Y4Zr3O12 crystallizes in the triclinic P-1 space group. There are four inequivalent Y sites. In the first Y site, Y(1) is bonded in a 7-coordinate geometry to one O(1), one O(2), one O(3), one O(6), one O(9), and two equivalent O(5) atoms. In the second Y site, Y(2) is bonded in a 7-coordinate geometry to one O(1), one O(11), one O(12), one O(5), one O(6), one O(7), and one O(9) atom. In the third Y site, Y(3) is bonded to one O(10), one O(11), one O(12), one O(3), one O(7), one O(8), and one O(9) atom to form distorted YO7 pentagonal bipyramids that share  a cornercorner with one Zr(1)O6 octahedra and  an edgeedge with one Zr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the fourth Y site, Y(4) is bonded in a 7-coordinate geometry to one O(11), one O(12), one O(8), two equivalent O(10), and two equivalent O(4) atoms. There are three inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to one O(1), one O(11), one O(2), one O(3), one O(4), and one O(7) atom to form ZrO6 octahedra that share  a cornercorner with one Y(3)O7 pentagonal bipyramid and  an edgeedge with one Y(3)O7 pentagonal bipyramid. In the second Zr site, Zr(2) is bonded in a 7-coordinate geometry to one O(1), one O(10), 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(2), one O(5), one O(7), one O(9), and two equivalent O(6) atoms. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Y(1), one Y(2), one Zr(1), and one Zr(2) atom to form distorted OY2Zr2 tetrahedra that share  a cornercorner with one O(10)Y3Zr tetrahedra,  a cornercorner with one O(5)Y3Zr tetrahedra, corners with two equivalent O(6)Y2Zr2 tetrahedra, corners with two equivalent O(8)Y2Zr2 tetrahedra, corners with two equivalent O(11)Y3Zr tetrahedra, corners with two equivalent O(9)Y3Zr tetrahedra,  an edgeedge with one O(4)Y2Zr2 tetrahedra,  an edgeedge with one O(7)Y2Zr2 tetrahedra,  an edgeedge with one O(12)Y3Zr tetrahedra, and  an edgeedge with one O(5)Y3Zr tetrahedra. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Y(1), one Zr(1), and one Zr(3) atom. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Y(1), one Y(3), one Zr(1), and one Zr(2) atom. In the fourth O site, O(4) is bonded to two equivalent Y(4), one Zr(1), and one Zr(2) atom to form distorted OY2Zr2 tetrahedra that share  a cornercorner with one O(7)Y2Zr2 tetrahedra,  a cornercorner with one O(11)Y3Zr tetrahedra, corners with two equivalent O(8)Y2Zr2 tetrahedra, corners with three equivalent O(10)Y3Zr tetrahedra, corners with three equivalent O(12)Y3Zr tetrahedra,  an edgeedge with one O(1)Y2Zr2 tetrahedra,  an edgeedge with one O(4)Y2Zr2 tetrahedra,  an edgeedge with one O(8)Y2Zr2 tetrahedra,  an edgeedge with one O(10)Y3Zr tetrahedra, and  an edgeedge with one O(11)Y3Zr tetrahedra. In the fifth O site, O(5) is bonded to one Y(2), two equivalent Y(1), and one Zr(3) atom to form distorted OY3Zr tetrahedra that share  a cornercorner with one O(1)Y2Zr2 tetrahedra,  a cornercorner with one O(11)Y3Zr tetrahedra,  a cornercorner with