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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

S U ( 2 ) principal chiral model with tensor renormalization group on a cubic lattice

We study the continuous phase transition and thermodynamic observables in the three-dimensional Euclidean S U ( 2 ) principal chiral field model with the triad tensor renormalization group and the anisotropic tensor renormalization group methods. Using these methods, we find results that are consistent with previous Monte Carlo estimates and the predicted renormalization group scaling of the magnetization close to criticality. These results bring us one step closer to studying finite-density quantum chromodynamics in four dimensions using tensor network methods. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Theoretical antiferromagnetism of ordered face-centered cubic Cr-Ni alloys

Contrary to prior calculations, the Ni-rich ordered structures of the Cr-Ni alloy system are found to be antiferromagnetic under semilocal density-functional theory. The optimization of local magnetic moments significantly increases the driving force for the formation of CrNi 2 , the only experimentally observed intermetallic phase. This structure's ab initio magnetism appears well described by a Heisenberg Hamiltonian with longitudinal spin fluctuations; itinerant Cr moments are induced only by the strength of exchange interactions. The role of magnetism at temperature is less clear and several scenarios are considered based on a review of experimental literature, specifically a failure of the theory, the existence of an overlooked magnetic phase transition, and the coupling of antiferromagnetism to chemical ordering. In conclusion, implications for related commercial and high-entropy alloys are discussed for each case.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Cubical moderators for the Neutron Target Demonstator (NTD)

Neutron capture cross sections of unstable isotopes are important for neutron induced nucleosynthesis as well as for technological applications. The traditional time-of-flight method reaches its limits once the necessary detection of the reaction products is hampered by the size (mass) of the sample. Several factors may limit the sample mass: The decay properties of radioactive isotopes interfere with the signals from the neutron capture or neutron-induced fission reactions; The limited range of charged reaction products requires a thin sample. In both cases, an increased neutron fluence at the sample position with ever improved neutron sources overcomes the lack of reaction rate. Reference proposed a combination of a radioactive beam facility, an ion storage ring and a spallation neutron source surrounded by neutron moderator. This idea is part of the LANSCE strategy to stay a worldwide leader for neutron induced research. Figure 1 shows a sketch of the proposed future setup.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Investigation of novel twinning in additive body centered cubic titanium (Fiscal Year 2024 Final Report)

This report summarizes the result of a one year seedling project to investigate unusual twinning behavior in shock loaded additive Ti5552. The twinning behavior only occurs when the β phase of Ti5553 is metastable, and it appears to be a type of double twin involving two different twin variants, first a {332}⟨113⟩ twin forms before being consumed by a specific {112}⟨111⟩ twin variant to create a 20 o . This behavior has only been detected during shock loading around incipient spall damage. The twinning is investigated by performing postmortem EBSD and PED analysis of gas-gun loaded specimens and preliminary molecular dynamics simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Y2Zr24O51 by Materials Project

