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DOE OSTI2020

Materials Data on Hf2N2O by Materials Project

Hf2ON2 is Ilmenite-like structured and crystallizes in the monoclinic P2/c space group. The structure is three-dimensional. there are two inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded to three N3- and three equivalent O2- atoms to form a mixture of distorted face, edge, and corner-sharing HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 47–63°. There are a spread of Hf–N bond distances ranging from 2.06–2.23 Å. There are a spread of Hf–O bond distances ranging from 2.12–2.31 Å. In the second Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form distorted HfN5O octahedra that share corners with nine HfN3O3 octahedra, edges with three HfN3O3 octahedra, and a faceface with one HfN5O octahedra. The corner-sharing octahedra tilt angles range from 47–63°. There are a spread of Hf–N bond distances ranging from 2.10–2.29 Å. The Hf–O bond length is 2.17 Å. There are three inequivalent N3- sites. In the first N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with four equivalent OHf4 trigonal pyramids, corners with eight NHf4 trigonal pyramids, an edgeedge with one OHf4 trigonal pyramid, and edges with three NHf4 trigonal pyramids. In the second N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with four equivalent OHf4 trigonal pyramids, corners with eight equivalent NHf4 trigonal pyramids, edges with two equivalent NHf4 trigonal pyramids, and edges with two equivalent OHf4 trigonal pyramids. In the third N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with four equivalent NHf4 trigonal pyramids, corners with eight equivalent OHf4 trigonal pyramids, and edges with four NHf4 trigonal pyramids. O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share corners with two equivalent OHf4 trigonal pyramids, corners with ten NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two equivalent OHf4 trigonal pyramids.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf3N2O3 by Materials Project

Hf3N2O3 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are six inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded to two N3- and four O2- atoms to form distorted HfN2O4 octahedra that share corners with four HfN2O4 octahedra and edges with six HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 28–41°. There are one shorter (2.07 Å) and one longer (2.19 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.05–2.24 Å. In the second Hf4+ site, Hf4+ is bonded to three N3- and three O2- atoms to form distorted HfN3O3 octahedra that share corners with four HfN3O3 octahedra and edges with six HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 26–58°. There are two shorter (2.10 Å) and one longer (2.19 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.09–2.31 Å. In the third Hf4+ site, Hf4+ is bonded to three N3- and three O2- atoms to form distorted HfN3O3 octahedra that share corners with four HfN3O3 octahedra and edges with six HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 21–58°. There are one shorter (2.04 Å) and two longer (2.14 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.03–2.39 Å. In the fourth Hf4+ site, Hf4+ is bonded to two N3- and four O2- atoms to form a mixture of distorted corner and edge-sharing HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 21–35°. Both Hf–N bond lengths are 2.15 Å. There are a spread of Hf–O bond distances ranging from 2.10–2.12 Å. In the fifth Hf4+ site, Hf4+ is bonded to three N3- and three O2- atoms to form a mixture of distorted corner and edge-sharing HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 28–57°. There are two shorter (2.11 Å) and one longer (2.18 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.09–2.42 Å. In the sixth Hf4+ site, Hf4+ is bonded to two N3- and four O2- atoms to form a mixture of distorted corner and edge-sharing HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 28–57°. There are one shorter (2.04 Å) and one longer (2.22 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.09–2.25 Å. There are four inequivalent N3- sites. In the first N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one OHf4 trigonal pyramid, corners with two equivalent NHf4 trigonal pyramids, and edges with two equivalent NHf4 trigonal pyramids. In the second N3- site, N3- is bonded in a 3-coordinate geometry to three Hf4+ atoms. In the third N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent NHf4 tetrahedra, a cornercorner with one NHf4 trigonal pyramid, and edges with two equivalent OHf4 trigonal pyramids. In the fourth N3- site, N3- is bonded to four Hf4+ atoms to form a mixture of distorted corner and edge-sharing NHf4 trigonal pyramids. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share a cornercorner with one NHf4 trigonal pyramid, corners with two equivalent OHf4 trigonal pyramids, and edges with two equivalent NHf4 tetrahedra. In the second O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the third O2- site, O2- is bonded in a 3-coordinate geometry to three Hf4+ atoms. In the fourth O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the fifth O2- site, O2- is bonded in a distorted T-shaped geometry to three Hf4+ atoms. In the sixth O2- site, O2- is bonded in a distorted T-shaped geometry to three Hf4+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf2N2O by Materials Project

Hf2ON2 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are eight inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to six N3- and one O2- atom. There are a spread of Hf–N bond distances ranging from 2.14–2.71 Å. The Hf–O bond length is 2.14 Å. In the second Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to five N3- and two O2- atoms. There are a spread of Hf–N bond distances ranging from 2.13–2.30 Å. There are one shorter (2.16 Å) and one longer (2.44 Å) Hf–O bond lengths. In the third Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to five N3- and two O2- atoms. There are a spread of Hf–N bond distances ranging from 2.13–2.35 Å. There are one shorter (2.17 Å) and one longer (2.56 Å) Hf–O bond lengths. In the fourth Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to five N3- and two O2- atoms. There are a spread of Hf–N bond distances ranging from 2.10–2.27 Å. There are one shorter (2.27 Å) and one longer (2.45 Å) Hf–O bond lengths. In the fifth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form a mixture of edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 60–64°. There are a spread of Hf–N bond distances ranging from 2.12–2.20 Å. There are one shorter (2.14 Å) and one longer (2.15 Å) Hf–O bond lengths. In the sixth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form a mixture of edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 60–62°. There are a spread of Hf–N bond distances ranging from 2.12–2.22 Å. There are one shorter (2.12 Å) and one longer (2.17 Å) Hf–O bond lengths. In the seventh Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to four N3- and three O2- atoms. There are a spread of Hf–N bond distances ranging from 2.10–2.61 Å. There are a spread of Hf–O bond distances ranging from 2.18–2.27 Å. In the eighth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 60–64°. There are a spread of Hf–N bond distances ranging from 2.14–2.18 Å. There are one shorter (2.15 Å) and one longer (2.17 Å) Hf–O bond lengths. There are eight inequivalent N3- sites. In the first N3- site, N3- is bonded to five Hf4+ atoms to form distorted NHf5 trigonal bipyramids that share corners with four equivalent NHf5 square pyramids, a cornercorner with one NHf4 tetrahedra, corners with two equivalent OHf4 tetrahedra, edges with two equivalent NHf5 square pyramids, edges with two NHf4 tetrahedra, and edges with two equivalent NHf5 trigonal bipyramids. In the second N3- site, N3- is bonded to five Hf4+ atoms to form distorted NHf5 square pyramids that share a cornercorner with one OHf4 tetrahedra, corners with two equivalent NHf4 tetrahedra, corners with four equivalent NHf5 trigonal bipyramids, edges with two equivalent NHf5 square pyramids, edges with two NHf4 tetrahedra, and edges with two equivalent NHf5 trigonal bipyramids. In the third N3- site, N3- is bonded to five Hf4+ atoms to form distorted NHf5 trigonal bipyramids that share corners with four equivalent NHf5 square pyramids, corners with three NHf4 tetrahedra, edges with two equivalent NHf5 square pyramids, an edgeedge with one NHf4 tetrahedra, an edgeedge with one OHf4 tetrahedra, and edges with two equivalent NHf5 trigonal bipyramids. In the fourth N3- site, N3- is bonded to five Hf4+ atoms to form distorted NHf5 square pyramids that share corners with three NHf4 tetrahedra, corners with four equivalent NHf5 trigonal bipyramids, edges with two equivalent NHf5 square pyramids, an edgeedge with one NHf4 tetrahedra, an edgeedge with one OHf4 tetrahedra, and edges with two equivalent NHf5 trigonal bipyramids. In the fifth N3- site, N3- is bonded in a 5-coordinate geometry to five Hf4+ atoms. In the sixth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent NHf5 square pyramids, corners with two equivalent OHf4 tetrahedra, corners with four NHf4 tetrahedra, a cornercorner with one NHf5 trigonal bipyramid, an edgeedge with one NHf5 square pyramid, and an edgeedge with one NHf5 trigonal bipyramid. In the seventh N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent NHf5 square pyramids, corners with two equivalent OHf4 tetrahedra, corners with four NHf4 tetrahedra, a cornercorner with one NHf5 trigonal bipyramid, an edgeedge with one NHf5 square pyramid, and an edgeedge with one NHf5 trigonal bipyramid. In the eighth N3- site, N3- is bonded to four Hf4+ atoms to form NHf4 tetrahedra that share a cornercorner with one NHf5 square pyramid, corners with two equivalent OHf4 tetrahedra, corners with four NHf4 tetrahedra, corners with two equivalent NHf5 trigonal bipyramids, an edgeedge with one NHf5 square pyramid, and an edgeedge with one NHf5 trigonal bipyramid. There are four inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the second O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 tetrahedra that share a cornercorner with one NHf5 square pyramid, corners with six NHf4 tetrahedra, corners with two equivalent NHf5 trigonal bipyramids, an edgeedge with one NHf5 square pyramid, and an edgeedge with one NHf5 trigonal bipyramid. In the third O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the fourth O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf2N2O by Materials Project

