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DOE OSTI2020

Materials Data on HfMg30BO31 by Materials Project

Mg30HfO31B crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional and consists of one boron molecule and one Mg30HfO31 framework. In the Mg30HfO31 framework, there are sixteen inequivalent Mg sites. In the first Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with two equivalent HfO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.02–2.15 Å. In the second 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, 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 2.01–2.19 Å. In the third 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 ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.02–2.17 Å. In the fourth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.12–2.16 Å. In the fifth 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 2.13–2.15 Å. In the sixth 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 MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.11 Å) and four longer (2.14 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 six MgO6 octahedra, an edgeedge with one HfO6 octahedra, edges with seven MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 3–13°. There are a spread of Mg–O bond distances ranging from 2.07–2.24 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–4°. There are a spread of Mg–O bond distances ranging from 2.13–2.17 Å. In the ninth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–8°. There are a spread of Mg–O bond distances ranging from 2.11–2.17 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Mg–O bond distances ranging from 2.09–2.20 Å. In the eleventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with nine MgO6 octahedra, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 2–8°. There are a spread of Mg–O bond distances ranging from 2.12–2.17 Å. In the twelfth 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 2.10–2.20 Å. In the thirteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–9°. There are a spread of Mg–O bond distances ranging from 2.13–2.18 Å. In the fourteenth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, an edgeedge with one HfO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Mg–O bond distances ranging from 2.13–2.19 Å. In the fifteenth 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 1–9°. There are a spread of Mg–O bond distances ranging from 2.12–2.18 Å. In the sixteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.11–2.19 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Hf–O bond distances ranging from 2.10–2.19 Å. There are seventeen inequivalent O sites. In the first O site, O is bonded to five Mg atoms to form distorted OMg5 square pyramids that share corners with two equivalent OMg6 octahedra, corners with five OMg5 square pyramids, and edges with eight OMg6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OHfMg5 octahedra, corners with two equivalent OMg5 square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5 square pyramids. 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 five Mg atoms to form distorted OMg5 square pyramids that share corners with four OMg6 octahedra, corners with five OMg5 square pyramids, and edges with eight OMg6 octahedra. The corner-sharing octahedra tilt angles range from 4–5°. In the fifth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with two equivalent OHfMg5 octahedra, corners with two equivalent OMg5 square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5 square pyramids. The corner-sharing octahedral tilt angles are 0°. In the sixth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5 square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. In the seventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 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 eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra, edges with eight OMg6 octahedra, and edges with three OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 2–6°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra, edges with nine OMg6 octahedra, and edges with three OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 2–6°. In the tenth O site, O is bonded to five Mg atoms to form distorted OMg5 square pyramids that share corners with four OHfMg5 octahedra, corners with five OMg5 square pyramids, and edges with seven OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 5–8°. In the eleventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with four OHfMg5 octahedra, corners with two equivalent OMg5 square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 0–4°. In the twelfth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5 square pyramids, edges with nine OMg6 octahedra, and edges with two OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. In the thirteenth 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 0–4°. In the fourteenth O site, O is bonded to five Mg atoms to form distorted OMg5 square pyramids that share corners with four OHfMg5 octahedra, corners with five OMg5 square pyramids, and edges with eight OMg6 octahedra. The corner-sharing octahedra tilt angles range from 6–8°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with four OHfMg5 octahedra, corners with two equivalent OMg5 square pyramids, edges with nine OHfMg5 octahedra, and edges with two equivalent OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. In the sixteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5 square pyramids, edges with ten OMg6 octahedra, and edges with two OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. In the seventeenth 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°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMg30BO31 by Materials Project

