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DOE OSTI2020

Materials Data on K9Ta10O30 by Materials Project

K9Ta10O30 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are five inequivalent K sites. In the first K site, K is bonded to twelve O atoms to form KO12 cuboctahedra that share corners with eleven KO12 cuboctahedra, faces with five KO12 cuboctahedra, and faces with eight TaO6 octahedra. There are a spread of K–O bond distances ranging from 2.83–2.85 Å. In the second K site, K is bonded to twelve O atoms to form KO12 cuboctahedra that share corners with eleven KO12 cuboctahedra, faces with five KO12 cuboctahedra, and faces with eight TaO6 octahedra. There are a spread of K–O bond distances ranging from 2.83–2.85 Å. In the third K site, K is bonded to twelve O atoms to form KO12 cuboctahedra that share corners with ten KO12 cuboctahedra, faces with six KO12 cuboctahedra, and faces with eight TaO6 octahedra. There are a spread of K–O bond distances ranging from 2.82–2.85 Å. In the fourth K site, K is bonded to twelve O atoms to form KO12 cuboctahedra that share corners with ten KO12 cuboctahedra, faces with six KO12 cuboctahedra, and faces with eight TaO6 octahedra. There are two shorter (2.82 Å) and ten longer (2.85 Å) K–O bond lengths. In the fifth K site, K is bonded to twelve O atoms to form KO12 cuboctahedra that share corners with eleven KO12 cuboctahedra, faces with five KO12 cuboctahedra, and faces with eight TaO6 octahedra. There are a spread of K–O bond distances ranging from 2.83–2.85 Å. There are five inequivalent Ta sites. In the first Ta site, Ta is bonded to six O atoms to form TaO6 octahedra that share corners with six TaO6 octahedra and faces with seven KO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Ta–O bond distances ranging from 1.99–2.03 Å. In the second Ta site, Ta is bonded to six O atoms to form TaO6 octahedra that share corners with six TaO6 octahedra and faces with seven KO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Ta–O bond distances ranging from 1.99–2.04 Å. In the third Ta site, Ta is bonded to six O atoms to form TaO6 octahedra that share corners with six TaO6 octahedra and faces with seven KO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Ta–O bond distances ranging from 1.99–2.03 Å. In the fourth Ta site, Ta is bonded to six O atoms to form TaO6 octahedra that share corners with six TaO6 octahedra and faces with eight KO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are five shorter (2.01 Å) and one longer (2.02 Å) Ta–O bond lengths. In the fifth Ta site, Ta is bonded to six O atoms to form TaO6 octahedra that share corners with six TaO6 octahedra and faces with seven KO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Ta–O bond distances ranging from 1.99–2.03 Å. There are sixteen inequivalent O sites. In the first O site, O is bonded in a distorted linear geometry to three K and two Ta atoms. In the second O site, O is bonded in a distorted linear geometry to three K and two Ta atoms. In the third O site, O is bonded in a distorted linear geometry to four K and two Ta atoms. In the fourth O site, O is bonded in a distorted linear geometry to three K and two Ta atoms. In the fifth O site, O is bonded in a distorted linear geometry to four K and two Ta atoms. In the sixth O site, O is bonded in a distorted linear geometry to four K and two Ta atoms. In the seventh O site, O is bonded in a distorted linear geometry to four K and two equivalent Ta atoms. In the eighth O site, O is bonded in a distorted linear geometry to four K and two Ta atoms. In the ninth O site, O is bonded in a distorted linear geometry to four K and two Ta atoms. In the tenth O site, O is bonded in a distorted linear geometry to four K and two Ta atoms. In the eleventh O site, O is bonded in a distorted linear geometry to four K and two Ta atoms. In the twelfth O site, O is bonded in a distorted linear geometry to three K and two Ta atoms. In the thirteenth O site, O is bonded in a distorted linear geometry to three K and two Ta atoms. In the fourteenth O site, O is bonded in a distorted linear geometry to four K and two Ta atoms. In the fifteenth O site, O is bonded in a distorted linear geometry to four K and two equivalent Ta atoms. In the sixteenth O site, O is bonded in a distorted linear geometry to three K and two Ta atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K16Na9(Tl6Cd)3 by Materials Project

K16Na9(CdTl6)3 crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. there are four inequivalent K sites. In the first K site, K is bonded in a 4-coordinate geometry to six K, four Na, and six Tl atoms. There are a spread of K–K bond distances ranging from 4.06–4.45 Å. There are two shorter (4.10 Å) and two longer (4.13 Å) K–Na bond lengths. There are a spread of K–Tl bond distances ranging from 3.99–4.20 Å. In the second K site, K is bonded in a 4-coordinate geometry to five K, four equivalent Na, two equivalent Cd, and six Tl atoms. There are two shorter (4.11 Å) and three longer (4.19 Å) K–K bond lengths. All K–Na bond lengths are 4.20 Å. Both K–Cd bond lengths are 3.96 Å. There are two shorter (4.10 Å) and four longer (4.20 Å) K–Tl bond lengths. In the third K site, K is bonded in a 3-coordinate geometry to three K and four Tl atoms. There are a spread of K–Tl bond distances ranging from 3.82–4.06 Å. In the fourth K site, K is bonded in a 6-coordinate geometry to three equivalent K and six equivalent Tl atoms. All K–Tl bond lengths are 3.84 Å. There are two inequivalent Na sites. In the first Na site, Na is bonded in a 6-coordinate geometry to four K, one Cd, and five Tl atoms. The Na–Cd bond length is 3.18 Å. There are a spread of Na–Tl bond distances ranging from 3.26–3.46 Å. In the second Na site, Na is bonded in a 12-coordinate geometry to four equivalent K and six Tl atoms. There are four shorter (3.32 Å) and two longer (3.43 Å) Na–Tl bond lengths. Cd is bonded in a 12-coordinate geometry to two equivalent K, two equivalent Na, and six Tl atoms. There are four shorter (3.18 Å) and two longer (3.39 Å) Cd–Tl bond lengths. There are five inequivalent Tl sites. In the first Tl site, Tl is bonded to six K, three equivalent Na, and three equivalent Tl atoms to form a mixture of distorted face and corner-sharing TlK6Na3Tl3 cuboctahedra. All Tl–Tl bond lengths are 3.25 Å. In the second Tl site, Tl is bonded in a 12-coordinate geometry to three equivalent K, three equivalent Na, three equivalent Cd, and three equivalent Tl atoms. All Tl–Tl bond lengths are 3.32 Å. In the third Tl site, Tl is bonded in a 12-coordinate geometry to six K, two equivalent Na, two equivalent Cd, and two Tl atoms. The Tl–Tl bond length is 3.21 Å. In the fourth Tl site, Tl is bonded in a 3-coordinate geometry to three equivalent K, three Na, and two Tl atoms. The Tl–Tl bond length is 3.24 Å. In the fifth Tl site, Tl is bonded to six K, three equivalent Na, and three equivalent Tl atoms to form a mixture of distorted face and corner-sharing TlK6Na3Tl3 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2023

The 𝑚=2 amplituhedron and the hypersimplex: Signs, clusters, tilings, Eulerian numbers