Hf2ON2 is Ilmenite-like structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are eight inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted face, edge, and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 44–64°. There are a spread of Hf–N bond distances ranging from 2.07–2.25 Å. There are one shorter (2.16 Å) and one longer (2.39 Å) Hf–O bond lengths. In the second Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted face, edge, and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 42–66°. There are a spread of Hf–N bond distances ranging from 2.09–2.33 Å. There are one shorter (2.08 Å) and one longer (2.27 Å) Hf–O bond lengths. In the third Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted face, edge, and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 46–66°. There are a spread of Hf–N bond distances ranging from 2.09–2.29 Å. There are one shorter (2.14 Å) and one longer (2.32 Å) Hf–O bond lengths. In the fourth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted face, edge, and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 44–66°. There are a spread of Hf–N bond distances ranging from 2.04–2.23 Å. There are one shorter (2.17 Å) and one longer (2.44 Å) Hf–O bond lengths. In the fifth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted face, edge, and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 42–64°. There are a spread of Hf–N bond distances ranging from 2.06–2.24 Å. There are one shorter (2.15 Å) and one longer (2.35 Å) Hf–O bond lengths. In the sixth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted face, edge, and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 47–67°. There are a spread of Hf–N bond distances ranging from 2.09–2.30 Å. There are one shorter (2.08 Å) and one longer (2.26 Å) Hf–O bond lengths. In the seventh Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted face, edge, and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 45–67°. There are a spread of Hf–N bond distances ranging from 2.04–2.24 Å. There are one shorter (2.17 Å) and one longer (2.38 Å) Hf–O bond lengths. In the eighth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted face, edge, and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 46–66°. There are a spread of Hf–N bond distances ranging from 2.08–2.30 Å. There are one shorter (2.13 Å) and one longer (2.32 Å) Hf–O bond lengths. There are eight inequivalent N3- sites. In the first N3- site, N3- is bonded to four Hf4+ atoms to form a mixture of distorted edge and corner-sharing NHf4 trigonal pyramids. In the second N3- site, N3- is bonded to four Hf4+ atoms to form a mixture of distorted edge and corner-sharing NHf4 trigonal pyramids. In the third N3- site, N3- is bonded to four Hf4+ atoms to form a mixture of distorted edge and corner-sharing NHf4 trigonal pyramids. In the fourth N3- site, N3- is bonded in a distorted see-saw-like geometry to four Hf4+ atoms. In the fifth N3- site, N3- is bonded to four Hf4+ atoms to form a mixture of distorted edge and corner-sharing NHf4 trigonal pyramids. In the sixth N3- site, N3- is bonded to four Hf4+ atoms to form a mixture of distorted edge and corner-sharing NHf4 trigonal pyramids. In the seventh N3- site, N3- is bonded to four Hf4+ atoms to form a mixture of distorted edge and corner-sharing NHf4 trigonal pyramids. In the eighth N3- site, N3- is bonded in a distorted see-saw-like geometry to four Hf4+ atoms. There are four inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the second O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the third O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the fourth O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf2N2O by Materials Project

Hf2ON2 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. there are three inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded to four N3- and two equivalent O2- atoms to form a mixture of edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Hf–N bond distances ranging from 2.06–2.15 Å. Both Hf–O bond lengths are 2.35 Å. In the second Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to four N3- and three equivalent O2- atoms. There are a spread of Hf–N bond distances ranging from 2.14–2.31 Å. There are two shorter (2.18 Å) and one longer (2.46 Å) Hf–O bond lengths. In the third Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to five N3- and two O2- atoms. There are a spread of Hf–N bond distances ranging from 2.10–2.36 Å. There are one shorter (2.21 Å) and one longer (2.71 Å) Hf–O bond lengths. There are three inequivalent N3- sites. In the first N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent OHf6 octahedra, corners with four NHf4 tetrahedra, an edgeedge with one OHf6 octahedra, and an edgeedge with one NHf4 tetrahedra. The corner-sharing octahedral tilt angles are 11°. In the second N3- site, N3- is bonded to four Hf4+ atoms to form NHf4 tetrahedra that share a cornercorner with one OHf6 octahedra, corners with four NHf4 tetrahedra, edges with two equivalent OHf6 octahedra, and edges with two equivalent NHf4 tetrahedra. The corner-sharing octahedral tilt angles are 45°. In the third N3- site, N3- is bonded in a 5-coordinate geometry to five Hf4+ atoms. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the second O2- site, O2- is bonded to six Hf4+ atoms to form distorted OHf6 octahedra that share corners with six NHf4 tetrahedra, edges with two equivalent OHf6 octahedra, and edges with six NHf4 tetrahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf3N2O3 by Materials Project

Hf3N2O3 crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. there are two inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded to two equivalent N3- and four O2- atoms to form distorted HfN2O4 octahedra that share corners with four HfN2O4 octahedra and edges with six equivalent HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 25–35°. Both Hf–N bond lengths are 2.14 Å. There are two shorter (2.11 Å) and two longer (2.12 Å) Hf–O bond lengths. In the second Hf4+ site, Hf4+ is bonded to three equivalent N3- and three O2- atoms to form a mixture of distorted edge and corner-sharing HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 25–56°. There are two shorter (2.12 Å) and one longer (2.18 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.07–2.32 Å. N3- is bonded to four Hf4+ atoms to form a mixture of distorted edge and corner-sharing NHf4 trigonal pyramids. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the second O2- site, O2- is bonded in a distorted T-shaped geometry to three Hf4+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf2N2O by Materials Project

