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Mg(Hf) is Tetraauricupride structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. Mg is bonded in a body-centered cubic geometry to eight equivalent Hf atoms. All Mg–Hf bond lengths are 3.02 Å. Hf is bonded in a body-centered cubic geometry to eight equivalent Mg atoms.
Mg30HfVO32 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 VO6 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 2.11–2.15 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent VO6 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 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 (2.15 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 (2.15 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 VO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. There are a spread of Mg–O bond distances ranging from 2.11–2.19 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 0–2°. There are a spread of Mg–O bond distances ranging from 2.14–2.16 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 VO6 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 2.14–2.17 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 2.11–2.20 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. V is bonded to six O atoms to form VO6 octahedra that share corners with six MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. All V–O bond lengths are 2.19 Å. There are nine inequivalent O sites. In the first O site, O is bonded to five Mg and one V atom to form OMg5V octahedra that share corners with six OMg5V octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedral tilt angles are 0°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg5V 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 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 OMg5V octahedra. The corner-sharing octahedra tilt angles range from 1–3°. In the fifth O site, O is bonded to five Mg and one V atom to form a mixture of corner and edge-sharing OMg5V octahedra. The corner-sharing octahedra tilt angles range from 0–3°. In the sixth O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OMg5V octahedra and edges with twelve OMg6 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 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 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 five Mg and one V atom to form a mixture of corner and edge-sharing OMg5V octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are three shorter (2.11 Å) and two longer (2.17 Å) O–Mg bond lengths.
HfZn22 crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. Hf is bonded in a 4-coordinate geometry to sixteen Zn atoms. There are twelve shorter (3.01 Å) and four longer (3.06 Å) Hf–Zn bond lengths. There are four inequivalent Zn sites. In the first Zn site, Zn is bonded to twelve Zn atoms to form a mixture of distorted corner, edge, and face-sharing ZnZn12 cuboctahedra. There are a spread of Zn–Zn bond distances ranging from 2.51–2.84 Å. In the second Zn site, Zn is bonded in a 2-coordinate geometry to two equivalent Hf and twelve equivalent Zn atoms. All Zn–Zn bond lengths are 2.96 Å. In the third Zn site, Zn is bonded to twelve Zn atoms to form a mixture of corner, edge, and face-sharing ZnZn12 cuboctahedra. All Zn–Zn bond lengths are 2.85 Å. In the fourth Zn site, Zn is bonded to one Hf and eleven Zn atoms to form a mixture of distorted corner, edge, and face-sharing ZnHfZn11 cuboctahedra. There are a spread of Zn–Zn bond distances ranging from 2.53–2.97 Å.
Ho4HfAl15 is Uranium Silicide-derived structured and 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 to twelve Al atoms to form HoAl12 cuboctahedra that share corners with four equivalent HfAl12 cuboctahedra, corners with eight HoAl12 cuboctahedra, edges with twenty-four AlHo2Hf2Al8 cuboctahedra, a faceface with one HfAl12 cuboctahedra, faces with five HoAl12 cuboctahedra, and faces with twelve AlHo4Al8 cuboctahedra. There are a spread of Ho–Al bond distances ranging from 2.98–3.01 Å. In the second Ho site, Ho is bonded to twelve Al atoms to form HoAl12 cuboctahedra that share corners with twelve HoAl12 cuboctahedra, edges with twenty-four AlHo4Al8 cuboctahedra, faces