Th5Y2O13 crystallizes in the trigonal R3m space group. There are five inequivalent Th sites. In the first Th site, Th(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 Th site, Th(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 Th site, Th(3) is bonded in a body-centered cubic geometry to one O(10), one O(6), three equivalent O(7), and three equivalent O(9) atoms. In the fourth Th site, Th(4) is bonded in a body-centered cubic geometry to one O(12), one O(8), three equivalent O(11), and three equivalent O(13) atoms. In the fifth Th site, Th(5) is bonded in a body-centered cubic geometry to one O(11), one O(9), three equivalent O(10), and three equivalent O(8) atoms. There are two inequivalent Y sites. In the first Y site, Y(1) is bonded to one O(13), one O(2), and three equivalent O(12) 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 Th(1) and three equivalent Y(2) atoms to form OY3Th tetrahedra that share  a cornercorner with one O(4)Th4 tetrahedra, corners with three equivalent O(3)Th4 tetrahedra, corners with three equivalent O(2)Y4 tetrahedra, corners with six equivalent O(1)Y3Th tetrahedra, edges with three equivalent O(2)Y4 tetrahedra, and edges with three equivalent O(5)YTh3 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(13)YTh3 tetrahedra, corners with three equivalent O(1)Y3Th tetrahedra, corners with three equivalent O(12)Y3Th tetrahedra, corners with three equivalent O(5)YTh3 tetrahedra, corners with six equivalent O(2)Y4 tetrahedra, and edges with three equivalent O(1)Y3Th tetrahedra. In the third O site, O(3) is bonded to one Th(2) and three equivalent Th(1) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(7)Th4 tetrahedra, corners with three equivalent O(6)Th4 tetrahedra, corners with three equivalent O(1)Y3Th tetrahedra, corners with three equivalent O(5)YTh3 tetrahedra, corners with six equivalent O(3)Th4 tetrahedra, edges with three equivalent O(4)Th4 tetrahedra, and edges with three equivalent O(5)YTh3 tetrahedra. In the fourth O site, O(4) is bonded to one Th(1) and three equivalent Th(2) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(1)Y3Th tetrahedra, corners with three equivalent O(6)Th4 tetrahedra, corners with three equivalent O(7)Th4 tetrahedra, corners with three equivalent O(5)YTh3 tetrahedra, corners with six equivalent O(4)Th4 tetrahedra, edges with three equivalent O(3)Th4 tetrahedra, and edges with three equivalent O(6)Th4 tetrahedra. In the fifth O site, O(5) is bonded to three equivalent Th(1) and one Y(2) atom to form OYTh3 tetrahedra that share corners with three equivalent O(3)Th4 tetrahedra, corners with three equivalent O(4)Th4 tetrahedra, corners with three equivalent O(2)Y4 tetrahedra, corners with six equivalent O(5)YTh3 tetrahedra, edges with three equivalent O(3)Th4 tetrahedra, and edges with three equivalent O(1)Y3Th tetrahedra. In the sixth O site, O(6) is bonded to one Th(3) and three equivalent Th(2) atoms to form a mixture of edge and corner-sharing OTh4 tetrahedra. In the seventh O site, O(7) is bonded to one Th(2) and three equivalent Th(3) atoms to form a mixture of edge and corner-sharing OTh4 tetrahedra. In the eighth O site, O(8) is bonded to one Th(4) and three equivalent Th(5) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(12)Y3Th tetrahedra, corners with three equivalent O(10)Th4 tetrahedra, corners with three equivalent O(9)Th4 tetrahedra, corners with three equivalent O(13)YTh3 tetrahedra, corners with six equivalent O(8)Th4 tetrahedra, edges with three equivalent O(10)Th4 tetrahedra, and edges with three equivalent O(11)Th4 tetrahedra. In the ninth O site, O(9) is bonded to one Th(5) and three equivalent Th(3) atoms to form a mixture of edge and corner-sharing OTh4 tetrahedra. In the tenth O site, O(10) is bonded to one Th(3) and three equivalent