Zr3Yb4O12 crystallizes in the triclinic P-1 space group. There are two inequivalent Yb sites. In the first Yb site, Yb(1) is bonded to one O(1), one O(2), one O(4), two equivalent O(3), and two equivalent O(5) atoms to form distorted YbO7 pentagonal bipyramids that share  a cornercorner with one Yb(2)O7 hexagonal pyramid,  a cornercorner with one Zr(1)O6 octahedra, edges with three equivalent Yb(2)O7 hexagonal pyramids,  an edgeedge with one Zr(1)O6 octahedra, and edges with two equivalent Yb(1)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 50°. In the second Yb site, Yb(2) is bonded to one O(2), one O(3), one O(5), two equivalent O(1), and two equivalent O(6) atoms to form distorted YbO7 hexagonal pyramids that share  a cornercorner with one Zr(1)O6 octahedra,  a cornercorner with one Yb(1)O7 pentagonal bipyramid, edges with two equivalent Yb(2)O7 hexagonal pyramids,  an edgeedge with one Zr(1)O6 octahedra, and edges with three equivalent Yb(1)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 57°. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to two equivalent O(4), two equivalent O(5), and two equivalent O(6) atoms to form ZrO6 octahedra that share corners with two equivalent Yb(2)O7 hexagonal pyramids, corners with two equivalent Yb(1)O7 pentagonal bipyramids, edges with two equivalent Yb(2)O7 hexagonal pyramids, and edges with two equivalent Yb(1)O7 pentagonal bipyramids. In the second Zr site, Zr(2) is bonded in a 7-coordinate geometry to one O(1), one O(3), one O(6), two equivalent O(2), and two equivalent O(4) atoms. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Yb(1), two equivalent Yb(2), and one Zr(2) atom to form OYb3Zr tetrahedra that share corners with two equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(6)Yb2Zr2 tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids, corners with three equivalent O(4)YbZr3 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra, and  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid. In the second O site, O(2) is bonded to one Yb(1), one Yb(2), and two equivalent Zr(2) atoms to form distorted OYb2Zr2 trigonal pyramids that share corners with two equivalent O(6)Yb2Zr2 tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with three equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(4)YbZr3 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the third O site, O(3) is bonded to one Yb(2), two equivalent Yb(1), and one Zr(2) atom to form distorted OYb3Zr tetrahedra that share corners with three equivalent O(6)Yb2Zr2 tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(5)Yb3Zr tetrahedra, corners with two equivalent O(4)YbZr3 trigonal pyramids, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the fourth O site, O(4) is bonded to one Yb(1), one Zr(1), and two equivalent Zr(2) atoms to form distorted OYbZr3 trigonal pyramids that share corners with two equivalent O(6)Yb2Zr2 tetrahedra, corners with two equivalent O(3)Yb3Zr tetrahedra, corners with two equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra,  a cornercorner with one O(4)YbZr3 trigonal pyramid, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the fifth O site, O(5) is bonded to one Yb(2), two equivalent Yb(1), and one Zr(1) atom to form distorted OYb3Zr tetrahedra that share  a cornercorner with one O(5)Yb3Zr tetrahedra, corners with two equivalent O(6)Yb2Zr2 tetrahedra, corners with two equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with two equivalent O(4)YbZr3 trigonal pyramids, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the sixth O site, O(6) is bonded to two equivalent Yb(2), one Zr(1), and one Zr(2) atom to form OYb2Zr2 tetrahedra that share  a cornercorner with one O(6)Yb2Zr2 tetrahedra, corners with two equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with two equivalent O(2)Yb2Zr2 trigonal pyramids, corners with two equivalent O(4)YbZr3 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid.
