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Competing magnetic orders in quantum critical Sr 3 Ru 2 O 7

We investigated Sr 3 RuO 7 , a quantum critical metal that shows a metamagnetic quantum phase transition and electronic nematicity, through density functional calculations. These predict a ferromagnetic ground state in contrast to the experimentally observed paramagnetism, raising the question of competing magnetic states and associated fluctuations that may suppress magnetic order. We did a search to identify such low-energy antiferromagnetically ordered metastable states. We find that the lowest-energy antiferromagnetic state has a striped order. This corresponds to the E-type order that has been shown to be induced by Mn alloying. We also note significant transport anisotropy in this E-type ordered state. Furthermore, these results are discussed in relation to experimental observations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Experimental evidence for nonspherical magnetic form factor in Ru 3 +

The Mott insulator ..alpha..-RuCl3 has generated great interest in the community due to its possible field-induced Kitaev quantum spin liquid state. Despite enormous effort spent trying to obtain the form of the low-energy Hamiltonian, there is currently no agreed upon set of parameters which is able to explain all of the data. A key piece of missing information lies in the determination of the magnetic form factor of Ru3+, particularly for a true quantitative treatment of inelastic neutron scattering data. Here we present the experimentally derived magnetic form factor of Ru3+ in the low spin 4d5 state using polarized neutron diffraction within the paramagnetic regime on high-quality single crystals of ..alpha..-RuCl3. We observe strong evidence of an anisotropic form factor, expected of the spin-orbit coupled jeff=12 ground state. We model the static magnetization density in increasing complexity from simple isotropic cases, to a multipolar expansion, and, finally, ab initio calculations of the generalized jeff=12 ground state. Comparison of both single ion models and inclusion of Cl- anions support the presence of hybridization of Ru3+ with the surrounding Cl- ligands.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Long-range and local crystal structures of the S r 1 - x C a x Ru O 3 perovskites

Here, the crystal structures of the Sr 1–x Ca x RuO 3 (0 ≤ x ≤ 1) perovskites are investigated using both long-range and local structural probes. High-resolution synchrotron powder x-ray-diffraction characterization at ambient temperature shows that the materials have orthorhombic long-range crystal structures to high precision, and we support previous work showing that Ca 2+ substitution for Sr 2+ primarily changes the tilting of rigid corner-sharing RuO 6 octahedra at their shared oxygen vertices. X-ray pair-distribution function analysis for SrRuO 3 , CaRuO 3 , and one intermediate composition show them to display monoclinic symmetry at the local level; when averaged over different domain orientations this yields orthorhombic symmetry in the long range, and no long-range or local phase transitions are observed between 80 and 300 K for materials with intermediate compositions. High-resolution transmission electron microscopy shows that the Sr/Ca distribution is random at the nanoscale. Lastly, we plot magnetic characteristics such as the ferromagnetic T c , Curie-Weiss theta, effective moment, and ambient temperature susceptibility vs the octahedral tilt and unit-cell volume.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Materials Data on Er17(TeRu2)3 by Materials Project

