sharing OCaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the sixth O site, O is bonded to one Ca and five Mg atoms to form a mixture of edge and corner-sharing OCaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are two shorter (2.17 Å) and two longer (2.18 Å) O–Mg bond lengths. In the seventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OCaMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the eighth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on RbHfMg14O15 by Materials Project

RbMg14HfO15 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. Rb is bonded in a 5-coordinate geometry to five O atoms. There are two shorter (2.60 Å) and three longer (2.75 Å) Rb–O bond lengths. There are ten inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with eight MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 3°. There are a spread of Mg–O bond distances ranging from 2.00–2.18 Å. In the second Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 8°. There are a spread of Mg–O bond distances ranging from 2.01–2.09 Å. In the third Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share a cornercorner with one MgO6 octahedra, corners with four equivalent MgO5 square pyramids, and edges with four MgO6 octahedra. The corner-sharing octahedral tilt angles are 4°. There are a spread of Mg–O bond distances ranging from 1.98–2.24 Å. In the fourth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four equivalent MgO6 octahedra, a cornercorner with one MgO5 square pyramid, edges with six MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–9°. There are a spread of Mg–O bond distances ranging from 2.07–2.25 Å. In the fifth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share a cornercorner with one MgO6 octahedra, corners with two equivalent MgO5 square pyramids, and edges with four MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.03–2.09 Å. In the sixth Mg site, Mg is bonded in a distorted T-shaped geometry to three O atoms. There are two shorter (2.17 Å) and one longer (2.41 Å) Mg–O bond lengths. In the seventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, a cornercorner with one MgO5 square pyramid, edges with eight MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 4–12°. There are a spread of Mg–O bond distances ranging from 2.06–2.27 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, edges with six MgO6 octahedra, and edges with four MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 4–12°. There are a spread of Mg–O bond distances ranging from 2.08–2.53 Å. In the ninth Mg site, Mg is bonded in a rectangular see-saw-like geometry to four O atoms. There are a spread of Mg–O bond distances ranging from 2.04–2.10 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four equivalent MgO6 octahedra, edges with seven MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 3–11°. There are a spread of Mg–O bond distances ranging from 2.07–2.32 Å. Hf is bonded in a 4-coordinate geometry to four O atoms. There are two shorter (2.00 Å) and two longer (2.21 Å) Hf–O bond lengths. There are eleven inequivalent O sites. In the first O site, O is bonded to one Rb and five Mg atoms to form ORbMg5 octahedra that share corners with two equivalent ORbMg5 octahedra, a cornercorner with one OMg5 square pyramid, corners with four ORbHfMg3 trigonal bipyramids, edges with four OMg6 octahedra, and edges with four equivalent OMg5 square pyramids. The corner-sharing octahedral tilt angles are 6°. In the second O site, O is bonded to five Mg atoms to form OMg5 square pyramids that share a cornercorner with one ORbMg5 octahedra, corners with four OMg5 square pyramids, corners with four ORb2Mg3 trigonal bipyramids, and edges with eight OMg6 octahedra. The corner-sharing octahedral tilt angles are 0°. In the third O site, O is bonded to five Mg atoms to form OMg5 square pyramids that share corners with four OMg5 square pyramids, corners with four OHf2Mg3 trigonal bipyramids, and edges with eight OMg6 octahedra. In the fourth O site, O is bonded to five Mg atoms to form OMg5 square pyramids that share a cornercorner with one OMg6 octahedra, corners with four equivalent OMg5 square pyramids, and edges with six ORbMg5 octahedra. The corner-sharing octahedral tilt angles are 2°. In the fifth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four equivalent OMg6 octahedra, a cornercorner with one OMg5 square pyramid, edges with four OMg6 octahedra, edges with four OMg5 square pyramids, and edges with four ORb2Mg3 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 2–6°. In the sixth O site, O is bonded to two equivalent Rb and three Mg atoms to form ORb2Mg3 trigonal bipyramids that share corners with three ORbMg5 octahedra, corners with two equivalent OMg5 square pyramids, corners with four ORb2Mg3 trigonal bipyramids, edges with two equivalent OMg6 octahedra, and edges with four equivalent ORbHfMg3 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 0–53°. In the seventh O site, O is bonded to three Mg and two equivalent Hf atoms to form OHf2Mg3 trigonal bipyramids that share a cornercorner with one OMg6 octahedra, corners with two equivalent OMg5 square pyramids, corners with four OHf2Mg3 trigonal bipyramids, edges with two equivalent OMg6 octahedra, and edges with four equivalent ORbHfMg3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 0°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, a cornercorner with one ORb2Mg3 trigonal bipyramid, edges with eight ORbMg5 octahedra, and edges with four OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 3–4°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, a cornercorner with one OHf2Mg3 trigonal bipyramid, edges with six OMg6 octahedra, and edges with four OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 4–16°. In the tenth O site, O is bonded to one Rb, three Mg, and one Hf atom to form distorted ORbHfMg3 trigonal bipyramids that share corners with two ORbMg5 octahedra, corners with two OMg5 square pyramids, corners with four equivalent ORbHfMg3 trigonal bipyramids, edges with two equivalent OMg6 octahedra, and edges with four OHf2Mg3 trigonal bipyramids. The corner-sharing octahedra tilt angles range from 9–60°. In the eleventh O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four equivalent OMg6 octahedra, a cornercorner with one ORbHfMg3 trigonal bipyramid, edges with seven ORbMg5 octahedra, and edges with four OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 3–10°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfScSi2 by Materials Project