one O(12)Y3Zr tetrahedra, corners with two equivalent O(7)Y2Zr2 tetrahedra, corners with two equivalent O(9)Y3Zr tetrahedra, corners with three equivalent O(6)Y2Zr2 tetrahedra,  an edgeedge with one O(1)Y2Zr2 tetrahedra,  an edgeedge with one O(6)Y2Zr2 tetrahedra,  an edgeedge with one O(5)Y3Zr tetrahedra, and  an edgeedge with one O(9)Y3Zr tetrahedra. In the sixth O site, O(6) is bonded to one Y(1), one Y(2), and two equivalent Zr(3) atoms to form OY2Zr2 tetrahedra that share  a cornercorner with one O(7)Y2Zr2 tetrahedra,  a cornercorner with one O(11)Y3Zr tetrahedra,  a cornercorner with one O(12)Y3Zr tetrahedra, corners with two equivalent O(1)Y2Zr2 tetrahedra, corners with two equivalent O(9)Y3Zr tetrahedra, corners with three equivalent O(5)Y3Zr tetrahedra,  an edgeedge with one O(6)Y2Zr2 tetrahedra,  an edgeedge with one O(7)Y2Zr2 tetrahedra,  an edgeedge with one O(5)Y3Zr tetrahedra, and  an edgeedge with one O(9)Y3Zr tetrahedra. In the seventh O site, O(7) is bonded to one Y(2), one Y(3), one Zr(1), and one Zr(3) atom to form distorted OY2Zr2 tetrahedra that share  a cornercorner with one O(4)Y2Zr2 tetrahedra,  a cornercorner with one O(6)Y2Zr2 tetrahedra,  a cornercorner with one O(8)Y2Zr2 tetrahedra,  a cornercorner with one O(10)Y3Zr tetrahedra,  a cornercorner with one O(11)Y3Zr tetrahedra,  a cornercorner with one O(9)Y3Zr tetrahedra, corners with two equivalent O(12)Y3Zr tetrahedra, corners with two equivalent O(5)Y3Zr tetrahedra,  an edgeedge with one O(1)Y2Zr2 tetrahedra,  an edgeedge with one O(6)Y2Zr2 tetrahedra,  an edgeedge with one O(11)Y3Zr tetrahedra, and  an edgeedge with one O(9)Y3Zr tetrahedra. In the eighth O site, O(8) is bonded to one Y(3), one Y(4), and two equivalent Zr(2) atoms to form OY2Zr2 tetrahedra that share  a cornercorner with one O(7)Y2Zr2 tetrahedra,  a cornercorner with one O(9)Y3Zr tetrahedra, corners with two equivalent O(1)Y2Zr2 tetrahedra, corners with two equivalent O(4)Y2Zr2 tetrahedra, corners with two equivalent O(11)Y3Zr tetrahedra, corners with two equivalent O(12)Y3Zr tetrahedra, corners with three equivalent O(10)Y3Zr tetrahedra,  an edgeedge with one O(4)Y2Zr2 tetrahedra,  an edgeedge with one O(8)Y2Zr2 tetrahedra,  an edgeedge with one O(10)Y3Zr tetrahedra, and  an edgeedge with one O(12)Y3Zr tetrahedra. In the ninth O site, O(9) is bonded to one Y(1), one Y(2), one Y(3), and one Zr(3) atom to form OY3Zr tetrahedra that share  a cornercorner with one O(7)Y2Zr2 tetrahedra,  a cornercorner with one O(8)Y2Zr2 tetrahedra,  a cornercorner with one O(10)Y3Zr tetrahedra, corners with two equivalent O(1)Y2Zr2 tetrahedra, corners with two equivalent O(6)Y2Zr2 tetrahedra, corners with two equivalent O(11)Y3Zr tetrahedra, corners with two equivalent O(5)Y3Zr tetrahedra,  an edgeedge with one O(6)Y2Zr2 tetrahedra,  an edgeedge with one O(7)Y2Zr2 tetrahedra,  an edgeedge with one O(12)Y3Zr tetrahedra, and  an edgeedge with one O(5)Y3Zr tetrahedra. In the tenth O site, O(10) is bonded to one Y(3), two