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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Materials Data on KSeO4 by Materials Project

KSeO4 crystallizes in the orthorhombic Pbca space group. The structure is three-dimensional. there are two inequivalent K sites. In the first 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 2.76–3.29 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 2.75–3.18 Å. There are two 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 1.65–1.72 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 1.67–1.69 Å. There are eight inequivalent O sites. In the first O site, O is bonded in a 1-coordinate geometry to two K and one Se atom. In the second O site, O is bonded in a 1-coordinate geometry to three K and one Se atom. In the third O site, O is bonded in a distorted single-bond geometry to two K and one Se atom. In the fourth O site, O is bonded in a 1-coordinate geometry to two K and one Se atom. In the fifth O site, O is bonded in a 1-coordinate geometry to three K and one Se atom. In the sixth O site, O is bonded in a distorted single-bond geometry to two 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 single-bond geometry to two K and one Se atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K5U4VS4O33 by Materials Project

K5U4VS4O33 crystallizes in the tetragonal P4/n space group. The structure is three-dimensional. there are two 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 2.84–3.29 Å. In the second K site, K is bonded to twelve O atoms to form distorted KO12 cuboctahedra that share edges with four equivalent UO7 pentagonal bipyramids and edges with four equivalent SO4 tetrahedra. There are a spread of K–O bond distances ranging from 3.18–3.45 Å. U is bonded to seven O atoms to form distorted UO7 pentagonal bipyramids that share corners with two equivalent UO7 pentagonal bipyramids, corners with three equivalent SO4 tetrahedra, and an edgeedge with one KO12 cuboctahedra. There are a spread of U–O bond distances ranging from 1.82–2.48 Å. V is bonded in a 5-coordinate geometry to five O atoms. There is one shorter (1.63 Å) and four longer (1.89 Å) V–O bond length. S is bonded to four O atoms to form SO4 tetrahedra that share corners with three equivalent UO7 pentagonal bipyramids and an edgeedge with one KO12 cuboctahedra. There are a spread of S–O bond distances ranging from 1.46–1.51 Å. There are nine inequivalent O sites. In the first O site, O is bonded in a single-bond geometry to two equivalent K and one U atom. In the second O site, O is bonded in a 1-coordinate geometry to one K, one U, and one S atom. In the third O site, O is bonded in a single-bond geometry to two K atoms. In the fourth O site, O is bonded in a 3-coordinate geometry to one K, two equivalent U, and one V atom. In the fifth O site, O is bonded in a distorted single-bond geometry to one K, one U, and one S atom. In the sixth O site, O is bonded in a single-bond geometry to one V atom. In the seventh O site, O is bonded in a distorted single-bond geometry to one K and one U atom. In the eighth O site, O is bonded in a distorted single-bond geometry to two equivalent K and one S atom. In the ninth O site, O is bonded in a distorted single-bond geometry to one K, one U, and one S atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3Zr6BeCl15 by Materials Project

K3BeZr6Cl15 crystallizes in the monoclinic C2/c space group. The structure is three-dimensional. there are two inequivalent K sites. In the first K site, K is bonded in a 10-coordinate geometry to ten Cl atoms. There are a spread of K–Cl bond distances ranging from 3.37–3.75 Å. In the second K site, K is bonded in a 8-coordinate geometry to eight Cl atoms. There are a spread of K–Cl bond distances ranging from 3.16–3.74 Å. Be is bonded to six Zr atoms to form BeZr6 octahedra that share corners with two equivalent ClK4Zr2 octahedra and edges with two equivalent ClK2Zr2 trigonal pyramids. The corner-sharing octahedral tilt angles are 1°. There are two shorter (2.33 Å) and four longer (2.37 Å) Be–Zr bond lengths. There are three inequivalent Zr sites. In the first Zr site, Zr is bonded to one Be and five Cl atoms to form a mixture of corner and edge-sharing ZrBeCl5 octahedra. The corner-sharing octahedra tilt angles range from 0–52°. There are a spread of Zr–Cl bond distances ranging from 2.58–2.76 Å. In the second Zr site, Zr is bonded to one Be and five Cl atoms to form a mixture of corner and edge-sharing ZrBeCl5 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Zr–Cl bond distances ranging from 2.58–2.74 Å. In the third Zr site, Zr is bonded to one Be and five Cl atoms to form a mixture of corner and edge-sharing ZrBeCl5 octahedra. The corner-sharing octahedra tilt angles range from 0–52°. There are a spread of Zr–Cl bond distances ranging from 2.59–2.72 Å. There are eight inequivalent Cl sites. In the first Cl site, Cl is bonded in a distorted L-shaped geometry to two K and two Zr atoms. In the second Cl site, Cl is bonded to four K and two equivalent Zr atoms to form distorted ClK4Zr2 octahedra that share corners with two equivalent BeZr6 octahedra, corners with two equivalent ClK4Zr2 octahedra, corners with two equivalent ClK2Zr2 trigonal pyramids, and faces with two equivalent ClK2Zr2 trigonal pyramids. The corner-sharing octahedra tilt angles range from 1–23°. In the third Cl site, Cl is bonded in a 3-coordinate geometry to two K and two Zr atoms. In the fourth Cl site, Cl is bonded in a distorted trigonal non-coplanar geometry to one K and two Zr atoms. In the fifth Cl site, Cl is bonded to two K and two Zr atoms to form distorted ClK2Zr2 trigonal pyramids that share a cornercorner with one ClK4Zr2 octahedra, a cornercorner with one ClK2Zr2 trigonal pyramid, an edgeedge with one BeZr6 octahedra, and a faceface with one ClK4Zr2 octahedra. The corner-sharing octahedral tilt angles are 40°. In the sixth Cl site, Cl is bonded in a 3-coordinate geometry to one K and two Zr atoms. In the seventh Cl site, Cl is bonded in a distorted T-shaped geometry to one K and two Zr atoms. In the eighth Cl site, Cl is bonded in a distorted rectangular see-saw-like geometry to two K and two Zr atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Precise measurements of branching fractions for $ {\mathrm{D}}_{\mathrm{s}}^{+} $ meson decays to two pseudoscalar mesons