Y2Zr24O51 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. there are two inequivalent Y3+ sites. In the first Y3+ site, Y3+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Y–O bond distances ranging from 2.16–2.42 Å. In the second Y3+ site, Y3+ is bonded in a 6-coordinate geometry to six O2- atoms. There are two shorter (2.09 Å) and four longer (2.37 Å) Y–O bond lengths. There are twenty-four inequivalent Zr4+ sites. In the first Zr4+ site, Zr4+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.17–2.33 Å. In the second Zr4+ site, Zr4+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.11–2.42 Å. In the third Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.10 Å) and four longer (2.44 Å) Zr–O bond lengths. In the fourth Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.46 Å. In the fifth Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.46 Å. In the sixth Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.09 Å) and four longer (2.45 Å) Zr–O bond lengths. In the seventh Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.45 Å. In the eighth Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.45 Å. In the ninth Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.45 Å. In the tenth Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.45 Å. In the eleventh Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.10–2.45 Å. In the twelfth Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.10–2.43 Å. In the thirteenth Zr4+ site, Zr4+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.20–2.27 Å. In the fourteenth Zr4+ site, Zr4+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.13–2.39 Å. In the fifteenth Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.10–2.44 Å. In the sixteenth Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.45 Å. In the seventeenth Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.45 Å. In the eighteenth Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.45 Å. In the nineteenth Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.45 Å. In the twentieth Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.45 Å. In the twenty-first Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.45 Å. In the twenty-second Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.44 Å. In the twenty-third Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.44 Å. In the twenty-fourth Zr4+ site, Zr4+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Zr–O bond distances ranging from 2.10–2.43 Å. There are fifty-one inequivalent O2- sites. In the first O2- site, O2- is bonded to two equivalent Y3+ and two equivalent Zr4+ atoms to form OY2Zr2 tetrahedra that share corners with fourteen OZr4 tetrahedra and edges with five OY2Zr2 tetrahedra. In the second O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of corner and edge-sharing OZr4 tetrahedra. In the third O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of corner and edge-sharing OZr4 tetrahedra. In the fourth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the fifth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the sixth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the seventh O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the eighth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the ninth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the tenth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the eleventh O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the twelfth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the thirteenth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the fourteenth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the fifteenth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the sixteenth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the seventeenth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the eighteenth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the nineteenth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the twentieth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the twenty-first O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the twenty-second O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the twenty-third O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the twenty-fourth O2- site, O2- is bonded to four Zr4+ atoms to form distorted OZr4 tetrahedra that share corners with sixteen OY2Zr2 tetrahedra and edges with six OZr4 tetrahedra. In the twenty-fifth O2- site, O2- is bonded to two equivalent Y3+ and two equivalent Zr4+ atoms to form distorted OY2Zr2 tetrahedra that share corners with fourteen OZr4 tetrahedra and edges with five OY2Zr2 tetrahedra. In the twenty-sixth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of corner and edge-sharing OZr4 tetrahedra. In the twenty-seventh O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the twenty-eighth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the twenty-ninth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the thirtieth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the thirty-first O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the thirty-second O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the thirty-third O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the thirty-fourth O2- site, O2- is bonded to four Zr4+ atoms to form OZr4 tetrahedra that share corners with sixteen OY2Zr2 tetrahedra and edges with six OZr4 tetrahedra. In the thirty-fifth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the thirty-sixth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the thirty-seventh O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the thirty-eighth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the thirty-ninth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the fortieth O2- site, O2- is bonded to two equivalent Y3+ and two equivalent Zr4+ atoms to form a mixture of distorted corner and edge-sharing OY2Zr2 tetrahedra. In the forty-first O2- site, O2- is bonded to two equivalent Y3+ and two equivalent Zr4+ atoms to form OY2Zr2 tetrahedra that share corners with twelve OZr4 tetrahedra and edges with six OY4 tetrahedra. In the forty-second O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the forty-third O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the forty-fourth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the forty-fifth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the forty-sixth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the forty-seventh O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the forty-eighth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the forty-ninth O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra. In the fiftieth O2- site, O2- is bonded to four Y3+ atoms to form a mixture of corner and edge-sharing OY4 tetrahedra. In the fifty-first O2- site, O2- is bonded to four Zr4+ atoms to form a mixture of distorted corner and edge-sharing OZr4 tetrahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Y6Zr22O53 by Materials Project

