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Ultrafast vibrational dynamics of a trigonal planar anionic probe in ionic liquids (ILs): A two-dimensional infrared (2DIR) spectroscopic investigation

A major impediment limiting the widespread application of ionic liquids (ILs) is their high shear viscosity. Incorporation of a tricyanomethanide (TCM - ) anion in ILs leads to low shear viscosity and improvement of several characteristics suitable for large scale applications. However, properties including interactions of TCM - with the local environment and dynamics of TCM - have not been thoroughly investigated. Herein, we have studied the ultrafast dynamics of TCM - in several imidazolium ILs using linear IR and two-dimensional infrared spectroscopy techniques. The spectral diffusion dynamics of the CN stretching modes of TCM - in all ILs exhibit a nonexponential behavior with a short time component of ~2 ps and a long time component spanning ~9 ps to 14 ps. The TCM - vibrational probe reports a significantly faster relaxation of ILs compared to those observed previously using linear vibrational probes, such as thiocyanate and selenocyanate. Our results indicate a rapid relaxation of the local ion-cage structure embedding the vibrational probe in the ILs. The faster relaxation suggests that the lifetime of the local ion-cage structure decreases in the presence of TCM - in the ILs. Linear IR spectroscopic results show that the hydrogen-bonding interaction between TCM - and imidazolium cations in ILs is much weaker. Shorter ion-cage lifetimes together with weaker hydrogen-bonding interactions account for the low shear viscosity of TCM - based ILs compared to commonly used ILs. In addition, this work demonstrates that TCM - can be used as a potential vibrational reporter to study the structure and dynamics of ILs and other molecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Crystal structure of a trigonal polymorph of aquadioxidobis(pentane-2,4-dionato-κ 2 O , O ′)uranium(VI)

The title compound, [UO 2 (acac) 2 (H 2 O)] consists of a uranyl(VI) unit ([O=U=O] 2+ ) coordinated to two monoanionic acetylacetonate (acac, C 5 H 7 O 2 ) ligands and one water molecule. The asymmetric unit includes a one-half of a uranium atom, one oxido ion, one-half of a water molecule and one acac ligand. The coordination about the uranium atom is distorted pentagonal–bipyramidal. The acac ligands and O w atom comprise the equatorial plane, while the uranyl O atoms occupy the axial positions. Intermolecular hydrogen bonding between complexes results in the formation of two-dimensional hexagonal void channels along the c- axis direction with a diameter of 6.7 Å. The monoclinic ( P 2 1 / c space group) polymorph was reported by Alcock & Flanders [(1987). Acta Cryst. C 43 , 1480–1483].

Hernandez, Alejandro↗

Materials Data on Cd9(InSe2)20 by Materials Project

Cd9(InSe2)20 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are nine inequivalent Cd2+ sites. In the first Cd2+ site, Cd2+ is bonded to five Se+1.85- atoms to form distorted CdSe5 trigonal bipyramids that share corners with two CdSe5 trigonal bipyramids, corners with three InSe5 trigonal bipyramids, and edges with four InSe5 trigonal bipyramids. There are a spread of Cd–Se bond distances ranging from 2.64–3.17 Å. In the second Cd2+ site, Cd2+ is bonded to five Se+1.85- atoms to form distorted CdSe5 trigonal bipyramids that share corners with two CdSe5 trigonal bipyramids, corners with four InSe5 trigonal bipyramids, and edges with four InSe5 trigonal bipyramids. There are a spread of Cd–Se bond distances ranging from 2.63–3.28 Å. In the third Cd2+ site, Cd2+ is bonded to five Se+1.85- atoms to form distorted CdSe5 trigonal bipyramids that share corners with two CdSe5 trigonal bipyramids, corners with three InSe5 trigonal bipyramids, and edges with four InSe5 trigonal bipyramids. There are a spread of Cd–Se bond distances ranging from 2.64–3.17 Å. In the fourth Cd2+ site, Cd2+ is bonded to five Se+1.85- atoms to form CdSe5 trigonal bipyramids that share a cornercorner with one CdSe5 trigonal bipyramid, corners with two InSe5 trigonal bipyramids, and edges with four InSe5 trigonal bipyramids. There are a spread of Cd–Se bond distances ranging from 2.74–2.87 Å. In the fifth Cd2+ site, Cd2+ is bonded in a 5-coordinate geometry to five Se+1.85- atoms. There are a spread of Cd–Se bond distances ranging from 2.63–3.35 Å. In the sixth Cd2+ site, Cd2+ is bonded to five Se+1.85- atoms to form CdSe5 trigonal bipyramids that share corners with two CdSe5 trigonal bipyramids, corners with four InSe5 trigonal bipyramids, and edges with three InSe5 trigonal bipyramids. There are a spread of Cd–Se bond distances ranging from 2.71–2.88 Å. In the seventh Cd2+ site, Cd2+ is bonded to five Se+1.85- atoms to form CdSe5 trigonal bipyramids that share a cornercorner with one CdSe5 trigonal bipyramid, corners with four InSe5 trigonal bipyramids, and edges with four InSe5 trigonal bipyramids. There are a spread of Cd–Se bond distances ranging from 2.73–2.87 Å. In the eighth Cd2+ site, Cd2+ is bonded to five Se+1.85- atoms to form CdSe5 trigonal bipyramids that share a cornercorner with one CdSe5 trigonal bipyramid, corners with four InSe5 trigonal bipyramids, and edges with three InSe5 trigonal bipyramids. There are a spread of Cd–Se bond distances ranging from 2.69–2.89 Å. In the ninth Cd2+ site, Cd2+ is bonded to five Se+1.85- atoms to form CdSe5 trigonal bipyramids that share a cornercorner with one CdSe5 trigonal bipyramid, corners with four InSe5 trigonal bipyramids, and edges with four InSe5 trigonal bipyramids. There are a spread of Cd–Se bond distances ranging from 2.72–2.88 Å. There are twenty inequivalent In+2.80+ sites. In the first In+2.80+ site, In+2.80+ is bonded in a 5-coordinate geometry to five Se+1.85- atoms. There are a spread of In–Se bond distances ranging from 2.66–3.30 Å. In the second In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share corners with two CdSe5 trigonal bipyramids, corners with eight InSe5 trigonal bipyramids, and edges with two CdSe5 trigonal bipyramids. There are a spread of In–Se bond distances ranging from 2.64–3.06 Å. In the third In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share corners with two CdSe5 trigonal bipyramids, corners with seven InSe5 trigonal bipyramids, and edges with two CdSe5 trigonal bipyramids. There are a spread of In–Se bond distances ranging from 2.65–3.13 Å. In the fourth In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share corners with two CdSe5 trigonal bipyramids, corners with seven InSe5 trigonal bipyramids, and edges with two CdSe5 trigonal bipyramids. There are a spread of In–Se bond distances ranging from 2.65–3.05 Å. In the fifth In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share corners with two CdSe5 trigonal bipyramids, corners with seven InSe5 trigonal bipyramids, and edges with two CdSe5 trigonal bipyramids. There are a spread of In–Se bond distances ranging from 2.67–3.09 Å. In the sixth In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share a cornercorner with one CdSe5 trigonal bipyramid, corners with seven InSe5 trigonal bipyramids, and edges with two CdSe5 trigonal bipyramids. There are a spread of In–Se bond distances ranging from 2.65–3.06 Å. In the seventh In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share corners with two CdSe5 trigonal bipyramids, corners with eight InSe5 trigonal bipyramids, and edges with two CdSe5 trigonal bipyramids. There are a spread of In–Se bond distances ranging from 2.66–3.04 Å. In the eighth In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share a cornercorner with one CdSe5 trigonal bipyramid, corners with seven InSe5 trigonal bipyramids, and edges with two CdSe5 trigonal bipyramids. There are a spread of In–Se bond distances ranging from 2.65–3.06 Å. In the ninth In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share corners with two CdSe5 trigonal bipyramids, corners with eight InSe5 trigonal bipyramids, and an edgeedge with one CdSe5 trigonal bipyramid. There are a spread of In–Se bond distances ranging from 2.66–3.02 Å. In the tenth In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share a cornercorner with one CdSe5 trigonal bipyramid, corners with seven InSe5 trigonal bipyramids, and edges with two CdSe5 trigonal bipyramids. There are a spread of In–Se bond distances ranging from 2.62–3.11 Å. In the eleventh In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share a cornercorner with one CdSe5 trigonal bipyramid, corners with seven InSe5 trigonal bipyramids, and edges with two CdSe5 trigonal bipyramids. There are a spread of In–Se bond distances ranging from 2.66–3.07 Å. In the twelfth In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share a cornercorner with one CdSe5 trigonal bipyramid, corners with seven InSe5 trigonal bipyramids, and an edgeedge with one CdSe5 trigonal bipyramid. There are a spread of In–Se bond distances ranging from 2.63–3.03 Å. In the thirteenth In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share a cornercorner with one CdSe5 trigonal bipyramid, corners with seven InSe5 trigonal bipyramids, and an edgeedge with one CdSe5 trigonal bipyramid. There are a spread of In–Se bond distances ranging from 2.65–2.99 Å. In the fourteenth In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share corners with two CdSe5 trigonal bipyramids, corners with seven InSe5 trigonal bipyramids, and edges with two CdSe5 trigonal bipyramids. There are a spread of In–Se bond distances ranging from 2.65–3.02 Å. In the fifteenth In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share a cornercorner with one CdSe5 trigonal bipyramid, corners with seven InSe5 trigonal bipyramids, and edges with two CdSe5 trigonal bipyramids. There are a spread of In–Se bond distances ranging from 2.66–3.00 Å. In the sixteenth In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share a cornercorner with one CdSe5 trigonal bipyramid, corners with seven InSe5 trigonal bipyramids, and edges with two CdSe5 trigonal bipyramids. There are a spread of In–Se bond distances ranging from 2.66–3.01 Å. In the seventeenth In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share corners with two CdSe5 trigonal bipyramids, corners with eight InSe5 trigonal bipyramids, and an edgeedge with one CdSe5 trigonal bipyramid. There are a spread of In–Se bond distances ranging from 2.65–3.09 Å. In the eighteenth In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share corners with two CdSe5 trigonal bipyramids, corners with eight InSe5 trigonal bipyramids, and an edgeedge with one CdSe5 trigonal bipyramid. There are a spread of In–Se bond distances ranging from 2.66–3.09 Å. In the nineteenth In+2.80+ site, In+2.80+ is bonded in a 5-coordinate geometry to five Se+1.85- atoms. There are a spread of In–Se bond distances ranging from 2.66–3.28 Å. In the twentieth In+2.80+ site, In+2.80+ is bonded to five Se+1.85- atoms to form distorted InSe5 trigonal bipyramids that share corners with two CdSe5 trigonal bipyramids, corners with six InSe5 trigonal bipyramids, and an edgeedge with one CdSe5 trigonal bipyramid. There are a spread of In–Se bond distances ranging from 2.65–3.02 Å. There are forty inequivalent Se+1.85- sites. In the first Se+1.85- site, Se+1.85- is bonded to one Cd2+ and three In+2.80+ atoms to form distorted SeCdIn3 trigonal pyramids that share a cornercorner with one SeCd2In2 tetrahedra and corners with four SeCdIn3 trigonal pyramids. In the second Se+1.85- site, Se+1.85- is bonded in a 4-coordinate geometry to one Cd2+ and three In+2.80+ atoms. In the third Se+1.85- site, Se+1.85- is bonded in a distorted trigonal non-coplanar geometry to one Cd2+ and two In+2.80+ atoms. In the fourth Se+1.85- site, Se+1.85- is bonded in a 3-coordinate geometry to three In+2.80+ atoms. In the fifth Se+1.85- site, Se+1.85- is bonded in a distorted trigonal non-coplanar geometry to one Cd2+ and two In+2.80+ atoms. In the sixth Se+1.85- site, Se+1.85- is bonded in a 4-coordinate geometry to one Cd2+ and three In+2.80+ atoms. In the seventh Se+1.85- site, Se+1.85- is bonded to one Cd2+ and three In+2.80+ atoms to form distorted SeCdIn3 trigonal pyramids that share a cornercorner with one SeCd2In2 tetrahedra, corners with six SeCdIn3 trigonal pyramids, and an edgeedge with one SeCd2In2 tetrahedra. In the eighth Se+1.85- site, Se+1.85- is bonded in a 4-coordinate geometry to two Cd2+ and two In+2.80+ atoms. In the ninth Se+1.85- site, Se+1.85- is bonded to one Cd2+ and three In+2.80+ atoms to form distorted SeCdIn3 trigonal pyramids that share corners with two SeCd2In2 tetrahedra and corners with six SeCdIn3 trigonal pyramids. In the tenth Se+1.85- site, Se+1.85- is bonded to two Cd2+ and two In+2.80+ atoms to form a mixture of edge and corner-sharing SeCd2In2 tetrahedra. In the eleventh Se+1.85- site, Se+1.85- is bonded to one Cd2+ and three In+2.80+ atoms to form distorted SeCdIn3 trigonal pyramids that share a cornercorner with one SeCd2In2 tetrahedra, corners with six SeCdIn3 trigonal pyramids, and an edgeedge with one SeCd2In2 tetrahedra. In the twelfth Se+1.85- site, Se+1.85- is bonded in a distorted trigonal non-coplanar geometry to one Cd2+ and two In+2.80+ atoms. In the thirteenth Se+1.85- site, Se+1.85- is bonded to one Cd2+ and three In+2.80+ atoms to form distorted SeCdIn3 trigonal pyramids that share corners with two SeCd2In2 tetrahedra and corners with six SeCdIn3 trigonal pyramids. In the fourteenth Se+1.85- site, Se+1.85- is bonded in a distorted T-shaped geometry to one Cd2+ and two In+2.80+ atoms. In the fifteenth Se+1.85- site, Se+1.85- is bonded to one Cd2+ and three In+2.80+ atoms to form distorted SeCdIn3 trigonal pyramids that share a cornercorner with one SeCd2In2 tetrahedra, corners with seven SeCdIn3 trigonal pyramids, and an edgeedge with one SeCd2In2 tetrahedra. In the sixteenth Se+1.