equivalent Y(4), and one Zr(2) atom to form OY3Zr tetrahedra that share  a cornercorner with one O(1)Y2Zr2 tetrahedra,  a cornercorner with one O(7)Y2Zr2 tetrahedra,  a cornercorner with one O(11)Y3Zr tetrahedra,  a cornercorner with one O(9)Y3Zr tetrahedra, corners with two equivalent O(12)Y3Zr tetrahedra, corners with three equivalent O(4)Y2Zr2 tetrahedra, corners with three equivalent O(8)Y2Zr2 tetrahedra,  an edgeedge with one O(4)Y2Zr2 tetrahedra,  an edgeedge with one O(8)Y2Zr2 tetrahedra,  an edgeedge with one O(10)Y3Zr tetrahedra,  an edgeedge with one O(11)Y3Zr tetrahedra, and  an edgeedge with one O(12)Y3Zr tetrahedra. In the eleventh O site, O(11) is bonded to one Y(2), one Y(3), one Y(4), and one Zr(1) atom to form distorted OY3Zr tetrahedra that share  a cornercorner with one O(4)Y2Zr2 tetrahedra,  a cornercorner with one O(6)Y2Zr2 tetrahedra,  a cornercorner with one O(7)Y2Zr2 tetrahedra,  a cornercorner with one O(10)Y3Zr tetrahedra,  a cornercorner with one O(12)Y3Zr tetrahedra,  a cornercorner with one O(5)Y3Zr tetrahedra, corners with two equivalent O(1)Y2Zr2 tetrahedra, corners with two equivalent O(8)Y2Zr2 tetrahedra, corners with two equivalent O(9)Y3Zr tetrahedra,  an edgeedge with one O(4)Y2Zr2 tetrahedra,  an edgeedge with one O(7)Y2Zr2 tetrahedra,  an edgeedge with one O(10)Y3Zr tetrahedra, and  an edgeedge with one O(12)Y3Zr tetrahedra. In the twelfth O site, O(12) is bonded to one Y(2), one Y(3), one Y(4), and one Zr(2) atom to form distorted OY3Zr tetrahedra that share  a cornercorner with one O(6)Y2Zr2 tetrahedra,  a cornercorner with one O(11)Y3Zr tetrahedra,  a cornercorner with one O(5)Y3Zr tetrahedra, corners with two equivalent O(7)Y2Zr2 tetrahedra, corners with two equivalent O(8)Y2Zr2 tetrahedra, corners with two equivalent O(10)Y3Zr tetrahedra, corners with three equivalent O(4)Y2Zr2 tetrahedra,  an edgeedge with one O(1)Y2Zr2 tetrahedra,  an edgeedge with one O(8)Y2Zr2 tetrahedra,  an edgeedge with one O(10)Y3Zr tetrahedra,  an edgeedge with one O(11)Y3Zr tetrahedra, and  an edgeedge with one O(9)Y3Zr tetrahedra.
Y4Zr3O12 crystallizes in the triclinic P-1 space group. There are four inequivalent Y sites. In the first Y site, Y(1) is bonded in a 7-coordinate geometry to one O(1), one O(2), one O(3), one O(6), one O(9), and two equivalent O(5) atoms. The Y(1)-O(1) bond length is 2.24 Å. The Y(1)-O(2) bond length is 2.30 Å. The Y(1)-O(3) bond length is 2.62 Å. The Y(1)-O(6) bond length is 2.37 Å. The Y(1)-O(9) bond length is 2.20 Å. There is one shorter (2.27 Å) and one longer (2.34 Å) Y(1)-O(5) bond length. In the second Y site, Y(2) is bonded in a 7-coordinate geometry to one O(1), one O(11), one O(12), one O(5), one O(6), one O(7), and one O(9) atom. The Y(2)-O(1) bond length is 2.25 Å. The Y(2)-O(11) bond length is 2.25 Å. The Y(2)-O(12) bond length is 2.29 Å. The Y(2)-O(5) bond length is 2.39 Å. The Y(2)-O(6) bond length is 2.23 Å. The Y(2)-O(7) bond length is 2.57 Å. The Y(2)-O(9) bond length is 