LiMg6BO7 crystallizes in the tetragonal P4mm space group. Li(1) is bonded to one O(1) and four equivalent O(4) atoms to form LiO5 square pyramids that share  a cornercorner with one Mg(1)O5 square pyramid, corners with four equivalent Li(1)O5 square pyramids, and edges with four equivalent Mg(4)O6 octahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1) and four equivalent O(5) atoms to form MgO5 square pyramids that share  a cornercorner with one Li(1)O5 square pyramid, corners with four equivalent Mg(1)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(2)O5 square pyramids. In the second Mg site, Mg(2) is bonded to one O(2) and four equivalent O(5) atoms to form distorted MgO5 square pyramids that share corners with four equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(2)O5 square pyramids, and edges with four equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles are 79°. In the third Mg site, Mg(3) is bonded in a distorted T-shaped geometry to one O(4) and two equivalent O(2) atoms. In the fourth Mg site, Mg(4) 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 four equivalent Mg(4)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Li(1)O5 square pyramids, and edges with two equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 4-20°. B(1) is bonded in a distorted single-bond geometry to one O(3) and four equivalent O(4) atoms. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Mg(1), and four equivalent Mg(4) atoms to form OLiMg5 octahedra that share corners with four equivalent O(1)LiMg5 octahedra, edges with four equivalent O(4)Li2Mg2B2 octahedra, edges with four equivalent O(3)Mg4B square pyramids, and edges with four equivalent O(5)Mg5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 4°. In the second O site, O(2) is bonded to one Mg(2) and four equivalent Mg(3) atoms to form distorted OMg5 square pyramids that share corners with four equivalent O(4)Li2Mg2B2 octahedra, corners with four equivalent O(2)Mg5 square pyramids, and corners with four equivalent O(5)Mg5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 78°. In the third O site, O(3) is bonded to four equivalent Mg(4) and one B(1) atom to form distorted OMg4B square pyramids that share corners with four equivalent O(3)Mg4B square pyramids, corners with four equivalent O(5)Mg5 trigonal bipyramids, edges with four equivalent O(4)Li2Mg2B2 octahedra, and edges with four equivalent O(1)LiMg5 octahedra. In the fourth O site, O(4) is bonded to two equivalent Li(1), one Mg(3), one Mg(4), and two equivalent B(1) atoms to form OLi2Mg2B2 octahedra that share corners with four equivalent O(4)Li2Mg2B2 octahedra, corners with two equivalent O(2)Mg5 square pyramids,  a cornercorner with one O(5)Mg5 trigonal bipyramid, edges with two equivalent O(1)LiMg5 octahedra, edges with four equivalent O(4)Li2Mg2B2 octahedra, and edges with two equivalent O(3)Mg4B square pyramids. The corner-sharing octahedral tilt angles range from 8-20°. In the fifth O site, O(5) is bonded to one Mg(4), two equivalent Mg(1), and two equivalent Mg(2) atoms to form OMg5 trigonal bipyramids that share  a cornercorner with one O(4)Li2Mg2B2 octahedra, corners with two equivalent O(3)Mg4B square pyramids, corners with two equivalent O(2)Mg5 square pyramids, corners with four equivalent O(5)Mg5 trigonal bipyramids, edges with two equivalent O(1)LiMg5 octahedra, and edges with four equivalent O(5)Mg5 trigonal bipyramids. The corner-sharing octahedra are not tilted.
LiMg6BO7 crystallizes in the tetragonal P4mm space group. Li(1) is bonded to one O(1) and four equivalent O(4) atoms to form LiO5 square pyramids that share  a cornercorner with one Mg(1)O5 square pyramid, corners with four equivalent Li(1)O5 square pyramids, and edges with four equivalent Mg(4)O6 octahedra. The Li(1)-O(1) bond length is 2.06 Å. All Li(1)-O(4) bond lengths are 2.06 Å. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1) and four equivalent O(5) atoms to form MgO5 square pyramids that share  a cornercorner with one Li(1)O5 square pyramid, corners with four equivalent Mg(1)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(2)O5 square pyramids. The Mg(1)-O(1) bond length is 2.10 Å. All Mg(1)-O(5) bond lengths are 2.06 Å. In the second Mg site, Mg(2) is bonded to one O(2) and four equivalent O(5) atoms to form distorted MgO5 square pyramids that share corners with four equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(2)O5 square pyramids, and edges with four equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles are 79°. The Mg(2)-O(2) bond length is 2.01 Å. All Mg(2)-O(5) bond lengths are 2.10 Å. In the third Mg site, Mg(3) is bonded in a distorted T-shaped geometry to one O(4) and two equivalent O(2) atoms. The Mg(3)-O(4) bond length is 2.02 Å. Both Mg(3)-O(2) bond lengths are 2.10 Å. In the fourth Mg site, Mg(4) 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 four equivalent Mg(4)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Li(1)O5 square pyramids, and edges with two equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 4-20°. The Mg(4)-O(4) bond length is 2.11 Å. The Mg(4)-O(5) bond length is 2.13 Å. Both Mg(4)-O(1) bond lengths are 2.06 Å. Both Mg(4)-O(3) bond lengths are 2.09 Å. B(1) is bonded in a distorted single-bond geometry to one O(3) and four equivalent O(4) atoms. The B(1)-O(3) bond length is 1.38 Å. All B(1)-O(4) bond lengths are 2.09 Å. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Mg(1), and four equivalent Mg(4) atoms to form OLiMg5 octahedra that share corners with four equivalent O(1)LiMg5 octahedra, edges with four equivalent O(4)Li2Mg2B2 octahedra, edges with four equivalent O(3)Mg4B square pyramids, and edges with four equivalent O(5)Mg5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 4°. In the second O site, O(2) is bonded to one Mg(2) and four equivalent Mg(3) atoms to form distorted OMg5 square pyramids that share corners with four equivalent O(4)Li2Mg2B2 octahedra, corners with four equivalent O(2)Mg5 square pyramids, and corners with four equivalent O(5)Mg5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 78°. In the third O site, O(3) is bonded to four equivalent Mg(4) and one B(1) atom to form distorted OMg4B square pyramids that share corners with four equivalent O(3)Mg4B square pyramids, corners with four equivalent O(5)Mg5 trigonal bipyramids, edges with four equivalent O(4)Li2Mg2B2 octahedra, and edges with four equivalent O(1)LiMg5 octahedra. In the fourth O site, O(4) is bonded to two equivalent Li(1), one Mg(3), one Mg(4), and two equivalent B(1) atoms to form OLi2Mg2B2 octahedra that share corners with four equivalent O(4)Li2Mg2B2 octahedra, corners with two equivalent O(2)Mg5 square pyramids,  a cornercorner with one O(5)Mg5 trigonal bipyramid, edges with two equivalent O(1)LiMg5 octahedra, edges with four equivalent O(4)Li2Mg2B2 octahedra, and edges with two equivalent O(3)Mg4B square pyramids. The corner-sharing octahedral tilt angles range from 8-20°. In the fifth O site, O(5) is bonded to one Mg(4), two equivalent Mg(1), and two equivalent Mg(2) atoms to form OMg5 trigonal bipyramids that share  a cornercorner with one O(4)Li2Mg2B2 octahedra, corners with two equivalent O(3)Mg4B square pyramids, corners with two equivalent O(2)Mg5 square pyramids, corners with four equivalent O(5)Mg5 trigonal bipyramids, edges with two equivalent O(1)LiMg5 octahedra, and edges with four equivalent O(5)Mg5 trigonal bipyramids. The corner-sharing octahedra are not tilted.