MgU7Zr3O20 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(18), one O(19), two equivalent O(15), and two equivalent O(20) atoms to form distorted MgO6 octahedra that share edges with two equivalent U(6)O7 hexagonal pyramids, edges with two equivalent Zr(3)O7 hexagonal pyramids, and edges with two equivalent Mg(1)O6 octahedra. There are seven inequivalent U sites. In the first U site, U(1) is bonded in a body-centered cubic geometry to one O(1), one O(6), one O(7), one O(9), two equivalent O(13), and two equivalent O(5) atoms. In the second U site, U(2) is bonded in a body-centered cubic geometry to one O(12), one O(3), one O(7), one O(9), two equivalent O(11), and two equivalent O(4) atoms. In the third U site, U(3) is bonded in a body-centered cubic geometry to one O(10), one O(12), one O(14), one O(3), two equivalent O(17), and two equivalent O(8) atoms. In the fourth U site, U(4) is bonded in a body-centered cubic geometry to one O(11), one O(13), one O(17), one O(4), two equivalent O(3), and two equivalent O(9) atoms. In the fifth U site, U(5) is bonded in a 7-coordinate geometry to one O(16), one O(19), one O(8), two equivalent O(10), and two equivalent O(15) atoms. In the sixth U site, U(6) is bonded to one O(10), one O(14), one O(15), two equivalent O(16), and two equivalent O(19) atoms to form distorted UO7 hexagonal pyramids that share edges with two equivalent U(6)O7 hexagonal pyramids and edges with two equivalent Mg(1)O6 octahedra. In the seventh U site, U(7) is bonded in a 7-coordinate geometry to one O(1), one O(18), one O(6), two equivalent O(2), and two equivalent O(20) atoms. There are three inequivalent Zr sites. In the first Zr site, Zr(1) is bonded in a 7-coordinate geometry to one O(13), one O(4), one O(5), two equivalent O(1), and two equivalent O(7) atoms. In the second Zr site, Zr(2) is bonded in a body-centered cubic geometry to one O(11), one O(16), one O(17), one O(8), two equivalent O(12), and two equivalent O(14) atoms. In the third Zr site, Zr(3) is bonded to one O(2), one O(20), one O(5), two equivalent O(18), and two equivalent O(6) atoms to form distorted ZrO7 hexagonal pyramids that share edges with two equivalent Zr(3)O7 hexagonal pyramids and edges with two equivalent Mg(1)O6 octahedra. There are twenty inequivalent O sites. In the first O site, O(1) is bonded to one U(1), one U(7), and two equivalent Zr(1) atoms to form OZr2U2 tetrahedra that share  a cornercorner with one O(9)U4 tetrahedra, corners with two equivalent O(1)Zr2U2 tetrahedra, corners with two equivalent O(4)ZrU3 tetrahedra, corners with three equivalent O(7)Zr2U2 tetrahedra, corners with four equivalent O(5)Zr2U2 tetrahedra,  an edgeedge with one O(6)Zr2U2 tetrahedra,  an edgeedge with one O(7)Zr2U2 tetrahedra, and edges with two equivalent O(13)ZrU3 tetrahedra. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to two equivalent U(7) and one Zr(3) atom. In the third O site, O(3) is bonded to one U(2), one U(3), and two equivalent U(4) atoms to form OU4 tetrahedra that share  a cornercorner with one O(10)U4 tetrahedra,  a cornercorner with one O(14)Zr2U2 tetrahedra,  a cornercorner with one O(7)Zr2U2 tetrahedra, corners with two equivalent O(3)U4 tetrahedra, corners with two equivalent O(13)ZrU3 tetrahedra, corners with two equivalent O(8)ZrU3 tetrahedra, corners with three equivalent O(9)U4 tetrahedra, corners with four equivalent O(11)ZrU3 tetrahedra,  an edgeedge with one O(9)U4 tetrahedra,  an