The hypersimplex Δ <#comment/> k + 1 , n \Delta _{k+1,n} is the image of the positive Grassmannian G r k + 1 , n ≥ <#comment/> 0 Gr^{\geq 0}_{k+1,n} under the moment map. It is a polytope of dimension n − <#comment/> 1 n-1 in R n \mathbb {R}^n . Meanwhile, the amplituhedron A n , k , 2 ( Z ) \mathcal {A}_{n,k,2}(Z) is the projection of the positive Grassmannian G r k , n ≥ <#comment/> 0 Gr^{\geq 0}_{k,n} into the Grassmannian G r k , k + 2 Gr_{k,k+2} under a map Z ~ <#comment/> \tilde {Z} induced by a positive matrix Z ∈ <#comment/> M a t n , k + 2 > 0 Z\in Mat_{n,k+2}^{>0} . Introduced in the context of scattering amplitudes , it is not a polytope, and has full dimension 2 k 2k inside G r k , k + 2 Gr_{k,k+2} . Nevertheless, there seem to be remarkable connections between these two objects via T-duality , as conjectured by Łukowski, Parisi, and Williams [Int. Math. Res. Not. (2023)]. In this paper we use ideas from oriented matroid theory, total positivity, and the geometry of the hypersimplex and positroid polytopes to obtain a deeper understanding of the amplituhedron. We show that the inequalities cutting out positroid polytopes —images of positroid cells of G r k + 1 , n ≥ <#comment/> 0 Gr^{\geq 0}_{k+1,n} under the moment map—translate into sign conditions characterizing the T-dual Grasstopes —images of positroid cells of G r k , n ≥ <#comment/> 0 Gr^{\geq 0}_{k,n} under Z ~ <#comment/> \tilde {Z} . Moreover, we subdivide the amplituhedron into chambers , just as the hypersimplex can be subdivided into simplices, with both chambers and simplices enumerated by the Eulerian numbers. We use these properties to prove the main conjecture of Łukowski, Parisi, and Williams [Int. Math. Res. Not. (2023)]: a collection of positroid polytopes is a tiling of the hypersimplex if and only if the collection of T-dual Grasstopes is a tiling of the amplituhedron A n , k , 2 ( Z ) \mathcal {A}_{n,k,2}(Z) for all Z Z . Moreover, we prove Arkani-Hamed–Thomas–Trnka’s conjectural sign-flip characterization of A n , k , 2 \mathcal {A}_{n,k,2} , and Łukowski–Parisi–Spradlin–Volovich’s conjectures on m = 2 m=2 cluster adjacency and on positroid tiles for A n , k , 2 \mathcal {A}_{n,k,2} (images of 2 k 2k -dimensional positroid cells which map injectively into A n , k , 2 \mathcal {A}_{n,k,2} ). Finally, we introduce new cluster structures in the amplituhedron.

Parisi, Matteo↗
DOE OSTI2020

Materials Data on K7As2W8O39 by Materials Project

K7W8As2O39 crystallizes in the monoclinic P2_1/m space group. The structure is three-dimensional. there are four inequivalent K sites. In the first K site, K is bonded in a 8-coordinate geometry to eight O atoms. There are a spread of K–O bond distances ranging from 2.73–3.35 Å. In the second K site, K is bonded in a 6-coordinate geometry to seven O atoms. There are a spread of K–O bond distances ranging from 2.65–3.43 Å. In the third K site, K is bonded in a 8-coordinate geometry to eight O atoms. There are a spread of K–O bond distances ranging from 2.74–3.35 Å. In the fourth K site, K is bonded in a 2-coordinate geometry to nine O atoms. There are a spread of K–O bond distances ranging from 2.66–3.27 Å. There are four inequivalent W sites. In the first W site, W is bonded to six O atoms to form distorted edge-sharing WO6 octahedra. There are a spread of W–O bond distances ranging from 1.78–2.32 Å. In the second W site, W is bonded in a 6-coordinate geometry to six O atoms. There are a spread of W–O bond distances ranging from 1.77–2.35 Å. In the third W site, W is bonded in a 6-coordinate geometry to six O atoms. There are a spread of W–O bond distances ranging from 1.76–2.37 Å. In the fourth W site, W is bonded in a 6-coordinate geometry to six O atoms. There are a spread of W–O bond distances ranging from 1.75–2.36 Å. There are two inequivalent As sites. In the first As site, As is bonded in a distorted trigonal non-coplanar geometry to three O atoms. There is one shorter (1.79 Å) and two longer (1.87 Å) As–O bond length. In the second As site, As is bonded in a trigonal non-coplanar geometry to three O atoms. There is one shorter (1.68 Å) and two longer (1.80 Å) As–O bond length. There are twenty-two inequivalent O sites. In the first O site, O is bonded in a 1-coordinate geometry to two K and one W atom. In the second O site, O is bonded in a bent 120 degrees geometry to two equivalent W atoms. In the third O site, O is bonded in a 1-coordinate geometry to one K, two equivalent W, and one As atom. In the fourth O site, O is bonded in a bent 150 degrees geometry to one K and two W atoms. In the fifth O site, O is bonded in a 2-coordinate geometry to one K and one W atom. In the sixth O site, O is bonded in a 2-coordinate geometry to one K and one W atom. In the seventh O site, O is bonded in a 3-coordinate geometry to one K and two W atoms. In the eighth O site, O is bonded in a distorted rectangular see-saw-like geometry to three W and one As atom. In the ninth O site, O is bonded in a bent 120 degrees geometry to two W atoms. In the tenth O site, O is bonded in a bent 120 degrees geometry to two W atoms. In the eleventh O site, O is bonded in a distorted trigonal planar geometry to one K, one W, and one As atom. In the twelfth O site, O is bonded in a distorted bent 150 degrees geometry to one K and two equivalent W atoms. In the thirteenth O site, O is bonded in a 1-coordinate geometry to two K and one W atom. In the fourteenth O site, O is bonded in a 4-coordinate geometry to two K and two W atoms. In the fifteenth O site, O is bonded in a distorted bent 150 degrees geometry to one K and two equivalent W atoms. In the sixteenth O site, O is bonded in a single-bond geometry to two equivalent K and one As atom. In the seventeenth O site, O is bonded in a distorted bent 120 degrees geometry to two K and one W atom. In the eighteenth O site, O is bonded in a 4-coordinate geometry to three K and one W atom. In the nineteenth O site, O is bonded in a T-shaped geometry to three K atoms. In the twentieth O site, O is bonded in a 3-coordinate geometry to three K atoms. In the twenty-first O site, O is bonded in a water-like geometry to one K and one O atom. The O–O bond length is 1.23 Å. In the twenty-second O site, O is bonded in a distorted L-shaped geometry to two K atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K4Th(S2O9)2 by Materials Project

K4Th(S2O9)2 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are five inequivalent K sites. In the first K site, K is bonded to six O atoms to form distorted KO6 pentagonal pyramids that share corners with two equivalent KO7 hexagonal pyramids and corners with five SO4 tetrahedra. There are a spread of K–O bond distances ranging from 2.67–2.90 Å. In the second K site, K is bonded in a 7-coordinate geometry to seven O atoms. There are a spread of K–O bond distances ranging from 2.76–3.16 Å. In the third K site, K is bonded in a 8-coordinate geometry to six O atoms. There are a spread of K–O bond distances ranging from 2.74–2.80 Å. In the fourth K site, K is bonded in a distorted q6 geometry to ten O atoms. There are a spread of K–O bond distances ranging from 2.85–3.11 Å. In the fifth K site, K is bonded to seven O atoms to form distorted KO7 hexagonal pyramids that share corners with two equivalent KO6 pentagonal pyramids, corners with five SO4 tetrahedra, and an edgeedge with one SO4 tetrahedra. There are a spread of K–O bond distances ranging from 2.74–2.96 Å. Th is bonded in a 9-coordinate geometry to nine O atoms. There are a spread of Th–O bond distances ranging from 2.39–2.51 Å. There are four inequivalent S sites. In the first S site, S is bonded to four O atoms to form SO4 tetrahedra that share a cornercorner with one KO7 hexagonal pyramid and a cornercorner with one KO6 pentagonal pyramid. There are a spread of S–O bond distances ranging from 1.47–1.52 Å. In the second S site, S is bonded to four O atoms to form SO4 tetrahedra that share a cornercorner with one KO7 hexagonal pyramid and a cornercorner with one KO6 pentagonal pyramid. There are a spread of S–O bond distances ranging from 1.46–1.54 Å. In the third S site, S is bonded to four O atoms to form SO4 tetrahedra that share corners with two equivalent KO7 hexagonal pyramids and corners with two equivalent KO6 pentagonal pyramids. There are a spread of S–O bond distances ranging from 1.46–1.53 Å. In the fourth S site, S is bonded to four O atoms to form SO4 tetrahedra that share a cornercorner with one KO7 hexagonal pyramid, a cornercorner with one KO6 pentagonal pyramid, and an edgeedge with one KO7 hexagonal pyramid. There are a spread of S–O bond distances ranging from 1.47–1.56 Å. There are eighteen inequivalent O sites. In the first O site, O is bonded in a 1-coordinate geometry to one K, one Th, and one S atom. In the second O site, O is bonded in a distorted bent 150 degrees geometry to one Th and one S atom. In the third O site, O is bonded in a 1-coordinate geometry to two K and one S atom. In the fourth O site, O is bonded in a distorted single-bond geometry to two K and one S atom. In the fifth O site, O is bonded in a distorted single-bond geometry to one Th and one S atom. In the sixth O site, O is bonded in a 1-coordinate geometry to one K, one Th, and one S atom. In the seventh O site, O is bonded in a distorted single-bond geometry to three K and one S atom. In the eighth O site, O is bonded in a distorted single-bond geometry to two K and one S atom. In the ninth O site, O is bonded in a distorted single-bond geometry to three K and one S atom. In the tenth O site, O is bonded in a distorted single-bond geometry to two K and one S atom. In the eleventh O site, O is bonded in a distorted single-bond geometry to two K, one Th, and one S atom. In the twelfth O site, O is bonded in a distorted single-bond geometry to one K, one Th, and one S atom. In the thirteenth O site, O is bonded in a distorted bent 150 degrees geometry to one Th and one S atom. In the fourteenth O site, O is bonded in a distorted single-bond geometry to three K and one S atom. In the fifteenth O site, O is bonded in a distorted single-bond geometry to two K and one S atom. In the sixteenth O site, O is bonded in a distorted single-bond geometry to two K and one S atom. In the seventeenth O site, O is bonded in a bent 150 degrees geometry to one K and one Th atom. In the eighteenth O site, O is bonded in a bent 120 degrees geometry to one K and one Th atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K4Mo6PtO26 by Materials Project