We measure the branching fractions for seven $D$$^{+}_{s}$ two-body decays to pseudo-scalar mesons, by analyzing data collected at √s = 4.178 ~ 4.226 GeV with the BESIII detector at the BEPCII collider. The branching fractions are determined to be $$ {\displaystyle \begin{array}{c}\mathcal{B}\left({D}_s^{+}\to {K}^{+}\eta \hbox{'}\right)=\left(2.68\pm 0.17\pm 0.17\pm 0.08\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to \eta \hbox{'}{\pi}^{+}\right)=\left(37.8\pm 0.4\pm 2.1\pm 1.2\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}^{+}\eta \right)=\left(1.62\pm 0.10\pm 0.03\pm 0.05\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to \eta {\pi}^{+}\right)=\left(17.41\pm 0.18\pm 0.27\pm 0.54\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}^{+}{K}_S^0\right)=\left(15.02\pm 0.10\pm 0.27\pm 0.47\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}_S^0{\pi}^{+}\right)=\left(1.109\pm 0.034\pm 0.023\pm 0.035\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}^{+}{\pi}^0\right)=\left(0.748\pm 0.049\pm 0.018\pm 0.035\right)\times {10}^{-3},\end{array}} $$ B D s + → K + η ' = 2.68 ± 0.17 ± 0.17 ± 0.08 × 10 - 3 , B D s + → η ' π + = 37.8 ± 0.4 ± 2.1 ± 1.2 × 10 - 3 , B D s + → K + η = 1.62 ± 0.10 ± 0.03 ± 0.05 × 10 - 3 , B D s + → η π + = 17.41 ± 0.18 ± 0.27 ± 0.54 × 10 - 3 , B D s + → K + K S 0 = 15.02 ± 0.10 ± 0.27 ± 0.47 × 10 - 3 , B D s + → K S 0 π + = 1.109 ± 0.034 ± 0.023 ± 0.035 × 10 - 3 , B D s + → K + π 0 = 0.748 ± 0.049 ± 0.018 ± 0.035 × 10 - 3 , where the first uncertainties are statistical, the second are systematic, and the third are from external input branching fraction of the normalization mode $ {D}_s^{+} $ D s + → K + K - π + . Precision of our measurements is significantly improved compared with that of the current world average values.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Emerging Potassium Metal Anodes: Perspectives on Control of the Electrochemical Interfaces

Potassium metal acts as the anode in emerging potassium metal batteries (KMBs). It further serves as the counter-electrode for potassium ion battery (KIB) half-cells, with its reliable performance being critical for assessing the working electrode material. This first-of-its-kind critical review focuses on the dual challenge of controlling the potassium metal-substrate and the potassium metal-electrolyte interface so as to prevent dendrites. The discussion begins with a comparison of the physical and chemical properties of K metal anodes versus the much oft studied Li and Na metal anodes. Based on established descriptions for root causes of dendrites, the problem should be less severe for K than for Li or Na, while in fact the opposite is observed. The key reason that the K metal surface rapidly becomes dendritic in common electrolytes is its unstable solid electrolyte interphase (SEI). An unstable SEI layer is defined as being non self-passivating. No SEI is perfectly stable during cycling, and all SEI structures are heterogenous both vertically and horizontally relative to the electrolyte interface. The difference between a "stable" and an "unstable" SEI may be viewed as the relative degree to which during cycling it thickens and becomes further heterogeneous. The unstable SEI on K metal leads to a number of interrelated problems, such as low cycling Coulombic efficiency (CE), a severe impedance rise, large overpotentials, and possibly electrical shorting; all of which have been reported to occur as early as in the first ten plating/stripping cycles. Many of the traditional "interface fixes" employed for Li and Na metal anodes, such as various artificial SEIs, surface membranes, barrier layers, the secondary separators, etc. have not been attempted or optimized for the case of K. This is an important area for further exploration, with an understanding that success may come harder than with Li due to K-based SEI reactivity with both ether and ester solvents. The second critical problem with K metal anodes is that they do not thermally or electrochemically wet a standard (untreated) Cu foil current collector. Published experimental and modeling research directly highlights the weak bonding between the K atoms and a Cu surface. Existing surface treatment approaches that achieve improved K wetting are discussed, along with the general design rules for future studies. Also discussed are geometry-based methods to tune nucleation, as well dual approaches where nucleation and SEI structure are tuned through complementary schemes to achieve extended half-cell and full battery stability. We hypothesize that K metal never achieves a planar wetting morphology even at cycle one making the dendrites "baked-in". We propose that classical thin films growth models, Frank van der Merwe (F-M), Volmer Weber (V-W), and Stranski-Krastanov (S-K) can be employed to describe early stage plating behavior. It is demonstrated that island-like V-W growth is the applicable description for the natural plating behavior of K on pristine Cu. Moving forward, there are three inter-related thrusts to be pursued: First, K salt - based electrolyte formulations have to mature and become further tailored to handle the increased reactivity of a metal rather than an ion anode. Second, the K-based SEI structure needs to be further understood and ultimately tuned to be less reactive. Third, the energetics of the K metal - current collector interface must be controlled to promote planar wetting/dewetting throughout cycling.