edgeedge with one O(12)Zr2U2 tetrahedra, edges with two equivalent O(17)ZrU3 tetrahedra, and edges with two equivalent O(4)ZrU3 tetrahedra. In the fourth O site, O(4) is bonded to one U(4), two equivalent U(2), and one Zr(1) atom to form OZrU3 tetrahedra that share  a cornercorner with one O(5)Zr2U2 tetrahedra,  a cornercorner with one O(17)ZrU3 tetrahedra, corners with two equivalent O(1)Zr2U2 tetrahedra, corners with two equivalent O(12)Zr2U2 tetrahedra, corners with two equivalent O(4)ZrU3 tetrahedra, corners with three equivalent O(11)ZrU3 tetrahedra, corners with four equivalent O(9)U4 tetrahedra,  an edgeedge with one O(11)ZrU3 tetrahedra,  an edgeedge with one O(13)ZrU3 tetrahedra, edges with two equivalent O(3)U4 tetrahedra, and edges with two equivalent O(7)Zr2U2 tetrahedra. In the fifth O site, O(5) is bonded to two equivalent U(1), one Zr(1), and one Zr(3) atom to form OZr2U2 tetrahedra that share  a cornercorner with one O(4)ZrU3 tetrahedra, corners with two equivalent O(9)U4 tetrahedra, corners with two equivalent O(5)Zr2U2 tetrahedra, corners with three equivalent O(13)ZrU3 tetrahedra, corners with four equivalent O(1)Zr2U2 tetrahedra,  an edgeedge with one O(13)ZrU3 tetrahedra, edges with two equivalent O(6)Zr2U2 tetrahedra, and edges with two equivalent O(7)Zr2U2 tetrahedra. In the sixth O site, O(6) is bonded to one U(1), one U(7), and two equivalent Zr(3) atoms to form OZr2U2 tetrahedra that share  a cornercorner with one O(9)U4 tetrahedra,  a cornercorner with one O(7)Zr2U2 tetrahedra, corners with two equivalent O(6)Zr2U2 tetrahedra, corners with two equivalent O(13)ZrU3 tetrahedra,  an edgeedge with one O(1)Zr2U2 tetrahedra, and edges with two equivalent O(5)Zr2U2 tetrahedra. In the seventh O site, O(7) is bonded to one U(1), one U(2), and two equivalent Zr(1) atoms to form OZr2U2 tetrahedra that share  a cornercorner with one O(3)U4 tetrahedra,  a cornercorner with one O(12)Zr2U2 tetrahedra,  a cornercorner with one O(6)Zr2U2 tetrahedra, corners with two equivalent O(7)Zr2U2 tetrahedra, corners with two equivalent O(11)ZrU3 tetrahedra, corners with three equivalent O(1)Zr2U2 tetrahedra, corners with four equivalent O(13)ZrU3 tetrahedra,  an edgeedge with one O(9)U4 tetrahedra,  an edgeedge with one O(1)Zr2U2 tetrahedra, edges with two equivalent O(5)Zr2U2 tetrahedra, and edges with two equivalent O(4)ZrU3 tetrahedra. In the eighth O site, O(8) is bonded to one U(5), two equivalent U(3), and one Zr(2) atom to form OZrU3 tetrahedra that share  a cornercorner with one O(11)ZrU3 tetrahedra, corners with two equivalent O(3)U4 tetrahedra, corners with two equivalent O(8)ZrU3 tetrahedra, corners with three equivalent O(17)ZrU3 tetrahedra, corners with four equivalent O(14)Zr2U2 tetrahedra, corners with two equivalent O(15)Mg2U3 trigonal bipyramids,  an edgeedge with one O(16)ZrU3 tetrahedra,  an edgeedge with one O(17)ZrU3 tetrahedra, edges with two equivalent O(10)U4 tetrahedra, and edges with two equivalent O(12)Zr2U2 tetrahedra. In the ninth O site, O(9) is bonded to one U(1), one U(2), and two equivalent U(4) atoms to form OU4 tetrahedra that share  a cornercorner with one O(1)Zr2U2 tetrahedra,  a cornercorner with one O(12)Zr2U2 tetrahedra,  a cornercorner with one O(6)Zr2U2 tetrahedra, corners with two equivalent O(9)U4 tetrahedra, corners with two equivalent O(5)Zr2U2 tetrahedra, corners with two equivalent O(17)ZrU3 tetrahedra, corners with three equivalent O(3)U4 tetrahedra, corners