MgZr2(BiO4)2 crystallizes in the monoclinic C2 space group. Mg(1) is bonded to two equivalent O(2) and two equivalent O(3) atoms to form MgO4 tetrahedra that share corners with two equivalent Zr(2)O6 octahedra, corners with two equivalent Bi(2)O6 pentagonal pyramids, and  an edgeedge with one Zr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms to form ZrO6 octahedra that share edges with two equivalent Zr(2)O6 octahedra, edges with two equivalent Bi(2)O6 pentagonal pyramids, and  an edgeedge with one Mg(1)O4 tetrahedra. In the second Zr site, Zr(2) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms to form distorted ZrO6 octahedra that share corners with two equivalent Bi(2)O6 pentagonal pyramids, corners with two equivalent Mg(1)O4 tetrahedra, edges with two equivalent Zr(1)O6 octahedra, and edges with two equivalent Bi(2)O6 pentagonal pyramids. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a 6-coordinate geometry to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms. In the second Bi site, Bi(2) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms to form distorted BiO6 pentagonal pyramids that share corners with two equivalent Zr(2)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra, edges with two equivalent Zr(1)O6 octahedra, and edges with two equivalent Zr(2)O6 octahedra. The corner-sharing octahedral tilt angles are 40°. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Zr(1), one Zr(2), one Bi(1), and one Bi(2) atom to form distorted corner-sharing OZr2Bi2 trigonal pyramids. In the second O site, O(2) is bonded in a distorted T-shaped geometry to one Mg(1), one Zr(1), and one Bi(1) atom. In the third O site, O(3) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Zr(2), and one Bi(2) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Zr(1), one Zr(2), one Bi(1), and one Bi(2) atom.
MgZr2(BiO4)2 crystallizes in the monoclinic C2 space group. Mg(1) is bonded to two equivalent O(2) and two equivalent O(3) atoms to form MgO4 tetrahedra that share corners with two equivalent Zr(2)O6 octahedra, corners with two equivalent Bi(2)O6 pentagonal pyramids, and  an edgeedge with one Zr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. Both Mg(1)-O(2) bond lengths are 2.02 Å. Both Mg(1)-O(3) bond lengths are 1.98 Å. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms to form ZrO6 octahedra that share edges with two equivalent Zr(2)O6 octahedra, edges with two equivalent Bi(2)O6 pentagonal pyramids, and  an edgeedge with one Mg(1)O4 tetrahedra. Both Zr(1)-O(1) bond lengths are 2.14 Å. Both Zr(1)-O(2) bond lengths are 2.04 Å. Both Zr(1)-O(4) bond lengths are 2.21 Å. In the second Zr site, Zr(2) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms to form distorted ZrO6 octahedra that share corners with two equivalent Bi(2)O6 pentagonal pyramids, corners with two equivalent Mg(1)O4 tetrahedra, edges with two equivalent Zr(1)O6 octahedra, and edges with two equivalent Bi(2)O6 pentagonal pyramids. Both Zr(2)-O(1) bond lengths are 2.36 Å. Both Zr(2)-O(3) bond lengths are 2.02 Å. Both Zr(2)-O(4) bond lengths are 2.11 Å. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a 6-coordinate geometry to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms. Both Bi(1)-O(1) bond lengths are 2.35 Å. Both Bi(1)-O(2) bond lengths are 2.34 Å. Both Bi(1)-O(4) bond lengths are 2.65 Å. In the second Bi site, Bi(2) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms to form distorted BiO6 pentagonal pyramids that share corners with two equivalent Zr(2)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra, edges with two equivalent Zr(1)O6 octahedra, and edges with two equivalent Zr(2)O6 octahedra. The corner-sharing octahedral tilt angles are 40°. Both Bi(2)-O(1) bond lengths are 2.42 Å. Both Bi(2)-O(3) bond lengths are 2.37 Å. Both Bi(2)-O(4) bond lengths are 2.32 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Zr(1), one Zr(2), one Bi(1), and one Bi(2) atom to form distorted corner-sharing OZr2Bi2 trigonal pyramids. In the second O site, O(2) is bonded in a distorted T-shaped geometry to one Mg(1), one Zr(1), and one Bi(1) atom. In the third O site, O(3) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Zr(2), and one Bi(2) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Zr(1), one Zr(2), one Bi(1), and one Bi(2) atom.