Er17Ru6Te3 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are thirty-four inequivalent Er sites. In the first Er site, Er is bonded in a 2-coordinate geometry to three Ru and one Te atom. There are two shorter (2.81 Å) and one longer (3.39 Å) Er–Ru bond lengths. The Er–Te bond length is 3.16 Å. In the second Er site, Er is bonded in a 5-coordinate geometry to three Ru and two equivalent Te atoms. There are two shorter (2.92 Å) and one longer (3.18 Å) Er–Ru bond lengths. Both Er–Te bond lengths are 3.51 Å. In the third Er site, Er is bonded in a 2-coordinate geometry to three Ru and two equivalent Te atoms. There are a spread of Er–Ru bond distances ranging from 2.90–3.60 Å. There are one shorter (3.46 Å) and one longer (3.49 Å) Er–Te bond lengths. In the fourth Er site, Er is bonded to three Ru and one Te atom to form a mixture of distorted edge and corner-sharing ErTeRu3 tetrahedra. There are two shorter (2.85 Å) and one longer (2.98 Å) Er–Ru bond lengths. The Er–Te bond length is 3.14 Å. In the fifth Er site, Er is bonded in a 2-coordinate geometry to three Ru and two equivalent Te atoms. There are two shorter (2.82 Å) and one longer (3.49 Å) Er–Ru bond lengths. There are one shorter (3.40 Å) and one longer (3.43 Å) Er–Te bond lengths. In the sixth Er site, Er is bonded in a 4-coordinate geometry to three Ru and one Te atom. There are a spread of Er–Ru bond distances ranging from 2.86–3.21 Å. The Er–Te bond length is 3.13 Å. In the seventh Er site, Er is bonded in a 2-coordinate geometry to three Ru and two equivalent Te atoms. There are two shorter (2.82 Å) and one longer (3.48 Å) Er–Ru bond lengths. Both Er–Te bond lengths are 3.41 Å. In the eighth Er site, Er is bonded in a 6-coordinate geometry to four Ru and two equivalent Te atoms. There are a spread of Er–Ru bond distances ranging from 2.87–3.08 Å. Both Er–Te bond lengths are 3.32 Å. In the ninth Er site, Er is bonded in a 2-coordinate geometry to three Ru and two equivalent Te atoms. There are a spread of Er–Ru bond distances ranging from 2.81–3.46 Å. There are one shorter (3.34 Å) and one longer (3.36 Å) Er–Te bond lengths. In the tenth Er site, Er is bonded in a 4-coordinate geometry to three Ru and one Te atom. There are a spread of Er–Ru bond distances ranging from 2.87–3.19 Å. The Er–Te bond length is 3.15 Å. In the eleventh Er site, Er is bonded in a 2-coordinate geometry to three Ru and two equivalent Te atoms. There are a spread of Er–Ru bond distances ranging from 2.79–3.64 Å. Both Er–Te bond lengths are 3.35 Å. In the twelfth Er site, Er is bonded to three Ru and one Te atom to form distorted corner-sharing ErTeRu3 tetrahedra. There are two shorter (2.87 Å) and one longer (2.93 Å) Er–Ru bond lengths. The Er–Te bond length is 3.12 Å. In the thirteenth Er site, Er is bonded in a 6-coordinate geometry to four Ru and two equivalent Te atoms. There are a spread of Er–Ru bond distances ranging from 2.87–3.09 Å. There are one shorter (3.30 Å) and one longer (3.32 Å) Er–Te bond lengths. In the fourteenth Er site, Er is bonded to three Ru and one Te atom to form a mixture of distorted edge and corner-sharing ErTeRu3 tetrahedra. There are two shorter (2.85 Å) and one longer (2.88 Å) Er–Ru bond lengths. The Er–Te bond length is 3.16 Å. In the fifteenth Er site, Er is bonded in a 5-coordinate geometry to three Ru and two equivalent Te atoms. There are two shorter (2.91 Å) and one longer (3.23 Å) Er–Ru bond lengths. There are one shorter (3.37 Å) and one longer (3.39 Å) Er–Te bond lengths. In the sixteenth Er site, Er is bonded in a 2-coordinate geometry to three Ru and two equivalent Te atoms. There are a spread of Er–Ru bond distances ranging from 2.90–3.27 Å. There are one shorter (3.38 Å) and one longer (3.39 Å) Er–Te bond lengths. In the seventeenth Er site, Er is bonded in a 5-coordinate geometry to three Ru and two equivalent Te atoms. There are two shorter (2.93 Å) and one longer (3.15 Å) Er–Ru bond lengths. There are one shorter (3.51 Å) and one longer (3.53 Å) Er–Te bond lengths. In the eighteenth Er site, Er is bonded in a 6-coordinate geometry to four Ru and two equivalent Te atoms. There are a spread of Er–Ru bond distances ranging from 2.87–3.10 Å. There are one shorter (3.32 Å) and one longer (3.33 Å) Er–Te bond lengths. In the nineteenth Er site, Er is bonded in a 4-coordinate geometry to three Ru and one Te atom. There are two shorter (2.82 Å) and one longer (3.25 Å) Er–Ru bond lengths. The Er–Te bond length is 3.12 Å. In the twentieth Er site, Er is bonded in a 2-coordinate geometry to three Ru and two equivalent Te atoms. There are two shorter (2.82 Å) and one longer (3.47 Å) Er–Ru bond lengths. Both Er–Te bond lengths are 3.34 Å. In the twenty-first Er site, Er is bonded in a 5-coordinate geometry to three