Ce5Y2O13 crystallizes in the trigonal R3m space group. There are five inequivalent Ce sites. In the first Ce site, Ce(1) is bonded in a body-centered cubic geometry to one O(1), one O(4), three equivalent O(3), and three equivalent O(5) atoms. In the second Ce site, Ce(2) is bonded in a body-centered cubic geometry to one O(3), one O(7), three equivalent O(4), and three equivalent O(6) atoms. In the third Ce site, Ce(3) is bonded in a body-centered cubic geometry to one O(6), one O(9), three equivalent O(10), and three equivalent O(7) atoms. In the fourth Ce site, Ce(4) is bonded in a body-centered cubic geometry to one O(10), one O(12), three equivalent O(8), and three equivalent O(9) atoms. In the fifth Ce site, Ce(5) is bonded in a body-centered cubic geometry to one O(13), one O(8), three equivalent O(11), and three equivalent O(12) atoms. There are two inequivalent Y sites. In the first Y site, Y(1) is bonded to one O(11), one O(2), and three equivalent O(13) atoms to form corner-sharing YO5 trigonal bipyramids. In the second Y site, Y(2) is bonded in a 7-coordinate geometry to one O(5), three equivalent O(1), and three equivalent O(2) atoms. There are thirteen inequivalent O sites. In the first O site, O(1) is bonded to one Ce(1) and three equivalent Y(2) atoms to form OCeY3 tetrahedra that share  a cornercorner with one O(4)Ce4 tetrahedra, corners with three equivalent O(3)Ce4 tetrahedra, corners with three equivalent O(2)Y4 tetrahedra, corners with six equivalent O(1)CeY3 tetrahedra, edges with three equivalent O(5)Ce3Y tetrahedra, and edges with three equivalent O(2)Y4 tetrahedra. In the second O site, O(2) is bonded to one Y(1) and three equivalent Y(2) atoms to form distorted OY4 tetrahedra that share  a cornercorner with one O(11)Ce3Y tetrahedra, corners with three equivalent O(5)Ce3Y tetrahedra, corners with three equivalent O(1)CeY3 tetrahedra, corners with six equivalent O(2)Y4 tetrahedra, corners with three equivalent O(13)CeY3 trigonal pyramids, and edges with three equivalent O(1)CeY3 tetrahedra. In the third O site, O(3) is bonded to one Ce(2) and three equivalent Ce(1) atoms to form OCe4 tetrahedra that share  a cornercorner with one O(7)Ce4 tetrahedra, corners with three equivalent O(5)Ce3Y tetrahedra, corners with three equivalent O(6)Ce4 tetrahedra, corners with three equivalent O(1)CeY3 tetrahedra, corners with six equivalent O(3)Ce4 tetrahedra, edges with three equivalent O(5)Ce3Y tetrahedra, and edges with three equivalent O(4)Ce4 tetrahedra. In the fourth O site, O(4) is bonded to one Ce(1) and three equivalent Ce(2) atoms to form OCe4 tetrahedra that share  a cornercorner with one O(1)CeY3 tetrahedra, corners with three equivalent O(5)Ce3Y tetrahedra, corners with three equivalent O(6)Ce4 tetrahedra, corners with three equivalent O(7)Ce4 tetrahedra, corners with six equivalent O(4)Ce4 tetrahedra, edges with three equivalent O(3)Ce4 tetrahedra, and edges with three equivalent O(6)Ce4 tetrahedra. In the fifth O site, O(5) is bonded to three equivalent Ce(1) and one Y(2) atom to form OCe3Y tetrahedra that share corners with three equivalent O(3)Ce4 tetrahedra, corners with three equivalent O(4)Ce4 tetrahedra, corners with three equivalent O(2)Y4 tetrahedra, corners with six equivalent O(5)Ce3Y tetrahedra, edges with three equivalent O(3)Ce4 tetrahedra, and edges with three equivalent O(1)CeY3 tetrahedra. In the sixth O site, O(6) is bonded to one Ce(3) and three equivalent Ce(2) atoms to form a mixture of corner and edge-sharing OCe4 tetrahedra. In the seventh O site, O(7) is bonded to one Ce(2) and three equivalent Ce(3) atoms to form a mixture of corner and edge-sharing OCe4 tetrahedra. In the eighth O site, O(8) is bonded to one Ce(5) and three equivalent Ce(4) atoms to form OCe4 tetrahedra that share corners with three equivalent O(11)Ce3Y tetrahedra, corners with three equivalent O(10)Ce4 tetrahedra, corners with three equivalent O(9)Ce4 tetrahedra, corners with six equivalent O(8)Ce4 tetrahedra,  a cornercorner with one O(13)CeY3 trigonal pyramid, edges with three equivalent O(12)Ce4 tetrahedra, and edges with three equivalent O(9)Ce4 tetrahedra. In the ninth