36 MATERIALS SCIENCE↗

Materials Data on LiMg7N5 by Materials Project

LiMg7N5 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are six inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded in a distorted trigonal non-coplanar geometry to three N3- atoms. There are a spread of Li–N bond distances ranging from 2.01–2.18 Å. In the second Li1+ site, Li1+ is bonded to four N3- atoms to form distorted LiN4 trigonal pyramids that share corners with four MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with six MgN4 trigonal pyramids, edges with three MgN4 tetrahedra, and an edgeedge with one MgN4 trigonal pyramid. There are a spread of Li–N bond distances ranging from 2.10–2.38 Å. In the third Li1+ site, Li1+ is bonded to four N3- atoms to form distorted LiN4 trigonal pyramids that share corners with five MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with four MgN4 trigonal pyramids, edges with three MgN4 tetrahedra, and an edgeedge with one MgN4 trigonal pyramid. There are a spread of Li–N bond distances ranging from 2.07–2.37 Å. In the fourth Li1+ site, Li1+ is bonded in a trigonal non-coplanar geometry to three N3- atoms. There are a spread of Li–N bond distances ranging from 2.04–2.11 Å. In the fifth Li1+ site, Li1+ is bonded in a bent 120 degrees geometry to two N3- atoms. There are one shorter (1.96 Å) and one longer (2.04 Å) Li–N bond lengths. In the sixth Li1+ site, Li1+ is bonded to four N3- atoms to form distorted LiN4 trigonal pyramids that share corners with two MgN4 tetrahedra, corners with five MgN4 trigonal pyramids, edges with three MgN4 tetrahedra, and an edgeedge with one MgN4 trigonal pyramid. There are a spread of Li–N bond distances ranging from 2.12–2.29 Å. There are forty-two inequivalent Mg2+ sites. In the first Mg2+ site, Mg2+ is bonded to four N3- atoms to form distorted MgN4 trigonal pyramids that share corners with six MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with five MgN4 trigonal pyramids, edges with two MgN4 tetrahedra, and edges with two MgN4 trigonal pyramids. There are a spread of Mg–N bond distances ranging from 2.10–2.23 Å. In the second Mg2+ site, Mg2+ is bonded to four N3- atoms to form distorted MgN4 trigonal pyramids that share corners with five MgN4 tetrahedra, corners with two LiN4 trigonal pyramids, corners with three MgN4 trigonal pyramids, edges with three MgN4 tetrahedra, and an edgeedge with one MgN4 trigonal pyramid. There are a spread of Mg–N bond distances ranging from 2.08–2.28 Å. In the third Mg2+ site, Mg2+ is bonded to four N3- atoms to form distorted MgN4 tetrahedra that share corners with four MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with seven MgN4 trigonal pyramids, edges with two MgN4 tetrahedra, and edges with two MgN4 trigonal pyramids. There are a spread of Mg–N bond distances ranging from 2.08–2.20 Å. In the fourth Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 trigonal pyramids that share corners with seven MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with four MgN4 trigonal pyramids, an edgeedge with one MgN4 tetrahedra, and edges with three MgN4 trigonal pyramids. There are a spread of Mg–N bond distances ranging from 2.12–2.22 Å. In the fifth Mg2+ site, Mg2+ is bonded to four N3- atoms to form distorted MgN4 tetrahedra that share corners with five MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with five MgN4 trigonal pyramids, an edgeedge with one MgN4 tetrahedra, an edgeedge with one LiN4 trigonal pyramid, and an edgeedge with one MgN4 trigonal pyramid. There are a spread of Mg–N bond distances ranging from 2.08–2.24 Å. In the sixth Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 tetrahedra that share corners with six MgN4 tetrahedra, corners with six MgN4 trigonal pyramids, edges with three MgN4 tetrahedra, and an edgeedge with one LiN4 trigonal pyramid. There are a spread of Mg–N bond distances ranging from 2.09–2.24 Å. In the seventh Mg2+ site, Mg2+ is bonded to four N3- atoms to form distorted MgN4 trigonal pyramids that share corners with five MgN4 tetrahedra, corners with two MgN4 trigonal pyramids, an edgeedge with one MgN4 tetrahedra, an edgeedge with one LiN4 trigonal pyramid, and an edgeedge with one MgN4 trigonal pyramid. There are a spread of Mg–N bond distances ranging from 2.12–2.26 Å. In the eighth Mg2+ site, Mg2+ is bonded in a trigonal planar geometry to three N3- atoms. There are a spread of Mg–N bond distances ranging from 2.05–2.08 Å. In the ninth Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 tetrahedra that share corners with six MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with three MgN4 trigonal pyramids, an edgeedge with one MgN4 tetrahedra, an edgeedge with one LiN4 trigonal pyramid, and an edgeedge with one MgN4 trigonal pyramid. There are a spread of Mg–N bond distances ranging from 2.06–2.22 Å. In the tenth Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 trigonal pyramids that share corners with six MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with four MgN4 trigonal pyramids, an edgeedge with one MgN4 tetrahedra, and edges with two MgN4 trigonal pyramids. There are a spread of Mg–N bond distances ranging from 2.09–2.23 Å. In the eleventh Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 tetrahedra that share corners with five MgN4 tetrahedra, corners with two LiN4 trigonal pyramids, corners with five MgN4 trigonal pyramids, edges with three MgN4 tetrahedra, and an edgeedge with one MgN4 trigonal pyramid. There are a spread of Mg–N bond distances ranging from 2.10–2.18 Å. In the twelfth Mg2+ site, Mg2+ is bonded in a trigonal non-coplanar geometry to three N3- atoms. There are a spread of Mg–N bond distances ranging from 2.00–2.17 Å. In the thirteenth Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 trigonal pyramids that share corners with four MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with five MgN4 trigonal pyramids, edges with three MgN4 tetrahedra, and an edgeedge with one MgN4 trigonal pyramid. There are a spread of Mg–N bond distances ranging from 2.10–2.23 Å. In the fourteenth Mg2+ site, Mg2+ is bonded to four N3- atoms to form a mixture of edge and corner-sharing MgN4 tetrahedra. There are a spread of Mg–N bond distances ranging from 2.14–2.19 Å. In the fifteenth Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 tetrahedra that share corners with six MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with two MgN4 trigonal pyramids, an edgeedge with one MgN4 tetrahedra, an edgeedge with one LiN4 trigonal pyramid, and edges with two MgN4 trigonal pyramids. There are a spread of Mg–N bond distances ranging from 2.10–2.25 Å. In the sixteenth Mg2+ site, Mg2+ is bonded to four N3- atoms to form distorted MgN4 tetrahedra that share corners with six MgN4 tetrahedra, corners with two MgN4 trigonal pyramids, an edgeedge with one MgN4 tetrahedra, an edgeedge with one LiN4 trigonal pyramid, and an edgeedge with one MgN4 trigonal pyramid. There are a spread of Mg–N bond distances ranging from 2.05–2.27 Å. In the seventeenth Mg2+ site, Mg2+ is bonded in a trigonal non-coplanar geometry to three N3- atoms. There are a spread of Mg–N bond distances ranging from 2.07–2.09 Å. In the eighteenth Mg2+ site, Mg2+ is bonded to four N3- atoms to form a mixture of edge and corner-sharing MgN4 tetrahedra. There are a spread of Mg–N bond distances ranging from 2.15–2.18 Å. In the nineteenth Mg2+ site, Mg2+ is bonded in a trigonal non-coplanar geometry to three N3- atoms. There are a spread of Mg–N bond distances ranging from 2.01–2.14 Å. In the twentieth Mg2+ site, Mg2+ is bonded to four N3- atoms to form distorted MgN4 tetrahedra that share corners with five MgN4 tetrahedra, corners with two MgN4 trigonal pyramids, an edgeedge with one LiN4 trigonal pyramid, and edges with two MgN4 trigonal pyramids. There are a spread of Mg–N bond distances ranging from 2.05–2.25 Å. In the twenty-first Mg2+ site, Mg2+ is bonded in a trigonal planar geometry to three N3- atoms. There are one shorter (2.06 Å) and two longer (2.12 Å) Mg–N bond lengths. In the twenty-second Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 trigonal pyramids that share corners with six MgN4 tetrahedra, corners with five MgN4 trigonal pyramids, an edgeedge with one MgN4 tetrahedra, an edgeedge with one LiN4 trigonal pyramid, and edges with two MgN4 trigonal pyramids. There are a spread of Mg–N bond distances ranging from 2.11–2.21 Å. In the twenty-third Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 tetrahedra that share corners with five MgN4 tetrahedra, corners with three MgN4 trigonal pyramids, an edgeedge with one LiN4 trigonal pyramid, and edges with two MgN4 trigonal pyramids. There are a spread of Mg–N bond distances ranging from 2.10–2.23 Å. In the twenty-fourth Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 trigonal pyramids that share corners with four MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with five MgN4 trigonal pyramids, edges with two MgN4 tetrahedra, and an edgeedge with one MgN4 trigonal pyramid. There are a spread of Mg–N bond distances ranging from 2.10–2.26 Å. In the twenty-fifth Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 tetrahedra that share corners with four MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with seven MgN4 trigonal pyramids, an edgeedge with one MgN4 tetrahedra, and edges with three MgN4 trigonal pyramids. There are a spread of Mg–N bond distances ranging from 2.12–2.20 Å. In the twenty-sixth Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 tetrahedra that share a cornercorner with one MgN4 tetrahedra, corners with two LiN4 trigonal pyramids, corners with four MgN4 trigonal pyramids, edges with three MgN4 tetrahedra, and an edgeedge with one MgN4 trigonal pyramid. There are a spread of Mg–N bond distances ranging from 2.11–2.22 Å. In the twenty-seventh Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 trigonal pyramids that share corners with six MgN4 tetrahedra, corners with two LiN4 trigonal pyramids, corners with four MgN4 trigonal pyramids, edges with three MgN4 tetrahedra, and an edgeedge with one MgN4 trigonal pyramid. There are a spread of Mg–N bond distances ranging from 2.11–2.24 Å. In the twenty-eighth Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 trigonal pyramids that share corners with five MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with six MgN4 trigonal pyramids, an edgeedge with one MgN4 tetrahedra, and edges with three MgN4 trigonal pyramids. There are a spread of Mg–N bond distances ranging from 2.12–2.20 Å. In the twenty-ninth Mg2+ site, Mg2+ is bonded to four N3- atoms to form distorted MgN4 trigonal pyramids that share corners with two MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with four MgN4 trigonal pyramids, and edges with three MgN4 tetrahedra. There are a spread of Mg–N bond distances ranging from 2.11–2.23 Å. In the thirtieth Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 trigonal pyramids that share corners with three MgN4 tetrahedra, corners with two LiN4 trigonal pyramids, corners with four MgN4 trigonal pyramids, and edges with two MgN4 tetrahedra. There are a spread of Mg–N bond distances ranging from 2.08–2.30 Å. In the thirty-first Mg2+ site, Mg2+ is bonded to four N3- atoms to form MgN4 trigonal pyramids that share corners with three MgN4 tetrahedra, a cornercorner with one LiN4 trigonal pyramid, corners with three MgN4 trigonal pyramids, and edges with three MgN4 tetrahedra. There are a spread of Mg–N bond distances ranging from 2.06–2.28 Å. In the thirty-second Mg2+ site, Mg2+ is bonded to four N3- atoms to form distorted Mg