Ru and two equivalent Te atoms. There are a spread of Er–Ru bond distances ranging from 2.90–3.28 Å. There are one shorter (3.36 Å) and one longer (3.40 Å) Er–Te bond lengths. In the twenty-second Er site, Er is bonded in a 5-coordinate geometry to three Ru and two equivalent Te atoms. There are a spread of Er–Ru bond distances ranging from 2.90–3.31 Å. There are one shorter (3.35 Å) and one longer (3.37 Å) Er–Te bond lengths. In the twenty-third Er site, Er is bonded to three Ru and one Te atom to form a mixture of distorted edge and corner-sharing ErTeRu3 tetrahedra. There are two shorter (2.80 Å) and one longer (3.02 Å) Er–Ru bond lengths. The Er–Te bond length is 3.13 Å. In the twenty-fourth Er site, Er is bonded in a 6-coordinate geometry to four Ru and two equivalent Te atoms. There are a spread of Er–Ru bond distances ranging from 2.88–3.09 Å. Both Er–Te bond lengths are 3.33 Å. In the twenty-fifth Er site, Er is bonded in a rectangular see-saw-like geometry to two Ru and two Te atoms. There are one shorter (3.12 Å) and one longer (3.13 Å) Er–Ru bond lengths. Both Er–Te bond lengths are 3.26 Å. In the twenty-sixth Er site, Er is bonded to three Ru and one Te atom to form distorted corner-sharing ErTeRu3 tetrahedra. There are two shorter (2.87 Å) and one longer (2.93 Å) Er–Ru bond lengths. The Er–Te bond length is 3.12 Å. In the twenty-seventh Er site, Er is bonded to three Ru and one Te atom to form a mixture of distorted edge and corner-sharing ErTeRu3 tetrahedra. There are a spread of Er–Ru bond distances ranging from 2.79–3.00 Å. The Er–Te bond length is 3.13 Å. In the twenty-eighth Er site, Er is bonded to three Ru and one Te atom to form a mixture of distorted edge and corner-sharing ErTeRu3 tetrahedra. There are a spread of Er–Ru bond distances ranging from 2.84–2.97 Å. The Er–Te bond length is 3.14 Å. In the twenty-ninth Er site, Er is bonded to three Ru and one Te atom to form a mixture of distorted edge and corner-sharing ErTeRu3 tetrahedra. There are two shorter (2.85 Å) and one longer (2.87 Å) Er–Ru bond lengths. The Er–Te bond length is 3.16 Å. In the thirtieth Er site, Er is bonded in a 2-coordinate geometry to three Ru and two equivalent Te atoms. There are a spread of Er–Ru bond distances ranging from 2.78–3.61 Å. There are one shorter (3.36 Å) and one longer (3.37 Å) Er–Te bond lengths. In the thirty-first Er site, Er is bonded in a 2-coordinate geometry to three Ru and one Te atom. There are a spread of Er–Ru bond distances ranging from 2.81–3.39 Å. The Er–Te bond length is 3.16 Å. In the thirty-second Er site, Er is bonded in a 4-coordinate geometry to three Ru and one Te atom. There are two shorter (2.82 Å) and one longer (3.25 Å) Er–Ru bond lengths. The Er–Te bond length is 3.12 Å. In the thirty-third Er site, Er is bonded in a rectangular see-saw-like geometry to two Ru and two Te atoms. Both Er–Ru bond lengths are 3.19 Å. There are one shorter (3.18 Å) and one longer (3.19 Å) Er–Te bond lengths. In the thirty-fourth Er site, Er is bonded in a 2-coordinate geometry to three Ru and two equivalent Te atoms. There are two shorter (2.90 Å) and one longer (3.61 Å) Er–Ru bond lengths. There are one shorter (3.47 Å) and one longer (3.48 Å) Er–Te bond lengths. There are twelve inequivalent Ru sites. In the first Ru site, Ru is bonded in a 8-coordinate geometry to eight Er atoms. In the second Ru site, Ru is bonded in a 9-coordinate geometry to nine Er atoms. In the third Ru site, Ru is bonded in a 9-coordinate geometry to eight Er atoms. In the fourth Ru site, Ru is bonded in a 9-coordinate geometry to nine Er atoms. In the fifth Ru site, Ru is bonded in a 7-coordinate geometry to nine Er atoms. In the sixth Ru site, Ru is bonded in a 7-coordinate geometry to nine Er atoms. In the seventh Ru site, Ru is bonded in a 9-coordinate geometry to nine Er atoms. In the eighth Ru site, Ru is bonded in a 9-coordinate geometry to nine Er atoms. In the ninth Ru site, Ru is bonded in a 8-coordinate geometry to eight Er atoms. In the tenth Ru site, Ru is bonded in a 9-coordinate geometry to nine Er atoms. In the eleventh Ru site, Ru is bonded in a 9-coordinate geometry to nine Er atoms. In the twelfth Ru site, Ru is bonded in a 9-coordinate geometry to eight Er atoms. There are six inequivalent Te sites. In the first Te site, Te is bonded in a 9-coordinate geometry to nine Er atoms. In the second Te site, Te is bonded in a 9-coordinate geometry to nine Er atoms. In the third Te site, Te is bonded in a 9-coordinate geometry to nine Er atoms. In the fourth Te site, Te is bonded in a 9-coordinate geometry to nine Er atoms. In the fifth Te site, Te is bonded in a 9-coordinate geometry to nine Er atoms. In the sixth Te site, Te is bonded in a 9-coordinate geometry to nine Er atoms.

