Dy2Ce5O13 crystallizes in the trigonal R3m space group. There are two inequivalent Dy sites. In the first Dy site, Dy(1) is bonded to one O(13), one O(2), and three equivalent O(11) atoms to form corner-sharing DyO5 trigonal bipyramids. In the second Dy site, Dy(2) is bonded in a 7-coordinate geometry to one O(4), three equivalent O(1), and three equivalent O(2) atoms. 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(5), three equivalent O(3), and three equivalent O(4) atoms. In the second Ce site, Ce(2) is bonded in a body-centered cubic geometry to one O(3), one O(6), three equivalent O(5), and three equivalent O(7) atoms. In the third Ce site, Ce(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 Ce site, Ce(4) is bonded in a body-centered cubic geometry to one O(12), one O(8), three equivalent O(10), and three equivalent O(9) atoms. In the fifth Ce site, Ce(5) is bonded in a body-centered cubic geometry to one O(10), one O(11), three equivalent O(12), and three equivalent O(13) atoms. There are thirteen inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Dy(2) and one Ce(1) atom to form OCeDy3 tetrahedra that share  a cornercorner with one O(5)Ce4 tetrahedra, corners with three equivalent O(3)Ce4 tetrahedra, corners with three equivalent O(2)Dy4 tetrahedra, corners with six equivalent O(1)CeDy3 tetrahedra, edges with three equivalent O(4)Ce3Dy tetrahedra, and edges with three equivalent O(2)Dy4 tetrahedra. In the second O site, O(2) is bonded to one Dy(1) and three equivalent Dy(2) atoms to form distorted ODy4 tetrahedra that share  a cornercorner with one O(13)Ce3Dy tetrahedra, corners with three equivalent O(4)Ce3Dy tetrahedra, corners with three equivalent O(1)CeDy3 tetrahedra, corners with six equivalent O(2)Dy4 tetrahedra, corners with three equivalent O(11)CeDy3 trigonal pyramids, and edges with three equivalent O(1)CeDy3 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(6)Ce4 tetrahedra, corners with three equivalent O(4)Ce3Dy tetrahedra, corners with three equivalent O(7)Ce4 tetrahedra, corners with three equivalent O(1)CeDy3 tetrahedra, corners with six equivalent O(3)Ce4 tetrahedra, edges with three equivalent O(4)Ce3Dy tetrahedra, and edges with three equivalent O(5)Ce4 tetrahedra. In the fourth O site, O(4) is bonded to one Dy(2) and three equivalent Ce(1) atoms to form OCe3Dy tetrahedra that share corners with three equivalent O(3)Ce4 tetrahedra, corners with three equivalent O(5)Ce4 tetrahedra, corners with three equivalent O(2)Dy4 tetrahedra, corners with six equivalent O(4)Ce3Dy tetrahedra, edges with three equivalent O(3)Ce4 tetrahedra, and edges with three equivalent O(1)CeDy3 tetrahedra. In the fifth O site, O(5) is bonded to one Ce(1) and three equivalent Ce(2) atoms to form OCe4 tetrahedra that share  a cornercorner with one O(1)CeDy3 tetrahedra, corners with three equivalent O(4)Ce3Dy tetrahedra, corners with three equivalent O(6)Ce4 tetrahedra, corners with three equivalent O(7)Ce4 tetrahedra, corners with six equivalent O(5)Ce4 tetrahedra, edges with three equivalent O(3)Ce4 tetrahedra, and edges with three equivalent O(7)Ce4 tetrahedra. In the sixth O site, O(6) is bonded to one Ce(2) and three equivalent Ce(3) atoms to form a mixture of edge and corner-sharing OCe4 tetrahedra. In the seventh O site, O(7) is bonded to one Ce(3) and three equivalent Ce(2) atoms to form a mixture of edge and corner-sharing OCe4 tetrahedra. In the eighth O site, O(8) is bonded to one Ce(4) and three equivalent Ce(3) atoms to form a mixture of edge and corner-sharing OCe4 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 edge and corner-sharing OCe4 tetrahedra. In the tenth O site, O(10) is bonded to one Ce(5) and three equivalent Ce(4) atoms to form OCe4 tetrahedra that share corners with three equivalent O(13)Ce3Dy tetrahedra, corners with three equivalent