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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

The Impact of High-Dimensional Phase Space Correlations on the Beam Dynamics in a Linear Accelerator

Hadron beams develop intensity-dependent transverse-longitudinal correlations within radio-frequency quadrupole (RFQ) accelerating structures. These correlations are only visible in six-dimensional phase space and are destroyed by reconstructions from low-dimensional projections. In this work, we estimate the effect of artificial decorrelation on the beam dynamics in the Spallation Neutron Source (SNS) linac and Beam Test Facility (BTF). We show that the evolution of a realistic initial distribution and its decorrelated twin converge during the early acceleration stages; thus, low-dimensional projections are probably sufficient for detailed predictions in high-power linacs.

Hoover, Austin↗
DOE OSTI2025

A Solution to the Hierarchy Problem with Non-Linear Quantum Mechanics

We argue that the hierarchy problem of the standard model of particle physics can be solved by adding a state-dependent term to the Higgs sector. We present an example of a scalar field with a Higgs-like potential with an additional term proportional to the expectation value of the squared Higgs field operator. We show that the mass can be parametrically lighter than the theory's energy-momentum cutoff without fine tuning. We find the Higgs mass can be technically natural, even with a Planck-scale cutoff. The simplest version of the theory may not be distinguishable from the standard model at colliders, but other versions might. In addition, some aspects of cosmological evolution can be different in this model, in some cases radically.

Kaplan, David E. [Johns Hopkins U.; Tokyo U., IPMU↗
DOE OSTI2026

Modeling of a Four-Stage Linear Ionization Cooling Channel for a Muon Collider in G4Beamline

A previous study of an eight-stage rectilinear ionization cooling channel in the ICOOL software demonstrated a five-order-of-magnitude reduction in a muon beam’s 6D emittance. In this study, we look to compare the ways ICOOL and Muons, Inc.’s g4Beamline software model ionization cooling by comparing their modeling of the first four stages to this optimized cooling channel constructed in ICOOL. We begin by identifying the parameters used to construct the optimized ionization cooling channel in ICOOL. We then reconstruct this beam in g4Beamline with identical parameter specifications and simulate the cooling of an identical input beam. Finally, we compare the two simulations based on their beam transmission, longitudinal emittance, and transverse emittance along the channel length. Through this process, we demonstrate that G4Beamline accurately reproduces transverse cooling results but predicts systematically different longitudinal emittance evolution while maintaining similar overall cooling performance, reproducing a 97.9% reduction in 6D emittance over four stages.

Keeler, Dominic [Purdue U., West Lafayette] (ORCID↗
DOE OSTI2020

Materials Data on TlP4(W5O17)4 by Materials Project

TlP4(W5O17)4 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are twenty inequivalent W sites. In the first W site, W is bonded to six O atoms to form WO6 octahedra that share corners with five WO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 3–21°. There are a spread of W–O bond distances ranging from 1.84–2.05 Å. In the second W site, W is bonded to six O atoms to form WO6 octahedra that share corners with five WO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 4–14°. There are a spread of W–O bond distances ranging from 1.87–2.03 Å. In the third W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 0–15°. There are a spread of W–O bond distances ranging from 1.92–1.98 Å. In the fourth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 1–12°. There are a spread of W–O bond distances ranging from 1.90–1.99 Å. In the fifth W site, W is bonded to six O atoms to form WO6 octahedra that share corners with three WO6 octahedra and corners with three PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 2–21°. There are a spread of W–O bond distances ranging from 1.82–2.11 Å. In the sixth W site, W is bonded to six O atoms to form WO6 octahedra that share corners with three WO6 octahedra and corners with three PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 1–14°. There are a spread of W–O bond distances ranging from 1.85–2.06 Å. In the seventh W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 2–18°. There are a spread of W–O bond distances ranging from 1.86–2.04 Å. In the eighth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 1–13°. There are a spread of W–O bond distances ranging from 1.87–2.02 Å. In the ninth W site, W is bonded to six O atoms to form WO6 octahedra that share corners with five WO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 6–21°. There are a spread of W–O bond distances ranging from 1.85–2.10 Å. In the tenth W site, W is bonded to six O atoms to form WO6 octahedra that share corners with five WO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 5–14°. There are a spread of W–O bond distances ranging from 1.86–2.05 Å. In the eleventh W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 0–14°. There are a spread of W–O bond distances ranging from 1.91–1.98 Å. In the twelfth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 2–14°. There are a spread of W–O bond distances ranging from 1.92–1.96 Å. In the thirteenth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 1–14°. There are a spread of W–O bond distances ranging from 1.90–1.99 Å. In the fourteenth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 0–14°. There are a spread of W–O bond distances ranging from 1.91–2.01 Å. In the fifteenth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 2–16°. There are a spread of W–O bond distances ranging from 1.89–2.03 Å. In the sixteenth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 0–13°. There are a spread of W–O bond distances ranging from 1.92–1.98 Å. In the seventeenth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 2–21°. There are a spread of W–O bond distances ranging from 1.86–2.09 Å. In the eighteenth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 1–14°. There are a spread of W–O bond distances ranging from 1.88–2.01 Å. In the nineteenth W site, W is bonded to six O atoms to form WO6 octahedra that share corners with three WO6 octahedra and corners with three PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 2–17°. There are a spread of W–O bond distances ranging from 1.82–2.08 Å. In the twentieth W site, W is bonded to six O atoms to form WO6 octahedra that share corners with three WO6 octahedra and corners with three PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 1–13°. There are a spread of W–O bond distances ranging from 1.85–2.06 Å. Tl is bonded in a 2-coordinate geometry to two O atoms. There are one shorter (2.64 Å) and one longer (2.69 Å) Tl–O bond lengths. There are four inequivalent P sites. In the first P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with four WO6 octahedra. The corner-sharing octahedra tilt angles range from 9–22°. There is two shorter (1.53 Å) and two longer (1.54 Å) P–O bond length. In the second P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with four WO6 octahedra. The corner-sharing octahedra tilt angles range from 10–23°. All P–O bond lengths are 1.54 Å. In the third P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with four WO6 octahedra. The corner-sharing octahedra tilt angles range from 8–28°. There are a spread of P–O bond distances ranging from 1.53–1.56 Å. In the fourth P site, P is bonded to four O atoms to form PO4 tetrahedra that share corners with four WO6 octahedra. The corner-sharing octahedra tilt angles range from 9–23°. There is three shorter (1.54 Å) and one longer (1.55 Å) P–O bond length. There are sixty-eight inequivalent O sites. In the first O site, O is bonded in a linear geometry to two W atoms. In the second O site, O is bonded in a linear geometry to two W atoms. In the third O site, O is bonded in a linear geometry to two W atoms. In the fourth O site, O is bonded in a linear geometry to two W atoms. In the fifth O site, O is bonded in a linear geometry to two W atoms. In the sixth O site, O is bonded in a linear geometry to two W atoms. In the seventh O site, O is bonded in a linear geometry to two W atoms. In the eighth O site, O is bonded in a linear geometry to two W atoms. In the ninth O site, O is bonded in a linear geometry to two W atoms. In the tenth O site, O is bonded in a linear geometry to two W atoms. In the eleventh O site, O is bonded in a linear geometry to two W atoms. In the twelfth O site, O is bonded in a linear geometry to two W atoms. In the thirteenth O site, O is bonded in a bent 150 degrees geometry to two W atoms. In the fourteenth O site, O is bonded in a linear geometry to two W atoms. In the fifteenth O site, O is bonded in a linear geometry to two W atoms. In the sixteenth O site, O is bonded in a linear geometry to two W atoms. In the seventeenth O site, O is bonded in a linear geometry to two W atoms. In the eighteenth O site, O is bonded in a linear geometry to two W atoms. In the nineteenth O site, O is bonded in a bent 150 degrees geometry to two W atoms. In the twentieth O site, O is bonded in a linear geometry to two W atoms. In the twenty-first O site, O is bonded in a linear geometry to two W atoms. In the twenty-second O site, O is bonded in a linear geometry to two W atoms. In the twenty-third O site, O is bonded in a linear geometry to one W and one P atom. In the twenty-fourth O site, O is bonded in a linear geometry to one W and one P atom. In the twenty-fifth O site, O is bonded in a distorted T-shaped geometry to one W, one Tl, and one P atom. In the twenty-sixth O site, O is bonded in a linear geometry to one W and one P atom. In the twenty-seventh O site, O is bonded in a bent 150 degrees geometry to one W and one P atom. In the twenty-eighth O site, O is bonded in a bent 150 degrees geometry to one W and one P atom. In the twenty-ninth O site, O is bonded in a linear geometry to two W atoms. In the thirtieth O site, O is bonded in a linear geometry to two W atoms. In the thirty-first O site, O is bonded in a bent 150 degrees geometry to one W and one P atom. In the thirty-second O site, O is bonded in a bent 150 degrees geometry to one W and one P atom. In the thirty-third O site, O is bonded in a linear geometry to two W atoms. In the thirty-fourth O site, O is bonded in a linear geometry to two W atoms. In the thirty-fifth O site, O is bonded in a linear geometry to two W atoms. In the thirty-sixth O site, O is bonded in a linear geometry to two W atoms. In the thirty-seventh O site, O is bonded in a linear geometry to one W and one P atom. In the thirty-eighth O site, O is bonded in a 2-coordinate geometry to one W and one P atom. In the thirty-ninth O site, O is bonded in a linear geometry to two W atoms. In the fortieth O site, O is bonded in a linear geometry to two W atoms. In the forty-first O site, O is bonded in a distorted bent 150 degrees geometry to one W and one P atom. In the forty-second O site, O is bonded in a bent 150 degrees geometry to one W and one P atom. In the forty-third O site, O is bonded in a linear geometry to two W atoms. In the forty-fourth O site, O is bonded in a linear geometry to two W atoms. In the forty-fifth O site, O is bonded in a linear geometry to two W atoms. In the forty-sixth O site, O is bonded in a linear geometry to two W atoms. In the forty-seventh O site, O is bonded in a linear geometry to two W atoms. In the forty-eighth O site, O is bonded in a linear geometry to two W atoms. In the forty-ninth O site, O is bonded in a linear geometry to two W atoms. In the fiftieth O site, O is bonded in a linear geometry to two W atoms. In the fifty-first O site, O is bonded in a distorted linear geometry to one W and one P atom. In the fifty-second O site, O is bonded in a linear geometry to one W and one P atom. In the fifty-third O site, O is bonded in a 1-coordinate geometry to one W, one Tl, and one P atom. In the fifty-fourth O site, O is bonded in a bent 150 degrees geometry to one W and one P atom. In the fifty-fifth O site, O is bonded in a linear geometry to two W atoms. In the fifty-sixth O site, O is bonded in a linear geometry to two W atoms. In the fifty-seventh O site, O is bonded in a linear geometry to two W atoms. In the fifty-eighth O site, O is bonded in a linear geometry to two W atoms. In the fifty-ninth O site, O is bonded in a bent 150 degrees geometry to two W atoms. In the sixtieth O site, O is bonded in a linear geometry to two W atoms. In the sixty-first O site, O is bonded in a linear geometry to two W atoms. In the sixty-second O site, O is bonded in a linear geometry to two W atoms. In the sixty-third O site, O is bonded in a linear geometry to two W atoms. In the sixty-fourth O site, O is bonded in a linear geometry to two W atoms. In the sixty-fifth O site, O is bonded in a linear geometry to two W atoms. In the sixty-sixth O site, O is bonded in a linear geometry to two W atoms. In the sixty-seventh O site, O is bonded in a linear geometry to two W atoms. In the sixty-eighth O site, O is bonded in a linear geometry to two W atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on CrN2 by Materials Project