25 ENERGY STORAGE↗
DOE OSTI2024

Intertwined charge and spin density waves in a topological kagome material

Using neutrons and x rays we show the topological kagome antiferromagnet Mn 3 Sn for T < 285 K forms a homogeneous spin and charge ordered state comprising a longitudinally polarized spin density wave with wave vector k β = k β c ̂ , a helical modulated version of the room temperature antichiral magnetic order with k χ = k χ c ̂ , and charge density waves with wave vectors 2 k β , 2 k χ , and k β + k χ . Though k χ and k β coincide for 200 K < T < 230 K , they exhibit distinct continuous T dependencies before locking to commensurate values of k β = 1 12 c * and k χ = 5 48 c * at low T . Density functional theory indicates this complex modulated state may be associated with the nesting of Fermi surfaces from correlated flat kagome bands, which host Weyl nodes that are annihilated as it forms. Published by the American Physical Society 2024

Chen, Y. (ORCID:0000000177169179)↗
DOE OSTI2026

Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth

Matrix chain multiplication -- computing $\mathcal{W} = M^{(0)}\cdots M^{(K-1)}$ where $M^{(k)} \in \mathbb{R}^{P_k \times P_{k+1}}$-- arises in scientific computing, machine learning, and graph analysis. Despite the importance of this problem, for chains of distinct matrices, the classical number of operations grows linearly with the chain length $K$ and polynomially in the matrix dimensions. We present \emph{Two-Tower Matrix Multiplication}, a quantum subroutine that encodes the product $\mathcal{W}$ of the $K$ matrices into a quantum state in circuit depth $\mathcal{O}(\max_{k} \mathrm{polylog} (P_k P_{k+1}))$, which is independent of~$K$ within the QRAM-based state-preparation model, whereas the qubit count is $\mathcal{O}\bigl(\sum_{k} \log P_k \bigr)$; the total gate count remains linear in $K$, so the gain is in the circuit depth. The construction interleaves state-preparation operators across two layers; within each layer, all operators act on disjoint registers and execute in parallel. This subroutine can be specialized for the chain-vector case, which computes the product of $K-1$ matrices applied to a vector. We prove the correctness of the subroutine for all $K$ and provide two implementations using the Qiskit and QCLAB frameworks. The subroutine is applicable to any downstream quantum algorithm that operates on a matrix encoded in the statevector, including norm estimation, graph-matrix powers, linear system solving, and quantum machine learning kernels.

Antonioli, Giacomo [Pisa U.] (ORCID:00090000668703↗
DOE OSTI2023

Rubidium and potassium isotopic variations in chondrites and Mars: Accretion signatures and planetary overprints

As moderately volatile elements, isotopes of Rb and K can trace volatilization processes in planetary bodies. Rubidium isotopic data are however very scarce, especially for non-carbonaceous meteorites. Here, in this study, we report combined Rb and K isotopic data (δ 87/85 Rb and δ 41/39 Κ) for 7 ordinary, 6 enstatite, and 4 Martian meteorite falls to understand the causes for the variations in volatile abundances and isotopic compositions. Bulk Rb and K isotopic compositions of planetary bodies are estimated to be (Table 1): Mars +0.10 ± 0.03 ‰ for Rb and -0.26 ± 0.05 ‰ for K, bulk OCs $-0.12^{+0.15}_{-0.24}$ ‰ for Rb and $-0.72^{+0.28}_{-0.41}$ ‰ for K, bulk ECs $-0.02^{+0.29}_{-0.26}$ ‰ for Rb and $-0.33^{+0.37}_{-0.23}$ ‰ for K. The bulk K isotopic compositions of subgroup OCs are estimated to be $-0.72^{+0.26}_{-0.55}$ ‰ for H chondrites, $-0.71^{+0.23}_{-0.39}$ ‰ for L chondrites, and $-0.77^{+0.63}_{-0.30}$ ‰ for LL chondrites. A broad correlation between the Rb and K isotopic compositions of planetary bodies is observed. The correlation follows a slope that is consistent with kinetic evaporation and condensation processes, suggesting volatility-controlled mass-dependent isotope fractionation (as opposed to nucleosynthetic anomalies). Individual ordinary and enstatite chondrites show large Rb and K isotopic variations (-1.02 to +0.29 ‰ for Rb and -0.91 to -0.15 ‰ for K). Samples of lower metamorphic grades display correlated elemental and isotopic fractionations between Rb and K, while samples of higher metamorphic grades show great scatter, suggesting that chondrite parent-body processes have decoupled the two elements and their isotopes at the sample scale. Several processes could have contributed to the observed isotopic variations of Rb and K, including (i) chondrule “nugget effect”, (ii) volatilization during parent-body thermal metamorphism (heat-induced vaporization and gas transport within parent bodies), (iii) thermal diffusion during parent-body metamorphism, and (iv) impact/shock heating. Quantitative modeling of the first two processes suggests that neither of them could produce isotopic variations large enough to explain the observed isotopic variations. Volatilization during parent-body thermal metamorphism [the scenario (ii)], which has been commonly invoked to explain the isotopic variations of volatile elements, is gas transport-limited and its effect on isotopic fractionations of moderately volatile elements should be negligible. Modeling of diffusion processes suggests that (iii) could produce K isotopic variation comparable to the observed variation. The large isotopic variations in non-carbonaceous meteorites are thus most likely due to diffusive redistribution of K and Rb during metamorphism and/or shock-induced heating and vaporization.

58 GEOSCIENCES↗
DOE OSTI2023

Accessing the strong interaction between Λ baryons and charged kaons with the femtoscopy technique at the LHC

The interaction between baryons and kaons/antikaons is a crucial ingredient for the strangeness $S$ = 0 and $S$ = -2 sector of the meson–baryon interaction at low energies. In particular, the $Λ\overline{K}$ might help in understanding the origin of states such as the $Ξ$(1620), whose nature and properties are still under debate. Experimental data on $Λ–K$ and $Λ–\overline{K}$ systems are scarce, leading to large uncertainties and tension between the available theoretical predictions constrained by such data. In this Letter we present the measurements of $Λ–K$ + ⊕ $\overline{Λ}–K$ - and $Λ–K$ - ⊕ $\overline{Λ}–K$ + correlations obtained in the high multiplicity triggered data sample in pp collisions at $\sqrt{s}$ = 13 TeV recorded by ALICE at the LHC. The correlation function for both pairs is modeled using the Lednický–Lyuboshits analytical formula and the corresponding scattering parameters are extracted. The $Λ–K$ - ⊕ $\overline{Λ}–K$ + correlations show the presence of several structures at relative momenta k above 200 MeV/c, compatible with the $Ω$ baryon, the $Ξ$(1690), and $Ξ$(1820) resonances decaying into $Λ–K$ - pairs. The low $k^*$ region in the $Λ–K$ - ⊕ $\overline{Λ}–K$ + also exhibits the presence of the $Ξ$(1620) state, expected to strongly couple to the measured pair. The presented data allow to access the $ΛK$ + and $ΛK$ - strong interaction with an unprecedented precision and deliver the first experimental observation of the $Ξ$(1620) decaying into $ΛK$ - .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Materials Data on KGa3 by Materials Project