36 MATERIALS SCIENCE↗

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 a mixture of distorted edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 51–59°. There are a spread of Hf–N bond distances ranging from 2.09–2.24 Å. There are one shorter (2.18 Å) and one longer (2.27 Å) Hf–O bond lengths. In the second 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 51–57°. There are a spread of Hf–N bond distances ranging from 2.10–2.18 Å. There are one shorter (2.23 Å) and one longer (2.26 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 edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 50–59°. There are a spread of Hf–N bond distances ranging from 2.09–2.19 Å. There are one shorter (2.23 Å) and one longer (2.28 Å) Hf–O bond lengths. In the fourth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form HfN4O2 octahedra that share corners with six HfN4O2 octahedra and edges with six HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 52–59°. There are a spread of Hf–N bond distances ranging from 2.08–2.20 Å. There are one shorter (2.24 Å) and one longer (2.29 Å) Hf–O bond lengths. In the fifth 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 51–53°. There are a spread of Hf–N bond distances ranging from 2.13–2.16 Å. There are a spread of Hf–O bond distances ranging from 2.09–2.21 Å. In the sixth 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 52–54°. There are a spread of Hf–N bond distances ranging from 2.13–2.21 Å. There are one shorter (2.15 Å) and one longer (2.17 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 edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 53–56°. There are a spread of Hf–N bond distances ranging from 2.11–2.22 Å. There are one shorter (2.23 Å) and one longer (2.25 Å) Hf–O bond lengths. In the eighth 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 51–58°. There are a spread of Hf–N bond distances ranging from 2.07–2.14 Å. There are two shorter (2.19 Å) and one longer (2.30 Å) Hf–O bond lengths. In the ninth 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 52–58°. There are a spread of Hf–N bond distances ranging from 2.13–2.23 Å. The Hf–O bond length is 2.24 Å. In the tenth 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 52–57°. There are a spread of Hf–N bond distances ranging from 2.11–2.22 Å. There are a spread of Hf–O bond distances ranging from 2.13–2.19 Å. In the eleventh 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 53–55°. There are a spread of Hf–N bond distances ranging from 2.11–2.25 Å. The Hf–O bond length is 2.31 Å. In the twelfth 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 51–55°. There are a spread of Hf–N bond distances ranging from 2.08–2.18 Å. There are one shorter (2.18 Å) and one longer (2.34 Å) Hf–O bond lengths. In the thirteenth 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 54–58°. There are a spread of Hf–N bond distances ranging from 2.09–2.20 Å. There are one shorter (2.26 Å) and one longer (2.28 Å) Hf–O bond lengths. In the fourteenth 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 51–57°. There are a spread of Hf–N bond distances ranging from 2.15–2.20 Å. There are one shorter (2.16 Å) and one longer (2.18 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 53–57°. There are a spread of Hf–N bond distances ranging from 2.12–2.22 Å. The Hf–O bond length is 2.28 Å. In the sixteenth 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 50–59°. There are a spread of Hf–N bond distances ranging from 2.11–2.19 Å. There are one shorter (2.20 Å) and one longer (2.24 Å) Hf–O bond lengths. There are sixteen 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 NHf4 tetrahedra, corners with five NHf4 trigonal pyramids, corners with six OHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, 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 corners with six NHf4 trigonal pyramids, corners with six OHf4 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 two OHf4 trigonal pyramids, corners with ten NHf4 trigonal pyramids, an edgeedge with one NHf4 trigonal pyramid, and edges with three OHf4 trigonal pyramids. In the fourth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with six NHf4 trigonal pyramids, corners with six OHf4 trigonal pyramids, an edgeedge with one OHf4 trigonal pyramid, and edges with three NHf4 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, corners with two OHf4 trigonal pyramids, corners with nine NHf4 trigonal pyramids, an edgeedge with one NHf4 trigonal pyramid, and edges with three OHf4 trigonal pyramids. In the sixth N3- site, N3- is bonded to four Hf4+ atoms to form NHf4 trigonal pyramids that share corners with four 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 seventh 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 five NHf4 trigonal pyramids, corners with six OHf4 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, corners with five NHf4 trigonal pyramids, corners with six OHf4 trigonal pyramids, an edgeedge with one OHf4 trigonal pyramid, and edges with three NHf4 trigonal pyramids. In the ninth 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 five NHf4 trigonal pyramids, corners with six OHf4 trigonal pyramids, an edgeedge with one OHf4 trigonal pyramid, and edges with three 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, corners with two OHf4 trigonal pyramids, corners with nine NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 trigonal pyramids. In the eleventh N3- site, N3- is bonded to four Hf4+ atoms to form NHf4 trigonal pyramids that share a cornercorner with one NHf4 tetrahedra, corners with five NHf4 trigonal pyramids, corners with six OHf4 trigonal pyramids, an edgeedge with one OHf4 trigonal pyramid, and edges with three 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 five NHf4 trigonal pyramids, corners with six OHf4 trigonal pyramids, and edges with four 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 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 fourteenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with six NHf4 trigonal pyramids, corners with six OHf4 trigonal pyramids, an edgeedge with one NHf4 tetrahedra, an edgeedge with one OHf4 trigonal pyramid, and edges with two 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 NHf4 tetrahedra, corners with four 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 sixteenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with two OHf4 trigonal pyramids, corners with ten NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 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 four OHf4 trigonal pyramids, corners with eight 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 second O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share corners with four OHf4 trigonal pyramids, corners with eight NHf4 trigonal pyramids, and edges with four NHf4 trigonal pyramids. In the third 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 OHf4 trigonal pyramids, corners with nine NHf4 trigonal pyramids, an edgeedge with one OHf4 trigonal pyramid, and edges with three NHf4 trigonal pyramids. In the fourth O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share corners with two OHf4 trigonal pyramids, corners with ten NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 trigonal pyramids. In the fifth O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share corners with two OHf4 trigonal pyramids, corners with ten NHf4 trigonal pyramids, an edgeedge with one NHf4 tetrahedra, an edgeedge with one OHf4 trigonal pyramid, and edges wi

36 MATERIALS SCIENCE↗

Materials Data on Li6FeO5F by Materials Project

Li6FeO5F crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are twelve inequivalent Li sites. In the first Li site, Li is bonded to three O and one F atom to form distorted LiO3F tetrahedra that share corners with two FeO4 tetrahedra, corners with five LiO3F trigonal pyramids, and edges with three LiO3F trigonal pyramids. There are a spread of Li–O bond distances ranging from 1.90–2.05 Å. The Li–F bond length is 1.99 Å. In the second Li site, Li is bonded to four O atoms to form LiO4 trigonal pyramids that share corners with three equivalent FeO4 tetrahedra, corners with five LiO3F trigonal pyramids, an edgeedge with one LiO3F tetrahedra, and an edgeedge with one LiO3F trigonal pyramid. There are a spread of Li–O bond distances ranging from 1.93–2.06 Å. In the third Li site, Li is bonded to three O and one F atom to form LiO3F trigonal pyramids that share corners with three equivalent FeO4 tetrahedra, corners with five LiO4 trigonal pyramids, edges with two LiO3F tetrahedra, and an edgeedge with one LiO3F trigonal pyramid. There is two shorter (1.97 Å) and one longer (1.98 Å) Li–O bond length. The Li–F bond length is 2.10 Å. In the fourth Li site, Li is bonded in a distorted rectangular see-saw-like geometry to three O and one F atom. There is one shorter (1.96 Å) and two longer (1.98 Å) Li–O bond length. The Li–F bond length is 2.03 Å. In the fifth Li site, Li is bonded to three O and one F atom to form distorted LiO3F trigonal pyramids that share corners with two FeO4 tetrahedra, corners with three equivalent LiO3F tetrahedra, a cornercorner with one LiO3F trigonal pyramid, and edges with three LiO3F trigonal pyramids. There are a spread of Li–O bond distances ranging from 1.94–2.04 Å. The Li–F bond length is 1.90 Å. In the sixth Li site, Li is bonded to three O and one F atom to form distorted LiO3F trigonal pyramids that share corners with two LiO3F tetrahedra, corners with five LiO4 trigonal pyramids, an edgeedge with one LiO3F tetrahedra, an edgeedge with one FeO4 tetrahedra, and an edgeedge with one LiO3F trigonal pyramid. There are a spread of Li–O bond distances ranging from 1.90–2.00 Å. The Li–F bond length is 1.91 Å. In the seventh Li site, Li is bonded to three O and one F atom to form distorted LiO3F tetrahedra that share corners with two FeO4 tetrahedra, corners with three equivalent LiO3F tetrahedra, corners with four LiO3F trigonal pyramids, and edges with three LiO4 trigonal pyramids. There are a spread of Li–O bond distances ranging from 1.90–2.05 Å. The Li–F bond length is 1.98 Å. In the eighth Li site, Li is bonded to three O and one F atom to form distorted LiO3F tetrahedra that share corners with two FeO4 tetrahedra, corners with three equivalent LiO3F tetrahedra, corners with five LiO3F trigonal pyramids, and edges with three LiO4 trigonal pyramids. There are a spread of Li–O bond distances ranging from 1.95–2.08 Å. The Li–F bond length is 1.90 Å. In the ninth Li site, Li is bonded to three O and one F atom to form LiO3F trigonal pyramids that share corners with three equivalent FeO4 tetrahedra, corners with five LiO4 trigonal pyramids, an edgeedge with one LiO3F tetrahedra, and an edgeedge with one LiO3F trigonal pyramid. There are a spread of Li–O bond distances ranging from 1.95–2.00 Å. The Li–F bond length is 2.11 Å. In the tenth Li site, Li is bonded to four O atoms to form LiO4 trigonal pyramids that share corners with three equivalent FeO4 tetrahedra, corners with five LiO3F trigonal pyramids, edges with two LiO3F tetrahedra, and an edgeedge with one LiO3F trigonal pyramid. There are a spread of Li–O bond distances ranging from 1.92–2.02 Å. In the eleventh Li site, Li is bonded to three O and one F atom to form distorted LiO3F trigonal pyramids that share corners with three LiO3F tetrahedra, corners with five LiO4 trigonal pyramids, an edgeedge with one FeO4 tetrahedra, edges with two LiO3F tetrahedra, and an edgeedge with one LiO3F trigonal pyramid. There are a spread of Li–O bond distances ranging from 1.90–1.97 Å. The Li–F bond length is 1.91 Å. In the twelfth Li site, Li is bonded to three O and one F atom to form distorted LiO3F trigonal pyramids that share corners with two FeO4 tetrahedra, corners with six LiO3F tetrahedra, a cornercorner with one LiO3F trigonal pyramid, and edges with three LiO4 trigonal pyramids. There is two shorter (1.92 Å) and one longer (1.93 Å) Li–O bond length. The Li–F bond length is 2.04 Å. There are two inequivalent Fe sites. In the first Fe site, Fe is bonded to four O atoms to form FeO4 tetrahedra that share corners with three LiO3F tetrahedra, corners with eight LiO4 trigonal pyramids, and an edgeedge with one LiO3F trigonal pyramid. There are a spread of Fe–O bond distances ranging from 1.79–1.83 Å. In the second Fe site, Fe is bonded to four O atoms to form FeO4 tetrahedra that share corners with three LiO3F tetrahedra, corners with eight LiO3F trigonal pyramids, and an edgeedge with one LiO3F trigonal pyramid. There are a spread of Fe–O bond distances ranging from 1.79–1.82 Å. There are ten inequivalent O sites. In the first O site, O is bonded to four Li and one Fe atom to form distorted OLi4Fe trigonal bipyramids that share corners with two equivalent FLi5 trigonal bipyramids, corners with three OLi4Fe trigonal bipyramids, corners with four OLi3Fe trigonal pyramids, an edgeedge with one FLi5 trigonal bipyramid, and edges with two OLi5 trigonal bipyramids. In the second O site, O is bonded to four Li and one Fe atom to form distorted OLi4Fe trigonal bipyramids that share corners with two equivalent FLi5 trigonal bipyramids, corners with three OLi5 trigonal bipyramids, corners with four OLi3Fe trigonal pyramids, an edgeedge with one FLi5 trigonal bipyramid, and edges with two OLi5 trigonal bipyramids. In the third O site, O is bonded to three Li and one Fe atom to form distorted OLi3Fe trigonal pyramids that share corners with five OLi4Fe trigonal bipyramids, corners with three equivalent OLi3Fe trigonal pyramids, an edgeedge with one OLi5 trigonal bipyramid, and an edgeedge with one FLi5 trigonal bipyramid. In the fourth O site, O is bonded to three Li and one Fe atom to form OLi3Fe trigonal pyramids that share corners with five OLi4Fe trigonal bipyramids, corners with three equivalent OLi3Fe trigonal pyramids, an edgeedge with one OLi5 trigonal bipyramid, and an edgeedge with one FLi5 trigonal bipyramid. In the fifth O site, O is bonded to five Li atoms to form distorted OLi5 trigonal bipyramids that share corners with two equivalent FLi5 trigonal bipyramids, corners with three OLi4Fe trigonal bipyramids, an edgeedge with one FLi5 trigonal bipyramid, edges with two OLi4Fe trigonal bipyramids, and edges with two OLi3Fe trigonal pyramids. In the sixth O site, O is bonded to three Li and one Fe atom to form OLi3Fe trigonal pyramids that share corners with five OLi4Fe trigonal bipyramids, corners with three equivalent OLi3Fe trigonal pyramids, an edgeedge with one OLi5 trigonal bipyramid, and an edgeedge with one FLi5 trigonal bipyramid. In the seventh O site, O is bonded to four Li and one Fe atom to form OLi4Fe trigonal bipyramids that share a cornercorner with one FLi5 trigonal bipyramid, corners with two OLi4Fe trigonal bipyramids, corners with six OLi3Fe trigonal pyramids, an edgeedge with one FLi5 trigonal bipyramid, and edges with two OLi5 trigonal bipyramids. In the eighth O site, O is bonded to five Li atoms to form distorted OLi5 trigonal bipyramids that share corners with two equivalent FLi5 trigonal bipyramids, corners with three OLi4Fe trigonal bipyramids, an edgeedge with one FLi5 trigonal bipyramid, edges with two OLi4Fe trigonal bipyramids, and edges with two OLi3Fe trigonal pyramids. In the ninth O site, O is bonded to four Li and one Fe atom to form OLi4Fe trigonal bipyramids that share a cornercorner with one FLi5 trigonal bipyramid, corners with two OLi4Fe trigonal bipyramids, corners with six OLi3Fe trigonal pyramids, an edgeedge with one FLi5 trigonal bipyramid, and edges with two OLi5 trigonal bipyramids. In the tenth O site, O is bonded to three Li and one Fe atom to form OLi3Fe trigonal pyramids that share corners with five OLi4Fe trigonal bipyramids, corners with three equivalent OLi3Fe trigonal pyramids, an edgeedge with one OLi5 trigonal bipyramid, and an edgeedge with one FLi5 trigonal bipyramid. There are two inequivalent F sites. In the first F site, F is bonded to five Li atoms to form distorted FLi5 trigonal bipyramids that share corners with five OLi5 trigonal bipyramids, edges with three OLi4Fe trigonal bipyramids, and edges with two OLi3Fe trigonal pyramids. In the second F site, F is bonded to five Li atoms to form distorted FLi5 trigonal bipyramids that share corners with five OLi5 trigonal bipyramids, edges with three OLi4Fe trigonal bipyramids, and edges with two OLi3Fe trigonal pyramids.