Y6Zr22O53 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. there are six inequivalent Y sites. In the first Y site, Y is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Y–O bond distances ranging from 2.20–2.60 Å. In the second Y site, Y is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Y–O bond distances ranging from 2.22–2.60 Å. In the third Y site, Y is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Y–O bond distances ranging from 2.13–2.45 Å. In the fourth Y site, Y is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Y–O bond distances ranging from 2.22–2.60 Å. In the fifth Y site, Y is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Y–O bond distances ranging from 2.12–2.44 Å. In the sixth Y site, Y is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Y–O bond distances ranging from 2.07–2.40 Å. There are twenty-two inequivalent Zr sites. In the first Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.12–2.43 Å. In the second Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.08–2.47 Å. In the third Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.08–2.45 Å. In the fourth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.08–2.48 Å. In the fifth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.08–2.47 Å. In the sixth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.08–2.47 Å. In the seventh Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.08–2.48 Å. In the eighth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.45 Å. In the ninth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.13–2.40 Å. In the tenth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.11–2.48 Å. In the eleventh Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.10–2.50 Å. In the twelfth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.10–2.51 Å. In the thirteenth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.10–2.51 Å. In the fourteenth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.10–2.51 Å. In the fifteenth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.12–2.48 Å. In the sixteenth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.16–2.40 Å. In the seventeenth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.10–2.51 Å. In the eighteenth Zr site, Zr is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Zr–O bond distances ranging from 2.01–2.37 Å. In the nineteenth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.20–2.32 Å. In the twentieth Zr site, Zr is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Zr–O bond distances ranging from 2.00–2.36 Å. In the twenty-first Zr site, Zr is bonded in a 6-coordinate geometry to six O atoms. There are a spread of Zr–O bond distances ranging from 2.01–2.37 Å. In the twenty-second Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.19–2.33 Å. There are fifty-three inequivalent O sites. In the first O site, O is bonded to four Zr atoms to form distorted OZr4 tetrahedra that share corners with sixteen OY2Zr2 tetrahedra and edges with six OZr4 tetrahedra. In the second O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the third O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the fourth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the fifth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the sixth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the seventh O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the eighth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the ninth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the tenth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the eleventh O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the twelfth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the thirteenth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the fourteenth O site, O is bonded in a 4-coordinate geometry to two equivalent Y and two equivalent Zr atoms. In the fifteenth O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the sixteenth O site, O is bonded in a 4-coordinate geometry to two equivalent Y and two equivalent Zr atoms. In the seventeenth O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the eighteenth O site, O is bonded in a 4-coordinate geometry to two equivalent Y and two equivalent Zr atoms. In the nineteenth O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of distorted edge and corner-sharing OY2Zr2 tetrahedra. In the twentieth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the twenty-first O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the twenty-second O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the twenty-third O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the twenty-fourth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the twenty-fifth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the twenty-sixth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the twenty-seventh O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the twenty-eighth O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the twenty-ninth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the thirtieth O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the thirty-first O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the thirty-second O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the thirty-third O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the thirty-fourth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the thirty-fifth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the thirty-sixth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the thirty-seventh O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the thirty-eighth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the thirty-ninth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the fortieth O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the forty-first O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the forty-second O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the forty-third O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the forty-fourth O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the forty-fifth O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the forty-sixth O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the forty-seventh O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the forty-eighth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the forty-ninth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the fiftieth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the fifty-first O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form OY2Zr2 tetrahedra that share corners with fourteen OY2Zr2 tetrahedra and edges with five OZr4 tetrahedra. In the fifty-second O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the fifty-third O site, O is bonded to two equivalent Y and two equivalent Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Y2Zr9O22 by Materials Project

