Lu4Zr3O12 crystallizes in the triclinic P-1 space group. There are four inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 7-coordinate geometry to one O(1), one O(10), one O(2), one O(3), one O(7), and two equivalent O(5) atoms. In the second Lu site, Lu(2) is bonded in a 7-coordinate geometry to one O(1), one O(10), one O(12), one O(5), one O(6), one O(7), and one O(9) atom. In the third Lu site, Lu(3) is bonded in a 7-coordinate geometry to one O(10), one O(11), one O(12), one O(3), one O(6), one O(8), and one O(9) atom. In the fourth Lu site, Lu(4) is bonded in a 7-coordinate geometry to one O(12), one O(8), one O(9), two equivalent O(11), and two equivalent O(4) atoms. There are three inequivalent Zr sites. In the first Zr site, Zr(1) is bonded in an octahedral geometry to one O(1), one O(2), one O(3), one O(4), one O(6), and one O(9) atom. In the second Zr site, Zr(2) is bonded in a 7-coordinate geometry to one O(1), one O(11), one O(12), one O(3), one O(4), and two equivalent O(8) atoms. In the third Zr site, Zr(3) is bonded in a 6-coordinate geometry to one O(10), one O(2), one O(5), one O(6), and two equivalent O(7) atoms. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Lu(1), one Lu(2), one Zr(1), and one Zr(2) atom to form distorted OLu2Zr2 tetrahedra that share  a cornercorner with one O(11)Lu3Zr tetrahedra,  a cornercorner with one O(5)Lu3Zr tetrahedra, corners with two equivalent O(7)Lu2Zr2 tetrahedra, corners with two equivalent O(8)Lu2Zr2 tetrahedra, corners with two equivalent O(10)Lu3Zr tetrahedra, corners with two equivalent O(9)Lu3Zr tetrahedra,  an edgeedge with one O(4)Lu2Zr2 tetrahedra,  an edgeedge with one O(6)Lu2Zr2 tetrahedra,  an edgeedge with one O(12)Lu3Zr tetrahedra, and  an edgeedge with one O(5)Lu3Zr tetrahedra. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Lu(1), one Zr(1), and one Zr(3) atom. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Lu(1), one Lu(3), one Zr(1), and one Zr(2) atom. In the fourth O site, O(4) is bonded to two equivalent Lu(4), one Zr(1), and one Zr(2) atom to form distorted OLu2Zr2 tetrahedra that share  a cornercorner with one O(6)Lu2Zr2 tetrahedra,  a cornercorner with one O(9)Lu3Zr tetrahedra, corners with two equivalent O(8)Lu2Zr2 tetrahedra, corners with three equivalent O(11)Lu3Zr tetrahedra, corners with three equivalent O(12)Lu3Zr tetrahedra,  an edgeedge with one O(1)Lu2Zr2 tetrahedra,  an edgeedge with one O(4)Lu2Zr2 tetrahedra,  an edgeedge with one O(8)Lu2Zr2 tetrahedra,  an edgeedge with one O(11)Lu3Zr tetrahedra, and  an edgeedge with one O(9)Lu3Zr tetrahedra. In the fifth O site, O(5) is bonded to one Lu(2), two equivalent Lu(1), and one Zr(3) atom to form distorted OLu3Zr tetrahedra that share  a cornercorner with one O(1)Lu2Zr2 tetrahedra,  a cornercorner with one O(12)Lu3Zr tetrahedra,  a cornercorner with one O(9)Lu3Zr tetrahedra, corners with two equivalent O(6)Lu2Zr2 tetrahedra, corners with two equivalent O(10)Lu3Zr tetrahedra, corners