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Late-formed haloes prefer to host quiescent central galaxies – I. Observational results

ABSTRACT The star formation and quenching of central galaxies are regulated by the assembly histories of their host haloes. In this work, we use the central stellar mass to halo mass ratio as a proxy of halo formation time, and we devise three different models, from the physical hydrodynamical simulation to the empirical statistical model, to demonstrate its robustness. With this proxy, we inferred the dependence of the central galaxy properties on the formation time of their host haloes using the SDSS main galaxy sample, where central galaxies are identified with the halo-based group finder. We found that central galaxies living in late-formed haloes have higher quiescent fractions and lower spiral fractions than their early-formed counterparts by $\lesssim 8~{{\ \rm per\ cent}}$ . Finally, we demonstrate that the group finding algorithm has a negligible impact on our results.

Astronomy & Astrophysics↗

Materials Data on U(HO)8 by Materials Project

U(HO)8 crystallizes in the monoclinic C2/c space group. The structure is three-dimensional. U is bonded to eight O atoms to form distorted edge-sharing UO8 hexagonal bipyramids. There are a spread of U–O bond distances ranging from 1.83–2.43 Å. There are four inequivalent H sites. In the first H site, H is bonded in a distorted linear geometry to two O atoms. There is one shorter (1.01 Å) and one longer (1.66 Å) H–O bond length. In the second H site, H is bonded in a single-bond geometry to one O atom. The H–O bond length is 0.99 Å. In the third H site, H is bonded in a single-bond geometry to one O atom. The H–O bond length is 0.99 Å. In the fourth H site, H is bonded in a single-bond geometry to two O atoms. There is one shorter (1.00 Å) and one longer (1.75 Å) H–O bond length. There are four inequivalent O sites. In the first O site, O is bonded in a 4-coordinate geometry to two equivalent U, one H, and one O atom. The O–O bond length is 1.45 Å. In the second O site, O is bonded in a single-bond geometry to one U atom. In the third O site, O is bonded in a distorted water-like geometry to one U and two H atoms. In the fourth O site, O is bonded in a distorted water-like geometry to three H atoms.

36 MATERIALS SCIENCE↗

Materials Data on LaPr3(CoP)8 by Materials Project

Pr3La(CoP)8 crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are two inequivalent Pr3+ sites. In the first Pr3+ site, Pr3+ is bonded in a body-centered cubic geometry to eight P3- atoms. All Pr–P bond lengths are 3.08 Å. In the second Pr3+ site, Pr3+ is bonded in a body-centered cubic geometry to eight equivalent P3- atoms. All Pr–P bond lengths are 3.09 Å. La3+ is bonded in a body-centered cubic geometry to eight equivalent P3- atoms. All La–P bond lengths are 3.10 Å. There are two inequivalent Co+1.50+ sites. In the first Co+1.50+ site, Co+1.50+ is bonded to four P3- atoms to form a mixture of edge and corner-sharing CoP4 tetrahedra. All Co–P bond lengths are 2.25 Å. In the second Co+1.50+ site, Co+1.50+ is bonded to four P3- atoms to form a mixture of edge and corner-sharing CoP4 tetrahedra. There are two shorter (2.25 Å) and two longer (2.26 Å) Co–P bond lengths. There are four inequivalent P3- sites. In the first P3- site, P3- is bonded in a 4-coordinate geometry to four equivalent La3+ and four equivalent Co+1.50+ atoms. In the second P3- site, P3- is bonded in a 9-coordinate geometry to four equivalent Pr3+ and four equivalent Co+1.50+ atoms. In the third P3- site, P3- is bonded in a 9-coordinate geometry to four equivalent Pr3+ and four equivalent Co+1.50+ atoms. In the fourth P3- site, P3- is bonded in a 9-coordinate geometry to four equivalent Pr3+ and four equivalent Co+1.50+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Li3(WO3)8 by Materials Project

Li3(WO3)8 crystallizes in the orthorhombic Pmmm space group. The structure is three-dimensional. there are three inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded in a distorted square co-planar geometry to four equivalent O2- atoms. All Li–O bond lengths are 2.15 Å. In the second Li1+ site, Li1+ is bonded in a distorted square co-planar geometry to four equivalent O2- atoms. All Li–O bond lengths are 2.15 Å. In the third Li1+ site, Li1+ is bonded in a distorted square co-planar geometry to four equivalent O2- atoms. All Li–O bond lengths are 2.16 Å. W+5.62+ is bonded to six O2- atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 26–31°. There are a spread of W–O bond distances ranging from 1.93–1.97 Å. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two equivalent W+5.62+ atoms. In the second O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two equivalent W+5.62+ atoms. In the third O2- site, O2- is bonded in a 4-coordinate geometry to one Li1+ and two equivalent W+5.62+ atoms. In the fourth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Li1+ and two equivalent W+5.62+ atoms. In the fifth O2- site, O2- is bonded in a bent 150 degrees geometry to two equivalent W+5.62+ atoms. In the sixth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Li1+ and two equivalent W+5.62+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Mg(TiS2)8 by Materials Project

