RbMg14BO16 crystallizes in the tetragonal P4/mmm space group. Rb(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form RbO6 octahedra that share corners with two equivalent Rb(1)O6 octahedra; corners with four equivalent Mg(1)O6 octahedra; edges with four equivalent Mg(4)O6 octahedra; and edges with eight Mg(2,2)O6 octahedra. The corner-sharing octahedra are not tilted. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1); two O(2,2); and two equivalent O(5) atoms to form distorted MgO6 octahedra that share corners with two equivalent Rb(1)O6 octahedra; corners with two equivalent Mg(1)O6 octahedra; edges with four Mg(2,2)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 Mg(2,2)O6 octahedra; edges with two equivalent Rb(1)O6 octahedra; edges with two equivalent Mg(1)O6 octahedra; edges with two Mg(2,2)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 0-13°. In the third 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 Mg(2,2)O6 octahedra; edges with two equivalent Rb(1)O6 octahedra; edges with two equivalent Mg(1)O6 octahedra; edges with two Mg(2,2)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 0-13°. In the fourth 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 a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles range from 0-17°. In the fifth 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 Rb(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 2-20°. B(1) is bonded in a square co-planar geometry to four O(2,2) atoms. There are seven inequivalent O sites. In the first O site, O(1) is bonded to one Rb(1), one Mg(1), two equivalent Mg(2), and two equivalent Mg(4) atoms to form distorted ORbMg5 octahedra that share corners with two equivalent O(2)Mg5B octahedra, corners with four equivalent O(1)RbMg5 octahedra, edges with two equivalent O(2)Mg5B octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(4)Rb2Mg4 octahedra, edges with two equivalent O(1)RbMg5 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-16°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one B(1) atom to form distorted OMg5B octahedra that share corners with two equivalent O(1)RbMg5 octahedra; corners with four O(2,2)Mg5B octahedra; edges with two equivalent O(2)Mg5B octahedra; edges with two equivalent O(5)Mg6 octahedra; edges with two equivalent O(1)RbMg5 octahedra; and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-17°. In the third O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one B(1) atom to form distorted OMg5B octahedra that share corners with two equivalent O(1)RbMg5 octahedra; corners with four O(2,2)Mg5B octahedra; edges with two equivalent O(2)Mg5B octahedra; edges with two equivalent O(5)Mg6 octahedra; edges with two equivalent O(1)RbMg5 octahedra; and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-17°. In the fourth 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)Rb2Mg4 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)Mg5B octahedra, and edges with four equivalent O(1)RbMg5 octahedra. The corner-sharing octahedral tilt angles range from 1-4°. In the fifth O site, O(4) is bonded to two equivalent Rb(1) and four Mg(2,2) atoms to form ORb2Mg4 octahedra that share corners with two equivalent O(4)Rb2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)RbMg5 octahedra. The corner-sharing octahedra are not tilted. In the sixth O site, O(5) is bonded to two equivalent Mg(1); two Mg(2,2); and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(5)Mg6 octahedra; corners with two equivalent O(4)Rb2Mg4 octahedra; edges with four O(2,2)Mg5B octahedra; edges with four equivalent O(3)Mg6 octahedra; and edges with four equivalent O(1)RbMg5 octahedra. The corner-sharing octahedra are not tilted. In the seventh O site, O(6) is bonded in a distorted square co-planar geometry to four equivalent Mg(3) atoms.