with three equivalent O(7)Lu2Zr2 tetrahedra,  an edgeedge with one O(1)Lu2Zr2 tetrahedra,  an edgeedge with one O(7)Lu2Zr2 tetrahedra,  an edgeedge with one O(10)Lu3Zr tetrahedra, and  an edgeedge with one O(5)Lu3Zr tetrahedra. In the sixth O site, O(6) is bonded to one Lu(2), one Lu(3), one Zr(1), and one Zr(3) atom to form distorted OLu2Zr2 tetrahedra that share  a cornercorner with one O(4)Lu2Zr2 tetrahedra,  a cornercorner with one O(7)Lu2Zr2 tetrahedra,  a cornercorner with one O(8)Lu2Zr2 tetrahedra,  a cornercorner with one O(10)Lu3Zr tetrahedra,  a cornercorner with one O(11)Lu3Zr tetrahedra,  a cornercorner with one O(9)Lu3Zr tetrahedra, corners with two equivalent O(12)Lu3Zr tetrahedra, corners with two equivalent O(5)Lu3Zr tetrahedra,  an edgeedge with one O(1)Lu2Zr2 tetrahedra,  an edgeedge with one O(7)Lu2Zr2 tetrahedra,  an edgeedge with one O(10)Lu3Zr tetrahedra, and  an edgeedge with one O(9)Lu3Zr tetrahedra. In the seventh O site, O(7) is bonded to one Lu(1), one Lu(2), and two equivalent Zr(3) atoms to form OLu2Zr2 tetrahedra that share  a cornercorner with one O(6)Lu2Zr2 tetrahedra,  a cornercorner with one O(12)Lu3Zr tetrahedra,  a cornercorner with one O(9)Lu3Zr tetrahedra, corners with two equivalent O(1)Lu2Zr2 tetrahedra, corners with two equivalent O(10)Lu3Zr tetrahedra, corners with three equivalent O(5)Lu3Zr tetrahedra,  an edgeedge with one O(6)Lu2Zr2 tetrahedra,  an edgeedge with one O(7)Lu2Zr2 tetrahedra,  an edgeedge with one O(10)Lu3Zr tetrahedra, and  an edgeedge with one O(5)Lu3Zr tetrahedra. In the eighth O site, O(8) is bonded to one Lu(3), one Lu(4), and two equivalent Zr(2) atoms to form OLu2Zr2 tetrahedra that share  a cornercorner with one O(6)Lu2Zr2 tetrahedra,  a cornercorner with one O(10)Lu3Zr tetrahedra, corners with two equivalent O(1)Lu2Zr2 tetrahedra, corners with two equivalent O(4)Lu2Zr2 tetrahedra, corners with two equivalent O(12)Lu3Zr tetrahedra, corners with two equivalent O(9)Lu3Zr tetrahedra, corners with three equivalent O(11)Lu3Zr tetrahedra,  an edgeedge with one O(4)Lu2Zr2 tetrahedra,  an edgeedge with one O(8)Lu2Zr2 tetrahedra,  an edgeedge with one O(11)Lu3Zr tetrahedra, and  an edgeedge with one O(12)Lu3Zr tetrahedra. In the ninth O site, O(9) is bonded to one Lu(2), one Lu(3), one Lu(4), and one Zr(1) atom to form distorted OLu3Zr tetrahedra that share  a cornercorner with one O(4)Lu2Zr2 tetrahedra,  a cornercorner with one O(6)Lu2Zr2 tetrahedra,  a cornercorner with one O(7)Lu2Zr2 tetrahedra,  a cornercorner with one O(11)Lu3Zr tetrahedra,  a cornercorner with one O(12)Lu3Zr tetrahedra,  a cornercorner with one O(5)Lu3Zr tetrahedra, corners with two equivalent O(1)Lu2Zr2 tetrahedra, corners with two equivalent O(8)Lu2Zr2 tetrahedra, corners with two equivalent O(10)Lu3Zr tetrahedra,  an edgeedge with one O(4)Lu2Zr2 tetrahedra,  an edgeedge with one O(6)Lu2Zr2 tetrahedra,  an edgeedge with one O(11)Lu3Zr tetrahedra, and  an edgeedge with one O(12)Lu3Zr tetrahedra. In