Mg(TiS2)8 crystallizes in the orthorhombic Pnnm space group. The structure is three-dimensional. Mg2+ is bonded to six S2- atoms to form MgS6 octahedra that share corners with six TiS6 octahedra and edges with six TiS6 octahedra. The corner-sharing octahedra tilt angles range from 2–4°. There are two shorter (2.52 Å) and four longer (2.53 Å) Mg–S bond lengths. There are four inequivalent Ti+3.75+ sites. In the first Ti+3.75+ site, Ti+3.75+ is bonded to six S2- atoms to form TiS6 octahedra that share an edgeedge with one MgS6 octahedra and edges with six TiS6 octahedra. There are a spread of Ti–S bond distances ranging from 2.39–2.51 Å. In the second Ti+3.75+ site, Ti+3.75+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with two equivalent MgS6 octahedra and edges with six TiS6 octahedra. The corner-sharing octahedral tilt angles are 4°. There are a spread of Ti–S bond distances ranging from 2.38–2.50 Å. In the third Ti+3.75+ site, Ti+3.75+ is bonded to six S2- atoms to form TiS6 octahedra that share edges with two equivalent MgS6 octahedra and edges with six TiS6 octahedra. There are two shorter (2.45 Å) and four longer (2.46 Å) Ti–S bond lengths. In the fourth Ti+3.75+ site, Ti+3.75+ is bonded to six S2- atoms to form TiS6 octahedra that share corners with two equivalent MgS6 octahedra and edges with six TiS6 octahedra. The corner-sharing octahedral tilt angles are 2°. There are two shorter (2.43 Å) and four longer (2.44 Å) Ti–S bond lengths. There are six inequivalent S2- sites. In the first S2- site, S2- is bonded in a distorted T-shaped geometry to three Ti+3.75+ atoms. In the second S2- site, S2- is bonded in a rectangular see-saw-like geometry to one Mg2+ and three Ti+3.75+ atoms. In the third S2- site, S2- is bonded in a distorted T-shaped geometry to three Ti+3.75+ atoms. In the fourth S2- site, S2- is bonded in a distorted T-shaped geometry to three Ti+3.75+ atoms. In the fifth S2- site, S2- is bonded in a rectangular see-saw-like geometry to one Mg2+ and three Ti+3.75+ atoms. In the sixth S2- site, S2- is bonded in a distorted T-shaped geometry to three Ti+3.75+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Li3(WO3)8 by Materials Project

Li3(WO3)8 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. there are two inequivalent Li1+ sites. In the first Li1+ site, Li1+ is bonded in a distorted rectangular see-saw-like geometry to four O2- atoms. There are two shorter (2.09 Å) and two longer (2.16 Å) Li–O bond lengths. In the second Li1+ site, Li1+ is bonded in a distorted square co-planar geometry to four equivalent O2- atoms. All Li–O bond lengths are 2.14 Å. There are three inequivalent W+5.62+ sites. In the first W+5.62+ site, W+5.62+ is bonded to six O2- atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 28–33°. There is two shorter (1.94 Å) and four longer (1.95 Å) W–O bond length. In the second W+5.62+ site, W+5.62+ is bonded to six O2- atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 25–35°. There are a spread of W–O bond distances ranging from 1.94–2.04 Å. In the third W+5.62+ site, W+5.62+ is bonded to six O2- atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 23–35°. There are a spread of W–O bond distances ranging from 1.86–2.02 Å. There are eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a 3-coordinate geometry to one Li1+ and two W+5.62+ atoms. In the second O2- site, O2- is bonded in a bent 150 degrees geometry to two W+5.62+ atoms. In the third O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two equivalent W+5.62+ atoms. In the fourth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two equivalent W+5.62+ atoms. In the fifth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two equivalent W+5.62+ atoms. In the sixth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two equivalent W+5.62+ atoms. In the seventh O2- site, O2- is bonded in a 4-coordinate geometry to one Li1+ and two W+5.62+ atoms. In the eighth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Li1+ and two W+5.62+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on NaSr7Cu8(SF)8 by Materials Project

NaSr7Cu8(SF)8 crystallizes in the tetragonal P4mm space group. The structure is three-dimensional. Na1+ is bonded in a 4-coordinate geometry to four equivalent S2- and four equivalent F1- atoms. All Na–S bond lengths are 3.35 Å. All Na–F bond lengths are 2.34 Å. There are three inequivalent Sr2+ sites. In the first Sr2+ site, Sr2+ is bonded in a 4-coordinate geometry to four S2- and four F1- atoms. There are one shorter (3.18 Å) and three longer (3.20 Å) Sr–S bond lengths. There are two shorter (2.43 Å) and two longer (2.46 Å) Sr–F bond lengths. In the second Sr2+ site, Sr2+ is bonded in a 4-coordinate geometry to four equivalent S2- and four F1- atoms. All Sr–S bond lengths are 3.20 Å. There are two shorter (2.45 Å) and two longer (2.47 Å) Sr–F bond lengths. In the third Sr2+ site, Sr2+ is bonded in a 4-coordinate geometry to four equivalent S2- and four equivalent F1- atoms. All Sr–S bond lengths are 3.17 Å. All Sr–F bond lengths are 2.47 Å. There are two inequivalent Cu+1.12+ sites. In the first Cu+1.12+ site, Cu+1.12+ is bonded to four S2- atoms to form a mixture of edge and corner-sharing CuS4 tetrahedra. There are a spread of Cu–S bond distances ranging from 2.39–2.43 Å. In the second Cu+1.12+ site, Cu+1.12+ is bonded to four S2- atoms to form a mixture of edge and corner-sharing CuS4 tetrahedra. There are a spread of Cu–S bond distances ranging from 2.40–2.44 Å. There are four inequivalent S2- sites. In the first S2- site, S2- is bonded in a 4-coordinate geometry to one Na1+, three Sr2+, and four Cu+1.12+ atoms. In the second S2- site, S2- is bonded in a 4-coordinate geometry to four equivalent Sr2+ and four equivalent Cu+1.12+ atoms. In the third S2- site, S2- is bonded in a 4-coordinate geometry to four equivalent Sr2+ and four Cu+1.12+ atoms. In the fourth S2- site, S2- is bonded in a 4-coordinate geometry to four equivalent Sr2+ and four equivalent Cu+1.12+ atoms. There are two inequivalent F1- sites. In the first F1- site, F1- is bonded to four Sr2+ atoms to form a mixture of edge and corner-sharing FSr4 tetrahedra. In the second F1- site, F1- is bonded to one Na1+ and three Sr2+ atoms to form a mixture of edge and corner-sharing FNaSr3 tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on BaSr3Cu8(BO3)8 by Materials Project