with four equivalent O(4)ZrU3 tetrahedra,  an edgeedge with one O(3)U4 tetrahedra,  an edgeedge with one O(7)Zr2U2 tetrahedra, edges with two equivalent O(11)ZrU3 tetrahedra, and edges with two equivalent O(13)ZrU3 tetrahedra. In the tenth O site, O(10) is bonded to one U(3), one U(6), and two equivalent U(5) atoms to form OU4 tetrahedra that share  a cornercorner with one O(3)U4 tetrahedra,  a cornercorner with one O(12)Zr2U2 tetrahedra, corners with two equivalent O(10)U4 tetrahedra, corners with two equivalent O(17)ZrU3 tetrahedra, corners with four equivalent O(16)ZrU3 tetrahedra, corners with three equivalent O(15)Mg2U3 trigonal bipyramids,  an edgeedge with one O(14)Zr2U2 tetrahedra, edges with two equivalent O(8)ZrU3 tetrahedra, and  an edgeedge with one O(15)Mg2U3 trigonal bipyramid. In the eleventh O site, O(11) is bonded to one U(4), two equivalent U(2), and one Zr(2) atom to form OZrU3 tetrahedra that share  a cornercorner with one O(13)ZrU3 tetrahedra,  a cornercorner with one O(16)ZrU3 tetrahedra,  a cornercorner with one O(8)ZrU3 tetrahedra, corners with two equivalent O(14)Zr2U2 tetrahedra, corners with two equivalent O(7)Zr2U2 tetrahedra, corners with two equivalent O(11)ZrU3 tetrahedra, corners with three equivalent O(4)ZrU3 tetrahedra, corners with four equivalent O(3)U4 tetrahedra,  an edgeedge with one O(17)ZrU3 tetrahedra,  an edgeedge with one O(4)ZrU3 tetrahedra, edges with two equivalent O(9)U4 tetrahedra, and edges with two equivalent O(12)Zr2U2 tetrahedra. In the twelfth O site, O(12) is bonded to one U(2), one U(3), and two equivalent Zr(2) atoms to form OZr2U2 tetrahedra that share  a cornercorner with one O(10)U4 tetrahedra,  a cornercorner with one O(9)U4 tetrahedra,  a cornercorner with one O(7)Zr2U2 tetrahedra, corners with two equivalent O(12)Zr2U2 tetrahedra, corners with two equivalent O(16)ZrU3 tetrahedra, corners with two equivalent O(4)ZrU3 tetrahedra, corners with three equivalent O(14)Zr2U2 tetrahedra, corners with four equivalent O(17)ZrU3 tetrahedra,  an edgeedge with one O(3)U4 tetrahedra,  an edgeedge with one O(14)Zr2U2 tetrahedra, edges with two equivalent O(11)ZrU3 tetrahedra, and edges with two equivalent O(8)ZrU3 tetrahedra. In the thirteenth O site, O(13) is bonded to one U(4), two equivalent U(1), and one Zr(1) atom to form OZrU3 tetrahedra that share  a cornercorner with one O(11)ZrU3 tetrahedra,  a cornercorner with one O(17)ZrU3 tetrahedra, corners with two equivalent O(3)U4 tetrahedra, corners with two equivalent O(6)Zr2U2 tetrahedra, corners with two equivalent O(13)ZrU3 tetrahedra, corners with three equivalent O(5)Zr2U2 tetrahedra, corners with four equivalent O(7)Zr2U2 tetrahedra,  an edgeedge with one O(5)Zr2U2 tetrahedra,  an edgeedge with one O(4)ZrU3 tetrahedra, edges with two equivalent O(9)U4 tetrahedra, and edges with two equivalent O(1)Zr2U2 tetrahedra. In the fourteenth O site, O(14) is bonded to one U(3), one U(6), and two equivalent Zr(2) atoms to form OZr2U2 tetrahedra that share  a cornercorner with one O(3)U4 tetrahedra, corners with two equivalent O(14)Zr2U2 tetrahedra, corners with two equivalent O(11)ZrU3 tetrahedra, corners with three equivalent O(12)Zr2U2 tetrahedra, corners with four equivalent O(8)ZrU3 tetrahedra,  a cornercorner with one O(15)Mg2U3 trigonal bipyramid,  an edgeedge with one O(10)U4 tetrahedra,  an edgeedge with one O(12)Zr2U2 tetrahedra, edges with two equivalent O(16)ZrU3 tetrahedra, and edges with two