CrN2 is High (Orthorhombic) Tridymite-like structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are twenty-four inequivalent Cr6+ sites. In the first Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.68–1.81 Å. In the second Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.68–1.81 Å. In the third Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.68–1.80 Å. In the fourth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.66–1.78 Å. In the fifth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.65–1.78 Å. In the sixth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.65–1.78 Å. In the seventh Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.66–1.78 Å. In the eighth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.68–1.81 Å. In the ninth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.65–1.78 Å. In the tenth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.68–1.81 Å. In the eleventh Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.66–1.78 Å. In the twelfth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.68–1.81 Å. In the thirteenth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.65–1.78 Å. In the fourteenth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.66–1.78 Å. In the fifteenth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.66–1.78 Å. In the sixteenth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.68–1.81 Å. In the seventeenth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.68–1.80 Å. In the eighteenth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.68–1.81 Å. In the nineteenth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.65–1.78 Å. In the twentieth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.68–1.80 Å. In the twenty-first Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.66–1.78 Å. In the twenty-second Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.68–1.81 Å. In the twenty-third Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.65–1.78 Å. In the twenty-fourth Cr6+ site, Cr6+ is bonded to four N3- atoms to form corner-sharing CrN4 tetrahedra. There are a spread of Cr–N bond distances ranging from 1.68–1.81 Å. There are forty-eight inequivalent N3- sites. In the first N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the second N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the third N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the fourth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the fifth N3- site, N3- is bonded in a bent 150 degrees geometry to two Cr6+ atoms. In the sixth N3- site, N3- is bonded in a bent 150 degrees geometry to two Cr6+ atoms. In the seventh N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the eighth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the ninth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the tenth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the eleventh N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the twelfth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the thirteenth N3- site, N3- is bonded in a bent 150 degrees geometry to two Cr6+ atoms. In the fourteenth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the fifteenth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the sixteenth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the seventeenth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the eighteenth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the nineteenth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the twentieth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the twenty-first N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the twenty-second N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the twenty-third N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the twenty-fourth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the twenty-fifth N3- site, N3- is bonded in a bent 150 degrees geometry to two Cr6+ atoms. In the twenty-sixth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the twenty-seventh N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the twenty-eighth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the twenty-ninth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the thirtieth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the thirty-first N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the thirty-second N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the thirty-third N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the thirty-fourth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the thirty-fifth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the thirty-sixth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the thirty-seventh N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the thirty-eighth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the thirty-ninth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the fortieth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the forty-first N3- site, N3- is bonded in a bent 150 degrees geometry to two Cr6+ atoms. In the forty-second N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the forty-third N3- site, N3- is bonded in a bent 150 degrees geometry to two Cr6+ atoms. In the forty-fourth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the forty-fifth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the forty-sixth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the forty-seventh N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms. In the forty-eighth N3- site, N3- is bonded in a linear geometry to two Cr6+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Zn(W18O49)2 by Materials Project