Y2Zr9O22 is Fluorite-derived structured and crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are four inequivalent Y sites. In the first Y site, Y is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Y–O bond distances ranging from 2.28–2.45 Å. In the second Y site, Y is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Y–O bond distances ranging from 2.29–2.44 Å. In the third Y site, Y is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Y–O bond distances ranging from 2.30–2.39 Å. In the fourth Y site, Y is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Y–O bond distances ranging from 2.30–2.43 Å. There are eighteen inequivalent Zr sites. In the first Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.13–2.36 Å. In the second Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.13–2.35 Å. In the third Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.17–2.39 Å. In the fourth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.15–2.31 Å. In the fifth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.18–2.37 Å. In the sixth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.18–2.33 Å. In the seventh Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.18–2.32 Å. In the eighth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.18–2.45 Å. In the ninth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.15–2.35 Å. In the tenth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.12–2.38 Å. In the eleventh Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.15–2.33 Å. In the twelfth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.14–2.31 Å. In the thirteenth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.17–2.27 Å. In the fourteenth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.18–2.27 Å. In the fifteenth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.13–2.36 Å. In the sixteenth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.16–2.44 Å. In the seventeenth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.17–2.34 Å. In the eighteenth Zr site, Zr is bonded in a body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.18–2.33 Å. There are forty-four inequivalent O sites. In the first O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the second O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the third O site, O is bonded to two equivalent Y and two Zr atoms to form OY2Zr2 tetrahedra that share corners with sixteen OYZr3 tetrahedra and edges with six OY2Zr2 tetrahedra. In the fourth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the fifth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the sixth O site, O is bonded to two equivalent Y and two Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the seventh O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the eighth O site, O is bonded to four Zr atoms to form OZr4 tetrahedra that share corners with sixteen OYZr3 tetrahedra and edges with six OZr4 tetrahedra. In the ninth O site, O is bonded to four Zr atoms to form OZr4 tetrahedra that share corners with sixteen OZr4 tetrahedra and edges with six OY2Zr2 tetrahedra. In the tenth O site, O is bonded to four Zr atoms to form OZr4 tetrahedra that share corners with sixteen OY2Zr2 tetrahedra and edges with six OYZr3 tetrahedra. In the eleventh O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the twelfth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the thirteenth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the fourteenth O site, O is bonded to one Y and three Zr atoms to form a mixture of edge and corner-sharing OYZr3 tetrahedra. In the fifteenth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the sixteenth O site, O is bonded to one Y and three Zr atoms to form OYZr3 tetrahedra that share corners with sixteen OZr4 tetrahedra and edges with six OY2Zr2 tetrahedra. In the seventeenth O site, O is bonded to one Y and three Zr atoms to form OYZr3 tetrahedra that share corners with sixteen OYZr3 tetrahedra and edges with six OY2Zr2 tetrahedra. In the eighteenth O site, O is bonded to one Y and three Zr atoms to form OYZr3 tetrahedra that share corners with sixteen OYZr3 tetrahedra and edges with six OY2Zr2 tetrahedra. In the nineteenth O site, O is bonded to four Zr atoms to form OZr4 tetrahedra that share corners with sixteen OYZr3 tetrahedra and edges with six OZr4 tetrahedra. In the twentieth O site, O is bonded to one Y and three Zr atoms to form OYZr3 tetrahedra that share corners with sixteen OZr4 tetrahedra and edges with six OYZr3 tetrahedra. In the twenty-first O site, O is bonded to four Zr atoms to form OZr4 tetrahedra that share corners with sixteen OYZr3 tetrahedra and edges with six OZr4 tetrahedra. In the twenty-second O site, O is bonded to one Y and three Zr atoms to form OYZr3 tetrahedra that share corners with sixteen OZr4 tetrahedra and edges with six OYZr3 tetrahedra. In the twenty-third O site, O is bonded to one Y and three Zr atoms to form a mixture of edge and corner-sharing OYZr3 tetrahedra. In the twenty-fourth O site, O is bonded to one Y and three Zr atoms to form a mixture of edge and corner-sharing OYZr3 tetrahedra. In the twenty-fifth O site, O is bonded to one Y and three Zr atoms to form a mixture of edge and corner-sharing OYZr3 tetrahedra. In the twenty-sixth O site, O is bonded to one Y and three Zr atoms to form a mixture of edge and corner-sharing OYZr3 tetrahedra. In the twenty-seventh O site, O is bonded to one Y and three Zr atoms to form a mixture of edge and corner-sharing OYZr3 tetrahedra. In the twenty-eighth O site, O is bonded to one Y and three Zr atoms to form OYZr3 tetrahedra that share corners with sixteen OYZr3 tetrahedra and edges with six OY2Zr2 tetrahedra. In the twenty-ninth O site, O is bonded to one Y and three Zr atoms to form OYZr3 tetrahedra that share corners with sixteen OY2Zr2 tetrahedra and edges with six OYZr3 tetrahedra. In the thirtieth O site, O is bonded to one Y and three Zr atoms to form OYZr3 tetrahedra that share corners with sixteen OY2Zr2 tetrahedra and edges with six OYZr3 tetrahedra. In the thirty-first O site, O is bonded to one Y and three Zr atoms to form OYZr3 tetrahedra that share corners with sixteen OZr4 tetrahedra and edges with six OY2Zr2 tetrahedra. In the thirty-second O site, O is bonded to one Y and three Zr atoms to form a mixture of edge and corner-sharing OYZr3 tetrahedra. In the thirty-third O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the thirty-fourth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the thirty-fifth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the thirty-sixth O site, O is bonded to two equivalent Y and two Zr atoms to form OY2Zr2 tetrahedra that share corners with sixteen OZr4 tetrahedra and edges with six OY2Zr2 tetrahedra. In the thirty-seventh O site, O is bonded to four Zr atoms to form OZr4 tetrahedra that share corners with sixteen OYZr3 tetrahedra and edges with six OZr4 tetrahedra. In the thirty-eighth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the thirty-ninth O site, O is bonded to two equivalent Y and two Zr atoms to form OY2Zr2 tetrahedra that share corners with sixteen OZr4 tetrahedra and edges with six OYZr3 tetrahedra. In the fortieth O site, O is bonded to two equivalent Y and two Zr atoms to form OY2Zr2 tetrahedra that share corners with sixteen OY2Zr2 tetrahedra and edges with six OYZr3 tetrahedra. In the forty-first O site, O is bonded to two equivalent Y and two Zr atoms to form a mixture of edge and corner-sharing OY2Zr2 tetrahedra. In the forty-second O site, O is bonded to two equivalent Y and two Zr atoms to form OY2Zr2 tetrahedra that share corners with sixteen OZr4 tetrahedra and edges with six OY2Zr2 tetrahedra. In the forty-third O site, O is bonded to two equivalent Y and two Zr atoms to form OY2Zr2 tetrahedra that share corners with sixteen OY2Zr2 tetrahedra and edges with six OYZr3 tetrahedra. In the forty-fourth O site, O is bonded to four Zr atoms to form OZr4 tetrahedra that share corners with sixteen OY2Zr2 tetrahedra and edges with six OZr4 tetrahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Pr5Mo3O16 by Materials Project