with six HoAl12 cuboctahedra, and faces with twelve AlHo4Al8 cuboctahedra. There are a spread of Ho–Al bond distances ranging from 2.98–3.00 Å. Hf is bonded to twelve Al atoms to form HfAl12 cuboctahedra that share corners with four equivalent HfAl12 cuboctahedra, corners with eight equivalent HoAl12 cuboctahedra, edges with twenty-four AlHo2Hf2Al8 cuboctahedra, faces with two equivalent HoAl12 cuboctahedra, faces with four equivalent HfAl12 cuboctahedra, and faces with twelve AlHo2Hf2Al8 cuboctahedra. There are eight shorter (2.91 Å) and four longer (2.98 Å) Hf–Al bond lengths. There are six inequivalent Al sites. In the first Al site, Al is bonded to four equivalent Hf and eight equivalent Al atoms to form AlHf4Al8 cuboctahedra that share corners with twelve AlHf4Al8 cuboctahedra, edges with eight equivalent HoAl12 cuboctahedra, edges with sixteen equivalent AlHo2Hf2Al8 cuboctahedra, faces with four equivalent HfAl12 cuboctahedra, and faces with fourteen AlHo2Hf2Al8 cuboctahedra. All Al–Al bond lengths are 2.91 Å. In the second Al site, Al is bonded to four equivalent Ho and eight Al atoms to form distorted AlHo4Al8 cuboctahedra that share corners with twelve AlHf4Al8 cuboctahedra, edges with four equivalent HoAl12 cuboctahedra, edges with four equivalent HfAl12 cuboctahedra, edges with sixteen AlHo2Hf2Al8 cuboctahedra, faces with four equivalent HoAl12 cuboctahedra, and faces with fourteen AlHf4Al8 cuboctahedra. There are four shorter (2.99 Å) and four longer (3.02 Å) Al–Al bond lengths. In the third Al site, Al is bonded to four equivalent Ho and eight Al atoms to form distorted AlHo4Al8 cuboctahedra that share corners with twelve AlHo4Al8 cuboctahedra, edges with eight HoAl12 cuboctahedra, edges with sixteen AlHo4Al8 cuboctahedra, faces with four equivalent HoAl12 cuboctahedra, and faces with fourteen AlHo4Al8 cuboctahedra. All Al–Al bond lengths are 2.99 Å. In the fourth Al site, Al is bonded to two equivalent Ho, two equivalent Hf, and eight Al atoms to form distorted AlHo2Hf2Al8 cuboctahedra that share corners with twelve AlHo2Hf2Al8 cuboctahedra, edges with four equivalent HoAl12 cuboctahedra, edges with four equivalent HfAl12 cuboctahedra, edges with sixteen AlHf4Al8 cuboctahedra, faces with two equivalent HoAl12 cuboctahedra, faces with two equivalent HfAl12 cuboctahedra, and faces with fourteen AlHf4Al8 cuboctahedra. All Al–Al bond lengths are 2.98 Å. In the fifth Al site, Al is bonded to four Ho and eight Al atoms to form distorted AlHo4Al8 cuboctahedra that share corners with twelve AlHo2Hf2Al8 cuboctahedra, edges with eight HoAl12 cuboctahedra, edges with sixteen AlHo4Al8 cuboctahedra, faces with four HoAl12 cuboctahedra, and faces with fourteen AlHo4Al8 cuboctahedra. All Al–Al bond lengths are 2.98 Å. In the sixth Al site, Al is bonded to four equivalent Ho and eight Al atoms to form distorted AlHo4Al8 cuboctahedra that share corners with twelve AlHo4Al8 cuboctahedra, edges with eight equivalent HoAl12 cuboctahedra, edges with sixteen AlHo4Al8 cuboctahedra, faces with four equivalent HoAl12 cuboctahedra, and faces with fourteen AlHo4Al8 cuboctahedra. All Al–Al bond lengths are 2.98 Å.
Hf2NiS4 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. Hf is bonded to six S atoms to form HfS6 octahedra that share corners with six equivalent NiS6 octahedra, edges with six equivalent HfS6 octahedra, and a faceface with one NiS6 octahedra. The corner-sharing octahedra tilt angles range from 47–49°. There are a spread of Hf–S bond distances ranging from 2.54–2.58 Å. Ni is bonded to six S atoms to form NiS6 octahedra that share corners with twelve equivalent HfS6 octahedra, edges with two equivalent NiS6 octahedra, and faces with two equivalent HfS6 octahedra. The corner-sharing octahedra tilt angles range from 47–49°. There are two shorter (2.39 Å) and four longer (2.46 Å) Ni–S bond lengths. There are two inequivalent S sites. In the first S site, S is bonded in a rectangular see-saw-like geometry to three equivalent Hf and one Ni atom. In the second S site, S is bonded to three equivalent Hf and two equivalent Ni atoms to form a mixture of distorted corner and edge-sharing SHf3Ni2 square pyramids.