Hf2ON2 crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are six inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded to four N3- and two equivalent O2- atoms to form distorted HfN4O2 octahedra that share corners with two equivalent HfN2O4 octahedra and edges with three HfN4O2 octahedra. The corner-sharing octahedral tilt angles are 5°. There are a spread of Hf–N bond distances ranging from 2.06–2.13 Å. Both Hf–O bond lengths are 2.49 Å. In the second Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to four N3- and three O2- atoms. There are a spread of Hf–N bond distances ranging from 2.17–2.40 Å. There are two shorter (2.18 Å) and one longer (2.43 Å) Hf–O bond lengths. In the third Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to six N3- and one O2- atom. There are a spread of Hf–N bond distances ranging from 2.09–2.41 Å. The Hf–O bond length is 2.71 Å. In the fourth Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to five N3- and two O2- atoms. There are a spread of Hf–N bond distances ranging from 2.13–2.30 Å. There are one shorter (2.19 Å) and one longer (2.67 Å) Hf–O bond lengths. In the fifth Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to five N3- and two O2- atoms. There are a spread of Hf–N bond distances ranging from 2.12–2.39 Å. There are one shorter (2.20 Å) and one longer (2.33 Å) Hf–O bond lengths. In the sixth Hf4+ site, Hf4+ is bonded to two N3- and four O2- atoms to form a mixture of corner and edge-sharing HfN2O4 octahedra. The corner-sharing octahedral tilt angles are 5°. There are one shorter (2.06 Å) and one longer (2.16 Å) Hf–N bond lengths. There are two shorter (2.05 Å) and two longer (2.27 Å) Hf–O bond lengths. There are six inequivalent N3- sites. In the first N3- site, N3- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the second N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent NHf4 tetrahedra, a cornercorner with one OHf4 trigonal pyramid, corners with two equivalent NHf4 trigonal pyramids, and edges with two equivalent NHf4 tetrahedra. In the third N3- site, N3- is bonded in a 5-coordinate geometry to five Hf4+ atoms. In the fourth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with three NHf4 tetrahedra, corners with two equivalent NHf4 trigonal pyramids, and edges with two equivalent OHf4 trigonal pyramids. In the fifth N3- site, N3- is bonded in a 5-coordinate geometry to five Hf4+ atoms. In the sixth N3- site, N3- is bonded to four Hf4+ atoms to form NHf4 tetrahedra that share corners with two equivalent NHf4 tetrahedra, a cornercorner with one NHf4 trigonal pyramid, corners with two equivalent OHf4 trigonal pyramids, and edges with two equivalent NHf4 tetrahedra. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share corners with three NHf4 tetrahedra, corners with two equivalent OHf4 trigonal pyramids, and edges with two equivalent NHf4 trigonal pyramids. In the second O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the third O2- site, O2- is bonded in a 6-coordinate geometry to six Hf4+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf3N2O3 by Materials Project

Hf3N2O3 crystallizes in the orthorhombic Cmc2_1 space group. The structure is three-dimensional. there are three inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded to two N3- and four O2- atoms to form a mixture of distorted edge and corner-sharing HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 28–35°. There are one shorter (2.05 Å) and one longer (2.23 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.07–2.24 Å. In the second Hf4+ site, Hf4+ is bonded in a 6-coordinate geometry to three N3- and three O2- atoms. There are one shorter (2.04 Å) and two longer (2.13 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.03–2.52 Å. In the third Hf4+ site, Hf4+ is bonded to two N3- and four O2- atoms to form a mixture of distorted edge and corner-sharing HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 28–41°. There are one shorter (2.08 Å) and one longer (2.20 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.06–2.24 Å. There are two inequivalent N3- sites. In the first N3- site, N3- is bonded in a 3-coordinate geometry to three Hf4+ atoms. In the second N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent NHf4 tetrahedra, a cornercorner with one OHf4 trigonal pyramid, and edges with two equivalent OHf4 trigonal pyramids. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted T-shaped geometry to three Hf4+ atoms. In the second O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share a cornercorner with one NHf4 tetrahedra, corners with two equivalent OHf4 trigonal pyramids, and edges with two equivalent NHf4 tetrahedra. In the third O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf2N2O by Materials Project

Hf2ON2 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. there are two inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to five N3- and two equivalent O2- atoms. There are a spread of Hf–N bond distances ranging from 2.07–2.50 Å. There are one shorter (2.09 Å) and one longer (2.10 Å) Hf–O bond lengths. In the second Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to five N3- and two equivalent O2- atoms. There are a spread of Hf–N bond distances ranging from 2.06–2.49 Å. There are one shorter (2.09 Å) and one longer (2.47 Å) Hf–O bond lengths. There are two inequivalent N3- sites. In the first N3- site, N3- is bonded to six Hf4+ atoms to form NHf6 octahedra that share corners with six equivalent NHf4 tetrahedra, edges with six equivalent NHf6 octahedra, and edges with three equivalent NHf4 tetrahedra. In the second N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with six equivalent NHf6 octahedra, corners with two equivalent NHf4 tetrahedra, edges with three equivalent NHf6 octahedra, and an edgeedge with one NHf4 tetrahedra. The corner-sharing octahedra tilt angles range from 10–57°. O2- is bonded in a 3-coordinate geometry to four Hf4+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf5N5O2 by Materials Project

Hf5N5O2 crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are five inequivalent Hf sites. In the first Hf site, Hf is bonded to five N and one O atom to form a mixture of edge and corner-sharing HfN5O octahedra. The corner-sharing octahedra tilt angles range from 2–59°. There are a spread of Hf–N bond distances ranging from 2.16–2.22 Å. The Hf–O bond length is 2.18 Å. In the second Hf site, Hf is bonded in a 7-coordinate geometry to five N and two equivalent O atoms. There are a spread of Hf–N bond distances ranging from 2.26–2.41 Å. Both Hf–O bond lengths are 2.22 Å. In the third Hf site, Hf is bonded in a 7-coordinate geometry to five N and two equivalent O atoms. There are a spread of Hf–N bond distances ranging from 2.25–2.38 Å. Both Hf–O bond lengths are 2.23 Å. In the fourth Hf site, Hf is bonded to five N and one O atom to form a mixture of edge and corner-sharing HfN5O octahedra. The corner-sharing octahedra tilt angles range from 2–59°. There are a spread of Hf–N bond distances ranging from 2.16–2.22 Å. The Hf–O bond length is 2.16 Å. In the fifth Hf site, Hf is bonded to four N and two O atoms to form HfN4O2 octahedra that share corners with two HfN5O octahedra and edges with two equivalent HfN4O2 octahedra. The corner-sharing octahedral tilt angles are 59°. There are two shorter (2.19 Å) and two longer (2.20 Å) Hf–N bond lengths. There are one shorter (2.11 Å) and one longer (2.12 Å) Hf–O bond lengths. There are five inequivalent N sites. In the first N site, N is bonded in a square co-planar geometry to four Hf atoms. In the second N site, N is bonded to five Hf atoms to form distorted NHf5 square pyramids that share corners with four equivalent OHf4 tetrahedra, corners with six NHf5 trigonal bipyramids, edges with two equivalent NHf5 square pyramids, edges with three OHf4 tetrahedra, and edges with four NHf5 trigonal bipyramids. In the third N site, N is bonded to five Hf atoms to form NHf5 trigonal bipyramids that share corners with two equivalent NHf5 square pyramids, corners with five OHf4 tetrahedra, corners with two equivalent NHf5 trigonal bipyramids, an edgeedge with one NHf5 square pyramid, an edgeedge with one OHf4 tetrahedra, and edges with four NHf5 trigonal bipyramids. In the fourth N site, N is bonded to five Hf atoms to form NHf5 trigonal bipyramids that share corners with two equivalent NHf5 square pyramids, corners with five OHf4 tetrahedra, corners with two equivalent NHf5 trigonal bipyramids, an edgeedge with one OHf4 tetrahedra, and edges with five NHf5 trigonal bipyramids. In the fifth N site, N is bonded to five Hf atoms to form distorted NHf5 trigonal bipyramids that share corners with two equivalent NHf5 square pyramids, corners with four equivalent OHf4 tetrahedra, corners with four NHf5 trigonal bipyramids, edges with three equivalent NHf5 square pyramids, edges with three OHf4 tetrahedra, and edges with three NHf5 trigonal bipyramids. There are two inequivalent O sites. In the first O site, O is bonded to four Hf atoms to form OHf4 tetrahedra that share corners with three OHf4 tetrahedra, corners with nine NHf5 trigonal bipyramids, edges with two equivalent NHf5 square pyramids, and edges with two NHf5 trigonal bipyramids. In the second O site, O is bonded to four Hf atoms to form OHf4 tetrahedra that share corners with four equivalent NHf5 square pyramids, corners with three OHf4 tetrahedra, corners with five NHf5 trigonal bipyramids, an edgeedge with one NHf5 square pyramid, and edges with three NHf5 trigonal bipyramids.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf3N2O3 by Materials Project