ScHfSi2 crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. Sc is bonded in a 5-coordinate geometry to seven Si atoms. There are a spread of Sc–Si bond distances ranging from 2.71–2.93 Å. Hf is bonded in a 5-coordinate geometry to seven Si atoms. There are a spread of Hf–Si bond distances ranging from 2.73–2.91 Å. There are two inequivalent Si sites. In the first Si site, Si is bonded in a 9-coordinate geometry to four equivalent Sc, three equivalent Hf, and two equivalent Si atoms. Both Si–Si bond lengths are 2.46 Å. In the second Si site, Si is bonded in a 9-coordinate geometry to three equivalent Sc, four equivalent Hf, and two equivalent Si atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ho2Hf2O5 by Materials Project

Ho2Hf2O5 crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are two inequivalent Ho sites. In the first Ho site, Ho is bonded in a distorted body-centered cubic geometry to eight equivalent O atoms. All Ho–O bond lengths are 2.82 Å. In the second Ho site, Ho is bonded to twelve O atoms to form HoO12 cuboctahedra that share corners with four equivalent HoO12 cuboctahedra, faces with four equivalent HoO12 cuboctahedra, and faces with eight equivalent HfO5 square pyramids. There are eight shorter (2.71 Å) and four longer (2.90 Å) Ho–O bond lengths. Hf is bonded to five O atoms to form HfO5 square pyramids that share corners with five equivalent HfO5 square pyramids and faces with four equivalent HoO12 cuboctahedra. There are four shorter (2.07 Å) and one longer (2.08 Å) Hf–O bond lengths. There are two inequivalent O sites. In the first O site, O is bonded to four Ho and two equivalent Hf atoms to form a mixture of distorted edge, face, and corner-sharing OHo4Hf2 octahedra. The corner-sharing octahedra tilt angles range from 0–65°. In the second O site, O is bonded in a linear geometry to four equivalent Ho and two equivalent Hf atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on RbHfMg6O7 by Materials Project

RbMg6HfO7 crystallizes in the tetragonal P4mm space group. The structure is two-dimensional and consists of one RbMg6HfO7 sheet oriented in the (0, 0, 1) direction. Rb is bonded in a 4-coordinate geometry to four equivalent O atoms. All Rb–O bond lengths are 2.91 Å. There are four inequivalent Mg sites. In the first Mg site, Mg is bonded to five O atoms to form a mixture of distorted corner and edge-sharing MgO5 square pyramids. There are one shorter (1.97 Å) and four longer (2.11 Å) Mg–O bond lengths. In the second Mg site, Mg is bonded to five O atoms to form a mixture of distorted corner and edge-sharing MgO5 trigonal bipyramids. There are one shorter (2.05 Å) and four longer (2.12 Å) Mg–O bond lengths. In the third Mg site, Mg is bonded in a single-bond geometry to one O atom. The Mg–O bond length is 2.04 Å. In the fourth Mg site, Mg is bonded to five O atoms to form a mixture of distorted corner and edge-sharing MgO5 trigonal bipyramids. There are a spread of Mg–O bond distances ranging from 1.99–2.13 Å. Hf is bonded in a 5-coordinate geometry to five O atoms. There are one shorter (1.89 Å) and four longer (2.11 Å) Hf–O bond lengths. There are five inequivalent O sites. In the first O site, O is bonded to five Mg atoms to form distorted corner-sharing OMg5 trigonal bipyramids. In the second O site, O is bonded to four equivalent Rb and one Hf atom to form a mixture of distorted corner and edge-sharing ORb4Hf square pyramids. In the third O site, O is bonded in a 5-coordinate geometry to five Mg atoms. In the fourth O site, O is bonded in a 3-coordinate geometry to one Mg and two equivalent Hf atoms. In the fifth O site, O is bonded to five Mg atoms to form a mixture of distorted corner and edge-sharing OMg5 trigonal bipyramids.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on CeHfMg30O32 by Materials Project