K4Mo6PtO26 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are four inequivalent K sites. In the first K site, K is bonded in a 7-coordinate geometry to seven O atoms. There are a spread of K–O bond distances ranging from 2.69–3.07 Å. In the second K site, K is bonded in a 7-coordinate geometry to seven O atoms. There are a spread of K–O bond distances ranging from 2.78–3.29 Å. In the third K site, K is bonded in a 8-coordinate geometry to eight O atoms. There are a spread of K–O bond distances ranging from 2.75–3.10 Å. In the fourth K site, K is bonded in a 6-coordinate geometry to six O atoms. There are a spread of K–O bond distances ranging from 2.78–3.19 Å. There are six inequivalent Mo sites. In the first Mo site, Mo is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Mo–O bond distances ranging from 1.74–2.31 Å. In the second Mo site, Mo is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Mo–O bond distances ranging from 1.73–2.33 Å. In the third Mo site, Mo is bonded in a 4-coordinate geometry to six O atoms. There are a spread of Mo–O bond distances ranging from 1.74–2.44 Å. In the fourth Mo site, Mo is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Mo–O bond distances ranging from 1.74–2.41 Å. In the fifth Mo site, Mo is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Mo–O bond distances ranging from 1.74–2.31 Å. In the sixth Mo site, Mo is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Mo–O bond distances ranging from 1.73–2.32 Å. Pt is bonded in an octahedral geometry to six O atoms. There are a spread of Pt–O bond distances ranging from 1.87–2.05 Å. There are twenty-six inequivalent O sites. In the first O site, O is bonded in a distorted single-bond geometry to one K and one Mo atom. In the second O site, O is bonded in a distorted single-bond geometry to one K and one Mo atom. In the third O site, O is bonded in a distorted single-bond geometry to two K and one Mo atom. In the fourth O site, O is bonded in a distorted bent 120 degrees geometry to one K and one Mo atom. In the fifth O site, O is bonded in a distorted single-bond geometry to one K and one Mo atom. In the sixth O site, O is bonded in a distorted single-bond geometry to two K and one Mo atom. In the seventh O site, O is bonded in a distorted single-bond geometry to two K and one Mo atom. In the eighth O site, O is bonded in a distorted bent 150 degrees geometry to one K and one Mo atom. In the ninth O site, O is bonded in a distorted single-bond geometry to two K and one Mo atom. In the tenth O site, O is bonded in a 1-coordinate geometry to two K and one Mo atom. In the eleventh O site, O is bonded in a distorted single-bond geometry to three K and one Mo atom. In the twelfth O site, O is bonded in a distorted bent 120 degrees geometry to one K and one Mo atom. In the thirteenth O site, O is bonded in a bent 120 degrees geometry to two Mo atoms. In the fourteenth O site, O is bonded in a distorted bent 120 degrees geometry to one K and two Mo atoms. In the fifteenth O site, O is bonded in a distorted water-like geometry to one Mo and one Pt atom. In the sixteenth O site, O is bonded in a distorted trigonal planar geometry to one K and two Mo atoms. In the seventeenth O site, O is bonded in a bent 120 degrees geometry to two Mo atoms. In the eighteenth O site, O is bonded in a bent 120 degrees geometry to two Mo atoms. In the nineteenth O site, O is bonded in a distorted single-bond geometry to one K, one Mo, and one Pt atom. In the twentieth O site, O is bonded in a distorted trigonal planar geometry to one K and two Mo atoms. In the twenty-first O site, O is bonded in a distorted trigonal non-coplanar geometry to two Mo and one Pt atom. In the twenty-second O site, O is bonded in a distorted trigonal non-coplanar geometry to two Mo and one Pt atom. In the twenty-third O site, O is bonded to three Mo and one Pt atom to form distorted corner-sharing OMo3Pt trigonal pyramids. In the twenty-fourth O site, O is bonded to three Mo and one Pt atom to form distorted corner-sharing OMo3Pt trigonal pyramids. In the twenty-fifth O site, O is bonded in a distorted T-shaped geometry to three K atoms. In the twenty-sixth O site, O is bonded in a bent 120 degrees geometry to two K atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K4Cd2S4O19 by Materials Project

K4Cd2S4O19 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. there are four inequivalent K sites. In the first K site, K is bonded in a 8-coordinate geometry to nine O atoms. There are a spread of K–O bond distances ranging from 2.75–3.34 Å. In the second K site, K is bonded in a 9-coordinate geometry to nine O atoms. There are a spread of K–O bond distances ranging from 2.72–3.34 Å. In the third K site, K is bonded in a 7-coordinate geometry to seven O atoms. There are a spread of K–O bond distances ranging from 2.74–3.30 Å. In the fourth K site, K is bonded in a 9-coordinate geometry to nine O atoms. There are a spread of K–O bond distances ranging from 2.70–3.24 Å. There are two inequivalent Cd sites. In the first Cd site, Cd is bonded to five O atoms to form distorted CdO5 square pyramids that share corners with five SO4 tetrahedra. There are a spread of Cd–O bond distances ranging from 2.24–2.33 Å. In the second Cd site, Cd is bonded to five O atoms to form distorted CdO5 square pyramids that share corners with five SO4 tetrahedra. There are a spread of Cd–O bond distances ranging from 2.20–2.34 Å. There are four inequivalent S sites. In the first S site, S is bonded to four O atoms to form SO4 tetrahedra that share corners with two equivalent CdO5 square pyramids. There are a spread of S–O bond distances ranging from 1.47–1.51 Å. In the second S site, S is bonded to four O atoms to form SO4 tetrahedra that share corners with three CdO5 square pyramids. There are a spread of S–O bond distances ranging from 1.47–1.51 Å. In the third S site, S is bonded to four O atoms to form SO4 tetrahedra that share corners with three CdO5 square pyramids. There are a spread of S–O bond distances ranging from 1.48–1.51 Å. In the fourth S site, S is bonded to four O atoms to form SO4 tetrahedra that share corners with two CdO5 square pyramids. There are a spread of S–O bond distances ranging from 1.47–1.51 Å. There are nineteen inequivalent O sites. In the first O site, O is bonded in a 1-coordinate geometry to two K, one Cd, and one S atom. In the second O site, O is bonded in a distorted single-bond geometry to one O atom. The O–O bond length is 1.24 Å. In the third O site, O is bonded in a 3-coordinate geometry to one K, one Cd, and one S atom. In the fourth O site, O is bonded in a distorted single-bond geometry to three K and one S atom. In the fifth O site, O is bonded in a 1-coordinate geometry to two K, one Cd, and one S atom. In the sixth O site, O is bonded in a distorted single-bond geometry to three K and one S atom. In the seventh O site, O is bonded in a 3-coordinate geometry to one K, one Cd, and one S atom. In the eighth O site, O is bonded in a 1-coordinate geometry to one K, one Cd, and one S atom. In the ninth O site, O is bonded in a distorted trigonal non-coplanar geometry to two K and one S atom. In the tenth O site, O is bonded in a 2-coordinate geometry to one K, one Cd, and one S atom. In the eleventh O site, O is bonded in a distorted single-bond geometry to four K and one S atom. In the twelfth O site, O is bonded in a distorted L-shaped geometry to three K atoms. In the thirteenth O site, O is bonded in a 1-coordinate geometry to two K, one Cd, and one S atom. In the fourteenth O site, O is bonded in a 3-coordinate geometry to one K, one Cd, and one S atom. In the fifteenth O site, O is bonded in a distorted single-bond geometry to three K and one S atom. In the sixteenth O site, O is bonded in a distorted single-bond geometry to two K and one S atom. In the seventeenth O site, O is bonded in a 1-coordinate geometry to one K, one Cd, and one S atom. In the eighteenth O site, O is bonded in a water-like geometry to one K and one O atom. In the nineteenth O site, O is bonded in a 3-coordinate geometry to one K, one Cd, and one S atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K4XeO15 by Materials Project

