Th5La2O13 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(2), 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(5), one O(6), three equivalent O(4), and three equivalent O(7) atoms. In the third Th site, Th(3) is bonded in a body-centered cubic geometry to one O(7), one O(9), three equivalent O(6), and three equivalent O(8) atoms. In the fourth Th site, Th(4) is bonded in a body-centered cubic geometry to one O(13), one O(8), three equivalent O(10), and three equivalent O(9) atoms. In the fifth Th site, Th(5) is bonded in a body-centered cubic geometry to one O(10), one O(12), three equivalent O(11), and three equivalent O(13) atoms. There are two inequivalent La sites. In the first La site, La(1) is bonded to one O(1), one O(11), and three equivalent O(12) atoms to form distorted corner-sharing LaO5 trigonal bipyramids. In the second La site, La(2) is bonded in a 7-coordinate geometry to one O(3), 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 La(1) and three equivalent La(2) atoms to form distorted OLa4 tetrahedra that share  a cornercorner with one O(11)LaTh3 tetrahedra, corners with three equivalent O(12)La3Th tetrahedra, corners with three equivalent O(2)La3Th tetrahedra, corners with three equivalent O(3)LaTh3 tetrahedra, corners with six equivalent O(1)La4 tetrahedra, and edges with three equivalent O(2)La3Th tetrahedra. In the second O site, O(2) is bonded to one Th(1) and three equivalent La(2) atoms to form OLa3Th tetrahedra that share  a cornercorner with one O(4)Th4 tetrahedra, corners with three equivalent O(1)La4 tetrahedra, corners with three equivalent O(5)Th4 tetrahedra, corners with six equivalent O(2)La3Th tetrahedra, edges with three equivalent O(1)La4 tetrahedra, and edges with three equivalent O(3)LaTh3 tetrahedra. In the third O site, O(3) is bonded to three equivalent Th(1) and one La(2) atom to form OLaTh3 tetrahedra that share corners with three equivalent O(1)La4 tetrahedra, corners with three equivalent O(4)Th4 tetrahedra, corners with three equivalent O(5)Th4 tetrahedra, corners with six equivalent O(3)LaTh3 tetrahedra, edges with three equivalent O(2)La3Th tetrahedra, and edges with three equivalent O(5)Th4 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(2)La3Th tetrahedra, corners with three equivalent O(3)LaTh3 tetrahedra, corners with three equivalent O(6)Th4 tetrahedra, corners with three equivalent O(7)Th4 tetrahedra, corners with six equivalent O(4)Th4 tetrahedra, edges with three equivalent O(5)Th4 tetrahedra, and edges with three equivalent O(7)Th4 tetrahedra. In the fifth O site, O(5) is bonded to one Th(2) and three equivalent Th(1) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(6)Th4 tetrahedra, corners with three equivalent O(2)La3Th tetrahedra, corners with three equivalent O(3)LaTh3 tetrahedra, corners with three equivalent O(7)Th4 tetrahedra, corners with six equivalent O(5)Th4 tetrahedra, edges with three equivalent O(3)LaTh3 tetrahedra, and edges with three equivalent O(4)Th4 tetrahedra. In the sixth O site, O(6) is bonded to one Th(2) and three equivalent Th(3) atoms to form a mixture of corner and edge-sharing OTh4 tetrahedra. In the seventh O site, O(7) is bonded to one Th(3) and three equivalent Th(2) atoms to form a mixture of corner and edge-sharing OTh4 tetrahedra. In the eighth O site, O(8) is bonded to one Th(4) and three equivalent Th(3) atoms to form a mixture of corner and edge-sharing OTh4 tetrahedra. In the ninth O site, O(9) is bonded to one Th(3) and three equivalent Th(4) atoms to form a mixture of corner and edge-sharing OTh4 tetrahedra. In the tenth O site, O(10) is bonded to one Th(5) and three equivalent Th(4) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(12)La3Th tetrahedra, corners with three equivalent O(11)LaTh3 tetrahedra, corners with three equivalent O(8)Th4 tetrahedra, corners with three equivalent O(9)Th4 tetrahedra, corners with six equivalent O(10)Th4 tetrahedra, edges