the tenth O site, O(10) is bonded to one Lu(1), one Lu(2), one Lu(3), and one Zr(3) atom to form OLu3Zr tetrahedra that share  a cornercorner with one O(6)Lu2Zr2 tetrahedra,  a cornercorner with one O(8)Lu2Zr2 tetrahedra,  a cornercorner with one O(11)Lu3Zr tetrahedra, corners with two equivalent O(1)Lu2Zr2 tetrahedra, corners with two equivalent O(7)Lu2Zr2 tetrahedra, corners with two equivalent O(5)Lu3Zr tetrahedra, corners with two equivalent O(9)Lu3Zr tetrahedra,  an edgeedge with one O(6)Lu2Zr2 tetrahedra,  an edgeedge with one O(7)Lu2Zr2 tetrahedra,  an edgeedge with one O(12)Lu3Zr tetrahedra, and  an edgeedge with one O(5)Lu3Zr tetrahedra. In the eleventh O site, O(11) is bonded to one Lu(3), two equivalent Lu(4), and one Zr(2) atom to form OLu3Zr tetrahedra that share  a cornercorner with one O(1)Lu2Zr2 tetrahedra,  a cornercorner with one O(6)Lu2Zr2 tetrahedra,  a cornercorner with one O(10)Lu3Zr tetrahedra,  a cornercorner with one O(9)Lu3Zr tetrahedra, corners with two equivalent O(12)Lu3Zr tetrahedra, corners with three equivalent O(4)Lu2Zr2 tetrahedra, corners with three equivalent O(8)Lu2Zr2 tetrahedra,  an edgeedge with one O(4)Lu2Zr2 tetrahedra,  an edgeedge with one O(8)Lu2Zr2 tetrahedra,  an edgeedge with one O(11)Lu3Zr tetrahedra,  an edgeedge with one O(12)Lu3Zr tetrahedra, and  an edgeedge with one O(9)Lu3Zr tetrahedra. In the twelfth O site, O(12) is bonded to one Lu(2), one Lu(3), one Lu(4), and one Zr(2) atom to form distorted OLu3Zr tetrahedra that share  a cornercorner with one O(7)Lu2Zr2 tetrahedra,  a cornercorner with one O(5)Lu3Zr tetrahedra,  a cornercorner with one O(9)Lu3Zr tetrahedra, corners with two equivalent O(6)Lu2Zr2 tetrahedra, corners with two equivalent O(8)Lu2Zr2 tetrahedra, corners with two equivalent O(11)Lu3Zr tetrahedra, corners with three equivalent O(4)Lu2Zr2 tetrahedra,  an edgeedge with one O(1)Lu2Zr2 tetrahedra,  an edgeedge with one O(8)Lu2Zr2 tetrahedra,  an edgeedge with one O(10)Lu3Zr tetrahedra,  an edgeedge with one O(11)Lu3Zr tetrahedra, and  an edgeedge with one O(9)Lu3Zr tetrahedra.
Lu4Zr3O12 crystallizes in the triclinic P-1 space group. There are four inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 7-coordinate geometry to one O(1), one O(10), one O(2), one O(3), one O(7), and two equivalent O(5) atoms. The Lu(1)-O(1) bond length is 2.17 Å. The Lu(1)-O(10) bond length is 2.13 Å. The Lu(1)-O(2) bond length is 2.22 Å. The Lu(1)-O(3) bond length is 2.61 Å. The Lu(1)-O(7) bond length is 2.32 Å. There is one shorter (2.23 Å) and one longer (2.24 Å) Lu(1)-O(5) bond length. In the second Lu site, Lu(2) is bonded in a 7-coordinate geometry to one O(1), one O(10), one O(12), one O(5), one O(6), one O(7), and one O(9) atom. The Lu(2)-O(1) bond length is 2.19 Å. The Lu(2)-O(10) bond length is 2.21 Å. The Lu(2)-O(12) bond length is 2.23 Å. The Lu(2)-O(5) bond length is 2.33 Å. The Lu(2)-O(6) bond length is 2.57 Å. The Lu(2)-O(7) bond length is 2.17 Å. The Lu(2)-O(9) bond