K6Mg(BiO4)2 crystallizes in the triclinic P1 space group. There are six inequivalent K sites. In the first K site, K(1) is bonded in a 5-coordinate geometry to one O(1), one O(3), one O(4), one O(5), and one O(8) atom. In the second K site, K(2) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(3), one O(5), and one O(8) atom. In the third K site, K(3) is bonded in a 5-coordinate geometry to one O(1), one O(5), one O(6), one O(7), and one O(8) atom. In the fourth K site, K(4) is bonded to one O(2), one O(5), one O(6), one O(7), and one O(8) atom to form distorted KO5 trigonal bipyramids that share  a cornercorner with one K(5)O5 trigonal bipyramid, corners with three equivalent Bi(2)O5 trigonal bipyramids, and  an edgeedge with one K(5)O5 trigonal bipyramid. In the fifth K site, K(5) is bonded to one O(1), one O(2), one O(3), one O(5), and one O(6) atom to form distorted KO5 trigonal bipyramids that share  a cornercorner with one K(4)O5 trigonal bipyramid,  a cornercorner with one Bi(2)O5 trigonal bipyramid,  an edgeedge with one K(4)O5 trigonal bipyramid, and  an edgeedge with one Bi(2)O5 trigonal bipyramid. In the sixth K site, K(6) is bonded in a 5-coordinate geometry to one O(2), one O(3), one O(4), one O(6), and one O(7) atom. Mg(1) is bonded in a distorted trigonal planar geometry to one O(2), one O(4), and one O(6) atom. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a 5-coordinate geometry to one O(2), one O(4), one O(6), one O(7), and one O(8) atom. In the second Bi site, Bi(2) is bonded to one O(1), one O(3), one O(5), one O(7), and one O(8) atom to form BiO5 trigonal bipyramids that share  a cornercorner with one K(5)O5 trigonal bipyramid, corners with three equivalent K(4)O5 trigonal bipyramids, and  an edgeedge with one K(5)O5 trigonal bipyramid. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to one K(1), one K(2), one K(3), one K(5), and one Bi(2) atom. In the second O site, O(2) is bonded in a 6-coordinate geometry to one K(2), one K(4), one K(5), one K(6), one Mg(1), and one Bi(1) atom. In the third O site, O(3) is bonded to one K(1), one K(2), one K(5), one K(6), and one Bi(2) atom to form distorted OK4Bi trigonal bipyramids that share  a cornercorner with one O(8)K4Bi2 octahedra, corners with two equivalent O(5)K5Bi octahedra, corners with two equivalent O(7)K3Bi2 square pyramids,  an edgeedge with one O(8)K4Bi2 octahedra, and  an edgeedge with one O(5)K5Bi octahedra. The corner-sharing octahedral tilt angles range from 13-78°. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one K(1), one K(6), one Mg(1), and one Bi(1) atom. In the fifth O site, O(5) is bonded to one K(1), one K(2), one K(3), one K(4), one K(5), and one Bi(2) atom to form distorted OK5Bi octahedra that share  a cornercorner with one O(8)K4Bi2 octahedra,  a cornercorner with one O(7)K3Bi2 square pyramid, corners with two equivalent O(3)K4Bi trigonal bipyramids, edges with two equivalent O(8)K4Bi2 octahedra,  an edgeedge with one O(7)K3Bi2 square pyramid, and  an edgeedge with one O(3)K4Bi trigonal bipyramid. The corner-sharing octahedral tilt angles are 16°. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to one K(3), one K(4), one K(5), one K(6), one Mg(1), and one Bi(1) atom. In the seventh O site, O(7) is bonded to one K(3), one K(4), one K(6), one Bi(1), and one Bi(2) atom to form distorted OK3Bi2 square pyramids that share  a cornercorner with one O(5)K5Bi octahedra, corners with two equivalent O(3)K4Bi trigonal bipyramids,  an edgeedge with one O(5)K5Bi octahedra, and edges with two equivalent O(8)K4Bi2 octahedra. The corner-sharing octahedral tilt angles are 52°. In the eighth O site, O(8) is bonded to one K(1), one K(2), one K(3), one K(4), one Bi(1), and one Bi(2) atom to form distorted OK4Bi2 octahedra that share  a cornercorner with one O(5)K5Bi octahedra,  a cornercorner with one O(3)K4Bi trigonal bipyramid, edges with two equivalent O(5)K5Bi octahedra, edges with two equivalent O(7)K3Bi2 square pyramids, and  an edgeedge with one O(3)K4Bi trigonal bipyramid. The corner-sharing octahedral tilt angles are 16°.
K6Mg(BiO4)2 crystallizes in the triclinic P1 space group. There are six inequivalent K sites. In the first K site, K(1) is bonded in a 5-coordinate geometry to one O(1), one O(3), one O(4), one O(5), and one O(8) atom. The K(1)-O(1) bond length is 2.68 Å. The K(1)-O(3) bond length is 2.67 Å. The K(1)-O(4) bond length is 2.68 Å. The K(1)-O(5) bond length is 2.88 Å. The K(1)-O(8) bond length is 2.94 Å. In the second K site, K(2) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(3), one O(5), and one O(8) atom. The K(2)-O(1) bond length is 2.51 Å. The K(2)-O(2) bond length is 3.19 Å. The K(2)-O(3) bond length is 2.69 Å. The K(2)-O(5) bond length is 2.73 Å. The K(2)-O(8) bond length is 2.79 Å. In the third K site, K(3) is bonded in a 5-coordinate geometry to one O(1), one O(5), one O(6), one O(7), and one O(8) atom. The K(3)-O(1) bond length is 2.80 Å. The K(3)-O(5) bond length is 2.69 Å. The K(3)-O(6) bond length is 2.70 Å. The K(3)-O(7) bond length is 2.77 Å. The K(3)-O(8) bond length is 2.81 Å. In the fourth K site, K(4) is bonded to one O(2), one O(5), one O(6), one O(7), and one O(8) atom to form distorted KO5 trigonal bipyramids that share  a cornercorner with one K(5)O5 trigonal bipyramid, corners with three equivalent Bi(2)O5 trigonal bipyramids, and  an edgeedge with one K(5)O5 trigonal bipyramid. The K(4)-O(2) bond length is 2.82 Å. The K(4)-O(5) bond length is 2.95 Å. The K(4)-O(6) bond length is 3.00 Å. The K(4)-O(7) bond length is 2.90 Å. The K(4)-O(8) bond length is 2.95 Å. In the fifth K site, K(5) is bonded to one O(1), one O(2), one O(3), one O(5), and one O(6) atom to form distorted KO5 trigonal bipyramids that share  a cornercorner with one K(4)O5 trigonal bipyramid,  a cornercorner with one Bi(2)O5 trigonal bipyramid,  an edgeedge with one K(4)O5 trigonal bipyramid, and  an edgeedge with one Bi(2)O5 trigonal bipyramid. The K(5)-O(1) bond length is 2.71 Å. The K(5)-O(2) bond length is 2.96 Å. The K(5)-O(3) bond length is 2.76 Å. The K(5)-O(5) bond length is 2.98 Å. The K(5)-O(6) bond length is 2.87 Å. In the sixth K site, K(6) is bonded in a 5-coordinate geometry to one O(2), one O(3), one O(4), one O(6), and one O(7) atom. The K(6)-O(2) bond length is 3.05 Å. The K(6)-O(3) bond length is 2.65 Å. The K(6)-O(4) bond length is 2.82 Å. The K(6)-O(6) bond length is 2.77 Å. The K(6)-O(7) bond length is 2.90 Å. Mg(1) is bonded in a distorted trigonal planar geometry to one O(2), one O(4), and one O(6) atom. The Mg(1)-O(2) bond length is 1.94 Å. The Mg(1)-O(4) bond length is 1.92 Å. The Mg(1)-O(6) bond length is 1.93 Å. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a 5-coordinate geometry to one O(2), one O(4), one O(6), one O(7), and one O(8) atom. The Bi(1)-O(2) bond length is 2.28 Å. The Bi(1)-O(4) bond length is 2.25 Å. The Bi(1)-O(6) bond length is 2.46 Å. The Bi(1)-O(7) bond length is 2.33 Å. The Bi(1)-O(8) bond length is 2.45 Å. In the second Bi site, Bi(2) is bonded to one O(1), one O(3), one O(5), one O(7), and one O(8) atom to form BiO5 trigonal bipyramids that share  a cornercorner with one K(5)O5 trigonal bipyramid, corners with three equivalent K(4)O5 trigonal bipyramids, and  an edgeedge with one K(5)O5 trigonal bipyramid. The Bi(2)-O(1) bond length is 2.08 Å. The Bi(2)-O(3) bond length is 2.06 Å. The Bi(2)-O(5) bond length is 2.12 Å. The Bi(2)-O(7) bond length is 2.17 Å. The Bi(2)-O(8) bond length is 2.22 Å. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to one K(1), one K(2), one K(3), one K(5), and one Bi(2) atom. In the second O site, O(2) is bonded in a 6-coordinate geometry to one K(2), one K(4), one K(5), one K(6), one Mg(1), and one Bi(1) atom. In the third O site, O(3) is bonded to one K(1), one K(2), one K(5), one K(6), and one Bi(2) atom to form distorted OK4Bi trigonal bipyramids that share  a cornercorner with one O(8)K4Bi2 octahedra, corners with two equivalent O(5)K5Bi octahedra, corners with two equivalent O(7)K3Bi2 square pyramids,  an edgeedge with one O(8)K4Bi2 octahedra, and  an edgeedge with one O(5)K5Bi octahedra. The corner-sharing octahedral tilt angles range from 13-78°. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one K(1), one K(6), one Mg(1), and one Bi(1) atom. In the fifth O site, O(5) is bonded to one K(1), one K(2), one K(3), one K(4), one K(5), and one Bi(2) atom to form distorted OK5Bi octahedra that share  a cornercorner with one O(8)K4Bi2 octahedra,  a cornercorner with one O(7)K3Bi2 square pyramid, corners with two equivalent O(3)K4Bi trigonal bipyramids, edges with two equivalent O(8)K4Bi2 octahedra,  an edgeedge with one O(7)K3Bi2 square pyramid, and  an edgeedge with one O(3)K4Bi trigonal bipyramid. The corner-sharing octahedral tilt angles are 16°. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to one K(3), one K(4), one K(5), one K(6), one Mg(1), and one Bi(1) atom. In the seventh O site, O(7) is bonded to one K(3), one K(4), one K(6), one Bi(1), and one Bi(2) atom to form distorted OK3Bi2 square pyramids that share  a cornercorner with one O(5)K5Bi octahedra, corners with two equivalent O(3)K4Bi trigonal bipyramids,  an edgeedge with one O(5)K5Bi octahedra, and edges with two equivalent O(8)K4Bi2 octahedra. The corner-sharing octahedral tilt angles are 52°. In the eighth O site, O(8) is bonded to one K(1), one K(2), one K(3), one K(4), one Bi(1), and one Bi(2) atom to form distorted OK4Bi2 octahedra that share  a cornercorner with one O(5)K5Bi octahedra,  a cornercorner with one O(3)K4Bi trigonal bipyramid, edges with two equivalent O(5)K5Bi octahedra, edges with two equivalent O(7)K3Bi2 square pyramids, and  an edgeedge with one O(3)K4Bi trigonal bipyramid. The corner-sharing octahedral tilt angles are 16°.