Hf3N2O3 crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are six inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded to two N3- and four O2- atoms to form a mixture of distorted edge and corner-sharing HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 28–52°. There are one shorter (2.12 Å) and one longer (2.19 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.08–2.22 Å. In the second Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 25–52°. There are a spread of Hf–N bond distances ranging from 2.11–2.25 Å. There are one shorter (2.08 Å) and one longer (2.18 Å) Hf–O bond lengths. In the third Hf4+ site, Hf4+ is bonded to two N3- and four O2- atoms to form a mixture of distorted edge and corner-sharing HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 24–36°. There are one shorter (2.12 Å) and one longer (2.19 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.07–2.13 Å. In the fourth Hf4+ site, Hf4+ is bonded to three N3- and three O2- atoms to form a mixture of distorted edge and corner-sharing HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 25–40°. There are one shorter (2.11 Å) and two longer (2.16 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.06–2.29 Å. In the fifth Hf4+ site, Hf4+ is bonded to three N3- and three O2- atoms to form distorted HfN3O3 octahedra that share corners with four HfN2O4 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 24–58°. There are two shorter (2.12 Å) and one longer (2.16 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.06–2.32 Å. In the sixth Hf4+ site, Hf4+ is bonded to two equivalent N3- and four O2- atoms to form a mixture of distorted edge and corner-sharing HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 24–58°. Both Hf–N bond lengths are 2.13 Å. There are a spread of Hf–O bond distances ranging from 2.00–2.27 Å. There are four inequivalent N3- sites. In the first N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent NHf4 tetrahedra, corners with two NHf4 trigonal pyramids, and edges with two equivalent OHf4 trigonal pyramids. In the second N3- site, N3- is bonded to four Hf4+ atoms to form a mixture of distorted edge and corner-sharing NHf4 trigonal pyramids. In the third N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one NHf4 tetrahedra, corners with three NHf4 trigonal pyramids, edges with two equivalent NHf4 trigonal pyramids, and edges with two equivalent OHf4 trigonal pyramids. In the fourth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one OHf4 trigonal pyramid, corners with two equivalent NHf4 trigonal pyramids, and edges with four NHf4 trigonal pyramids. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted T-shaped geometry to three Hf4+ atoms. In the second O2- site, O2- is bonded in a distorted T-shaped geometry to three Hf4+ atoms. In the third O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Hf4+ atoms. In the fourth O2- site, O2- is bonded in a distorted T-shaped geometry to three Hf4+ atoms. In the fifth O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share a cornercorner with one NHf4 trigonal pyramid, corners with two equivalent OHf4 trigonal pyramids, edges with two equivalent NHf4 tetrahedra, and edges with two equivalent NHf4 trigonal pyramids. In the sixth O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf5N5O2 by Materials Project

Hf5N5O2 crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are five inequivalent Hf sites. In the first Hf site, Hf is bonded to six N atoms to form HfN6 octahedra that share corners with three HfN5O octahedra and edges with five HfN6 octahedra. The corner-sharing octahedra tilt angles range from 7–57°. There are a spread of Hf–N bond distances ranging from 2.10–2.30 Å. In the second Hf site, Hf is bonded in a 7-coordinate geometry to five N and three O atoms. There are four shorter (2.28 Å) and one longer (2.81 Å) Hf–N bond lengths. There are two shorter (2.20 Å) and one longer (2.48 Å) Hf–O bond lengths. In the third Hf site, Hf is bonded in a 7-coordinate geometry to five N and two equivalent O atoms. There are a spread of Hf–N bond distances ranging from 2.15–2.45 Å. Both Hf–O bond lengths are 2.36 Å. In the fourth Hf site, Hf is bonded to five N and one O atom to form a mixture of corner and edge-sharing HfN5O octahedra. The corner-sharing octahedra tilt angles range from 7–61°. There are a spread of Hf–N bond distances ranging from 2.17–2.21 Å. The Hf–O bond length is 2.18 Å. In the fifth Hf site, Hf is bonded to three N and three O atoms to form HfN3O3 octahedra that share corners with two HfN6 octahedra and edges with two equivalent HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 57–61°. There are one shorter (2.05 Å) and two longer (2.15 Å) Hf–N bond lengths. There are one shorter (2.17 Å) and two longer (2.25 Å) Hf–O bond lengths. There are five inequivalent N sites. In the first N site, N is bonded in a distorted rectangular see-saw-like geometry to five Hf atoms. In the second N site, N is bonded to five Hf atoms to form NHf5 trigonal bipyramids that share a cornercorner with one OHf4 tetrahedra, corners with four equivalent NHf4 tetrahedra, corners with two equivalent NHf5 trigonal bipyramids, corners with two equivalent OHf5 trigonal bipyramids, an edgeedge with one NHf4 tetrahedra, an edgeedge with one OHf5 trigonal bipyramid, and edges with four NHf5 trigonal bipyramids. In the third N site, N is bonded to five Hf atoms to form NHf5 trigonal bipyramids that share a cornercorner with one NHf4 tetrahedra, corners with four equivalent OHf4 tetrahedra, corners with two equivalent NHf5 trigonal bipyramids, corners with two equivalent OHf5 trigonal bipyramids, an edgeedge with one OHf4 tetrahedra, and edges with five NHf5 trigonal bipyramids. In the fourth N site, N is bonded to five Hf atoms to form distorted NHf5 trigonal bipyramids that share corners with four equivalent OHf4 tetrahedra, corners with two equivalent OHf5 trigonal bipyramids, corners with four NHf5 trigonal bipyramids, an edgeedge with one OHf4 tetrahedra, edges with two equivalent NHf4 tetrahedra, edges with three NHf5 trigonal bipyramids, and edges with three equivalent OHf5 trigonal bipyramids. In the fifth N site, N is bonded to four Hf atoms to form NHf4 tetrahedra that share a cornercorner with one OHf4 tetrahedra, corners with two equivalent NHf4 tetrahedra, corners with four equivalent OHf5 trigonal bipyramids, corners with five NHf5 trigonal bipyramids, an edgeedge with one OHf5 trigonal bipyramid, and edges with three NHf5 trigonal bipyramids. There are two inequivalent O sites. In the first O site, O is bonded to four Hf atoms to form OHf4 tetrahedra that share a cornercorner with one NHf4 tetrahedra, corners with two equivalent OHf4 tetrahedra, corners with nine NHf5 trigonal bipyramids, edges with two NHf5 trigonal bipyramids, and edges with two equivalent OHf5 trigonal bipyramids. In the second O site, O is bonded to five Hf atoms to form distorted OHf5 trigonal bipyramids that share corners with four equivalent NHf4 tetrahedra, corners with six NHf5 trigonal bipyramids, an edgeedge with one NHf4 tetrahedra, edges with two equivalent OHf4 tetrahedra, edges with two equivalent OHf5 trigonal bipyramids, and edges with four NHf5 trigonal bipyramids.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf2N2O by Materials Project