36 MATERIALS SCIENCE↗

Materials Data on Na11(Ru4O9)4 by Materials Project

Na11(Ru4O9)4 is Orthorhombic Perovskite-like structured and crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are eleven inequivalent Na1+ sites. In the first Na1+ site, Na1+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Na–O bond distances ranging from 2.34–2.60 Å. In the second Na1+ site, Na1+ is bonded in a 7-coordinate geometry to eight O2- atoms. There are a spread of Na–O bond distances ranging from 2.36–2.88 Å. In the third Na1+ site, Na1+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Na–O bond distances ranging from 2.34–2.78 Å. In the fourth Na1+ site, Na1+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Na–O bond distances ranging from 2.38–2.82 Å. In the fifth Na1+ site, Na1+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Na–O bond distances ranging from 2.43–2.78 Å. In the sixth Na1+ site, Na1+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Na–O bond distances ranging from 2.43–3.09 Å. In the seventh Na1+ site, Na1+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Na–O bond distances ranging from 2.41–2.69 Å. In the eighth Na1+ site, Na1+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Na–O bond distances ranging from 2.37–2.72 Å. In the ninth Na1+ site, Na1+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Na–O bond distances ranging from 2.36–2.57 Å. In the tenth Na1+ site, Na1+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Na–O bond distances ranging from 2.37–2.56 Å. In the eleventh Na1+ site, Na1+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Na–O bond distances ranging from 2.31–2.51 Å. There are sixteen inequivalent Ru+3.81+ sites. In the first Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing RuO6 octahedra. The corner-sharing octahedra tilt angles range from 43–47°. There are a spread of Ru–O bond distances ranging from 1.92–2.16 Å. In the second Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing RuO6 octahedra. The corner-sharing octahedra tilt angles range from 44–49°. There are a spread of Ru–O bond distances ranging from 1.93–2.13 Å. In the third Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing RuO6 octahedra. The corner-sharing octahedra tilt angles range from 39–47°. There are a spread of Ru–O bond distances ranging from 1.94–2.14 Å. In the fourth Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing RuO6 octahedra. The corner-sharing octahedra tilt angles range from 43–52°. There are a spread of Ru–O bond distances ranging from 1.94–2.12 Å. In the fifth Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing RuO6 octahedra. The corner-sharing octahedra tilt angles range from 46–48°. There are a spread of Ru–O bond distances ranging from 1.92–2.09 Å. In the sixth Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing RuO6 octahedra. The corner-sharing octahedra tilt angles range from 44–45°. There are a spread of Ru–O bond distances ranging from 1.91–2.07 Å. In the seventh Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing RuO6 octahedra. The corner-sharing octahedra tilt angles range from 47–48°. There are a spread of Ru–O bond distances ranging from 1.93–2.09 Å. In the eighth Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing RuO6 octahedra. The corner-sharing octahedra tilt angles range from 44–46°. There are a spread of Ru–O bond distances ranging from 1.92–2.08 Å. In the ninth Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing RuO6 octahedra. The corner-sharing octahedra tilt angles range from 44–48°. There are a spread of Ru–O bond distances ranging from 2.00–2.08 Å. In the tenth Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing RuO6 octahedra. The corner-sharing octahedra tilt angles range from 44–47°. There are a spread of Ru–O bond distances ranging from 1.98–2.07 Å. In the eleventh Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing RuO6 octahedra. The corner-sharing octahedra tilt angles range from 44–47°. There are a spread of Ru–O bond distances ranging from 1.99–2.09 Å. In the twelfth Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing RuO6 octahedra. The corner-sharing octahedra tilt angles range from 44–48°. There are a spread of Ru–O bond distances ranging from 1.98–2.09 Å. In the thirteenth Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing RuO6 octahedra. The corner-sharing octahedra tilt angles range from 47–52°. There are a spread of Ru–O bond distances ranging from 1.99–2.07 Å. In the fourteenth Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing RuO6 octahedra. The corner-sharing octahedra tilt angles range from 39–44°. There are a spread of Ru–O bond distances ranging from 1.92–2.07 Å. In the fifteenth Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form edge-sharing RuO6 octahedra. There are a spread of Ru–O bond distances ranging from 2.03–2.09 Å. In the sixteenth Ru+3.81+ site, Ru+3.81+ is bonded to six O2- atoms to form edge-sharing RuO6 octahedra. There are a spread of Ru–O bond distances ranging from 2.03–2.08 Å. There are thirty-six inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to one Na1+ and three Ru+3.81+ atoms. In the second O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+ and three Ru+3.81+ atoms. In the third O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+ and three Ru+3.81+ atoms. In the fourth O2- site, O2- is bonded in a 4-coordinate geometry to one Na1+ and three Ru+3.81+ atoms. In the fifth O2- site, O2- is bonded to four Na1+ and two Ru+3.81+ atoms to form distorted ONa4Ru2 pentagonal pyramids that share corners with two equivalent ONa2Ru3 square pyramids, an edgeedge with one ONa2Ru3 square pyramid, and an edgeedge with one ONa3Ru2 trigonal bipyramid. In the sixth O2- site, O2- is bonded in a 6-coordinate geometry to four Na1+ and two Ru+3.81+ atoms. In the seventh O2- site, O2- is bonded to three Na1+ and two Ru+3.81+ atoms to form distorted ONa3Ru2 trigonal bipyramids that share corners with four ONa2Ru3 trigonal bipyramids and an edgeedge with one ONa4Ru2 pentagonal pyramid. In the eighth O2- site, O2- is bonded in a 5-coordinate geometry to three Na1+ and two Ru+3.81+ atoms. In the ninth O2- site, O2- is bonded in a 5-coordinate geometry to one Na1+ and three Ru+3.81+ atoms. In the tenth O2- site, O2- is bonded to two Na1+ and three Ru+3.81+ atoms to form distorted ONa2Ru3 trigonal bipyramids that share corners with four ONa3Ru2 trigonal bipyramids and edges with four ONa2Ru3 trigonal bipyramids. In the eleventh O2- site, O2- is bonded in a 5-coordinate geometry to two Na1+ and three Ru+3.81+ atoms. In the twelfth O2- site, O2- is bonded in a 5-coordinate geometry to two Na1+ and three Ru+3.81+ atoms. In the thirteenth O2- site, O2- is bonded to two Na1+ and three Ru+3.81+ atoms to form distorted ONa2Ru3 trigonal bipyramids that share corners with three ONa3Ru2 trigonal bipyramids and an edgeedge with one ONa2Ru3 trigonal bipyramid. In the fourteenth O2- site, O2- is bonded in a 5-coordinate geometry to two Na1+ and three Ru+3.81+ atoms. In the fifteenth O2- site, O2- is bonded in a 5-coordinate geometry to two Na1+ and three Ru+3.81+ atoms. In the sixteenth O2- site, O2- is bonded in a 5-coordinate geometry to two Na1+ and three Ru+3.81+ atoms. In the seventeenth O2- site, O2- is bonded to two Na1+ and three Ru+3.81+ atoms to form a mixture of distorted corner and edge-sharing ONa2Ru3 trigonal bipyramids. In the eighteenth O2- site, O2- is bonded to two Na1+ and three Ru+3.81+ atoms to form a mixture of distorted corner and edge-sharing ONa2Ru3 trigonal bipyramids. In the nineteenth O2- site, O2- is bonded in a 5-coordinate geometry to two Na1+ and three Ru+3.81+ atoms. In the twentieth O2- site, O2- is bonded to two Na1+ and three Ru+3.81+ atoms to form a mixture of distorted corner and edge-sharing ONa2Ru3 trigonal bipyramids. In the twenty-first O2- site, O2- is bonded in a 5-coordinate geometry to three Na1+ and two Ru+3.81+ atoms. In the twenty-second O2- site, O2- is bonded in a 5-coordinate geometry to three Na1+ and two Ru+3.81+ atoms. In the twenty-third O2- site, O2- is bonded to three Na1+ and two Ru+3.81+ atoms to form distorted ONa3Ru2 trigonal bipyramids that share corners with six ONa3Ru2 trigonal bipyramids and edges with two ONa2Ru3 trigonal bipyramids. In the twenty-fourth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+ and two Ru+3.81+ atoms. In the twenty-fifth O2- site, O2- is bonded to two Na1+ and three Ru+3.81+ atoms to form a mixture of distorted corner and edge-sharing ONa2Ru3 trigonal bipyramids. In the twenty-sixth O2- site, O2- is bonded to two Na1+ and three Ru+3.81+ atoms to form a mixture of distorted corner and edge-sharing ONa2Ru3 trigonal bipyramids. In the twenty-seventh O2- site, O2- is bonded to two Na1+ and three Ru+3.81+ atoms to form a mixture of distorted corner and edge-sharing ONa2Ru3 trigonal bipyramids. In the twenty-eighth O2- site, O2- is bonded to two Na1+ and three Ru+3.81+ atoms to form distorted edge-sharing ONa2Ru3 trigonal bipyramids. In the twenty-ninth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+ and two Ru+3.81+ atoms. In the thirtieth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+ and two Ru+3.81+ atoms. In the thirty-first O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+ and two Ru+3.81+ atoms. In the thirty-second O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+ and two Ru+3.81+ atoms. In the thirty-third O2- site, O2- is bonded to two Na1+ and three Ru+3.81+ atoms to form distorted ONa2Ru3 square pyramids that share a cornercorner with one ONa2Ru3 trigonal bipyramid, an edgeedge with one ONa4Ru2 pentagonal pyramid, edges with two equivalent ONa2Ru3 square pyramids, and edges with two ONa2Ru3 trigonal bipyramids. In the thirty-fourth O2- site, O2- is bonded to two Na1+ and three Ru+3.81+ atoms to form distorted ONa2Ru3 square pyramids that share corners with two equivalent ONa4Ru2 pentagonal pyramids, a cornercorner with one ONa2Ru3 trigonal bipyramid, edges with two equivalent ONa2Ru3 square pyramids, and edges with two ONa2Ru3 trigonal bipyramids. In the thirty-fifth O2- site, O2- is bonded in a distorted see-saw-like geometry to one Na1+ and three Ru+3.81+ atoms. In the thirty-sixth O2- site, O2- is bonded in a 4-coordinate geometry to two Na1+ and three Ru+3.81+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Sm8Al53Si17Ru12 by Materials Project