Mg30HfBO31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. there are sixteen inequivalent Mg sites. In the first 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 0–1°. There are a spread of Mg–O bond distances ranging from 1.97–2.22 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 octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.11–2.20 Å. In the third Mg site, Mg is bonded to one B and five O atoms to form a mixture of distorted corner and edge-sharing MgBO5 octahedra. The corner-sharing octahedral tilt angles are 0°. The Mg–B bond length is 2.35 Å. There are a spread of Mg–O bond distances ranging from 2.00–2.23 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 MgBO5 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.10–2.20 Å. In the fifth 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 0–1°. There are a spread of Mg–O bond distances ranging from 2.07–2.19 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 0–1°. There are a spread of Mg–O bond distances ranging from 2.12–2.16 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 HfO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–15°. There are a spread of Mg–O bond distances ranging from 2.04–2.31 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra and edges with twelve MgBO5 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. There are a spread of Mg–O bond distances ranging from 2.13–2.19 Å. In the ninth Mg site, Mg is bonded to one B and five O atoms to form MgBO5 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with ten MgBO5 octahedra. The corner-sharing octahedra tilt angles range from 2–15°. The Mg–B bond length is 2.23 Å. There are a spread of Mg–O bond distances ranging from 2.10–2.19 Å. In the tenth 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 0–3°. There are a spread of Mg–O bond distances ranging from 2.12–2.18 Å. In the eleventh 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 ten MgBO5 octahedra. The corner-sharing octahedra tilt angles range from 1–10°. There are a spread of Mg–O bond distances ranging from 2.03–2.30 Å. In the twelfth 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 0–5°. There are a spread of Mg–O bond distances ranging from 2.12–2.19 Å. In the thirteenth Mg site, Mg is bonded to one B and five O atoms to form a mixture of corner and edge-sharing MgBO5 octahedra. The corner-sharing octahedra tilt angles range from 0–12°. The Mg–B bond length is 2.26 Å. There are a spread of Mg–O bond distances ranging from 2.05–2.22 Å. In the fourteenth 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 2–6°. There are a spread of Mg–O bond distances ranging from 2.08–2.23 Å. In the fifteenth 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 0–10°. There are a spread of Mg–O bond distances ranging from 2.09–2.20 Å. In the sixteenth 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 1–6°. There are a spread of Mg–O bond distances ranging from 2.08–2.21 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with four MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Hf–O bond distances ranging from 2.03–2.14 Å. B is bonded to five Mg atoms to form BMg5 square pyramids that share corners with four OHfMg5 octahedra, corners with five OMg5 square pyramids, and edges with eight OMg6 octahedra. The corner-sharing octahedra tilt angles range from 4–9°. There are seventeen inequivalent O sites. In the first O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with four OMg6 octahedra, corners with two equivalent BMg5 square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OHfMg4 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent BMg5 square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. In the third 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 0–3°. In the fourth O site, O is bonded to five Mg atoms to form OMg5 square pyramids that share corners with four OHfMg5 octahedra, a cornercorner with one BMg5 square pyramid, corners with four OHfMg4 square pyramids, and edges with eight OMg6 octahedra. The corner-sharing octahedra tilt angles range from 4–7°. In the fifth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with four OHfMg5 octahedra, corners with two equivalent OMg5 square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OHfMg4 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. In the sixth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5 square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. In the seventh 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 0–3°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra, edges with nine OHfMg5 octahedra, an edgeedge with one BMg5 square pyramid, and edges with two OHfMg4 square pyramids. The corner-sharing octahedra tilt angles range from 2–9°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra, edges with nine OHfMg5 octahedra, and edges with three OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 2–9°. In the tenth O site, O is bonded to four Mg and one Hf atom to form OHfMg4 square pyramids that share corners with four OMg6 octahedra, a cornercorner with one BMg5 square pyramid, corners with four OMg5 square pyramids, and edges with eight OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 3–13°. In the eleventh O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OHfMg4 square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 0–4°. In the twelfth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OHfMg4 square pyramids, edges with ten OHfMg5 octahedra, an edgeedge with one BMg5 square pyramid, and an edgeedge with one OMg5 square pyramid. The corner-sharing octahedra tilt angles range from 2–4°. In the thirteenth 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 fourteenth O site, O is bonded to five Mg atoms to form OMg5 square pyramids that share corners with four OHfMg5 octahedra, a cornercorner with one BMg5 square pyramid, corners with four OMg5 square pyramids, and edges with eight OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with four OHfMg5 octahedra, corners with two equivalent OMg5 square pyramids, edges with ten OHfMg5 octahedra, and edges with two equivalent OHfMg4 square pyramids. The corner-sharing octahedra tilt angles range from 0–5°. In the sixteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5 square pyramids, edges with ten OMg6 octahedra, an edgeedge with one BMg5 square pyramid, and an edgeedge with one OMg5 square pyramid. The corner-sharing octahedra tilt angles range from 1–2°. In the seventeenth 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 0–5°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMg30BO31 by Materials Project