KGa3 crystallizes in the tetragonal I-4m2 space group. The structure is three-dimensional. there are two inequivalent K sites. In the first K site, K is bonded in a 12-coordinate geometry to three K and twelve Ga atoms. There are one shorter (3.69 Å) and two longer (3.70 Å) K–K bond lengths. There are a spread of K–Ga bond distances ranging from 3.70–3.74 Å. In the second K site, K is bonded in a 12-coordinate geometry to four equivalent K and twelve Ga atoms. There are four shorter (3.57 Å) and eight longer (3.77 Å) K–Ga bond lengths. There are three inequivalent Ga sites. In the first Ga site, Ga is bonded in a 9-coordinate geometry to three K and six Ga atoms. There are a spread of Ga–Ga bond distances ranging from 2.62–2.82 Å. In the second Ga site, Ga is bonded in a 10-coordinate geometry to five K and five Ga atoms. There are one shorter (2.47 Å) and one longer (2.52 Å) Ga–Ga bond lengths. In the third Ga site, Ga is bonded in a distorted body-centered cubic geometry to four equivalent K and four equivalent Ga atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3Bi by Materials Project

K3Bi crystallizes in the hexagonal P6_3cm space group. The structure is three-dimensional. there are four inequivalent K sites. In the first K site, K is bonded in a trigonal planar geometry to three equivalent Bi atoms. All K–Bi bond lengths are 3.61 Å. In the second K site, K is bonded in a trigonal planar geometry to three equivalent Bi atoms. All K–Bi bond lengths are 3.62 Å. In the third K site, K is bonded in a 3-coordinate geometry to three equivalent Bi atoms. There are one shorter (3.67 Å) and two longer (3.96 Å) K–Bi bond lengths. In the fourth K site, K is bonded in a 2-coordinate geometry to two equivalent Bi atoms. There are one shorter (3.68 Å) and one longer (3.88 Å) K–Bi bond lengths. Bi is bonded in a 8-coordinate geometry to eight K atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K2S2NO7 by Materials Project

K2NS2O7 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are two 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 2.75–3.36 Å. In the second K site, K is bonded in a 10-coordinate geometry to ten O atoms. There are a spread of K–O bond distances ranging from 2.72–3.35 Å. N is bonded in a trigonal planar geometry to two S and one O atom. There is one shorter (1.85 Å) and one longer (1.86 Å) N–S bond length. The N–O bond length is 1.26 Å. There are two inequivalent S sites. In the first S site, S is bonded to one N and three O atoms to form corner-sharing SNO3 tetrahedra. There is one shorter (1.45 Å) and two longer (1.46 Å) S–O bond length. In the second S site, S is bonded to one N and three O atoms to form corner-sharing SNO3 tetrahedra. There are a spread of S–O bond distances ranging from 1.45–1.47 Å. There are seven inequivalent O sites. In the first O site, O is bonded in a distorted single-bond geometry to two equivalent K and one S atom. In the second O site, O is bonded in a single-bond geometry to three K and one S atom. In the third O site, O is bonded in a distorted single-bond geometry to three K 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 distorted single-bond geometry to two K and one S atom. In the sixth O site, O is bonded in a distorted single-bond geometry to two K and one N atom. In the seventh O site, O is bonded in a distorted single-bond geometry to three K and one S atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K2TiOF4 by Materials Project