Mg30HfCoO32 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 CoO6 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 2.02–2.21 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent CoO6 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 (2.17 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 2.13–2.17 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 (2.19 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 HfO6 octahedra, an edgeedge with one CoO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 5–12°. There are a spread of Mg–O bond distances ranging from 2.07–2.25 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 2–5°. There are a spread of Mg–O bond distances ranging from 2.13–2.17 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 CoO6 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 2.11–2.19 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 3–7°. There are a spread of Mg–O bond distances ranging from 2.08–2.22 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 four shorter (2.09 Å) and two longer (2.11 Å) Hf–O bond lengths. Co is bonded to six O atoms to form CoO6 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 (2.25 Å) and four longer (2.28 Å) Co–O bond lengths. There are ten inequivalent O sites. In the first O site, O is bonded to five Mg and one Co atom to form a mixture of corner and edge-sharing OMg5Co 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 OMg5Co 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 0–4°. In the fourth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg5Co octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are two shorter (2.08 Å) and two longer (2.19 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 OMg5Co octahedra. The corner-sharing octahedra tilt angles range from 2–8°. In the sixth O site, O is bonded to five Mg and one Co atom to form a mixture of corner and edge-sharing OMg5Co octahedra. The corner-sharing octahedra tilt angles range from 0–10°. In the seventh O site, O is bonded to five Mg and one Co atom to form a mixture of corner and edge-sharing OMg5Co octahedra. The corner-sharing octahedra tilt angles range from 0–10°. There are two shorter (2.07 Å) and two longer (2.14 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 OMg5Co octahedra and edges with twelve OMg6 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 a mixture of corner and edge-sharing OMg6 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 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°.
Hf2Pt3 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Hf is bonded in a 9-coordinate geometry to nine Pt atoms. There are a spread of Hf–Pt bond distances ranging from 2.76–2.96 Å. There are two inequivalent Pt sites. In the first Pt site, Pt is bonded in a distorted body-centered cubic geometry to eight equivalent Hf atoms. In the second Pt site, Pt is bonded in a 10-coordinate geometry to five equivalent Hf atoms.
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 MgO6 octahedra, corners with two equivalent CeO6 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 2.05–2.20 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent 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 (2.02 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 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 2.13–2.19 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 (2.17 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 CeO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. There are a spread of Mg–O bond distances ranging from 2.14–2.23 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 0–2°. There are two shorter (2.16 Å) and four longer (2.18 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 CeO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–4°. There are a spread of Mg–O bond distances ranging from 2.09–2.24 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 0–3°. 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 six MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. All Ce–O bond lengths are 2.31 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 (2.14 Å) and four longer (2.23 Å) Hf–O bond lengths. There are eleven 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 OCeMg5 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 OCeMg5 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 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 equivalent OMg6 octahedra and edges with twelve OCeMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the fifth O site, O is bonded to five Mg and one Ce atom to form a mixture of corner and edge-sharing OCeMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the sixth O site, O is bonded to five Mg and one Ce atom to form a mixture of corner and edge-sharing OCeMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are two shorter (2.23 Å) and two longer (2.24 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 OCeMg5 octahedra and edges with twelve 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 a mixture of corner and edge-sharing 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 a mixture of corner and edge-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are two shorter (2.09 Å) and two longer (2.18 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°. 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 two shorter (2.12 Å) and two longer (2.18 Å) O–Mg bond lengths.