equivalent O(17)ZrU3 tetrahedra. In the fifteenth O site, O(15) is bonded to two equivalent Mg(1), one U(6), and two equivalent U(5) atoms to form distorted OMg2U3 trigonal bipyramids that share  a cornercorner with one O(14)Zr2U2 tetrahedra, corners with two equivalent O(8)ZrU3 tetrahedra, corners with three equivalent O(10)U4 tetrahedra,  an edgeedge with one O(10)U4 tetrahedra, edges with two equivalent O(16)ZrU3 tetrahedra, and edges with two equivalent O(15)Mg2U3 trigonal bipyramids. In the sixteenth O site, O(16) is bonded to one U(5), two equivalent U(6), and one Zr(2) atom to form OZrU3 tetrahedra that share  a cornercorner with one O(11)ZrU3 tetrahedra,  a cornercorner with one O(17)ZrU3 tetrahedra, corners with two equivalent O(12)Zr2U2 tetrahedra, corners with two equivalent O(16)ZrU3 tetrahedra, corners with four equivalent O(10)U4 tetrahedra,  an edgeedge with one O(8)ZrU3 tetrahedra, edges with two equivalent O(14)Zr2U2 tetrahedra, and edges with two equivalent O(15)Mg2U3 trigonal bipyramids. In the seventeenth O site, O(17) is bonded to one U(4), two equivalent U(3), and one Zr(2) atom to form OZrU3 tetrahedra that share  a cornercorner with one O(13)ZrU3 tetrahedra,  a cornercorner with one O(16)ZrU3 tetrahedra,  a cornercorner with one O(4)ZrU3 tetrahedra, corners with two equivalent O(10)U4 tetrahedra, corners with two equivalent O(9)U4 tetrahedra, corners with two equivalent O(17)ZrU3 tetrahedra, corners with three equivalent O(8)ZrU3 tetrahedra, corners with four equivalent O(12)Zr2U2 tetrahedra,  an edgeedge with one O(11)ZrU3 tetrahedra,  an edgeedge with one O(8)ZrU3 tetrahedra, edges with two equivalent O(3)U4 tetrahedra, and edges with two equivalent O(14)Zr2U2 tetrahedra. In the eighteenth O site, O(18) is bonded in a distorted see-saw-like geometry to one Mg(1), one U(7), and two equivalent Zr(3) atoms. In the nineteenth O site, O(19) is bonded in a 4-coordinate geometry to one Mg(1), one U(5), and two equivalent U(6) atoms. In the twentieth O site, O(20) is bonded in a 3-coordinate geometry to two equivalent Mg(1), two equivalent U(7), and one Zr(3) atom.
MgU7Zr3O20 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(18), one O(19), two equivalent O(15), and two equivalent O(20) atoms to form distorted MgO6 octahedra that share edges with two equivalent U(6)O7 hexagonal pyramids, edges with two equivalent Zr(3)O7 hexagonal pyramids, and edges with two equivalent Mg(1)O6 octahedra. The Mg(1)-O(18) bond length is 2.03 Å. The Mg(1)-O(19) bond length is 2.09 Å. There is one shorter (2.65 Å) and one longer (2.67 Å) Mg(1)-O(15) bond length. There is one shorter (2.16 Å) and one longer (2.17 Å) Mg(1)-O(20) bond length. There are seven inequivalent U sites. In the first U site, U(1) is bonded in a body-centered cubic geometry to one O(1), one O(6), one O(7), one O(9), two equivalent O(13), and two equivalent O(5) atoms. The U(1)-O(1) bond length is 2.47 Å. The U(1)-O(6) bond length is 2.31 Å. The U(1)-O(7) bond length is 2.37 Å. The U(1)-O(9) bond length is 2.38 Å. There is one shorter (2.29 Å) and one longer (2.30 Å) U(1)-O(13) bond length. Both U(1)-O(5) bond lengths are 2.41 Å. In the second U site, U(2) is bonded in a body-centered cubic geometry to one O(12), one O(3), one O(7), one O(9), two equivalent O(11), and two equivalent O(4) atoms. The U(2)-O(12) bond length is 2.42 Å. The U(2)-O(3) bond length is 2.30 Å. The U(2)-O(7) bond length is 2.39 Å. The U(2)-O(9) bond length is 2.31 