XeK4O15 crystallizes in the orthorhombic Pca2_1 space group. The structure is three-dimensional. Xe is bonded in a distorted bent 150 degrees geometry to two K atoms. There are one shorter (3.54 Å) and one longer (3.67 Å) Xe–K bond lengths. There are four inequivalent K sites. In the first K site, K is bonded in a 7-coordinate geometry to one Xe and six O atoms. There are a spread of K–O bond distances ranging from 2.67–3.10 Å. In the second K site, K is bonded in a 1-coordinate geometry to nine O atoms. There are a spread of K–O bond distances ranging from 2.66–3.17 Å. In the third K site, K is bonded in a 9-coordinate geometry to nine O atoms. There are a spread of K–O bond distances ranging from 2.75–3.08 Å. In the fourth K site, K is bonded in a 6-coordinate geometry to one Xe and six O atoms. There are a spread of K–O bond distances ranging from 2.66–3.13 Å. There are fifteen inequivalent O sites. In the first O site, O is bonded in a 4-coordinate geometry to three K and one O atom. The O–O bond length is 1.31 Å. In the second O site, O is bonded in a distorted trigonal planar geometry to one K and two O atoms. There is one shorter (1.35 Å) and one longer (1.39 Å) O–O bond length. In the third O site, O is bonded in a distorted rectangular see-saw-like geometry to three K and one O atom. The O–O bond length is 1.32 Å. In the fourth O site, O is bonded in a 1-coordinate geometry to two K and one O atom. The O–O bond length is 1.30 Å. In the fifth O site, O is bonded in a distorted bent 120 degrees geometry to one K and one O atom. The O–O bond length is 1.27 Å. In the sixth O site, O is bonded in a 4-coordinate geometry to three K and one O atom. In the seventh O site, O is bonded in a 4-coordinate geometry to three K and one O atom. The O–O bond length is 1.28 Å. In the eighth O site, O is bonded in a distorted see-saw-like geometry to three K and one O atom. In the ninth O site, O is bonded in a distorted T-shaped geometry to two K and one O atom. In the tenth O site, O is bonded in a 3-coordinate geometry to two K and one O atom. The O–O bond length is 1.27 Å. In the eleventh O site, O is bonded in an L-shaped geometry to one K and one O atom. In the twelfth O site, O is bonded in a 2-coordinate geometry to two K and one O atom. In the thirteenth O site, O is bonded in a distorted bent 150 degrees geometry to one K and one O atom. In the fourteenth O site, O is bonded in a distorted T-shaped geometry to two K and one O atom. In the fifteenth O site, O is bonded in a bent 120 degrees geometry to one K and one O atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K2Al2(SiO4)3 by Materials Project

K2Al2(SiO4)3 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are four inequivalent K sites. In the first K site, K is bonded in a 6-coordinate geometry to six O atoms. There are a spread of K–O bond distances ranging from 2.71–3.15 Å. In the second K site, K is bonded in a 6-coordinate geometry to six O atoms. There are a spread of K–O bond distances ranging from 2.70–3.10 Å. In the third K site, K is bonded in a 6-coordinate geometry to six O atoms. There are a spread of K–O bond distances ranging from 2.71–3.13 Å. In the fourth K site, K is bonded in a 6-coordinate geometry to six O atoms. There are a spread of K–O bond distances ranging from 2.72–3.09 Å. There are four inequivalent Al sites. In the first Al site, Al is bonded to four O atoms to form AlO4 tetrahedra that share corners with four SiO4 tetrahedra. There are a spread of Al–O bond distances ranging from 1.75–1.77 Å. In the second Al site, Al is bonded to four O atoms to form AlO4 tetrahedra that share corners with four SiO4 tetrahedra. There are a spread of Al–O bond distances ranging from 1.75–1.77 Å. In the third Al site, Al is bonded to four O atoms to form AlO4 tetrahedra that share corners with four SiO4 tetrahedra. There are a spread of Al–O bond distances ranging from 1.75–1.77 Å. In the fourth Al site, Al is bonded to four O atoms to form AlO4 tetrahedra that share corners with four SiO4 tetrahedra. There are a spread of Al–O bond distances ranging from 1.75–1.77 Å. There are six inequivalent Si sites. In the first Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share corners with two AlO4 tetrahedra and corners with two SiO4 tetrahedra. There is one shorter (1.63 Å) and three 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 two AlO4 tetrahedra and corners with two SiO4 tetrahedra. There is one shorter (1.63 Å) and three longer (1.64 Å) Si–O bond length. In the third Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share a cornercorner with one SiO4 tetrahedra and corners with three AlO4 tetrahedra. There are a spread of Si–O bond distances ranging from 1.63–1.65 Å. In the fourth Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share a cornercorner with one SiO4 tetrahedra and corners with three AlO4 tetrahedra. There are a spread of Si–O bond distances ranging from 1.63–1.65 Å. In the fifth Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share a cornercorner with one SiO4 tetrahedra and corners with three AlO4 tetrahedra. There are a spread of Si–O bond distances ranging from 1.63–1.65 Å. In the sixth Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share a cornercorner with one SiO4 tetrahedra and corners with three AlO4 tetrahedra. There are a spread of Si–O bond distances ranging from 1.63–1.65 Å. There are twenty-four inequivalent O sites. In the first O site, O is bonded in a bent 150 degrees geometry to one Al and one Si atom. In the second O site, O is bonded in a bent 150 degrees geometry to one Al and one Si atom. In the third O site, O is bonded in a bent 150 degrees geometry to one Al and one Si atom. In the fourth O site, O is bonded in a bent 150 degrees geometry to one Al and one Si atom. In the fifth O site, O is bonded in a 2-coordinate geometry to two K, one Al, and one Si atom. In the sixth O site, O is bonded in a 2-coordinate geometry to two K, one Al, and one Si atom. In the seventh O site, O is bonded in a 2-coordinate geometry to two K, one Al, and one Si atom. In the eighth O site, O is bonded in a 2-coordinate geometry to two K, one Al, and one Si atom. In the ninth O site, O is bonded in a 2-coordinate geometry to one K, one Al, and one Si atom. In the tenth O site, O is bonded in a 2-coordinate geometry to one K, one Al, and one Si atom. In the eleventh O site, O is bonded in a 2-coordinate geometry to one K, one Al, and one Si atom. In the twelfth O site, O is bonded in a 2-coordinate geometry to one K, one Al, and one Si atom. In the thirteenth O site, O is bonded in a 3-coordinate geometry to one K, one Al, and one Si atom. In the fourteenth O site, O is bonded in a 3-coordinate geometry to one K, one Al, and one Si atom. In the fifteenth O site, O is bonded in a 3-coordinate geometry to one K, one Al, and one Si atom. In the sixteenth O site, O is bonded in a 3-coordinate geometry to one K, one Al, and one Si atom. In the seventeenth O site, O is bonded in a bent 150 degrees geometry to two Si atoms. In the eighteenth O site, O is bonded in a bent 150 degrees geometry to two Si atoms. In the nineteenth O site, O is bonded in a bent 150 degrees geometry to two Si atoms. In the twentieth O site, O is bonded in a bent 150 degrees geometry to two Si atoms. In the twenty-first O site, O is bonded in a 2-coordinate geometry to two K atoms. In the twenty-second O site, O is bonded in a 2-coordinate geometry to two K atoms. In the twenty-third O site, O is bonded in a 2-coordinate geometry to two K atoms. In the twenty-fourth O site, O is bonded in a 2-coordinate geometry to two K atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KPO4 by Materials Project