Sm8Ru12Al53Si17 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are eight inequivalent Sm sites. In the first Sm site, Sm is bonded in a 12-coordinate geometry to nine Al and three Si atoms. There are a spread of Sm–Al bond distances ranging from 3.16–3.23 Å. All Sm–Si bond lengths are 2.99 Å. In the second Sm site, Sm is bonded in a 12-coordinate geometry to nine Al and three Si atoms. There are a spread of Sm–Al bond distances ranging from 3.15–3.24 Å. There are one shorter (2.98 Å) and two longer (2.99 Å) Sm–Si bond lengths. In the third Sm site, Sm is bonded in a 12-coordinate geometry to nine Al and three Si atoms. There are a spread of Sm–Al bond distances ranging from 3.13–3.25 Å. All Sm–Si bond lengths are 2.98 Å. In the fourth Sm site, Sm is bonded in a 12-coordinate geometry to nine Al and three Si atoms. There are a spread of Sm–Al bond distances ranging from 3.14–3.26 Å. There are a spread of Sm–Si bond distances ranging from 2.97–2.99 Å. In the fifth Sm site, Sm is bonded in a 12-coordinate geometry to nine Al and three Si atoms. There are a spread of Sm–Al bond distances ranging from 3.14–3.25 Å. All Sm–Si bond lengths are 2.97 Å. In the sixth Sm site, Sm is bonded in a 12-coordinate geometry to nine Al and three Si atoms. There are a spread of Sm–Al bond distances ranging from 3.14–3.24 Å. There are a spread of Sm–Si bond distances ranging from 2.97–2.99 Å. In the seventh Sm site, Sm is bonded in a 12-coordinate geometry to nine Al and three Si atoms. There are a spread of Sm–Al bond distances ranging from 3.15–3.24 Å. There are a spread of Sm–Si bond distances ranging from 2.97–2.99 Å. In the eighth Sm site, Sm is bonded in a 12-coordinate geometry to nine Al and three Si atoms. There are a spread of Sm–Al bond distances ranging from 3.14–3.24 Å. There are two shorter (2.98 Å) and one longer (2.99 Å) Sm–Si bond lengths. There are twelve inequivalent Ru sites. In the first Ru site, Ru is bonded in a 9-coordinate geometry to nine Al atoms. There are a spread of Ru–Al bond distances ranging from 2.47–2.63 Å. In the second Ru site, Ru is bonded in a 9-coordinate geometry to nine Al atoms. There are a spread of Ru–Al bond distances ranging from 2.46–2.63 Å. In the third Ru site, Ru is bonded in a 9-coordinate geometry to nine Al atoms. There are a spread of Ru–Al bond distances ranging from 2.45–2.63 Å. In the fourth Ru site, Ru is bonded in a 9-coordinate geometry to nine Al atoms. There are a spread of Ru–Al bond distances ranging from 2.47–2.62 Å. In the fifth Ru site, Ru is bonded in a 9-coordinate geometry to eight Al and one Si atom. There are a spread of Ru–Al bond distances ranging from 2.59–2.63 Å. The Ru–Si bond length is 2.40 Å. In the sixth Ru site, Ru is bonded in a 9-coordinate geometry to eight Al and one Si atom. There are a spread of Ru–Al bond distances ranging from 2.60–2.62 Å. The Ru–Si bond length is 2.39 Å. In the seventh Ru site, Ru is bonded in a 9-coordinate geometry to eight Al and one Si atom. There are a spread of Ru–Al bond distances ranging from 2.59–2.64 Å. The Ru–Si bond length is 2.40 Å. In the eighth Ru site, Ru is bonded in a 9-coordinate geometry to eight Al and one Si atom. There are a spread of Ru–Al bond distances ranging from 2.59–2.63 Å. The Ru–Si bond length is 2.40 Å. In the ninth Ru site, Ru is bonded in a 9-coordinate geometry to eight Al and one Si atom. There are a spread of Ru–Al bond distances ranging from 2.58–2.62 Å. The Ru–Si bond length is 2.39 Å. In the tenth Ru site, Ru is bonded in a 9-coordinate geometry to eight Al and one Si atom. There are a spread of Ru–Al bond distances ranging from 2.59–2.65 Å. The Ru–Si bond length is 2.40 Å. In the eleventh Ru site, Ru is bonded in a 9-coordinate geometry to eight Al and one Si atom. There are a spread of Ru–Al bond distances ranging from 2.60–2.62 Å. The Ru–Si bond length is 2.39 Å. In the twelfth Ru site, Ru is bonded in a 9-coordinate geometry to eight Al and one Si atom. There are a spread of Ru–Al bond distances ranging from 2.58–2.63 Å. The Ru–Si bond length is 2.41 Å. There are fifty-three inequivalent Al sites. In the first Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, and one Si atom. The Al–Si bond length is 2.59 Å. In the second Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, one Al, and one Si atom. The Al–Al bond length is 2.75 Å. The Al–Si bond length is 2.58 Å. In the third Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, and one Si atom. The Al–Si bond length is 2.58 Å. In the fourth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, four Al, and three Si atoms. There are two shorter (2.75 Å) and two longer (2.90 Å) Al–Al bond lengths. There are a spread of Al–Si bond distances ranging from 2.58–2.77 Å. In the fifth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, two Al, and two Si atoms. Both Al–Al bond lengths are 2.74 Å. There are one shorter (2.58 Å) and one longer (2.91 Å) Al–Si bond lengths. In the sixth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, two Al, and two Si atoms. There are one shorter (2.75 Å) and one longer (2.77 Å) Al–Al bond lengths. There are one shorter (2.60 Å) and one longer (2.86 Å) Al–Si bond lengths. In the seventh Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, two Al, and three Si atoms. Both Al–Al bond lengths are 2.75 Å. There are a spread of Al–Si bond distances ranging from 2.59–2.81 Å. In the eighth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, four Al, and three Si atoms. There are a spread of Al–Al bond distances ranging from 2.76–2.92 Å. There are a spread of Al–Si bond distances ranging from 2.59–2.80 Å. In the ninth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, one Al, and three Si atoms. The Al–Al bond length is 2.77 Å. There are a spread of Al–Si bond distances ranging from 2.60–2.77 