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DOE OSTI2020

Materials Data on HfV2 by Materials Project

HfV2 is Cubic Laves structured and crystallizes in the orthorhombic Imma space group. The structure is three-dimensional. Hf is bonded in a 12-coordinate geometry to four equivalent Hf and twelve V atoms. There are two shorter (3.15 Å) and two longer (3.19 Å) Hf–Hf bond lengths. There are a spread of Hf–V bond distances ranging from 3.01–3.06 Å. There are two inequivalent V sites. In the first V site, V is bonded to six equivalent Hf and six V atoms to form a mixture of edge, face, and corner-sharing VHf6V6 cuboctahedra. There are four shorter (2.58 Å) and two longer (2.63 Å) V–V bond lengths. In the second V site, V is bonded to six equivalent Hf and six V atoms to form a mixture of edge, face, and corner-sharing VHf6V6 cuboctahedra. Both V–V bond lengths are 2.56 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMg by Materials Project

Mg(Hf) is Protactinium-derived structured and crystallizes in the hexagonal P6_3mc space group. The structure is three-dimensional. Mg is bonded in a 10-coordinate geometry to six equivalent Mg and four equivalent Hf atoms. All Mg–Mg bond lengths are 3.03 Å. There are one shorter (3.07 Å) and three longer (3.17 Å) Mg–Hf bond lengths. Hf is bonded in a 10-coordinate geometry to four equivalent Mg and six equivalent Hf atoms. All Hf–Hf bond lengths are 3.03 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMn by Materials Project

HfMn crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. Hf is bonded in a 6-coordinate geometry to eight equivalent Hf and six Mn atoms. There are four shorter (3.03 Å) and four longer (3.25 Å) Hf–Hf bond lengths. There are two shorter (2.86 Å) and four longer (2.91 Å) Hf–Mn bond lengths. There are two inequivalent Mn sites. In the first Mn site, Mn is bonded to six equivalent Hf and six equivalent Mn atoms to form a mixture of face and corner-sharing MnHf6Mn6 cuboctahedra. All Mn–Mn bond lengths are 2.48 Å. In the second Mn site, Mn is bonded to six equivalent Hf and six Mn atoms to form a mixture of distorted face and corner-sharing MnHf6Mn6 cuboctahedra. All Mn–Mn bond lengths are 2.54 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfZr(CoSb)2 by Materials Project

HfZr(CoSb)2 is half-Heusler-derived structured and crystallizes in the trigonal R3m space group. The structure is three-dimensional. Hf is bonded in a body-centered cubic geometry to four Co and four Sb atoms. There are one shorter (2.76 Å) and three longer (2.80 Å) Hf–Co bond lengths. There are one shorter (2.78 Å) and three longer (2.79 Å) Hf–Sb bond lengths. Zr is bonded in a body-centered cubic geometry to four Co and four Sb atoms. There are three shorter (2.81 Å) and one longer (2.82 Å) Zr–Co bond lengths. All Zr–Sb bond lengths are 2.82 Å. There are two inequivalent Co sites. In the first Co site, Co is bonded to one Hf and three equivalent Zr atoms to form distorted CoHfZr3 tetrahedra that share corners with four equivalent SbHfZr3 tetrahedra, corners with twelve CoHfZr3 tetrahedra, and edges with six SbHf3Zr tetrahedra. In the second Co site, Co is bonded to three equivalent Hf and one Zr atom to form distorted CoHf3Zr tetrahedra that share corners with four equivalent SbHf3Zr tetrahedra, corners with twelve CoHfZr3 tetrahedra, and edges with six SbHf3Zr tetrahedra. There are two inequivalent Sb sites. In the first Sb site, Sb is bonded to three equivalent Hf and one Zr atom to form distorted SbHf3Zr tetrahedra that share corners with four equivalent CoHf3Zr tetrahedra, corners with twelve SbHf3Zr tetrahedra, and edges with six CoHfZr3 tetrahedra. In the second Sb site, Sb is bonded to one Hf and three equivalent Zr atoms to form distorted SbHfZr3 tetrahedra that share corners with four equivalent CoHfZr3 tetrahedra, corners with twelve SbHf3Zr tetrahedra, and edges with six CoHfZr3 tetrahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf6Be15Co8 by Materials Project