Zn(W18O49)2 crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are eighteen inequivalent W sites. In the first W site, W is bonded to six O atoms to form WO6 octahedra that share corners with six WO6 octahedra and an edgeedge with one WO7 pentagonal bipyramid. The corner-sharing octahedra tilt angles range from 9–38°. There are a spread of W–O bond distances ranging from 1.82–2.15 Å. In the second W site, W is bonded to six O atoms to form WO6 octahedra that share corners with six WO6 octahedra and an edgeedge with one WO7 pentagonal bipyramid. The corner-sharing octahedra tilt angles range from 9–38°. There are a spread of W–O bond distances ranging from 1.82–2.13 Å. In the third W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 6–27°. There are a spread of W–O bond distances ranging from 1.84–2.06 Å. In the fourth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 6–27°. There are a spread of W–O bond distances ranging from 1.84–2.07 Å. In the fifth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 3–49°. There are a spread of W–O bond distances ranging from 1.93–2.22 Å. In the sixth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 2–49°. There are a spread of W–O bond distances ranging from 1.93–2.23 Å. In the seventh W site, W is bonded to six O atoms to form WO6 octahedra that share corners with six WO6 octahedra and an edgeedge with one WO7 pentagonal bipyramid. The corner-sharing octahedra tilt angles range from 6–37°. There are a spread of W–O bond distances ranging from 1.83–2.09 Å. In the eighth W site, W is bonded to six O atoms to form WO6 octahedra that share corners with six WO6 octahedra and an edgeedge with one WO7 pentagonal bipyramid. The corner-sharing octahedra tilt angles range from 5–37°. There are a spread of W–O bond distances ranging from 1.83–2.05 Å. In the ninth W site, W is bonded to seven O atoms to form WO7 pentagonal bipyramids that share corners with two equivalent WO7 pentagonal bipyramids and edges with five WO6 octahedra. There are a spread of W–O bond distances ranging from 1.93–2.13 Å. In the tenth W site, W is bonded to seven O atoms to form WO7 pentagonal bipyramids that share corners with two equivalent WO7 pentagonal bipyramids and edges with five WO6 octahedra. There are a spread of W–O bond distances ranging from 1.93–2.12 Å. In the eleventh W site, W is bonded to six O atoms to form WO6 octahedra that share corners with six WO6 octahedra and an edgeedge with one WO7 pentagonal bipyramid. The corner-sharing octahedra tilt angles range from 1–38°. There are a spread of W–O bond distances ranging from 1.93–2.09 Å. In the twelfth W site, W is bonded to six O atoms to form WO6 octahedra that share corners with six WO6 octahedra and an edgeedge with one WO7 pentagonal bipyramid. The corner-sharing octahedra tilt angles range from 1–36°. There are a spread of W–O bond distances ranging from 1.93–2.12 Å. In the thirteenth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 1–15°. There are a spread of W–O bond distances ranging from 1.87–2.04 Å. In the fourteenth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 4–26°. There are a spread of W–O bond distances ranging from 1.83–2.11 Å. In the fifteenth W site, W is bonded to six O atoms to form WO6 octahedra that share corners with six WO6 octahedra and an edgeedge with one WO7 pentagonal bipyramid. The corner-sharing octahedra tilt angles range from 4–38°. There are a spread of W–O bond distances ranging from 1.85–2.07 Å. In the sixteenth W site, W is bonded to six O atoms to form WO6 octahedra that share corners with six WO6 octahedra and an edgeedge with one WO7 pentagonal bipyramid. The corner-sharing octahedra tilt angles range from 6–38°. There are a spread of W–O bond distances ranging from 1.84–2.10 Å. In the seventeenth W site, W is bonded to six O atoms to form WO6 octahedra that share corners with six WO6 octahedra, an edgeedge with one WO6 octahedra, and an edgeedge with one WO7 pentagonal bipyramid. The corner-sharing octahedra tilt angles range from 1–49°. There are a spread of W–O bond distances ranging from 1.93–2.08 Å. In the eighteenth W site, W is bonded to six O atoms to form WO6 octahedra that share corners with six WO6 octahedra, an edgeedge with one WO6 octahedra, and an edgeedge with one WO7 pentagonal bipyramid. The corner-sharing octahedra tilt angles range from 1–49°. There are a spread of W–O bond distances ranging from 1.93–2.09 Å. Zn is bonded in a 4-coordinate geometry to four O atoms. There are a spread of Zn–O bond distances ranging from 2.00–2.26 Å. There are sixty-one inequivalent O sites. In the first O site, O is bonded in a linear geometry to two W atoms. In the second O site, O is bonded in a linear geometry to two equivalent W atoms. In the third O site, O is bonded in a linear geometry to two equivalent W atoms. In the fourth O site, O is bonded in a linear geometry to two equivalent W atoms. In the fifth O site, O is bonded in a distorted trigonal planar geometry to three W atoms. In the sixth O site, O is bonded in a distorted trigonal planar geometry to three W atoms. In the seventh O site, O is bonded in a linear geometry to two equivalent W atoms. In the eighth O site, O is bonded in a linear geometry to two equivalent W atoms. In the ninth O site, O is bonded in a linear geometry to two equivalent W atoms. In the tenth O site, O is bonded in a linear geometry to two equivalent W atoms. In the eleventh O site, O is bonded in a linear geometry to two W atoms. In the twelfth O site, O is bonded in a linear geometry to two W atoms. In the thirteenth O site, O is bonded in a linear geometry to two W atoms. In the fourteenth O site, O is bonded in a linear geometry to two W atoms. In the fifteenth O site, O is bonded in a linear geometry to two W atoms. In the sixteenth O site, O is bonded in a distorted trigonal planar geometry to three W atoms. In the seventeenth O site, O is bonded in a distorted trigonal planar geometry to three W atoms. In the eighteenth O site, O is bonded in a linear geometry to two equivalent W atoms. In the nineteenth O site, O is bonded in a linear geometry to two equivalent W atoms. In the twentieth O site, O is bonded in a linear geometry to two equivalent W atoms. In the twenty-first O site, O is bonded in a linear geometry to two equivalent W atoms. In the twenty-second O site, O is bonded in a distorted trigonal planar geometry to three W atoms. In the twenty-third O site, O is bonded in a distorted trigonal planar geometry to three W atoms. In the twenty-fourth O site, O is bonded in a linear geometry to two equivalent W atoms. In the twenty-fifth O site, O is bonded in a linear geometry to two equivalent W atoms. In the twenty-sixth O site, O is bonded in a T-shaped geometry to two equivalent W and one Zn atom. In the twenty-seventh O site, O is bonded in a linear geometry to two equivalent W atoms. In the twenty-eighth O site, O is bonded in a linear geometry to two equivalent W atoms. In the twenty-ninth O site, O is bonded in a linear geometry to two equivalent W atoms. In the thirtieth O site, O is bonded in a linear geometry to two equivalent W atoms. In the thirty-first O site, O is bonded in a linear geometry to two equivalent W atoms. In the thirty-second O site, O is bonded in a distorted trigonal non-coplanar geometry to three W atoms. In the thirty-third O site, O is bonded in a distorted trigonal non-coplanar geometry to three W atoms. In the thirty-fourth O site, O is bonded in a linear geometry to two W atoms. In the thirty-fifth O site, O is bonded in a linear geometry to two W atoms. In the thirty-sixth O site, O is bonded in a linear geometry to two W atoms. In the thirty-seventh O site, O is bonded in a distorted T-shaped geometry to two W and one Zn atom. In the thirty-eighth O site, O is bonded in a linear geometry to two equivalent W atoms. In the thirty-ninth O site, O is bonded in a linear geometry to two equivalent W atoms. In the fortieth O site, O is bonded in a linear geometry to two equivalent W atoms. In the forty-first O site, O is bonded in a bent 150 degrees geometry to two W atoms. In the forty-second O site, O is bonded in a bent 150 degrees geometry to two W atoms. In the forty-third O site, O is bonded in a linear geometry to two W atoms. In the forty-fourth O site, O is bonded in a linear geometry to two W atoms. In the forty-fifth O site, O is bonded in a linear geometry to two equivalent W atoms. In the forty-sixth O site, O is bonded in a linear geometry to two equivalent W atoms. In the forty-seventh O site, O is bonded in a linear geometry to two equivalent W atoms. In the forty-eighth O site, O is bonded in a linear geometry to two equivalent W atoms. In the forty-ninth O site, O is bonded in a linear geometry to two equivalent W atoms. In the fiftieth O site, O is bonded in a distorted trigonal planar geometry to three W atoms. In the fifty-first O site, O is bonded in a distorted trigonal planar geometry to three W atoms. In the fifty-second O site, O is bonded in a distorted trigonal non-coplanar geometry to three W atoms. In the fifty-third O site, O is bonded in a distorted trigonal non-coplanar geometry to three W atoms. In the fifty-fourth O site, O is bonded in a bent 150 degrees geometry to two W atoms. In the fifty-fifth O site, O is bonded in a bent 150 degrees geometry to two W atoms. In the fifty-sixth O site, O is bonded in a bent 150 degrees geometry to two W atoms. In the fifty-seventh O site, O is bonded in a bent 150 degrees geometry to two W atoms. In the fifty-eighth O site, O is bonded in a linear geometry to two equivalent W atoms. In the fifty-ninth O site, O is bonded in a linear geometry to two equivalent W atoms. In the sixtieth O site, O is bonded in a T-shaped geometry to two equivalent W and one Zn atom. In the sixty-first O site, O is bonded in a linear geometry to two W atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on W25O73 by Materials Project