2.29 Å. In the third Y site, Y(3) is bonded to one O(10), one O(11), one O(12), one O(3), one O(7), one O(8), and one O(9) atom to form distorted YO7 pentagonal bipyramids that share  a cornercorner with one Zr(1)O6 octahedra and  an edgeedge with one Zr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. The Y(3)-O(10) bond length is 2.18 Å. The Y(3)-O(11) bond length is 2.46 Å. The Y(3)-O(12) bond length is 2.32 Å. The Y(3)-O(3) bond length is 2.34 Å. The Y(3)-O(7) bond length is 2.34 Å. The Y(3)-O(8) bond length is 2.38 Å. The Y(3)-O(9) bond length is 2.26 Å. In the fourth Y site, Y(4) is bonded in a 7-coordinate geometry to one O(11), one O(12), one O(8), two equivalent O(10), and two equivalent O(4) atoms. The Y(4)-O(11) bond length is 2.27 Å. The Y(4)-O(12) bond length is 2.40 Å. The Y(4)-O(8) bond length is 2.21 Å. There is one shorter (2.26 Å) and one longer (2.28 Å) Y(4)-O(10) bond length. There is one shorter (2.29 Å) and one longer (2.58 Å) Y(4)-O(4) bond length. There are three inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to one O(1), one O(11), one O(2), one O(3), one O(4), and one O(7) atom to form ZrO6 octahedra that share  a cornercorner with one Y(3)O7 pentagonal bipyramid and  an edgeedge with one Y(3)O7 pentagonal bipyramid. The Zr(1)-O(1) bond length is 2.08 Å. The Zr(1)-O(11) bond length is 2.09 Å. The Zr(1)-O(2) bond length is 2.08 Å. The Zr(1)-O(3) bond length is 2.10 Å. The Zr(1)-O(4) bond length is 2.14 Å. The Zr(1)-O(7) bond length is 2.15 Å. In the second Zr site, Zr(2) is bonded in a 7-coordinate geometry to one O(1), one O(10), 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(10) bond length is 2.19 Å. The Zr(2)-O(12) bond length is 2.07 Å. The Zr(2)-O(3) bond length is 2.17 Å. The Zr(2)-O(4) bond length is 2.12 Å. There is one shorter (2.16 Å) and one longer (2.23 Å) Zr(2)-O(8) bond length. In the third Zr site, Zr(3) is bonded in a 6-coordinate geometry to one O(2), one O(5), one O(7), one O(9), and two equivalent O(6) atoms. The Zr(3)-O(2) bond length is 2.12 Å. The Zr(3)-O(5) bond length is 2.07 Å. The Zr(3)-O(7) bond length is 2.11 Å. The Zr(3)-O(9) bond length is 2.17 Å. There is one shorter (2.10 Å) and one longer (2.21 Å) Zr(3)-O(6) bond length. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Y(1), one Y(2), one Zr(1), and one Zr(2) atom to form distorted OY2Zr2 tetrahedra that share  a cornercorner with one O(10)Y3Zr tetrahedra,  a cornercorner with one O(5)Y3Zr tetrahedra, corners with two equivalent O(6)Y2Zr2 tetrahedra, corners with two equivalent O(8)Y2Zr2 tetrahedra, corners with two equivalent O(11)Y3Zr tetrahedra, corners with two equivalent O(9)Y3Zr tetrahedra,  an edgeedge with one O(4)Y2Zr2 tetrahedra,  an edgeedge with one O(7)Y2Zr2 tetrahedra,  an edgeedge with one O(12)Y3Zr tetrahedra, and  an edgeedge with one O(5)Y3Zr tetrahedra. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Y(1), one Zr(1), and one Zr(3) atom. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Y(1), one Y(3), one Zr(1), and one Zr(2) atom. In the fourth O site, O(4) is bonded to two equivalent Y(4), one Zr(1), and one Zr(2) atom to form distorted OY2Zr2 tetrahedra that share  a cornercorner with one O(7)Y2Zr2 tetrahedra,  a cornercorner with one O(11)Y3Zr tetrahedra, corners with two equivalent O(8)Y2Zr2 tetrahedra, corners with three equivalent O(10)Y3Zr tetrahedra, corners with three equivalent O(12)Y3Zr tetrahedra,  an edgeedge with one O(1)Y2Zr2 tetrahedra,  an edgeedge with one O(4)Y2Zr2 tetrahedra,  an edgeedge with one O(8)Y2Zr2 tetrahedra,  an edgeedge with one O(10)Y3Zr tetrahedra, and  an edgeedge with one O(11)Y3Zr tetrahedra. In the fifth O site, O(5) is bonded to one Y(2), two equivalent Y(1), and one Zr(3) atom to form distorted OY3Zr tetrahedra that share  a cornercorner with one O(1)Y2Zr2 tetrahedra,  a cornercorner with one O(11)Y3Zr tetrahedra,  a cornercorner with one O(12)Y3Zr tetrahedra, corners with two equivalent O(7)Y2Zr2 tetrahedra, corners with two equivalent O(9)Y3Zr tetrahedra, corners with three equivalent O(6)Y2Zr2 tetrahedra,  an edgeedge with one O(1)Y2Zr2 tetrahedra,  an edgeedge with one O(6)Y2Zr2 tetrahedra,  an edgeedge with one O(5)Y3Zr tetrahedra, and  an edgeedge with one O(9)Y3Zr tetrahedra. In the sixth O site, O(6) is bonded to one Y(1), one Y(2), and two equivalent Zr(3) atoms to form OY2Zr2 tetrahedra that share  a cornercorner with one O(7)Y2Zr2 tetrahedra,  a cornercorner with one O(11)Y3Zr tetrahedra,  a cornercorner with one O(12)Y3Zr tetrahedra, corners with two equivalent O(1)Y2Zr2 tetrahedra, corners with two equivalent O(9)Y3Zr tetrahedra, corners with three equivalent O(5)Y3Zr tetrahedra,  an edgeedge with one O(6)Y2Zr2 tetrahedra,  an edgeedge with one O(7)Y2Zr2 tetrahedra,  an edgeedge with one O(5)Y3Zr tetrahedra, and  an edgeedge with one O(9)Y3Zr tetrahedra. In the seventh O site, O(7) is bonded to one Y(2), one Y(3), one Zr(1), and one Zr(3) atom to form distorted OY2Zr2 tetrahedra that share  a cornercorner with one O(4)Y2Zr2 tetrahedra,  a cornercorner with one O(6)Y2Zr2 tetrahedra,  a cornercorner with one O(8)Y2Zr2 tetrahedra,  a cornercorner with one O(10)Y3Zr tetrahedra,  a cornercorner with one O(11)Y3Zr tetrahedra,  a cornercorner with one O(9)Y3Zr tetrahedra, corners with two equivalent O(12)Y3Zr tetrahedra, corners with two equivalent O(5)Y3Zr tetrahedra,  an edgeedge with one O(1)Y2Zr2 tetrahedra,  an edgeedge with one O(6)Y2Zr2 tetrahedra,  an edgeedge with one O(11)Y3Zr tetrahedra, and  an edgeedge with one O(9)Y3Zr tetrahedra. In the eighth O site, O(8) is bonded to one Y(3), one Y(4), and two equivalent Zr(2) atoms to form OY2Zr2 tetrahedra that share  a cornercorner with one O(7)Y2Zr2 tetrahedra,  a cornercorner with one O(9)Y3Zr tetrahedra, corners with two equivalent O(1)Y2Zr2 tetrahedra, corners with two equivalent O(4)Y2Zr2 tetrahedra, corners with two equivalent O(11)Y3Zr tetrahedra, corners with two equivalent O(12)Y3Zr tetrahedra, corners with three