O site, O(9) is bonded to one Ce(3) and three equivalent Ce(4) atoms to form a mixture of corner and edge-sharing OCe4 tetrahedra. In the tenth O site, O(10) is bonded to one Ce(4) and three equivalent Ce(3) atoms to form a mixture of corner and edge-sharing OCe4 tetrahedra. In the eleventh O site, O(11) is bonded to three equivalent Ce(5) and one Y(1) atom to form OCe3Y tetrahedra that share  a cornercorner with one O(2)Y4 tetrahedra, corners with three equivalent O(12)Ce4 tetrahedra, corners with three equivalent O(8)Ce4 tetrahedra, corners with six equivalent O(11)Ce3Y tetrahedra, edges with three equivalent O(12)Ce4 tetrahedra, and edges with three equivalent O(13)CeY3 trigonal pyramids. In the twelfth O site, O(12) is bonded to one Ce(4) and three equivalent Ce(5) atoms to form OCe4 tetrahedra that share  a cornercorner with one O(10)Ce4 tetrahedra, corners with three equivalent O(11)Ce3Y tetrahedra, corners with three equivalent O(9)Ce4 tetrahedra, corners with six equivalent O(12)Ce4 tetrahedra, corners with three equivalent O(13)CeY3 trigonal pyramids, edges with three equivalent O(11)Ce3Y tetrahedra, and edges with three equivalent O(8)Ce4 tetrahedra. In the thirteenth O site, O(13) is bonded to one Ce(5) and three equivalent Y(1) atoms to form distorted OCeY3 trigonal pyramids that share  a cornercorner with one O(8)Ce4 tetrahedra, corners with three equivalent O(12)Ce4 tetrahedra, corners with three equivalent O(2)Y4 tetrahedra, corners with six equivalent O(13)CeY3 trigonal pyramids, and edges with three equivalent O(11)Ce3Y tetrahedra.
Ce5Y2O13 crystallizes in the trigonal R3m space group. There are five inequivalent Ce sites. In the first Ce site, Ce(1) is bonded in a body-centered cubic geometry to one O(1), one O(4), three equivalent O(3), and three equivalent O(5) atoms. The Ce(1)-O(1) bond length is 2.34 Å. The Ce(1)-O(4) bond length is 2.45 Å. All Ce(1)-O(3) bond lengths are 2.37 Å. All Ce(1)-O(5) bond lengths are 2.33 Å. In the second Ce site, Ce(2) is bonded in a body-centered cubic geometry to one O(3), one O(7), three equivalent O(4), and three equivalent O(6) atoms. The Ce(2)-O(3) bond length is 2.32 Å. The Ce(2)-O(7) bond length is 2.45 Å. All Ce(2)-O(4) bond lengths are 2.33 Å. All Ce(2)-O(6) bond lengths are 2.37 Å. In the third Ce site, Ce(3) is bonded in a body-centered cubic geometry to one O(6), one O(9), three equivalent O(10), and three equivalent O(7) atoms. The Ce(3)-O(6) bond length is 2.33 Å. The Ce(3)-O(9) bond length is 2.45 Å. All Ce(3)-O(10) bond lengths are 2.37 Å. All Ce(3)-O(7) bond lengths are 2.33 Å. In the fourth Ce site, Ce(4) is bonded in a body-centered cubic geometry to one O(10), one O(12), three equivalent O(8), and three equivalent O(9) atoms. The Ce(4)-O(10) bond length is 2.33 Å. The Ce(4)-O(12) bond length is 2.43 Å. All Ce(4)-O(8) bond lengths are 2.37 Å. All Ce(4)-O(9) bond lengths are 2.33 Å. In the fifth Ce site, Ce(5) is bonded in a body-centered cubic geometry to one O(13), one O(8), three equivalent O(11), and three equivalent O(12) atoms. The Ce(5)-O(13) bond length is 2.76 Å. The Ce(5)-O(8) bond length is 2.31 Å. All Ce(5)-O(11) bond lengths are 2.36 Å. All Ce(5)-O(12) bond lengths are 2.33 Å. There are two inequivalent Y sites. In the first Y site, Y(1) is bonded to one O(11), one O(2), and three equivalent O(13) atoms to form corner-sharing YO5 trigonal bipyramids. The Y(1)-O(11) bond length is 2.34 Å. The Y(1)-O(2) bond length is 2.13 Å. All Y(1)-O(13) bond lengths are 2.25 Å. In the second Y site, Y(2) is bonded in a 7-coordinate geometry to one O(5), three equivalent O(1), and three equivalent O(2) atoms. The Y(2)-O(5) bond length is 2.28 Å. All Y(2)-O(1) bond lengths are 2.31 Å. All Y(2)-O(2) bond lengths are 2.54 Å. There are thirteen inequivalent O sites. In the first O site, O(1) is bonded to one Ce(1) and three equivalent Y(2) atoms to form OCeY3 tetrahedra that share  a cornercorner with one O(4)Ce4 tetrahedra, corners with three equivalent O(3)Ce4 tetrahedra, corners with three equivalent O(2)Y4 tetrahedra, corners with six equivalent O(1)CeY3 tetrahedra, edges with three equivalent O(5)Ce3Y tetrahedra, and edges