BaSr3Cu8(BO3)8 crystallizes in the orthorhombic P222 space group. The structure is three-dimensional. Ba2+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are four shorter (2.75 Å) and four longer (2.80 Å) Ba–O bond lengths. There are three inequivalent Sr2+ sites. In the first Sr2+ site, Sr2+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are four shorter (2.66 Å) and four longer (2.72 Å) Sr–O bond lengths. In the second Sr2+ site, Sr2+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are four shorter (2.65 Å) and four longer (2.72 Å) Sr–O bond lengths. In the third Sr2+ site, Sr2+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are four shorter (2.66 Å) and four longer (2.73 Å) Sr–O bond lengths. There are two inequivalent Cu2+ sites. In the first Cu2+ site, Cu2+ is bonded in a square co-planar geometry to four O2- atoms. There are a spread of Cu–O bond distances ranging from 1.94–1.97 Å. In the second Cu2+ site, Cu2+ is bonded in a rectangular see-saw-like geometry to four O2- atoms. There are a spread of Cu–O bond distances ranging from 1.94–1.99 Å. There are two inequivalent B3+ sites. In the first B3+ site, B3+ is bonded in a trigonal planar geometry to three O2- atoms. There is one shorter (1.38 Å) and two longer (1.39 Å) B–O bond length. In the second B3+ site, B3+ is bonded in a trigonal planar geometry to three O2- atoms. There is one shorter (1.37 Å) and two longer (1.39 Å) B–O bond length. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal planar geometry to two equivalent Cu2+ and one B3+ atom. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to two equivalent Cu2+ and one B3+ atom. In the third O2- site, O2- is bonded in a 1-coordinate geometry to two Sr2+, one Cu2+, and one B3+ atom. In the fourth O2- site, O2- is bonded in a 1-coordinate geometry to one Ba2+, one Sr2+, one Cu2+, and one B3+ atom. In the fifth O2- site, O2- is bonded in a 1-coordinate geometry to two Sr2+, one Cu2+, and one B3+ atom. In the sixth O2- site, O2- is bonded in a 1-coordinate geometry to one Ba2+, one Sr2+, one Cu2+, and one B3+ atom.

36 MATERIALS SCIENCE↗

Materials Data on Mg7(SiO3)8 by Materials Project

Mg7(SiO3)8 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. there are four inequivalent Mg sites. In the first Mg site, Mg is bonded in a rectangular see-saw-like geometry to four O atoms. There are two shorter (2.01 Å) and two longer (2.08 Å) Mg–O bond lengths. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six SiO4 tetrahedra and edges with three MgO6 octahedra. There are a spread of Mg–O bond distances ranging from 2.05–2.16 Å. In the third Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four equivalent SiO4 tetrahedra and edges with six MgO6 octahedra. There are two shorter (2.08 Å) and four longer (2.12 Å) Mg–O bond lengths. In the fourth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four SiO4 tetrahedra and edges with five MgO6 octahedra. There are a spread of Mg–O bond distances ranging from 2.06–2.11 Å. There are two inequivalent Si sites. In the first Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share corners with three MgO6 octahedra and corners with three SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 59–62°. There is two shorter (1.63 Å) and two longer (1.64 Å) Si–O bond length. In the second Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share corners with three MgO6 octahedra and corners with two equivalent SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 39–60°. There are a spread of Si–O bond distances ranging from 1.61–1.67 Å. There are seven inequivalent O sites. In the first O site, O is bonded in a bent 150 degrees geometry to two equivalent Si atoms. In the second O site, O is bonded in a trigonal non-coplanar geometry to three Mg atoms. In the third O site, O is bonded in a bent 150 degrees geometry to two Si atoms. In the fourth O site, O is bonded in a distorted trigonal non-coplanar geometry to two Mg and one Si atom. In the fifth O site, O is bonded to three Mg and one Si atom to form a mixture of distorted corner and edge-sharing OMg3Si tetrahedra. In the sixth O site, O is bonded in a rectangular see-saw-like geometry to three Mg and one Si atom. In the seventh O site, O is bonded in a bent 150 degrees geometry to two Si atoms.

36 MATERIALS SCIENCE↗

Materials Data on Mn2Fe5(SiO3)8 by Materials Project

Mn2Fe5(SiO3)8 crystallizes in the orthorhombic Pnnm space group. The structure is three-dimensional. Mn2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Mn–O bond distances ranging from 2.09–2.63 Å. There are three inequivalent Fe+2.40+ sites. In the first Fe+2.40+ site, Fe+2.40+ is bonded to six O2- atoms to form FeO6 octahedra that share corners with four SiO4 tetrahedra and edges with five FeO6 octahedra. There are a spread of Fe–O bond distances ranging from 1.96–2.17 Å. In the second Fe+2.40+ site, Fe+2.40+ is bonded to six O2- atoms to form FeO6 octahedra that share corners with four equivalent SiO4 tetrahedra and edges with six FeO6 octahedra. There are two shorter (2.09 Å) and four longer (2.18 Å) Fe–O bond lengths. In the third Fe+2.40+ site, Fe+2.40+ is bonded to six O2- atoms to form FeO6 octahedra that share corners with six SiO4 tetrahedra and edges with three FeO6 octahedra. There are a spread of Fe–O bond distances ranging from 2.10–2.21 Å. There are two inequivalent Si4+ sites. In the first Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with three FeO6 octahedra and corners with two equivalent SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 35–59°. There are a spread of Si–O bond distances ranging from 1.63–1.67 Å. In the second Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with three FeO6 octahedra and corners with three SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 56–63°. There are a spread of Si–O bond distances ranging from 1.63–1.65 Å. There are seven inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one Mn2+ and two Si4+ atoms. In the second O2- site, O2- is bonded in a bent 150 degrees geometry to two Si4+ atoms. In the third O2- site, O2- is bonded in a distorted T-shaped geometry to three Fe+2.40+ atoms. In the fourth O2- site, O2- is bonded in a distorted T-shaped geometry to one Mn2+, one Fe+2.40+, and one Si4+ atom. In the fifth O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to one Mn2+, two Fe+2.40+, and one Si4+ atom. In the sixth O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to three Fe+2.40+ and one Si4+ atom. In the seventh O2- site, O2- is bonded in a bent 150 degrees geometry to two equivalent Si4+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Fe7(SiO3)8 by Materials Project