Å. There is one shorter (2.30 Å) and one longer (2.31 Å) U(2)-O(11) bond length. Both U(2)-O(4) bond lengths are 2.34 Å. In the third U site, U(3) is bonded in a body-centered cubic geometry to one O(10), one O(12), one O(14), one O(3), two equivalent O(17), and two equivalent O(8) atoms. The U(3)-O(10) bond length is 2.45 Å. The U(3)-O(12) bond length is 2.34 Å. The U(3)-O(14) bond length is 2.32 Å. The U(3)-O(3) bond length is 2.35 Å. Both U(3)-O(17) bond lengths are 2.32 Å. Both U(3)-O(8) bond lengths are 2.31 Å. In the fourth U site, U(4) is bonded in a body-centered cubic geometry to one O(11), one O(13), one O(17), one O(4), two equivalent O(3), and two equivalent O(9) atoms. The U(4)-O(11) bond length is 2.34 Å. The U(4)-O(13) bond length is 2.49 Å. The U(4)-O(17) bond length is 2.38 Å. The U(4)-O(4) bond length is 2.35 Å. Both U(4)-O(3) bond lengths are 2.32 Å. There is one shorter (2.30 Å) and one longer (2.31 Å) U(4)-O(9) bond length. In the fifth U site, U(5) is bonded in a 7-coordinate geometry to one O(16), one O(19), one O(8), two equivalent O(10), and two equivalent O(15) atoms. The U(5)-O(16) bond length is 2.28 Å. The U(5)-O(19) bond length is 2.77 Å. The U(5)-O(8) bond length is 2.35 Å. Both U(5)-O(10) bond lengths are 2.28 Å. There is one shorter (2.40 Å) and one longer (2.42 Å) U(5)-O(15) bond length. In the sixth U site, U(6) is bonded to one O(10), one O(14), one O(15), two equivalent O(16), and two equivalent O(19) atoms to form distorted UO7 hexagonal pyramids that share edges with two equivalent U(6)O7 hexagonal pyramids and edges with two equivalent Mg(1)O6 octahedra. The U(6)-O(10) bond length is 2.26 Å. The U(6)-O(14) bond length is 2.30 Å. The U(6)-O(15) bond length is 2.29 Å. Both U(6)-O(16) bond lengths are 2.32 Å. Both U(6)-O(19) bond lengths are 2.33 Å. In the seventh U site, U(7) is bonded in a 7-coordinate geometry to one O(1), one O(18), one O(6), two equivalent O(2), and two equivalent O(20) atoms. The U(7)-O(1) bond length is 2.29 Å. The U(7)-O(18) bond length is 2.62 Å. The U(7)-O(6) bond length is 2.29 Å. Both U(7)-O(2) bond lengths are 2.18 Å. Both U(7)-O(20) bond lengths are 2.82 Å. There are three inequivalent Zr sites. In the first Zr site, Zr(1) is bonded in a 7-coordinate geometry to one O(13), one O(4), one O(5), two equivalent O(1), and two equivalent O(7) atoms. The Zr(1)-O(13) bond length is 2.17 Å. The Zr(1)-O(4) bond length is 2.14 Å. The Zr(1)-O(5) bond length is 2.23 Å. There is one shorter (2.31 Å) and one longer (2.33 Å) Zr(1)-O(1) bond length. There is one shorter (2.22 Å) and one longer (2.23 Å) Zr(1)-O(7) bond length. In the second Zr site, Zr(2) is bonded in a body-centered cubic geometry to one O(11), one O(16), one O(17), one O(8), two equivalent O(12), and two equivalent O(14) atoms. The Zr(2)-O(11) bond length is 2.26 Å. The Zr(2)-O(16) bond length is 2.27 Å. The Zr(2)-O(17) bond length is 2.23 Å. The Zr(2)-O(8) bond length is 2.30 Å. Both Zr(2)-O(12) bond lengths are 2.24 Å. There is one shorter (2.27 Å) and one longer (2.28 Å) Zr(2)-O(14) bond length. In the third Zr site, Zr(3) is bonded to one O(2), one O(20), one O(5), two equivalent O(18), and two equivalent O(6) atoms to form distorted ZrO7 hexagonal pyramids that share edges with two equivalent Zr(3)O7 hexagonal pyramids and edges with two equivalent Mg(1)O6 octahedra. The Zr(3)-O(2) bond length is 2.13 Å. The Zr(3)-O(20) bond length is 2.13 Å. The Zr(3)-O(5) bond length is 2.13 Å. There