length is 2.18 Å. In the third Lu site, Lu(3) is bonded in a 7-coordinate geometry to one O(10), one O(11), one O(12), one O(3), one O(6), one O(8), and one O(9) atom. The Lu(3)-O(10) bond length is 2.22 Å. The Lu(3)-O(11) bond length is 2.13 Å. The Lu(3)-O(12) bond length is 2.24 Å. The Lu(3)-O(3) bond length is 2.23 Å. The Lu(3)-O(6) bond length is 2.23 Å. The Lu(3)-O(8) bond length is 2.33 Å. The Lu(3)-O(9) bond length is 2.48 Å. In the fourth Lu site, Lu(4) is bonded in a 7-coordinate geometry to one O(12), one O(8), one O(9), two equivalent O(11), and two equivalent O(4) atoms. The Lu(4)-O(12) bond length is 2.32 Å. The Lu(4)-O(8) bond length is 2.16 Å. The Lu(4)-O(9) bond length is 2.20 Å. There is one shorter (2.20 Å) and one longer (2.22 Å) Lu(4)-O(11) bond length. There is one shorter (2.21 Å) and one longer (2.58 Å) Lu(4)-O(4) bond length. There are three inequivalent Zr sites. In the first Zr site, Zr(1) is bonded in an octahedral geometry to one O(1), one O(2), one O(3), one O(4), one O(6), and one O(9) atom. The Zr(1)-O(1) bond length is 2.07 Å. The Zr(1)-O(2) bond length is 2.09 Å. The Zr(1)-O(3) bond length is 2.10 Å. The Zr(1)-O(4) bond length is 2.11 Å. The Zr(1)-O(6) bond length is 2.13 Å. The Zr(1)-O(9) bond length is 2.07 Å. In the second Zr site, Zr(2) is bonded in a 7-coordinate geometry to one O(1), one O(11), one O(12), one O(3), one O(4), and two equivalent O(8) atoms. The Zr(2)-O(1) bond length is 2.52 Å. The Zr(2)-O(11) bond length is 2.20 Å. The Zr(2)-O(12) bond length is 2.06 Å. The Zr(2)-O(3) bond length is 2.14 Å. The Zr(2)-O(4) bond length is 2.11 Å. There is one shorter (2.15 Å) and one longer (2.21 Å) Zr(2)-O(8) bond length. In the third Zr site, Zr(3) is bonded in a 6-coordinate geometry to one O(10), one O(2), one O(5), one O(6), and two equivalent O(7) atoms. The Zr(3)-O(10) bond length is 2.19 Å. The Zr(3)-O(2) bond length is 2.13 Å. The Zr(3)-O(5) bond length is 2.06 Å. The Zr(3)-O(6) bond length is 2.09 Å. There is one shorter (2.12 Å) and one longer (2.20 Å) Zr(3)-O(7) bond length. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Lu(1), one Lu(2), one Zr(1), and one Zr(2) atom to form distorted OLu2Zr2 tetrahedra that share  a cornercorner with one O(11)Lu3Zr tetrahedra,  a cornercorner with one O(5)Lu3Zr tetrahedra, corners with two equivalent O(7)Lu2Zr2 tetrahedra, corners with two equivalent O(8)Lu2Zr2 tetrahedra, corners with two equivalent O(10)Lu3Zr tetrahedra, corners with two equivalent O(9)Lu3Zr tetrahedra,  an edgeedge with one O(4)Lu2Zr2 tetrahedra,  an edgeedge with one O(6)Lu2Zr2 tetrahedra,  an edgeedge with one O(12)Lu3Zr tetrahedra, and  an edgeedge with one O(5)Lu3Zr tetrahedra. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Lu(1), one Zr(1), and one Zr(3) atom. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Lu(1), one Lu(3), one Zr(1), and one Zr(2) atom. In the fourth O site, O(4) is bonded to two equivalent Lu(4), one Zr(1), and one Zr(2) atom to form distorted OLu2Zr2 tetrahedra that share  a cornercorner with one O(6)Lu2Zr2 tetrahedra,  a cornercorner with one O(9)Lu3Zr tetrahedra, corners with two equivalent O(8)Lu2Zr2 tetrahedra, corners with three equivalent O(11)Lu3Zr tetrahedra, corners with three equivalent O(12)Lu3Zr tetrahedra,  an edgeedge with one O(1)Lu2Zr2 tetrahedra,  an edgeedge with one O(4)Lu2Zr2 tetrahedra,  an edgeedge with one O(8)Lu2Zr2 tetrahedra,  an edgeedge with one O(11)Lu3Zr tetrahedra, and  an edgeedge with one O(9)Lu3Zr tetrahedra. In the fifth O site, O(5) is bonded to one Lu(2), two equivalent Lu(1), and one Zr(3) atom to form distorted OLu3Zr tetrahedra that share  a cornercorner with one O(1)Lu2Zr2 tetrahedra,  a cornercorner with one O(12)Lu3Zr tetrahedra,  a cornercorner with one O(9)Lu3Zr tetrahedra, corners with two equivalent O(6)Lu2Zr2 tetrahedra, corners with two equivalent O(10)Lu3Zr tetrahedra, corners with three equivalent O(7)Lu2Zr2 tetrahedra,  an edgeedge with one O(1)Lu2Zr2 tetrahedra,  an edgeedge with one O(7)Lu2Zr2 tetrahedra,  an edgeedge with one O(10)Lu3Zr tetrahedra, and  an edgeedge with one O(5)Lu3Zr tetrahedra. In the sixth O site, O(6) is bonded to one Lu(2), one Lu(3), one Zr(1), and one Zr(3) atom to form distorted OLu2Zr2 tetrahedra that share  a cornercorner with one O(4)Lu2Zr2 tetrahedra,  a cornercorner with one O(7)Lu2Zr2 tetrahedra,  a cornercorner with one O(8)Lu2Zr2 tetrahedra,  a cornercorner with one O(10)Lu3Zr tetrahedra,  a cornercorner with one O(11)Lu3Zr tetrahedra,  a cornercorner with one O(9)Lu3Zr tetrahedra, corners with two equivalent O(12)Lu3Zr tetrahedra, corners with two equivalent O(5)Lu3Zr tetrahedra,  an edgeedge with one O(1)Lu2Zr2 tetrahedra,  an edgeedge with one O(7)Lu2Zr2 tetrahedra,  an edgeedge with one O(10)Lu3Zr tetrahedra, and  an edgeedge with one O(9)Lu3Zr tetrahedra. In the seventh O site, O(7) is bonded to one Lu(1), one Lu(2), and two equivalent Zr(3) atoms to form OLu2Zr2 tetrahedra that share  a cornercorner with one O(6)Lu2Zr2 tetrahedra,  a cornercorner with one O(12)Lu3Zr tetrahedra,  a cornercorner with one O(9)Lu3Zr tetrahedra, corners with two equivalent O(1)Lu2Zr2 tetrahedra, corners with two equivalent O(10)Lu3Zr tetrahedra, corners with three equivalent O(5)Lu3Zr tetrahedra,  an edgeedge with one O(6)Lu2Zr2 tetrahedra,  an edgeedge with one O(7)Lu2Zr2 tetrahedra,  an edgeedge with one O(10)Lu3Zr tetrahedra, and  an edgeedge with one O(5)Lu3Zr tetrahedra. In the eighth O site, O(8) is bonded to one Lu(3), one Lu(4), and two equivalent Zr(2) atoms to form OLu2Zr2 tetrahedra that share  a cornercorner with one O(6)Lu2Zr2 tetrahedra,  a cornercorner with one O(10)Lu3Zr tetrahedra, corners with two equivalent O(1)Lu2Zr2 tetrahedra, corners with two equivalent O(4)Lu2Zr2 tetrahedra, corners with two equivalent O(12)Lu3Zr tetrahedra, corners with two equivalent O(9)Lu3Zr tetrahedra, corners with three equivalent O(11)Lu3Zr tetrahedra,  an edgeedge with one O(4)Lu2Zr2 tetrahedra,  