O(8)Ce4 tetrahedra, corners with three equivalent O(9)Ce4 tetrahedra, corners with six equivalent O(10)Ce4 tetrahedra,  a cornercorner with one O(11)CeDy3 trigonal pyramid, edges with three equivalent O(12)Ce4 tetrahedra, and edges with three equivalent O(9)Ce4 tetrahedra. In the eleventh O site, O(11) is bonded to three equivalent Dy(1) and one Ce(5) atom to form distorted OCeDy3 trigonal pyramids that share  a cornercorner with one O(10)Ce4 tetrahedra, corners with three equivalent O(12)Ce4 tetrahedra, corners with three equivalent O(2)Dy4 tetrahedra, corners with six equivalent O(11)CeDy3 trigonal pyramids, and edges with three equivalent O(13)Ce3Dy tetrahedra. 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(8)Ce4 tetrahedra, corners with three equivalent O(13)Ce3Dy tetrahedra, corners with three equivalent O(9)Ce4 tetrahedra, corners with six equivalent O(12)Ce4 tetrahedra, corners with three equivalent O(11)CeDy3 trigonal pyramids, edges with three equivalent O(13)Ce3Dy tetrahedra, and edges with three equivalent O(10)Ce4 tetrahedra. In the thirteenth O site, O(13) is bonded to one Dy(1) and three equivalent Ce(5) atoms to form OCe3Dy tetrahedra that share  a cornercorner with one O(2)Dy4 tetrahedra, corners with three equivalent O(10)Ce4 tetrahedra, corners with three equivalent O(12)Ce4 tetrahedra, corners with six equivalent O(13)Ce3Dy tetrahedra, edges with three equivalent O(12)Ce4 tetrahedra, and edges with three equivalent O(11)CeDy3 trigonal pyramids.
Dy2Ce5O13 crystallizes in the trigonal R3m space group. There are two inequivalent Dy sites. In the first Dy site, Dy(1) is bonded to one O(13), one O(2), and three equivalent O(11) atoms to form corner-sharing DyO5 trigonal bipyramids. The Dy(1)-O(13) bond length is 2.34 Å. The Dy(1)-O(2) bond length is 2.13 Å. All Dy(1)-O(11) bond lengths are 2.24 Å. In the second Dy site, Dy(2) is bonded in a 7-coordinate geometry to one O(4), three equivalent O(1), and three equivalent O(2) atoms. The Dy(2)-O(4) bond length is 2.26 Å. All Dy(2)-O(1) bond lengths are 2.31 Å. All Dy(2)-O(2) bond lengths are 2.54 Å. 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(5), three equivalent O(3), and three equivalent O(4) atoms. The Ce(1)-O(1) bond length is 2.33 Å. The Ce(1)-O(5) bond length is 2.45 Å. All Ce(1)-O(3) bond lengths are 2.37 Å. All Ce(1)-O(4) 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(6), three equivalent O(5), and three equivalent O(7) atoms. The Ce(2)-O(3) bond length is 2.33 Å. The Ce(2)-O(6) bond length is 2.44 Å. All Ce(2)-O(5) bond lengths are 2.33 Å. All Ce(2)-O(7) bond lengths are 2.37 Å. In the third Ce site, Ce(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 Ce(3)-O(7) bond length is 2.33 Å. The Ce(3)-O(9) bond length is 2.44 Å. All Ce(3)-O(6) bond lengths are 2.33 Å. All Ce(3)-O(8) bond lengths are 2.37 Å. In the fourth Ce site, Ce(4) is bonded in a body-centered cubic geometry to one O(12), one O(8), three equivalent O(10), and three equivalent O(9) atoms. The Ce(4)-O(12) bond length is 2.43 Å. The Ce(4)-O(8) bond length is 2.33 Å. All Ce(4)-O(10) 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(10), one O(11), three equivalent O(12), and three equivalent O(13) atoms. The Ce(5)-O(10) bond length is 2.31 Å. The Ce(5)-O(11) bond length is 2.76 Å. All Ce(5)-O(12) bond lengths are 2.33 Å. All Ce(5)-O(13) bond lengths are 2.36 Å. There are thirteen inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Dy(2) and one Ce(1) atom to form OCeDy3 tetrahedra that share  a cornercorner with one O(5)Ce4 tetrahedra, corners with three equivalent O(3)Ce4 tetrahedra, corners with three equivalent O(2)Dy4 tetrahedra, corners with six equivalent O(1)CeDy3 tetrahedra, edges with three equivalent O(4)Ce3Dy tetrahedra, and edges with three equivalent O(2)Dy4 tetrahedra. In the second O site, O(2) is bonded to one