Hf2ON2 is beta indium sulfide-derived structured and crystallizes in the tetragonal I4_1/amd space group. The structure is three-dimensional. there are three inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded to four equivalent N3- and two equivalent O2- atoms to form HfN4O2 octahedra that share corners with four equivalent HfN4 tetrahedra and edges with six HfN4O2 octahedra. All Hf–N bond lengths are 2.21 Å. Both Hf–O bond lengths are 2.08 Å. In the second Hf4+ site, Hf4+ is bonded to four N3- and two equivalent O2- atoms to form HfN4O2 octahedra that share corners with four equivalent HfN4 tetrahedra and edges with six HfN4O2 octahedra. There are a spread of Hf–N bond distances ranging from 2.19–2.23 Å. Both Hf–O bond lengths are 2.10 Å. In the third Hf4+ site, Hf4+ is bonded to four N3- atoms to form corner-sharing HfN4 tetrahedra. The corner-sharing octahedra tilt angles range from 57–58°. There are two shorter (2.08 Å) and two longer (2.09 Å) Hf–N bond lengths. There are two inequivalent N3- sites. In the first N3- site, N3- is bonded to four Hf4+ atoms to form a mixture of distorted corner and edge-sharing NHf4 trigonal pyramids. In the second N3- site, N3- is bonded in a distorted rectangular see-saw-like geometry to four Hf4+ atoms. O2- is bonded in a distorted trigonal non-coplanar geometry to three Hf4+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf2N2O by Materials Project

Hf2ON2 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are two inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded to six N3- atoms to form a mixture of edge and corner-sharing HfN6 octahedra. The corner-sharing octahedral tilt angles are 4°. There are a spread of Hf–N bond distances ranging from 2.10–2.48 Å. In the second Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to four N3- and three equivalent O2- atoms. There are a spread of Hf–N bond distances ranging from 2.17–2.63 Å. There are two shorter (2.01 Å) and one longer (2.21 Å) Hf–O bond lengths. There are two inequivalent N3- sites. In the first N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent NHf6 octahedra, corners with four equivalent NHf4 tetrahedra, and edges with five equivalent NHf6 octahedra. The corner-sharing octahedra tilt angles range from 9–11°. In the second N3- site, N3- is bonded to six Hf4+ atoms to form distorted NHf6 octahedra that share corners with two equivalent NHf6 octahedra, corners with two equivalent NHf4 tetrahedra, edges with six equivalent NHf6 octahedra, and edges with five equivalent NHf4 tetrahedra. The corner-sharing octahedral tilt angles are 4°. O2- is bonded in a distorted trigonal non-coplanar geometry to three equivalent Hf4+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf2N2O by Materials Project