Mg30HfO32C crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional and consists of one medicinal charcoal molecule and one Mg30HfO32 framework. In the Mg30HfO32 framework, there are eight inequivalent Mg sites. In the first 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 1.94–2.23 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 four shorter (2.13 Å) and two 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 (2.11 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 (2.14 Å) and two 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, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–17°. There are a spread of Mg–O bond distances ranging from 2.07–2.30 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 2.13–2.20 Å. In the seventh 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 2–12°. There are a spread of Mg–O bond distances ranging from 2.12–2.19 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 2–4°. There are a spread of Mg–O bond distances ranging from 2.09–2.18 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with four equivalent MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (1.98 Å) and four longer (2.11 Å) Hf–O bond lengths. There are ten inequivalent O sites. In the first O site, O is bonded to five Mg atoms to form 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 5–7°. In the second 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 0–3°. In the third 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 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 0–3°. Both O–Mg bond lengths are 2.20 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 0–3°. There are two shorter (2.09 Å) and two longer (2.20 Å) O–Mg bond lengths. In the sixth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six equivalent OMg6 octahedra, edges with nine OHfMg5 octahedra, and edges with three OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 1–7°. In the seventh O site, O is bonded to four equivalent Mg and one Hf atom to form OHfMg4 square pyramids that share corners with four equivalent OMg6 octahedra, corners with five OHfMg4 square pyramids, and edges with eight OMg6 octahedra. The corner-sharing octahedral tilt angles are 13°. In the eighth 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, and edges with two equivalent OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. 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 0–3°. 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 0–3°. The O–Mg bond length is 2.13 Å.
Mg30HfMnO32 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 MnO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.10 Å) and two longer (2.16 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 MnO6 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 (2.17 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 2.12–2.17 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 (2.14 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 HfO6 octahedra, an edgeedge with one MnO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–4°. There are a spread of Mg–O bond distances ranging from 2.13–2.18 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 1–2°. There are a spread of Mg–O bond distances ranging from 2.14–2.17 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 MnO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are one shorter (2.13 Å) and five longer (2.16 Å) Mg–O bond lengths. 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 2.10–2.21 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 (2.11 Å) and four longer (2.21 Å) Hf–O bond lengths. Mn is bonded to six O atoms to form MnO6 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 (2.20 Å) and four longer (2.21 Å) Mn–O bond lengths. There are eleven inequivalent O sites. In the first O site, O is bonded to five Mg and one Mn atom to form OMg5Mn octahedra that share corners with six OMg5Mn 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 OMg5Mn 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 OMg5Mn octahedra. The corner-sharing octahedra tilt angles range from 1–4°. In the fifth O site, O is bonded to five Mg and one Mn atom to form a mixture of edge and corner-sharing OMg5Mn octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the sixth O site, O is bonded to five Mg and one Mn atom to form a mixture of edge and corner-sharing OMg5Mn octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are two shorter (2.13 Å) and two longer (2.16 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 OMg5Mn 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°. 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 0–2°. There are two shorter (2.13 Å) and one longer (2.14 Å) O–Mg bond lengths. 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 0–2°. Both O–Mg bond lengths are 2.11 Å.
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 MgO6 octahedra, corners with two equivalent HfO6 octahedra, corners with two equivalent SnO6 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 1.98–2.20 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent 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 (1.99 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 corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.14 Å) and two longer (2.16 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 (2.09 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 SnO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–10°. There are four shorter (2.16 Å) and two 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 corner and edge-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 SnO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. There are a spread of Mg–O bond distances ranging from 2.12–2.22 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 1–3°. There are a spread of Mg–O bond distances ranging from 2.13–2.21 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 (2.17 Å) and two longer (2.25 Å) Hf–O bond lengths. Sn is bonded to six O atoms to form SnO6 octahedra that share corners with six MgO6 octahedra and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. All Sn–O bond lengths are 2.35 Å. There are eleven 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 OMg5Sn 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 OMg5Sn 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 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 OMg5Sn 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 (2.14 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 OMg5Sn octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the sixth O site, O is bonded to five Mg and one Sn atom to form a mixture of corner and edge-sharing OMg5Sn octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the seventh 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 OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. 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 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 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°. Both O–Mg bond lengths are 2.13 Å. In the eleventh O site, O is bonded to five Mg and one Sn atom to form a mixture of corner and edge-sharing OMg5Sn octahedra. The corner-sharing octahedra tilt angles range from 0–5°. There are a spread of O–Mg bond distances ranging from 1.98–2.22 Å.