Dy(1) and three equivalent Dy(2) atoms to form distorted ODy4 tetrahedra that share  a cornercorner with one O(13)Ce3Dy tetrahedra, corners with three equivalent O(4)Ce3Dy tetrahedra, corners with three equivalent O(1)CeDy3 tetrahedra, corners with six equivalent O(2)Dy4 tetrahedra, corners with three equivalent O(11)CeDy3 trigonal pyramids, and edges with three equivalent O(1)CeDy3 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(6)Ce4 tetrahedra, corners with three equivalent O(4)Ce3Dy tetrahedra, corners with three equivalent O(7)Ce4 tetrahedra, corners with three equivalent O(1)CeDy3 tetrahedra, corners with six equivalent O(3)Ce4 tetrahedra, edges with three equivalent O(4)Ce3Dy tetrahedra, and edges with three equivalent O(5)Ce4 tetrahedra. In the fourth O site, O(4) is bonded to one Dy(2) and three equivalent Ce(1) atoms to form OCe3Dy tetrahedra that share corners with three equivalent O(3)Ce4 tetrahedra, corners with three equivalent O(5)Ce4 tetrahedra, corners with three equivalent O(2)Dy4 tetrahedra, corners with six equivalent O(4)Ce3Dy tetrahedra, edges with three equivalent O(3)Ce4 tetrahedra, and edges with three equivalent O(1)CeDy3 tetrahedra. In the fifth O site, O(5) is bonded to one Ce(1) and three equivalent Ce(2) atoms to form OCe4 tetrahedra that share  a cornercorner with one O(1)CeDy3 tetrahedra, corners with three equivalent O(4)Ce3Dy tetrahedra, corners with three equivalent O(6)Ce4 tetrahedra, corners with three equivalent O(7)Ce4 tetrahedra, corners with six equivalent O(5)Ce4 tetrahedra, edges with three equivalent O(3)Ce4 tetrahedra, and edges with three equivalent O(7)Ce4 tetrahedra. In the sixth O site, O(6) is bonded to one Ce(2) and three equivalent Ce(3) atoms to form a mixture of edge and corner-sharing OCe4 tetrahedra. In the seventh O site, O(7) is bonded to one Ce(3) and three equivalent Ce(2) atoms to form a mixture of edge and corner-sharing OCe4 tetrahedra. In the eighth O site, O(8) is bonded to one Ce(4) and three equivalent Ce(3) atoms to form a mixture of edge and corner-sharing OCe4 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 edge and corner-sharing OCe4 tetrahedra. In the tenth O site, O(10) is bonded to one Ce(5) and three equivalent Ce(4) atoms to form OCe4 tetrahedra that share corners with three equivalent O(13)Ce3Dy tetrahedra, corners with three equivalent O(8)Ce4 tetrahedra, corners with three equivalent O(9)Ce4 tetrahedra, corners with six equivalent O(10)Ce4 tetrahedra,  a cornercorner with one O(11)CeDy3 trigonal pyramid, edges with three equivalent O(12)Ce4 tetrahedra, and edges with three equivalent O(9)Ce4 tetrahedra. In the eleventh O site, O(11) is bonded to three equivalent Dy(1) and one Ce(5) atom to form distorted OCeDy3 trigonal pyramids that share  a cornercorner with one O(10)Ce4 tetrahedra, corners with three equivalent O(12)Ce4 tetrahedra, corners with three equivalent O(2)Dy4 tetrahedra, corners with six equivalent O(11)CeDy3 trigonal pyramids, and edges with three equivalent O(13)Ce3Dy tetrahedra. 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(8)Ce4 tetrahedra, corners with three equivalent O(13)Ce3Dy tetrahedra, corners with three equivalent O(9)Ce4 tetrahedra, corners with six equivalent O(12)Ce4 tetrahedra, corners with three equivalent O(11)CeDy3 trigonal pyramids, edges with three equivalent O(13)Ce3Dy tetrahedra, and edges with three equivalent O(10)Ce4 tetrahedra. In the thirteenth O site, O(13) is bonded to one Dy(1) and three equivalent Ce(5) atoms to form OCe3Dy tetrahedra that share  a cornercorner with one O(2)Dy4 tetrahedra, corners with three equivalent O(10)Ce4 tetrahedra, corners with three equivalent O(12)Ce4 tetrahedra, corners with six equivalent O(13)Ce3Dy tetrahedra, edges with three equivalent O(12)Ce4 tetrahedra, and edges with three equivalent O(11)CeDy3 trigonal pyramids.