Å. In the tenth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, four Al, and three Si atoms. There are a spread of Al–Al bond distances ranging from 2.75–2.90 Å. There are a spread of Al–Si bond distances ranging from 2.59–2.77 Å. In the eleventh Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, two Al, and three Si atoms. Both Al–Al bond lengths are 2.76 Å. There are a spread of Al–Si bond distances ranging from 2.58–2.79 Å. In the twelfth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, two Al, and three Si atoms. There are one shorter (2.73 Å) and one longer (2.74 Å) Al–Al bond lengths. There are a spread of Al–Si bond distances ranging from 2.57–2.88 Å. In the thirteenth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, four Al, and three Si atoms. There are one shorter (2.74 Å) and one longer (2.75 Å) Al–Al bond lengths. There are a spread of Al–Si bond distances ranging from 2.59–2.82 Å. In the fourteenth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, three Al, and three Si atoms. There are one shorter (2.73 Å) and one longer (2.74 Å) Al–Al bond lengths. There are a spread of Al–Si bond distances ranging from 2.58–2.89 Å. In the fifteenth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, two Al, and three Si atoms. Both Al–Al bond lengths are 2.74 Å. There are a spread of Al–Si bond distances ranging from 2.58–2.86 Å. In the sixteenth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, one Al, and two Si atoms. The Al–Al bond length is 2.74 Å. There are one shorter (2.59 Å) and one longer (2.88 Å) Al–Si bond lengths. In the seventeenth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, two Al, and three Si atoms. The Al–Al bond length is 2.73 Å. There are a spread of Al–Si bond distances ranging from 2.58–2.83 Å. In the eighteenth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, one Al, and two Si atoms. The Al–Al bond length is 2.75 Å. There are one shorter (2.59 Å) and one longer (2.88 Å) Al–Si bond lengths. In the nineteenth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, four Al, and three Si atoms. There are one shorter (2.74 Å) and one longer (2.75 Å) Al–Al bond lengths. There are a spread of Al–Si bond distances ranging from 2.59–2.75 Å. In the twentieth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, two Al, and two Si atoms. Both Al–Al bond lengths are 2.75 Å. There are one shorter (2.59 Å) and one longer (2.89 Å) Al–Si bond lengths. In the twenty-first Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, two Al, and two Si atoms. Both Al–Al bond lengths are 2.76 Å. There are one shorter (2.60 Å) and one longer (2.86 Å) Al–Si bond lengths. In the twenty-second Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, and two Si atoms. There are one shorter (2.58 Å) and one longer (2.83 Å) Al–Si bond lengths. In the twenty-third Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, two Al, and one Si atom. Both Al–Al bond lengths are 2.77 Å. The Al–Si bond length is 2.60 Å. In the twenty-fourth Al site, Al is bonded in a 3-coordinate geometry to one Sm, two Ru, and two Si atoms. There are one shorter (2.58 Å) and one longer (2.88 Å) Al–Si bond lengths. In the twenty-fifth Al site, Al is bonded in a 3-coordinate geometry to two Sm, two Ru, three Al, and one Si atom. There are a spread of Al–Al bond distances ranging from 2.61–2.90 Å. The Al–Si bond length is 2.64 Å. In the twenty-sixth Al site, Al is bonded in a 3-coordinate geometry to two Sm, two Ru, two Al, and one Si atom. The Al–Al bond length is 2.91 Å. The Al–Si bond length is 2.64 Å. In the twenty-seventh Al site, Al is bonded in a 3-coordinate geometry to two Sm, two Ru, two Al, and one Si atom. There are one shorter (2.61 Å) and one longer (2.91 Å) Al–Al bond lengths. The Al–Si bond length is 2.66 Å. In the twenty-eighth Al site, Al is bonded in a 3-coordinate geometry to two Sm, two Ru, two Al, and one Si atom. The Al–Al bond length is 2.91 Å. The Al–Si bond length is 2.66 Å. In the twenty-ninth Al site, Al is bonded in a 3-coordinate geometry to two Sm, two Ru, and one Si atom. The Al–Si bond length is 2.65 Å. In the thirtieth Al site, Al is bonded in a 3-coordinate geometry to two Sm, two Ru, five Al, and one Si atom. There are one shorter (2.62 Å) and one longer (2.90 Å) Al–Al bond lengths. The Al–Si bond length is 2.65 Å. In the thirty-first Al site, Al is bonded in a 3-coordinate geometry to two Sm, two Ru, five Al, and one Si atom. Both Al–Al bond lengths are 2.90 Å. The Al–Si bond length is 2.65 Å. In the thirty-second Al site, Al is bonded in a 3-coordinate geometry to two Sm, two Ru, three Al, and one Si atom. There are one shorter (2.61 Å) and one longer (2.92 Å) Al–Al bond lengths. The Al–Si bond length is 2.65 Å. In the thirty-third Al site, Al is bonded in a 3-coordinate geometry to two Sm, two Ru, five Al, and one Si atom. There are one shorter (2.61 Å) and two longer (2.91 Å) Al–Al bond lengths. The Al–Si bond length is 2.66 Å. In the thirty-fourth Al site, Al is bonded in a 3-coordinate geometry to two Sm, two Ru, three Al, and one Si atom. The Al–Al bond length is 2.94 Å. The Al–Si bond length is 2.65 Å. In the thirty-fifth Al site, Al is bonded in a 3-coordinate geometry to two Sm, two Ru, five Al, and one Si atom. The Al–Al bond length is 2.61 Å. The Al–Si bond length is 2.66 Å. In the thirty-sixth Al site, Al is bonded in a 3-coordinate geometry to two Sm, two Ru, five Al, and one Si atom. There are one shorter (2.62 Å) and one longer (2.89 Å) Al–Al bond lengths. The Al–Si bond length is 2.65 Å. In the thirty-seventh Al site, Al is bonded in a 3-coordinate geometry to two Sm, two Ru, five Al, and one Si atom. There are one shorter (2.62 Å) and one longer (2.91 Å) Al–Al bond lengths. The Al–Si bond length is 2.66 Å. In the thirty-eighth Al site, Al is bonded in a 3-coordina