Fe7(SiO3)8 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. there are four inequivalent Fe+2.29+ sites. In the first Fe+2.29+ site, Fe+2.29+ is bonded in a distorted rectangular see-saw-like geometry to four O2- atoms. There are two shorter (2.03 Å) and two longer (2.17 Å) Fe–O bond lengths. In the second Fe+2.29+ site, Fe+2.29+ is bonded to six O2- atoms to form FeO6 octahedra that share corners with six SiO4 tetrahedra and edges with three FeO6 octahedra. There are a spread of Fe–O bond distances ranging from 2.09–2.22 Å. In the third Fe+2.29+ site, Fe+2.29+ is bonded to six O2- atoms to form FeO6 octahedra that share corners with four equivalent SiO4 tetrahedra and edges with six FeO6 octahedra. There are two shorter (1.95 Å) and four longer (2.11 Å) Fe–O bond lengths. In the fourth Fe+2.29+ site, Fe+2.29+ is bonded to six O2- atoms to form FeO6 octahedra that share corners with four SiO4 tetrahedra and edges with five FeO6 octahedra. There are a spread of Fe–O bond distances ranging from 2.01–2.22 Å. There are two inequivalent Si4+ sites. In the first Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with three FeO6 octahedra and corners with three SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 59–60°. There are a spread of Si–O bond distances ranging from 1.62–1.65 Å. In the second Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with three FeO6 octahedra and corners with two equivalent SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 38–60°. There are a spread of Si–O bond distances ranging from 1.63–1.66 Å. There are seven inequivalent O2- sites. In the first O2- site, O2- is bonded in a bent 150 degrees geometry to two equivalent Si4+ atoms. In the second O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three Fe+2.29+ atoms. In the third O2- site, O2- is bonded in a bent 150 degrees geometry to two Si4+ atoms. In the fourth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to two Fe+2.29+ and one Si4+ atom. In the fifth O2- site, O2- is bonded in a 4-coordinate geometry to three Fe+2.29+ and one Si4+ atom. In the sixth O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to three Fe+2.29+ and one Si4+ atom. In the seventh O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two Si4+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Ga6AgSb7(TeCl3)8 by Materials Project

AgGa6Sb7(TeCl3)8 crystallizes in the triclinic P1 space group. The structure is three-dimensional. Ag1+ is bonded in a 6-coordinate geometry to six Cl1- atoms. There are a spread of Ag–Cl bond distances ranging from 2.57–3.18 Å. There are six inequivalent Ga3+ sites. In the first Ga3+ site, Ga3+ is bonded in a tetrahedral geometry to four Cl1- atoms. There are a spread of Ga–Cl bond distances ranging from 2.17–2.24 Å. In the second Ga3+ site, Ga3+ is bonded in a tetrahedral geometry to four Cl1- atoms. There are a spread of Ga–Cl bond distances ranging from 2.17–2.23 Å. In the third Ga3+ site, Ga3+ is bonded in a tetrahedral geometry to four Cl1- atoms. There are a spread of Ga–Cl bond distances ranging from 2.19–2.24 Å. In the fourth Ga3+ site, Ga3+ is bonded in a tetrahedral geometry to four Cl1- atoms. There are a spread of Ga–Cl bond distances ranging from 2.18–2.22 Å. In the fifth Ga3+ site, Ga3+ is bonded in a tetrahedral geometry to four Cl1- atoms. There are a spread of Ga–Cl bond distances ranging from 2.18–2.22 Å. In the sixth Ga3+ site, Ga3+ is bonded in a tetrahedral geometry to four Cl1- atoms. There are a spread of Ga–Cl bond distances ranging from 2.18–2.22 Å. There are seven inequivalent Sb3+ sites. In the first Sb3+ site, Sb3+ is bonded in a 4-coordinate geometry to three Te2- and two Cl1- atoms. There are a spread of Sb–Te bond distances ranging from 2.89–2.98 Å. There are one shorter (3.17 Å) and one longer (3.36 Å) Sb–Cl bond lengths. In the second Sb3+ site, Sb3+ is bonded in a 4-coordinate geometry to three Te2- and one Cl1- atom. There are a spread of Sb–Te bond distances ranging from 2.88–2.97 Å. The Sb–Cl bond length is 3.18 Å. In the third Sb3+ site, Sb3+ is bonded in an octahedral geometry to six Te2- atoms. There are three shorter (3.06 Å) and three longer (3.07 Å) Sb–Te bond lengths. In the fourth Sb3+ site, Sb3+ is bonded in a 4-coordinate geometry to three Te2- and three Cl1- atoms. There are a spread of Sb–Te bond distances ranging from 2.89–2.91 Å. There are a spread of Sb–Cl bond distances ranging from 3.32–3.40 Å. In the fifth Sb3+ site, Sb3+ is bonded in a 6-coordinate geometry to three Te2- atoms. There are one shorter (2.89 Å) and two longer (2.91 Å) Sb–Te bond lengths. In the sixth Sb3+ site, Sb3+ is bonded in a rectangular see-saw-like geometry to three Te2- and one Cl1- atom. There are one shorter (2.88 Å) and two longer (2.92 Å) Sb–Te bond lengths. The Sb–Cl bond length is 3.23 Å. In the seventh Sb3+ site, Sb3+ is bonded in a rectangular see-saw-like geometry to three Te2- and one Cl1- atom. There are a spread of Sb–Te bond distances ranging from 2.89–2.92 Å. The Sb–Cl bond length is 3.22 Å. There are eight inequivalent Te2- sites. In the first Te2- site, Te2- is bonded in a 7-coordinate geometry to three Sb3+ and four Cl1- atoms. There are a spread of Te–Cl bond distances ranging from 3.66–4.02 Å. In the second Te2- site, Te2- is bonded in a 7-coordinate geometry to three Sb3+ and four Cl1- atoms. There are a spread of Te–Cl bond distances ranging from 3.66–4.02 Å. In the third Te2- site, Te2- is bonded in a 9-coordinate geometry to three Sb3+ and six Cl1- atoms. There are a spread of Te–Cl bond distances ranging from 3.59–4.15 Å. In the fourth Te2- site, Te2- is bonded in a 9-coordinate geometry to three Sb3+ and six Cl1- atoms. There are a spread of Te–Cl bond distances ranging from 3.59–4.19 Å. In the fifth Te2- site, Te2- is bonded in a 4-coordinate geometry to three Sb3+ and one Cl1- atom. The Te–Cl bond length is 3.82 Å. In the sixth Te2- site, Te2- is bonded in a 4-coordinate geometry to three Sb3+ and one Cl1- atom. The Te–Cl bond length is 3.82 Å. In the seventh Te2- site, Te2- is bonded in a 8-coordinate geometry to three Sb3+ and five Cl1- atoms. There are a spread of Te–Cl bond distances ranging from 3.85–4.13 Å. In the eighth Te2- site, Te2- is bonded in a 8-coordinate geometry to three Sb3+ and five Cl1- atoms. There are a spread of Te–Cl bond distances ranging from 3.86–4.13 Å. There are twenty-four inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded in a single-bond geometry to one Ga3+ and two Te2- atoms. In the second Cl1- site, Cl1- is bonded in a single-bond geometry to one Ga3+, one Sb3+, and two Te2- atoms. In the third Cl1- site, Cl1- is bonded in a distorted single-bond geometry to one Ga3+, one Sb3+, and three Te2- atoms. In the fourth Cl1- site, Cl1- is bonded in a distorted single-bond geometry to one Ga3+, one Sb3+, and three Te2- atoms. In the fifth Cl1- site, Cl1- is bonded in a single-bond geometry to one Ga3+ and one Sb3+ atom. In the sixth Cl1- site, Cl1- is bonded in a distorted single-bond geometry to one Ag1+ and one Ga3+ atom. In the seventh Cl1- site, Cl1- is bonded in a single-bond geometry to one Ga3+ and one Te2- atom. In the eighth Cl1- site, Cl1- is bonded in a single-bond geometry to one Ga3+ and one Te2- atom. In the ninth Cl1- site, Cl1- is bonded in a single-bond geometry to one Ga3+ and two Te2- atoms. In the tenth Cl1- site, Cl1- is bonded in a single-bond geometry to one Ga3+ and two Te2- atoms. In the eleventh Cl1- site, Cl1- is bonded in a bent 120 degrees geometry to one Ag1+ and one Ga3+ atom. In the twelfth Cl1- site, Cl1- is bonded in a water-like geometry to one Ag1+ and one Ga3+ atom. In the thirteenth Cl1- site, Cl1- is bonded in a single-bond geometry to one Ga3+ and one Te2- atom. In the fourteenth Cl1- site, Cl1- is bonded in a single-bond geometry to one Ga3+ and one Te2- atom. In the fifteenth Cl1- site, Cl1- is bonded in a 1-coordinate geometry to one Ag1+, one Ga3+, one Sb3+, and one Te2- atom. In the sixteenth Cl1- site, Cl1- is bonded in a distorted single-bond geometry to one Ag1+, one Ga3+, and one Te2- atom. In the seventeenth Cl1- site, Cl1- is bonded in a single-bond geometry to one Ga3+ and two Te2- atoms. In the eighteenth Cl1- site, Cl1- is bonded in a distorted single-bond geometry to one Ag1+, one Ga3+, and two Te2- atoms. In the nineteenth Cl1- site, Cl1- is bonded in a single-bond geometry to one Ga3+ and one Te2- atom. In the twentieth Cl1- site, Cl1- is bonded in a single-bond geometry to one Ga3+ and one Te2- atom. In the twenty-first Cl1- site, Cl1- is bonded in a single-bond geometry to one Ga3+ and two Te2- atoms. In the twenty-second Cl1- site, Cl1- is bonded in a single-bond geometry to one Ga3+, one Sb3+, and two Te2- atoms. In the twenty-third Cl1- site, Cl1- is bonded in a distorted single-bond geometry to one Ga3+, one Sb3+, and one Te2- atom. In the twenty-fourth Cl1- site, Cl1- is bonded in a distorted single-bond geometry to one Ga3+, one Sb3+, and one Te2- atom.