W25O73 is alpha Rhenium trioxide-like structured and crystallizes in the monoclinic P2/c space group. The structure is three-dimensional. there are thirteen inequivalent W sites. In the first W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 0–6°. There are a spread of W–O bond distances ranging from 1.86–2.04 Å. In the second W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 1–6°. There are a spread of W–O bond distances ranging from 1.89–2.01 Å. In the third W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 2–10°. There are a spread of W–O bond distances ranging from 1.84–2.09 Å. In the fourth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 1–10°. There are a spread of W–O bond distances ranging from 1.84–2.09 Å. In the fifth W site, W is bonded to six O atoms to form a mixture of distorted edge and corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 2–32°. There are a spread of W–O bond distances ranging from 1.83–2.19 Å. In the sixth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. There are a spread of W–O bond distances ranging from 1.89–2.01 Å. In the seventh W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of W–O bond distances ranging from 1.89–1.97 Å. In the eighth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 1–10°. There are a spread of W–O bond distances ranging from 1.86–2.08 Å. In the ninth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of W–O bond distances ranging from 1.89–1.97 Å. In the tenth W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 2–9°. There are a spread of W–O bond distances ranging from 1.86–2.06 Å. In the eleventh W site, W is bonded to six O atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. There are a spread of W–O bond distances ranging from 1.88–2.00 Å. In the twelfth W site, W is bonded to six O atoms to form a mixture of edge and corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 1–32°. There are a spread of W–O bond distances ranging from 1.82–2.18 Å. In the thirteenth W site, W is bonded to six O atoms to form a mixture of edge and corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 7–27°. There are a spread of W–O bond distances ranging from 1.84–2.10 Å. There are thirty-seven inequivalent O sites. In the first O site, O is bonded in a linear geometry to two W atoms. In the second O site, O is bonded in a linear geometry to two W atoms. In the third O site, O is bonded in a linear geometry to two equivalent W atoms. In the fourth O site, O is bonded in a linear geometry to two W atoms. In the fifth O site, O is bonded in a linear geometry to two W atoms. In the sixth O site, O is bonded in a linear geometry to two W atoms. In the seventh O site, O is bonded in a linear geometry to two W atoms. In the eighth O site, O is bonded in a linear geometry to two equivalent W atoms. In the ninth O site, O is bonded in a linear 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 linear geometry to two equivalent W atoms. In the twelfth O site, O is bonded in a linear geometry to two W atoms. In the thirteenth O site, O is bonded in a linear geometry to two equivalent W atoms. In the fourteenth O site, O is bonded in a linear geometry to two equivalent W atoms. In the fifteenth O site, O is bonded in a linear geometry to two W atoms. In the sixteenth O site, O is bonded in a linear geometry to two W atoms. In the seventeenth O site, O is bonded in a linear geometry to two W atoms. In the eighteenth O site, O is bonded in a linear geometry to two W atoms. In the nineteenth O site, O is bonded in a linear geometry to two equivalent W atoms. In the twentieth O site, O is bonded in a linear geometry to two W atoms. In the twenty-first O site, O is bonded in a linear geometry to two W atoms. In the twenty-second O site, O is bonded in a linear geometry to two equivalent W atoms. In the twenty-third O site, O is bonded in a linear geometry to two W atoms. In the twenty-fourth O site, O is bonded in a linear geometry to two W atoms. In the twenty-fifth O site, O is bonded in a distorted trigonal non-coplanar geometry to three W atoms. In the twenty-sixth O site, O is bonded in a linear geometry to two equivalent W atoms. In the twenty-seventh O site, O is bonded in a linear geometry to two W atoms. In the twenty-eighth O site, O is bonded in a distorted T-shaped geometry to three W atoms. In the twenty-ninth O site, O is bonded in a linear geometry to two W atoms. In the thirtieth O site, O is bonded in a linear geometry to two equivalent W atoms. In the thirty-first O site, O is bonded in a linear geometry to two equivalent W atoms. In the thirty-second O site, O is bonded in a linear geometry to two equivalent W atoms. In the thirty-third O site, O is bonded in a linear geometry to two W atoms. In the thirty-fourth O site, O is bonded in a linear geometry to two W atoms. In the thirty-fifth O site, O is bonded in a linear geometry to two W atoms. In the thirty-sixth O site, O is bonded in a linear geometry to two equivalent W atoms. In the thirty-seventh O site, O is bonded in a linear geometry to two equivalent W atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Nb20(O13F7)3 by Materials Project

Nb20(O13F7)3 crystallizes in the orthorhombic Pmmm space group. The structure is three-dimensional. there are eleven inequivalent Nb+4.95+ sites. In the first Nb+4.95+ site, Nb+4.95+ is bonded to four O2- and two F1- atoms to form corner-sharing NbO4F2 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (1.94 Å) and two longer (2.07 Å) Nb–O bond lengths. Both Nb–F bond lengths are 2.04 Å. In the second Nb+4.95+ site, Nb+4.95+ is bonded to three O2- and three F1- atoms to form corner-sharing NbO3F3 octahedra. The corner-sharing octahedra tilt angles range from 0–16°. There is one shorter (1.79 Å) and two longer (1.96 Å) Nb–O bond length. There are two shorter (2.08 Å) and one longer (2.18 Å) Nb–F bond lengths. In the third Nb+4.95+ site, Nb+4.95+ is bonded to four O2- and two equivalent F1- atoms to form corner-sharing NbO4F2 octahedra. The corner-sharing octahedra tilt angles range from 0–15°. There are a spread of Nb–O bond distances ranging from 1.81–2.21 Å. Both Nb–F bond lengths are 2.08 Å. In the fourth Nb+4.95+ site, Nb+4.95+ is bonded to four O2- and two equivalent F1- atoms to form corner-sharing NbO4F2 octahedra. The corner-sharing octahedra tilt angles range from 0–15°. There are a spread of Nb–O bond distances ranging from 1.80–2.20 Å. Both Nb–F bond lengths are 2.08 Å. In the fifth Nb+4.95+ site, Nb+4.95+ is bonded to four O2- and two equivalent F1- atoms to form distorted corner-sharing NbO4F2 octahedra. The corner-sharing octahedra tilt angles range from 0–16°. There are a spread of Nb–O bond distances ranging from 1.79–2.21 Å. Both Nb–F bond lengths are 2.08 Å. In the sixth Nb+4.95+ site, Nb+4.95+ is bonded to four O2- and two equivalent F1- atoms to form corner-sharing NbO4F2 octahedra. The corner-sharing octahedra tilt angles range from 0–15°. There are a spread of Nb–O bond distances ranging from 1.80–2.21 Å. Both Nb–F bond lengths are 2.08 Å. In the seventh Nb+4.95+ site, Nb+4.95+ is bonded to four O2- and two equivalent F1- atoms to form corner-sharing NbO4F2 octahedra. The corner-sharing octahedra tilt angles range from 0–15°. There are a spread of Nb–O bond distances ranging from 1.81–2.20 Å. Both Nb–F bond lengths are 2.08 Å. In the eighth Nb+4.95+ site, Nb+4.95+ is bonded to four O2- and two equivalent F1- atoms to form corner-sharing NbO4F2 octahedra. The corner-sharing octahedra tilt angles range from 0–14°. There are a spread of Nb–O bond distances ranging from 1.81–2.20 Å. Both Nb–F bond lengths are 2.07 Å. In the ninth Nb+4.95+ site, Nb+4.95+ is bonded to four O2- and two equivalent F1- atoms to form corner-sharing NbO4F2 octahedra. The corner-sharing octahedra tilt angles range from 0–12°. There are a spread of Nb–O bond distances ranging from 1.84–2.19 Å. Both Nb–F bond lengths are 2.07 Å. In the tenth Nb+4.95+ site, Nb+4.95+ is bonded to four O2- and two equivalent F1- atoms to form corner-sharing NbO4F2 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. There are a spread of Nb–O bond distances ranging from 1.89–2.14 Å. Both Nb–F bond lengths are 2.07 Å. In the eleventh Nb+4.95+ site, Nb+4.95+ is bonded to four O2- and two equivalent F1- atoms to form corner-sharing NbO4F2 octahedra. The corner-sharing octahedral tilt angles are 0°. There is two shorter (1.94 Å) and two longer (2.02 Å) Nb–O bond length. Both Nb–F bond lengths are 2.07 Å. There are twenty-one inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted linear geometry to two Nb+4.95+ atoms. In the second O2- site, O2- is bonded in a distorted linear geometry to two Nb+4.95+ atoms. In the third O2- site, O2- is bonded in a distorted linear geometry to two Nb+4.95+ atoms. In the fourth O2- site, O2- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the fifth O2- site, O2- is bonded in a distorted linear geometry to two Nb+4.95+ atoms. In the sixth O2- site, O2- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the seventh O2- site, O2- is bonded in a distorted linear geometry to two Nb+4.95+ atoms. In the eighth O2- site, O2- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the ninth O2- site, O2- is bonded in a distorted linear geometry to two Nb+4.95+ atoms. In the tenth O2- site, O2- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the eleventh O2- site, O2- is bonded in a distorted linear geometry to two Nb+4.95+ atoms. In the twelfth O2- site, O2- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the thirteenth O2- site, O2- is bonded in a linear geometry to two Nb+4.95+ atoms. In the fourteenth O2- site, O2- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the fifteenth O2- site, O2- is bonded in a linear geometry to two Nb+4.95+ atoms. In the sixteenth O2- site, O2- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the seventeenth O2- site, O2- is bonded in a distorted linear geometry to two equivalent Nb+4.95+ atoms. In the eighteenth O2- site, O2- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the nineteenth O2- site, O2- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the twentieth O2- site, O2- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the twenty-first O2- site, O2- is bonded in a distorted linear geometry to two equivalent Nb+4.95+ atoms. There are twelve inequivalent F1- sites. In the first F1- site, F1- is bonded in a linear geometry to two Nb+4.95+ atoms. The F–Nb bond length is 2.18 Å. In the second F1- site, F1- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the third F1- site, F1- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the fourth F1- site, F1- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the fifth F1- site, F1- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the sixth F1- site, F1- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the seventh F1- site, F1- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the eighth F1- site, F1- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the ninth F1- site, F1- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the tenth F1- site, F1- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the eleventh F1- site, F1- is bonded in a linear geometry to two equivalent Nb+4.95+ atoms. In the twelfth F1- site, F1- is bonded in a linear geometry to two Nb+4.95+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Os5C17O16 by Materials Project