is one shorter (2.26 Å) and one longer (2.27 Å) Zr(3)-O(18) bond length. There is one shorter (2.30 Å) and one longer (2.31 Å) Zr(3)-O(6) bond length. There are twenty inequivalent O sites. In the first O site, O(1) is bonded to one U(1), one U(7), and two equivalent Zr(1) atoms to form OZr2U2 tetrahedra that share  a cornercorner with one O(9)U4 tetrahedra, corners with two equivalent O(1)Zr2U2 tetrahedra, corners with two equivalent O(4)ZrU3 tetrahedra, corners with three equivalent O(7)Zr2U2 tetrahedra, corners with four equivalent O(5)Zr2U2 tetrahedra,  an edgeedge with one O(6)Zr2U2 tetrahedra,  an edgeedge with one O(7)Zr2U2 tetrahedra, and edges with two equivalent O(13)ZrU3 tetrahedra. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to two equivalent U(7) and one Zr(3) atom. In the third O site, O(3) is bonded to one U(2), one U(3), and two equivalent U(4) atoms to form OU4 tetrahedra that share  a cornercorner with one O(10)U4 tetrahedra,  a cornercorner with one O(14)Zr2U2 tetrahedra,  a cornercorner with one O(7)Zr2U2 tetrahedra, corners with two equivalent O(3)U4 tetrahedra, corners with two equivalent O(13)ZrU3 tetrahedra, corners with two equivalent O(8)ZrU3 tetrahedra, corners with three equivalent O(9)U4 tetrahedra, corners with four equivalent O(11)ZrU3 tetrahedra,  an edgeedge with one O(9)U4 tetrahedra,  an edgeedge with one O(12)Zr2U2 tetrahedra, edges with two equivalent O(17)ZrU3 tetrahedra, and edges with two equivalent O(4)ZrU3 tetrahedra. In the fourth O site, O(4) is bonded to one U(4), two equivalent U(2), and one Zr(1) atom to form OZrU3 tetrahedra that share  a cornercorner with one O(5)Zr2U2 tetrahedra,  a cornercorner with one O(17)ZrU3 tetrahedra, corners with two equivalent O(1)Zr2U2 tetrahedra, corners with two equivalent O(12)Zr2U2 tetrahedra, corners with two equivalent O(4)ZrU3 tetrahedra, corners with three equivalent O(11)ZrU3 tetrahedra, corners with four equivalent O(9)U4 tetrahedra,  an edgeedge with one O(11)ZrU3 tetrahedra,  an edgeedge with one O(13)ZrU3 tetrahedra, edges with two equivalent O(3)U4 tetrahedra, and edges with two equivalent O(7)Zr2U2 tetrahedra. In the fifth O site, O(5) is bonded to two equivalent U(1), one Zr(1), and one Zr(3) atom to form OZr2U2 tetrahedra that share  a cornercorner with one O(4)ZrU3 tetrahedra, corners with two equivalent O(9)U4 tetrahedra, corners with two equivalent O(5)Zr2U2 tetrahedra, corners with three equivalent O(13)ZrU3 tetrahedra, corners with four equivalent O(1)Zr2U2 tetrahedra,  an edgeedge with one O(13)ZrU3 tetrahedra, edges with two equivalent O(6)Zr2U2 tetrahedra, and edges with two equivalent O(7)Zr2U2 tetrahedra. In the sixth O site, O(6) is bonded to one U(1), one U(7), and two equivalent Zr(3) atoms to form OZr2U2 tetrahedra that share  a cornercorner with one O(9)U4 tetrahedra,  a cornercorner with one O(7)Zr2U2 tetrahedra, corners with two equivalent O(6)Zr2U2 tetrahedra, corners with two equivalent O(13)ZrU3 tetrahedra,  an edgeedge with one O(1)Zr2U2 tetrahedra, and edges with two equivalent O(5)Zr2U2 tetrahedra. In the seventh O site, O(7) is bonded to one U(1), one U(2), and two equivalent Zr(1) atoms to form OZr2U2 tetrahedra that share  a cornercorner with one O(3)U4 tetrahedra,  a cornercorner with one O(12)Zr2U2 tetrahedra,  a cornercorner with one O(6)Zr2U2 tetrahedra, corners with two equivalent O(7)Zr2U2 tetrahedra, corners with two equivalent O(11)ZrU3 tetrahedra, corners with three