36 MATERIALS SCIENCE↗

Materials Data on Gd5P12Ru19 by Materials Project

Gd5Ru19P12 crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. there are three inequivalent Gd sites. In the first Gd site, Gd is bonded in a 2-coordinate geometry to ten Ru and six P atoms. There are a spread of Gd–Ru bond distances ranging from 3.04–3.38 Å. There are four shorter (3.06 Å) and two longer (3.11 Å) Gd–P bond lengths. In the second Gd site, Gd is bonded in a 2-coordinate geometry to ten Ru and six P atoms. There are a spread of Gd–Ru bond distances ranging from 3.05–3.37 Å. There are four shorter (3.06 Å) and two longer (3.11 Å) Gd–P bond lengths. In the third Gd site, Gd is bonded in a 6-coordinate geometry to nine Ru and six P atoms. There are four shorter (3.14 Å) and five longer (3.15 Å) Gd–Ru bond lengths. All Gd–P bond lengths are 2.99 Å. There are eleven inequivalent Ru sites. In the first Ru site, Ru is bonded in a distorted single-bond geometry to six Ru and five P atoms. There are two shorter (2.85 Å) and four longer (2.89 Å) Ru–Ru bond lengths. There are a spread of Ru–P bond distances ranging from 2.27–2.82 Å. In the second Ru site, Ru is bonded in a distorted single-bond geometry to six Ru and five P atoms. There are two shorter (2.85 Å) and four longer (2.89 Å) Ru–Ru bond lengths. There are one shorter (2.28 Å) and four longer (2.81 Å) Ru–P bond lengths. In the third Ru site, Ru is bonded in a 12-coordinate geometry to two Gd, four Ru, and four P atoms. There are two shorter (2.83 Å) and two longer (2.84 Å) Ru–Ru bond lengths. There are a spread of Ru–P bond distances ranging from 2.30–2.35 Å. In the fourth Ru site, Ru is bonded in a 12-coordinate geometry to two equivalent Gd, four equivalent Ru, and four P atoms. All Ru–Ru bond lengths are 2.83 Å. There are two shorter (2.30 Å) and two longer (2.35 Å) Ru–P bond lengths. In the fifth Ru site, Ru is bonded in a 12-coordinate geometry to three Gd, five Ru, and four P atoms. Both Ru–Ru bond lengths are 2.83 Å. There are a spread of Ru–P bond distances ranging from 2.37–2.41 Å. In the sixth Ru site, Ru is bonded in a 12-coordinate geometry to three Gd, five Ru, and four P atoms. Both Ru–Ru bond lengths are 2.82 Å. There are a spread of Ru–P bond distances ranging from 2.37–2.41 Å. In the seventh Ru site, Ru is bonded in a 12-coordinate geometry to three Gd, five Ru, and four P atoms. Both Ru–Ru bond lengths are 2.82 Å. There are a spread of Ru–P bond distances ranging from 2.37–2.41 Å. In the eighth Ru site, Ru is bonded in a 12-coordinate geometry to three Gd, five Ru, and four P atoms. The Ru–Ru bond length is 2.73 Å. There are a spread of Ru–P bond distances ranging from 2.31–2.51 Å. In the ninth Ru site, Ru is bonded in a 12-coordinate geometry to three Gd, five Ru, and four P atoms. The Ru–Ru bond length is 2.73 Å. There are a spread of Ru–P bond distances ranging from 2.31–2.52 Å. In the tenth Ru site, Ru is bonded in a 12-coordinate geometry to three Gd, five Ru, and four P atoms. There are a spread of Ru–P bond distances ranging from 2.31–2.52 Å. In the eleventh Ru site, Ru is bonded in a 9-coordinate geometry to six Gd and three P atoms. All Ru–P bond lengths are 2.33 Å. There are seven inequivalent P sites. In the first P site, P is bonded in a 9-coordinate geometry to four Gd and five Ru atoms. In the second P site, P is bonded in a 9-coordinate geometry to four equivalent Gd and five Ru atoms. In the third P site, P is bonded in a 9-coordinate geometry to two equivalent Gd and seven Ru atoms. In the fourth P site, P is bonded in a 9-coordinate geometry to two equivalent Gd and seven Ru atoms. In the fifth P site, P is bonded in a 9-coordinate geometry to two equivalent Gd and seven Ru atoms. In the sixth P site, P is bonded in a 9-coordinate geometry to two equivalent Gd and seven Ru atoms. In the seventh P site, P is bonded in a 9-coordinate geometry to two equivalent Gd and seven Ru atoms.