Hf2ON2 is Ilmenite-like structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are sixteen inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form HfN4O2 octahedra that share corners with six HfN3O3 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 53–55°. There are a spread of Hf–N bond distances ranging from 2.09–2.18 Å. There are one shorter (2.25 Å) and one longer (2.26 Å) Hf–O bond lengths. In the second Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form distorted HfN4O2 octahedra that share corners with six HfN3O3 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 52–56°. There are a spread of Hf–N bond distances ranging from 2.09–2.16 Å. There are one shorter (2.28 Å) and one longer (2.33 Å) Hf–O bond lengths. In the third Hf4+ site, Hf4+ is bonded to three N3- and three O2- atoms to form a mixture of distorted edge and corner-sharing HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 51–56°. There are a spread of Hf–N bond distances ranging from 2.09–2.21 Å. There are one shorter (2.12 Å) and two longer (2.19 Å) Hf–O bond lengths. In the fourth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form distorted HfN4O2 octahedra that share corners with six HfN3O3 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 51–57°. There are a spread of Hf–N bond distances ranging from 2.13–2.27 Å. There are one shorter (2.11 Å) and one longer (2.24 Å) Hf–O bond lengths. In the fifth Hf4+ site, Hf4+ is bonded to three N3- and three O2- atoms to form distorted HfN3O3 octahedra that share corners with six HfN3O3 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 51–55°. There are a spread of Hf–N bond distances ranging from 2.09–2.17 Å. There are a spread of Hf–O bond distances ranging from 2.13–2.22 Å. In the sixth Hf4+ site, Hf4+ is bonded to three N3- and three O2- atoms to form distorted HfN3O3 octahedra that share corners with six HfN4O2 octahedra and edges with six HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 49–59°. There are a spread of Hf–N bond distances ranging from 2.08–2.12 Å. There are a spread of Hf–O bond distances ranging from 2.19–2.27 Å. In the seventh Hf4+ site, Hf4+ is bonded to three N3- and three O2- atoms to form a mixture of edge and corner-sharing HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 51–58°. All Hf–N bond lengths are 2.10 Å. There are a spread of Hf–O bond distances ranging from 2.21–2.24 Å. In the eighth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form a mixture of edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 53–57°. There are a spread of Hf–N bond distances ranging from 2.09–2.16 Å. There are one shorter (2.24 Å) and one longer (2.26 Å) Hf–O bond lengths. In the ninth Hf4+ site, Hf4+ is bonded to three N3- and three O2- atoms to form distorted HfN3O3 octahedra that share corners with six HfN4O2 octahedra and edges with six HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 49–55°. There are a spread of Hf–N bond distances ranging from 2.11–2.20 Å. There are two shorter (2.14 Å) and one longer (2.19 Å) Hf–O bond lengths. In the tenth Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form HfN5O octahedra that share corners with six HfN4O2 octahedra and edges with six HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 54–59°. There are a spread of Hf–N bond distances ranging from 2.09–2.22 Å. The Hf–O bond length is 2.33 Å. In the eleventh Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form distorted HfN4O2 octahedra that share corners with six HfN4O2 octahedra and edges with six HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 52–55°. There are a spread of Hf–N bond distances ranging from 2.08–2.18 Å. There are one shorter (2.21 Å) and one longer (2.29 Å) Hf–O bond lengths. In the twelfth Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form a mixture of distorted edge and corner-sharing HfN5O octahedra. The corner-sharing octahedra tilt angles range from 52–55°. There are a spread of Hf–N bond distances ranging from 2.13–2.27 Å. The Hf–O bond length is 2.21 Å. In the thirteenth Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form a mixture of distorted edge and corner-sharing HfN5O octahedra. The corner-sharing octahedra tilt angles range from 51–58°. There are a spread of Hf–N bond distances ranging from 2.13–2.29 Å. The Hf–O bond length is 2.20 Å. In the fourteenth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form distorted HfN4O2 octahedra that share corners with six HfN4O2 octahedra and edges with six HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 52–54°. There are a spread of Hf–N bond distances ranging from 2.12–2.20 Å. There are one shorter (2.14 Å) and one longer (2.21 Å) Hf–O bond lengths. In the fifteenth Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form a mixture of distorted edge and corner-sharing HfN5O octahedra. The corner-sharing octahedra tilt angles range from 51–56°. There are a spread of Hf–N bond distances ranging from 2.12–2.23 Å. The Hf–O bond length is 2.25 Å. In the sixteenth Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form distorted HfN5O octahedra that share corners with six HfN3O3 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 51–59°. There are a spread of Hf–N bond distances ranging from 2.10–2.23 Å. The Hf–O bond length is 2.27 Å. There are sixteen inequivalent N3- sites. In the first N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share a cornercorner with one OHf4 tetrahedra, corners with three OHf4 trigonal pyramids, corners with eight NHf4 trigonal pyramids, an edgeedge with one NHf4 tetrahedra, an edgeedge with one NHf4 trigonal pyramid, and edges with two OHf4 trigonal pyramids. In the second N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one OHf4 tetrahedra, corners with two NHf4 tetrahedra, corners with four OHf4 trigonal pyramids, corners with five NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 trigonal pyramids. In the third N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with three OHf4 trigonal pyramids, corners with nine NHf4 trigonal pyramids, an edgeedge with one NHf4 tetrahedra, an edgeedge with one OHf4 tetrahedra, and edges with two OHf4 trigonal pyramids. In the fourth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one NHf4 tetrahedra, corners with four OHf4 trigonal pyramids, corners with seven NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 trigonal pyramids. In the fifth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one NHf4 tetrahedra, a cornercorner with one OHf4 tetrahedra, corners with three OHf4 trigonal pyramids, corners with seven NHf4 trigonal pyramids, an edgeedge with one OHf4 trigonal pyramid, and edges with three NHf4 trigonal pyramids. In the sixth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one OHf4 tetrahedra, corners with two NHf4 tetrahedra, corners with four OHf4 trigonal pyramids, corners with five NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 trigonal pyramids. In the seventh N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one NHf4 tetrahedra, a cornercorner with one OHf4 tetrahedra, corners with four OHf4 trigonal pyramids, corners with six NHf4 trigonal pyramids, an edgeedge with one OHf4 trigonal pyramid, and edges with three NHf4 trigonal pyramids. In the eighth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one NHf4 tetrahedra, a cornercorner with one OHf4 tetrahedra, corners with four OHf4 trigonal pyramids, corners with six NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 trigonal pyramids. In the ninth N3- site, N3- is bonded to four Hf4+ atoms to form NHf4 trigonal pyramids that share a cornercorner with one OHf4 tetrahedra, corners with two NHf4 tetrahedra, corners with four OHf4 trigonal pyramids, corners with five NHf4 trigonal pyramids, and edges with four NHf4 trigonal pyramids. In the tenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one NHf4 tetrahedra, a cornercorner with one OHf4 tetrahedra, corners with three OHf4 trigonal pyramids, corners with seven NHf4 trigonal pyramids, an edgeedge with one OHf4 trigonal pyramid, and edges with three NHf4 trigonal pyramids. In the eleventh N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with two NHf4 tetrahedra, corners with four OHf4 trigonal pyramids, corners with six NHf4 trigonal pyramids, an edgeedge with one OHf4 tetrahedra, an edgeedge with one OHf4 trigonal pyramid, and edges with two NHf4 trigonal pyramids. In the twelfth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one NHf4 tetrahedra, corners with four OHf4 trigonal pyramids, corners with seven NHf4 trigonal pyramids, an edgeedge with one NHf4 tetrahedra, an edgeedge with one OHf4 trigonal pyramid, and edges with two NHf4 trigonal pyramids. In the thirteenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one NHf4 tetrahedra, corners with three OHf4 trigonal pyramids, corners with eight NHf4 trigonal pyramids, an edgeedge with one NHf4 trigonal pyramid, and edges with three OHf4 trigonal pyramids. In the fourteenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with three OHf4 trigonal pyramids, corners with nine NHf4 trigonal pyramids, an edgeedge with one OHf4 tetrahedra, and edges with three NHf4 trigonal pyramids. In the fifteenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one OHf4 tetrahedra, corners with three OHf4 trigonal pyramids, corners with eight NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 trigonal pyramids. In the sixteenth N3- site, N3- is bonded to four Hf4+ atoms to form NHf4 trigonal pyramids that share corners with two NHf4 tetrahedra, corners with four OHf4 trigonal pyramids, corners with six NHf4 trigonal pyramids, an edgeedge with one OHf4 trigonal pyramid, and edges with three NHf4 trigonal pyramids. There are eight inequivalent O2- sites. In the first O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share corners with two NHf4 tetrahedra, corners with four OHf4 trigonal pyramids, corners with six NHf4 trigonal pyramids, and edges with four NHf4 trigonal pyramids. In the second O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share a cornercorner with one NHf4 tetrahedra, a cornercorner with one OHf4 tetrahedra, corners with four OHf4 trigonal pyramids, corners with six NHf4 trigonal pyramids, an edgeedge with one NHf4 tetrahedra, and edges with three NHf4 trigonal pyramids. In the third O2- site, O2- is bonded to fo