equivalent O(1)Zr2U2 tetrahedra, corners with four equivalent O(13)ZrU3 tetrahedra,  an edgeedge with one O(9)U4 tetrahedra,  an edgeedge with one O(1)Zr2U2 tetrahedra, edges with two equivalent O(5)Zr2U2 tetrahedra, and edges with two equivalent O(4)ZrU3 tetrahedra. In the eighth O site, O(8) is bonded to one U(5), two equivalent U(3), and one Zr(2) atom to form OZrU3 tetrahedra that share  a cornercorner with one O(11)ZrU3 tetrahedra, corners with two equivalent O(3)U4 tetrahedra, corners with two equivalent O(8)ZrU3 tetrahedra, corners with three equivalent O(17)ZrU3 tetrahedra, corners with four equivalent O(14)Zr2U2 tetrahedra, corners with two equivalent O(15)Mg2U3 trigonal bipyramids,  an edgeedge with one O(16)ZrU3 tetrahedra,  an edgeedge with one O(17)ZrU3 tetrahedra, edges with two equivalent O(10)U4 tetrahedra, and edges with two equivalent O(12)Zr2U2 tetrahedra. In the ninth O site, O(9) is bonded to one U(1), one U(2), and two equivalent U(4) atoms to form OU4 tetrahedra that share  a cornercorner with one O(1)Zr2U2 tetrahedra,  a cornercorner with one O(12)Zr2U2 tetrahedra,  a cornercorner with one O(6)Zr2U2 tetrahedra, corners with two equivalent O(9)U4 tetrahedra, corners with two equivalent O(5)Zr2U2 tetrahedra, corners with two equivalent O(17)ZrU3 tetrahedra, corners with three equivalent O(3)U4 tetrahedra, corners with four equivalent O(4)ZrU3 tetrahedra,  an edgeedge with one O(3)U4 tetrahedra,  an edgeedge with one O(7)Zr2U2 tetrahedra, edges with two equivalent O(11)ZrU3 tetrahedra, and edges with two equivalent O(13)ZrU3 tetrahedra. In the tenth O site, O(10) is bonded to one U(3), one U(6), and two equivalent U(5) atoms to form OU4 tetrahedra that share  a cornercorner with one O(3)U4 tetrahedra,  a cornercorner with one O(12)Zr2U2 tetrahedra, corners with two equivalent O(10)U4 tetrahedra, corners with two equivalent O(17)ZrU3 tetrahedra, corners with four equivalent O(16)ZrU3 tetrahedra, corners with three equivalent O(15)Mg2U3 trigonal bipyramids,  an edgeedge with one O(14)Zr2U2 tetrahedra, edges with two equivalent O(8)ZrU3 tetrahedra, and  an edgeedge with one O(15)Mg2U3 trigonal bipyramid. In the eleventh O site, O(11) is bonded to one U(4), two equivalent U(2), and one Zr(2) atom to form OZrU3 tetrahedra that share  a cornercorner with one O(13)ZrU3 tetrahedra,  a cornercorner with one O(16)ZrU3 tetrahedra,  a cornercorner with one O(8)ZrU3 tetrahedra, corners with two equivalent O(14)Zr2U2 tetrahedra, corners with two equivalent O(7)Zr2U2 tetrahedra, corners with two equivalent O(11)ZrU3 tetrahedra, corners with three equivalent O(4)ZrU3 tetrahedra, corners with four equivalent O(3)U4 tetrahedra,  an edgeedge with one O(17)ZrU3 tetrahedra,  an edgeedge with one O(4)ZrU3 tetrahedra, edges with two equivalent O(9)U4 tetrahedra, and edges with two equivalent O(12)Zr2U2 tetrahedra. In the twelfth O site, O(12) is bonded to one U(2), one U(3), and two equivalent Zr(2) atoms to form OZr2U2 tetrahedra that share  a cornercorner with one O(10)U4 tetrahedra,  a cornercorner with one O(9)U4 tetrahedra,  a cornercorner with one O(7)Zr2U2 tetrahedra, corners with two equivalent O(12)Zr2U2 tetrahedra, corners with two equivalent O(16)ZrU3 tetrahedra, corners with two equivalent O(4)ZrU3 tetrahedra, corners with three equivalent O(14)Zr2U2 tetrahedra, corners with four equivalent O(17)ZrU3 tetrahedra,  an edgeedge with one O(3)U4 tetrahedra,  an edgeedge with one O(14)Zr2U2 tetrahedra, edges