36 MATERIALS SCIENCE↗

Materials Data on Ti2N2O by Materials Project

Ti2N2O is Ilmenite-like structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are sixteen inequivalent Ti4+ sites. In the first Ti4+ site, Ti4+ is bonded to three N3- and three O2- atoms to form TiN3O3 octahedra that share corners with five TiN3O3 octahedra, a cornercorner with one TiN3O3 pentagonal pyramid, edges with five TiN4O2 octahedra, and an edgeedge with one TiN3O3 pentagonal pyramid. The corner-sharing octahedra tilt angles range from 49–56°. There are a spread of Ti–N bond distances ranging from 1.95–1.99 Å. There are a spread of Ti–O bond distances ranging from 2.07–2.13 Å. In the second Ti4+ site, Ti4+ is bonded to three N3- and three O2- atoms to form distorted TiN3O3 pentagonal pyramids that share corners with six TiN3O3 octahedra and edges with six TiN4O2 octahedra. The corner-sharing octahedra tilt angles range from 47–54°. There are a spread of Ti–N bond distances ranging from 1.94–2.03 Å. There are a spread of Ti–O bond distances ranging from 2.04–2.15 Å. In the third Ti4+ site, Ti4+ is bonded to three N3- and three O2- atoms to form distorted TiN3O3 octahedra that share corners with four TiN3O3 octahedra, corners with two TiN3O3 pentagonal pyramids, and edges with six TiN5O octahedra. The corner-sharing octahedra tilt angles range from 48–50°. There are one shorter (1.97 Å) and two longer (2.03 Å) Ti–N bond lengths. There are a spread of Ti–O bond distances ranging from 2.02–2.12 Å. In the fourth Ti4+ site, Ti4+ is bonded to four N3- and two O2- atoms to form distorted TiN4O2 octahedra that share corners with six TiN5O octahedra, edges with four TiN3O3 octahedra, and edges with two TiN3O3 pentagonal pyramids. The corner-sharing octahedra tilt angles range from 52–57°. There are a spread of Ti–N bond distances ranging from 1.98–2.07 Å. There are one shorter (2.11 Å) and one longer (2.16 Å) Ti–O bond lengths. In the fifth Ti4+ site, Ti4+ is bonded to three N3- and three O2- atoms to form a mixture of distorted edge and corner-sharing TiN3O3 pentagonal pyramids. The corner-sharing octahedra tilt angles range from 46–55°. There are a spread of Ti–N bond distances ranging from 1.94–2.04 Å. There are a spread of Ti–O bond distances ranging from 2.03–2.15 Å. In the sixth Ti4+ site, Ti4+ is bonded to five N3- and one O2- atom to form distorted TiN5O octahedra that share corners with six TiN4O2 octahedra, edges with four TiN3O3 octahedra, and edges with two TiN3O3 pentagonal pyramids. The corner-sharing octahedra tilt angles range from 52–56°. There are a spread of Ti–N bond distances ranging from 2.00–2.10 Å. The Ti–O bond length is 2.13 Å. In the seventh Ti4+ site, Ti4+ is bonded to three N3- and three O2- atoms to form distorted TiN3O3 octahedra that share corners with four TiN3O3 octahedra, corners with two TiN3O3 pentagonal pyramids, and edges with six TiN4O2 octahedra. The corner-sharing octahedra tilt angles range from 49–52°. There are a spread of Ti–N bond distances ranging from 1.99–2.06 Å. There are two shorter (2.03 Å) and one longer (2.08 Å) Ti–O bond lengths. In the eighth Ti4+ site, Ti4+ is bonded to four N3- and two O2- atoms to form TiN4O2 octahedra that share corners with five TiN3O3 octahedra, a cornercorner with one TiN3O3 pentagonal pyramid, edges with five TiN4O2 octahedra, and an edgeedge with one TiN3O3 pentagonal pyramid. The corner-sharing octahedra tilt angles range from 48–55°. There are a spread of Ti–N bond distances ranging from 1.95–2.07 Å. There are one shorter (2.08 Å) and one longer (2.15 Å) Ti–O bond lengths. In the ninth Ti4+ site, Ti4+ is bonded to five N3- and one O2- atom to form a mixture of distorted edge and corner-sharing TiN5O octahedra. The corner-sharing octahedra tilt angles range from 53–56°. There are a spread of Ti–N bond distances ranging from 2.01–2.09 Å. The Ti–O bond length is 2.12 Å. In the tenth Ti4+ site, Ti4+ is bonded to three N3- and three O2- atoms to form a mixture of distorted edge and corner-sharing TiN3O3 octahedra. The corner-sharing octahedra tilt angles range from 48–52°. There are a spread of Ti–N bond distances ranging from 1.97–2.09 Å. There are a spread of Ti–O bond distances ranging from 2.03–2.10 Å. In the eleventh Ti4+ site, Ti4+ is bonded to four N3- and two O2- atoms to form TiN4O2 octahedra that share corners with five TiN4O2 octahedra, a cornercorner with one TiN3O3 pentagonal pyramid, edges with five TiN3O3 octahedra, and an edgeedge with one TiN3O3 pentagonal pyramid. The corner-sharing octahedra tilt angles range from 52–57°. There are a spread of Ti–N bond distances ranging from 1.96–2.08 Å. There are one shorter (2.11 Å) and one longer (2.15 Å) Ti–O bond lengths. In the twelfth Ti4+ site, Ti4+ is bonded to five N3- and one O2- atom to form TiN5O octahedra that share corners with five TiN4O2 octahedra, a cornercorner with one TiN3O3 pentagonal pyramid, edges with five TiN3O3 octahedra, and an edgeedge with one TiN3O3 pentagonal pyramid. The corner-sharing octahedra tilt angles range from 50–56°. There are a spread of Ti–N bond distances ranging from 1.95–2.07 Å. The Ti–O bond length is 2.17 Å. In the thirteenth Ti4+ site, Ti4+ is bonded to four N3- and two O2- atoms to form distorted TiN4O2 octahedra that share corners with six TiN4O2 octahedra and edges with six TiN3O3 octahedra. The corner-sharing octahedra tilt angles range from 52–54°. There are a spread of Ti–N bond distances ranging from 2.01–2.09 Å. There are one shorter (2.05 Å) and one longer (2.08 Å) Ti–O bond lengths. In the fourteenth Ti4+ site, Ti4+ is bonded to five N3- and one O2- atom to form a mixture of distorted edge and corner-sharing TiN5O octahedra. The corner-sharing octahedra tilt angles range from 50–52°. There are a spread of Ti–N bond distances ranging from 2.00–2.06 Å. The Ti–O bond length is 2.12 Å. In the fifteenth Ti4+ site, Ti4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted edge and corner-sharing TiN4O2 octahedra. The corner-sharing octahedra tilt angles range from 52–55°. There are a spread of Ti–N bond distances ranging from 1.98–2.09 Å. There are one shorter (2.09 Å) and one longer (2.13 Å) Ti–O bond lengths. In the sixteenth Ti4+ site, Ti4+ is bonded to six N3- atoms to form a mixture of distorted edge and corner-sharing TiN6 octahedra. The corner-sharing octahedra tilt angles range from 53–54°. There are a spread of Ti–N bond distances ranging from 2.05–2.10 Å. There are sixteen inequivalent N3- sites. In the first N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with two OTi4 trigonal pyramids, corners with ten NTi4 trigonal pyramids, and edges with four OTi4 trigonal pyramids. In the second N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with three OTi4 trigonal pyramids, corners with nine NTi4 trigonal pyramids, an edgeedge with one NTi4 trigonal pyramid, and edges with three OTi4 trigonal pyramids. In the third N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share a cornercorner with one OTi4 trigonal pyramid, corners with eleven NTi4 trigonal pyramids, and edges with four OTi4 trigonal pyramids. In the fourth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with two OTi4 trigonal pyramids, corners with ten NTi4 trigonal pyramids, edges with two NTi4 trigonal pyramids, and edges with two OTi4 trigonal pyramids. In the fifth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share a cornercorner with one OTi4 trigonal pyramid, corners with eleven NTi4 trigonal pyramids, an edgeedge with one NTi4 trigonal pyramid, and edges with three OTi4 trigonal pyramids. In the sixth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with two OTi4 trigonal pyramids, corners with ten NTi4 trigonal pyramids, an edgeedge with one NTi4 trigonal pyramid, and edges with three OTi4 trigonal pyramids. In the seventh N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with five NTi4 trigonal pyramids, corners with seven OTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the eighth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with three OTi4 trigonal pyramids, corners with nine NTi4 trigonal pyramids, edges with two NTi4 trigonal pyramids, and edges with two OTi4 trigonal pyramids. In the ninth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with two OTi4 trigonal pyramids, corners with ten NTi4 trigonal pyramids, an edgeedge with one NTi4 trigonal pyramid, and edges with three OTi4 trigonal pyramids. In the tenth N3- site, N3- is bonded to four Ti4+ atoms to form NTi4 trigonal pyramids that share corners with five NTi4 trigonal pyramids, corners with seven OTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the eleventh N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with two OTi4 trigonal pyramids, corners with ten NTi4 trigonal pyramids, edges with two NTi4 trigonal pyramids, and edges with two OTi4 trigonal pyramids. In the twelfth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with three OTi4 trigonal pyramids, corners with nine NTi4 trigonal pyramids, edges with two NTi4 trigonal pyramids, and edges with two OTi4 trigonal pyramids. In the thirteenth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with six NTi4 trigonal pyramids, corners with six OTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the fourteenth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with two OTi4 trigonal pyramids, corners with ten NTi4 trigonal pyramids, edges with two NTi4 trigonal pyramids, and edges with two OTi4 trigonal pyramids. In the fifteenth N3- site, N3- is bonded to four Ti4+ atoms to form NTi4 trigonal pyramids that share corners with six NTi4 trigonal pyramids, corners with six OTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the sixteenth N3- site, N3- is bonded to four Ti4+ atoms to form NTi4 trigonal pyramids that share a cornercorner with one OTi4 trigonal pyramid, corners with eleven NTi4 trigonal pyramids, edges with two NTi4 trigonal pyramids, and edges with two OTi4 trigonal pyramids. There are eight inequivalent O2- sites. In the first O2- site, O2- is bonded to four Ti4+ atoms to form OTi4 trigonal pyramids that share corners with six NTi4 trigonal pyramids, corners with six OTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the second O2- site, O2- is bonded to four Ti4+ atoms to form OTi4 trigonal pyramids that share corners with six NTi4 trigonal pyramids, corners with six OTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the third O2- site, O2- is bonded to four Ti4+ atoms to form OTi4 trigonal pyramids that share corners with five NTi4 trigonal pyramids, corners with seven OTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the fourth O2- site, O2- is bonded to four Ti4+ atoms to form OTi4 trigonal pyramids that share corners with five OTi4 trigonal pyramids, corners with seven NTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the fifth O2- site, O2- is bonded to four Ti4+ atoms to form distorted OTi4 trigonal pyramids that share corners with six NTi4 trigonal pyramids, corners with six OTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the sixth O2- site, O2- is bonded to four Ti4+ atoms to form distorted OTi4 trigonal pyramids that share corners with six NTi4 trigonal