KPO4 crystallizes in the monoclinic P2_1 space group. The structure is three-dimensional. there are four inequivalent K sites. In the first K site, K is bonded in a 7-coordinate geometry to eight O atoms. There are a spread of K–O bond distances ranging from 2.77–3.25 Å. In the second K site, K is bonded in a 7-coordinate geometry to seven O atoms. There are a spread of K–O bond distances ranging from 2.85–3.00 Å. In the third K site, K is bonded in a 8-coordinate geometry to eight O atoms. There are a spread of K–O bond distances ranging from 2.83–3.10 Å. In the fourth K site, K is bonded in a 8-coordinate geometry to eight O atoms. There are a spread of K–O bond distances ranging from 2.82–3.25 Å. There are four inequivalent P sites. In the first P site, P is bonded in a tetrahedral geometry to four O atoms. There are a spread of P–O bond distances ranging from 1.53–1.55 Å. In the second P site, P is bonded in a tetrahedral geometry to four O atoms. There is one shorter (1.53 Å) and three longer (1.55 Å) P–O bond length. In the third P site, P is bonded in a tetrahedral geometry to four O atoms. There is one shorter (1.54 Å) and three longer (1.55 Å) P–O bond length. In the fourth P site, P is bonded in a tetrahedral geometry to four O atoms. There is three shorter (1.54 Å) and one longer (1.55 Å) P–O bond length. There are sixteen inequivalent O sites. In the first O site, O is bonded in a distorted single-bond geometry to two K and one P atom. In the second O site, O is bonded in a distorted single-bond geometry to one K and one P atom. In the third O site, O is bonded in a distorted single-bond geometry to two K and one P atom. In the fourth O site, O is bonded in a distorted single-bond geometry to two K and one P atom. In the fifth O site, O is bonded in a single-bond geometry to two K and one P atom. In the sixth O site, O is bonded in a distorted single-bond geometry to three K and one P atom. In the seventh O site, O is bonded in a distorted single-bond geometry to two K and one P atom. In the eighth O site, O is bonded in a distorted single-bond geometry to two K and one P atom. In the ninth O site, O is bonded in a distorted single-bond geometry to one K and one P atom. In the tenth O site, O is bonded in a distorted single-bond geometry to two K and one P atom. In the eleventh O site, O is bonded in a distorted single-bond geometry to two K and one P atom. In the twelfth O site, O is bonded in a distorted single-bond geometry to three K and one P atom. In the thirteenth O site, O is bonded in a distorted single-bond geometry to two K and one P atom. In the fourteenth O site, O is bonded in a distorted single-bond geometry to two K and one P atom. In the fifteenth O site, O is bonded in a distorted single-bond geometry to two K and one P atom. In the sixteenth O site, O is bonded in a distorted single-bond geometry to one K and one P atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K4PSe3O16 by Materials Project

K4PSe3O16 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are four inequivalent K sites. In the first K site, K is bonded in a 8-coordinate geometry to eight O atoms. There are a spread of K–O bond distances ranging from 2.77–3.05 Å. In the second K site, K is bonded in a 8-coordinate geometry to eight O atoms. There are a spread of K–O bond distances ranging from 2.81–3.04 Å. In the third K site, K is bonded in a 6-coordinate geometry to six O atoms. There are a spread of K–O bond distances ranging from 2.78–2.96 Å. In the fourth K site, K is bonded in a 6-coordinate geometry to six O atoms. There are a spread of K–O bond distances ranging from 2.78–2.93 Å. P is bonded in a tetrahedral geometry to four O atoms. There are a spread of P–O bond distances ranging from 1.53–1.55 Å. There are three inequivalent Se sites. In the first Se site, Se is bonded in a tetrahedral geometry to four O atoms. There are a spread of Se–O bond distances ranging from 1.65–1.71 Å. In the second Se site, Se is bonded in a tetrahedral geometry to four O atoms. There are a spread of Se–O bond distances ranging from 1.66–1.71 Å. In the third Se site, Se is bonded in a tetrahedral geometry to four O atoms. There are a spread of Se–O bond distances ranging from 1.67–1.69 Å. There are sixteen inequivalent O sites. In the first O site, O is bonded in a distorted single-bond geometry to two K and one P atom. In the second O site, O is bonded in a distorted single-bond geometry to two K and one Se atom. In the third O site, O is bonded in a distorted single-bond geometry to one K and one P atom. In the fourth O site, O is bonded in a 2-coordinate geometry to one K and one Se atom. In the fifth O site, O is bonded in a distorted bent 120 degrees geometry to one K and one Se atom. In the sixth O site, O is bonded in a bent 120 degrees geometry to one K and one Se atom. In the seventh O site, O is bonded in a distorted trigonal planar geometry to two K and one Se atom. In the eighth O site, O is bonded in a distorted trigonal planar geometry to two K and one Se atom. In the ninth O site, O is bonded in a distorted single-bond geometry to one K and one P atom. In the tenth O site, O is bonded in a 1-coordinate geometry to one K and one Se atom. In the eleventh O site, O is bonded in a 4-coordinate geometry to three K and one Se atom. In the twelfth O site, O is bonded in a 4-coordinate geometry to three K and one Se atom. In the thirteenth O site, O is bonded in a distorted single-bond geometry to two K and one P atom. In the fourteenth O site, O is bonded in a distorted single-bond geometry to two K and one Se atom. In the fifteenth O site, O is bonded in a 1-coordinate geometry to two K and one Se atom. In the sixteenth O site, O is bonded in a 1-coordinate geometry to two K and one Se atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K23Na8(CdIn4)12 by Materials Project

Na8K23Cd12In48 is Bergman Structure: Mg32(Al,Zn)49 Bergman-derived structured and crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. there are four inequivalent K sites. In the first K site, K is bonded in a 12-coordinate geometry to four K, one Na, two equivalent Cd, and nine In atoms. There are a spread of K–K bond distances ranging from 3.93–4.18 Å. The K–Na bond length is 3.89 Å. Both K–Cd bond lengths are 3.91 Å. There are a spread of K–In bond distances ranging from 3.66–3.90 Å. In the second K site, K is bonded in a 10-coordinate geometry to four equivalent K and ten In atoms. There are a spread of K–In bond distances ranging from 3.78–4.03 Å. In the third K site, K is bonded in a 12-coordinate geometry to three equivalent K and twelve In atoms. There are three shorter (3.58 Å) and nine longer (3.71 Å) K–In bond lengths. In the fourth K site, K is bonded in a 2-coordinate geometry to eight Na atoms. There are two shorter (3.70 Å) and six longer (4.22 Å) K–Na bond lengths. There are two inequivalent Na sites. In the first Na site, Na is bonded in a 10-coordinate geometry to three K, four equivalent Cd, and six In atoms. All Na–Cd bond lengths are 3.46 Å. There are two shorter (3.63 Å) and four longer (3.66 Å) Na–In bond lengths. In the second Na site, Na is bonded in a 6-coordinate geometry to one K, one Na, six equivalent Cd, and six equivalent In atoms. The Na–Na bond length is 3.29 Å. All Na–Cd bond lengths are 3.44 Å. All Na–In bond lengths are 3.64 Å. Cd is bonded in a 12-coordinate geometry to two equivalent K, three Na, and three In atoms. There are one shorter (3.11 Å) and two longer (3.13 Å) Cd–In bond lengths. There are five inequivalent In sites. In the first In site, In is bonded in a 11-coordinate geometry to three K, two equivalent Na, one Cd, and five In atoms. There are a spread of In–In bond distances ranging from 3.10–3.21 Å. In the second In site, In is bonded in a distorted q6 geometry to four K, one Na, and six In atoms. There are a spread of In–In bond distances ranging from 3.04–3.21 Å. In the third In site, In is bonded in a 11-coordinate geometry to five K and six In atoms. There are one shorter (3.07 Å) and one longer (3.16 Å) In–In bond lengths. In the fourth In site, In is bonded to eight K and four In atoms to form a mixture of edge and face-sharing InK8In4 cuboctahedra. Both In–In bond lengths are 3.19 Å. In the fifth In site, In is bonded in a distorted q6 geometry to four K, two equivalent Na, four equivalent Cd, and two equivalent In atoms. Both In–In bond lengths are 3.24 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K4Pb9 by Materials Project

