KMg14BiO16 is Caswellsilverite-derived structured and crystallizes in the tetragonal P4/mmm space group. K(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form KO6 octahedra that share corners with two equivalent K(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(2)O6 octahedra. The corner-sharing octahedra are not tilted. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent K(1)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Bi(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(3)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedra are not tilted. In the second Mg site, Mg(2) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(3)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, edges with two equivalent K(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the third Mg site, Mg(3) is bonded to one O(5), one O(6), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Bi(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. In the fourth Mg site, Mg(4) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with six equivalent Mg(4)O6 octahedra,  an edgeedge with one K(1)O6 octahedra,  an edgeedge with one Bi(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-15°. Bi(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form BiO6 octahedra that share corners with two equivalent Bi(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. There are six inequivalent O sites. In the first O site, O(1) is bonded to one K(1), one Mg(1), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OKMg5 octahedra that share corners with two equivalent O(2)Mg5Bi octahedra, corners with four equivalent O(1)KMg5 octahedra, edges with two equivalent O(4)K2Mg4 octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with two equivalent O(2)Mg5Bi octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Bi(1) atom to form OMg5Bi octahedra that share corners with two equivalent O(1)KMg5 octahedra, corners with four equivalent O(2)Mg5Bi octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with two equivalent O(6)Mg4Bi2 octahedra, edges with two equivalent O(2)Mg5Bi octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the third O site, O(3) is bonded to two equivalent Mg(2), two equivalent Mg(3), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with six equivalent O(3)Mg6 octahedra,  an edgeedge with one O(4)K2Mg4 octahedra,  an edgeedge with one O(6)Mg4Bi2 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)KMg5 octahedra, and edges with four equivalent O(2)Mg5Bi octahedra. The corner-sharing octahedral tilt angles range from 2-9°. In the fourth O site, O(4) is bonded to two equivalent K(1) and four equivalent Mg(2) atoms to form OK2Mg4 octahedra that share corners with two equivalent O(4)K2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)KMg5 octahedra. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to two equivalent Mg(1), two equivalent Mg(2), and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(4)K2Mg4 octahedra, corners with two equivalent O(6)Mg4Bi2 octahedra, corners with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)KMg5 octahedra, edges with four equivalent O(2)Mg5Bi octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to four equivalent Mg(3) and two equivalent Bi(1) atoms to form OMg4Bi2 octahedra that share corners with two equivalent O(6)Mg4Bi2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)Mg5Bi octahedra. The corner-sharing octahedra are not tilted.
KMg14BiO16 is Caswellsilverite-derived structured and crystallizes in the tetragonal P4/mmm space group. K(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form KO6 octahedra that share corners with two equivalent K(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(2)O6 octahedra. The corner-sharing octahedra are not tilted. Both K(1)-O(4) bond lengths are 2.24 Å. All K(1)-O(1) bond lengths are 2.40 Å. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent K(1)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Bi(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(3)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedra are not tilted. Both Mg(1)-O(1) bond lengths are 1.98 Å. Both Mg(1)-O(2) bond lengths are 2.08 Å. Both Mg(1)-O(5) bond lengths are 2.24 Å. In the second Mg site, Mg(2) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(3)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, edges with two equivalent K(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. The Mg(2)-O(4) bond length is 2.18 Å. The Mg(2)-O(5) bond length is 2.21 Å. Both Mg(2)-O(1) bond lengths are 2.25 Å. Both Mg(2)-O(3) bond lengths are 2.21 Å. In the third Mg site, Mg(3) is bonded to one O(5), one O(6), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Bi(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. The Mg(3)-O(5) bond length is 2.05 Å. The Mg(3)-O(6) bond length is 2.34 Å. Both Mg(3)-O(2) bond lengths are 2.24 Å. Both Mg(3)-O(3) bond lengths are 2.18 Å. In the fourth Mg site, Mg(4) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with six equivalent Mg(4)O6 octahedra,  an edgeedge with one K(1)O6 octahedra,  an edgeedge with one Bi(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-15°. Both Mg(4)-O(1) bond lengths are 2.14 Å. Both Mg(4)-O(2) bond lengths are 2.27 Å. Both Mg(4)-O(3) bond lengths are 2.25 Å. Bi(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form BiO6 octahedra that share corners with two equivalent Bi(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. Both Bi(1)-O(6) bond lengths are 2.24 Å. All Bi(1)-O(2) bond lengths are 2.31 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded to one K(1), one Mg(1), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OKMg5 octahedra that share corners with two equivalent O(2)Mg5Bi octahedra, corners with four equivalent O(1)KMg5 octahedra, edges with two equivalent O(4)K2Mg4 octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with two equivalent O(2)Mg5Bi octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Bi(1) atom to form OMg5Bi octahedra that share corners with two equivalent O(1)KMg5 octahedra, corners with four equivalent O(2)Mg5Bi octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with two equivalent O(6)Mg4Bi2 octahedra, edges with two equivalent O(2)Mg5Bi octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the third O site, O(3) is bonded to two equivalent Mg(2), two equivalent Mg(3), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with six equivalent O(3)Mg6 octahedra,  an edgeedge with one O(4)K2Mg4 octahedra,  an edgeedge with one O(6)Mg4Bi2 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)KMg5 octahedra, and edges with four equivalent O(2)Mg5Bi octahedra. The corner-sharing octahedral tilt angles range from 2-9°. In the fourth O site, O(4) is bonded to two equivalent K(1) and four equivalent Mg(2) atoms to form OK2Mg4 octahedra that share corners with two equivalent O(4)K2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)KMg5 octahedra. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to two equivalent Mg(1), two equivalent Mg(2), and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(4)K2Mg4 octahedra, corners with two equivalent O(6)Mg4Bi2 octahedra, corners with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)KMg5 octahedra, edges with four equivalent O(2)Mg5Bi octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to four equivalent Mg(3) and two equivalent Bi(1) atoms to form OMg4Bi2 octahedra that share corners with two equivalent O(6)Mg4Bi2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)Mg5Bi octahedra. The corner-sharing octahedra are not tilted.