Mg30HfSbO32 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 SbO6 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 1.88–2.25 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 2.10–2.20 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 (2.12 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 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 SbO6 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 2.10–2.27 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 1–5°. 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 SbO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–14°. There are a spread of Mg–O bond distances ranging from 2.15–2.21 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 3–4°. 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 two equivalent SbO6 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 (1.98 Å) and four longer (2.15 Å) Hf–O bond lengths. Sb is bonded to six O atoms to form SbO6 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 (2.37 Å) and four longer (2.47 Å) Sb–O bond lengths. There are eleven inequivalent O sites. In the first O site, O is bonded to five Mg and one Sb atom to form distorted OMg5Sb octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg5Sb 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 OMg5Sb octahedra and edges with twelve OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. 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 0–8°. 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 0–3°. Both O–Mg bond lengths are 2.19 Å. In the fifth O site, O is bonded to five Mg and one Sb atom to form a mixture of distorted edge and corner-sharing OMg5Sb octahedra. The corner-sharing octahedra tilt angles range from 0–8°. There are a spread of O–Mg bond distances ranging from 1.88–2.21 Å. 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 0–3°. 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 OMg5Sb 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 Sb atom to form distorted OHfMg4Sb octahedra that share corners with six OHfMg4Sb octahedra and edges with twelve OMg5Sb 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 OHfMg4Sb octahedra and edges with twelve OMg5Sb 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 edge and corner-sharing OMg6 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 a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. The O–Mg bond length is 2.18 Å.
Mg30HfTiO32 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 TiO6 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 TiO6 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 (2.17 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°. All Mg–O bond lengths are 2.15 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 HfO6 octahedra, an edgeedge with one TiO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 3–8°. There are a spread of Mg–O bond distances ranging from 2.10–2.21 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 1–3°. There are two shorter (2.14 Å) and four longer (2.16 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 TiO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. There are a spread of Mg–O bond distances ranging from 2.14–2.16 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 2–4°. There are a spread of Mg–O bond distances ranging from 2.10–2.20 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 (2.13 Å) and two longer (2.15 Å) Hf–O bond lengths. Ti is bonded to six O atoms to form TiO6 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 (2.24 Å) and four longer (2.25 Å) Ti–O bond lengths. There are ten inequivalent O sites. In the first O site, O is bonded to five Mg and one Ti atom to form OMg5Ti octahedra that share corners with six OMg5Ti 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 OMg5Ti 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 OMg5Ti octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are two shorter (2.10 Å) and two longer (2.16 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 OMg5Ti octahedra. The corner-sharing octahedra tilt angles range from 1–5°. In the sixth O site, O is bonded to five Mg and one Ti atom to form a mixture of edge and corner-sharing OMg5Ti octahedra. The corner-sharing octahedra tilt angles range from 0–6°. In the seventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OMg5Ti octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. 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 0–4°. 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 0–3°. In the tenth O site, O is bonded to five Mg and one Ti atom to form a mixture of edge and corner-sharing OMg5Ti octahedra. The corner-sharing octahedra tilt angles range from 0–6°. There are a spread of O–Mg bond distances ranging from 2.05–2.16 Å.