an edgeedge with one O(8)Lu2Zr2 tetrahedra,  an edgeedge with one O(11)Lu3Zr tetrahedra, and  an edgeedge with one O(12)Lu3Zr tetrahedra. In the ninth O site, O(9) is bonded to one Lu(2), one Lu(3), one Lu(4), and one Zr(1) atom to form distorted OLu3Zr tetrahedra that share  a cornercorner with one O(4)Lu2Zr2 tetrahedra,  a cornercorner with one O(6)Lu2Zr2 tetrahedra,  a cornercorner with one O(7)Lu2Zr2 tetrahedra,  a cornercorner with one O(11)Lu3Zr tetrahedra,  a cornercorner with one O(12)Lu3Zr tetrahedra,  a cornercorner with one O(5)Lu3Zr tetrahedra, corners with two equivalent O(1)Lu2Zr2 tetrahedra, corners with two equivalent O(8)Lu2Zr2 tetrahedra, corners with two equivalent O(10)Lu3Zr tetrahedra,  an edgeedge with one O(4)Lu2Zr2 tetrahedra,  an edgeedge with one O(6)Lu2Zr2 tetrahedra,  an edgeedge with one O(11)Lu3Zr tetrahedra, and  an edgeedge with one O(12)Lu3Zr tetrahedra. In the tenth O site, O(10) is bonded to one Lu(1), one Lu(2), one Lu(3), and one Zr(3) atom to form OLu3Zr tetrahedra that share  a cornercorner with one O(6)Lu2Zr2 tetrahedra,  a cornercorner with one O(8)Lu2Zr2 tetrahedra,  a cornercorner with one O(11)Lu3Zr tetrahedra, corners with two equivalent O(1)Lu2Zr2 tetrahedra, corners with two equivalent O(7)Lu2Zr2 tetrahedra, corners with two equivalent O(5)Lu3Zr tetrahedra, corners with two equivalent O(9)Lu3Zr tetrahedra,  an edgeedge with one O(6)Lu2Zr2 tetrahedra,  an edgeedge with one O(7)Lu2Zr2 tetrahedra,  an edgeedge with one O(12)Lu3Zr tetrahedra, and  an edgeedge with one O(5)Lu3Zr tetrahedra. In the eleventh O site, O(11) is bonded to one Lu(3), two equivalent Lu(4), and one Zr(2) atom to form OLu3Zr tetrahedra that share  a cornercorner with one O(1)Lu2Zr2 tetrahedra,  a cornercorner with one O(6)Lu2Zr2 tetrahedra,  a cornercorner with one O(10)Lu3Zr tetrahedra,  a cornercorner with one O(9)Lu3Zr tetrahedra, corners with two equivalent O(12)Lu3Zr tetrahedra, corners with three equivalent O(4)Lu2Zr2 tetrahedra, corners with three equivalent O(8)Lu2Zr2 tetrahedra,  an edgeedge with one O(4)Lu2Zr2 tetrahedra,  an edgeedge with one O(8)Lu2Zr2 tetrahedra,  an edgeedge with one O(11)Lu3Zr tetrahedra,  an edgeedge with one O(12)Lu3Zr tetrahedra, and  an edgeedge with one O(9)Lu3Zr tetrahedra. In the twelfth O site, O(12) is bonded to one Lu(2), one Lu(3), one Lu(4), and one Zr(2) atom to form distorted OLu3Zr tetrahedra that share  a cornercorner with one O(7)Lu2Zr2 tetrahedra,  a cornercorner with one O(5)Lu3Zr tetrahedra,  a cornercorner with one O(9)Lu3Zr tetrahedra, corners with two equivalent O(6)Lu2Zr2 tetrahedra, corners with two equivalent O(8)Lu2Zr2 tetrahedra, corners with two equivalent O(11)Lu3Zr tetrahedra, corners with three equivalent O(4)Lu2Zr2 tetrahedra,  an edgeedge with one O(1)Lu2Zr2 tetrahedra,  an edgeedge with one O(8)Lu2Zr2 tetrahedra,  an edgeedge with one O(10)Lu3Zr tetrahedra,  an edgeedge with one O(11)Lu3Zr tetrahedra, and  an edgeedge with one O(9)Lu3Zr tetrahedra.