K2TiOF4 crystallizes in the orthorhombic Pna2_1 space group. The structure is three-dimensional. there are eight inequivalent K1+ sites. In the first K1+ site, K1+ is bonded in a 10-coordinate geometry to two O2- and eight F1- atoms. There are one shorter (3.04 Å) and one longer (3.07 Å) K–O bond lengths. There are a spread of K–F bond distances ranging from 2.65–3.13 Å. In the second K1+ site, K1+ is bonded in a 11-coordinate geometry to three O2- and eight F1- atoms. There are a spread of K–O bond distances ranging from 2.91–3.18 Å. There are a spread of K–F bond distances ranging from 2.75–3.29 Å. In the third K1+ site, K1+ is bonded in a 11-coordinate geometry to two O2- and nine F1- atoms. There are one shorter (3.20 Å) and one longer (3.27 Å) K–O bond lengths. There are a spread of K–F bond distances ranging from 2.63–3.17 Å. In the fourth K1+ site, K1+ is bonded in a 10-coordinate geometry to two O2- and eight F1- atoms. There are one shorter (3.00 Å) and one longer (3.07 Å) K–O bond lengths. There are a spread of K–F bond distances ranging from 2.65–3.15 Å. In the fifth K1+ site, K1+ is bonded in a 11-coordinate geometry to two O2- and nine F1- atoms. There are one shorter (3.23 Å) and one longer (3.31 Å) K–O bond lengths. There are a spread of K–F bond distances ranging from 2.64–3.21 Å. In the sixth K1+ site, K1+ is bonded in a 8-coordinate geometry to eight F1- atoms. There are a spread of K–F bond distances ranging from 2.70–2.89 Å. In the seventh K1+ site, K1+ is bonded in a 7-coordinate geometry to seven F1- atoms. There are a spread of K–F bond distances ranging from 2.70–2.89 Å. In the eighth K1+ site, K1+ is bonded in a 11-coordinate geometry to two O2- and nine F1- atoms. There are one shorter (3.11 Å) and one longer (3.21 Å) K–O bond lengths. There are a spread of K–F bond distances ranging from 2.69–3.38 Å. There are four inequivalent Ti4+ sites. In the first Ti4+ site, Ti4+ is bonded to two O2- and four F1- atoms to form corner-sharing TiO2F4 octahedra. The corner-sharing octahedra tilt angles range from 2–7°. There is one shorter (1.86 Å) and one longer (1.87 Å) Ti–O bond length. There are a spread of Ti–F bond distances ranging from 1.92–2.02 Å. In the second Ti4+ site, Ti4+ is bonded to two O2- and four F1- atoms to form corner-sharing TiO2F4 octahedra. The corner-sharing octahedra tilt angles range from 2–3°. There is one shorter (1.87 Å) and one longer (1.88 Å) Ti–O bond length. There are a spread of Ti–F bond distances ranging from 1.90–1.99 Å. In the third Ti4+ site, Ti4+ is bonded to two O2- and four F1- atoms to form corner-sharing TiO2F4 octahedra. The corner-sharing octahedra tilt angles range from 4–7°. There is one shorter (1.86 Å) and one longer (1.87 Å) Ti–O bond length. There are a spread of Ti–F bond distances ranging from 1.92–2.02 Å. In the fourth Ti4+ site, Ti4+ is bonded to two O2- and four F1- atoms to form corner-sharing TiO2F4 octahedra. The corner-sharing octahedra tilt angles range from 3–4°. There is one shorter (1.87 Å) and one longer (1.88 Å) Ti–O bond length. There is one shorter (1.90 Å) and three longer (1.98 Å) Ti–F bond length. There are four inequivalent O2- sites. In the first O2- site, O2- is bonded in a linear geometry to four K1+ and two Ti4+ atoms. In the second O2- site, O2- is bonded in a linear geometry to three K1+ and two Ti4+ atoms. In the third O2- site, O2- is bonded in a distorted linear geometry to three K1+ and two Ti4+ atoms. In the fourth O2- site, O2- is bonded in a linear geometry to three K1+ and two Ti4+ atoms. There are sixteen inequivalent F1- sites. In the first F1- site, F1- is bonded in a 1-coordinate geometry to four K1+ and one Ti4+ atom. In the second F1- site, F1- is bonded in a 1-coordinate geometry to four K1+ and one Ti4+ atom. In the third F1- site, F1- is bonded in a distorted single-bond geometry to four K1+ and one Ti4+ atom. In the fourth F1- site, F1- is bonded in a 1-coordinate geometry to four K1+ and one Ti4+ atom. In the fifth F1- site, F1- is bonded in a 1-coordinate geometry to four K1+ and one Ti4+ atom. In the sixth F1- site, F1- is bonded in a 1-coordinate geometry to five K1+ and one Ti4+ atom. In the seventh F1- site, F1- is bonded in a 5-coordinate geometry to five K1+ and one Ti4+ atom. In the eighth F1- site, F1- is bonded in a 1-coordinate geometry to four K1+ and one Ti4+ atom. In the ninth F1- site, F1- is bonded in a 1-coordinate geometry to five K1+ and one Ti4+ atom. In the tenth F1- site, F1- is bonded in a 1-coordinate geometry to four K1+ and one Ti4+ atom. In the eleventh F1- site, F1- is bonded in a 1-coordinate geometry to four K1+ and one Ti4+ atom. In the twelfth F1- site, F1- is bonded in a 1-coordinate geometry to three K1+ and one Ti4+ atom. In the thirteenth F1- site, F1- is bonded in a 1-coordinate geometry to four K1+ and one Ti4+ atom. In the fourteenth F1- site, F1- is bonded in a distorted single-bond geometry to four K1+ and one Ti4+ atom. In the fifteenth F1- site, F1- is bonded in a 1-coordinate geometry to four K1+ and one Ti4+ atom. In the sixteenth F1- site, F1- is bonded in a 1-coordinate geometry to four K1+ and one Ti4+ atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K6Fe24S26Cl by Materials Project

K6Fe24S26Cl crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. there are two inequivalent K sites. In the first K site, K is bonded in a 9-coordinate geometry to eight S and one Cl atom. There are a spread of K–S bond distances ranging from 3.17–3.33 Å. The K–Cl bond length is 2.98 Å. In the second K site, K is bonded in a 9-coordinate geometry to eight S and one Cl atom. There are four shorter (3.18 Å) and four longer (3.37 Å) K–S bond lengths. The K–Cl bond length is 3.04 Å. There are two inequivalent Fe sites. In the first Fe site, Fe is bonded to four S atoms to form a mixture of edge and corner-sharing FeS4 tetrahedra. There are a spread of Fe–S bond distances ranging from 2.15–2.19 Å. In the second Fe site, Fe is bonded to four S atoms to form a mixture of edge and corner-sharing FeS4 tetrahedra. There are a spread of Fe–S bond distances ranging from 2.15–2.19 Å. There are five inequivalent S sites. In the first S site, S is bonded in a 4-coordinate geometry to four equivalent Fe atoms. In the second S site, S is bonded in a 6-coordinate geometry to two equivalent K and four equivalent Fe atoms. In the third S site, S is bonded in a 5-coordinate geometry to one K and four equivalent Fe atoms. In the fourth S site, S is bonded in a 6-coordinate geometry to two equivalent K and four equivalent Fe atoms. In the fifth S site, S is bonded in a 6-coordinate geometry to three K and three Fe atoms. Cl is bonded in an octahedral geometry to six K atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K2NaH10IO10 by Materials Project