Mg30HfBO31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. there are sixteen 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 BO6 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 2.02–2.17 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent HfO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.10–2.16 Å. In the third 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 BO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.02–2.17 Å. In the fourth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one HfO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.13–2.16 Å. In the fifth 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 a spread of Mg–O bond distances ranging from 2.12–2.16 Å. In the sixth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.12–2.15 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 BO6 octahedra, edges with eight MgO6 octahedra, an edgeedge with one HfO5 square pyramid, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–10°. There are a spread of Mg–O bond distances ranging from 2.09–2.22 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.14–2.16 Å. In the ninth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one HfO5 square pyramid, corners with four MgO5 square pyramids, an edgeedge with one BO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–10°. There are a spread of Mg–O bond distances ranging from 2.07–2.19 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Mg–O bond distances ranging from 2.13–2.17 Å. In the eleventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one BO6 octahedra, edges with nine MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one HfO5 square pyramid. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of Mg–O bond distances ranging from 2.10–2.20 Å. In the twelfth 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 1–2°. There are a spread of Mg–O bond distances ranging from 2.13–2.16 Å. In the thirteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one BO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–8°. There are a spread of Mg–O bond distances ranging from 2.13–2.16 Å. In the fourteenth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, a cornercorner with one HfO5 square pyramid, corners with four MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 1°. There are a spread of Mg–O bond distances ranging from 2.11–2.22 Å. In the fifteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one BO6 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 2.13–2.16 Å. In the sixteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, an edgeedge with one MgO5 square pyramid, and an edgeedge with one HfO5 square pyramid. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 2.11–2.17 Å. Hf is bonded to five O atoms to form HfO5 square pyramids that share corners with two equivalent MgO6 octahedra, corners with two equivalent BO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–6°. There are a spread of Hf–O bond distances ranging from 2.03–2.27 Å. B is bonded to six O atoms to form distorted BO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent HfO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of B–O bond distances ranging from 2.26–2.28 Å. There are seventeen inequivalent O sites. In the first O site, O is bonded to five Mg and one B atom to form distorted OMg5B square pyramids that share corners with two equivalent OMg6 octahedra, corners with two equivalent OMg5B square pyramids, edges with eight OMg6 octahedra, and edges with four OHfMg4B square pyramids. The corner-sharing octahedral tilt angles are 5°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5B square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5B square pyramids. The corner-sharing octahedral tilt angles are 0°. 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 octahedral tilt angles are 0°. In the fourth O site, O is bonded to five Mg and one B atom to form distorted OMg5B square pyramids that share corners with four OHfMg5 octahedra, corners with two equivalent OMg5B square pyramids, edges with eight OMg6 octahedra, and edges with four OHfMg4B square pyramids. The corner-sharing octahedra tilt angles range from 2–4°. In the fifth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with two equivalent OMg6 octahedra, corners with two equivalent OMg5B square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OHfMg4B square pyramids. The corner-sharing octahedral tilt angles are 1°. In the sixth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5B square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5B square pyramids. The corner-sharing octahedra tilt angles range from 0–1°. In the seventh 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 eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra, edges with eight OMg6 octahedra, and edges with three OMg5B square pyramids. 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 OMg6 octahedra, edges with nine OHfMg5 octahedra, and edges with three OMg5B square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. In the tenth O site, O is bonded to four Mg, one Hf, and one B atom to form distorted OHfMg4B square pyramids that share corners with four OMg6 octahedra, corners with two equivalent OHfMg4B square pyramids, edges with seven OHfMg5 octahedra, and edges with four OMg5B square pyramids. The corner-sharing octahedra tilt angles range from 7–8°. In the eleventh O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OHfMg4B square pyramids, edges with ten OMg6 octahedra, and edges with two equivalent OMg5B square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. In the twelfth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OHfMg4B square pyramids, edges with nine OHfMg5 octahedra, and edges with two OMg5B square pyramids. The corner-sharing octahedra tilt angles range from 0–2°. In the thirteenth 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°. In the fourteenth O site, O is bonded to five Mg and one B atom to form distorted OMg5B square pyramids that share corners with four OHfMg5 octahedra, corners with two equivalent OMg5B square pyramids, edges with eight OMg6 octahedra, and edges with four OMg5B square pyramids. The corner-sharing octahedra tilt angles range from 3–5°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with four OHfMg5 octahedra, corners with two equivalent OMg5B square pyramids, edges with nine OMg6 octahedra, and edges with two equivalent OHfMg4B square pyramids. The corner-sharing octahedra tilt angles range from 0–9°. In the sixteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OMg6 octahedra, corners with two equivalent OMg5B square pyramids, edges with ten OMg6 octahedra, and edges with two OMg5B square pyramids. The corner-sharing octahedral tilt angles are 0°. In the seventeenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with eleven OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°.

36 MATERIALS SCIENCE↗