with three equivalent O(2)Y4 tetrahedra. In the second O site, O(2) is bonded to one Y(1) and three equivalent Y(2) atoms to form distorted OY4 tetrahedra that share  a cornercorner with one O(11)Ce3Y tetrahedra, corners with three equivalent O(5)Ce3Y tetrahedra, corners with three equivalent O(1)CeY3 tetrahedra, corners with six equivalent O(2)Y4 tetrahedra, corners with three equivalent O(13)CeY3 trigonal pyramids, and edges with three equivalent O(1)CeY3 tetrahedra. In the third O site, O(3) is bonded to one Ce(2) and three equivalent Ce(1) atoms to form OCe4 tetrahedra that share  a cornercorner with one O(7)Ce4 tetrahedra, corners with three equivalent O(5)Ce3Y tetrahedra, corners with three equivalent O(6)Ce4 tetrahedra, corners with three equivalent O(1)CeY3 tetrahedra, corners with six equivalent O(3)Ce4 tetrahedra, edges with three equivalent O(5)Ce3Y tetrahedra, and edges with three equivalent O(4)Ce4 tetrahedra. In the fourth O site, O(4) is bonded to one Ce(1) and three equivalent Ce(2) atoms to form OCe4 tetrahedra that share  a cornercorner with one O(1)CeY3 tetrahedra, corners with three equivalent O(5)Ce3Y tetrahedra, corners with three equivalent O(6)Ce4 tetrahedra, corners with three equivalent O(7)Ce4 tetrahedra, corners with six equivalent O(4)Ce4 tetrahedra, edges with three equivalent O(3)Ce4 tetrahedra, and edges with three equivalent O(6)Ce4 tetrahedra. In the fifth O site, O(5) is bonded to three equivalent Ce(1) and one Y(2) atom to form OCe3Y tetrahedra that share corners with three equivalent O(3)Ce4 tetrahedra, corners with three equivalent O(4)Ce4 tetrahedra, corners with three equivalent O(2)Y4 tetrahedra, corners with six equivalent O(5)Ce3Y tetrahedra, edges with three equivalent O(3)Ce4 tetrahedra, and edges with three equivalent O(1)CeY3 tetrahedra. In the sixth O site, O(6) is bonded to one Ce(3) and three equivalent Ce(2) atoms to form a mixture of corner and edge-sharing OCe4 tetrahedra. In the seventh O site, O(7) is bonded to one Ce(2) and three equivalent Ce(3) atoms to form a mixture of corner and edge-sharing OCe4 tetrahedra. In the eighth O site, O(8) is bonded to one Ce(5) and three equivalent Ce(4) atoms to form OCe4 tetrahedra that share corners with three equivalent O(11)Ce3Y tetrahedra, corners with three equivalent O(10)Ce4 tetrahedra, corners with three equivalent O(9)Ce4 tetrahedra, corners with six equivalent O(8)Ce4 tetrahedra,  a cornercorner with one O(13)CeY3 trigonal pyramid, edges with three equivalent O(12)Ce4 tetrahedra, and edges with three equivalent O(9)Ce4 tetrahedra. In the ninth O site, O(9) is bonded to one Ce(3) and three equivalent Ce(4) atoms to form a mixture of corner and edge-sharing OCe4 tetrahedra. In the tenth O site, O(10) is bonded to one Ce(4) and three equivalent Ce(3) atoms to form a mixture of corner and edge-sharing OCe4 tetrahedra. In the eleventh O site, O(11) is bonded to three equivalent Ce(5) and one Y(1) atom to form OCe3Y tetrahedra that share  a cornercorner with one O(2)Y4 tetrahedra, corners with three equivalent O(12)Ce4 tetrahedra, corners with three equivalent O(8)Ce4 tetrahedra, corners with six equivalent O(11)Ce3Y tetrahedra, edges with three equivalent O(12)Ce4 tetrahedra, and edges with three equivalent O(13)CeY3 trigonal pyramids. In the twelfth O site, O(12) is bonded to one Ce(4) and three equivalent Ce(5) atoms to form OCe4 tetrahedra that share  a cornercorner with one O(10)Ce4 tetrahedra, corners with three equivalent O(11)Ce3Y tetrahedra, corners with three equivalent O(9)Ce4 tetrahedra, corners with six equivalent O(12)Ce4 tetrahedra, corners with three equivalent O(13)CeY3 trigonal pyramids, edges with three equivalent O(11)Ce3Y tetrahedra, and edges with three equivalent O(8)Ce4 tetrahedra. In the thirteenth O site, O(13) is bonded to one Ce(5) and three equivalent Y(1) atoms to form distorted OCeY3 trigonal pyramids that share  a cornercorner with one O(8)Ce4 tetrahedra, corners with three equivalent O(12)Ce4 tetrahedra, corners with three equivalent O(2)Y4 tetrahedra, corners with six equivalent O(13)CeY3 trigonal pyramids, and edges with three equivalent O(11)Ce3Y tetrahedra.