K2NaH10O10I crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are two 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 2.75–2.97 Å. In the second K site, K is bonded in a 2-coordinate geometry to three O atoms. There are a spread of K–O bond distances ranging from 2.71–2.91 Å. Na is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Na–O bond distances ranging from 2.38–2.49 Å. There are ten 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 (1.02 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 1.00 Å. In the third H site, H is bonded in a distorted linear geometry to two O atoms. There is one shorter (1.02 Å) and one longer (1.63 Å) H–O bond length. In the fourth H site, H is bonded in a single-bond geometry to one O atom. The H–O bond length is 0.98 Å. In the fifth 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 sixth 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 seventh H site, H is bonded in a single-bond geometry to two O atoms. There is one shorter (1.01 Å) and one longer (1.72 Å) H–O bond length. In the eighth 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 ninth H site, H is bonded in a distorted single-bond geometry to two O atoms. There is one shorter (1.01 Å) and one longer (1.66 Å) H–O bond length. In the tenth H site, H is bonded in a single-bond geometry to two O atoms. There is one shorter (1.00 Å) and one longer (1.74 Å) H–O bond length. There are ten inequivalent O sites. In the first O site, O is bonded in a distorted single-bond geometry to one K, one Na, one H, and one I atom. The O–I bond length is 2.01 Å. In the second O site, O is bonded in a distorted single-bond geometry to one K, one Na, one H, and one I atom. The O–I bond length is 2.03 Å. In the third O site, O is bonded in a 1-coordinate geometry to one I atom. The O–I bond length is 1.89 Å. In the fourth O site, O is bonded in a 4-coordinate geometry to one K, two H, and one I atom. The O–I bond length is 1.87 Å. In the fifth O site, O is bonded in a 2-coordinate geometry to one K, two H, and one I atom. The O–I bond length is 1.87 Å. In the sixth O site, O is bonded in a 1-coordinate geometry to three K, one H, and one I atom. The O–I bond length is 1.86 Å. In the seventh O site, O is bonded in a distorted water-like geometry to one K, one Na, and two H atoms. In the eighth O site, O is bonded in a distorted water-like geometry to one K, one Na, and two H atoms. In the ninth O site, O is bonded in a water-like geometry to one Na and two H atoms. In the tenth O site, O is bonded in a distorted water-like geometry to one Na and two H atoms. I is bonded in an octahedral geometry to six O atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K7H12Pt4C16(N8O3)2 by Materials Project

K7Pt4C16H12(N8O3)2 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are seven inequivalent K1+ sites. In the first K1+ site, K1+ is bonded to three N3- and two O2- atoms to form distorted edge-sharing KN3O2 square pyramids. There are a spread of K–N bond distances ranging from 2.85–3.03 Å. There are one shorter (2.85 Å) and one longer (2.94 Å) K–O bond lengths. In the second K1+ site, K1+ is bonded in a 6-coordinate geometry to five N3- and one O2- atom. There are a spread of K–N bond distances ranging from 2.81–3.25 Å. The K–O bond length is 2.79 Å. In the third K1+ site, K1+ is bonded in a distorted rectangular see-saw-like geometry to two N3- and two O2- atoms. There are one shorter (2.92 Å) and one longer (3.25 Å) K–N bond lengths. There are one shorter (2.70 Å) and one longer (2.86 Å) K–O bond lengths. In the fourth K1+ site, K1+ is bonded in a distorted rectangular see-saw-like geometry to two N3- and two O2- atoms. There are one shorter (2.92 Å) and one longer (3.26 Å) K–N bond lengths. There are one shorter (2.71 Å) and one longer (2.87 Å) K–O bond lengths. In the fifth K1+ site, K1+ is bonded in a distorted rectangular see-saw-like geometry to two N3- and two O2- atoms. There are one shorter (2.90 Å) and one longer (2.92 Å) K–N bond lengths. There are one shorter (2.82 Å) and one longer (2.84 Å) K–O bond lengths. In the sixth K1+ site, K1+ is bonded in a 6-coordinate geometry to five N3- and one O2- atom. There are a spread of K–N bond distances ranging from 2.81–3.23 Å. The K–O bond length is 2.76 Å. In the seventh K1+ site, K1+ is bonded to three N3- and two O2- atoms to form distorted edge-sharing KN3O2 square pyramids. There are a spread of K–N bond distances ranging from 2.84–3.04 Å. There are one shorter (2.84 Å) and one longer (2.93 Å) K–O bond lengths. There are four inequivalent Pt2- sites. In the first Pt2- site, Pt2- is bonded in a square co-planar geometry to two C+3.06+ and two N3- atoms. Both Pt–C bond lengths are 2.01 Å. Both Pt–N bond lengths are 1.99 Å. In the second Pt2- site, Pt2- is bonded in a rectangular see-saw-like geometry to two C+3.06+ and two N3- atoms. There are one shorter (2.00 Å) and one longer (2.01 Å) Pt–C bond lengths. Both Pt–N bond lengths are 1.98 Å. In the third Pt2- site, Pt2- is bonded in a square co-planar geometry to two C+3.06+ and two equivalent N3- atoms. Both Pt–C bond lengths are 2.01 Å. Both Pt–N bond lengths are 1.99 Å. In the fourth Pt2- site, Pt2- is bonded in a rectangular see-saw-like geometry to two C+3.06+ and two N3- atoms. There are one shorter (2.00 Å) and one longer (2.01 Å) Pt–C bond lengths. There is one shorter (1.98 Å) and one longer (1.99 Å) Pt–N bond length. There are fourteen inequivalent C+3.06+ sites. In the first C+3.06+ site, C+3.06+ is bonded in a linear geometry to one Pt2- and one N3- atom. The C–N bond length is 1.17 Å. In the second C+3.06+ site, C+3.06+ is bonded in a single-bond geometry to one N3- atom. The C–N bond length is 1.18 Å. In the third C+3.06+ site, C+3.06+ is bonded in a linear geometry to one Pt2- and one N3- atom. The C–N bond length is 1.17 Å. In the fourth C+3.06+ site, C+3.06+ is bonded in a single-bond geometry to one N3- atom. The C–N bond length is 1.18 Å. In the fifth C+3.06+ site, C+3.06+ is bonded in a linear geometry to one Pt2- and one N3- atom. The C–N bond length is 1.17 Å. In the sixth C+3.06+ site, C+3.06+ is bonded in a distorted linear geometry to one Pt2- and one N3- atom. The C–N bond length is 1.17 Å. In the seventh C+3.06+ site, C+3.06+ is bonded in a single-bond geometry to one N3- atom. The C–N bond length is 1.18 Å. In the eighth C+3.06+ site, C+3.06+ is bonded in a single-bond geometry to one N3- atom. The C–N bond length is 1.18 Å. In the ninth C+3.06+ site, C+3.06+ is bonded in a distorted linear geometry to one Pt2- and one N3- atom. The C–N bond length is 1.17 Å. In the tenth C+3.06+ site, C+3.06+ is bonded in a linear geometry to one Pt2- and one N3- atom. The C–N bond length is 1.17 Å. In the eleventh C+3.06+ site, C+3.06+ is bonded in a single-bond geometry to one N3- atom. The C–N bond length is 1.18 Å. In the twelfth C+3.06+ site, C+3.06+ is bonded in a linear geometry to one Pt2- and one N3- atom. The C–N bond length is 1.17 Å. In the thirteenth C+3.06+ site, C+3.06+ is bonded in a single-bond geometry to one N3- atom. The C–N bond length is 1.18 Å. In the fourteenth C+3.06+ site, C+3.06+ is bonded in a linear geometry to one Pt2- and one N3- atom. The C–N bond length is 1.17 Å. There are fifteen inequivalent N3- sites. In the first N3- site, N3- is bonded in a 1-coordinate geometry to three K1+ and one C+3.06+ atom. In the second N3- site, N3- is bonded in a linear geometry to one Pt2- and one C+3.06+ atom. In the third N3- site, N3- is bonded in a distorted single-bond geometry to three K1+ and one C+3.06+ atom. In the fourth N3- site, N3- is bonded in a linear geometry to one Pt2- and one C+3.06+ atom. In the fifth N3- site, N3- is bonded in a 1-coordinate geometry to three K1+ and one C+3.06+ atom. In the sixth N3- site, N3- is bonded in a single-bond geometry to two K1+ and one C+3.06+ atom. In the seventh N3- site, N3- is bonded in a linear geometry to one Pt2- and one C+3.06+ atom. The N–C bond length is 1.18 Å. In the eighth N3- site, N3- is bonded in a linear geometry to one Pt2- and one C+3.06+ atom. In the ninth N3- site, N3- is bonded in a distorted linear geometry to one Pt2- and one C+3.06+ atom. In the tenth N3- site, N3- is bonded in a distorted single-bond geometry to two K1+ and one C+3.06+ atom. In the eleventh N3- site, N3- is bonded in a 1-coordinate geometry to three K1+ and one C+3.06+ atom. In the twelfth N3- site, N3- is bonded in a linear geometry to one Pt2- and one C+3.06+ atom. In the thirteenth N3- site, N3- is bonded in a distorted single-bond geometry to three K1+ and one C+3.06+ atom. In the fourteenth N3- site, N3- is bonded in a linear geometry to one Pt2- and one C+3.06+ atom. In the fifteenth N3- site, N3- is bonded in a 1-coordinate geometry to three K1+ and one C+3.06+ atom. There are twelve 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 0.98 Å. In the third 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 fourth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the fifth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the sixth 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 seventh 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 eighth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the ninth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. In the tenth 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 eleventh 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 twelfth H1+ site, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.98 Å. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted water-like geometry to two K1+ and two H1+ atoms. In the second O2- site, O2- is bonded in a water-like geometry to two K1+ and two H1+ atoms. In the third O2- site, O2- is bonded in a distorted water-like geometry to two K1+ and two H1+ atoms. In the fourth O2- site, O2- is bonded in a distorted water-like geometry to two K1+ and two H1+ atoms. In the fifth O2- site, O2- is bonded in a water-like geometry to two K1+ and two H1+ atoms. In the sixth O2- site, O2- is bonded in a distorted water-like geometry to two K1+ and two H1+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K2BaNa2Ti4(SiO4)8 by Materials Project