36 MATERIALS SCIENCE↗

Materials Data on Ba4PrY(CuO2)8 by Materials Project

Ba4PrY(CuO2)8 crystallizes in the monoclinic P2/m space group. The structure is three-dimensional. there are two inequivalent Ba2+ sites. In the first Ba2+ site, Ba2+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Ba–O bond distances ranging from 2.78–3.03 Å. In the second Ba2+ site, Ba2+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of Ba–O bond distances ranging from 2.78–3.06 Å. Pr4+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are four shorter (2.50 Å) and four longer (2.51 Å) Pr–O bond lengths. Y3+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are four shorter (2.40 Å) and four longer (2.43 Å) Y–O bond lengths. There are four inequivalent Cu+2.12+ sites. In the first Cu+2.12+ site, Cu+2.12+ is bonded in a square co-planar geometry to four O2- atoms. There are a spread of Cu–O bond distances ranging from 1.85–1.97 Å. In the second Cu+2.12+ site, Cu+2.12+ is bonded in a square co-planar geometry to four O2- atoms. There are a spread of Cu–O bond distances ranging from 1.85–1.97 Å. In the third Cu+2.12+ site, Cu+2.12+ is bonded to five O2- atoms to form corner-sharing CuO5 square pyramids. There are a spread of Cu–O bond distances ranging from 1.96–2.30 Å. In the fourth Cu+2.12+ site, Cu+2.12+ is bonded to five O2- atoms to form corner-sharing CuO5 square pyramids. There are a spread of Cu–O bond distances ranging from 1.96–2.30 Å. There are seven inequivalent O2- sites. In the first O2- site, O2- is bonded in a 6-coordinate geometry to two Ba2+, one Pr4+, one Y3+, and two equivalent Cu+2.12+ atoms. In the second O2- site, O2- is bonded to four Ba2+ and two Cu+2.12+ atoms to form a mixture of distorted corner and edge-sharing OBa4Cu2 octahedra. The corner-sharing octahedral tilt angles are 11°. In the third O2- site, O2- is bonded to four Ba2+ and two Cu+2.12+ atoms to form a mixture of distorted corner and edge-sharing OBa4Cu2 octahedra. The corner-sharing octahedral tilt angles are 11°. In the fourth O2- site, O2- is bonded in a distorted T-shaped geometry to two equivalent Ba2+ and three Cu+2.12+ atoms. In the fifth O2- site, O2- is bonded in a distorted T-shaped geometry to two equivalent Ba2+ and three Cu+2.12+ atoms. In the sixth O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Ba2+, two equivalent Y3+, and two Cu+2.12+ atoms. In the seventh O2- site, O2- is bonded in a 6-coordinate geometry to two equivalent Ba2+, two equivalent Pr4+, and two Cu+2.12+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on NaAl6Sb7(TeCl3)8 by Materials Project