Mg30CeHfO32 is alpha Po-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are eight inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent CeO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.00–2.21 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.13–2.17 Å. In the third Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.14 Å) and two longer (2.19 Å) Mg–O bond lengths. In the fourth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.16 Å) and two longer (2.17 Å) Mg–O bond lengths. In the fifth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one CeO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Mg–O bond distances ranging from 2.08–2.25 Å. In the sixth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.15–2.18 Å. In the seventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one CeO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. There are a spread of Mg–O bond distances ranging from 2.10–2.24 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Mg–O bond distances ranging from 2.12–2.22 Å. Ce is bonded to six O atoms to form CeO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.27 Å) and four longer (2.34 Å) Ce–O bond lengths. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with two equivalent CeO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.09 Å) and four longer (2.21 Å) Hf–O bond lengths. There are fourteen inequivalent O sites. In the first O site, O is bonded to five Mg and one Ce atom to form OCeMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OCeMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the second O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OCeMg5 octahedra and edges with twelve OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the third O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. Both O–Mg bond lengths are 2.18 Å. In the fourth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. Both O–Mg bond lengths are 2.18 Å. In the fifth O site, O is bonded to five Mg and one Ce atom to form a mixture of edge and corner-sharing OCeMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of O–Mg bond distances ranging from 2.00–2.24 Å. In the sixth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OCeMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are two shorter (2.10 Å) and two longer (2.18 Å) O–Mg bond lengths. In the seventh O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are two shorter (2.12 Å) and two longer (2.18 Å) O–Mg bond lengths. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six equivalent OMg6 octahedra and edges with twelve OCeMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. In the ninth O site, O is bonded to four equivalent Mg, one Ce, and one Hf atom to form OCeHfMg4 octahedra that share corners with six OCeHfMg4 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the tenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OCeHfMg4 octahedra and edges with twelve OCeMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the eleventh O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the twelfth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. The O–Mg bond length is 2.20 Å. In the thirteenth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. The O–Mg bond length is 2.17 Å. In the fourteenth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of O–Mg bond distances ranging from 2.10–2.20 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMg30SiO32 by Materials Project

Mg30HfSiO32 is alpha Po-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are eight inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 octahedra, corners with two equivalent SiO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.06–2.16 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent SiO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.08 Å) and four longer (2.16 Å) Mg–O bond lengths. In the third Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.15 Å) and two longer (2.16 Å) Mg–O bond lengths. In the fourth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.10 Å) and four longer (2.16 Å) Mg–O bond lengths. In the fifth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, an edgeedge with one SiO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–7°. There are a spread of Mg–O bond distances ranging from 2.12–2.19 Å. In the sixth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.15–2.17 Å. In the seventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one SiO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. There are a spread of Mg–O bond distances ranging from 2.14–2.18 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–2°. There are a spread of Mg–O bond distances ranging from 2.12–2.20 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with six MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.16 Å) and two longer (2.22 Å) Hf–O bond lengths. Si is bonded to six O atoms to form SiO6 octahedra that share corners with six MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. All Si–O bond lengths are 2.25 Å. There are ten inequivalent O sites. In the first O site, O is bonded to five Mg and one Si atom to form OMg5Si octahedra that share corners with six OMg5Si octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg5Si octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the third O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedral tilt angles are 0°. In the fourth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six equivalent OMg6 octahedra and edges with twelve OMg5Si octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fifth O site, O is bonded to five Mg and one Si atom to form a mixture of edge and corner-sharing OMg5Si octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the sixth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OMg5Si octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the seventh O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. Both O–Mg bond lengths are 2.12 Å. In the tenth O site, O is bonded to five Mg and one Si atom to form a mixture of edge and corner-sharing OMg5Si octahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of O–Mg bond distances ranging from 2.06–2.18 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMg30SnO32 by Materials Project