Mg30HfCuO32 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 CuO6 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 2.01–2.21 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent CuO6 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 (2.03 Å) and four longer (2.18 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 2.13–2.17 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 (2.19 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 HfO6 octahedra, an edgeedge with one CuO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 5–13°. 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 corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. There are a spread of Mg–O bond distances ranging from 2.13–2.17 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 CuO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 1–10°. There are a spread of Mg–O bond distances ranging from 2.12–2.19 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 2–7°. There are a spread of Mg–O bond distances ranging from 2.09–2.22 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 four shorter (2.09 Å) and two longer (2.11 Å) Hf–O bond lengths. Cu is bonded to six O atoms to form CuO6 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 (2.27 Å) and four longer (2.30 Å) Cu–O bond lengths. There are twelve inequivalent O sites. In the first O site, O is bonded to five Mg and one Cu atom to form OMg5Cu octahedra that share corners with six OMg5Cu 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 OMg5Cu 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 0–3°. In the fourth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg5Cu octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are two shorter (2.09 Å) and two longer (2.19 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 OMg5Cu octahedra. The corner-sharing octahedra tilt angles range from 2–8°. In the sixth O site, O is bonded to five Mg and one Cu atom to form a mixture of corner and edge-sharing OMg5Cu octahedra. The corner-sharing octahedra tilt angles range from 0–10°. In the seventh O site, O is bonded to five Mg and one Cu atom to form a mixture of corner and edge-sharing OMg5Cu octahedra. The corner-sharing octahedra tilt angles range from 0–10°. There are two shorter (2.08 Å) and two longer (2.14 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 OMg5Cu octahedra and edges with twelve OMg6 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 a mixture of corner and edge-sharing OMg6 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 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 five Mg and one Cu atom to form a mixture of corner and edge-sharing OMg5Cu octahedra. The corner-sharing octahedra tilt angles range from 0–10°. There are one shorter (2.01 Å) and two longer (2.14 Å) O–Mg bond lengths. In the twelfth O site, O is bonded to five Mg and one Cu atom to form a mixture of corner and edge-sharing OMg5Cu octahedra. The corner-sharing octahedra tilt angles range from 0–10°. There are a spread of O–Mg bond distances ranging from 2.01–2.14 Å.
HfBi3 is Uranium Silicide-like structured and crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Hf is bonded to twelve Bi atoms to form HfBi12 cuboctahedra that share corners with four equivalent HfBi12 cuboctahedra, edges with eight equivalent HfBi12 cuboctahedra, edges with sixteen equivalent BiHf4Bi8 cuboctahedra, faces with four equivalent HfBi12 cuboctahedra, and faces with eight equivalent BiHf4Bi8 cuboctahedra. There are four shorter (3.27 Å) and eight longer (3.51 Å) Hf–Bi bond lengths. There are two inequivalent Bi sites. In the first Bi site, Bi is bonded to four equivalent Hf and eight Bi atoms to form distorted BiHf4Bi8 cuboctahedra that share corners with twelve equivalent BiHf4Bi8 cuboctahedra, edges with eight equivalent HfBi12 cuboctahedra, edges with eight equivalent BiHf4Bi8 cuboctahedra, faces with four equivalent HfBi12 cuboctahedra, and faces with ten equivalent BiHf4Bi8 cuboctahedra. There are four shorter (3.27 Å) and four longer (3.51 Å) Bi–Bi bond lengths. In the second Bi site, Bi is bonded in a square co-planar geometry to four equivalent Hf and eight equivalent Bi atoms.