Os5C17O16 crystallizes in the triclinic P-1 space group. The structure is zero-dimensional and consists of four Os5C17O16 clusters. In two of the Os5C17O16 clusters, there are five inequivalent Os2- sites. In the first Os2- site, Os2- is bonded to five C+2.47+ atoms to form corner-sharing OsC5 trigonal bipyramids. There are a spread of Os–C bond distances ranging from 1.93–2.26 Å. In the second Os2- site, Os2- is bonded in a distorted rectangular see-saw-like geometry to four C+2.47+ atoms. There are a spread of Os–C bond distances ranging from 1.90–2.11 Å. In the third Os2- site, Os2- is bonded in a rectangular see-saw-like geometry to four C+2.47+ atoms. There is three shorter (1.92 Å) and one longer (2.01 Å) Os–C bond length. In the fourth Os2- site, Os2- is bonded to four C+2.47+ atoms to form distorted corner-sharing OsC4 trigonal pyramids. There are a spread of Os–C bond distances ranging from 1.91–2.02 Å. In the fifth Os2- site, Os2- is bonded in a distorted rectangular see-saw-like geometry to four C+2.47+ atoms. There are a spread of Os–C bond distances ranging from 1.90–2.11 Å. There are seventeen inequivalent C+2.47+ sites. In the first C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the second C+2.47+ site, C+2.47+ is bonded in a linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.17 Å. In the third C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.15 Å. In the fourth C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the fifth C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.17 Å. In the sixth C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.15 Å. In the seventh C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the eighth C+2.47+ site, C+2.47+ is bonded in a linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the ninth C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the tenth C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.17 Å. In the eleventh C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the twelfth C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.17 Å. In the thirteenth C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the fourteenth C+2.47+ site, C+2.47+ is bonded in a linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the fifteenth C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.17 Å. In the sixteenth C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.17 Å. In the seventeenth C+2.47+ site, C+2.47+ is bonded in a trigonal bipyramidal geometry to five Os2- atoms. There are sixteen inequivalent O2- sites. In the first O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the second O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the third O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the fourth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the fifth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the sixth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the seventh O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the eighth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the ninth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the tenth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the eleventh O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the twelfth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the thirteenth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the fourteenth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the fifteenth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the sixteenth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In two of the Os5C17O16 clusters, there are five inequivalent Os2- sites. In the first Os2- site, Os2- is bonded in a rectangular see-saw-like geometry to four C+2.47+ atoms. There are a spread of Os–C bond distances ranging from 1.90–2.11 Å. In the second Os2- site, Os2- is bonded in a rectangular see-saw-like geometry to four C+2.47+ atoms. There are a spread of Os–C bond distances ranging from 1.91–2.00 Å. In the third Os2- site, Os2- is bonded in a rectangular see-saw-like geometry to four C+2.47+ atoms. There are a spread of Os–C bond distances ranging from 1.90–2.12 Å. In the fourth Os2- site, Os2- is bonded in a trigonal bipyramidal geometry to five C+2.47+ atoms. There are a spread of Os–C bond distances ranging from 1.93–2.26 Å. In the fifth Os2- site, Os2- is bonded in a distorted rectangular see-saw-like geometry to four C+2.47+ atoms. There are a spread of Os–C bond distances ranging from 1.91–2.01 Å. There are seventeen inequivalent C+2.47+ sites. In the first C+2.47+ site, C+2.47+ is bonded in a linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the second C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.17 Å. In the third C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the fourth C+2.47+ site, C+2.47+ is bonded in a linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the fifth C+2.47+ site, C+2.47+ is bonded in a linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the sixth C+2.47+ site, C+2.47+ is bonded in a linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the seventh C+2.47+ site, C+2.47+ is bonded in a linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the eighth C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the ninth C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.15 Å. In the tenth C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the eleventh C+2.47+ site, C+2.47+ is bonded in a linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.17 Å. In the twelfth C+2.47+ site, C+2.47+ is bonded in a linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.17 Å. In the thirteenth C+2.47+ site, C+2.47+ is bonded in a trigonal bipyramidal geometry to five Os2- atoms. In the fourteenth C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.15 Å. In the fifteenth C+2.47+ site, C+2.47+ is bonded in a distorted linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.16 Å. In the sixteenth C+2.47+ site, C+2.47+ is bonded in a linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.17 Å. In the seventeenth C+2.47+ site, C+2.47+ is bonded in a linear geometry to one Os2- and one O2- atom. The C–O bond length is 1.17 Å. There are sixteen inequivalent O2- sites. In the first O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the second O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the third O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the fourth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the fifth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the sixth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the seventh O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the eighth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the ninth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the tenth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the eleventh O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the twelfth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the thirteenth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the fourteenth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the fifteenth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom. In the sixteenth O2- site, O2- is bonded in a single-bond geometry to one C+2.47+ atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on NaP4(W3O11)4 by Materials Project