36 MATERIALS SCIENCE↗

Materials Data on La19(RuO6)8 by Materials Project

La19(RuO6)8 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are nineteen inequivalent La3+ sites. In the first La3+ site, La3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of La–O bond distances ranging from 2.38–2.83 Å. In the second La3+ site, La3+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of La–O bond distances ranging from 2.38–3.11 Å. In the third La3+ site, La3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of La–O bond distances ranging from 2.35–2.82 Å. In the fourth La3+ site, La3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of La–O bond distances ranging from 2.37–2.77 Å. In the fifth La3+ site, La3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of La–O bond distances ranging from 2.41–2.82 Å. In the sixth La3+ site, La3+ is bonded in a 7-coordinate geometry to eight O2- atoms. There are a spread of La–O bond distances ranging from 2.38–3.03 Å. In the seventh La3+ site, La3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of La–O bond distances ranging from 2.33–2.92 Å. In the eighth La3+ site, La3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of La–O bond distances ranging from 2.37–2.81 Å. In the ninth La3+ site, La3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of La–O bond distances ranging from 2.43–2.57 Å. In the tenth La3+ site, La3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of La–O bond distances ranging from 2.43–2.58 Å. In the eleventh La3+ site, La3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of La–O bond distances ranging from 2.38–2.97 Å. In the twelfth La3+ site, La3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of La–O bond distances ranging from 2.32–2.92 Å. In the thirteenth La3+ site, La3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of La–O bond distances ranging from 2.35–2.61 Å. In the fourteenth La3+ site, La3+ is bonded in a 7-coordinate geometry to eight O2- atoms. There are a spread of La–O bond distances ranging from 2.38–3.00 Å. In the fifteenth La3+ site, La3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of La–O bond distances ranging from 2.42–3.01 Å. In the sixteenth La3+ site, La3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of La–O bond distances ranging from 2.36–2.70 Å. In the seventeenth La3+ site, La3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of La–O bond distances ranging from 2.37–2.81 Å. In the eighteenth La3+ site, La3+ is bonded in a 9-coordinate geometry to eight O2- atoms. There are a spread of La–O bond distances ranging from 2.37–2.94 Å. In the nineteenth La3+ site, La3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of La–O bond distances ranging from 2.41–2.74 Å. There are eight inequivalent Ru+4.88+ sites. In the first Ru+4.88+ site, Ru+4.88+ is bonded in an octahedral geometry to six O2- atoms. There are a spread of Ru–O bond distances ranging from 1.92–2.03 Å. In the second Ru+4.88+ site, Ru+4.88+ is bonded in an octahedral geometry to six O2- atoms. There are a spread of Ru–O bond distances ranging from 1.95–2.01 Å. In the third Ru+4.88+ site, Ru+4.88+ is bonded in an octahedral geometry to six O2- atoms. There are a spread of Ru–O bond distances ranging from 1.96–2.02 Å. In the fourth Ru+4.88+ site, Ru+4.88+ is bonded in an octahedral geometry to six O2- atoms. There are a spread of Ru–O bond distances ranging from 1.98–2.05 Å. In the fifth Ru+4.88+ site, Ru+4.88+ is bonded in an octahedral geometry to six O2- atoms. There are a spread of Ru–O bond distances ranging from 1.98–2.05 Å. In the sixth Ru+4.88+ site, Ru+4.88+ is bonded in an octahedral geometry to six O2- atoms. There are a spread of Ru–O bond distances ranging from 1.94–2.06 Å. In the seventh Ru+4.88+ site, Ru+4.88+ is bonded in an octahedral geometry to six O2- atoms. There are a spread of Ru–O bond distances ranging from 1.95–2.02 Å. In the eighth Ru+4.88+ site, Ru+4.88+ is bonded in an octahedral geometry to six O2- atoms. There are a spread of Ru–O bond distances ranging from 1.94–2.01 Å. There are forty-eight inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the second O2- site, O2- is bonded in a 4-coordinate geometry to four La3+ and one Ru+4.88+ atom. In the third O2- site, O2- is bonded to three La3+ and one Ru+4.88+ atom to form a mixture of distorted corner and edge-sharing OLa3Ru trigonal pyramids. In the fourth O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the fifth O2- site, O2- is bonded to three La3+ and one Ru+4.88+ atom to form distorted corner-sharing OLa3Ru trigonal pyramids. In the sixth O2- site, O2- is bonded to three La3+ and one Ru+4.88+ atom to form a mixture of distorted corner and edge-sharing OLa3Ru tetrahedra. In the seventh O2- site, O2- is bonded to three La3+ and one Ru+4.88+ atom to form a mixture of distorted corner and edge-sharing OLa3Ru trigonal pyramids. In the eighth O2- site, O2- is bonded to three La3+ and one Ru+4.88+ atom to form a mixture of distorted corner and edge-sharing OLa3Ru trigonal pyramids. In the ninth O2- site, O2- is bonded in a 3-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the tenth O2- site, O2- is bonded in a distorted trigonal planar geometry to two La3+ and one Ru+4.88+ atom. In the eleventh O2- site, O2- is bonded to three La3+ and one Ru+4.88+ atom to form a mixture of distorted corner and edge-sharing OLa3Ru trigonal pyramids. In the twelfth O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to two La3+ and one Ru+4.88+ atom. In the thirteenth O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the fourteenth O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the fifteenth O2- site, O2- is bonded in a 4-coordinate geometry to four La3+ and one Ru+4.88+ atom. In the sixteenth O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the seventeenth O2- site, O2- is bonded in a distorted T-shaped geometry to two La3+ and one Ru+4.88+ atom. In the eighteenth O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the nineteenth O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the twentieth O2- site, O2- is bonded in a distorted rectangular see-saw-like geometry to three La3+ and one Ru+4.88+ atom. In the twenty-first O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the twenty-second O2- site, O2- is bonded in a 3-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the twenty-third O2- site, O2- is bonded in a 5-coordinate geometry to four La3+ and one Ru+4.88+ atom. In the twenty-fourth O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the twenty-fifth O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the twenty-sixth O2- site, O2- is bonded in a 5-coordinate geometry to four La3+ and one Ru+4.88+ atom. In the twenty-seventh O2- site, O2- is bonded to three La3+ and one Ru+4.88+ atom to form a mixture of distorted corner and edge-sharing OLa3Ru trigonal pyramids. In the twenty-eighth O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the twenty-ninth O2- site, O2- is bonded in a distorted see-saw-like geometry to three La3+ and one Ru+4.88+ atom. In the thirtieth O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the thirty-first O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the thirty-second O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the thirty-third O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the thirty-fourth O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the thirty-fifth O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the thirty-sixth O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the thirty-seventh O2- site, O2- is bonded in a distorted T-shaped geometry to two La3+ and one Ru+4.88+ atom. In the thirty-eighth O2- site, O2- is bonded to three La3+ and one Ru+4.88+ atom to form a mixture of distorted corner and edge-sharing OLa3Ru trigonal pyramids. In the thirty-ninth O2- site, O2- is bonded in a distorted trigonal planar geometry to two La3+ and one Ru+4.88+ atom. In the fortieth O2- site, O2- is bonded in a 3-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the forty-first O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom. In the forty-second O2- site, O2- is bonded to three La3+ and one Ru+4.88+ atom to form a mixture of distorted corner and edge-sharing OLa3Ru trigonal pyramids. In the forty-third O2- site, O2- is bonded to three La3+ and one Ru+4.88+ atom to form a mixture of distorted corner and edge-sharing OLa3Ru tetrahedra. In the forty-fourth O2- site, O2- is bonded to three La3+ and one Ru+4.88+ atom to form a mixture of distorted corner and edge-sharing OLa3Ru trigonal pyramids. In the forty-fifth O2- site, O2- is bonded in a 5-coordinate geometry to four La3+ and one Ru+4.88+ atom. In the forty-sixth O2- site, O2- is bonded to three La3+ and one Ru+4.88+ atom to form a mixture of distorted corner and edge-sharing OLa3Ru tetrahedra. In the forty-seventh O2- site, O2- is bonded in a 5-coordinate geometry to four La3+ and one Ru+4.88+ atom. In the forty-eighth O2- site, O2- is bonded in a 4-coordinate geometry to three La3+ and one Ru+4.88+ atom.

36 MATERIALS SCIENCE↗