36 MATERIALS SCIENCE↗

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 a mixture of edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 52–58°. There are a spread of Hf–N bond distances ranging from 2.10–2.20 Å. There are one shorter (2.22 Å) and one longer (2.25 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 51–56°. There are a spread of Hf–N bond distances ranging from 2.09–2.20 Å. There are one shorter (2.20 Å) and one longer (2.31 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 edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 52–56°. There are a spread of Hf–N bond distances ranging from 2.10–2.19 Å. There are one shorter (2.22 Å) and one longer (2.26 Å) Hf–O bond lengths. 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 52–54°. There are a spread of Hf–N bond distances ranging from 2.11–2.17 Å. There are a spread of Hf–O bond distances ranging from 2.15–2.19 Å. In the fifth 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 51–59°. There are a spread of Hf–N bond distances ranging from 2.08–2.11 Å. There are a spread of Hf–O bond distances ranging from 2.17–2.29 Å. In the sixth 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 52–57°. There are a spread of Hf–N bond distances ranging from 2.11–2.20 Å. There are one shorter (2.21 Å) and one longer (2.23 Å) Hf–O bond lengths. In the seventh Hf4+ site, Hf4+ is bonded to three N3- and three O2- atoms to form HfN3O3 octahedra that share corners with six HfN3O3 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 52–59°. There are one shorter (2.08 Å) and two longer (2.09 Å) Hf–N bond lengths. There are two shorter (2.23 Å) and one longer (2.25 Å) Hf–O bond lengths. In the eighth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form HfN4O2 octahedra that share corners with six HfN4O2 octahedra and edges with six HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 53–57°. There are a spread of Hf–N bond distances ranging from 2.09–2.19 Å. There are one shorter (2.26 Å) and one longer (2.27 Å) Hf–O bond lengths. In the ninth 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 53–56°. There are a spread of Hf–N bond distances ranging from 2.10–2.17 Å. There are one shorter (2.18 Å) and one longer (2.30 Å) Hf–O bond lengths. In the tenth Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form a mixture of edge and corner-sharing HfN5O octahedra. The corner-sharing octahedra tilt angles range from 54–59°. There are a spread of Hf–N bond distances ranging from 2.11–2.20 Å. The Hf–O bond length is 2.27 Å. In the eleventh 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 51–54°. There are a spread of Hf–N bond distances ranging from 2.08–2.17 Å. There are one shorter (2.18 Å) and one longer (2.28 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 53–58°. There are a spread of Hf–N bond distances ranging from 2.14–2.25 Å. The Hf–O bond length is 2.22 Å. In the thirteenth 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 51–59°. There are a spread of Hf–N bond distances ranging from 2.10–2.23 Å. There are one shorter (2.19 Å) and one longer (2.21 Å) Hf–O bond lengths. In the fourteenth 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 2.13–2.21 Å. The Hf–O bond length is 2.23 Å. In the fifteenth 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 51–57°. There are a spread of Hf–N bond distances ranging from 2.14–2.19 Å. Both Hf–O bond lengths are 2.17 Å. In the sixteenth 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 52–56°. There are a spread of Hf–N bond distances ranging from 2.11–2.25 Å. There are one shorter (2.14 Å) and one longer (2.24 Å) Hf–O bond lengths. There are sixteen 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 two NHf4 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 second N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share a cornercorner with one NHf4 tetrahedra, corners with five NHf4 trigonal pyramids, corners with six OHf4 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 a cornercorner with one NHf4 tetrahedra, corners with five OHf4 trigonal pyramids, corners with six NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, 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 five 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 fifth 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 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 NHf4 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 seventh 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 five NHf4 trigonal pyramids, corners with six OHf4 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 corners with five NHf4 trigonal pyramids, corners with seven OHf4 trigonal pyramids, edges with two NHf4 tetrahedra, an edgeedge with one NHf4 trigonal pyramid, and an edgeedge with one OHf4 trigonal pyramid. In the ninth 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, edges with two NHf4 trigonal pyramids, and edges with two OHf4 trigonal pyramids. In the tenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with five NHf4 trigonal pyramids, corners with seven OHf4 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 five NHf4 trigonal pyramids, corners with seven OHf4 trigonal pyramids, an edgeedge with one NHf4 tetrahedra, and edges with three NHf4 trigonal pyramids. In the twelfth N3- site, N3- is bonded to four Hf4+ atoms to form NHf4 trigonal pyramids that share a cornercorner with one NHf4 tetrahedra, corners with five NHf4 trigonal pyramids, corners with six OHf4 trigonal pyramids, and edges with four 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 five OHf4 trigonal pyramids, corners with six NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two 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 four 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 fifteenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with four 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 sixteenth 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 two OHf4 trigonal pyramids, corners with nine NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 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, corners with three OHf4 trigonal pyramids, corners with eight 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 third O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share corners with two NHf4 tetrahedra, a cornercorner with one OHf4 trigonal pyramid, corners with nine NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 trigonal pyramids. In the fourth 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 OHf4 trigonal pyramids, corners with nine 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 fifth O2- si

36 MATERIALS SCIENCE↗

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 distorted HfN4O2 octahedra that share corners with six HfN3O3 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 51–54°. There are a spread of Hf–N bond distances ranging from 2.11–2.24 Å. There are one shorter (2.12 Å) and one longer (2.23 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 edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 51–58°. There are a spread of Hf–N bond distances ranging from 2.12–2.17 Å. There are one shorter (2.23 Å) and one longer (2.25 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 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 2.09–2.20 Å. There are one shorter (2.18 Å) and one longer (2.29 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 edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 53–58°. There are a spread of Hf–N bond distances ranging from 2.13–2.26 Å. There are one shorter (2.12 Å) and one longer (2.21 Å) Hf–O bond lengths. In the fifth 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 51–57°. There are a spread of Hf–N bond distances ranging from 2.07–2.13 Å. There are a spread of Hf–O bond distances ranging from 2.18–2.28 Å. In the sixth 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 54–57°. There are a spread of Hf–N bond distances ranging from 2.10–2.17 Å. Both Hf–O bond lengths are 2.27 Å. In the seventh 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 53–58°. There are a spread of Hf–N bond distances ranging from 2.09–2.17 Å. There are one shorter (2.26 Å) and one longer (2.27 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 edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 53–58°. There are a spread of Hf–N bond distances ranging from 2.10–2.19 Å. There are one shorter (2.23 Å) and one longer (2.27 Å) Hf–O bond lengths. In the ninth 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 51–57°. There are a spread of Hf–N bond distances ranging from 2.10–2.18 Å. There are one shorter (2.24 Å) and one longer (2.26 Å) Hf–O bond lengths. In the tenth 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 53–56°. There are one shorter (2.08 Å) and three longer (2.16 Å) Hf–N bond lengths. There are one shorter (2.20 Å) and one longer (2.32 Å) Hf–O bond lengths. In the eleventh 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 51–54°. There are a spread of Hf–N bond distances ranging from 2.13–2.20 Å. There are a spread of Hf–O bond distances ranging from 2.13–2.16 Å. 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 53–58°. There are a spread of Hf–N bond distances ranging from 2.13–2.29 Å. The Hf–O bond length is 2.22 Å. In the thirteenth 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 50–58°. There are a spread of Hf–N bond distances ranging from 2.10–2.27 Å. There are one shorter (2.19 Å) and one longer (2.21 Å) Hf–O bond lengths. In the fourteenth 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 52–56°. There are a spread of Hf–N bond distances ranging from 2.13–2.23 Å. The Hf–O bond length is 2.22 Å. In the fifteenth 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 50–54°. There are a spread of Hf–N bond distances ranging from 2.10–2.16 Å. There are a spread of Hf–O bond distances ranging from 2.14–2.21 Å. In the sixteenth 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 54–58°. There are a spread of Hf–N bond distances ranging from 2.12–2.23 Å. The Hf–O bond length is 2.32 Å. There are sixteen 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 five NHf4 trigonal pyramids, corners with seven OHf4 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 three NHf4 tetrahedra, a cornercorner with one OHf4 trigonal pyramid, corners with eight NHf4 trigonal pyramids, and edges with four 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 two NHf4 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 fourth 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, 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, 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 sixth 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 seventh N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with three NHf4 tetrahedra, corners with three OHf4 trigonal pyramids, corners with six NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 trigonal pyramids. In the eighth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with five NHf4 trigonal pyramids, corners with seven OHf4 trigonal pyramids, edges with three NHf4 tetrahedra, and an edgeedge with one OHf4 trigonal pyramid. In the ninth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra 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 tenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with three NHf4 tetrahedra, corners with three OHf4 trigonal pyramids, corners with six NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 trigonal pyramids. In the eleventh N3- site, N3- is bonded to four Hf4+ atoms to form NHf4 trigonal pyramids that share corners with five NHf4 trigonal pyramids, corners with seven OHf4 trigonal pyramids, an edgeedge with one NHf4 tetrahedra, and edges with three NHf4 trigonal pyramids. In the twelfth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra 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 thirteenth N3- site, N3- is bonded to four Hf4+ atoms to form NHf4 trigonal pyramids that share corners with five 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 fourteenth 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, edges with two NHf4 trigonal pyramids, and edges with two OHf4 trigonal pyramids. In the fifteenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with three NHf4 tetrahedra, a cornercorner with one OHf4 trigonal pyramid, 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 distorted NHf4 tetrahedra that share corners with two NHf4 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. 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 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 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 four OHf4 trigonal pyramids, corners with seven 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 four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share corners with three NHf4 tetrahedra, corners with three OHf4 trigonal pyramids, corners with six NHf4 trigonal pyramids, and edges with four NHf4 trigonal pyramids. In the fourth 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, an edgeedge with one NHf4 tetrahedra, an edgeedge with one OHf4 trigonal pyramid, and edges with two NHf4 trigonal pyramids. In the fifth O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share corners with five OHf4 trigonal