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf2N2O by Materials Project

Hf2ON2 crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are twelve inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to three N3- and four O2- atoms. There are a spread of Hf–N bond distances ranging from 2.09–2.48 Å. There are two shorter (2.15 Å) and two longer (2.29 Å) Hf–O bond lengths. In the second Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to three N3- and four O2- atoms. There are a spread of Hf–N bond distances ranging from 2.11–2.30 Å. There are two shorter (2.14 Å) and two longer (2.33 Å) Hf–O bond lengths. In the third Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form HfN5O octahedra that share corners with four HfN4O2 octahedra and edges with three HfN5O octahedra. The corner-sharing octahedra tilt angles range from 9–72°. There are three shorter (2.11 Å) and two longer (2.29 Å) Hf–N bond lengths. The Hf–O bond length is 2.18 Å. In the fourth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form a mixture of corner and edge-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 9–62°. There are two shorter (2.13 Å) and two longer (2.28 Å) Hf–N bond lengths. There are one shorter (2.09 Å) and one longer (2.15 Å) Hf–O bond lengths. In the fifth Hf4+ site, Hf4+ is bonded to four N3- and two equivalent O2- atoms to form distorted HfN4O2 octahedra that share corners with four HfN5O octahedra and edges with two equivalent HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 62–72°. There are a spread of Hf–N bond distances ranging from 2.13–2.34 Å. Both Hf–O bond lengths are 2.16 Å. In the sixth Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to five N3- and two equivalent O2- atoms. There are a spread of Hf–N bond distances ranging from 2.14–2.42 Å. Both Hf–O bond lengths are 2.14 Å. In the seventh Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to three N3- and four O2- atoms. There are two shorter (2.06 Å) and one longer (2.18 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.22–2.41 Å. In the eighth Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to four N3- and three O2- atoms. There are a spread of Hf–N bond distances ranging from 2.04–2.79 Å. There are two shorter (2.33 Å) and one longer (2.55 Å) Hf–O bond lengths. In the ninth Hf4+ site, Hf4+ is bonded to six N3- atoms to form HfN6 octahedra that share corners with two equivalent HfN5O octahedra and edges with three HfN6 octahedra. The corner-sharing octahedral tilt angles are 17°. There are a spread of Hf–N bond distances ranging from 2.11–2.31 Å. In the tenth Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form a mixture of corner and edge-sharing HfN5O octahedra. The corner-sharing octahedral tilt angles are 17°. There are a spread of Hf–N bond distances ranging from 2.09–2.29 Å. The Hf–O bond length is 2.18 Å. In the eleventh Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to six N3- and one O2- atom. There are a spread of Hf–N bond distances ranging from 2.16–2.38 Å. The Hf–O bond length is 2.28 Å. In the twelfth Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to five N3- and two O2- atoms. There are a spread of Hf–N bond distances ranging from 2.15–2.46 Å. There are one shorter (2.22 Å) and one longer (2.25 Å) Hf–O bond lengths. There are twelve inequivalent N3- sites. In the first N3- site, N3- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the second N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent NHf5 square pyramids, corners with two equivalent NHf4 tetrahedra, corners with two equivalent OHf4 tetrahedra, corners with two equivalent OHf5 trigonal bipyramids, corners with two equivalent OHf4 trigonal pyramids, an edgeedge with one NHf5 square pyramid, and edges with two equivalent OHf4 tetrahedra. In the third N3- site, N3- is bonded to five Hf4+ atoms to form NHf5 square pyramids that share corners with three NHf4 tetrahedra, corners with four OHf4 tetrahedra, edges with two equivalent NHf5 square pyramids, an edgeedge with one NHf4 tetrahedra, and edges with two equivalent OHf4 tetrahedra. In the fourth N3- site, N3- is bonded in a 5-coordinate geometry to five Hf4+ atoms. In the fifth N3- site, N3- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the sixth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share a cornercorner with one NHf5 square pyramid, corners with five NHf4 tetrahedra, corners with two equivalent OHf4 trigonal pyramids, edges with two equivalent NHf5 square pyramids, and edges with two equivalent OHf4 tetrahedra. In the seventh N3- site, N3- is bonded to five Hf4+ atoms to form NHf5 square pyramids that share a cornercorner with one OHf4 tetrahedra, corners with six NHf4 tetrahedra, a cornercorner with one OHf4 trigonal pyramid, edges with two equivalent NHf5 square pyramids, and edges with three NHf4 tetrahedra. In the eighth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent NHf5 square pyramids, corners with four NHf4 tetrahedra, a cornercorner with one OHf5 trigonal bipyramid, a cornercorner with one OHf4 trigonal pyramid, an edgeedge with one NHf5 square pyramid, and edges with two equivalent NHf4 tetrahedra. In the ninth N3- site, N3- is bonded in a 4-coordinate geometry to five Hf4+ atoms. In the tenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent NHf5 square pyramids, corners with two equivalent OHf4 tetrahedra, corners with three NHf4 tetrahedra, corners with two equivalent OHf5 trigonal bipyramids, and edges with two equivalent OHf4 tetrahedra. In the eleventh N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent NHf5 square pyramids, corners with two equivalent OHf4 tetrahedra, corners with four NHf4 tetrahedra, edges with two equivalent NHf4 tetrahedra, and edges with two equivalent OHf5 trigonal bipyramids. In the twelfth N3- site, N3- is bonded in a 5-coordinate geometry to five Hf4+ atoms. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded to five Hf4+ atoms to form distorted OHf5 trigonal bipyramids that share corners with four OHf4 tetrahedra, corners with five NHf4 tetrahedra, edges with two equivalent NHf4 tetrahedra, edges with two OHf4 tetrahedra, and edges with two equivalent OHf5 trigonal bipyramids. In the second O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 tetrahedra that share corners with two equivalent NHf5 square pyramids, corners with two equivalent NHf4 tetrahedra, corners with four OHf4 tetrahedra, corners with two equivalent OHf5 trigonal bipyramids, edges with two equivalent NHf4 tetrahedra, and an edgeedge with one OHf5 trigonal bipyramid. In the third O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 tetrahedra that share corners with two equivalent NHf5 square pyramids, corners with two equivalent NHf4 tetrahedra, corners with three OHf4 tetrahedra, corners with two equivalent OHf5 trigonal bipyramids, edges with two equivalent NHf4 tetrahedra, and an edgeedge with one OHf5 trigonal bipyramid. In the fourth O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 tetrahedra that share a cornercorner with one NHf5 square pyramid, corners with two equivalent NHf4 tetrahedra, corners with three OHf4 tetrahedra, a cornercorner with one OHf4 trigonal pyramid, edges with two equivalent NHf5 square pyramids, and edges with two equivalent NHf4 tetrahedra. In the fifth O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share a cornercorner with one NHf5 square pyramid, a cornercorner with one OHf4 tetrahedra, corners with five NHf4 tetrahedra, and corners with two equivalent OHf4 trigonal pyramids. In the sixth O2- site, O2- is bonded in a 5-coordinate geometry to five Hf4+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Hf2N2O by Materials Project