Be15Hf6Co8 crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. there are three inequivalent Be sites. In the first Be site, Be is bonded to four equivalent Be, four equivalent Hf, and four equivalent Co atoms to form a mixture of face and corner-sharing BeHf4Be4Co4 cuboctahedra. All Be–Be bond lengths are 2.24 Å. All Be–Hf bond lengths are 2.77 Å. All Be–Co bond lengths are 2.37 Å. In the second Be site, Be is bonded in a body-centered cubic geometry to eight equivalent Co atoms. All Be–Co bond lengths are 2.36 Å. In the third Be site, Be is bonded in a distorted q6 geometry to six Be, three equivalent Hf, and three equivalent Co atoms. All Be–Be bond lengths are 2.23 Å. All Be–Hf bond lengths are 2.77 Å. All Be–Co bond lengths are 2.31 Å. Hf is bonded in a 12-coordinate geometry to eight Be and four equivalent Co atoms. All Hf–Co bond lengths are 2.63 Å. Co is bonded in a 10-coordinate geometry to seven Be and three equivalent Hf atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMg by Materials Project

Mg(Hf) is beta-prime cadmium gold structured and crystallizes in the orthorhombic Pmma space group. The structure is three-dimensional. Mg is bonded to four equivalent Mg and eight equivalent Hf atoms to form MgHf8Mg4 cuboctahedra that share corners with eight equivalent HfHf4Mg8 cuboctahedra, corners with ten equivalent MgHf8Mg4 cuboctahedra, edges with six equivalent MgHf8Mg4 cuboctahedra, edges with twelve equivalent HfHf4Mg8 cuboctahedra, faces with eight equivalent HfHf4Mg8 cuboctahedra, and faces with twelve equivalent MgHf8Mg4 cuboctahedra. There are two shorter (3.16 Å) and two longer (3.22 Å) Mg–Mg bond lengths. There are a spread of Mg–Hf bond distances ranging from 3.08–3.12 Å. Hf is bonded to eight equivalent Mg and four equivalent Hf atoms to form HfHf4Mg8 cuboctahedra that share corners with eight equivalent MgHf8Mg4 cuboctahedra, corners with ten equivalent HfHf4Mg8 cuboctahedra, edges with six equivalent HfHf4Mg8 cuboctahedra, edges with twelve equivalent MgHf8Mg4 cuboctahedra, faces with eight equivalent MgHf8Mg4 cuboctahedra, and faces with twelve equivalent HfHf4Mg8 cuboctahedra. There are two shorter (3.16 Å) and two longer (3.22 Å) Hf–Hf bond lengths.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMg14AlO16 by Materials Project