Mg30HfSnO32 is alpha Po-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are eight inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent SnO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (1.98 Å) and four longer (2.19 Å) Mg–O bond lengths. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.10–2.18 Å. In the third Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.14 Å) and two longer (2.17 Å) Mg–O bond lengths. In the fourth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.16 Å) and two longer (2.17 Å) Mg–O bond lengths. In the fifth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, an edgeedge with one SnO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–8°. There are a spread of Mg–O bond distances ranging from 2.08–2.26 Å. In the sixth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.16–2.18 Å. In the seventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one SnO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–7°. There are a spread of Mg–O bond distances ranging from 2.13–2.21 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Mg–O bond distances ranging from 2.14–2.20 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with two equivalent SnO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.02 Å) and four longer (2.24 Å) Hf–O bond lengths. Sn is bonded to six O atoms to form SnO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.32 Å) and four longer (2.35 Å) Sn–O bond lengths. There are ten inequivalent O sites. In the first O site, O is bonded to five Mg and one Sn atom to form OMg5Sn octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg5Sn octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the second O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OMg5Sn octahedra and edges with twelve OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the third O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. Both O–Mg bond lengths are 2.17 Å. In the fourth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the fifth O site, O is bonded to five Mg and one Sn atom to form a mixture of edge and corner-sharing OMg5Sn octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of O–Mg bond distances ranging from 1.98–2.21 Å. In the sixth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OMg5Sn octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the seventh O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six equivalent OMg6 octahedra and edges with twelve OMg5Sn octahedra. The corner-sharing octahedra tilt angles range from 1–6°. In the eighth O site, O is bonded to four equivalent Mg, one Hf, and one Sn atom to form OHfMg4Sn octahedra that share corners with six OHfMg4Sn octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg4Sn octahedra and edges with twelve OMg5Sn octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the tenth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on LaHfMg30O32 by Materials Project

Mg30LaHfO32 is alpha Po-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are eight inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent LaO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 1.99–2.23 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.15–2.18 Å. In the third Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.15 Å) and two longer (2.20 Å) Mg–O bond lengths. In the fourth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.17 Å) and two longer (2.18 Å) Mg–O bond lengths. In the fifth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one LaO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Mg–O bond distances ranging from 2.07–2.28 Å. In the sixth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.16–2.19 Å. In the seventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one LaO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–5°. There are a spread of Mg–O bond distances ranging from 2.10–2.26 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. There are a spread of Mg–O bond distances ranging from 2.12–2.23 Å. La is bonded to six O atoms to form LaO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.30 Å) and four longer (2.36 Å) La–O bond lengths. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with two equivalent LaO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.07 Å) and four longer (2.19 Å) Hf–O bond lengths. There are fifteen inequivalent O sites. In the first O site, O is bonded to five Mg and one La atom to form OLaMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OLaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the second O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OLaMg5 octahedra and edges with twelve OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the third O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. Both O–Mg bond lengths are 2.19 Å. In the fourth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. Both O–Mg bond lengths are 2.19 Å. In the fifth O site, O is bonded to five Mg and one La atom to form a mixture of edge and corner-sharing OLaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of O–Mg bond distances ranging from 1.99–2.26 Å. In the sixth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OLaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are two shorter (2.10 Å) and two longer (2.19 Å) O–Mg bond lengths. In the seventh O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are two shorter (2.12 Å) and two longer (2.19 Å) O–Mg bond lengths. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six equivalent OMg6 octahedra and edges with twelve OLaMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–6°. In the ninth O site, O is bonded to four equivalent Mg, one La, and one Hf atom to form OLaHfMg4 octahedra that share corners with six OLaHfMg4 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the tenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OLaHfMg4 octahedra and edges with twelve OLaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the eleventh O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OLaHfMg4 octahedra and edges with twelve OLaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are two shorter (2.07 Å) and two longer (2.19 Å) O–Mg bond lengths. In the twelfth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the thirteenth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. The O–Mg bond length is 2.21 Å. In the fourteenth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. The O–Mg bond length is 2.18 Å. In the fifteenth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of O–Mg bond distances ranging from 2.10–2.21 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on SrHfMg30O32 by Materials Project