Mg30HfNiO32 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 NiO6 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 2.01–2.22 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent NiO6 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 (2.17 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 2.12–2.18 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 (2.13 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 HfO6 octahedra, an edgeedge with one NiO6 octahedra, and edges with ten MgO6 octahedra. The corner-sharing octahedra tilt angles range from 5–13°. 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 2–5°. There are a spread of Mg–O bond distances ranging from 2.13–2.18 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 NiO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–10°. There are a spread of Mg–O bond distances ranging from 2.13–2.19 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 2–7°. There are a spread of Mg–O bond distances ranging from 2.09–2.23 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 (2.10 Å) Hf–O bond lengths. Ni is bonded to six O atoms to form NiO6 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 (2.21 Å) and four longer (2.30 Å) Ni–O bond lengths. There are twelve inequivalent O sites. In the first O site, O is bonded to five Mg and one Ni atom to form OMg5Ni octahedra that share corners with six OMg5Ni 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 OMg5Ni 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 0–3°. In the fourth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg5Ni octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are two shorter (2.09 Å) and two longer (2.19 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 OMg5Ni octahedra. The corner-sharing octahedra tilt angles range from 2–8°. In the sixth O site, O is bonded to five Mg and one Ni atom to form a mixture of edge and corner-sharing OMg5Ni octahedra. The corner-sharing octahedra tilt angles range from 0–11°. In the seventh O site, O is bonded to five Mg and one Ni atom to form a mixture of edge and corner-sharing OMg5Ni octahedra. The corner-sharing octahedra tilt angles range from 0–11°. There are two shorter (2.08 Å) and two longer (2.13 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 OMg5Ni 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 0–6°. 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 a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. There are one shorter (2.14 Å) and two longer (2.15 Å) O–Mg bond lengths. 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 0–6°. Both O–Mg bond lengths are 2.09 Å.
Hf2FeC2S crystallizes in the trigonal P3m1 space group. The structure is two-dimensional and consists of one Hf2FeC2S sheet oriented in the (0, 0, 1) direction. there are two inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded to three equivalent C4- and three equivalent S2- atoms to form edge-sharing HfC3S3 octahedra. All Hf–C bond lengths are 2.38 Å. All Hf–S bond lengths are 2.62 Å. In the second Hf4+ site, Hf4+ is bonded in a 3-coordinate geometry to three equivalent C4- and three equivalent S2- atoms. All Hf–C bond lengths are 2.09 Å. All Hf–S bond lengths are 2.82 Å. Fe2+ is bonded in a trigonal non-coplanar geometry to three equivalent C4- atoms. All Fe–C bond lengths are 2.02 Å. There are two inequivalent C4- sites. In the first C4- site, C4- is bonded to three equivalent Hf4+ and three equivalent Fe2+ atoms to form distorted edge-sharing CHf3Fe3 octahedra. In the second C4- site, C4- is bonded in a trigonal non-coplanar geometry to three equivalent Hf4+ atoms. S2- is bonded in a 6-coordinate geometry to six Hf4+ atoms.
Mg30HfO32C crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional and consists of one methane molecule and one Mg30HfO32 framework. In the Mg30HfO32 framework, 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, 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 1.89–2.24 Å. In the second 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 (2.02 Å) and four longer (2.18 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 2.08–2.19 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 (2.14 Å) and two longer (2.15 Å) Mg–O bond lengths. In the fifth Mg site, Mg is bonded to six O atoms to form distorted 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 7–23°. There are a spread of Mg–O bond distances ranging from 2.07–2.31 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 2–7°. There are a spread of Mg–O bond distances ranging from 2.13–2.19 Å. In the seventh 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 3–17°. There are a spread of Mg–O bond distances ranging from 2.10–2.20 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 0–8°. There are a spread of Mg–O bond distances ranging from 2.08–2.24 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 four shorter (2.08 Å) and two longer (2.10 Å) Hf–O bond lengths. There are ten inequivalent O sites. In the first O site, O is bonded to five Mg atoms to form OMg5 square pyramids that share corners with four equivalent OMg6 octahedra, corners with five OMg5 square pyramids, and edges with eight OMg6 octahedra. The corner-sharing octahedral tilt angles are 6°. 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 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 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 equivalent OMg6 octahedra, edges with nine OMg6 octahedra, and edges with three OMg5 square pyramids. The corner-sharing octahedra tilt angles range from 3–11°. In the fifth O site, O is bonded to five Mg atoms to form 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 10–17°. In the sixth 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 0–7°. In the seventh 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 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 0–7°. In the ninth 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°. There are one shorter (2.15 Å) and two longer (2.17 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 0–7°. Both O–Mg bond lengths are 2.08 Å.