Hf2ON2 crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are twelve inequivalent Hf4+ sites. In the first Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to three N3- and four O2- atoms. There are a spread of Hf–N bond distances ranging from 2.06–2.49 Å. There are two shorter (2.16 Å) and two longer (2.28 Å) Hf–O bond lengths. In the second Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to three N3- and four O2- atoms. There are two shorter (2.14 Å) and one longer (2.30 Å) Hf–N bond lengths. There are two shorter (2.14 Å) and two longer (2.33 Å) Hf–O bond lengths. In the third Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form HfN5O octahedra that share corners with two equivalent HfN4O2 octahedra, a cornercorner with one HfN5O2 pentagonal bipyramid, edges with three HfN5O octahedra, and edges with two equivalent HfN4O3 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 10°. There are a spread of Hf–N bond distances ranging from 2.10–2.31 Å. The Hf–O bond length is 2.15 Å. In the fourth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form HfN4O2 octahedra that share corners with two equivalent HfN5O octahedra, a cornercorner with one HfN5O2 pentagonal bipyramid, edges with three HfN5O octahedra, and edges with two equivalent HfN4O3 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 10°. There are two shorter (2.13 Å) and two longer (2.27 Å) Hf–N bond lengths. There are one shorter (2.08 Å) and one longer (2.14 Å) Hf–O bond lengths. In the fifth Hf4+ site, Hf4+ is bonded in a 6-coordinate geometry to three N3- and three O2- atoms. There are one shorter (2.08 Å) and two longer (2.29 Å) Hf–N bond lengths. There are two shorter (2.11 Å) and one longer (2.29 Å) Hf–O bond lengths. In the sixth Hf4+ site, Hf4+ is bonded to four N3- and three O2- atoms to form distorted HfN4O3 pentagonal bipyramids that share a cornercorner with one HfN6 octahedra, edges with four HfN5O octahedra, and edges with two equivalent HfN4O3 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 50°. There are a spread of Hf–N bond distances ranging from 2.10–2.37 Å. There are two shorter (2.16 Å) and one longer (2.24 Å) Hf–O bond lengths. In the seventh Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to five N3- and two O2- atoms. There are a spread of Hf–N bond distances ranging from 2.09–2.41 Å. There are one shorter (2.24 Å) and one longer (2.46 Å) Hf–O bond lengths. In the eighth Hf4+ site, Hf4+ is bonded in a 6-coordinate geometry to three N3- and three O2- atoms. There are one shorter (2.05 Å) and two longer (2.19 Å) Hf–N bond lengths. There are two shorter (2.21 Å) and one longer (2.43 Å) Hf–O bond lengths. In the ninth Hf4+ site, Hf4+ is bonded to six N3- atoms to form HfN6 octahedra that share corners with two equivalent HfN6 octahedra, a cornercorner with one HfN4O3 pentagonal bipyramid, and edges with three HfN6 octahedra. The corner-sharing octahedral tilt angles are 15°. There are a spread of Hf–N bond distances ranging from 2.13–2.29 Å. In the tenth Hf4+ site, Hf4+ is bonded to six N3- atoms to form HfN6 octahedra that share corners with two equivalent HfN6 octahedra, edges with three HfN6 octahedra, and edges with two equivalent HfN5O2 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 15°. There are a spread of Hf–N bond distances ranging from 2.10–2.31 Å. In the eleventh Hf4+ site, Hf4+ is bonded in a 7-coordinate geometry to six N3- and one O2- atom. There are a spread of Hf–N bond distances ranging from 2.15–2.37 Å. The Hf–O bond length is 2.28 Å. In the twelfth Hf4+ site, Hf4+ is bonded to five N3- and two O2- atoms to form distorted HfN5O2 pentagonal bipyramids that share corners with two HfN4O2 octahedra, edges with two equivalent HfN6 octahedra, and edges with two equivalent HfN5O2 pentagonal bipyramids. The corner-sharing octahedra tilt angles range from 38–42°. There are a spread of Hf–N bond distances ranging from 2.14–2.34 Å. There are one shorter (2.21 Å) and one longer (2.29 Å) Hf–O bond lengths. There are twelve inequivalent N3- sites. In the first N3- site, N3- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the second N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent NHf5 square pyramids, corners with two equivalent OHf5 square pyramids, corners with two equivalent NHf4 tetrahedra, corners with two equivalent OHf4 tetrahedra, a cornercorner with one OHf4 trigonal pyramid, an edgeedge with one NHf5 square pyramid, and edges with two equivalent OHf4 tetrahedra. In the third N3- site, N3- is bonded to five Hf4+ atoms to form NHf5 square pyramids that share corners with three NHf4 tetrahedra, corners with four OHf4 tetrahedra, a cornercorner with one OHf4 trigonal pyramid, edges with two equivalent NHf5 square pyramids, an edgeedge with one NHf4 tetrahedra, and edges with two equivalent OHf4 tetrahedra. In the fourth N3- site, N3- is bonded in a 5-coordinate geometry to five Hf4+ atoms. In the fifth N3- site, N3- is bonded to five Hf4+ atoms to form distorted NHf5 square pyramids that share corners with two equivalent OHf4 tetrahedra, corners with three NHf4 tetrahedra, corners with two equivalent OHf4 trigonal pyramids, corners with four NHf4 trigonal pyramids, edges with four NHf5 square pyramids, an edgeedge with one NHf4 tetrahedra, and an edgeedge with one OHf4 trigonal pyramid. In the sixth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with three NHf5 square pyramids, corners with three NHf4 tetrahedra, a cornercorner with one OHf4 trigonal pyramid, corners with two equivalent NHf4 trigonal pyramids, edges with three NHf5 square pyramids, and edges with two equivalent OHf4 tetrahedra. In the seventh N3- site, N3- is bonded to five Hf4+ atoms to form NHf5 square pyramids that share a cornercorner with one OHf4 tetrahedra, corners with four NHf4 tetrahedra, corners with four NHf4 trigonal pyramids, edges with four NHf5 square pyramids, edges with two equivalent NHf4 tetrahedra, and edges with two NHf4 trigonal pyramids. In the eighth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one OHf5 square pyramid, corners with four NHf5 square pyramids, corners with two equivalent NHf4 tetrahedra, corners with two equivalent OHf4 trigonal pyramids, corners with three NHf4 trigonal pyramids, an edgeedge with one NHf5 square pyramid, and edges with two equivalent NHf4 tetrahedra. In the ninth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share a cornercorner with one OHf5 square pyramid, corners with four NHf5 square pyramids, corners with two equivalent NHf4 tetrahedra, corners with two OHf4 tetrahedra, corners with three NHf4 trigonal pyramids, an edgeedge with one NHf5 square pyramid, and edges with two equivalent NHf4 tetrahedra. In the tenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent OHf5 square pyramids, corners with three NHf5 square pyramids, corners with two equivalent OHf4 tetrahedra, corners with three NHf4 tetrahedra, edges with two equivalent OHf4 tetrahedra, and edges with two equivalent NHf4 trigonal pyramids. In the eleventh N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with two equivalent NHf5 square pyramids, corners with two equivalent OHf4 tetrahedra, corners with four NHf4 tetrahedra, corners with two equivalent NHf4 trigonal pyramids, edges with two equivalent OHf5 square pyramids, and edges with two equivalent NHf4 trigonal pyramids. In the twelfth N3- site, N3- is bonded in a 5-coordinate geometry to five Hf4+ atoms. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded to five Hf4+ atoms to form distorted OHf5 square pyramids that share corners with four NHf4 tetrahedra, corners with four OHf4 tetrahedra, corners with two NHf4 trigonal pyramids, edges with two equivalent OHf5 square pyramids, edges with two equivalent NHf4 tetrahedra, and edges with two OHf4 tetrahedra. In the second O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 tetrahedra that share corners with two equivalent NHf5 square pyramids, corners with two equivalent OHf5 square pyramids, corners with two equivalent NHf4 tetrahedra, corners with four OHf4 tetrahedra, a cornercorner with one NHf4 trigonal pyramid, an edgeedge with one OHf5 square pyramid, and edges with two equivalent NHf4 tetrahedra. In the third O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 tetrahedra that share corners with two equivalent NHf5 square pyramids, corners with two equivalent OHf5 square pyramids, corners with two equivalent NHf4 tetrahedra, corners with three OHf4 tetrahedra, a cornercorner with one NHf4 trigonal pyramid, an edgeedge with one OHf5 square pyramid, and edges with two equivalent NHf4 tetrahedra. In the fourth O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 tetrahedra that share corners with three NHf5 square pyramids, corners with two equivalent NHf4 tetrahedra, corners with three OHf4 tetrahedra, corners with two equivalent OHf4 trigonal pyramids, edges with two equivalent NHf5 square pyramids, and edges with two equivalent NHf4 tetrahedra. In the fifth O2- site, O2- is bonded in a 4-coordinate geometry to four Hf4+ atoms. In the sixth O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share corners with three NHf5 square pyramids, corners with two NHf4 tetrahedra, corners with two equivalent OHf4 tetrahedra, corners with two equivalent NHf4 trigonal pyramids, corners with two equivalent OHf4 trigonal pyramids, and an edgeedge with one NHf5 square pyramid.

36 MATERIALS SCIENCE↗