36 MATERIALS SCIENCE↗

Materials Data on Zr2N2O by Materials Project

Zr2ON2 is Ilmenite-like structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are sixteen inequivalent Zr4+ sites. In the first Zr4+ site, Zr4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted corner and edge-sharing ZrN4O2 octahedra. The corner-sharing octahedra tilt angles range from 52–57°. There are a spread of Zr–N bond distances ranging from 2.15–2.26 Å. There are one shorter (2.23 Å) and one longer (2.26 Å) Zr–O bond lengths. In the second Zr4+ site, Zr4+ is bonded to four N3- and two O2- atoms to form a mixture of corner and edge-sharing ZrN4O2 octahedra. The corner-sharing octahedra tilt angles range from 53–58°. There are a spread of Zr–N bond distances ranging from 2.12–2.22 Å. There are one shorter (2.26 Å) and one longer (2.31 Å) Zr–O bond lengths. In the third Zr4+ site, Zr4+ is bonded to four N3- and two O2- atoms to form a mixture of corner and edge-sharing ZrN4O2 octahedra. The corner-sharing octahedra tilt angles range from 52–57°. There are two shorter (2.13 Å) and two longer (2.21 Å) Zr–N bond lengths. Both Zr–O bond lengths are 2.30 Å. In the fourth Zr4+ site, Zr4+ is bonded to five N3- and one O2- atom to form a mixture of corner and edge-sharing ZrN5O octahedra. The corner-sharing octahedra tilt angles range from 53–59°. There are a spread of Zr–N bond distances ranging from 2.13–2.25 Å. The Zr–O bond length is 2.33 Å. In the fifth Zr4+ site, Zr4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted corner and edge-sharing ZrN4O2 octahedra. The corner-sharing octahedra tilt angles range from 51–55°. There are a spread of Zr–N bond distances ranging from 2.16–2.28 Å. There are one shorter (2.15 Å) and one longer (2.27 Å) Zr–O bond lengths. In the sixth Zr4+ site, Zr4+ is bonded to four N3- and two O2- atoms to form distorted ZrN4O2 octahedra that share corners with five ZrN5O octahedra, a cornercorner with one ZrN4O2 pentagonal pyramid, and edges with six ZrN4O2 octahedra. The corner-sharing octahedra tilt angles range from 53–57°. There are a spread of Zr–N bond distances ranging from 2.11–2.24 Å. There are one shorter (2.26 Å) and one longer (2.32 Å) Zr–O bond lengths. In the seventh Zr4+ site, Zr4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted corner and edge-sharing ZrN4O2 octahedra. The corner-sharing octahedra tilt angles range from 52–59°. There are a spread of Zr–N bond distances ranging from 2.17–2.26 Å. There are one shorter (2.16 Å) and one longer (2.24 Å) Zr–O bond lengths. In the eighth Zr4+ site, Zr4+ is bonded to three N3- and three O2- atoms to form a mixture of distorted corner and edge-sharing ZrN3O3 octahedra. The corner-sharing octahedra tilt angles range from 49–57°. There are a spread of Zr–N bond distances ranging from 2.17–2.23 Å. There are a spread of Zr–O bond distances ranging from 2.15–2.22 Å. In the ninth Zr4+ site, Zr4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted corner and edge-sharing ZrN4O2 pentagonal pyramids. The corner-sharing octahedra tilt angles range from 50–55°. There are three shorter (2.19 Å) and one longer (2.22 Å) Zr–N bond lengths. There are one shorter (2.20 Å) and one longer (2.22 Å) Zr–O bond lengths. In the tenth Zr4+ site, Zr4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted corner and edge-sharing ZrN4O2 octahedra. The corner-sharing octahedra tilt angles range from 52–55°. There are a spread of Zr–N bond distances ranging from 2.17–2.25 Å. There are one shorter (2.20 Å) and one longer (2.22 Å) Zr–O bond lengths. In the eleventh Zr4+ site, Zr4+ is bonded to five N3- and one O2- atom to form a mixture of distorted corner and edge-sharing ZrN5O octahedra. The corner-sharing octahedra tilt angles range from 53–56°. There are a spread of Zr–N bond distances ranging from 2.14–2.25 Å. The Zr–O bond length is 2.32 Å. In the twelfth Zr4+ site, Zr4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted corner and edge-sharing ZrN4O2 octahedra. The corner-sharing octahedra tilt angles range from 51–56°. There are a spread of Zr–N bond distances ranging from 2.11–2.24 Å. There are one shorter (2.27 Å) and one longer (2.34 Å) Zr–O bond lengths. In the thirteenth Zr4+ site, Zr4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted corner and edge-sharing ZrN4O2 octahedra. The corner-sharing octahedra tilt angles range from 52–58°. There are a spread of Zr–N bond distances ranging from 2.15–2.32 Å. There are one shorter (2.17 Å) and one longer (2.27 Å) Zr–O bond lengths. In the fourteenth Zr4+ site, Zr4+ is bonded to three N3- and three O2- atoms to form a mixture of corner and edge-sharing ZrN3O3 octahedra. The corner-sharing octahedra tilt angles range from 53–55°. There are a spread of Zr–N bond distances ranging from 2.11–2.23 Å. There are a spread of Zr–O bond distances ranging from 2.18–2.29 Å. In the fifteenth Zr4+ site, Zr4+ is bonded to four N3- and two O2- atoms to form distorted ZrN4O2 octahedra that share corners with six ZrN4O2 octahedra, edges with five ZrN5O octahedra, and an edgeedge with one ZrN4O2 pentagonal pyramid. The corner-sharing octahedra tilt angles range from 52–56°. There are a spread of Zr–N bond distances ranging from 2.13–2.19 Å. There are one shorter (2.32 Å) and one longer (2.34 Å) Zr–O bond lengths. In the sixteenth Zr4+ site, Zr4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted corner and edge-sharing ZrN4O2 octahedra. The corner-sharing octahedra tilt angles range from 49–58°. There are a spread of Zr–N bond distances ranging from 2.14–2.26 Å. There are one shorter (2.24 Å) and one longer (2.25 Å) Zr–O bond lengths. There are sixteen inequivalent N3- sites. In the first N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 trigonal pyramids that share a cornercorner with one NZr4 tetrahedra, corners with five NZr4 trigonal pyramids, corners with six OZr4 trigonal pyramids, an edgeedge with one NZr4 tetrahedra, an edgeedge with one NZr4 trigonal pyramid, and edges with two OZr4 trigonal pyramids. In the second N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 trigonal pyramids that share a cornercorner with one NZr4 tetrahedra, corners with two OZr4 trigonal pyramids, corners with nine NZr4 trigonal pyramids, an edgeedge with one NZr4 trigonal pyramid, and edges with three OZr4 trigonal pyramids. In the third N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 trigonal pyramids that share corners with four OZr4 trigonal pyramids, corners with eight NZr4 trigonal pyramids, edges with two NZr4 trigonal pyramids, and edges with two OZr4 trigonal pyramids. In the fourth N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 trigonal pyramids that share a cornercorner with one NZr4 tetrahedra, corners with five OZr4 trigonal pyramids, corners with six NZr4 trigonal pyramids, an edgeedge with one OZr4 trigonal pyramid, and edges with three NZr4 trigonal pyramids. In the fifth N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 tetrahedra that share corners with four OZr4 trigonal pyramids, corners with eight NZr4 trigonal pyramids, an edgeedge with one NZr4 tetrahedra, an edgeedge with one NZr4 trigonal pyramid, and edges with two OZr4 trigonal pyramids. In the sixth N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 trigonal pyramids that share a cornercorner with one NZr4 tetrahedra, corners with three OZr4 trigonal pyramids, corners with eight NZr4 trigonal pyramids, an edgeedge with one NZr4 tetrahedra, an edgeedge with one NZr4 trigonal pyramid, and edges with two OZr4 trigonal pyramids. In the seventh N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 trigonal pyramids that share corners with two NZr4 tetrahedra, corners with four OZr4 trigonal pyramids, corners with six NZr4 trigonal pyramids, an edgeedge with one OZr4 trigonal pyramid, and edges with three NZr4 trigonal pyramids. In the eighth N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 trigonal pyramids that share a cornercorner with one NZr4 tetrahedra, corners with five NZr4 trigonal pyramids, corners with six OZr4 trigonal pyramids, an edgeedge with one OZr4 trigonal pyramid, and edges with three NZr4 trigonal pyramids. In the ninth N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 trigonal pyramids that share corners with two NZr4 tetrahedra, corners with four OZr4 trigonal pyramids, corners with six NZr4 trigonal pyramids, edges with two NZr4 trigonal pyramids, and edges with two OZr4 trigonal pyramids. In the tenth N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 trigonal pyramids that share a cornercorner with one NZr4 tetrahedra, corners with three OZr4 trigonal pyramids, corners with eight NZr4 trigonal pyramids, edges with two NZr4 trigonal pyramids, and edges with two OZr4 trigonal pyramids. In the eleventh N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 trigonal pyramids that share corners with two NZr4 tetrahedra, corners with four OZr4 trigonal pyramids, corners with six NZr4 trigonal pyramids, edges with two NZr4 trigonal pyramids, and edges with two OZr4 trigonal pyramids. In the twelfth N3- site, N3- is bonded to four Zr4+ atoms to form NZr4 trigonal pyramids that share a cornercorner with one NZr4 tetrahedra, corners with five NZr4 trigonal pyramids, corners with six OZr4 trigonal pyramids, and edges with four NZr4 trigonal pyramids. In the thirteenth N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 trigonal pyramids that share a cornercorner with one NZr4 tetrahedra, corners with five OZr4 trigonal pyramids, corners with six NZr4 trigonal pyramids, edges with two NZr4 trigonal pyramids, and edges with two OZr4 trigonal pyramids. In the fourteenth N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 tetrahedra that share corners with five OZr4 trigonal pyramids, corners with seven NZr4 trigonal pyramids, an edgeedge with one NZr4 tetrahedra, an edgeedge with one NZr4 trigonal pyramid, and edges with two OZr4 trigonal pyramids. In the fifteenth N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 trigonal pyramids that share corners with five OZr4 trigonal pyramids, corners with seven NZr4 trigonal pyramids, an edgeedge with one OZr4 trigonal pyramid, and edges with three NZr4 trigonal pyramids. In the sixteenth N3- site, N3- is bonded to four Zr4+ atoms to form distorted NZr4 trigonal pyramids that share a cornercorner with one NZr4 tetrahedra, corners with two OZr4 trigonal pyramids, corners with nine NZr4 trigonal pyramids, an edgeedge with one NZr4 trigonal pyramid, and edges with three OZr4 trigonal pyramids. There are eight inequivalent O2- sites. In the first O2- site, O2- is bonded to four Zr4+ atoms to form distorted OZr4 trigonal pyramids that share corners with two NZr4 tetrahedra, corners with three OZr4 trigonal pyramids, corners with seven NZr4 trigonal pyramids, an edgeedge with one OZr4 trigonal pyramid, and edges with three NZr4 trigonal pyramids. In the second O2- site, O2- is bonded to four Zr4+ atoms to form distorted OZr4 trigonal pyramids that share corners with two NZr4 tetrahedra, corners with three OZr4 trigonal pyramids, corners with seven NZr4 trigonal pyramids, and edges with four NZr4 trigonal pyramids. In the third O2- site, O2- is bonded to four Zr4+ atoms to form distorted OZr4 trigonal pyramids that share a cornercorner with one NZr4 tetrahedra, corners with three OZr4 trigonal pyramids, corners with eight NZr4 trigonal pyramids, an edgeedge with one NZr4 tetrahedra, an edgeedge with one OZr4 trigonal pyramid, and edges with two NZr4 trigonal pyramids. In the fourth O2- site, O2- is bonded to four Zr4+ atoms to form distorted OZr4 trigonal pyramids that share corners with five OZr4 trigonal pyramids, corners with seven

36 MATERIALS SCIENCE↗

Materials Data on Ti2N2O by Materials Project

Ti2N2O is Ilmenite-like structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are sixteen inequivalent Ti4+ sites. In the first Ti4+ site, Ti4+ is bonded to three N3- and three O2- atoms to form TiN3O3 octahedra that share corners with five TiN3O3 octahedra, a cornercorner with one TiN3O3 pentagonal pyramid, edges with five TiN4O2 octahedra, and an edgeedge with one TiN3O3 pentagonal pyramid. The corner-sharing octahedra tilt angles range from 47–54°. There are a spread of Ti–N bond distances ranging from 1.96–1.99 Å. There are a spread of Ti–O bond distances ranging from 2.07–2.12 Å. In the second Ti4+ site, Ti4+ is bonded to three N3- and three O2- atoms to form distorted TiN3O3 pentagonal pyramids that share corners with six TiN3O3 octahedra and edges with six TiN4O2 octahedra. The corner-sharing octahedra tilt angles range from 47–53°. There are a spread of Ti–N bond distances ranging from 1.94–2.03 Å. There are a spread of Ti–O bond distances ranging from 2.05–2.17 Å. In the third Ti4+ site, Ti4+ is bonded to four N3- and two O2- atoms to form distorted TiN4O2 octahedra that share corners with six TiN5O octahedra, edges with four TiN3O3 octahedra, and edges with two TiN3O3 pentagonal pyramids. The corner-sharing octahedra tilt angles range from 52–56°. There are a spread of Ti–N bond distances ranging from 1.98–2.07 Å. There are one shorter (2.13 Å) and one longer (2.14 Å) Ti–O bond lengths. In the fourth Ti4+ site, Ti4+ is bonded to three N3- and three O2- atoms to form distorted TiN3O3 octahedra that share corners with four TiN3O3 octahedra, corners with two TiN3O3 pentagonal pyramids, and edges with six TiN5O octahedra. The corner-sharing octahedra tilt angles range from 47–51°. There are a spread of Ti–N bond distances ranging from 2.02–2.05 Å. There are a spread of Ti–O bond distances ranging from 1.96–2.08 Å. In the fifth Ti4+ site, Ti4+ is bonded to three N3- and three O2- atoms to form a mixture of distorted edge and corner-sharing TiN3O3 pentagonal pyramids. The corner-sharing octahedra tilt angles range from 46–56°. There are a spread of Ti–N bond distances ranging from 1.92–2.04 Å. There are a spread of Ti–O bond distances ranging from 2.03–2.18 Å. In the sixth Ti4+ site, Ti4+ is bonded to five N3- and one O2- atom to form distorted TiN5O octahedra that share corners with six TiN4O2 octahedra, edges with four TiN3O3 octahedra, and edges with two TiN3O3 pentagonal pyramids. The corner-sharing octahedra tilt angles range from 52–56°. There are a spread of Ti–N bond distances ranging from 1.99–2.09 Å. The Ti–O bond length is 2.16 Å. In the seventh Ti4+ site, Ti4+ is bonded to three N3- and three O2- atoms to form distorted TiN3O3 octahedra that share corners with four TiN3O3 octahedra, corners with two TiN3O3 pentagonal pyramids, and edges with six TiN4O2 octahedra. The corner-sharing octahedra tilt angles range from 49–53°. There are two shorter (1.97 Å) and one longer (2.10 Å) Ti–N bond lengths. There are a spread of Ti–O bond distances ranging from 2.01–2.09 Å. In the eighth Ti4+ site, Ti4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted edge and corner-sharing TiN4O2 octahedra. The corner-sharing octahedra tilt angles range from 50–53°. There are a spread of Ti–N bond distances ranging from 2.03–2.05 Å. There are one shorter (2.04 Å) and one longer (2.05 Å) Ti–O bond lengths. In the ninth Ti4+ site, Ti4+ is bonded to four N3- and two O2- atoms to form TiN4O2 octahedra that share corners with five TiN3O3 octahedra, a cornercorner with one TiN3O3 pentagonal pyramid, edges with five TiN4O2 octahedra, and an edgeedge with one TiN3O3 pentagonal pyramid. The corner-sharing octahedra tilt angles range from 50–56°. There are a spread of Ti–N bond distances ranging from 1.95–2.07 Å. There are one shorter (2.08 Å) and one longer (2.16 Å) Ti–O bond lengths. In the tenth Ti4+ site, Ti4+ is bonded to four N3- and two O2- atoms to form TiN4O2 octahedra that share corners with five TiN4O2 octahedra, a cornercorner with one TiN3O3 pentagonal pyramid, edges with five TiN3O3 octahedra, and an edgeedge with one TiN3O3 pentagonal pyramid. The corner-sharing octahedra tilt angles range from 53–56°. There are a spread of Ti–N bond distances ranging from 2.01–2.08 Å. There are one shorter (2.02 Å) and one longer (2.05 Å) Ti–O bond lengths. In the eleventh Ti4+ site, Ti4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted edge and corner-sharing TiN4O2 octahedra. The corner-sharing octahedra tilt angles range from 51–58°. There are a spread of Ti–N bond distances ranging from 2.00–2.06 Å. There are one shorter (2.09 Å) and one longer (2.14 Å) Ti–O bond lengths. In the twelfth Ti4+ site, Ti4+ is bonded to five N3- and one O2- atom to form TiN5O octahedra that share corners with five TiN4O2 octahedra, a cornercorner with one TiN3O3 pentagonal pyramid, edges with five TiN3O3 octahedra, and an edgeedge with one TiN3O3 pentagonal pyramid. The corner-sharing octahedra tilt angles range from 51–58°. There are a spread of Ti–N bond distances ranging from 1.96–2.08 Å. The Ti–O bond length is 2.17 Å. In the thirteenth Ti4+ site, Ti4+ is bonded to five N3- and one O2- atom to form distorted TiN5O octahedra that share corners with six TiN4O2 octahedra and edges with six TiN3O3 octahedra. The corner-sharing octahedra tilt angles range from 52–54°. There are a spread of Ti–N bond distances ranging from 2.00–2.09 Å. The Ti–O bond length is 2.10 Å. In the fourteenth Ti4+ site, Ti4+ is bonded to five N3- and one O2- atom to form a mixture of distorted edge and corner-sharing TiN5O octahedra. The corner-sharing octahedra tilt angles range from 51–54°. There are a spread of Ti–N bond distances ranging from 2.00–2.08 Å. The Ti–O bond length is 2.10 Å. In the fifteenth Ti4+ site, Ti4+ is bonded to four N3- and two O2- atoms to form a mixture of distorted edge and corner-sharing TiN4O2 octahedra. The corner-sharing octahedra tilt angles range from 51–54°. There are a spread of Ti–N bond distances ranging from 1.98–2.07 Å. There are one shorter (2.09 Å) and one longer (2.13 Å) Ti–O bond lengths. In the sixteenth Ti4+ site, Ti4+ is bonded to five N3- and one O2- atom to form a mixture of distorted edge and corner-sharing TiN5O octahedra. The corner-sharing octahedra tilt angles range from 52–55°. There are a spread of Ti–N bond distances ranging from 2.01–2.11 Å. The Ti–O bond length is 2.10 Å. There are sixteen inequivalent N3- sites. In the first N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share a cornercorner with one OTi4 trigonal pyramid, corners with ten NTi4 trigonal pyramids, an edgeedge with one NTi4 trigonal pyramid, and edges with three OTi4 trigonal pyramids. In the second N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with three OTi4 trigonal pyramids, corners with eight NTi4 trigonal pyramids, an edgeedge with one NTi4 trigonal pyramid, and edges with two OTi4 trigonal pyramids. In the third N3- site, N3- is bonded to four Ti4+ atoms to form NTi4 trigonal pyramids that share corners with four OTi4 trigonal pyramids, corners with six NTi4 trigonal pyramids, an edgeedge with one OTi4 trigonal pyramid, and edges with three NTi4 trigonal pyramids. In the fourth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with two OTi4 trigonal pyramids, corners with ten NTi4 trigonal pyramids, an edgeedge with one NTi4 trigonal pyramid, and edges with three OTi4 trigonal pyramids. In the fifth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with two OTi4 trigonal pyramids, corners with ten NTi4 trigonal pyramids, an edgeedge with one NTi4 trigonal pyramid, and edges with two OTi4 trigonal pyramids. In the sixth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share a cornercorner with one OTi4 trigonal pyramid, corners with ten NTi4 trigonal pyramids, an edgeedge with one NTi4 trigonal pyramid, and edges with two OTi4 trigonal pyramids. In the seventh N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with four OTi4 trigonal pyramids, corners with six NTi4 trigonal pyramids, an edgeedge with one OTi4 trigonal pyramid, and edges with three NTi4 trigonal pyramids. In the eighth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with three OTi4 trigonal pyramids, corners with eight NTi4 trigonal pyramids, and edges with three NTi4 trigonal pyramids. In the ninth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with three OTi4 trigonal pyramids, corners with eight NTi4 trigonal pyramids, edges with two NTi4 trigonal pyramids, and edges with two OTi4 trigonal pyramids. In the tenth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with two OTi4 trigonal pyramids, corners with ten NTi4 trigonal pyramids, an edgeedge with one NTi4 trigonal pyramid, and edges with two OTi4 trigonal pyramids. In the eleventh N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with four OTi4 trigonal pyramids, corners with six NTi4 trigonal pyramids, an edgeedge with one OTi4 trigonal pyramid, and edges with three NTi4 trigonal pyramids. In the twelfth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with two OTi4 trigonal pyramids, corners with ten NTi4 trigonal pyramids, an edgeedge with one OTi4 trigonal pyramid, and edges with two NTi4 trigonal pyramids. In the thirteenth N3- site, N3- is bonded to four Ti4+ atoms to form NTi4 trigonal pyramids that share corners with five OTi4 trigonal pyramids, corners with six NTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the fourteenth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with two OTi4 trigonal pyramids, corners with ten NTi4 trigonal pyramids, edges with two NTi4 trigonal pyramids, and edges with two OTi4 trigonal pyramids. In the fifteenth N3- site, N3- is bonded to four Ti4+ atoms to form NTi4 trigonal pyramids that share corners with four OTi4 trigonal pyramids, corners with six NTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the sixteenth N3- site, N3- is bonded to four Ti4+ atoms to form distorted NTi4 trigonal pyramids that share corners with two OTi4 trigonal pyramids, corners with ten NTi4 trigonal pyramids, an edgeedge with one OTi4 trigonal pyramid, and edges with two NTi4 trigonal pyramids. There are eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a rectangular see-saw-like geometry to four Ti4+ atoms. In the second O2- site, O2- is bonded to four Ti4+ atoms to form OTi4 trigonal pyramids that share corners with five OTi4 trigonal pyramids, corners with six NTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the third O2- site, O2- is bonded to four Ti4+ atoms to form OTi4 trigonal pyramids that share corners with four OTi4 trigonal pyramids, corners with six NTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the fourth O2- site, O2- is bonded to four Ti4+ atoms to form OTi4 trigonal pyramids that share corners with three OTi4 trigonal pyramids, corners with eight NTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the fifth O2- site, O2- is bonded to four Ti4+ atoms to form distorted OTi4 trigonal pyramids that share corners with four OTi4 trigonal pyramids, corners with six NTi4 trigonal pyramids, and edges with four NTi4 trigonal pyramids. In the sixth O2- site, O2- is bonded to four Ti4+ atoms to form distorted OTi4