RbMg14BO16 crystallizes in the tetragonal P4/mmm space group. Rb(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form RbO6 octahedra that share corners with two equivalent Rb(1)O6 octahedra; corners with four equivalent Mg(1)O6 octahedra; edges with four equivalent Mg(4)O6 octahedra; and edges with eight Mg(2,2)O6 octahedra. The corner-sharing octahedra are not tilted. Both Rb(1)-O(4) bond lengths are 2.25 Å. All Rb(1)-O(1) bond lengths are 2.42 Å. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1); two O(2,2); and two equivalent O(5) atoms to form distorted MgO6 octahedra that share corners with two equivalent Rb(1)O6 octahedra; corners with two equivalent Mg(1)O6 octahedra; edges with four Mg(2,2)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 1.85 Å. Both Mg(1)-O(2,2) bond lengths are 2.54 Å. Both Mg(1)-O(5) bond lengths are 2.25 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 Mg(2,2)O6 octahedra; edges with two equivalent Rb(1)O6 octahedra; edges with two equivalent Mg(1)O6 octahedra; edges with two Mg(2,2)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 0-13°. The Mg(2)-O(4) bond length is 2.16 Å. The Mg(2)-O(5) bond length is 2.11 Å. Both Mg(2)-O(1) bond lengths are 2.27 Å. Both Mg(2)-O(3) bond lengths are 2.15 Å. In the third 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 Mg(2,2)O6 octahedra; edges with two equivalent Rb(1)O6 octahedra; edges with two equivalent Mg(1)O6 octahedra; edges with two Mg(2,2)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 0-13°. The Mg(2)-O(4) bond length is 2.16 Å. The Mg(2)-O(5) bond length is 2.11 Å. Both Mg(2)-O(1) bond lengths are 2.27 Å. Both Mg(2)-O(3) bond lengths are 2.15 Å. In the fourth 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 a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles range from 0-17°. The Mg(3)-O(5) bond length is 2.22 Å. The Mg(3)-O(6) bond length is 2.05 Å. Both Mg(3)-O(2) bond lengths are 2.27 Å. Both Mg(3)-O(3) bond lengths are 2.12 Å. In the fifth 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 Rb(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 2-20°. Both Mg(4)-O(1) bond lengths are 2.19 Å. Both Mg(4)-O(2) bond lengths are 2.13 Å. Both Mg(4)-O(3) bond lengths are 2.25 Å. B(1) is bonded in a square co-planar geometry to four O(2,2) atoms. All B(1)-O(2,2) bond lengths are 1.72 Å. There are seven inequivalent O sites. In the first O site, O(1) is bonded to one Rb(1), one Mg(1), two equivalent Mg(2), and two equivalent Mg(4) atoms to form distorted ORbMg5 octahedra that share corners with two equivalent O(2)Mg5B octahedra, corners with four equivalent O(1)RbMg5 octahedra, edges with two equivalent O(2)Mg5B octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(4)Rb2Mg4 octahedra, edges with two equivalent O(1)RbMg5 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-16°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one B(1) atom to form distorted OMg5B octahedra that share corners with two equivalent O(1)RbMg5 octahedra; corners with four O(2,2)Mg5B octahedra; edges with two equivalent O(2)Mg5B octahedra; edges with two equivalent O(5)Mg6 octahedra; edges with two equivalent O(1)RbMg5 octahedra; and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-17°. In the third O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one B(1) atom to form distorted OMg5B octahedra that share corners with two equivalent O(1)RbMg5 octahedra; corners with four O(2,2)Mg5B octahedra; edges with two equivalent O(2)Mg5B octahedra; edges with two equivalent O(5)Mg6 octahedra; edges with two equivalent O(1)RbMg5 octahedra; and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-17°. Both O(2)-Mg(3) bond lengths are 2.27 Å. Both O(2)-Mg(4) bond lengths are 2.13 Å. In the fourth 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)Rb2Mg4 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)Mg5B octahedra, and edges with four equivalent O(1)RbMg5 octahedra. The corner-sharing octahedral tilt angles range from 1-4°. In the fifth O site, O(4) is bonded to two equivalent Rb(1) and four Mg(2,2) atoms to form ORb2Mg4 octahedra that share corners with two equivalent O(4)Rb2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)RbMg5 octahedra. The corner-sharing octahedra are not tilted. In the sixth O site, O(5) is bonded to two equivalent Mg(1); two Mg(2,2); and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(5)Mg6 octahedra; corners with two equivalent O(4)Rb2Mg4 octahedra; edges with four O(2,2)Mg5B octahedra; edges with four equivalent O(3)Mg6 octahedra; and edges with four equivalent O(1)RbMg5 octahedra. The corner-sharing octahedra are not tilted. In the seventh O site, O(6) is bonded in a distorted square co-planar geometry to four equivalent Mg(3) atoms.