Pr5Mo3O16 crystallizes in the cubic Pn-3n space group. The structure is three-dimensional. there are nineteen inequivalent Pr3+ sites. In the first Pr3+ site, Pr3+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.40 Å) and four longer (2.63 Å) Pr–O bond lengths. In the second Pr3+ site, Pr3+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.40 Å) and four longer (2.63 Å) Pr–O bond lengths. In the third Pr3+ site, Pr3+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.40 Å) and four longer (2.63 Å) Pr–O bond lengths. In the fourth Pr3+ site, Pr3+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.40 Å) and four longer (2.63 Å) Pr–O bond lengths. In the fifth Pr3+ site, Pr3+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.40 Å) and four longer (2.63 Å) Pr–O bond lengths. In the sixth Pr3+ site, Pr3+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.40 Å) and four longer (2.63 Å) Pr–O bond lengths. In the seventh Pr3+ site, Pr3+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.40 Å) and four longer (2.63 Å) Pr–O bond lengths. In the eighth Pr3+ site, Pr3+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.40 Å) and four longer (2.63 Å) Pr–O bond lengths. In the ninth Pr3+ site, Pr3+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.40 Å) and four longer (2.63 Å) Pr–O bond lengths. In the tenth Pr3+ site, Pr3+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.40 Å) and four longer (2.63 Å) Pr–O bond lengths. In the eleventh Pr3+ site, Pr3+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.40 Å) and four longer (2.63 Å) Pr–O bond lengths. In the twelfth Pr3+ site, Pr3+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are two shorter (2.35 Å) and six longer (2.60 Å) Pr–O bond lengths. In the thirteenth Pr3+ site, Pr3+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are two shorter (2.35 Å) and six longer (2.60 Å) Pr–O bond lengths. In the fourteenth Pr3+ site, Pr3+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are two shorter (2.35 Å) and six longer (2.60 Å) Pr–O bond lengths. In the fifteenth Pr3+ site, Pr3+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are two shorter (2.35 Å) and six longer (2.60 Å) Pr–O bond lengths. In the sixteenth Pr3+ site, Pr3+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are two shorter (2.35 Å) and six longer (2.60 Å) Pr–O bond lengths. In the seventeenth Pr3+ site, Pr3+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are two shorter (2.35 Å) and six longer (2.60 Å) Pr–O bond lengths. In the eighteenth Pr3+ site, Pr3+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are two shorter (2.35 Å) and six longer (2.60 Å) Pr–O bond lengths. In the nineteenth Pr3+ site, Pr3+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are two shorter (2.35 Å) and six longer (2.60 Å) Pr–O bond lengths. There are eleven inequivalent Mo+5.67+ sites. In the first Mo+5.67+ site, Mo+5.67+ is bonded in a tetrahedral geometry to four equivalent O2- atoms. All Mo–O bond lengths are 1.83 Å. In the second Mo+5.67+ site, Mo+5.67+ is bonded in a tetrahedral geometry to four equivalent O2- atoms. All Mo–O bond lengths are 1.83 Å. In the third Mo+5.67+ site, Mo+5.67+ is bonded in a tetrahedral geometry to four equivalent O2- atoms. All Mo–O bond lengths are 1.83 Å. In the fourth Mo+5.67+ site, Mo+5.67+ is bonded in a tetrahedral geometry to four equivalent O2- atoms. All Mo–O bond lengths are 1.83 Å. In the fifth Mo+5.67+ site, Mo+5.67+ is bonded in a tetrahedral geometry to four equivalent O2- atoms. All Mo–O bond lengths are 1.83 Å. In the sixth Mo+5.67+ site, Mo+5.67+ is bonded in a tetrahedral geometry to four equivalent O2- atoms. All Mo–O bond lengths are 1.83 Å. In the seventh Mo+5.67+ site, Mo+5.67+ is bonded in a tetrahedral geometry to four equivalent O2- atoms. All Mo–O bond lengths are 1.83 Å. In the eighth Mo+5.67+ site, Mo+5.67+ is bonded in a tetrahedral geometry to four equivalent O2- atoms. All Mo–O bond lengths are 1.83 Å. In the ninth Mo+5.67+ site, Mo+5.67+ is bonded in a tetrahedral geometry to four equivalent O2- atoms. All Mo–O bond lengths are 1.83 Å. In the tenth Mo+5.67+ site, Mo+5.67+ is bonded in a tetrahedral geometry to four equivalent O2- atoms. All Mo–O bond lengths are 1.83 Å. In the eleventh Mo+5.67+ site, Mo+5.67+ is bonded in a tetrahedral geometry to four equivalent O2- atoms. All Mo–O bond lengths are 1.83 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a 1-coordinate geometry to two Pr3+ and one Mo+5.67+ atom. In the second O2- site, O2- is bonded to four Pr3+ atoms to form a mixture of corner and edge-sharing OPr4 tetrahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Zr19O40 by Materials Project