with two equivalent O(11)ZrU3 tetrahedra, and edges with two equivalent O(8)ZrU3 tetrahedra. In the thirteenth O site, O(13) is bonded to one U(4), two equivalent U(1), and one Zr(1) atom to form OZrU3 tetrahedra that share  a cornercorner with one O(11)ZrU3 tetrahedra,  a cornercorner with one O(17)ZrU3 tetrahedra, corners with two equivalent O(3)U4 tetrahedra, corners with two equivalent O(6)Zr2U2 tetrahedra, corners with two equivalent O(13)ZrU3 tetrahedra, corners with three equivalent O(5)Zr2U2 tetrahedra, corners with four equivalent O(7)Zr2U2 tetrahedra,  an edgeedge with one O(5)Zr2U2 tetrahedra,  an edgeedge with one O(4)ZrU3 tetrahedra, edges with two equivalent O(9)U4 tetrahedra, and edges with two equivalent O(1)Zr2U2 tetrahedra. In the fourteenth O site, O(14) is bonded to one U(3), one U(6), and two equivalent Zr(2) atoms to form OZr2U2 tetrahedra that share  a cornercorner with one O(3)U4 tetrahedra, corners with two equivalent O(14)Zr2U2 tetrahedra, corners with two equivalent O(11)ZrU3 tetrahedra, corners with three equivalent O(12)Zr2U2 tetrahedra, corners with four equivalent O(8)ZrU3 tetrahedra,  a cornercorner with one O(15)Mg2U3 trigonal bipyramid,  an edgeedge with one O(10)U4 tetrahedra,  an edgeedge with one O(12)Zr2U2 tetrahedra, edges with two equivalent O(16)ZrU3 tetrahedra, and edges with two equivalent O(17)ZrU3 tetrahedra. In the fifteenth O site, O(15) is bonded to two equivalent Mg(1), one U(6), and two equivalent U(5) atoms to form distorted OMg2U3 trigonal bipyramids that share  a cornercorner with one O(14)Zr2U2 tetrahedra, corners with two equivalent O(8)ZrU3 tetrahedra, corners with three equivalent O(10)U4 tetrahedra,  an edgeedge with one O(10)U4 tetrahedra, edges with two equivalent O(16)ZrU3 tetrahedra, and edges with two equivalent O(15)Mg2U3 trigonal bipyramids. In the sixteenth O site, O(16) is bonded to one U(5), two equivalent U(6), and one Zr(2) atom to form OZrU3 tetrahedra that share  a cornercorner with one O(11)ZrU3 tetrahedra,  a cornercorner with one O(17)ZrU3 tetrahedra, corners with two equivalent O(12)Zr2U2 tetrahedra, corners with two equivalent O(16)ZrU3 tetrahedra, corners with four equivalent O(10)U4 tetrahedra,  an edgeedge with one O(8)ZrU3 tetrahedra, edges with two equivalent O(14)Zr2U2 tetrahedra, and edges with two equivalent O(15)Mg2U3 trigonal bipyramids. In the seventeenth O site, O(17) is bonded to one U(4), two equivalent U(3), and one Zr(2) atom to form OZrU3 tetrahedra that share  a cornercorner with one O(13)ZrU3 tetrahedra,  a cornercorner with one O(16)ZrU3 tetrahedra,  a cornercorner with one O(4)ZrU3 tetrahedra, corners with two equivalent O(10)U4 tetrahedra, corners with two equivalent O(9)U4 tetrahedra, corners with two equivalent O(17)ZrU3 tetrahedra, corners with three equivalent O(8)ZrU3 tetrahedra, corners with four equivalent O(12)Zr2U2 tetrahedra,  an edgeedge with one O(11)ZrU3 tetrahedra,  an edgeedge with one O(8)ZrU3 tetrahedra, edges with two equivalent O(3)U4 tetrahedra, and edges with two equivalent O(14)Zr2U2 tetrahedra. In the eighteenth O site, O(18) is bonded in a distorted see-saw-like geometry to one Mg(1), one U(7), and two equivalent Zr(3) atoms. In the nineteenth O site, O(19) is bonded in a 4-coordinate geometry to one Mg(1), one U(5), and two equivalent U(6) atoms. In the twentieth O site, O(20) is bonded in a 3-coordinate geometry to two equivalent Mg(1), two equivalent U(7), and one Zr(3) atom.