equivalent O(10)Y3Zr tetrahedra,  an edgeedge with one O(4)Y2Zr2 tetrahedra,  an edgeedge with one O(8)Y2Zr2 tetrahedra,  an edgeedge with one O(10)Y3Zr tetrahedra, and  an edgeedge with one O(12)Y3Zr tetrahedra. In the ninth O site, O(9) is bonded to one Y(1), one Y(2), one Y(3), and one Zr(3) atom to form OY3Zr tetrahedra that share  a cornercorner with one O(7)Y2Zr2 tetrahedra,  a cornercorner with one O(8)Y2Zr2 tetrahedra,  a cornercorner with one O(10)Y3Zr tetrahedra, corners with two equivalent O(1)Y2Zr2 tetrahedra, corners with two equivalent O(6)Y2Zr2 tetrahedra, corners with two equivalent O(11)Y3Zr tetrahedra, corners with two equivalent O(5)Y3Zr tetrahedra,  an edgeedge with one O(6)Y2Zr2 tetrahedra,  an edgeedge with one O(7)Y2Zr2 tetrahedra,  an edgeedge with one O(12)Y3Zr tetrahedra, and  an edgeedge with one O(5)Y3Zr tetrahedra. In the tenth O site, O(10) is bonded to one Y(3), two equivalent Y(4), and one Zr(2) atom to form OY3Zr tetrahedra that share  a cornercorner with one O(1)Y2Zr2 tetrahedra,  a cornercorner with one O(7)Y2Zr2 tetrahedra,  a cornercorner with one O(11)Y3Zr tetrahedra,  a cornercorner with one O(9)Y3Zr tetrahedra, corners with two equivalent O(12)Y3Zr tetrahedra, corners with three equivalent O(4)Y2Zr2 tetrahedra, corners with three equivalent O(8)Y2Zr2 tetrahedra,  an edgeedge with one O(4)Y2Zr2 tetrahedra,  an edgeedge with one O(8)Y2Zr2 tetrahedra,  an edgeedge with one O(10)Y3Zr tetrahedra,  an edgeedge with one O(11)Y3Zr tetrahedra, and  an edgeedge with one O(12)Y3Zr tetrahedra. In the eleventh O site, O(11) is bonded to one Y(2), one Y(3), one Y(4), and one Zr(1) atom to form distorted OY3Zr tetrahedra that share  a cornercorner with one O(4)Y2Zr2 tetrahedra,  a cornercorner with one O(6)Y2Zr2 tetrahedra,  a cornercorner with one O(7)Y2Zr2 tetrahedra,  a cornercorner with one O(10)Y3Zr tetrahedra,  a cornercorner with one O(12)Y3Zr tetrahedra,  a cornercorner with one O(5)Y3Zr tetrahedra, corners with two equivalent O(1)Y2Zr2 tetrahedra, corners with two equivalent O(8)Y2Zr2 tetrahedra, corners with two equivalent O(9)Y3Zr tetrahedra,  an edgeedge with one O(4)Y2Zr2 tetrahedra,  an edgeedge with one O(7)Y2Zr2 tetrahedra,  an edgeedge with one O(10)Y3Zr tetrahedra, and  an edgeedge with one O(12)Y3Zr tetrahedra. In the twelfth O site, O(12) is bonded to one Y(2), one Y(3), one Y(4), and one Zr(2) atom to form distorted OY3Zr tetrahedra that share  a cornercorner with one O(6)Y2Zr2 tetrahedra,  a cornercorner with one O(11)Y3Zr tetrahedra,  a cornercorner with one O(5)Y3Zr tetrahedra, corners with two equivalent O(7)Y2Zr2 tetrahedra, corners with two equivalent O(8)Y2Zr2 tetrahedra, corners with two equivalent O(10)Y3Zr tetrahedra, corners with three equivalent O(4)Y2Zr2 tetrahedra,  an edgeedge with one O(1)Y2Zr2 tetrahedra,  an edgeedge with one O(8)Y2Zr2 tetrahedra,  an edgeedge with one O(10)Y3Zr tetrahedra,  an edgeedge with one O(11)Y3Zr tetrahedra, and  an edgeedge with one O(9)Y3Zr tetrahedra.