SrMg30HfO32 is alpha Po-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. Sr is bonded to six O atoms to form SrO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.31 Å) and four longer (2.35 Å) Sr–O bond lengths. There are eight inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent SrO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (1.99 Å) and four longer (2.20 Å) Mg–O bond lengths. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.10–2.18 Å. In the third Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.14 Å) and two longer (2.17 Å) Mg–O bond lengths. In the fourth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. All Mg–O bond lengths are 2.16 Å. In the fifth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one SrO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–7°. There are a spread of Mg–O bond distances ranging from 2.06–2.28 Å. In the sixth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Mg–O bond distances ranging from 2.15–2.19 Å. In the seventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one SrO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–6°. There are a spread of Mg–O bond distances ranging from 2.11–2.23 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Mg–O bond distances ranging from 2.14–2.20 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with two equivalent SrO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.02 Å) and four longer (2.24 Å) Hf–O bond lengths. There are fourteen inequivalent O sites. In the first O site, O is bonded to one Sr and five Mg atoms to form a mixture of edge and corner-sharing OSrMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the second O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OSrMg5 octahedra and edges with twelve OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the third O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. Both O–Mg bond lengths are 2.17 Å. In the fourth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. Both O–Mg bond lengths are 2.17 Å. In the fifth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are two shorter (2.11 Å) and two longer (2.17 Å) O–Mg bond lengths. In the sixth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are two shorter (2.14 Å) and two longer (2.17 Å) O–Mg bond lengths. In the seventh O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six equivalent OMg6 octahedra and edges with twelve OSrMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–6°. In the eighth O site, O is bonded to one Sr, four equivalent Mg, and one Hf atom to form OSrHfMg4 octahedra that share corners with six OSrHfMg4 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OSrHfMg4 octahedra and edges with twelve OSrMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the tenth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the eleventh O site, O is bonded to one Sr and five Mg atoms to form a mixture of edge and corner-sharing OSrMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are two shorter (2.17 Å) and two longer (2.23 Å) O–Mg bond lengths. In the twelfth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. The O–Mg bond length is 2.20 Å. In the thirteenth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. The O–Mg bond length is 2.18 Å. In the fourteenth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of O–Mg bond distances ranging from 2.11–2.20 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Tb4HfAl15 by Materials Project

Tb4HfAl15 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. there are two inequivalent Tb sites. In the first Tb site, Tb is bonded to twelve Al atoms to form TbAl12 cuboctahedra that share corners with six equivalent AlTb2Hf2Al8 cuboctahedra, corners with nine TbAl12 cuboctahedra, a faceface with one HfAl12 cuboctahedra, and faces with six TbAl12 cuboctahedra. There are a spread of Tb–Al bond distances ranging from 3.02–3.06 Å. In the second Tb site, Tb is bonded to twelve Al atoms to form TbAl12 cuboctahedra that share corners with twelve TbAl12 cuboctahedra, edges with six equivalent AlTb2Hf2Al8 cuboctahedra, faces with three equivalent TbAl12 cuboctahedra, faces with three equivalent HfAl12 cuboctahedra, and faces with three equivalent AlTb2Hf2Al8 cuboctahedra. There are a spread of Tb–Al bond distances ranging from 2.97–3.03 Å. Hf is bonded to twelve Al atoms to form HfAl12 cuboctahedra that share corners with six equivalent HfAl12 cuboctahedra, edges with six equivalent AlTb2Hf2Al8 cuboctahedra, faces with six equivalent AlTb2Hf2Al8 cuboctahedra, and faces with eight TbAl12 cuboctahedra. There are six shorter (2.99 Å) and six longer (3.03 Å) Hf–Al bond lengths. There are three inequivalent Al sites. In the first 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 four equivalent TbAl12 cuboctahedra, corners with six equivalent AlTb2Hf2Al8 cuboctahedra, edges with two equivalent HfAl12 cuboctahedra, edges with four equivalent TbAl12 cuboctahedra, edges with four equivalent AlTb2Hf2Al8 cuboctahedra, faces with two equivalent TbAl12 cuboctahedra, faces with two equivalent HfAl12 cuboctahedra, and faces with four equivalent AlTb2Hf2Al8 cuboctahedra. There are four shorter (2.86 Å) and four longer (3.03 Å) Al–Al bond lengths. In the second Al site, Al is bonded in a distorted square co-planar geometry to four Tb and two equivalent Al atoms. Both Al–Al bond lengths are 3.00 Å. In the third Al site, Al is bonded in a 4-coordinate geometry to three Tb, one Hf, and six Al atoms. Both Al–Al bond lengths are 2.77 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMg30NbO32 by Materials Project

