Mg14GaBO16 crystallizes in the orthorhombic Pmmm space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(6), and two equivalent O(9) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra are not tilted. In the second Mg site, Mg(2) is bonded to two equivalent O(2), two equivalent O(7), and two equivalent O(9) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Mg(2)O6 octahedra, corners with two equivalent Ga(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, edges with four equivalent Mg(6)O6 octahedra, and edges with four equivalent Mg(7)O6 octahedra. The corner-sharing octahedra are not tilted. In the third Mg site, Mg(3) is bonded to one O(4), one O(5), two equivalent O(3), and two equivalent O(8) atoms to form MgO6 octahedra that share corners with two equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, edges with two equivalent Mg(6)O6 octahedra, edges with two equivalent Ga(1)O6 octahedra, and edges with four equivalent Mg(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-15°. In the fourth Mg site, Mg(4) is bonded to one O(6), one O(7), two equivalent O(3), and two equivalent O(9) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the fifth Mg site, Mg(5) is bonded to one O(4), one O(6), two equivalent O(1), and two equivalent O(3) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. In the sixth Mg site, Mg(6) is bonded to one O(5), one O(7), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(5)O6 octahedra, corners with four equivalent Mg(6)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Ga(1)O6 octahedra, and edges with four equivalent Mg(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the seventh Mg site, Mg(7) is bonded to one O(1), one O(2), one O(8), one O(9), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with six equivalent Mg(7)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Ga(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, and edges with two equivalent Mg(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-14°. Ga(1) is bonded to two equivalent O(2), two equivalent O(5), and two equivalent O(8) atoms to form GaO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with two equivalent Ga(1)O6 octahedra, edges with four equivalent Mg(3)O6 octahedra, edges with four equivalent Mg(6)O6 octahedra, and edges with four equivalent Mg(7)O6 octahedra. The corner-sharing octahedra are not tilted. B(1) is bonded in a distorted linear geometry to two equivalent O(4) atoms. There are nine inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), two equivalent Mg(5), and two equivalent Mg(7) atoms to form distorted OMg5 square pyramids that share corners with two equivalent O(4)Mg4B2 octahedra, corners with two equivalent O(2)Mg5Ga octahedra, corners with two equivalent O(8)Mg4Ga square pyramids, corners with three equivalent O(1)Mg5 square pyramids, edges with two equivalent O(6)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 3-86°. In the second O site, O(2) is bonded to one Mg(2), two equivalent Mg(6), two equivalent Mg(7), and one Ga(1) atom to form OMg5Ga octahedra that share corners with four equivalent O(2)Mg5Ga octahedra, corners with two equivalent O(1)Mg5 square pyramids, edges with two equivalent O(5)Mg4Ga2 octahedra, edges with two equivalent O(7)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with two equivalent O(8)Mg4Ga square pyramids. The corner-sharing octahedral tilt angles range from 0-3°. In the third O site, O(3) is bonded to one Mg(3), one Mg(4), one Mg(5), one Mg(6), and two equivalent Mg(7) atoms to form OMg6 octahedra that share corners with six equivalent O(3)Mg6 octahedra,  an edgeedge with one O(4)Mg4B2 octahedra,  an edgeedge with one O(5)Mg4Ga2 octahedra,  an edgeedge with one O(6)Mg6 octahedra,  an edgeedge with one O(7)Mg6 octahedra, edges with two equivalent O(2)Mg5Ga octahedra, edges with two equivalent O(9)Mg6 octahedra, edges with two equivalent O(8)Mg4Ga square pyramids, and edges with two equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 1-4°. In the fourth O site, O(4) is bonded to two equivalent Mg(3), two equivalent Mg(5), and two equivalent B(1) atoms to form OMg4B2 octahedra that share corners with two equivalent O(4)Mg4B2 octahedra, corners with two equivalent O(5)Mg4Ga2 octahedra, corners with two equivalent O(6)Mg6 octahedra, corners with four equivalent O(8)Mg4Ga square pyramids, corners with four equivalent O(1)Mg5 square pyramids, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to two equivalent Mg(3), two equivalent Mg(6), and two equivalent Ga(1) atoms to form OMg4Ga2 octahedra that share corners with two equivalent O(4)Mg4B2 octahedra, corners with two equivalent O(5)Mg4Ga2 octahedra, corners with two equivalent O(7)Mg6 octahedra, edges with four equivalent O(2)Mg5Ga octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(8)Mg4Ga square pyramids. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to two equivalent Mg(1), two equivalent Mg(4), and two equivalent Mg(5) atoms to form OMg6 octahedra that share corners with two equivalent O(4)Mg4B2 octahedra, corners with two equivalent O(6)Mg6 octahedra, corners with two equivalent O(7)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, edges with four equivalent O(9)Mg6 octahedra, and edges with four equivalent O(1)Mg5 square pyramids. The corner-sharing octahedra are not tilted. In the seventh O site, O(7) is bonded to two equivalent Mg(2), two equivalent Mg(4), and two equivalent Mg(6) atoms to form OMg6 octahedra that share corners with two equivalent O(5)Mg4Ga2 octahedra, corners with two equivalent O(6)Mg6 octahedra, corners with two equivalent O(7)Mg6 octahedra, edges with four equivalent O(2)Mg5Ga octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(9)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the eighth O site, O(8) is bonded to two equivalent Mg(3), two equivalent Mg(7), and one Ga(1) atom to form OMg4Ga square pyramids that share corners with two equivalent O(4)Mg4B2 octahedra, corners with two equivalent O(9)Mg6 octahedra, corners with two equivalent O(1)Mg5 square pyramids, corners with three equivalent O(8)Mg4Ga square pyramids, edges with two equivalent O(5)Mg4Ga2 octahedra, edges with two equivalent O(2)Mg5Ga octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 9-82°. In the ninth O site, O(9) is bonded to one Mg(1), one Mg(2), two equivalent Mg(4), and two equivalent Mg(7) atoms to form OMg6 octahedra that share corners with four equivalent O(9)Mg6 octahedra, corners with two equivalent O(8)Mg4Ga square pyramids, edges with two equivalent O(2)Mg5Ga octahedra, edges with two equivalent O(6)Mg6 octahedra, edges with two equivalent O(7)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with two equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-4°.
Mg14GaBO16 crystallizes in the orthorhombic Pmmm space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(6), and two equivalent O(9) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedra are not tilted. Both Mg(1)-O(1) bond lengths are 1.99 Å. Both Mg(1)-O(6) bond lengths are 2.10 Å. Both Mg(1)-O(9) bond lengths are 2.16 Å. In the second Mg site, Mg(2) is bonded to two equivalent O(2), two equivalent O(7), and two equivalent O(9) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Mg(2)O6 octahedra, corners with two equivalent Ga(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, edges with four equivalent Mg(6)O6 octahedra, and edges with four equivalent Mg(7)O6 octahedra. The corner-sharing octahedra are not tilted. Both Mg(2)-O(2) bond lengths are 2.15 Å. Both Mg(2)-O(7) bond lengths are 2.10 Å. Both Mg(2)-O(9) bond lengths are 2.07 Å. In the third Mg site, Mg(3) is bonded to one O(4), one O(5), two equivalent O(3), and two equivalent O(8) atoms to form MgO6 octahedra that share corners with two equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, edges with two equivalent Mg(6)O6 octahedra, edges with two equivalent Ga(1)O6 octahedra, and edges with four equivalent Mg(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-15°. The Mg(3)-O(4) bond length is 2.06 Å. The Mg(3)-O(5) bond length is 2.17 Å. Both Mg(3)-O(3) bond lengths are 2.10 Å. Both Mg(3)-O(8) bond lengths are 2.12 Å. In the fourth Mg site, Mg(4) is bonded to one O(6), one O(7), two equivalent O(3), and two equivalent O(9) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. The Mg(4)-O(6) bond length is 2.09 Å. The Mg(4)-O(7) bond length is 2.14 Å. Both Mg(4)-O(3) bond lengths are 2.13 Å. Both Mg(4)-O(9) bond lengths are 2.10 Å. In the fifth Mg site, Mg(5) is bonded to one O(4), one O(6), two equivalent O(1), and two equivalent O(3) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. The Mg(5)-O(4) bond length is 2.08 Å. The Mg(5)-O(6) bond length is 2.14 Å. Both Mg(5)-O(1) bond lengths are 2.11 Å. Both Mg(5)-O(3) bond lengths are 2.12 Å. In the sixth Mg site, Mg(6) is bonded to one O(5), one O(7), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(5)O6 octahedra, corners with four equivalent Mg(6)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Ga(1)O6 octahedra, and edges with four equivalent Mg(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. The Mg(6)-O(5) bond length is 2.14 Å. The Mg(6)-O(7) bond length is 2.09 Å. Both Mg(6)-O(2) bond lengths are 2.10 Å. Both Mg(6)-O(3) bond lengths are 2.11 Å. In the seventh Mg site, Mg(7) is bonded to one O(1), one O(2), one O(8), one O(9), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with six equivalent Mg(7)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Ga(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, and edges with two equivalent Mg(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-14°. The Mg(7)-O(1) bond length is 2.08 Å. The Mg(7)-O(2) bond length is 2.16 Å. The Mg(7)-O(8) bond length is 2.12 Å. The Mg(7)-O(9) bond length is 2.12 Å. Both Mg(7)-O(3) bond lengths are 2.10 