K2Na2BaTi4(SiO4)8 crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are two 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 2.85–2.99 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 2.86–3.04 Å. Na is bonded to six O atoms to form distorted NaO6 octahedra that share corners with two equivalent TiO6 octahedra, corners with four SiO4 tetrahedra, and an edgeedge with one TiO6 octahedra. The corner-sharing octahedra tilt angles range from 53–64°. There are a spread of Na–O bond distances ranging from 2.33–2.90 Å. Ba is bonded in a 11-coordinate geometry to eleven O atoms. There are a spread of Ba–O bond distances ranging from 2.65–3.13 Å. There are two inequivalent Ti sites. In the first Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with two equivalent NaO6 octahedra, corners with two equivalent TiO6 octahedra, and corners with four SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 47–64°. There are a spread of Ti–O bond distances ranging from 1.82–2.17 Å. In the second Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with two equivalent TiO6 octahedra, corners with four SiO4 tetrahedra, and an edgeedge with one NaO6 octahedra. The corner-sharing octahedral tilt angles are 47°. There are a spread of Ti–O bond distances ranging from 1.87–2.05 Å. There are four inequivalent Si sites. In the first Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share a cornercorner with one NaO6 octahedra, corners with two TiO6 octahedra, and corners with two SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 39–75°. There are a spread of Si–O bond distances ranging from 1.63–1.67 Å. In the second Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share a cornercorner with one NaO6 octahedra, corners with two TiO6 octahedra, and corners with two SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 50–67°. There are a spread of Si–O bond distances ranging from 1.63–1.66 Å. In the third Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share a cornercorner with one NaO6 octahedra, corners with two TiO6 octahedra, and corners with two SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 45–64°. There is two shorter (1.63 Å) and two longer (1.66 Å) Si–O bond length. In the fourth Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share a cornercorner with one NaO6 octahedra, corners with two TiO6 octahedra, and corners with two SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 40–61°. There are a spread of Si–O bond distances ranging from 1.62–1.67 Å. There are eighteen inequivalent O sites. In the first O site, O is bonded in a 2-coordinate geometry to one Ba, one Ti, and one Si atom. In the second O site, O is bonded in a distorted bent 120 degrees geometry to one Ba, one Ti, and one Si atom. In the third O site, O is bonded in a distorted bent 120 degrees geometry to one Ba and two Ti atoms. In the fourth O site, O is bonded in a 2-coordinate geometry to one Na and two Ti atoms. In the fifth O site, O is bonded in a distorted bent 150 degrees geometry to one Ti and one Si atom. In the sixth O site, O is bonded in a 3-coordinate geometry to one Na, one Ti, and one Si atom. In the seventh O site, O is bonded in a distorted bent 120 degrees geometry to one K, one Ba, one Ti, and one Si atom. In the eighth O site, O is bonded in a distorted bent 150 degrees geometry to one K, one Ti, and one Si atom. In the ninth O site, O is bonded in a distorted bent 150 degrees geometry to two K and two equivalent Si atoms. In the tenth O site, O is bonded in a distorted bent 150 degrees geometry to two K and two equivalent Si atoms. In the eleventh O site, O is bonded in a distorted bent 150 degrees geometry to one Na and two Si atoms. In the twelfth O site, O is bonded in a bent 150 degrees geometry to two Si atoms. In the thirteenth O site, O is bonded in a distorted bent 150 degrees geometry to one K, one Ba, and two equivalent Si atoms. In the fourteenth O site, O is bonded in a 3-coordinate geometry to one K and two equivalent Si atoms. In the fifteenth O site, O is bonded in a distorted bent 150 degrees geometry to one Ti and one Si atom. In the sixteenth O site, O is bonded in a distorted trigonal planar geometry to one Na, one Ti, and one Si atom. In the seventeenth O site, O is bonded in a 2-coordinate geometry to one Na and one Ba atom. In the eighteenth O site, O is bonded in a distorted trigonal non-coplanar geometry to two K and one Na atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K4Ba2Na4Ti8MnSi16(W4O29)2 by Materials Project