NaP4(W3O11)4 crystallizes in the triclinic P1 space group. The structure is three-dimensional. Na1+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Na–O bond distances ranging from 2.42–2.72 Å. There are twelve inequivalent W+5.58+ sites. In the first W+5.58+ site, W+5.58+ is bonded to six O2- atoms to form WO6 octahedra that share corners with three WO6 octahedra and corners with three PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 0–20°. There are a spread of W–O bond distances ranging from 1.81–2.10 Å. In the second W+5.58+ site, W+5.58+ is bonded to six O2- atoms to form WO6 octahedra that share corners with three WO6 octahedra and corners with three PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 1–14°. There are a spread of W–O bond distances ranging from 1.84–2.05 Å. In the third W+5.58+ site, W+5.58+ is bonded to six O2- atoms to form WO6 octahedra that share corners with three WO6 octahedra and corners with three PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 2–17°. There are a spread of W–O bond distances ranging from 1.82–2.06 Å. In the fourth W+5.58+ site, W+5.58+ is bonded to six O2- atoms to form WO6 octahedra that share corners with three WO6 octahedra and corners with three PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 3–18°. There are a spread of W–O bond distances ranging from 1.83–2.12 Å. In the fifth W+5.58+ site, W+5.58+ is bonded to six O2- atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 0–17°. There are a spread of W–O bond distances ranging from 1.88–2.03 Å. In the sixth W+5.58+ site, W+5.58+ is bonded to six O2- atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 1–16°. There are a spread of W–O bond distances ranging from 1.87–2.02 Å. In the seventh W+5.58+ site, W+5.58+ is bonded to six O2- atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 2–17°. There are a spread of W–O bond distances ranging from 1.84–2.02 Å. In the eighth W+5.58+ site, W+5.58+ is bonded to six O2- atoms to form corner-sharing WO6 octahedra. The corner-sharing octahedra tilt angles range from 2–17°. There are a spread of W–O bond distances ranging from 1.85–2.03 Å. In the ninth W+5.58+ site, W+5.58+ is bonded to six O2- atoms to form WO6 octahedra that share corners with five WO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 4–18°. There are a spread of W–O bond distances ranging from 1.84–2.05 Å. In the tenth W+5.58+ site, W+5.58+ is bonded to six O2- atoms to form WO6 octahedra that share corners with five WO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 4–17°. There are a spread of W–O bond distances ranging from 1.84–2.07 Å. In the eleventh W+5.58+ site, W+5.58+ is bonded to six O2- atoms to form WO6 octahedra that share corners with five WO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 2–14°. There are a spread of W–O bond distances ranging from 1.85–2.03 Å. In the twelfth W+5.58+ site, W+5.58+ is bonded to six O2- atoms to form WO6 octahedra that share corners with five WO6 octahedra and a cornercorner with one PO4 tetrahedra. The corner-sharing octahedra tilt angles range from 2–20°. There are a spread of W–O bond distances ranging from 1.84–2.15 Å. There are four inequivalent P5+ sites. In the first P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four WO6 octahedra. The corner-sharing octahedra tilt angles range from 10–29°. There is three shorter (1.54 Å) and one longer (1.55 Å) P–O bond length. In the second P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four WO6 octahedra. The corner-sharing octahedra tilt angles range from 10–26°. There are a spread of P–O bond distances ranging from 1.53–1.56 Å. In the third P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four WO6 octahedra. The corner-sharing octahedra tilt angles range from 8–23°. There are a spread of P–O bond distances ranging from 1.53–1.55 Å. In the fourth P5+ site, P5+ is bonded to four O2- atoms to form PO4 tetrahedra that share corners with four WO6 octahedra. The corner-sharing octahedra tilt angles range from 10–30°. There is three shorter (1.53 Å) and one longer (1.57 Å) P–O bond length. There are forty-four inequivalent O2- sites. In the first O2- site, O2- is bonded in a 3-coordinate geometry to one Na1+, one W+5.58+, and one P5+ atom. In the second O2- site, O2- is bonded in a distorted linear geometry to one W+5.58+ and one P5+ atom. In the third O2- site, O2- is bonded in a distorted linear geometry to one W+5.58+ and one P5+ atom. In the fourth O2- site, O2- is bonded in a 1-coordinate geometry to one Na1+, one W+5.58+, and one P5+ atom. In the fifth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the sixth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the seventh O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the eighth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the ninth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the tenth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the eleventh O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the twelfth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the thirteenth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the fourteenth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the fifteenth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the sixteenth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the seventeenth O2- site, O2- is bonded in a distorted T-shaped geometry to one Na1+ and two W+5.58+ atoms. In the eighteenth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the nineteenth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the twentieth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the twenty-first O2- site, O2- is bonded in a 1-coordinate geometry to one Na1+, one W+5.58+, and one P5+ atom. In the twenty-second O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one W+5.58+ and one P5+ atom. In the twenty-third O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one W+5.58+ and one P5+ atom. In the twenty-fourth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one W+5.58+ and one P5+ atom. In the twenty-fifth O2- site, O2- is bonded in a 1-coordinate geometry to one Na1+, one W+5.58+, and one P5+ atom. In the twenty-sixth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one W+5.58+ and one P5+ atom. In the twenty-seventh O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one W+5.58+ and one P5+ atom. In the twenty-eighth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to one W+5.58+ and one P5+ atom. In the twenty-ninth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the thirtieth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the thirty-first O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the thirty-second O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the thirty-third O2- site, O2- is bonded in a 1-coordinate geometry to one Na1+, one W+5.58+, and one P5+ atom. In the thirty-fourth O2- site, O2- is bonded in a distorted linear geometry to one W+5.58+ and one P5+ atom. In the thirty-fifth O2- site, O2- is bonded in a distorted linear geometry to one W+5.58+ and one P5+ atom. In the thirty-sixth O2- site, O2- is bonded in a linear geometry to one W+5.58+ and one P5+ atom. In the thirty-seventh O2- site, O2- is bonded in a distorted T-shaped geometry to one Na1+ and two W+5.58+ atoms. In the thirty-eighth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the thirty-ninth O2- site, O2- is bonded in a distorted linear geometry to two W+5.58+ atoms. In the fortieth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two W+5.58+ atoms. In the forty-first O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the forty-second O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the forty-third O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms. In the forty-fourth O2- site, O2- is bonded in a linear geometry to two W+5.58+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ba3Na7Ti3Nb7O30 by Materials Project