Å. Ga(1) is bonded to two equivalent O(2), two equivalent O(5), and two equivalent O(8) atoms to form GaO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with two equivalent Ga(1)O6 octahedra, edges with four equivalent Mg(3)O6 octahedra, edges with four equivalent Mg(6)O6 octahedra, and edges with four equivalent Mg(7)O6 octahedra. The corner-sharing octahedra are not tilted. Both Ga(1)-O(2) bond lengths are 2.07 Å. Both Ga(1)-O(5) bond lengths are 2.10 Å. Both Ga(1)-O(8) bond lengths are 1.90 Å. B(1) is bonded in a distorted linear geometry to two equivalent O(4) atoms. Both B(1)-O(4) bond lengths are 2.10 Å. There are nine inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), two equivalent Mg(5), and two equivalent Mg(7) atoms to form distorted OMg5 square pyramids that share corners with two equivalent O(4)Mg4B2 octahedra, corners with two equivalent O(2)Mg5Ga octahedra, corners with two equivalent O(8)Mg4Ga square pyramids, corners with three equivalent O(1)Mg5 square pyramids, edges with two equivalent O(6)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 3-86°. In the second O site, O(2) is bonded to one Mg(2), two equivalent Mg(6), two equivalent Mg(7), and one Ga(1) atom to form OMg5Ga octahedra that share corners with four equivalent O(2)Mg5Ga octahedra, corners with two equivalent O(1)Mg5 square pyramids, edges with two equivalent O(5)Mg4Ga2 octahedra, edges with two equivalent O(7)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with two equivalent O(8)Mg4Ga square pyramids. The corner-sharing octahedral tilt angles range from 0-3°. In the third O site, O(3) is bonded to one Mg(3), one Mg(4), one Mg(5), one Mg(6), and two equivalent Mg(7) atoms to form OMg6 octahedra that share corners with six equivalent O(3)Mg6 octahedra,  an edgeedge with one O(4)Mg4B2 octahedra,  an edgeedge with one O(5)Mg4Ga2 octahedra,  an edgeedge with one O(6)Mg6 octahedra,  an edgeedge with one O(7)Mg6 octahedra, edges with two equivalent O(2)Mg5Ga octahedra, edges with two equivalent O(9)Mg6 octahedra, edges with two equivalent O(8)Mg4Ga square pyramids, and edges with two equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 1-4°. In the fourth O site, O(4) is bonded to two equivalent Mg(3), two equivalent Mg(5), and two equivalent B(1) atoms to form OMg4B2 octahedra that share corners with two equivalent O(4)Mg4B2 octahedra, corners with two equivalent O(5)Mg4Ga2 octahedra, corners with two equivalent O(6)Mg6 octahedra, corners with four equivalent O(8)Mg4Ga square pyramids, corners with four equivalent O(1)Mg5 square pyramids, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to two equivalent Mg(3), two equivalent Mg(6), and two equivalent Ga(1) atoms to form OMg4Ga2 octahedra that share corners with two equivalent O(4)Mg4B2 octahedra, corners with two equivalent O(5)Mg4Ga2 octahedra, corners with two equivalent O(7)Mg6 octahedra, edges with four equivalent O(2)Mg5Ga octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(8)Mg4Ga square pyramids. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to two equivalent Mg(1), two equivalent Mg(4), and two equivalent Mg(5) atoms to form OMg6 octahedra that share corners with two equivalent O(4)Mg4B2 octahedra, corners with two equivalent O(6)Mg6 octahedra, corners with two equivalent O(7)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, edges with four equivalent O(9)Mg6 octahedra, and edges with four equivalent O(1)Mg5 square pyramids. The corner-sharing octahedra are not tilted. In the seventh O site, O(7) is bonded to two equivalent Mg(2), two equivalent Mg(4), and two equivalent Mg(6) atoms to form OMg6 octahedra that share corners with two equivalent O(5)Mg4Ga2 octahedra, corners with two equivalent O(6)Mg6 octahedra, corners with two equivalent O(7)Mg6 octahedra, edges with four equivalent O(2)Mg5Ga octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(9)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the eighth O site, O(8) is bonded to two equivalent Mg(3), two equivalent Mg(7), and one Ga(1) atom to form OMg4Ga square pyramids that share corners with two equivalent O(4)Mg4B2 octahedra, corners with two equivalent O(9)Mg6 octahedra, corners with two equivalent O(1)Mg5 square pyramids, corners with three equivalent O(8)Mg4Ga square pyramids, edges with two equivalent O(5)Mg4Ga2 octahedra, edges with two equivalent O(2)Mg5Ga octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 9-82°. In the ninth O site, O(9) is bonded to one Mg(1), one Mg(2), two equivalent Mg(4), and two equivalent Mg(7) atoms to form OMg6 octahedra that share corners with four equivalent O(9)Mg6 octahedra, corners with two equivalent O(8)Mg4Ga square pyramids, edges with two equivalent O(2)Mg5Ga octahedra, edges with two equivalent O(6)Mg6 octahedra, edges with two equivalent O(7)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with two equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-4°.