Mg14HfAlO16 is Molybdenum Carbide MAX Phase-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are seven 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 AlO6 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 2.02–2.35 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with two equivalent AlO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–10°. There are a spread of Mg–O bond distances ranging from 2.15–2.17 Å. In the third Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with two equivalent HfO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. There are a spread of Mg–O bond distances ranging from 2.11–2.22 Å. In the fourth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with two equivalent HfO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. There are a spread of Mg–O bond distances ranging from 2.11–2.22 Å. In the fifth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with two equivalent HfO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. There are a spread of Mg–O bond distances ranging from 2.11–2.22 Å. In the sixth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with two equivalent HfO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. There are a spread of Mg–O bond distances ranging from 2.11–2.22 Å. In the seventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six equivalent MgO6 octahedra, an edgeedge with one HfO6 octahedra, an edgeedge with one AlO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–10°. There are two shorter (2.15 Å) and four longer (2.17 Å) Mg–O bond lengths. Hf is bonded to six O atoms to form HfO6 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 (2.15 Å) and four longer (2.31 Å) Hf–O bond lengths. Al is bonded to six O atoms to form AlO6 octahedra that share corners with two equivalent AlO6 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 (1.97 Å) and two longer (2.15 Å) Al–O bond lengths. There are ten inequivalent O sites. In the first O site, O is bonded to five Mg and one Al atom to form OMg5Al octahedra that share corners with six OMg5Al octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–10°. There are two shorter (2.16 Å) and one longer (2.35 Å) O–Mg bond lengths. In the second O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OMg5Al octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the third O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OMg5Al octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. Both O–Mg bond lengths are 2.17 Å. 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 OMg5Al octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the fifth O site, O is bonded to four equivalent Mg and two equivalent Al atoms to form OMg4Al2 octahedra that share corners with six OMg4Al2 octahedra and edges with twelve OMg5Al octahedra. 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 six OMg4Al2 octahedra and edges with twelve OHfMg5 octahedra. The corner-sharing octahedral tilt angles are 0°. In the seventh O site, O is bonded to four Mg and two equivalent Hf atoms to form OHf2Mg4 octahedra that share corners with six OMg6 octahedra and edges with twelve OHfMg5 octahedra. The corner-sharing octahedral tilt angles are 0°. In the eighth O site, O is bonded to five Mg and one Al atom to form a mixture of corner and edge-sharing OMg5Al octahedra. The corner-sharing octahedra tilt angles range from 0–10°. In the ninth O site, O is bonded to five Mg and one Hf atom to form a mixture of corner and edge-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. The O–Mg bond length is 2.02 Å. In the tenth O site, O is bonded to five Mg and one Hf atom to form a mixture of corner and edge-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. There are one shorter (2.02 Å) and two longer (2.17 Å) O–Mg bond lengths.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMg30AlO32 by Materials Project

Mg30HfAlO32 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 AlO6 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 2.04–2.30 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent AlO6 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 (2.27 Å) Mg–O bond lengths. 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 (2.17 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 (2.12 Å) and four longer (2.15 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 AlO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–7°. There are four shorter (2.14 Å) and two longer (2.16 Å) Mg–O bond lengths. 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 two shorter (2.14 Å) and four longer (2.15 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 AlO6 octahedra, and edges with eleven MgO6 octahedra. 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 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 2.11–2.19 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 (2.17 Å) and four longer (2.26 Å) Hf–O bond lengths. Al is bonded to six O atoms to form AlO6 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 (2.00 Å) and two longer (2.01 Å) Al–O bond lengths. There are eighteen inequivalent O sites. In the first O site, O is bonded to five Mg and one Al atom to form OMg5Al octahedra that share corners with six OMg5Al octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg5Al octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the third O site, O is bonded to five Mg and one Hf atom to form a mixture of corner and edge-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 OMg5Al octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the fifth O site, O is bonded to five Mg and one Al atom to form a mixture of corner and edge-sharing OMg5Al octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the sixth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OMg5Al octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. The O–Mg bond length is 2.04 Å. In the seventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OMg5Al octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. There are a spread of O–Mg bond distances ranging from 2.04–2.17 Å. In the eighth 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 ninth 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 (2.13 Å) and two longer (2.15 Å) O–Mg bond lengths. 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 0–1°. The O–Mg bond length is 2.14 Å. 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 0–1°. There are a spread of O–Mg bond distances ranging from 2.11–2.15 Å. In the twelfth O site, O is bonded to five Mg and one Al atom to form a mixture of corner and edge-sharing OMg5Al octahedra. The corner-sharing octahedra tilt angles range from 0–6°. There are two shorter (2.16 Å) and one longer (2.30 Å) O–Mg bond lengths. In the thirteenth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OMg5Al octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. Both O–Mg bond lengths are 2.17 Å. In the fourteenth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OMg5Al octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. There are two shorter (2.16 Å) and two longer (2.17 Å) O–Mg bond lengths. In the fifteenth 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 (2.13 Å) and one longer (2.17 Å) O–Mg bond lengths. In the sixteenth 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 2.11 Å. 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 0–4°. There are a spread of O–Mg bond distances ranging from 2.13–2.17 Å. In the eighteenth 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°. There are two shorter (2.11 Å) and two longer (2.15 Å) O–Mg bond lengths.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf6Be15Cu8 by Materials Project

