Mg14MnBiO16 is Molybdenum Carbide MAX Phase-derived structured and crystallizes in the tetragonal P4/mmm space group. 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 Mg(1)O6 octahedra, corners with two equivalent Mn(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 Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. 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 0-3°. 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 Mn(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 4-6°. Mn(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form MnO6 octahedra that share corners with two equivalent Mn(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. 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 Mg(1), two equivalent Mg(2), two equivalent Mg(4), and one Mn(1) atom to form OMg5Mn octahedra that share corners with two equivalent O(2)Mg5Bi octahedra, corners with four equivalent O(1)Mg5Mn octahedra, edges with two equivalent O(4)Mg4Mn2 octahedra, edges with two equivalent O(2)Mg5Bi octahedra, edges with two equivalent O(1)Mg5Mn 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 0-2°. 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)Mg5Mn octahedra, corners with four equivalent O(2)Mg5Bi octahedra, edges with two equivalent O(6)Mg4Bi2 octahedra, edges with two equivalent O(2)Mg5Bi octahedra, edges with two equivalent O(1)Mg5Mn 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 0-3°. 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(6)Mg4Bi2 octahedra,  an edgeedge with one O(4)Mg4Mn2 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)Mg5Bi octahedra, and edges with four equivalent O(1)Mg5Mn octahedra. The corner-sharing octahedral tilt angles range from 0-6°. In the fourth O site, O(4) is bonded to four equivalent Mg(2) and two equivalent Mn(1) atoms to form OMg4Mn2 octahedra that share corners with two equivalent O(4)Mg4Mn2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)Mg5Mn 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(6)Mg4Bi2 octahedra, corners with two equivalent O(4)Mg4Mn2 octahedra, corners with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)Mg5Bi octahedra, edges with four equivalent O(1)Mg5Mn 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.
Mg14MnBiO16 is Molybdenum Carbide MAX Phase-derived structured and crystallizes in the tetragonal P4/mmm space group. 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 Mg(1)O6 octahedra, corners with two equivalent Mn(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 2.15 Å. Both Mg(1)-O(2) bond lengths are 2.01 Å. Both Mg(1)-O(5) bond lengths are 2.23 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 Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. The Mg(2)-O(4) bond length is 2.18 Å. The Mg(2)-O(5) bond length is 2.19 Å. Both Mg(2)-O(1) bond lengths are 2.23 Å. Both Mg(2)-O(3) bond lengths are 2.18 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 0-3°. The Mg(3)-O(5) bond length is 2.07 Å. The Mg(3)-O(6) bond length is 2.31 Å. Both Mg(3)-O(2) bond lengths are 2.23 Å. Both Mg(3)-O(3) bond lengths are 2.19 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 Mn(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 4-6°. Both Mg(4)-O(1) bond lengths are 2.12 Å. Both Mg(4)-O(2) bond lengths are 2.25 Å. Both Mg(4)-O(3) bond lengths are 2.23 Å. Mn(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form MnO6 octahedra that share corners with two equivalent Mn(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 Mn(1)-O(4) bond lengths are 2.23 Å. All Mn(1)-O(1) bond lengths are 2.22 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 2.23 Å. All Bi(1)-O(2) bond lengths are 2.36 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(4), and one Mn(1) atom to form OMg5Mn octahedra that share corners with two equivalent O(2)Mg5Bi octahedra, corners with four equivalent O(1)Mg5Mn octahedra, edges with two equivalent O(4)Mg4Mn2 octahedra, edges with two equivalent O(2)Mg5Bi octahedra, edges with two equivalent O(1)Mg5Mn 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 0-2°. 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)Mg5Mn octahedra, corners with four equivalent O(2)Mg5Bi octahedra, edges with two equivalent O(6)Mg4Bi2 octahedra, edges with two equivalent O(2)Mg5Bi octahedra, edges with two equivalent O(1)Mg5Mn 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 0-3°. 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(6)Mg4Bi2 octahedra,  an edgeedge with one O(4)Mg4Mn2 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)Mg5Bi octahedra, and edges with four equivalent O(1)Mg5Mn octahedra. The corner-sharing octahedral tilt angles range from 0-6°. In the fourth O site, O(4) is bonded to four equivalent Mg(2) and two equivalent Mn(1) atoms to form OMg4Mn2 octahedra that share corners with two equivalent O(4)Mg4Mn2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)Mg5Mn 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(6)Mg4Bi2 octahedra, corners with two equivalent O(4)Mg4Mn2 octahedra, corners with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)Mg5Bi octahedra, edges with four equivalent O(1)Mg5Mn 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.