Zr3Yb4O12 crystallizes in the triclinic P-1 space group. There are two inequivalent Yb sites. In the first Yb site, Yb(1) is bonded to one O(1), one O(2), one O(4), two equivalent O(3), and two equivalent O(5) atoms to form distorted YbO7 pentagonal bipyramids that share  a cornercorner with one Yb(2)O7 hexagonal pyramid,  a cornercorner with one Zr(1)O6 octahedra, edges with three equivalent Yb(2)O7 hexagonal pyramids,  an edgeedge with one Zr(1)O6 octahedra, and edges with two equivalent Yb(1)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 50°. The Yb(1)-O(1) bond length is 2.27 Å. The Yb(1)-O(2) bond length is 2.46 Å. The Yb(1)-O(4) bond length is 2.38 Å. There is one shorter (2.35 Å) and one longer (2.36 Å) Yb(1)-O(3) bond length. There is one shorter (2.32 Å) and one longer (2.42 Å) Yb(1)-O(5) bond length. In the second Yb site, Yb(2) is bonded to one O(2), one O(3), one O(5), two equivalent O(1), and two equivalent O(6) atoms to form distorted YbO7 hexagonal pyramids that share  a cornercorner with one Zr(1)O6 octahedra,  a cornercorner with one Yb(1)O7 pentagonal bipyramid, edges with two equivalent Yb(2)O7 hexagonal pyramids,  an edgeedge with one Zr(1)O6 octahedra, and edges with three equivalent Yb(1)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 57°. The Yb(2)-O(2) bond length is 2.35 Å. The Yb(2)-O(3) bond length is 2.42 Å. The Yb(2)-O(5) bond length is 2.32 Å. There is one shorter (2.31 Å) and one longer (2.36 Å) Yb(2)-O(1) bond length. There is one shorter (2.30 Å) and one longer (2.43 Å) Yb(2)-O(6) bond length. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to two equivalent O(4), two equivalent O(5), and two equivalent O(6) atoms to form ZrO6 octahedra that share corners with two equivalent Yb(2)O7 hexagonal pyramids, corners with two equivalent Yb(1)O7 pentagonal bipyramids, edges with two equivalent Yb(2)O7 hexagonal pyramids, and edges with two equivalent Yb(1)O7 pentagonal bipyramids. Both Zr(1)-O(4) bond lengths are 2.14 Å. Both Zr(1)-O(5) bond lengths are 2.11 Å. Both Zr(1)-O(6) bond lengths are 2.10 Å. In the second Zr site, Zr(2) is bonded in a 7-coordinate geometry to one O(1), one O(3), one O(6), two equivalent O(2), and two equivalent O(4) atoms. The Zr(2)-O(1) bond length is 2.16 Å. The Zr(2)-O(3) bond length is 2.08 Å. The Zr(2)-O(6) bond length is 2.10 Å. There is one shorter (2.23 Å) and one longer (2.28 Å) Zr(2)-O(2) bond length. There is one shorter (2.17 Å) and one longer (2.36 Å) Zr(2)-O(4) bond length. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Yb(1), two equivalent Yb(2), and one Zr(2) atom to form OYb3Zr tetrahedra that share corners with two equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(6)Yb2Zr2 tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids, corners with three equivalent O(4)YbZr3 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra, and  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid. In the second O site, O(2) is bonded to one Yb(1), one Yb(2), and two equivalent Zr(2) atoms to form distorted OYb2Zr2 trigonal pyramids that share corners with two equivalent O(6)Yb2Zr2 tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with three equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(4)YbZr3 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the third O site, O(3) is bonded to one Yb(2), two equivalent Yb(1), and one Zr(2) atom to form distorted OYb3Zr tetrahedra that share corners with three equivalent O(6)Yb2Zr2 tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(5)Yb3Zr tetrahedra, corners with two equivalent O(4)YbZr3 trigonal pyramids, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the fourth O site, O(4) is bonded to one Yb(1), one Zr(1), and two equivalent Zr(2) atoms to form distorted OYbZr3 trigonal pyramids that share corners with two equivalent O(6)Yb2Zr2 tetrahedra, corners with two equivalent O(3)Yb3Zr tetrahedra, corners with two equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra,  a cornercorner with one O(4)YbZr3 trigonal pyramid, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the fifth O site, O(5) is bonded to one Yb(2), two equivalent Yb(1), and one Zr(1) atom to form distorted OYb3Zr tetrahedra that share  a cornercorner with one O(5)Yb3Zr tetrahedra, corners with two equivalent O(6)Yb2Zr2 tetrahedra, corners with two equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with two equivalent O(4)YbZr3 trigonal pyramids, corners with three equivalent O(2)Yb2Zr2 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(3)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra, and  an edgeedge with one O(4)YbZr3 trigonal pyramid. In the sixth O site, O(6) is bonded to two equivalent Yb(2), one Zr(1), and one Zr(2) atom to form OYb2Zr2 tetrahedra that share  a cornercorner with one O(6)Yb2Zr2 tetrahedra, corners with two equivalent O(5)Yb3Zr tetrahedra, corners with three equivalent O(1)Yb3Zr tetrahedra, corners with three equivalent O(3)Yb3Zr tetrahedra, corners with two equivalent O(2)Yb2Zr2 trigonal pyramids, corners with two equivalent O(4)YbZr3 trigonal pyramids,  an edgeedge with one O(6)Yb2Zr2 tetrahedra,  an edgeedge with one O(1)Yb3Zr tetrahedra,  an edgeedge with one O(5)Yb3Zr tetrahedra,  an edgeedge with one O(2)Yb2Zr2 trigonal pyramid, and  an edgeedge with one O(4)YbZr3 trigonal pyramid.