Be15Hf6Cu8 crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. there are three inequivalent Be sites. In the first Be site, Be is bonded to four equivalent Be, four equivalent Hf, and four equivalent Cu atoms to form a mixture of distorted face and corner-sharing BeHf4Be4Cu4 cuboctahedra. All Be–Be bond lengths are 2.27 Å. All Be–Hf bond lengths are 2.82 Å. All Be–Cu bond lengths are 2.41 Å. In the second Be site, Be is bonded in a body-centered cubic geometry to eight equivalent Cu atoms. All Be–Cu bond lengths are 2.36 Å. In the third Be site, Be is bonded in a 12-coordinate geometry to six Be, three equivalent Hf, and three equivalent Cu atoms. All Be–Be bond lengths are 2.32 Å. All Be–Hf bond lengths are 2.77 Å. All Be–Cu bond lengths are 2.37 Å. Hf is bonded in a 12-coordinate geometry to eight Be and four equivalent Cu atoms. All Hf–Cu bond lengths are 2.73 Å. Cu is bonded in a 10-coordinate geometry to seven Be and three equivalent Hf atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf6Be15Pd8 by Materials Project

Be15Hf6Pd8 crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. there are three inequivalent Be sites. In the first Be site, Be is bonded to four equivalent Be, four equivalent Hf, and four equivalent Pd atoms to form a mixture of distorted corner and face-sharing BeHf4Be4Pd4 cuboctahedra. All Be–Be bond lengths are 2.33 Å. All Be–Hf bond lengths are 2.92 Å. All Be–Pd bond lengths are 2.47 Å. In the second Be site, Be is bonded in a body-centered cubic geometry to eight equivalent Pd atoms. All Be–Pd bond lengths are 2.47 Å. In the third Be site, Be is bonded in a 3-coordinate geometry to six Be, three equivalent Hf, and three equivalent Pd atoms. All Be–Be bond lengths are 2.47 Å. All Be–Hf bond lengths are 2.81 Å. All Be–Pd bond lengths are 2.43 Å. Hf is bonded in a 8-coordinate geometry to eight Be and four equivalent Pd atoms. All Hf–Pd bond lengths are 2.86 Å. Pd is bonded in a 10-coordinate geometry to seven Be and three equivalent Hf atoms.

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 six MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. All Sr–O bond lengths are 2.34 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 SrO6 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 2.00–2.20 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 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 (1.99 Å) and four longer (2.21 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 2.12–2.19 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 (2.20 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 SrO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. There are four shorter (2.16 Å) and two longer (2.19 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 0–2°. 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 SrO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. There are a spread of Mg–O bond distances ranging from 2.11–2.21 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 0–4°. There are a spread of Mg–O bond distances ranging from 2.12–2.23 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 two shorter (2.12 Å) and four longer (2.20 Å) Hf–O bond lengths. There are thirteen inequivalent O sites. In the first O site, O is bonded to one Sr and five Mg atoms to form OSrMg5 octahedra that share corners with six OSrMg5 octahedra and edges with twelve OMg6 octahedra. 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 six OSrMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. 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 OSrMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are two shorter (2.12 Å) and two longer (2.14 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 OSrMg5 octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the sixth 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 0–4°. In the seventh 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 0–4°. There are two shorter (2.19 Å) and two longer (2.21 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 OSrMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. The O–Mg bond length is 2.14 Å. In the ninth 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 OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of O–Mg bond distances ranging from 2.14–2.20 Å. 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 0–4°. 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 0–3°. In the twelfth 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 OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. Both O–Mg bond lengths are 2.20 Å. In the thirteenth 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 OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are two shorter (2.16 Å) and two longer (2.20 Å) O–Mg bond lengths.