Mg30HfNbO32 is alpha Po-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are eight inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 octahedra, corners with two equivalent NbO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.05–2.17 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent NbO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.06 Å) and four longer (2.17 Å) Mg–O bond lengths. In the third Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.14–2.16 Å. In the fourth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.11 Å) and four longer (2.16 Å) Mg–O bond lengths. In the fifth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, an edgeedge with one NbO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–8°. There are a spread of Mg–O bond distances ranging from 2.13–2.19 Å. In the sixth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.15–2.17 Å. In the seventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one NbO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. There are a spread of Mg–O bond distances ranging from 2.14–2.19 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.12–2.20 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with six MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.16 Å) and two longer (2.21 Å) Hf–O bond lengths. Nb is bonded to six O atoms to form NbO6 octahedra that share corners with six MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. All Nb–O bond lengths are 2.27 Å. There are nine inequivalent O sites. In the first O site, O is bonded to five Mg and one Nb atom to form OMg5Nb octahedra that share corners with six OMg5Nb octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg5Nb octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the third O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the fourth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six equivalent OMg6 octahedra and edges with twelve OMg5Nb octahedra. The corner-sharing octahedra tilt angles range from 1–3°. In the fifth O site, O is bonded to five Mg and one Nb atom to form a mixture of edge and corner-sharing OMg5Nb octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the sixth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OMg5Nb octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the seventh O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the ninth O site, O is bonded to five Mg and one Nb atom to form a mixture of edge and corner-sharing OMg5Nb octahedra. The corner-sharing octahedra tilt angles range from 0–5°. There are a spread of O–Mg bond distances ranging from 2.05–2.19 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMg30CdO32 by Materials Project

Mg30HfCdO32 is Molybdenum Carbide MAX Phase-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are eight inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 octahedra, corners with two equivalent CdO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 1.94–2.24 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent CdO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (1.94 Å) and four longer (2.22 Å) Mg–O bond lengths. In the third Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.11–2.20 Å. In the fourth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.13 Å) and two longer (2.21 Å) Mg–O bond lengths. In the fifth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, an edgeedge with one CdO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 4–16°. There are a spread of Mg–O bond distances ranging from 2.12–2.23 Å. In the sixth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–4°. There are a spread of Mg–O bond distances ranging from 2.15–2.18 Å. In the seventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one CdO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–13°. There are a spread of Mg–O bond distances ranging from 2.15–2.19 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–7°. There are a spread of Mg–O bond distances ranging from 2.10–2.23 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with six MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.09 Å) and two longer (2.11 Å) Hf–O bond lengths. Cd is bonded to six O atoms to form CdO6 octahedra that share corners with six MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.38 Å) and four longer (2.40 Å) Cd–O bond lengths. There are eleven inequivalent O sites. In the first O site, O is bonded to five Mg and one Cd atom to form OMg5Cd octahedra that share corners with six OMg5Cd octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg5Cd octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the third O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fourth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg5Cd octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. There are two shorter (2.10 Å) and two longer (2.18 Å) O–Mg bond lengths. In the fifth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six equivalent OMg6 octahedra and edges with twelve OMg5Cd octahedra. The corner-sharing octahedra tilt angles range from 2–6°. In the sixth O site, O is bonded to five Mg and one Cd atom to form a mixture of distorted edge and corner-sharing OMg5Cd octahedra. The corner-sharing octahedra tilt angles range from 0–11°. In the seventh O site, O is bonded to five Mg and one Cd atom to form a mixture of distorted edge and corner-sharing OMg5Cd octahedra. The corner-sharing octahedra tilt angles range from 0–11°. There are two shorter (2.12 Å) and two longer (2.19 Å) O–Mg bond lengths. In the eighth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OMg5Cd octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–11°. In the ninth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the tenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the eleventh O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. There are two shorter (2.11 Å) and two longer (2.18 Å) O–Mg bond lengths.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on CsHfMg6O7 by Materials Project

