LiMg14HfO15 crystallizes in the orthorhombic Pmm2 space group. Li(1) is bonded to one O(2), two equivalent O(10), and two equivalent O(6) atoms to form LiO5 square pyramids that share corners with two equivalent Mg(1)O6 octahedra,  a cornercorner with one Mg(2)O5 square pyramid, corners with two equivalent Li(1)O5 square pyramids, corners with two equivalent Mg(9)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles are 2°. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(3), two equivalent O(10), and two equivalent O(7) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Hf(1)O6 octahedra, corners with two equivalent Li(1)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(6)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra, edges with four equivalent Mg(3)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedra are not tilted. In the second Mg site, Mg(2) is bonded to one O(2), two equivalent O(11), and two equivalent O(8) atoms to form MgO5 square pyramids that share corners with two equivalent Hf(1)O6 octahedra,  a cornercorner with one Li(1)O5 square pyramid, corners with two equivalent Mg(2)O5 square pyramids, corners with two equivalent Mg(9)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles are 1°. In the third Mg site, Mg(3) is bonded to one O(4), one O(5), one O(6), one O(7), and two equivalent O(10) atoms to form MgO6 octahedra that share corners with two equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(3)O6 octahedra,  an edgeedge with one Mg(6)O6 octahedra,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Li(1)O5 square pyramids, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-8°. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), one O(8), one O(9), and two equivalent O(11) atoms to form MgO6 octahedra that share corners with two equivalent Mg(3)O6 octahedra, corners with four equivalent Mg(4)O6 octahedra,  an edgeedge with one Mg(6)O6 octahedra,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-6°. In the fifth Mg site, Mg(5) is bonded in a square co-planar geometry to one O(6), one O(8), and two equivalent O(4) atoms. In the sixth Mg site, Mg(6) is bonded to one O(7), one O(9), two equivalent O(1), and two equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Mg(6)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, and edges with four equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. In the seventh Mg site, Mg(7) is bonded to one O(6), one O(8), two equivalent O(2), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with four equivalent Mg(10)O6 octahedra, edges with two equivalent Li(1)O5 square pyramids, and edges with two equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 5-7°. In the eighth Mg site, Mg(8) is bonded to one O(7), one O(9), two equivalent O(3), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(6)O6 octahedra, corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, and edges with four equivalent Mg(10)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. In the ninth Mg site, Mg(9) is bonded to one O(1), one O(10), one O(11), and two equivalent O(4) atoms to form MgO5 square pyramids that share corners with two equivalent Mg(10)O6 octahedra,  a cornercorner with one Li(1)O5 square pyramid,  a cornercorner with one Mg(2)O5 square pyramid, corners with three equivalent Mg(9)O5 square pyramids,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Hf(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-9°. In the tenth Mg site, Mg(10) is bonded to one O(10), one O(11), one O(2), one O(3), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with four equivalent Mg(10)O6 octahedra, corners with two equivalent Mg(9)O5 square pyramids,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Hf(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra,  an edgeedge with one Li(1)O5 square pyramid, and  an edgeedge with one Mg(2)O5 square pyramid. The corner-sharing octahedral tilt angles range from 5-9°. Hf(1) is bonded to one O(1), one O(3), two equivalent O(11), and two equivalent O(9) atoms to form HfO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Hf(1)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(6)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedra are not tilted. There are eleven inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), two equivalent Mg(6), two equivalent Mg(9), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(1)HfMg5 octahedra, corners with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(9)Hf2Mg4 octahedra, edges with two equivalent O(11)HfMg5 octahedra, edges with two equivalent O(10)LiMg5 octahedra, edges with two equivalent O(7)Mg6 octahedra, and edges with four equivalent O(4)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. In the second O site, O(2) is bonded to one Li(1), one Mg(2), two equivalent Mg(10), and two equivalent Mg(7) atoms to form OLiMg5 octahedra that share corners with two equivalent O(3)HfMg5 octahedra, corners with two equivalent O(2)LiMg5 octahedra, edges with two equivalent O(11)HfMg5 octahedra, edges with two equivalent O(6)Li2Mg4 octahedra, edges with two equivalent O(10)LiMg5 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles are 7°. In the third O site, O(3) is bonded to one Mg(1), two equivalent Mg(10), two equivalent Mg(8), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(1)HfMg5 octahedra, corners with two equivalent O(3)HfMg5 octahedra, corners with two equivalent O(2)LiMg5 octahedra, edges with two equivalent O(9)Hf2Mg4 octahedra, edges with two equivalent O(11)HfMg5 octahedra, edges with two equivalent O(10)LiMg5 octahedra, edges with two equivalent O(7)Mg6 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the fourth O site, O(4) is bonded to one Mg(3), one Mg(4), one Mg(5), one Mg(6), and two equivalent Mg(9) atoms to form OMg6 octahedra that share corners with two equivalent O(5)Mg6 octahedra, corners with four equivalent O(4)Mg6 octahedra,  an edgeedge with one O(9)Hf2Mg4 octahedra,  an edgeedge with one O(6)Li2Mg4 octahedra,  an edgeedge with one O(7)Mg6 octahedra,  an edgeedge with one O(8)Mg6 octahedra, edges with two equivalent O(1)HfMg5 octahedra, edges with two equivalent O(11)HfMg5 octahedra, and edges with two equivalent O(10)LiMg5 octahedra. The corner-sharing octahedral tilt angles range from 4-8°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), one Mg(7), one Mg(8), and two equivalent Mg(10) atoms to form OMg6 octahedra that share corners with two equivalent O(4)Mg6 octahedra, corners with four equivalent O(5)Mg6 octahedra,  an edgeedge with one O(9)Hf2Mg4 octahedra,  an edgeedge with one O(6)Li2Mg4 octahedra,  an edgeedge with one O(7)Mg6 octahedra,  an edgeedge with one O(8)Mg6 octahedra, edges with two equivalent O(11)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(10)LiMg5 octahedra, and edges with two equivalent O(2)LiMg5 octahedra. The corner-sharing octahedral tilt angles range from 4-7°. In the sixth O site, O(6) is bonded to two equivalent Li(1), one Mg(5), one Mg(7), and two equivalent Mg(3) atoms to form OLi2Mg4 octahedra that share corners with two equivalent O(6)Li2Mg4 octahedra, corners with two equivalent O(7)Mg6 octahedra, corners with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(2)LiMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(10)LiMg5 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the seventh O site, O(7) is bonded to one Mg(6), one Mg(8), two equivalent Mg(1), and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(9)Hf2Mg4 octahedra, corners with two equivalent O(6)Li2Mg4 octahedra, corners with two equivalent O(7)Mg6 octahedra, edges with two equivalent O(1)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(10)LiMg5 octahedra. The corner-sharing octahedra are not tilted. In the eighth O site, O(8) is bonded to one Mg(5), one Mg(7), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(9)Hf2Mg4 octahedra, corners with two equivalent O(6)Li2Mg4 octahedra, corners with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(2)LiMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(11)HfMg5 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the ninth O site, O(9) is bonded to one Mg(6), one Mg(8), two equivalent Mg(4), and two equivalent Hf(1) atoms to form OHf2Mg4 octahedra that share corners with two equivalent O(9)Hf2Mg4 