NaAl6Sb7(TeCl3)8 crystallizes in the triclinic P1 space group. The structure is three-dimensional. Na1+ is bonded to six Cl1- atoms to form distorted NaCl6 pentagonal pyramids that share corners with two AlCl4 tetrahedra and edges with two AlCl4 tetrahedra. There are a spread of Na–Cl bond distances ranging from 2.77–3.19 Å. There are six inequivalent Al3+ sites. In the first Al3+ site, Al3+ is bonded to four Cl1- atoms to form AlCl4 tetrahedra that share an edgeedge with one NaCl6 pentagonal pyramid. There are a spread of Al–Cl bond distances ranging from 2.15–2.17 Å. In the second Al3+ site, Al3+ is bonded to four Cl1- atoms to form AlCl4 tetrahedra that share a cornercorner with one NaCl6 pentagonal pyramid. There are a spread of Al–Cl bond distances ranging from 2.14–2.19 Å. In the third Al3+ site, Al3+ is bonded in a tetrahedral geometry to four Cl1- atoms. There are a spread of Al–Cl bond distances ranging from 2.14–2.18 Å. In the fourth Al3+ site, Al3+ is bonded in a tetrahedral geometry to four Cl1- atoms. There are a spread of Al–Cl bond distances ranging from 2.14–2.18 Å. In the fifth Al3+ site, Al3+ is bonded to four Cl1- atoms to form AlCl4 tetrahedra that share an edgeedge with one NaCl6 pentagonal pyramid. There are a spread of Al–Cl bond distances ranging from 2.12–2.19 Å. In the sixth Al3+ site, Al3+ is bonded to four Cl1- atoms to form AlCl4 tetrahedra that share a cornercorner with one NaCl6 pentagonal pyramid. There are a spread of Al–Cl bond distances ranging from 2.13–2.20 Å. There are seven inequivalent Sb3+ sites. In the first Sb3+ site, Sb3+ is bonded in a 4-coordinate geometry to three Te2- atoms. There are one shorter (2.89 Å) and two longer (2.90 Å) Sb–Te bond lengths. In the second Sb3+ site, Sb3+ is bonded in a 4-coordinate geometry to three Te2- atoms. There are one shorter (2.89 Å) and two longer (2.90 Å) Sb–Te bond lengths. In the third Sb3+ site, Sb3+ is bonded in a 4-coordinate geometry to three Te2- and one Cl1- atom. There are a spread of Sb–Te bond distances ranging from 2.88–2.98 Å. The Sb–Cl bond length is 3.11 Å. In the fourth Sb3+ site, Sb3+ is bonded in a 5-coordinate geometry to three Te2- and two Cl1- atoms. There are a spread of Sb–Te bond distances ranging from 2.88–2.99 Å. There are one shorter (3.08 Å) and one longer (3.32 Å) Sb–Cl bond lengths. In the fifth Sb3+ site, Sb3+ is bonded in an octahedral geometry to six Te2- atoms. There are a spread of Sb–Te bond distances ranging from 3.06–3.08 Å. In the sixth Sb3+ site, Sb3+ is bonded in a rectangular see-saw-like geometry to three Te2- and one Cl1- atom. There are a spread of Sb–Te bond distances ranging from 2.89–2.92 Å. The Sb–Cl bond length is 3.19 Å. In the seventh Sb3+ site, Sb3+ is bonded in a rectangular see-saw-like geometry to three Te2- and one Cl1- atom. There are a spread of Sb–Te bond distances ranging from 2.89–2.92 Å. The Sb–Cl bond length is 3.20 Å. There are eight inequivalent Te2- sites. In the first Te2- site, Te2- is bonded in a 9-coordinate geometry to three Sb3+ and six Cl1- atoms. There are a spread of Te–Cl bond distances ranging from 3.53–4.24 Å. In the second Te2- site, Te2- is bonded in a 9-coordinate geometry to three Sb3+ and six Cl1- atoms. There are a spread of Te–Cl bond distances ranging from 3.53–4.18 Å. In the third Te2- site, Te2- is bonded in a 7-coordinate geometry to three Sb3+ and four Cl1- atoms. There are a spread of Te–Cl bond distances ranging from 3.63–4.04 Å. In the fourth Te2- site, Te2- is bonded in a 7-coordinate geometry to three Sb3+ and four Cl1- atoms. There are a spread of Te–Cl bond distances ranging from 3.63–4.03 Å. In the fifth Te2- site, Te2- is bonded in a 4-coordinate geometry to three Sb3+ and one Cl1- atom. The Te–Cl bond length is 3.80 Å. In the sixth Te2- site, Te2- is bonded in a 4-coordinate geometry to three Sb3+ and one Cl1- atom. The Te–Cl bond length is 3.80 Å. In the seventh Te2- site, Te2- is bonded in a 8-coordinate geometry to three Sb3+ and five Cl1- atoms. There are a spread of Te–Cl bond distances ranging from 3.81–4.17 Å. In the eighth Te2- site, Te2- is bonded in a 8-coordinate geometry to three Sb3+ and five Cl1- atoms. There are a spread of Te–Cl bond distances ranging from 3.82–4.18 Å. There are twenty-four inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ and one Te2- atom. In the second Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ and one Te2- atom. In the third Cl1- site, Cl1- is bonded in a distorted single-bond geometry to one Al3+, one Sb3+, and one Te2- atom. In the fourth Cl1- site, Cl1- is bonded in a distorted single-bond geometry to one Al3+, one Sb3+, and one Te2- atom. In the fifth Cl1- site, Cl1- is bonded in a distorted single-bond geometry to one Na1+, one Al3+, and one Te2- atom. In the sixth Cl1- site, Cl1- is bonded in a distorted water-like geometry to one Na1+, one Al3+, and one Te2- atom. In the seventh Cl1- site, Cl1- is bonded in a distorted single-bond geometry to one Al3+, one Sb3+, and three Te2- atoms. In the eighth Cl1- site, Cl1- is bonded in a distorted single-bond geometry to one Al3+, one Sb3+, and three Te2- atoms. In the ninth Cl1- site, Cl1- is bonded in a distorted L-shaped geometry to one Na1+ and one Al3+ atom. In the tenth Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ and one Sb3+ atom. In the eleventh Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ and two Te2- atoms. In the twelfth Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ and two Te2- atoms. In the thirteenth Cl1- site, Cl1- is bonded in an L-shaped geometry to one Na1+ and one Al3+ atom. In the fourteenth Cl1- site, Cl1- is bonded in a bent 120 degrees geometry to one Na1+ and one Al3+ atom. In the fifteenth Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ and one Te2- atom. In the sixteenth Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ and one Te2- atom. In the seventeenth Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ and two Te2- atoms. In the eighteenth Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ and two Te2- atoms. In the nineteenth Cl1- site, Cl1- is bonded in a distorted L-shaped geometry to one Na1+, one Al3+, and two Te2- atoms. In the twentieth Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ and two Te2- atoms. In the twenty-first Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ and one Te2- atom. In the twenty-second Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ and one Te2- atom. In the twenty-third Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ and two Te2- atoms. In the twenty-fourth Cl1- site, Cl1- is bonded in a single-bond geometry to one Al3+ and two Te2- atoms.