CsMg6HfO7 crystallizes in the tetragonal P4mm space group. The structure is two-dimensional and consists of one CsMg6HfO7 sheet oriented in the (0, 0, 1) direction. Cs is bonded in a distorted square co-planar geometry to four equivalent O atoms. All Cs–O bond lengths are 3.00 Å. There are four inequivalent Mg sites. In the first Mg site, Mg is bonded to five O atoms to form a mixture of distorted edge and corner-sharing MgO5 trigonal bipyramids. There are one shorter (1.98 Å) and four longer (2.11 Å) Mg–O bond lengths. In the second Mg site, Mg is bonded to five O atoms to form a mixture of distorted edge and corner-sharing MgO5 trigonal bipyramids. There are one shorter (2.04 Å) and four longer (2.12 Å) Mg–O bond lengths. In the third Mg site, Mg is bonded in a single-bond geometry to one O atom. The Mg–O bond length is 2.03 Å. In the fourth Mg site, Mg is bonded to five O atoms to form a mixture of distorted edge and corner-sharing MgO5 trigonal bipyramids. There are a spread of Mg–O bond distances ranging from 1.99–2.14 Å. Hf is bonded in a 5-coordinate geometry to five O atoms. There are one shorter (1.89 Å) and four longer (2.12 Å) Hf–O bond lengths. There are five inequivalent O sites. In the first O site, O is bonded to five Mg atoms to form distorted corner-sharing OMg5 trigonal bipyramids. In the second O site, O is bonded in a distorted single-bond geometry to four equivalent Cs and one Hf atom. In the third O site, O is bonded in a 5-coordinate geometry to five Mg atoms. In the fourth O site, O is bonded in a 3-coordinate geometry to one Mg and two equivalent Hf atoms. In the fifth O site, O is bonded to five Mg atoms to form a mixture of distorted edge and corner-sharing OMg5 trigonal bipyramids.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfTi3 by Materials Project

HfTi3 is beta Cu3Ti-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Hf is bonded to twelve Ti atoms to form HfTi12 cuboctahedra that share corners with six equivalent HfTi12 cuboctahedra, corners with twelve TiHf4Ti8 cuboctahedra, edges with eighteen TiHf4Ti8 cuboctahedra, faces with eight equivalent HfTi12 cuboctahedra, and faces with twelve TiHf4Ti8 cuboctahedra. There are six shorter (2.98 Å) and six longer (3.01 Å) Hf–Ti bond lengths. There are two inequivalent Ti sites. In the first Ti site, Ti is bonded to four equivalent Hf and eight Ti atoms to form distorted TiHf4Ti8 cuboctahedra that share corners with four equivalent HfTi12 cuboctahedra, corners with fourteen TiHf4Ti8 cuboctahedra, edges with six equivalent HfTi12 cuboctahedra, edges with twelve TiHf4Ti8 cuboctahedra, faces with four equivalent HfTi12 cuboctahedra, and faces with sixteen TiHf4Ti8 cuboctahedra. There are a spread of Ti–Ti bond distances ranging from 2.91–3.11 Å. In the second Ti site, Ti is bonded to four equivalent Hf and eight equivalent Ti atoms to form distorted TiHf4Ti8 cuboctahedra that share corners with four equivalent HfTi12 cuboctahedra, corners with fourteen TiHf4Ti8 cuboctahedra, edges with six equivalent HfTi12 cuboctahedra, edges with twelve equivalent TiHf4Ti8 cuboctahedra, faces with four equivalent HfTi12 cuboctahedra, and faces with sixteen TiHf4Ti8 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMg30BiO32 by Materials Project

Mg30HfBiO32 is Caswellsilverite-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are eight inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent BiO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 1.87–2.27 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.10–2.20 Å. In the third Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.12 Å) and two longer (2.21 Å) Mg–O bond lengths. In the fourth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.15 Å) and four longer (2.17 Å) Mg–O bond lengths. In the fifth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, an edgeedge with one BiO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 4–13°. There are a spread of Mg–O bond distances ranging from 2.09–2.28 Å. In the sixth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Mg–O bond distances ranging from 2.16–2.20 Å. In the seventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one BiO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–14°. There are a spread of Mg–O bond distances ranging from 2.14–2.22 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–5°. There are a spread of Mg–O bond distances ranging from 2.12–2.24 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with two equivalent BiO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (1.97 Å) and four longer (2.15 Å) Hf–O bond lengths. Bi is bonded to six O atoms to form BiO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.39 Å) and four longer (2.48 Å) Bi–O bond lengths. There are eleven inequivalent O sites. In the first O site, O is bonded to five Mg and one Bi atom to form distorted OMg5Bi octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg5Bi octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the second O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OMg5Bi octahedra and edges with twelve OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the third O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the fourth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. Both O–Mg bond lengths are 2.19 Å. In the fifth O site, O is bonded to five Mg and one Bi atom to form a mixture of distorted corner and edge-sharing OMg5Bi octahedra. The corner-sharing octahedra tilt angles range from 0–8°. There are a spread of O–Mg bond distances ranging from 1.87–2.22 Å. In the sixth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are two shorter (2.12 Å) and two longer (2.19 Å) O–Mg bond lengths. In the seventh O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six equivalent OMg6 octahedra and edges with twelve OMg5Bi octahedra. The corner-sharing octahedra tilt angles range from 2–6°. In the eighth O site, O is bonded to four equivalent Mg, one Hf, and one Bi atom to form distorted OHfMg4Bi octahedra that share corners with six OHfMg4Bi octahedra and edges with twelve OMg5Bi octahedra. The corner-sharing octahedra tilt angles range from 0–10°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg4Bi octahedra and edges with twelve OMg5Bi octahedra. The corner-sharing octahedra tilt angles range from 0–10°. In the tenth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the eleventh O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. The O–Mg bond length is 2.18 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on BaHfMg30O32 by Materials Project