Th(5) atoms to form a mixture of edge and corner-sharing OTh4 tetrahedra. In the eleventh O site, O(11) is bonded to one Th(5) and three equivalent Th(4) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(9)Th4 tetrahedra, corners with three equivalent O(10)Th4 tetrahedra, corners with three equivalent O(12)Y3Th tetrahedra, corners with three equivalent O(13)YTh3 tetrahedra, corners with six equivalent O(11)Th4 tetrahedra, edges with three equivalent O(8)Th4 tetrahedra, and edges with three equivalent O(13)YTh3 tetrahedra. In the twelfth O site, O(12) is bonded to one Th(4) and three equivalent Y(1) atoms to form distorted OY3Th tetrahedra that share  a cornercorner with one O(8)Th4 tetrahedra, corners with three equivalent O(11)Th4 tetrahedra, corners with three equivalent O(2)Y4 tetrahedra, corners with six equivalent O(12)Y3Th tetrahedra, and edges with three equivalent O(13)YTh3 tetrahedra. In the thirteenth O site, O(13) is bonded to three equivalent Th(4) and one Y(1) atom to form OYTh3 tetrahedra that share  a cornercorner with one O(2)Y4 tetrahedra, corners with three equivalent O(11)Th4 tetrahedra, corners with three equivalent O(8)Th4 tetrahedra, corners with six equivalent O(13)YTh3 tetrahedra, edges with three equivalent O(11)Th4 tetrahedra, and edges with three equivalent O(12)Y3Th tetrahedra.
Th5Y2O13 crystallizes in the trigonal R3m space group. There are five inequivalent Th sites. In the first Th site, Th(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 Th(1)-O(1) bond length is 2.40 Å. The Th(1)-O(4) bond length is 2.51 Å. All Th(1)-O(3) bond lengths are 2.43 Å. All Th(1)-O(5) bond lengths are 2.39 Å. In the second Th site, Th(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 Th(2)-O(3) bond length is 2.40 Å. The Th(2)-O(7) bond length is 2.49 Å. All Th(2)-O(4) bond lengths are 2.39 Å. All Th(2)-O(6) bond lengths are 2.43 Å. In the third Th site, Th(3) is bonded in a body-centered cubic geometry to one O(10), one O(6), three equivalent O(7), and three equivalent O(9) atoms. The Th(3)-O(10) bond length is 2.49 Å. The Th(3)-O(6) bond length is 2.39 Å. All Th(3)-O(7) bond lengths are 2.39 Å. All Th(3)-O(9) bond lengths are 2.43 Å. In the fourth Th site, Th(4) is bonded in a body-centered cubic geometry to one O(12), one O(8), three equivalent O(11), and three equivalent O(13) atoms. The Th(4)-O(12) bond length is 2.75 Å. The Th(4)-O(8) bond length is 2.39 Å. All Th(4)-O(11) bond lengths are 2.40 Å. All Th(4)-O(13) bond lengths are 2.41 Å. In the fifth Th site, Th(5) is bonded in a body-centered cubic geometry to one O(11), one O(9), three equivalent O(10), and three equivalent O(8) atoms. The Th(5)-O(11) bond length is 2.48 Å. The Th(5)-O(9) bond length is 2.40 Å. All Th(5)-O(10) bond lengths are 2.40 Å. All Th(5)-O(8) bond lengths are 2.43 Å. There are two inequivalent Y sites. In the first Y site, Y(1) is bonded to one O(13), one O(2), and three equivalent O(12) atoms to form corner-sharing YO5 trigonal bipyramids. The Y(1)-O(13) bond length is 2.35 Å. The Y(1)-O(2) bond length is 2.12 Å. All Y(1)-O(12) bond lengths are 2.31 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 2.27 Å. All Y(2)-O(1) bond lengths are 2.35 Å. All Y(2)-O(2) bond lengths are 2.61 Å. There are thirteen inequivalent O sites. In the first O site, O(1) is bonded to one Th(1) and three equivalent Y(2) atoms to form OY3Th tetrahedra that share  a cornercorner with one O(4)Th4 tetrahedra, corners with three equivalent O(3)Th4 tetrahedra, corners with three equivalent O(2)Y4 tetrahedra, corners with six equivalent O(1)Y3Th tetrahedra, edges with three equivalent O(2)Y4 tetrahedra, and edges with three equivalent O(5)YTh3 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(13)YTh3 tetrahedra, corners with three equivalent O(1)Y3Th