octahedra, corners with two equivalent O(7)Mg6 octahedra, corners with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(1)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(11)HfMg5 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the tenth O site, O(10) is bonded to one Li(1), one Mg(1), one Mg(10), one Mg(9), and two equivalent Mg(3) atoms to form OLiMg5 octahedra that share corners with two equivalent O(11)HfMg5 octahedra, corners with four equivalent O(10)LiMg5 octahedra,  an edgeedge with one O(1)HfMg5 octahedra,  an edgeedge with one O(3)HfMg5 octahedra,  an edgeedge with one O(2)LiMg5 octahedra, edges with two equivalent O(6)Li2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with two equivalent O(7)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. In the eleventh O site, O(11) is bonded to one Mg(10), one Mg(2), one Mg(9), two equivalent Mg(4), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(10)LiMg5 octahedra, corners with four equivalent O(11)HfMg5 octahedra,  an edgeedge with one O(1)HfMg5 octahedra,  an edgeedge with one O(3)HfMg5 octahedra,  an edgeedge with one O(2)LiMg5 octahedra, edges with two equivalent O(9)Hf2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with two equivalent O(8)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 1-7°.
LiMg14HfO15 crystallizes in the orthorhombic Pmm2 space group. Li(1) is bonded to one O(2), two equivalent O(10), and two equivalent O(6) atoms to form LiO5 square pyramids that share corners with two equivalent Mg(1)O6 octahedra,  a cornercorner with one Mg(2)O5 square pyramid, corners with two equivalent Li(1)O5 square pyramids, corners with two equivalent Mg(9)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles are 2°. The Li(1)-O(2) bond length is 2.16 Å. Both Li(1)-O(10) bond lengths are 2.24 Å. Both Li(1)-O(6) bond lengths are 2.14 Å. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(3), two equivalent O(10), and two equivalent O(7) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Hf(1)O6 octahedra, corners with two equivalent Li(1)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(6)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra, edges with four equivalent Mg(3)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedra are not tilted. The Mg(1)-O(1) bond length is 2.17 Å. The Mg(1)-O(3) bond length is 2.16 Å. Both Mg(1)-O(10) bond lengths are 2.08 Å. Both Mg(1)-O(7) bond lengths are 2.14 Å. In the second Mg site, Mg(2) is bonded to one O(2), two equivalent O(11), and two equivalent O(8) atoms to form MgO5 square pyramids that share corners with two equivalent Hf(1)O6 octahedra,  a cornercorner with one Li(1)O5 square pyramid, corners with two equivalent Mg(2)O5 square pyramids, corners with two equivalent Mg(9)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles are 1°. The Mg(2)-O(2) bond length is 2.09 Å. Both Mg(2)-O(11) bond lengths are 2.16 Å. Both Mg(2)-O(8) bond lengths are 2.14 Å. In the third Mg site, Mg(3) is bonded to one O(4), one O(5), one O(6), one O(7), and two equivalent O(10) atoms to form MgO6 octahedra that share corners with two equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(3)O6 octahedra,  an edgeedge with one Mg(6)O6 octahedra,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Li(1)O5 square pyramids, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-8°. The Mg(3)-O(4) bond length is 2.17 Å. The Mg(3)-O(5) bond length is 2.16 Å. The Mg(3)-O(6) bond length is 2.09 Å. The Mg(3)-O(7) bond length is 2.23 Å. Both Mg(3)-O(10) bond lengths are 2.15 Å. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), one O(8), one O(9), and two equivalent O(11) atoms to form MgO6 octahedra that share corners with two equivalent Mg(3)O6 octahedra, corners with four equivalent Mg(4)O6 octahedra,  an edgeedge with one Mg(6)O6 octahedra,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-6°. The Mg(4)-O(4) bond length is 2.15 Å. The Mg(4)-O(5) bond length is 2.15 Å. The Mg(4)-O(8) bond length is 2.07 Å. The Mg(4)-O(9) bond length is 2.25 Å. Both Mg(4)-O(11) bond lengths are 2.15 Å. In the fifth Mg site, Mg(5) is bonded in a square co-planar geometry to one O(6), one O(8), and two equivalent O(4) atoms. The Mg(5)-O(6) bond length is 2.09 Å. The Mg(5)-O(8) bond length is 2.25 Å. Both Mg(5)-O(4) bond lengths are 2.19 Å. In the sixth Mg site, Mg(6) is bonded to one O(7), one O(9), two equivalent O(1), and two equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Mg(6)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, and edges with four equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. The Mg(6)-O(7) bond length is 2.06 Å. The Mg(6)-O(9) bond length is 2.26 Å. Both Mg(6)-O(1) bond lengths are 2.15 Å. Both Mg(6)-O(4) bond lengths are 2.13 Å. In the seventh Mg site, Mg(7) is bonded to one O(6), one O(8), two equivalent O(2), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with four equivalent Mg(10)O6 octahedra, edges with two equivalent Li(1)O5 square pyramids, and edges with two equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 5-7°. The Mg(7)-O(6) bond length is 2.09 Å. The Mg(7)-O(8) bond length is 2.20 Å. Both Mg(7)-O(2) bond lengths are 2.15 Å. Both Mg(7)-O(5) bond lengths are 2.17 Å. In the eighth Mg site, Mg(8) is bonded to one O(7), one O(9), two equivalent O(3), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(6)O6 octahedra, corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, and edges with four equivalent Mg(10)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. The Mg(8)-O(7) bond length is 2.06 Å. The Mg(8)-O(9) bond length is 2.24 Å. Both Mg(8)-O(3) bond lengths are 2.15 Å. Both Mg(8)-O(5) bond lengths are 2.15 Å. In the ninth Mg site, Mg(9) is bonded to one O(1), one O(10), one O(11), and two equivalent O(4) atoms to form MgO5 square pyramids that share corners with two equivalent Mg(10)O6 octahedra,  a cornercorner with one Li(1)O5 square pyramid,  a cornercorner with one Mg(2)O5 square pyramid, corners with three equivalent Mg(9)O5 square pyramids,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Hf(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-9°. The Mg(9)-O(1) bond length is 2.24 Å. The Mg(9)-O(10) bond length is 2.07 Å. The Mg(9)-O(11) bond length is 2.27 Å. Both Mg(9)-O(4) bond lengths are 2.15 Å. In the tenth Mg site, Mg(10) is bonded to one O(10), one O(11), one O(2), one O(3), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with four equivalent Mg(10)O6 octahedra, corners with two equivalent Mg(9)O5 square pyramids,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Hf(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra,  an edgeedge with one Li(1)O5 square pyramid, and  an edgeedge with one Mg(2)O5 square pyramid. The corner-sharing octahedral tilt angles range from 5-9°. The Mg(10)-O(10) bond length is 2.07 Å. The Mg(10)-O(11) bond length is 2.23 Å. The Mg(10)-O(2) bond length is 2.07 Å. The Mg(10)-O(3) bond length is 2.25 Å. Both Mg(10)-O(5) bond lengths are 2.15 Å. Hf(1) is bonded to one O(1), one O(3), two equivalent O(11), and two equivalent O(9) atoms to form HfO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Hf(1)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(6)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedra are not tilted. The Hf(1)-O(1) bond length is 2.15 Å. The Hf(1)-O(3) bond length is 2.15 Å. Both Hf(1)-O(11) bond lengths are 2.16 Å. Both Hf(1)-O(9) bond lengths are 2.14 Å. There are eleven inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), two equivalent Mg(6), two equivalent Mg(9), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(1)HfMg5 octahedra, corners with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(9)Hf2Mg4 octahedra, edges with two equivalent O(11)HfMg5 octahedra, edges with two equivalent O(10)LiMg5 octahedra, edges with two equivalent O(7)Mg6 octahedra, and edges with four equivalent O(4)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. In the second O site, O(2) is bonded to one Li(1), one Mg(2), two equivalent Mg(10), and two equivalent Mg(7) atoms to form OLiMg5 octahedra that share corners with two equivalent O(3)HfMg5 octahedra, corners with two equivalent O(2)LiMg5 octahedra, edges with two equivalent O(11)HfMg5 octahedra, edges with two equivalent O(6)Li2Mg4 octahedra, edges with two equivalent