BaMg30HfO32 is Molybdenum Carbide MAX Phase-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. Ba is bonded to six O atoms to form BaO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.40 Å) and four longer (2.44 Å) Ba–O bond lengths. There are eight inequivalent Mg sites. In the first Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent BaO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 1.93–2.25 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent HfO6 octahedra, corners with four MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.13–2.19 Å. In the third Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.14 Å) and two longer (2.21 Å) Mg–O bond lengths. In the fourth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. All Mg–O bond lengths are 2.18 Å. In the fifth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one BaO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–10°. There are a spread of Mg–O bond distances ranging from 2.06–2.32 Å. In the sixth Mg site, Mg is bonded to six O atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Mg–O bond distances ranging from 2.16–2.21 Å. In the seventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one BaO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–9°. There are a spread of Mg–O bond distances ranging from 2.11–2.27 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Mg–O bond distances ranging from 2.14–2.23 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with two equivalent BaO6 octahedra, corners with four equivalent MgO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (1.99 Å) and four longer (2.22 Å) Hf–O bond lengths. There are ten inequivalent O sites. In the first O site, O is bonded to one Ba and five Mg atoms to form OBaMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OBaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the second O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OBaMg5 octahedra and edges with twelve OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the third O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. Both O–Mg bond lengths are 2.19 Å. In the fourth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the fifth O site, O is bonded to one Ba and five Mg atoms to form a mixture of corner and edge-sharing OBaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of O–Mg bond distances ranging from 1.93–2.27 Å. In the sixth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OBaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the seventh O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six equivalent OMg6 octahedra and edges with twelve OBaMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–7°. In the eighth O site, O is bonded to one Ba, four equivalent Mg, and one Hf atom to form OBaHfMg4 octahedra that share corners with six OBaHfMg4 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OBaHfMg4 octahedra and edges with twelve OBaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the tenth O site, O is bonded to six Mg atoms to form a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on PrHfO4 by Materials Project

PrHfO4 crystallizes in the tetragonal I4_1/a space group. The structure is three-dimensional. there are four inequivalent Pr4+ sites. In the first Pr4+ site, Pr4+ is bonded in a body-centered cubic geometry to eight equivalent O2- atoms. There are four shorter (2.45 Å) and four longer (2.50 Å) Pr–O bond lengths. In the second Pr4+ site, Pr4+ is bonded in a body-centered cubic geometry to eight equivalent O2- atoms. There are four shorter (2.45 Å) and four longer (2.50 Å) Pr–O bond lengths. In the third Pr4+ site, Pr4+ is bonded in a body-centered cubic geometry to eight equivalent O2- atoms. There are four shorter (2.45 Å) and four longer (2.50 Å) Pr–O bond lengths. In the fourth Pr4+ site, Pr4+ is bonded in a body-centered cubic geometry to eight equivalent O2- atoms. There are four shorter (2.45 Å) and four longer (2.50 Å) Pr–O bond lengths. There are four inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded in a distorted tetrahedral geometry to four equivalent O2- atoms. All Hf–O bond lengths are 2.01 Å. In the second Hf4+ site, Hf4+ is bonded in a distorted tetrahedral geometry to four equivalent O2- atoms. All Hf–O bond lengths are 2.01 Å. In the third Hf4+ site, Hf4+ is bonded in a distorted tetrahedral geometry to four equivalent O2- atoms. All Hf–O bond lengths are 2.01 Å. In the fourth Hf4+ site, Hf4+ is bonded in a distorted tetrahedral geometry to four equivalent O2- atoms. All Hf–O bond lengths are 2.01 Å. O2- is bonded in a 1-coordinate geometry to two Pr4+ and one Hf4+ atom.

36 MATERIALS SCIENCE↗