Na7Ba3Ti3Nb7O30 is (Cubic) Perovskite-derived structured and crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are seven inequivalent Na1+ sites. In the first Na1+ site, Na1+ is bonded to twelve O2- atoms to form NaO12 cuboctahedra that share corners with four NaO12 cuboctahedra, corners with eight BaO12 cuboctahedra, faces with three NaO12 cuboctahedra, faces with three BaO12 cuboctahedra, faces with four TiO6 octahedra, and faces with four NbO6 octahedra. There are a spread of Na–O bond distances ranging from 2.78–2.89 Å. In the second Na1+ site, Na1+ is bonded to twelve O2- atoms to form NaO12 cuboctahedra that share corners with four BaO12 cuboctahedra, corners with eight NaO12 cuboctahedra, a faceface with one BaO12 cuboctahedra, faces with five NaO12 cuboctahedra, faces with two equivalent TiO6 octahedra, and faces with six NbO6 octahedra. There are a spread of Na–O bond distances ranging from 2.80–2.87 Å. In the third Na1+ site, Na1+ is bonded to twelve O2- atoms to form NaO12 cuboctahedra that share corners with four BaO12 cuboctahedra, corners with eight NaO12 cuboctahedra, a faceface with one BaO12 cuboctahedra, faces with five NaO12 cuboctahedra, faces with two equivalent TiO6 octahedra, and faces with six NbO6 octahedra. There are a spread of Na–O bond distances ranging from 2.80–2.87 Å. In the fourth Na1+ site, Na1+ is bonded to twelve O2- atoms to form NaO12 cuboctahedra that share corners with twelve NaO12 cuboctahedra, faces with six NaO12 cuboctahedra, and faces with eight NbO6 octahedra. There are a spread of Na–O bond distances ranging from 2.82–2.86 Å. In the fifth Na1+ site, Na1+ is bonded to twelve O2- atoms to form NaO12 cuboctahedra that share corners with two equivalent BaO12 cuboctahedra, corners with ten NaO12 cuboctahedra, a faceface with one BaO12 cuboctahedra, faces with five NaO12 cuboctahedra, and faces with eight NbO6 octahedra. There are a spread of Na–O bond distances ranging from 2.81–2.86 Å. In the sixth Na1+ site, Na1+ is bonded to twelve O2- atoms to form NaO12 cuboctahedra that share corners with twelve NaO12 cuboctahedra, faces with six NaO12 cuboctahedra, and faces with eight NbO6 octahedra. There are a spread of Na–O bond distances ranging from 2.82–2.86 Å. In the seventh Na1+ site, Na1+ is bonded to twelve O2- atoms to form NaO12 cuboctahedra that share corners with two equivalent BaO12 cuboctahedra, corners with ten NaO12 cuboctahedra, faces with six NaO12 cuboctahedra, and faces with eight NbO6 octahedra. There are a spread of Na–O bond distances ranging from 2.81–2.86 Å. There are three inequivalent Ba2+ sites. In the first Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with four BaO12 cuboctahedra, corners with eight NaO12 cuboctahedra, faces with three NaO12 cuboctahedra, faces with three BaO12 cuboctahedra, faces with four TiO6 octahedra, and faces with four NbO6 octahedra. There are a spread of Ba–O bond distances ranging from 2.78–2.91 Å. In the second Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with six NaO12 cuboctahedra, corners with six BaO12 cuboctahedra, a faceface with one NaO12 cuboctahedra, faces with five BaO12 cuboctahedra, faces with two equivalent NbO6 octahedra, and faces with six TiO6 octahedra. There are a spread of Ba–O bond distances ranging from 2.81–2.90 Å. In the third Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with six NaO12 cuboctahedra, corners with six BaO12 cuboctahedra, faces with two NaO12 cuboctahedra, faces with four BaO12 cuboctahedra, faces with two equivalent NbO6 octahedra, and faces with six TiO6 octahedra. There are a spread of Ba–O bond distances ranging from 2.80–2.90 Å. There are three inequivalent Ti4+ sites. In the first Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one NbO6 octahedra, corners with five TiO6 octahedra, faces with two equivalent NaO12 cuboctahedra, and faces with six BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Ti–O bond distances ranging from 1.97–2.06 Å. In the second Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with three TiO6 octahedra, corners with three NbO6 octahedra, faces with four NaO12 cuboctahedra, and faces with four BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Ti–O bond distances ranging from 1.96–2.08 Å. In the third Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with two NbO6 octahedra, corners with four TiO6 octahedra, faces with two equivalent NaO12 cuboctahedra, and faces with six BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Ti–O bond distances ranging from 1.95–2.06 Å. There are seven inequivalent Nb5+ sites. In the first Nb5+ site, Nb5+ is bonded to six O2- atoms to form NbO6 octahedra that share corners with three TiO6 octahedra, corners with three NbO6 octahedra, faces with four NaO12 cuboctahedra, and faces with four BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Nb–O bond distances ranging from 1.97–2.06 Å. In the second Nb5+ site, Nb5+ is bonded to six O2- atoms to form NbO6 octahedra that share a cornercorner with one TiO6 octahedra, corners with five NbO6 octahedra, and faces with eight NaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Nb–O bond distances ranging from 1.94–2.08 Å. In the third Nb5+ site, Nb5+ is bonded to six O2- atoms to form NbO6 octahedra that share corners with six NbO6 octahedra and faces with eight NaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Nb–O bond distances ranging from 2.00–2.02 Å. In the fourth Nb5+ site, Nb5+ is bonded to six O2- atoms to form NbO6 octahedra that share corners with six NbO6 octahedra and faces with eight NaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Nb–O bond distances ranging from 1.96–2.05 Å. In the fifth Nb5+ site, Nb5+ is bonded to six O2- atoms to form NbO6 octahedra that share corners with six NbO6 octahedra and faces with eight NaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Nb–O bond distances ranging from 1.99–2.02 Å. In the sixth Nb5+ site, Nb5+ is bonded to six O2- atoms to form NbO6 octahedra that share a cornercorner with one TiO6 octahedra, corners with five NbO6 octahedra, faces with two equivalent BaO12 cuboctahedra, and faces with six NaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Nb–O bond distances ranging from 1.99–2.05 Å. In the seventh Nb5+ site, Nb5+ is bonded to six O2- atoms to form NbO6 octahedra that share a cornercorner with one TiO6 octahedra, corners with five NbO6 octahedra, faces with two equivalent BaO12 cuboctahedra, and faces with six NaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Nb–O bond distances ranging from 1.97–2.03 Å. There are thirty inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted linear geometry to two equivalent Na1+, two equivalent Ba2+, one Ti4+, and one Nb5+ atom. In the second O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two Ti4+ atoms. In the third O2- site, O2- is bonded in a distorted linear geometry to two equivalent Na1+, two equivalent Ba2+, one Ti4+, and one Nb5+ atom. In the fourth O2- site, O2- is bonded to four Ba2+ and two Ti4+ atoms to form distorted edge-sharing OBa4Ti2 octahedra. In the fifth O2- site, O2- is bonded in a distorted linear geometry to four Ba2+, one Ti4+, and one Nb5+ atom. In the sixth O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two Nb5+ atoms. In the seventh O2- site, O2- is bonded in a distorted linear geometry to four Na1+, one Ti4+, and one Nb5+ atom. In the eighth O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two Nb5+ atoms. In the ninth O2- site, O2- is bonded in a distorted linear geometry to two equivalent Na1+, two equivalent Ba2+, one Ti4+, and one Nb5+ atom. In the tenth O2- site, O2- is bonded in a distorted linear geometry to two equivalent Na1+, two equivalent Ba2+, and two Ti4+ atoms. In the eleventh O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two Nb5+ atoms. In the twelfth O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two Nb5+ atoms. In the thirteenth O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two Nb5+ atoms. In the fourteenth O2- site, O2- is bonded in a distorted linear geometry to two equivalent Na1+, two equivalent Ba2+, one Ti4+, and one Nb5+ atom. In the fifteenth O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two Nb5+ atoms. In the sixteenth O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two Nb5+ atoms. In the seventeenth O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two Nb5+ atoms. In the eighteenth O2- site, O2- is bonded in a distorted linear geometry to two equivalent Na1+, two equivalent Ba2+, and two Nb5+ atoms. In the nineteenth O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two Nb5+ atoms. In the twentieth O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two Nb5+ atoms. In the twenty-first O2- site, O2- is bonded in a distorted linear geometry to one Na1+, three Ba2+, and two equivalent Ti4+ atoms. In the twenty-second O2- site, O2- is bonded in a distorted linear geometry to two Na1+, two Ba2+, and two equivalent Ti4+ atoms. In the twenty-third O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two equivalent Nb5+ atoms. In the twenty-fourth O2- site, O2- is bonded in a distorted linear geometry to one Na1+, three Ba2+, and two equivalent Ti4+ atoms. In the twenty-fifth O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two equivalent Nb5+ atoms. In the twenty-sixth O2- site, O2- is bonded in a distorted linear geometry to three Na1+, one Ba2+, and two equivalent Nb5+ atoms. In the twenty-seventh O2- site, O2- is bonded in a distorted linear geometry to two Na1+, two Ba2+, and two equivalent Nb5+ atoms. In the twenty-eighth O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two equivalent Nb5+ atoms. In the twenty-ninth O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two equivalent Nb5+ atoms. In the thirtieth O2- site, O2- is bonded in a distorted linear geometry to three Na1+, one Ba2+, and two equivalent Nb5+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ba7Na3Ti7Nb3O30 by Materials Project