36 MATERIALS SCIENCE↗

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 distorted HfN4O2 octahedra that share corners with six HfN3O3 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 50–57°. There are a spread of Hf–N bond distances ranging from 2.08–2.19 Å. There are one shorter (2.23 Å) and one longer (2.29 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 edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 52–58°. There are a spread of Hf–N bond distances ranging from 2.10–2.19 Å. There are one shorter (2.21 Å) and one longer (2.25 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 edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 53–56°. There are a spread of Hf–N bond distances ranging from 2.08–2.17 Å. There are one shorter (2.29 Å) and one longer (2.31 Å) Hf–O bond lengths. In the fourth Hf4+ site, Hf4+ is bonded to three N3- and three O2- atoms to form distorted HfN3O3 octahedra that share corners with six HfN5O 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 2.10–2.23 Å. There are a spread of Hf–O bond distances ranging from 2.11–2.23 Å. In the fifth 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 49–57°. There are a spread of Hf–N bond distances ranging from 2.08–2.21 Å. There are a spread of Hf–O bond distances ranging from 2.11–2.23 Å. In the sixth 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 53–56°. There are a spread of Hf–N bond distances ranging from 2.11–2.20 Å. The Hf–O bond length is 2.27 Å. In the seventh Hf4+ site, Hf4+ is bonded to three N3- and three O2- atoms to form HfN3O3 octahedra that share corners with six HfN4O2 octahedra and edges with six HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 51–58°. There are two shorter (2.07 Å) and one longer (2.12 Å) Hf–N bond lengths. There are one shorter (2.21 Å) and two longer (2.26 Å) Hf–O bond lengths. In the eighth Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form distorted HfN5O octahedra that share corners with six HfN4O2 octahedra and edges with six HfN3O3 octahedra. The corner-sharing octahedra tilt angles range from 53–58°. There are a spread of Hf–N bond distances ranging from 2.12–2.25 Å. The Hf–O bond length is 2.34 Å. In the ninth Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form a mixture of edge and corner-sharing HfN5O octahedra. The corner-sharing octahedra tilt angles range from 54–58°. There are a spread of Hf–N bond distances ranging from 2.10–2.23 Å. The Hf–O bond length is 2.30 Å. In the tenth 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 49–56°. There are a spread of Hf–N bond distances ranging from 2.12–2.20 Å. There are a spread of Hf–O bond distances ranging from 2.13–2.17 Å. In the eleventh 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 53–58°. There are a spread of Hf–N bond distances ranging from 2.10–2.18 Å. There are one shorter (2.26 Å) and one longer (2.27 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 52–58°. There are a spread of Hf–N bond distances ranging from 2.15–2.23 Å. The Hf–O bond length is 2.22 Å. In the thirteenth 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 49–57°. There are a spread of Hf–N bond distances ranging from 2.06–2.20 Å. There are a spread of Hf–O bond distances ranging from 2.13–2.24 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 HfN5O octahedra. The corner-sharing octahedra tilt angles range from 50–54°. There are a spread of Hf–N bond distances ranging from 2.16–2.18 Å. There are one shorter (2.16 Å) and one longer (2.17 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 49–57°. There are a spread of Hf–N bond distances ranging from 2.13–2.23 Å. The Hf–O bond length is 2.22 Å. In the sixteenth 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 53–58°. There are a spread of Hf–N bond distances ranging from 2.12–2.24 Å. There are one shorter (2.18 Å) and one longer (2.21 Å) Hf–O bond lengths. There are sixteen 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 NHf4 tetrahedra, corners with five NHf4 trigonal pyramids, corners with six OHf4 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 tetrahedra that share corners with two NHf4 tetrahedra, corners with two 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 third N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with two NHf4 tetrahedra, corners with two 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 fourth N3- site, N3- is bonded to four Hf4+ atoms to form NHf4 trigonal pyramids that share corners with six NHf4 trigonal pyramids, corners with six OHf4 trigonal pyramids, an edgeedge with one NHf4 tetrahedra, and edges with three NHf4 trigonal pyramids. In the fifth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with five 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 sixth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share a cornercorner with one NHf4 tetrahedra, corners with five OHf4 trigonal pyramids, corners with six 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, corners with five NHf4 trigonal pyramids, corners with six OHf4 trigonal pyramids, an edgeedge with one NHf4 tetrahedra, an edgeedge with one OHf4 trigonal pyramid, 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 corners with three NHf4 tetrahedra, corners with two OHf4 trigonal pyramids, corners with seven NHf4 trigonal pyramids, an edgeedge with one NHf4 trigonal pyramid, and edges with three OHf4 trigonal pyramids. In the ninth 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 OHf4 trigonal pyramids, corners with seven NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 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, corners with five 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 eleventh N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share a cornercorner with one NHf4 tetrahedra, corners with five OHf4 trigonal pyramids, corners with six NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 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 five NHf4 trigonal pyramids, corners with six OHf4 trigonal pyramids, an edgeedge with one NHf4 tetrahedra, and edges with three NHf4 trigonal pyramids. In the thirteenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with six NHf4 trigonal pyramids, corners with six OHf4 trigonal pyramids, an edgeedge with one OHf4 trigonal pyramid, and edges with three NHf4 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 NHf4 tetrahedra, corners with three OHf4 trigonal pyramids, corners with six NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 trigonal pyramids. In the fifteenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with three NHf4 tetrahedra, corners with three 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 sixteenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with two NHf4 tetrahedra, corners with two OHf4 trigonal pyramids, corners with eight NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 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 five OHf4 trigonal pyramids, corners with seven NHf4 trigonal pyramids, edges with two NHf4 tetrahedra, and edges with two NHf4 trigonal pyramids. In the second O2- site, O2- is bonded to four Hf4+ atoms to form OHf4 trigonal pyramids that share corners with five OHf4 trigonal pyramids, corners with seven 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 four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share corners with three NHf4 tetrahedra, corners with two 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 fourth O2- site, O2- is bonded to four Hf4+ atoms to form OHf4 trigonal pyramids that share corners with two NHf4 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