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 six MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.43 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 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 1.93–2.23 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent 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 (1.92 Å) and four longer (2.24 Å) Mg–O bond lengths. 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 a spread of Mg–O bond distances ranging from 2.11–2.21 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 (2.16 Å) and two longer (2.22 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 BaO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–11°. There are a spread of Mg–O bond distances ranging from 2.15–2.23 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 1–3°. There are four shorter (2.18 Å) and two longer (2.19 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 BaO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–10°. There are a spread of Mg–O bond distances ranging from 2.10–2.25 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 2.13–2.24 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 (2.13 Å) and four longer (2.19 Å) Hf–O bond lengths. There are fourteen 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 OBaMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OBaMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the third O site, O is bonded to five Mg and one Hf atom to form a mixture of corner and edge-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 OBaMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. All O–Mg bond lengths are 2.13 Å. 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 OBaMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the sixth 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 0–5°. In the seventh 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 0–5°. There are two shorter (2.23 Å) and two longer (2.25 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 OBaMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. The O–Mg bond length is 2.18 Å. In the ninth 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 OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of O–Mg bond distances ranging from 2.15–2.22 Å. 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 0–5°. 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 0–3°. In the twelfth 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°. There are two shorter (2.13 Å) and two longer (2.19 Å) O–Mg bond lengths. In the thirteenth 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 OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. Both O–Mg bond lengths are 2.22 Å. In the fourteenth 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 OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are two shorter (2.15 Å) and two longer (2.22 Å) O–Mg bond lengths.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfMg by Materials Project

Mg(Hf) is Tetraauricupride structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. Mg is bonded to four equivalent Mg and eight equivalent Hf atoms to form MgHf8Mg4 cuboctahedra that share corners with twelve equivalent MgHf8Mg4 cuboctahedra, edges with eight equivalent MgHf8Mg4 cuboctahedra, edges with sixteen equivalent HfHf4Mg8 cuboctahedra, faces with eight equivalent HfHf4Mg8 cuboctahedra, and faces with ten equivalent MgHf8Mg4 cuboctahedra. All Mg–Mg bond lengths are 3.12 Å. All Mg–Hf bond lengths are 3.14 Å. Hf is bonded to eight equivalent Mg and four equivalent Hf atoms to form HfHf4Mg8 cuboctahedra that share corners with twelve equivalent HfHf4Mg8 cuboctahedra, edges with eight equivalent HfHf4Mg8 cuboctahedra, edges with sixteen equivalent MgHf8Mg4 cuboctahedra, faces with eight equivalent MgHf8Mg4 cuboctahedra, and faces with ten equivalent HfHf4Mg8 cuboctahedra. All Hf–Hf bond lengths are 3.12 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Aqueous Zr/Hf IV ‐Oxo Cluster Speciation and Separation

Abstract Many industrial separations of chemically‐similar elements are achieved by solvent extraction, exploiting differences in speciation and solubility across aqueous‐organic interfaces. We recently identified [OM 4 (OH) 6 (SCN) 12 ] 4− (OM 4 , M=Zr/Hf IV ) tetrahedral oxoclusters as the main species in industrial processes that produce nuclear‐grade Zr and Hf from crude ore. However, isostructural/isoelectronic OM 4 ‐oxoclusters do not explain selective extraction of Hf into the organic phase. Here we have characterized heterometal Hf−Zr clusters in solution and the solid‐state yielding key information about their fundamentally different chemistry that engenders separation. Clusters prepared with both ammonium (industrial process) and tetramethylammonium counter cations revealed that 1) heterometal clusters (instead of a mixture of homometal clusters) assemble, and 2) Hf‐rich OM 4 selectively precipitates over Zr‐rich OM 4 , providing a separation process that does not require an organic extractant. Mass spectrometry, small‐angle X‐ray scattering, solution‐state 1 H nuclear magnetic resonance (NMR) spectroscopy, and solid‐state 17 O NMR evidence both mixed‐metal speciation and selective Hf‐precipitation. Raman spectroscopy suggests greater Zr‐ligand lability than Hf‐ligand lability, consistent with higher aqueous solubility of Zr‐rich clusters, enabling both extraction and precipitation‐based separation. Fundamentally, we also identify a key difference between these chemically similar elements that has enabled diversification of Zr‐polyoxocation chemistry over the last decade, while Hf‐polyoxocation chemistry lags.