36 MATERIALS SCIENCE↗

Materials Data on Ba4NdY(CuO2)8 by Materials Project

Ba4NdY(CuO2)8 crystallizes in the orthorhombic Pmmm space group. The structure is three-dimensional. there are two inequivalent Ba2+ sites. In the first Ba2+ site, Ba2+ is bonded in a distorted q6 geometry to ten O2- atoms. There are a spread of Ba–O bond distances ranging from 2.79–3.03 Å. In the second Ba2+ site, Ba2+ is bonded in a distorted q6 geometry to ten O2- atoms. There are a spread of Ba–O bond distances ranging from 2.79–2.99 Å. Nd3+ is bonded in a body-centered cubic geometry to eight O2- atoms. All Nd–O bond lengths are 2.48 Å. Y3+ is bonded in a body-centered cubic geometry to eight O2- atoms. All Y–O bond lengths are 2.44 Å. There are four inequivalent Cu+2.25+ sites. In the first Cu+2.25+ site, Cu+2.25+ is bonded to five O2- atoms to form corner-sharing CuO5 square pyramids. There are four shorter (1.98 Å) and one longer (2.29 Å) Cu–O bond lengths. In the second Cu+2.25+ site, Cu+2.25+ is bonded to five O2- atoms to form corner-sharing CuO5 square pyramids. There are a spread of Cu–O bond distances ranging from 1.97–2.27 Å. In the third Cu+2.25+ site, Cu+2.25+ is bonded in a square co-planar geometry to four O2- atoms. There are a spread of Cu–O bond distances ranging from 1.85–1.97 Å. In the fourth Cu+2.25+ site, Cu+2.25+ is bonded in a square co-planar geometry to four O2- atoms. There are a spread of Cu–O bond distances ranging from 1.84–1.97 Å. There are eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted T-shaped geometry to two equivalent Ba2+ and three Cu+2.25+ atoms. In the second O2- site, O2- is bonded in a distorted T-shaped geometry to two equivalent Ba2+ and three Cu+2.25+ atoms. In the third O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Ba2+, two equivalent Y3+, and two equivalent Cu+2.25+ atoms. In the fourth O2- site, O2- is bonded in a 6-coordinate geometry to two equivalent Ba2+, two equivalent Nd3+, and two equivalent Cu+2.25+ atoms. In the fifth O2- site, O2- is bonded to four equivalent Ba2+ and two Cu+2.25+ atoms to form a mixture of distorted edge and corner-sharing OBa4Cu2 octahedra. The corner-sharing octahedral tilt angles are 10°. In the sixth O2- site, O2- is bonded to four equivalent Ba2+ and two Cu+2.25+ atoms to form a mixture of distorted edge and corner-sharing OBa4Cu2 octahedra. The corner-sharing octahedral tilt angles are 10°. In the seventh O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Ba2+, two equivalent Y3+, and two equivalent Cu+2.25+ atoms. In the eighth O2- site, O2- is bonded in a 6-coordinate geometry to two equivalent Ba2+, two equivalent Nd3+, and two equivalent Cu+2.25+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on K3V5Te4(HO3)8 by Materials Project

K3V5Te4(HO3)8 crystallizes in the orthorhombic Pmmn space group. The structure is three-dimensional. there are three inequivalent K1+ sites. In the first K1+ site, K1+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are four shorter (2.79 Å) and four longer (2.83 Å) K–O bond lengths. In the second K1+ site, K1+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of K–O bond distances ranging from 2.90–3.28 Å. In the third K1+ site, K1+ is bonded in a 10-coordinate geometry to ten O2- atoms. There are a spread of K–O bond distances ranging from 2.78–3.33 Å. There are two inequivalent V5+ sites. In the first V5+ site, V5+ is bonded to six O2- atoms to form distorted VO6 octahedra that share a cornercorner with one VO4 tetrahedra and a faceface with one VO6 octahedra. There are a spread of V–O bond distances ranging from 1.66–2.26 Å. In the second V5+ site, V5+ is bonded to four O2- atoms to form corner-sharing VO4 tetrahedra. The corner-sharing octahedral tilt angles are 47°. There is two shorter (1.68 Å) and two longer (1.84 Å) V–O bond length. There are two inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. In the second H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. There are two inequivalent Te3+ sites. In the first Te3+ site, Te3+ is bonded in a 3-coordinate geometry to three O2- atoms. There is one shorter (1.90 Å) and two longer (1.93 Å) Te–O bond length. In the second Te3+ site, Te3+ is bonded in a 3-coordinate geometry to three O2- atoms. There is two shorter (1.92 Å) and one longer (1.94 Å) Te–O bond length. There are eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one K1+, two equivalent V5+, and one Te3+ atom. In the second O2- site, O2- is bonded in a distorted T-shaped geometry to three V5+ atoms. In the third O2- site, O2- is bonded in a distorted single-bond geometry to three K1+ and one V5+ atom. In the fourth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to two equivalent V5+ and one Te3+ atom. In the fifth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one K1+ and one V5+ atom. In the sixth O2- site, O2- is bonded in a bent 120 degrees geometry to one K1+, one V5+, and one Te3+ atom. In the seventh O2- site, O2- is bonded in a water-like geometry to two K1+ and two H1+ atoms. In the eighth O2- site, O2- is bonded in a bent 120 degrees geometry to one V5+ and one Te3+ atom.