tetrahedra, corners with three equivalent O(12)Y3Th tetrahedra, corners with three equivalent O(5)YTh3 tetrahedra, corners with six equivalent O(2)Y4 tetrahedra, and edges with three equivalent O(1)Y3Th tetrahedra. In the third O site, O(3) is bonded to one Th(2) and three equivalent Th(1) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(7)Th4 tetrahedra, corners with three equivalent O(6)Th4 tetrahedra, corners with three equivalent O(1)Y3Th tetrahedra, corners with three equivalent O(5)YTh3 tetrahedra, corners with six equivalent O(3)Th4 tetrahedra, edges with three equivalent O(4)Th4 tetrahedra, and edges with three equivalent O(5)YTh3 tetrahedra. In the fourth O site, O(4) is bonded to one Th(1) and three equivalent Th(2) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(1)Y3Th tetrahedra, corners with three equivalent O(6)Th4 tetrahedra, corners with three equivalent O(7)Th4 tetrahedra, corners with three equivalent O(5)YTh3 tetrahedra, corners with six equivalent O(4)Th4 tetrahedra, edges with three equivalent O(3)Th4 tetrahedra, and edges with three equivalent O(6)Th4 tetrahedra. In the fifth O site, O(5) is bonded to three equivalent Th(1) and one Y(2) atom to form OYTh3 tetrahedra that share corners with three equivalent O(3)Th4 tetrahedra, corners with three equivalent O(4)Th4 tetrahedra, corners with three equivalent O(2)Y4 tetrahedra, corners with six equivalent O(5)YTh3 tetrahedra, edges with three equivalent O(3)Th4 tetrahedra, and edges with three equivalent O(1)Y3Th tetrahedra. In the sixth O site, O(6) is bonded to one Th(3) and three equivalent Th(2) atoms to form a mixture of edge and corner-sharing OTh4 tetrahedra. In the seventh O site, O(7) is bonded to one Th(2) and three equivalent Th(3) atoms to form a mixture of edge and corner-sharing OTh4 tetrahedra. In the eighth O site, O(8) is bonded to one Th(4) and three equivalent Th(5) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(12)Y3Th tetrahedra, corners with three equivalent O(10)Th4 tetrahedra, corners with three equivalent O(9)Th4 tetrahedra, corners with three equivalent O(13)YTh3 tetrahedra, corners with six equivalent O(8)Th4 tetrahedra, edges with three equivalent O(10)Th4 tetrahedra, and edges with three equivalent O(11)Th4 tetrahedra. In the ninth O site, O(9) is bonded to one Th(5) and three equivalent Th(3) atoms to form a mixture of edge and corner-sharing OTh4 tetrahedra. In the tenth O site, O(10) is bonded to one Th(3) and three equivalent Th(5) atoms to form a mixture of edge and corner-sharing OTh4 tetrahedra. In the eleventh O site, O(11) is bonded to one Th(5) and three equivalent Th(4) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(9)Th4 tetrahedra, corners with three equivalent O(10)Th4 tetrahedra, corners with three equivalent O(12)Y3Th tetrahedra, corners with three equivalent O(13)YTh3 tetrahedra, corners with six equivalent O(11)Th4 tetrahedra, edges with three equivalent O(8)Th4 tetrahedra, and edges with three equivalent O(13)YTh3 tetrahedra. In the twelfth O site, O(12) is bonded to one Th(4) and three equivalent Y(1) atoms to form distorted OY3Th tetrahedra that share  a cornercorner with one O(8)Th4 tetrahedra, corners with three equivalent O(11)Th4 tetrahedra, corners with three equivalent O(2)Y4 tetrahedra, corners with six equivalent O(12)Y3Th tetrahedra, and edges with three equivalent O(13)YTh3 tetrahedra. In the thirteenth O site, O(13) is bonded to three equivalent Th(4) and one Y(1) atom to form OYTh3 tetrahedra that share  a cornercorner with one O(2)Y4 tetrahedra, corners with three equivalent O(11)Th4 tetrahedra, corners with three equivalent O(8)Th4 tetrahedra, corners with six equivalent O(13)YTh3 tetrahedra, edges with three equivalent O(11)Th4 tetrahedra, and edges with three equivalent O(12)Y3Th tetrahedra.