K4Pb9 is Magnesium tetraboride-like structured and crystallizes in the monoclinic P2_1/m space group. The structure is three-dimensional. there are five inequivalent K sites. In the first K site, K is bonded in a 8-coordinate geometry to eight Pb atoms. There are a spread of K–Pb bond distances ranging from 3.71–4.06 Å. In the second K site, K is bonded in a 7-coordinate geometry to seven Pb atoms. There are a spread of K–Pb bond distances ranging from 3.75–3.90 Å. In the third K site, K is bonded in a 8-coordinate geometry to eight Pb atoms. There are a spread of K–Pb bond distances ranging from 3.66–4.01 Å. In the fourth K site, K is bonded in a 8-coordinate geometry to eight Pb atoms. There are a spread of K–Pb bond distances ranging from 3.70–4.13 Å. In the fifth K site, K is bonded in a 7-coordinate geometry to seven Pb atoms. There are a spread of K–Pb bond distances ranging from 3.59–3.78 Å. There are twelve inequivalent Pb sites. In the first Pb site, Pb is bonded in a distorted body-centered cubic geometry to four K and four Pb atoms. There are two shorter (3.17 Å) and two longer (3.20 Å) Pb–Pb bond lengths. In the second Pb site, Pb is bonded in a 1-coordinate geometry to three K and five Pb atoms. There are a spread of Pb–Pb bond distances ranging from 3.15–3.52 Å. In the third Pb site, Pb is bonded in a 9-coordinate geometry to four K and five Pb atoms. There are two shorter (3.26 Å) and two longer (3.28 Å) Pb–Pb bond lengths. In the fourth Pb site, Pb is bonded in a 1-coordinate geometry to three K and five Pb atoms. There are a spread of Pb–Pb bond distances ranging from 3.15–3.48 Å. In the fifth Pb site, Pb is bonded in a 1-coordinate geometry to two K and four Pb atoms. There are a spread of Pb–Pb bond distances ranging from 3.16–3.23 Å. In the sixth Pb site, Pb is bonded in a 8-coordinate geometry to four K and four Pb atoms. There are one shorter (3.18 Å) and one longer (3.19 Å) Pb–Pb bond lengths. In the seventh Pb site, Pb is bonded in a 6-coordinate geometry to three K and three Pb atoms. There are one shorter (3.14 Å) and two longer (3.20 Å) Pb–Pb bond lengths. In the eighth Pb site, Pb is bonded in a 8-coordinate geometry to four K and four Pb atoms. There are one shorter (3.16 Å) and one longer (3.21 Å) Pb–Pb bond lengths. In the ninth Pb site, Pb is bonded in a 1-coordinate geometry to five K and four Pb atoms. In the tenth Pb site, Pb is bonded in a 2-coordinate geometry to three K and four Pb atoms. In the eleventh Pb site, Pb is bonded in a 1-coordinate geometry to four K and four Pb atoms. There are one shorter (3.16 Å) and one longer (3.23 Å) Pb–Pb bond lengths. In the twelfth Pb site, Pb is bonded in a 7-coordinate geometry to three K and four Pb atoms. The Pb–Pb bond length is 3.20 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K6Al32O51 by Materials Project

K6Al32O51 is beta indium sulfide-derived structured and crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are four inequivalent K sites. In the first K site, K is bonded in a 1-coordinate geometry to five O atoms. There are a spread of K–O bond distances ranging from 2.70–3.11 Å. In the second K site, K is bonded in a 5-coordinate geometry to five O atoms. There are a spread of K–O bond distances ranging from 2.52–3.08 Å. In the third K site, K is bonded in a 1-coordinate geometry to five O atoms. There are a spread of K–O bond distances ranging from 2.69–3.11 Å. In the fourth K site, K is bonded in a 5-coordinate geometry to five O atoms. There are a spread of K–O bond distances ranging from 2.52–3.08 Å. There are nineteen inequivalent Al sites. In the first Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with six AlO4 tetrahedra and edges with six AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.87–1.94 Å. In the second Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with five AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.85–2.03 Å. In the third Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with five AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.84–2.03 Å. In the fourth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with five AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.84–2.02 Å. In the fifth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with six AlO4 tetrahedra and edges with six AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.95 Å. In the sixth Al site, Al is bonded to four O atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 52–59°. There is three shorter (1.81 Å) and one longer (1.85 Å) Al–O bond length. In the seventh Al site, Al is bonded to four O atoms to form AlO4 tetrahedra that share corners with six AlO6 octahedra and a cornercorner with one AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 52–54°. There is three shorter (1.77 Å) and one longer (1.78 Å) Al–O bond length. In the eighth Al site, Al is bonded to four O atoms to form AlO4 tetrahedra that share corners with six AlO6 octahedra and a cornercorner with one AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 54–55°. There is one shorter (1.76 Å) and three longer (1.80 Å) Al–O bond length. In the ninth Al site, Al is bonded to four O atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 50–58°. There is one shorter (1.78 Å) and three longer (1.83 Å) Al–O bond length. In the tenth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with four AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.74–2.10 Å. In the eleventh Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with four AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.74–2.10 Å. In the twelfth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with five AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.84–2.03 Å. In the thirteenth Al site, Al is bonded to four O atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 49–63°. There are a spread of Al–O bond distances ranging from 1.80–1.94 Å. In the fourteenth Al site, Al is bonded to four O atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 50–59°. There is one shorter (1.79 Å) and three longer (1.83 Å) Al–O bond length. In the fifteenth Al site, Al is bonded to four O atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 54–55°. There is one shorter (1.67 Å) and three longer (1.82 Å) Al–O bond length. In the sixteenth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with five AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.83–2.05 Å. In the seventeenth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with four AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.74–2.11 Å. In the eighteenth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with five AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.84–2.02 Å. In the nineteenth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with five AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.83–2.05 Å. There are thirty inequivalent O sites. In the first O site, O is bonded in a 3-coordinate geometry to one K and three Al atoms. In the second O site, O is bonded in a 3-coordinate geometry to one K and three Al atoms. In the third O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the fourth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the fifth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the sixth O site, O is bonded in a distorted tetrahedral geometry to one K and three Al atoms. In the seventh O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the eighth O site, O is bonded in a distorted tetrahedral geometry to one K and three Al atoms. In the ninth O site, O is bonded in a linear geometry to two Al atoms. In the tenth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the eleventh O site, O is bonded in a 4-coordinate geometry to one K and three Al atoms. In the twelfth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the thirteenth O site, O is bonded in a 3-coordinate geometry to one K and three Al atoms. In the fourteenth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the fifteenth O site, O is bonded in a distorted trigonal non-coplanar geometry to one K and two Al atoms. In the sixteenth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the seventeenth O site, O is bonded in a 3-coordinate geometry to one K and three Al atoms. In the eighteenth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the nineteenth O site, O is bonded in a 4-coordinate geometry to one K and three Al atoms. In the twentieth O site, O is bonded in a single-bond geometry to six K and one Al atom. In the twenty-first O site, O is bonded in a distorted tetrahedral geometry to one K and three Al atoms. In the twenty-second O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the twenty-third O site, O is bonded in a 3-coordinate geometry to one K and three Al atoms. In the twenty-fourth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the twenty-fifth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the twenty-sixth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the twenty-seventh O site, O is bonded in a distorted trigonal non-coplanar geometry to one K and two equivalent Al atoms. In the twenty-eighth O site, O is bonded in a distorted tetrahedral geometry to one K and three Al atoms. In the twenty-ninth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the thirtieth O site, O is bonded in a 4-coordinate geometry to one K and three Al atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3NO by Materials Project