36 MATERIALS SCIENCE↗

Materials Data on KNaAs6(PbO3)8 by Materials Project

KNaAs6(PbO3)8 crystallizes in the trigonal P3 space group. The structure is three-dimensional. K1+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of K–O bond distances ranging from 2.74–3.08 Å. Na1+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Na–O bond distances ranging from 2.52–3.07 Å. There are four inequivalent Pb2+ sites. In the first Pb2+ site, Pb2+ is bonded to six O2- atoms to form distorted PbO6 pentagonal pyramids that share corners with four equivalent PbO6 pentagonal pyramids, corners with four AsO4 tetrahedra, and an edgeedge with one AsO4 tetrahedra. There are a spread of Pb–O bond distances ranging from 2.27–2.84 Å. In the second Pb2+ site, Pb2+ is bonded to six O2- atoms to form distorted PbO6 pentagonal pyramids that share corners with four equivalent PbO6 pentagonal pyramids, corners with four AsO4 tetrahedra, and an edgeedge with one AsO4 tetrahedra. There are a spread of Pb–O bond distances ranging from 2.28–2.84 Å. In the third Pb2+ site, Pb2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Pb–O bond distances ranging from 2.46–3.07 Å. In the fourth Pb2+ site, Pb2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Pb–O bond distances ranging from 2.48–3.06 Å. There are two inequivalent As5+ sites. In the first As5+ site, As5+ is bonded to four O2- atoms to form AsO4 tetrahedra that share corners with four PbO6 pentagonal pyramids and an edgeedge with one PbO6 pentagonal pyramid. There are a spread of As–O bond distances ranging from 1.72–1.74 Å. In the second As5+ site, As5+ is bonded to four O2- atoms to form AsO4 tetrahedra that share corners with four PbO6 pentagonal pyramids and an edgeedge with one PbO6 pentagonal pyramid. There are a spread of As–O bond distances ranging from 1.72–1.74 Å. There are eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a 1-coordinate geometry to one Na1+, two Pb2+, and one As5+ atom. In the second O2- site, O2- is bonded in a 1-coordinate geometry to one K1+, two Pb2+, and one As5+ atom. In the third O2- site, O2- is bonded in a 1-coordinate geometry to one K1+, two Pb2+, and one As5+ atom. In the fourth O2- site, O2- is bonded in a 1-coordinate geometry to one Na1+, two Pb2+, and one As5+ atom. In the fifth O2- site, O2- is bonded in a distorted single-bond geometry to one K1+, two Pb2+, and one As5+ atom. In the sixth O2- site, O2- is bonded in a distorted single-bond geometry to one Na1+, two Pb2+, and one As5+ atom. In the seventh O2- site, O2- is bonded in a distorted single-bond geometry to three Pb2+ and one As5+ atom. In the eighth O2- site, O2- is bonded in a distorted single-bond geometry to three Pb2+ and one As5+ atom.

36 MATERIALS SCIENCE↗

Materials Data on KNaP6(PbO3)8 by Materials Project

KNaP6(PbO3)8 crystallizes in the trigonal P3 space group. The structure is three-dimensional. K1+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of K–O bond distances ranging from 2.70–3.00 Å. Na1+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Na–O bond distances ranging from 2.52–2.98 Å. There are four inequivalent Pb2+ sites. In the first Pb2+ site, Pb2+ is bonded to six O2- atoms to form distorted PbO6 pentagonal pyramids that share corners with four equivalent PbO6 pentagonal pyramids, corners with four PO4 tetrahedra, and an edgeedge with one PO4 tetrahedra. There are a spread of Pb–O bond distances ranging from 2.29–2.82 Å. In the second Pb2+ site, Pb2+ is bonded to six O2- atoms to form distorted PbO6 pentagonal pyramids that share corners with four equivalent PbO6 pentagonal pyramids, corners with four PO4 tetrahedra, and an edgeedge with one PO4 tetrahedra. There are a spread of Pb–O bond distances ranging from 2.27–2.80 Å. In the third Pb2+ site, Pb2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Pb–O bond distances ranging from 2.49–2.98 Å. In the fourth Pb2+ site, Pb2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Pb–O bond distances ranging from 2.52–2.97 Å. There are two inequivalent P5+ sites. In the first P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four PbO6 pentagonal pyramids and an edgeedge with one PbO6 pentagonal pyramid. There are a spread of P–O bond distances ranging from 1.55–1.57 Å. In the second P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four PbO6 pentagonal pyramids and an edgeedge with one PbO6 pentagonal pyramid. There are a spread of P–O bond distances ranging from 1.54–1.57 Å. There are eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted single-bond geometry to one Na1+, two Pb2+, and one P5+ atom. In the second O2- site, O2- is bonded in a distorted single-bond geometry to one K1+, two Pb2+, and one P5+ atom. In the third O2- site, O2- is bonded in a 1-coordinate geometry to one Na1+, two Pb2+, and one P5+ atom. In the fourth O2- site, O2- is bonded in a distorted single-bond geometry to one K1+, two Pb2+, and one P5+ atom. In the fifth O2- site, O2- is bonded in a 1-coordinate geometry to one K1+, two Pb2+, and one P5+ atom. In the sixth O2- site, O2- is bonded in a 1-coordinate geometry to one Na1+, two Pb2+, and one P5+ atom. In the seventh O2- site, O2- is bonded in a distorted single-bond geometry to three Pb2+ and one P5+ atom. In the eighth O2- site, O2- is bonded in a distorted single-bond geometry to three Pb2+ and one P5+ atom.

36 MATERIALS SCIENCE↗