Roseborough, Alexander [Department of Chemistry Or↗
DOE OSTI2024

Bi-fidelity variational auto-encoder for uncertainty quantification

Quantifying the uncertainty of quantities of interest (QoIs) from physical systems is a primary objective in model validation. However, achieving this goal entails balancing the need for computational efficiency with the requirement for numerical accuracy. To address this trade-off, we propose a novel bi-fidelity formulation of variational auto-encoders (BF-VAE) designed to estimate the uncertainty associated with a QoI from low-fidelity (LF) and high-fidelity (HF) samples of the QoI. Here, this model allows for the approximation of the statistics of the HF QoI by leveraging information derived from its LF counterpart. Specifically, we design a bi-fidelity auto-regressive model in the latent space which is integrated within the VAE’s probabilistic encoder–decoder structure. An effective algorithm is proposed to maximize the variational lower bound of the HF log-likelihood in the presence of limited HF data, resulting in the synthesis of HF realizations with a reduced computational cost. Additionally, we introduce the concept of the bi-fidelity information bottleneck (BF-IB) to provide an information-theoretic interpretation of the proposed BF-VAE model. Our numerical results demonstrate that the BF-VAE leads to considerably improved accuracy, as compared to a VAE trained using only HF data, when limited HF data is available.

42 ENGINEERING↗
DOE OSTI2020

Materials Data on Hf3(Cu2Ge)2 by Materials Project

Hf3(Cu2Ge)2 crystallizes in the hexagonal P-62m space group. The structure is three-dimensional. Hf is bonded in a 5-coordinate geometry to seven Cu and four equivalent Ge atoms. There are a spread of Hf–Cu bond distances ranging from 2.63–3.04 Å. All Hf–Ge bond lengths are 2.78 Å. There are two inequivalent Cu sites. In the first Cu site, Cu is bonded in a distorted trigonal planar geometry to three equivalent Hf and six equivalent Cu atoms. All Cu–Cu bond lengths are 2.52 Å. In the second Cu site, Cu is bonded to six equivalent Hf, four Cu, and two equivalent Ge atoms to form a mixture of distorted corner, edge, and face-sharing CuHf6Cu4Ge2 cuboctahedra. Both Cu–Cu bond lengths are 2.66 Å. Both Cu–Ge bond lengths are 2.48 Å. Ge is bonded in a 9-coordinate geometry to six equivalent Hf and three equivalent Cu atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf2Al by Materials Project

Hf2Al is Khatyrkite structured and crystallizes in the tetragonal I4/mcm space group. The structure is three-dimensional. Hf is bonded in a 4-coordinate geometry to one Hf and four equivalent Al atoms. The Hf–Hf bond length is 2.93 Å. All Hf–Al bond lengths are 2.91 Å. Al is bonded in a 10-coordinate geometry to eight equivalent Hf and two equivalent Al atoms. Both Al–Al bond lengths are 2.61 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on HfPRu by Materials Project

HfRuP crystallizes in the hexagonal P-62m space group. The structure is three-dimensional. Hf is bonded in a 11-coordinate geometry to six equivalent Ru and five P atoms. There are two shorter (2.88 Å) and four longer (3.01 Å) Hf–Ru bond lengths. There are one shorter (2.68 Å) and four longer (2.71 Å) Hf–P bond lengths. Ru is bonded to six equivalent Hf, two equivalent Ru, and four P atoms to form a mixture of distorted corner, edge, and face-sharing RuHf6P4Ru2 cuboctahedra. Both Ru–Ru bond lengths are 2.75 Å. All Ru–P bond lengths are 2.47 Å. There are two inequivalent P sites. In the first P site, P is bonded in a 9-coordinate geometry to six equivalent Hf and three equivalent Ru atoms. In the second P site, P is bonded in a 9-coordinate geometry to three equivalent Hf and six equivalent Ru atoms.

36 MATERIALS SCIENCE↗