Na3Ba7Ti7Nb3O30 is (Cubic) Perovskite-derived structured and crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are three inequivalent Na1+ sites. In the first Na1+ site, Na1+ is bonded to twelve O2- atoms to form NaO12 cuboctahedra that share corners with four NaO12 cuboctahedra, corners with eight BaO12 cuboctahedra, faces with three NaO12 cuboctahedra, faces with three BaO12 cuboctahedra, faces with four TiO6 octahedra, and faces with four NbO6 octahedra. There are a spread of Na–O bond distances ranging from 2.77–2.93 Å. In the second Na1+ site, Na1+ is bonded to twelve O2- atoms to form NaO12 cuboctahedra that share corners with six NaO12 cuboctahedra, corners with six BaO12 cuboctahedra, faces with two BaO12 cuboctahedra, faces with four NaO12 cuboctahedra, faces with two equivalent TiO6 octahedra, and faces with six NbO6 octahedra. There are a spread of Na–O bond distances ranging from 2.78–2.89 Å. In the third Na1+ site, Na1+ is bonded to twelve O2- atoms to form NaO12 cuboctahedra that share corners with six NaO12 cuboctahedra, corners with six BaO12 cuboctahedra, a faceface with one BaO12 cuboctahedra, faces with five NaO12 cuboctahedra, faces with two equivalent TiO6 octahedra, and faces with six NbO6 octahedra. There are a spread of Na–O bond distances ranging from 2.78–2.89 Å. There are seven inequivalent Ba2+ sites. In the first Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with four BaO12 cuboctahedra, corners with eight NaO12 cuboctahedra, faces with three NaO12 cuboctahedra, faces with three BaO12 cuboctahedra, faces with four TiO6 octahedra, and faces with four NbO6 octahedra. There are a spread of Ba–O bond distances ranging from 2.77–2.95 Å. In the second Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with two equivalent NaO12 cuboctahedra, corners with ten BaO12 cuboctahedra, faces with six BaO12 cuboctahedra, and faces with eight TiO6 octahedra. There are a spread of Ba–O bond distances ranging from 2.84–2.88 Å. In the third Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with twelve BaO12 cuboctahedra, faces with six BaO12 cuboctahedra, and faces with eight TiO6 octahedra. There are a spread of Ba–O bond distances ranging from 2.83–2.87 Å. In the fourth Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with two equivalent NaO12 cuboctahedra, corners with ten BaO12 cuboctahedra, a faceface with one NaO12 cuboctahedra, faces with five BaO12 cuboctahedra, and faces with eight TiO6 octahedra. There are a spread of Ba–O bond distances ranging from 2.82–2.88 Å. In the fifth Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with twelve BaO12 cuboctahedra, faces with six BaO12 cuboctahedra, and faces with eight TiO6 octahedra. There are a spread of Ba–O bond distances ranging from 2.83–2.87 Å. In the sixth Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with four NaO12 cuboctahedra, corners with eight BaO12 cuboctahedra, a faceface with one NaO12 cuboctahedra, faces with five BaO12 cuboctahedra, faces with two equivalent NbO6 octahedra, and faces with six TiO6 octahedra. There are a spread of Ba–O bond distances ranging from 2.81–2.90 Å. In the seventh Ba2+ site, Ba2+ is bonded to twelve O2- atoms to form BaO12 cuboctahedra that share corners with four NaO12 cuboctahedra, corners with eight BaO12 cuboctahedra, a faceface with one NaO12 cuboctahedra, faces with five BaO12 cuboctahedra, faces with two equivalent NbO6 octahedra, and faces with six TiO6 octahedra. There are a spread of Ba–O bond distances ranging from 2.82–2.90 Å. There are seven inequivalent Ti4+ sites. In the first Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one NbO6 octahedra, corners with five TiO6 octahedra, faces with two equivalent NaO12 cuboctahedra, and faces with six BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Ti–O bond distances ranging from 1.96–2.08 Å. In the second Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and faces with eight BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Ti–O bond distances ranging from 1.99–2.06 Å. In the third Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and faces with eight BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Ti–O bond distances ranging from 1.98–2.05 Å. In the fourth Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one NbO6 octahedra, corners with five TiO6 octahedra, faces with two equivalent NaO12 cuboctahedra, and faces with six BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–2°. There are a spread of Ti–O bond distances ranging from 1.96–2.06 Å. In the fifth Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with six TiO6 octahedra and faces with eight BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are four shorter (2.01 Å) and two longer (2.02 Å) Ti–O bond lengths. In the sixth Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share corners with three TiO6 octahedra, corners with three NbO6 octahedra, faces with four NaO12 cuboctahedra, and faces with four BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Ti–O bond distances ranging from 1.96–2.09 Å. In the seventh Ti4+ site, Ti4+ is bonded to six O2- atoms to form TiO6 octahedra that share a cornercorner with one NbO6 octahedra, corners with five TiO6 octahedra, and faces with eight BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Ti–O bond distances ranging from 1.95–2.09 Å. There are three inequivalent Nb5+ sites. In the first Nb5+ site, Nb5+ is bonded to six O2- atoms to form NbO6 octahedra that share corners with three TiO6 octahedra, corners with three NbO6 octahedra, faces with four NaO12 cuboctahedra, and faces with four BaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Nb–O bond distances ranging from 1.97–2.06 Å. In the second Nb5+ site, Nb5+ is bonded to six O2- atoms to form NbO6 octahedra that share corners with two TiO6 octahedra, corners with four NbO6 octahedra, faces with two equivalent BaO12 cuboctahedra, and faces with six NaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Nb–O bond distances ranging from 1.95–2.08 Å. In the third Nb5+ site, Nb5+ is bonded to six O2- atoms to form NbO6 octahedra that share a cornercorner with one TiO6 octahedra, corners with five NbO6 octahedra, faces with two equivalent BaO12 cuboctahedra, and faces with six NaO12 cuboctahedra. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Nb–O bond distances ranging from 1.98–2.05 Å. There are thirty inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted linear geometry to one Na1+, three Ba2+, and two equivalent Ti4+ atoms. In the second O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two equivalent Ti4+ atoms. In the third O2- site, O2- is bonded in a distorted linear geometry to one Na1+, three Ba2+, and two equivalent Ti4+ atoms. In the fourth O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two equivalent Ti4+ atoms. In the fifth O2- site, O2- is bonded in a distorted linear geometry to three Na1+, one Ba2+, and two equivalent Nb5+ atoms. In the sixth O2- site, O2- is bonded in a distorted linear geometry to three Na1+, one Ba2+, and two equivalent Nb5+ atoms. In the seventh O2- site, O2- is bonded in a distorted linear geometry to two equivalent Na1+, two equivalent Ba2+, one Ti4+, and one Nb5+ atom. In the eighth O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two Ti4+ atoms. In the ninth O2- site, O2- is bonded to four Ba2+ and two Ti4+ atoms to form distorted edge-sharing OBa4Ti2 octahedra. In the tenth O2- site, O2- is bonded in a distorted linear geometry to two equivalent Na1+, two equivalent Ba2+, one Ti4+, and one Nb5+ atom. In the eleventh O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two Ti4+ atoms. In the twelfth O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two Ti4+ atoms. In the thirteenth O2- site, O2- is bonded in a distorted linear geometry to two equivalent Na1+, two equivalent Ba2+, one Ti4+, and one Nb5+ atom. In the fourteenth O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two Ti4+ atoms. In the fifteenth O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two Ti4+ atoms. In the sixteenth O2- site, O2- is bonded in a distorted linear geometry to two equivalent Na1+, two equivalent Ba2+, and two Ti4+ atoms. In the seventeenth O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two Ti4+ atoms. In the eighteenth O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two Ti4+ atoms. In the nineteenth O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two Ti4+ atoms. In the twentieth O2- site, O2- is bonded in a distorted linear geometry to two equivalent Na1+, two equivalent Ba2+, one Ti4+, and one Nb5+ atom. In the twenty-first O2- site, O2- is bonded in a distorted linear geometry to two equivalent Na1+, two equivalent Ba2+, and two Nb5+ atoms. In the twenty-second O2- site, O2- is bonded in a distorted linear geometry to four Ba2+, one Ti4+, and one Nb5+ atom. In the twenty-third O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two Nb5+ atoms. In the twenty-fourth O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two Ti4+ atoms. In the twenty-fifth O2- site, O2- is bonded in a distorted linear geometry to four Na1+, one Ti4+, and one Nb5+ atom. In the twenty-sixth O2- site, O2- is bonded in a distorted linear geometry to four Na1+ and two Nb5+ atoms. In the twenty-seventh O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two equivalent Ti4+ atoms. In the twenty-eighth O2- site, O2- is bonded in a distorted linear geometry to two Na1+, two Ba2+, and two equivalent Ti4+ atoms. In the twenty-ninth O2- site, O2- is bonded in a distorted linear geometry to four Ba2+ and two equivalent Ti4+ atoms. In the thirtieth O2- site, O2- is bonded in a distorted linear geometry to two Na1+, two Ba2+, and two equivalent Nb5+ atoms.

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