K3NO crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are fifteen inequivalent K1+ sites. In the first K1+ site, K1+ is bonded in a 3-coordinate geometry to one N1- and two equivalent O2- atoms. The K–N bond length is 3.21 Å. There are one shorter (2.56 Å) and one longer (2.66 Å) K–O bond lengths. In the second K1+ site, K1+ is bonded in a linear geometry to two equivalent O2- atoms. Both K–O bond lengths are 2.61 Å. In the third K1+ site, K1+ is bonded in a 3-coordinate geometry to one N1- and two equivalent O2- atoms. The K–N bond length is 3.23 Å. There are one shorter (2.56 Å) and one longer (2.66 Å) K–O bond lengths. In the fourth K1+ site, K1+ is bonded in a distorted square co-planar geometry to two N1- and two equivalent O2- atoms. There are one shorter (3.26 Å) and one longer (3.29 Å) K–N bond lengths. Both K–O bond lengths are 2.60 Å. In the fifth K1+ site, K1+ is bonded in a distorted rectangular see-saw-like geometry to two N1- and two equivalent O2- atoms. There are one shorter (3.24 Å) and one longer (3.30 Å) K–N bond lengths. Both K–O bond lengths are 2.60 Å. In the sixth K1+ site, K1+ is bonded in a distorted T-shaped geometry to one N1- and two equivalent O2- atoms. The K–N bond length is 3.14 Å. There are one shorter (2.57 Å) and one longer (2.67 Å) K–O bond lengths. In the seventh K1+ site, K1+ is bonded in a distorted rectangular see-saw-like geometry to two N1- and two equivalent O2- atoms. There are one shorter (3.29 Å) and one longer (3.30 Å) K–N bond lengths. There are one shorter (2.57 Å) and one longer (2.65 Å) K–O bond lengths. In the eighth K1+ site, K1+ is bonded in a distorted T-shaped geometry to one N1- and two equivalent O2- atoms. The K–N bond length is 3.13 Å. There are one shorter (2.57 Å) and one longer (2.68 Å) K–O bond lengths. In the ninth K1+ site, K1+ is bonded in a linear geometry to two equivalent O2- atoms. There are one shorter (2.60 Å) and one longer (2.61 Å) K–O bond lengths. In the tenth K1+ site, K1+ is bonded in a linear geometry to two equivalent O2- atoms. Both K–O bond lengths are 2.61 Å. In the eleventh K1+ site, K1+ is bonded in a distorted see-saw-like geometry to two equivalent N1- and two O2- atoms. There are one shorter (3.09 Å) and one longer (3.14 Å) K–N bond lengths. Both K–O bond lengths are 2.60 Å. In the twelfth K1+ site, K1+ is bonded in a distorted see-saw-like geometry to two equivalent N1- and two O2- atoms. There are one shorter (3.09 Å) and one longer (3.13 Å) K–N bond lengths. Both K–O bond lengths are 2.60 Å. In the thirteenth K1+ site, K1+ is bonded in a distorted see-saw-like geometry to two equivalent N1- and two O2- atoms. Both K–N bond lengths are 3.12 Å. Both K–O bond lengths are 2.60 Å. In the fourteenth K1+ site, K1+ is bonded in a distorted see-saw-like geometry to two equivalent N1- and two O2- atoms. There are one shorter (3.09 Å) and one longer (3.13 Å) K–N bond lengths. Both K–O bond lengths are 2.61 Å. In the fifteenth K1+ site, K1+ is bonded in a distorted see-saw-like geometry to two equivalent N1- and two O2- atoms. There are one shorter (3.12 Å) and one longer (3.13 Å) K–N bond lengths. Both K–O bond lengths are 2.60 Å. There are five inequivalent N1- sites. In the first N1- site, N1- is bonded in a 4-coordinate geometry to four K1+ atoms. In the second N1- site, N1- is bonded in a 4-coordinate geometry to four K1+ atoms. In the third N1- site, N1- is bonded in a 4-coordinate geometry to four K1+ atoms. In the fourth N1- site, N1- is bonded in a 4-coordinate geometry to four K1+ atoms. In the fifth N1- site, N1- is bonded in a 4-coordinate geometry to four K1+ atoms. There are five inequivalent O2- sites. In the first O2- site, O2- is bonded to six K1+ atoms to form corner-sharing OK6 octahedra. The corner-sharing octahedra tilt angles range from 11–14°. In the second O2- site, O2- is bonded to six K1+ atoms to form corner-sharing OK6 octahedra. The corner-sharing octahedra tilt angles range from 0–14°. In the third O2- site, O2- is bonded to six K1+ atoms to form corner-sharing OK6 octahedra. The corner-sharing octahedra tilt angles range from 11–14°. In the fourth O2- site, O2- is bonded to six K1+ atoms to form corner-sharing OK6 octahedra. The corner-sharing octahedra tilt angles range from 0–14°. In the fifth O2- site, O2- is bonded to six K1+ atoms to form corner-sharing OK6 octahedra. The corner-sharing octahedra tilt angles range from 1–14°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K9(Mo6S7)8 by Materials Project

K9(Mo6S7)8 is alpha Pu-derived structured and crystallizes in the trigonal P-3 space group. The structure is three-dimensional. there are five inequivalent K sites. In the first K site, K is bonded in a 6-coordinate geometry to nine S atoms. There are a spread of K–S bond distances ranging from 3.51–3.76 Å. In the second K site, K is bonded in a 4-coordinate geometry to four S atoms. There are one shorter (2.65 Å) and three longer (2.74 Å) K–S bond lengths. In the third K site, K is bonded in a distorted linear geometry to eight S atoms. There are a spread of K–S bond distances ranging from 2.88–3.77 Å. In the fourth K site, K is bonded in a 9-coordinate geometry to nine S atoms. There are six shorter (3.38 Å) and three longer (3.53 Å) K–S bond lengths. In the fifth K site, K is bonded in a hexagonal planar geometry to six equivalent S atoms. All K–S bond lengths are 3.54 Å. There are eight inequivalent Mo sites. In the first Mo site, Mo is bonded in a 3-coordinate geometry to three S atoms. There are a spread of Mo–S bond distances ranging from 2.34–2.55 Å. In the second Mo site, Mo is bonded in a 5-coordinate geometry to five S atoms. There are a spread of Mo–S bond distances ranging from 2.36–2.70 Å. In the third Mo site, Mo is bonded in a 5-coordinate geometry to four S atoms. There are a spread of Mo–S bond distances ranging from 2.39–2.92 Å. In the fourth Mo site, Mo is bonded in a 4-coordinate geometry to six S atoms. There are a spread of Mo–S bond distances ranging from 2.34–2.97 Å. In the fifth Mo site, Mo is bonded in a 4-coordinate geometry to four S atoms. There are a spread of Mo–S bond distances ranging from 2.42–2.56 Å. In the sixth Mo site, Mo is bonded in a 2-coordinate geometry to six S atoms. There are a spread of Mo–S bond distances ranging from 2.44–3.11 Å. In the seventh Mo site, Mo is bonded in a 4-coordinate geometry to four S atoms. There are a spread of Mo–S bond distances ranging from 2.34–2.47 Å. In the eighth Mo site, Mo is bonded to four S atoms to form distorted corner-sharing MoS4 trigonal pyramids. There are a spread of Mo–S bond distances ranging from 2.40–2.57 Å. There are twelve inequivalent S sites. In the first S site, S is bonded in a 5-coordinate geometry to one K and four Mo atoms. In the second S site, S is bonded in a 6-coordinate geometry to two K and four Mo atoms. In the third S site, S is bonded in a 4-coordinate geometry to one K and three Mo atoms. In the fourth S site, S is bonded in a 4-coordinate geometry to two equivalent K and three Mo atoms. In the fifth S site, S is bonded in a 4-coordinate geometry to one K and three Mo atoms. In the sixth S site, S is bonded in a distorted rectangular see-saw-like geometry to one K and three Mo atoms. In the seventh S site, S is bonded in a 5-coordinate geometry to one K and four Mo atoms. In the eighth S site, S is bonded in a 7-coordinate geometry to one K and six Mo atoms. In the ninth S site, S is bonded in a 6-coordinate geometry to six Mo atoms. In the tenth S site, S is bonded in a distorted rectangular see-saw-like geometry to one K and three equivalent Mo atoms. In the eleventh S site, S is bonded in a 4-coordinate geometry to one K and three equivalent Mo atoms. In the twelfth S site, S is bonded in a 7-coordinate geometry to one K and six Mo atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K6Zr3H8(OF)12 by Materials Project