Zr19O40 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are nineteen inequivalent Zr sites. In the first Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.10–2.42 Å. In the second Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.07–2.50 Å. In the third Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.43 Å. In the fourth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.08–2.47 Å. In the fifth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.07–2.47 Å. In the sixth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.10–2.43 Å. In the seventh Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.43 Å. In the eighth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.47 Å. In the ninth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.07–2.50 Å. In the tenth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.07–2.54 Å. In the eleventh Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.08–2.48 Å. In the twelfth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.09–2.43 Å. In the thirteenth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.06–2.57 Å. In the fourteenth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.07–2.46 Å. In the fifteenth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.08–2.47 Å. In the sixteenth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.07–2.49 Å. In the seventeenth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.07–2.45 Å. In the eighteenth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.08–2.49 Å. In the nineteenth Zr site, Zr is bonded in a distorted body-centered cubic geometry to eight O atoms. There are a spread of Zr–O bond distances ranging from 2.08–2.51 Å. There are forty inequivalent O sites. In the first O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the second O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the third O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the fourth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the fifth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the sixth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the seventh O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the eighth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the ninth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the tenth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the eleventh O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the twelfth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the thirteenth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the fourteenth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the fifteenth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the sixteenth O site, O is bonded in a trigonal non-coplanar geometry to three Zr atoms. In the seventeenth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the eighteenth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the nineteenth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the twentieth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the twenty-first O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the twenty-second O site, O is bonded in a trigonal non-coplanar geometry to three Zr atoms. In the twenty-third O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the twenty-fourth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the twenty-fifth O site, O is bonded in a trigonal non-coplanar geometry to three Zr atoms. In the twenty-sixth O site, O is bonded in a trigonal non-coplanar geometry to three Zr atoms. In the twenty-seventh O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the twenty-eighth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the twenty-ninth O site, O is bonded in a trigonal non-coplanar geometry to three Zr atoms. In the thirtieth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the thirty-first O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the thirty-second O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the thirty-third O site, O is bonded in a trigonal non-coplanar geometry to three Zr atoms. In the thirty-fourth O site, O is bonded to four Zr atoms to form a mixture of edge and corner-sharing OZr4 tetrahedra. In the thirty-fifth O site, O is bonded in a trigonal non-coplanar geometry to three Zr atoms. In the thirty-sixth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the thirty-seventh O site, O is bonded in a trigonal non-coplanar geometry to three Zr atoms. In the thirty-eighth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the thirty-ninth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra. In the fortieth O site, O is bonded to four Zr atoms to form a mixture of distorted edge and corner-sharing OZr4 tetrahedra.

36 MATERIALS SCIENCE↗