with three equivalent O(13)Th4 tetrahedra, and edges with three equivalent O(9)Th4 tetrahedra. In the eleventh O site, O(11) is bonded to three equivalent Th(5) and one La(1) atom to form OLaTh3 tetrahedra that share  a cornercorner with one O(1)La4 tetrahedra, corners with three equivalent O(10)Th4 tetrahedra, corners with three equivalent O(13)Th4 tetrahedra, corners with six equivalent O(11)LaTh3 tetrahedra, edges with three equivalent O(12)La3Th tetrahedra, and edges with three equivalent O(13)Th4 tetrahedra. In the twelfth O site, O(12) is bonded to one Th(5) and three equivalent La(1) atoms to form distorted OLa3Th tetrahedra that share  a cornercorner with one O(10)Th4 tetrahedra, corners with three equivalent O(1)La4 tetrahedra, corners with three equivalent O(13)Th4 tetrahedra, corners with six equivalent O(12)La3Th tetrahedra, and edges with three equivalent O(11)LaTh3 tetrahedra. In the thirteenth O site, O(13) is bonded to one Th(4) and three equivalent Th(5) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(8)Th4 tetrahedra, corners with three equivalent O(12)La3Th tetrahedra, corners with three equivalent O(11)LaTh3 tetrahedra, corners with three equivalent O(9)Th4 tetrahedra, corners with six equivalent O(13)Th4 tetrahedra, edges with three equivalent O(11)LaTh3 tetrahedra, and edges with three equivalent O(10)Th4 tetrahedra.
Th5La2O13 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(2), one O(4), three equivalent O(3), and three equivalent O(5) atoms. The Th(1)-O(2) bond length is 2.39 Å. The Th(1)-O(4) bond length is 2.48 Å. All Th(1)-O(3) bond lengths are 2.41 Å. All Th(1)-O(5) bond lengths are 2.45 Å. In the second Th site, Th(2) is bonded in a body-centered cubic geometry to one O(5), one O(6), three equivalent O(4), and three equivalent O(7) atoms. The Th(2)-O(5) bond length is 2.39 Å. The Th(2)-O(6) bond length is 2.50 Å. All Th(2)-O(4) bond lengths are 2.42 Å. All Th(2)-O(7) bond lengths are 2.45 Å. In the third Th site, Th(3) is bonded in a body-centered cubic geometry to one O(7), one O(9), three equivalent O(6), and three equivalent O(8) atoms. The Th(3)-O(7) bond length is 2.41 Å. The Th(3)-O(9) bond length is 2.51 Å. All Th(3)-O(6) bond lengths are 2.42 Å. All Th(3)-O(8) bond lengths are 2.46 Å. In the fourth Th site, Th(4) is bonded in a body-centered cubic geometry to one O(13), one O(8), three equivalent O(10), and three equivalent O(9) atoms. The Th(4)-O(13) bond length is 2.49 Å. The Th(4)-O(8) bond length is 2.41 Å. All Th(4)-O(10) bond lengths are 2.46 Å. All Th(4)-O(9) bond lengths are 2.42 Å. In the fifth Th site, Th(5) is bonded in a body-centered cubic geometry to one O(10), one O(12), three equivalent O(11), and three equivalent O(13) atoms. The Th(5)-O(10) bond length is 2.38 Å. The Th(5)-O(12) bond length is 2.71 Å. All Th(5)-O(11) bond lengths are 2.44 Å. All Th(5)-O(13) bond lengths are 2.42 Å. There are two inequivalent La sites. In the first La site, La(1) is bonded to one O(1), one O(11), and three equivalent O(12) atoms to form distorted corner-sharing LaO5 trigonal bipyramids. The La(1)-O(1) bond length is 2.22 Å. The La(1)-O(11) bond length is 2.45 Å. All La(1)-O(12) bond lengths are 2.36 Å. In the second La site, La(2) is bonded in a 7-coordinate geometry to one O(3), three equivalent O(1), and three equivalent O(2) atoms. The La(2)-O(3) bond length is 2.39 Å. All La(2)-O(1) bond lengths are 2.64 Å. All La(2)-O(2) bond lengths are 2.42 Å. There are thirteen inequivalent O sites. In the first O site, O(1) is bonded to one La(1) and three equivalent La(2) atoms to form distorted OLa4 tetrahedra that share  a cornercorner with one O(11)LaTh3 tetrahedra, corners with three equivalent O(12)La3Th tetrahedra, corners with three equivalent O(2)La3Th tetrahedra, corners with three equivalent O(3)LaTh3 tetrahedra, corners with six equivalent O(1)La4 tetrahedra, and edges with three equivalent O(2)La3Th tetrahedra. In the