K6Zr3H8(OF)12 crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. there are three inequivalent K sites. In the first K site, K is bonded in a 9-coordinate geometry to four O and five F atoms. There are a spread of K–O bond distances ranging from 2.95–3.27 Å. There are a spread of K–F bond distances ranging from 2.62–2.97 Å. In the second K site, K is bonded in a 8-coordinate geometry to three O and five F atoms. There are a spread of K–O bond distances ranging from 2.78–3.02 Å. There are a spread of K–F bond distances ranging from 2.61–3.09 Å. In the third K site, K is bonded in a 8-coordinate geometry to two O and six F atoms. There are one shorter (2.78 Å) and one longer (2.95 Å) K–O bond lengths. There are a spread of K–F bond distances ranging from 2.63–3.11 Å. There are two inequivalent Zr sites. In the first Zr site, Zr is bonded in a 8-coordinate geometry to four O and four F atoms. There are two shorter (2.20 Å) and two longer (2.24 Å) Zr–O bond lengths. There are a spread of Zr–F bond distances ranging from 2.08–2.15 Å. In the second Zr site, Zr is bonded in a 8-coordinate geometry to four O and four F atoms. There are a spread of Zr–O bond distances ranging from 2.18–2.22 Å. There are a spread of Zr–F bond distances ranging from 2.08–2.13 Å. There are six inequivalent H sites. In the first H site, H is bonded in a distorted single-bond geometry to two O atoms. There is one shorter (1.00 Å) and one longer (1.69 Å) H–O bond length. In the second H site, H is bonded in a distorted linear geometry to one O and one F atom. The H–O bond length is 1.00 Å. The H–F bond length is 1.58 Å. In the third H site, H is bonded in a single-bond geometry to one O atom. The H–O bond length is 1.00 Å. In the fourth 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 fifth 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 sixth H site, H is bonded in a single-bond geometry to two O atoms. There is one shorter (0.99 Å) and one longer (1.75 Å) H–O bond length. There are nine inequivalent O sites. In the first O site, O is bonded in a 5-coordinate geometry to two equivalent K, two Zr, and one O atom. The O–O bond length is 1.51 Å. In the second O site, O is bonded in a 4-coordinate geometry to one K, two Zr, and one O atom. In the third O site, O is bonded in a 4-coordinate geometry to two equivalent Zr, one H, and one O atom. The O–O bond length is 1.50 Å. In the fourth O site, O is bonded in a 4-coordinate geometry to two equivalent Zr, one H, and one O atom. In the fifth O site, O is bonded in a single-bond geometry to two equivalent K and one H atom. In the sixth O site, O is bonded in a single-bond geometry to two equivalent K and one H atom. In the seventh O site, O is bonded in a single-bond geometry to two K and one H atom. In the eighth O site, O is bonded in a water-like geometry to two equivalent K and two equivalent H atoms. In the ninth O site, O is bonded in a water-like geometry to two equivalent K and two H atoms. There are seven inequivalent F sites. In the first F site, F is bonded to three K and one Zr atom to form distorted corner-sharing FK3Zr tetrahedra. In the second F site, F is bonded in a 2-coordinate geometry to two K and one Zr atom. In the third F site, F is bonded to three K and one Zr atom to form distorted corner-sharing FK3Zr tetrahedra. In the fourth F site, F is bonded in a 4-coordinate geometry to two equivalent K, one Zr, and one H atom. In the fifth F site, F is bonded in a distorted single-bond geometry to four K and one Zr atom. In the sixth F site, F is bonded in a 1-coordinate geometry to two K and one Zr atom. In the seventh F site, F is bonded in a 4-coordinate geometry to three K and one Zr atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K6Mo7O34 by Materials Project

K6Mo7O34 crystallizes in the orthorhombic Ama2 space group. The structure is three-dimensional. there are four inequivalent K sites. In the first K site, K is bonded in a 8-coordinate geometry to eight O atoms. There are a spread of K–O bond distances ranging from 2.83–2.94 Å. In the second K site, K is bonded in a 8-coordinate geometry to eight O atoms. There are a spread of K–O bond distances ranging from 2.62–3.16 Å. In the third K site, K is bonded in a 8-coordinate geometry to eight O atoms. There are a spread of K–O bond distances ranging from 2.67–3.23 Å. In the fourth K site, K is bonded in a 7-coordinate geometry to seven O atoms. There are a spread of K–O bond distances ranging from 2.66–3.38 Å. There are four inequivalent Mo sites. In the first Mo site, Mo is bonded to seven O atoms to form distorted MoO7 pentagonal bipyramids that share a cornercorner with one OK2MoO tetrahedra. There are a spread of Mo–O bond distances ranging from 1.74–2.29 Å. In the second Mo site, Mo is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Mo–O bond distances ranging from 1.78–2.37 Å. In the third Mo site, Mo is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Mo–O bond distances ranging from 1.75–2.32 Å. In the fourth Mo site, Mo is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Mo–O bond distances ranging from 1.75–2.33 Å. There are twenty inequivalent O sites. In the first O site, O is bonded to two K, one Mo, and one O atom to form distorted OK2MoO tetrahedra that share a cornercorner with one MoO7 pentagonal bipyramid, a cornercorner with one OK2MoO tetrahedra, and a cornercorner with one OMo4 trigonal pyramid. The O–O bond length is 1.39 Å. In the second O site, O is bonded in a 3-coordinate geometry to one K, one Mo, and one O atom. In the third O site, O is bonded in a water-like geometry to two Mo atoms. In the fourth O site, O is bonded in a distorted single-bond geometry to two K and one Mo atom. In the fifth O site, O is bonded to four Mo atoms to form distorted OMo4 trigonal pyramids that share a cornercorner with one OK2MoO tetrahedra and a cornercorner with one OMo4 trigonal pyramid. In the sixth O site, O is bonded in a 3-coordinate geometry to one K and two Mo atoms. In the seventh O site, O is bonded in a distorted trigonal non-coplanar geometry to one K and two Mo atoms. In the eighth O site, O is bonded in a distorted trigonal non-coplanar geometry to three Mo atoms. In the ninth O site, O is bonded in a distorted rectangular see-saw-like geometry to one K and three Mo atoms. In the tenth O site, O is bonded in a 1-coordinate geometry to two K and one Mo atom. In the eleventh O site, O is bonded in a bent 120 degrees geometry to two equivalent Mo atoms. In the twelfth O site, O is bonded in a 1-coordinate geometry to two K and one Mo atom. In the thirteenth O site, O is bonded in a 1-coordinate geometry to two K and one Mo atom. In the fourteenth O site, O is bonded in a bent 120 degrees geometry to two equivalent Mo atoms. In the fifteenth O site, O is bonded in a distorted bent 120 degrees geometry to one K and one Mo atom. In the sixteenth O site, O is bonded in a distorted T-shaped geometry to three K atoms. In the seventeenth O site, O is bonded in a bent 120 degrees geometry to two equivalent O atoms. Both O–O bond lengths are 1.31 Å. In the eighteenth O site, O is bonded in a bent 120 degrees geometry to two K atoms. In the nineteenth O site, O is bonded in an L-shaped geometry to two K atoms. In the twentieth O site, O is bonded in a 4-coordinate geometry to three K and one O atom.

36 MATERIALS SCIENCE↗