K4Na4Ba2Ti8MnSi16(W4O29)2 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. there are two inequivalent K sites. In the first K site, K is bonded in a 9-coordinate geometry to five O atoms. There are a spread of K–O bond distances ranging from 2.84–3.26 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 2.75–3.27 Å. Na is bonded in a 3-coordinate geometry to one W and four O atoms. The Na–W bond length is 3.01 Å. There are a spread of Na–O bond distances ranging from 2.27–2.72 Å. Ba is bonded in a 4-coordinate geometry to four O atoms. There are two shorter (2.83 Å) and two longer (2.98 Å) Ba–O bond lengths. There are three inequivalent Ti sites. In the first Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with two equivalent TiO6 octahedra and corners with four SiO4 tetrahedra. The corner-sharing octahedral tilt angles are 39°. There are a spread of Ti–O bond distances ranging from 1.95–2.07 Å. In the second Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with two equivalent TiO6 octahedra, corners with four SiO4 tetrahedra, and an edgeedge with one MnO6 octahedra. The corner-sharing octahedral tilt angles are 55°. There are a spread of Ti–O bond distances ranging from 1.94–2.06 Å. In the third Ti site, Ti is bonded to six O atoms to form TiO6 octahedra that share corners with two TiO6 octahedra and corners with four SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 39–55°. There are a spread of Ti–O bond distances ranging from 1.79–2.29 Å. There are two inequivalent W sites. In the first W site, W is bonded in a 3-coordinate geometry to three O atoms. There are a spread of W–O bond distances ranging from 2.06–2.22 Å. In the second W site, W is bonded in a 4-coordinate geometry to one Na and three O atoms. There are a spread of W–O bond distances ranging from 2.32–2.51 Å. Mn is bonded to six O atoms to form MnO6 octahedra that share corners with four equivalent SiO4 tetrahedra and edges with two equivalent TiO6 octahedra. There are two shorter (2.09 Å) and four longer (2.24 Å) Mn–O bond lengths. There are four inequivalent Si sites. In the first Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share a cornercorner with one MnO6 octahedra, corners with two TiO6 octahedra, and corners with two SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 48–65°. There are a spread of Si–O bond distances ranging from 1.63–1.66 Å. In the second Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share corners with two TiO6 octahedra and corners with two SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 36–53°. There are a spread of Si–O bond distances ranging from 1.62–1.65 Å. In the third Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share corners with two TiO6 octahedra and corners with two SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 39–55°. There are a spread of Si–O bond distances ranging from 1.61–1.66 Å. In the fourth Si site, Si is bonded to four O atoms to form SiO4 tetrahedra that share corners with two TiO6 octahedra and corners with two SiO4 tetrahedra. The corner-sharing octahedra tilt angles range from 49–54°. There are a spread of Si–O bond distances ranging from 1.62–1.66 Å. There are seventeen inequivalent O sites. In the first O site, O is bonded in a 3-coordinate geometry to one Na, one Ti, and one Si atom. In the second O site, O is bonded in a 1-coordinate geometry to one K, one Ti, one W, and one Si atom. In the third O site, O is bonded in a 1-coordinate geometry to one K, one Ti, one W, and one Si atom. In the fourth O site, O is bonded in a trigonal non-coplanar geometry to two equivalent W and one Mn atom. In the fifth O site, O is bonded in a distorted bent 150 degrees geometry to one K and two equivalent Si atoms. In the sixth O site, O is bonded in a bent 150 degrees geometry to two Si atoms. In the seventh O site, O is bonded in a distorted bent 150 degrees geometry to two Ti atoms. In the eighth O site, O is bonded in a distorted bent 150 degrees geometry to one K and two equivalent Si atoms. In the ninth O site, O is bonded in a distorted bent 150 degrees geometry to two equivalent K and two equivalent Si atoms. In the tenth O site, O is bonded in a 2-coordinate geometry to one K and two equivalent Si atoms. In the eleventh O site, O is bonded in a 2-coordinate geometry to one K, one Ba, one Ti, and one Si atom. In the twelfth O site, O is bonded in a 3-coordinate geometry to one Ti, one Mn, and one Si atom. In the thirteenth O site, O is bonded in a 4-coordinate geometry to two equivalent Na and two Si atoms. In the fourteenth O site, O is bonded in a distorted trigonal non-coplanar geometry to one Na, one Ti, and one Si atom. In the fifteenth O site, O is bonded in a distorted bent 150 degrees geometry to one Ti, one W, and one Si atom. In the sixteenth O site, O is bonded in a 2-coordinate geometry to one Ba, one Ti, and one Si atom. In the seventeenth O site, O is bonded in a 4-coordinate geometry to two Ti and two W atoms.

36 MATERIALS SCIENCE↗