36 MATERIALS SCIENCE↗

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 two N3- and four O2- atoms to form a mixture of edge and corner-sharing HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 51–55°. There are one shorter (2.12 Å) and one longer (2.15 Å) Hf–N bond lengths. There are a spread of Hf–O bond distances ranging from 2.10–2.15 Å. 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 HfN2O4 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 52–57°. There are a spread of Hf–N bond distances ranging from 2.12–2.24 Å. There are one shorter (2.13 Å) and one longer (2.23 Å) Hf–O bond lengths. In the third 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 HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 52–58°. There are a spread of Hf–N bond distances ranging from 2.13–2.24 Å. There are one shorter (2.14 Å) and one longer (2.18 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 HfN2O4 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 49–56°. There are a spread of Hf–N bond distances ranging from 2.13–2.22 Å. There are one shorter (2.15 Å) and one longer (2.18 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 HfN4O2 octahedra and edges with six HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 49–59°. There are a spread of Hf–N bond distances ranging from 2.07–2.20 Å. There are a spread of Hf–O bond distances ranging from 2.11–2.24 Å. In the sixth 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 HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 49–57°. There are a spread of Hf–N bond distances ranging from 2.10–2.19 Å. There are one shorter (2.19 Å) and one longer (2.28 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 edge and corner-sharing HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 54–57°. There are a spread of Hf–N bond distances ranging from 2.16–2.20 Å. There are one shorter (2.15 Å) and one longer (2.17 Å) Hf–O bond lengths. In the eighth Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form a mixture of edge and corner-sharing HfN5O octahedra. The corner-sharing octahedra tilt angles range from 52–56°. There are a spread of Hf–N bond distances ranging from 2.11–2.21 Å. The Hf–O bond length is 2.29 Å. In the ninth 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 HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 50–57°. There are a spread of Hf–N bond distances ranging from 2.13–2.22 Å. There are one shorter (2.13 Å) and one longer (2.25 Å) Hf–O bond lengths. In the tenth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form distorted HfN4O2 octahedra that share corners with six HfN2O4 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 50–59°. There are a spread of Hf–N bond distances ranging from 2.09–2.25 Å. There are one shorter (2.24 Å) and one longer (2.27 Å) Hf–O bond lengths. In the eleventh Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form a mixture of edge and corner-sharing HfN5O octahedra. The corner-sharing octahedra tilt angles range from 55–59°. There are a spread of Hf–N bond distances ranging from 2.11–2.22 Å. The Hf–O bond length is 2.33 Å. In the twelfth Hf4+ site, Hf4+ is bonded to four N3- and two O2- atoms to form distorted HfN4O2 octahedra that share corners with six HfN2O4 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 49–59°. There are a spread of Hf–N bond distances ranging from 2.09–2.23 Å. There are one shorter (2.22 Å) and one longer (2.28 Å) Hf–O bond lengths. In the thirteenth 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 HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 50–58°. There are a spread of Hf–N bond distances ranging from 2.08–2.18 Å. There are one shorter (2.26 Å) and one longer (2.29 Å) Hf–O bond lengths. In the fourteenth Hf4+ site, Hf4+ is bonded to five N3- and one O2- atom to form distorted HfN5O octahedra that share corners with six HfN4O2 octahedra and edges with six HfN2O4 octahedra. The corner-sharing octahedra tilt angles range from 52–59°. There are a spread of Hf–N bond distances ranging from 2.12–2.27 Å. The Hf–O bond length is 2.23 Å. In the fifteenth Hf4+ site, Hf4+ is bonded to three N3- and three O2- atoms to form distorted HfN3O3 octahedra that share corners with six HfN2O4 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 50–56°. There are a spread of Hf–N bond distances ranging from 2.07–2.15 Å. There are a spread of Hf–O bond distances ranging from 2.13–2.25 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 HfN2O4 octahedra and edges with six HfN4O2 octahedra. The corner-sharing octahedra tilt angles range from 51–56°. There are a spread of Hf–N bond distances ranging from 2.15–2.24 Å. The Hf–O bond length is 2.18 Å. There are sixteen 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 NHf4 tetrahedra, corners with four OHf4 trigonal pyramids, corners with seven NHf4 trigonal pyramids, an edgeedge with one NHf4 trigonal pyramid, and edges with three OHf4 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 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 third N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 tetrahedra that share corners with four OHf4 trigonal pyramids, corners with eight NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, 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 corners with four OHf4 trigonal pyramids, corners with eight 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 corners with four 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 sixth 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, 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, corners with five 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, corners with four 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 ninth 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 OHf4 trigonal pyramid, and edges with three 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, corners with five 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 eleventh N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with five OHf4 trigonal pyramids, corners with seven NHf4 trigonal pyramids, and edges with four 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 trigonal pyramid, and edges with three OHf4 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 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 fourteenth 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 OHf4 trigonal pyramid, 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 corners with four 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 sixteenth N3- site, N3- is bonded to four Hf4+ atoms to form distorted NHf4 trigonal pyramids that share corners with four OHf4 trigonal pyramids, corners with eight NHf4 trigonal pyramids, edges with two NHf4 trigonal pyramids, and edges with two OHf4 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 a cornercorner with one NHf4 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 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 five 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 third O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share corners with five OHf4 trigonal pyramids, corners with seven NHf4 trigonal pyramids, an edgeedge with one NHf4 tetrahedra, and edges with three NHf4 trigonal pyramids. In the fourth O2- site, O2- is bonded to four Hf4+ atoms to form distorted OHf4 trigonal pyramids that share corners with five O

36 MATERIALS SCIENCE↗

Materials Data on KMn2O4 by Materials Project

KMn2O4 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are eight inequivalent K1+ sites. In the first K1+ site, K1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of K–O bond distances ranging from 2.42–2.65 Å. In the second K1+ site, K1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of K–O bond distances ranging from 2.42–2.64 Å. In the third K1+ site, K1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of K–O bond distances ranging from 2.42–2.65 Å. In the fourth K1+ site, K1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of K–O bond distances ranging from 2.42–2.64 Å. In the fifth K1+ site, K1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of K–O bond distances ranging from 2.42–2.65 Å. In the sixth K1+ site, K1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of K–O bond distances ranging from 2.42–2.65 Å. In the seventh K1+ site, K1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of K–O bond distances ranging from 2.42–2.65 Å. In the eighth K1+ site, K1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of K–O bond distances ranging from 2.41–2.65 Å. There are sixteen inequivalent Mn+3.50+ sites. In the first Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of distorted corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 49–53°. There are a spread of Mn–O bond distances ranging from 1.92–2.32 Å. In the second Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 46–50°. There are a spread of Mn–O bond distances ranging from 1.93–2.13 Å. In the third Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 46–50°. There are a spread of Mn–O bond distances ranging from 1.93–2.13 Å. In the fourth Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of distorted corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 50–52°. There are a spread of Mn–O bond distances ranging from 1.92–2.32 Å. In the fifth Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of distorted corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 50–52°. There are a spread of Mn–O bond distances ranging from 1.92–2.34 Å. In the sixth Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 46–50°. There are a spread of Mn–O bond distances ranging from 1.93–2.14 Å. In the seventh Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 46–50°. There are a spread of Mn–O bond distances ranging from 1.93–2.13 Å. In the eighth Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of distorted corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 50–52°. There are a spread of Mn–O bond distances ranging from 1.92–2.33 Å. In the ninth Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 46–50°. There are a spread of Mn–O bond distances ranging from 1.93–2.13 Å. In the tenth Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of distorted corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 50–52°. There are a spread of Mn–O bond distances ranging from 1.92–2.33 Å. In the eleventh Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of distorted corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 49–52°. There are a spread of Mn–O bond distances ranging from 1.92–2.33 Å. In the twelfth Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 46–50°. There are a spread of Mn–O bond distances ranging from 1.93–2.15 Å. In the thirteenth Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of distorted corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 50–53°. There are a spread of Mn–O bond distances ranging from 1.92–2.34 Å. In the fourteenth Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 46–50°. There are a spread of Mn–O bond distances ranging from 1.93–2.12 Å. In the fifteenth Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 46–50°. There are a spread of Mn–O bond distances ranging from 1.93–2.13 Å. In the sixteenth Mn+3.50+ site, Mn+3.50+ is bonded to six O2- atoms to form a mixture of distorted corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra tilt angles range from 50–52°. There are a spread of Mn–O bond distances ranging from 1.92–2.33 Å. There are thirty-two inequivalent O2- sites. In the first O2- site, O2- is bonded to one K1+ and three Mn+3.50+ atoms to form distorted OKMn3 trigonal pyramids that share corners with three OK2Mn3 trigonal bipyramids, corners with two OKMn3 trigonal pyramids, and edges with five OK2Mn3 trigonal bipyramids. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to three Mn+3.50+ atoms. In the third O2- site, O2- is bonded in a distorted trigonal planar geometry to three Mn+3.50+ atoms. In the fourth O2- site, O2- is bonded to one K1+ and three Mn+3.50+ atoms to form distorted OKMn3 trigonal pyramids that share corners with three OK2Mn3 trigonal bipyramids, corners with two OKMn3 trigonal pyramids, and edges with five OK2Mn3 trigonal bipyramids. In the fifth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Mn+3.50+ atoms. In the sixth O2- site, O2- is bonded to one K1+ and three Mn+3.50+ atoms to form distorted OKMn3 trigonal pyramids that share corners with three OK2Mn3 trigonal bipyramids, corners with two OKMn3 trigonal pyramids, and edges with five OK2Mn3 trigonal bipyramids. In the seventh O2- site, O2- is bonded to one K1+ and three Mn+3.50+ atoms to form distorted OKMn3 trigonal pyramids that share corners with three OK2Mn3 trigonal bipyramids, corners with two OKMn3 trigonal pyramids, and edges with five OK2Mn3 trigonal bipyramids. In the eighth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Mn+3.50+ atoms. In the ninth O2- site, O2- is bonded to one K1+ and three Mn+3.50+ atoms to form distorted OKMn3 trigonal pyramids that share corners with three OK2Mn3 trigonal bipyramids, corners with two OKMn3 trigonal pyramids, and edges with five OK2Mn3 trigonal bipyramids. In the tenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Mn+3.50+ atoms. In the eleventh O2- site, O2- is bonded in a distorted trigonal planar geometry to three Mn+3.50+ atoms. In the twelfth O2- site, O2- is bonded to one K1+ and three Mn+3.50+ atoms to form distorted OKMn3 trigonal pyramids that share corners with three OK2Mn3 trigonal bipyramids, corners with two OKMn3 trigonal pyramids, and edges with five OK2Mn3 trigonal bipyramids. In the thirteenth O2- site, O2- is bonded to one K1+ and three Mn+3.50+ atoms to form distorted OKMn3 trigonal pyramids that share corners with three OK2Mn3 trigonal bipyramids, corners with two OKMn3 trigonal pyramids, and edges with five OK2Mn3 trigonal bipyramids. In the fourteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Mn+3.50+ atoms. In the fifteenth O2- site, O2- is bonded in a distorted trigonal planar geometry to three Mn+3.50+ atoms. In the sixteenth O2- site, O2- is bonded to one K1+ and three Mn+3.50+ atoms to form distorted OKMn3 trigonal pyramids that share corners with three OK2Mn3 trigonal bipyramids, corners with two OKMn3 trigonal pyramids, and edges with five OK2Mn3 trigonal bipyramids. In the seventeenth O2- site, O2- is bonded to two K1+ and three Mn+3.50+ atoms to form distorted OK2Mn3 trigonal bipyramids that share corners with four OK2Mn3 trigonal bipyramids, corners with three OKMn3 trigonal pyramids, edges with four OK2Mn3 trigonal bipyramids, and edges with two OKMn3 trigonal pyramids. In the eighteenth O2- site, O2- is bonded to two K1+ and three Mn+3.50+ atoms to form distorted OK2Mn3 trigonal bipyramids that share corners with four OK2Mn3 trigonal bipyramids, edges with four OK2Mn3 trigonal bipyramids, and edges with three OKMn3 trigonal pyramids. In the nineteenth O2- site, O2- is bonded to two K1+ and three Mn+3.50+ atoms to form distorted OK2Mn3 trigonal bipyramids that share corners with four OK2Mn3 trigonal bipyramids, corners with three OKMn3 trigonal pyramids, edges with four OK2Mn3 trigonal bipyramids, and edges with two OKMn3 trigonal pyramids. In the twentieth O2- site, O2- is bonded to two K1+ and three Mn+3.50+ atoms to form distorted OK2Mn3 trigonal bipyramids that share corners with four OK2Mn3 trigonal bipyramids, edges with four OK2Mn3 trigonal bipyramids, and edges with three OKMn3 trigonal pyramids. In the twenty-first O2- site, O2- is bonded to two K1+ and three Mn+3.50+ atoms to form distorted OK2Mn3 trigonal bipyramids that share corners with four OK2Mn3 trigonal bipyramids, edges with four OK2Mn3 trigonal bipyramids, and edges with three OKMn3 trigonal pyramids. In the twenty-second O2- site, O2- is bonded to two K1+ and three Mn+3.50+ atoms to form distorted OK2Mn3 trigonal bipyramids that share corners with four OK2Mn3 trigonal bipyramids, corners with three OKMn3 trigonal pyramids, edges with four OK2Mn3 trigonal bipyramids, and edges with two OKMn3 trigonal pyramids. In the twenty-third O2- site, O2- is bonded to two K1+ and three Mn+3.50+ atoms to form distorted OK2Mn3 trigonal bipyramids that share corners with four OK2Mn3 trigonal bipyramids, edges with four OK2Mn3 trigonal bipyramids, and edges with three OKMn3 trigonal pyramids. In the twenty-fourth O2- site, O2- is bonded to two K1+ and three Mn+3.50+ atoms to form distorted OK2Mn3 trigonal bipyramids that share corners with four OK2Mn3 trigonal bipyramids, corners with three OKMn3 trigonal pyramids, edges with four OK2Mn3 trigonal bipyramids, and edges with two OKMn3 trigonal pyramids. In the twenty-fifth O2- site, O2- is bonded to two K1+ and three Mn+3.50+ atoms to form distorted OK2Mn3 trigonal bipyramids that share corners with four OK2Mn3 trigonal bipyramids, edges with four OK2Mn3 trigonal bipyramids, and edges with three OKMn3 trigonal pyramids. In the twenty-sixth O2- site, O2- is bonded to two K1+ and three Mn+3.50+ atoms to form distorted OK2Mn3 trigonal bipyramids that share corners with four OK2Mn3 trigonal bipyramids, corners with three OKMn3 trigonal pyramids, edges with four OK2Mn3 trigonal bipyramids, and edges with two OKMn3 trigonal pyramids. In the twenty-seventh O2- site, O2- is bonded to two K1+ and three Mn+3.50+ atoms to form distorted OK2Mn3 trigonal bipyramids that share corners with four OK2Mn3 trigonal bipyramids, corners with three OKMn3 trigonal pyramids, edges with four OK2Mn3 trigonal bipyramids, and edges with two OKMn3 trigonal pyramids. In the twenty-eighth O2- site, O2- is bonded to two K1+ and three Mn+3.50+ atoms to form distorted OK2Mn3 trigonal bipyramids that share corners with four OK2Mn3 trigonal bipyramids, edges with four OK2Mn3 trigonal bipyramids, and

36 MATERIALS SCIENCE↗