second O site, O(2) is bonded to one Th(1) and three equivalent La(2) atoms to form OLa3Th tetrahedra that share  a cornercorner with one O(4)Th4 tetrahedra, corners with three equivalent O(1)La4 tetrahedra, corners with three equivalent O(5)Th4 tetrahedra, corners with six equivalent O(2)La3Th tetrahedra, edges with three equivalent O(1)La4 tetrahedra, and edges with three equivalent O(3)LaTh3 tetrahedra. In the third O site, O(3) is bonded to three equivalent Th(1) and one La(2) atom to form OLaTh3 tetrahedra that share corners with three equivalent O(1)La4 tetrahedra, corners with three equivalent O(4)Th4 tetrahedra, corners with three equivalent O(5)Th4 tetrahedra, corners with six equivalent O(3)LaTh3 tetrahedra, edges with three equivalent O(2)La3Th tetrahedra, and edges with three equivalent O(5)Th4 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(2)La3Th tetrahedra, corners with three equivalent O(3)LaTh3 tetrahedra, corners with three equivalent O(6)Th4 tetrahedra, corners with three equivalent O(7)Th4 tetrahedra, corners with six equivalent O(4)Th4 tetrahedra, edges with three equivalent O(5)Th4 tetrahedra, and edges with three equivalent O(7)Th4 tetrahedra. In the fifth O site, O(5) is bonded to one Th(2) and three equivalent Th(1) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(6)Th4 tetrahedra, corners with three equivalent O(2)La3Th tetrahedra, corners with three equivalent O(3)LaTh3 tetrahedra, corners with three equivalent O(7)Th4 tetrahedra, corners with six equivalent O(5)Th4 tetrahedra, edges with three equivalent O(3)LaTh3 tetrahedra, and edges with three equivalent O(4)Th4 tetrahedra. In the sixth O site, O(6) is bonded to one Th(2) and three equivalent Th(3) atoms to form a mixture of corner and edge-sharing OTh4 tetrahedra. In the seventh O site, O(7) is bonded to one Th(3) and three equivalent Th(2) atoms to form a mixture of corner and edge-sharing OTh4 tetrahedra. In the eighth O site, O(8) is bonded to one Th(4) and three equivalent Th(3) atoms to form a mixture of corner and edge-sharing OTh4 tetrahedra. In the ninth O site, O(9) is bonded to one Th(3) and three equivalent Th(4) atoms to form a mixture of corner and edge-sharing OTh4 tetrahedra. In the tenth O site, O(10) is bonded to one Th(5) and three equivalent Th(4) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(12)La3Th tetrahedra, corners with three equivalent O(11)LaTh3 tetrahedra, corners with three equivalent O(8)Th4 tetrahedra, corners with three equivalent O(9)Th4 tetrahedra, corners with six equivalent O(10)Th4 tetrahedra, edges with three equivalent O(13)Th4 tetrahedra, and edges with three equivalent O(9)Th4 tetrahedra. In the eleventh O site, O(11) is bonded to three equivalent Th(5) and one La(1) atom to form OLaTh3 tetrahedra that share  a cornercorner with one O(1)La4 tetrahedra, corners with three equivalent O(10)Th4 tetrahedra, corners with three equivalent O(13)Th4 tetrahedra, corners with six equivalent O(11)LaTh3 tetrahedra, edges with three equivalent O(12)La3Th tetrahedra, and edges with three equivalent O(13)Th4 tetrahedra. In the twelfth O site, O(12) is bonded to one Th(5) and three equivalent La(1) atoms to form distorted OLa3Th tetrahedra that share  a cornercorner with one O(10)Th4 tetrahedra, corners with three equivalent O(1)La4 tetrahedra, corners with three equivalent O(13)Th4 tetrahedra, corners with six equivalent O(12)La3Th tetrahedra, and edges with three equivalent O(11)LaTh3 tetrahedra. In the thirteenth O site, O(13) is bonded to one Th(4) and three equivalent Th(5) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(8)Th4 tetrahedra, corners with three equivalent O(12)La3Th tetrahedra, corners with three equivalent O(11)LaTh3 tetrahedra, corners with three equivalent O(9)Th4 tetrahedra, corners with six equivalent O(13)Th4 tetrahedra, edges with three equivalent O(11)LaTh3 tetrahedra, and edges with three equivalent O(10)Th4 tetrahedra.