O(10)LiMg5 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles are 7°. In the third O site, O(3) is bonded to one Mg(1), two equivalent Mg(10), two equivalent Mg(8), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(1)HfMg5 octahedra, corners with two equivalent O(3)HfMg5 octahedra, corners with two equivalent O(2)LiMg5 octahedra, edges with two equivalent O(9)Hf2Mg4 octahedra, edges with two equivalent O(11)HfMg5 octahedra, edges with two equivalent O(10)LiMg5 octahedra, edges with two equivalent O(7)Mg6 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the fourth O site, O(4) is bonded to one Mg(3), one Mg(4), one Mg(5), one Mg(6), and two equivalent Mg(9) atoms to form OMg6 octahedra that share corners with two equivalent O(5)Mg6 octahedra, corners with four equivalent O(4)Mg6 octahedra,  an edgeedge with one O(9)Hf2Mg4 octahedra,  an edgeedge with one O(6)Li2Mg4 octahedra,  an edgeedge with one O(7)Mg6 octahedra,  an edgeedge with one O(8)Mg6 octahedra, edges with two equivalent O(1)HfMg5 octahedra, edges with two equivalent O(11)HfMg5 octahedra, and edges with two equivalent O(10)LiMg5 octahedra. The corner-sharing octahedral tilt angles range from 4-8°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), one Mg(7), one Mg(8), and two equivalent Mg(10) atoms to form OMg6 octahedra that share corners with two equivalent O(4)Mg6 octahedra, corners with four equivalent O(5)Mg6 octahedra,  an edgeedge with one O(9)Hf2Mg4 octahedra,  an edgeedge with one O(6)Li2Mg4 octahedra,  an edgeedge with one O(7)Mg6 octahedra,  an edgeedge with one O(8)Mg6 octahedra, edges with two equivalent O(11)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(10)LiMg5 octahedra, and edges with two equivalent O(2)LiMg5 octahedra. The corner-sharing octahedral tilt angles range from 4-7°. In the sixth O site, O(6) is bonded to two equivalent Li(1), one Mg(5), one Mg(7), and two equivalent Mg(3) atoms to form OLi2Mg4 octahedra that share corners with two equivalent O(6)Li2Mg4 octahedra, corners with two equivalent O(7)Mg6 octahedra, corners with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(2)LiMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(10)LiMg5 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the seventh O site, O(7) is bonded to one Mg(6), one Mg(8), two equivalent Mg(1), and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(9)Hf2Mg4 octahedra, corners with two equivalent O(6)Li2Mg4 octahedra, corners with two equivalent O(7)Mg6 octahedra, edges with two equivalent O(1)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(10)LiMg5 octahedra. The corner-sharing octahedra are not tilted. In the eighth O site, O(8) is bonded to one Mg(5), one Mg(7), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(9)Hf2Mg4 octahedra, corners with two equivalent O(6)Li2Mg4 octahedra, corners with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(2)LiMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(11)HfMg5 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the ninth O site, O(9) is bonded to one Mg(6), one Mg(8), two equivalent Mg(4), and two equivalent Hf(1) atoms to form OHf2Mg4 octahedra that share corners with two equivalent O(9)Hf2Mg4 octahedra, corners with two equivalent O(7)Mg6 octahedra, corners with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(1)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(11)HfMg5 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the tenth O site, O(10) is bonded to one Li(1), one Mg(1), one Mg(10), one Mg(9), and two equivalent Mg(3) atoms to form OLiMg5 octahedra that share corners with two equivalent O(11)HfMg5 octahedra, corners with four equivalent O(10)LiMg5 octahedra,  an edgeedge with one O(1)HfMg5 octahedra,  an edgeedge with one O(3)HfMg5 octahedra,  an edgeedge with one O(2)LiMg5 octahedra, edges with two equivalent O(6)Li2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with two equivalent O(7)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. In the eleventh O site, O(11) is bonded to one Mg(10), one Mg(2), one Mg(9), two equivalent Mg(4), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(10)LiMg5 octahedra, corners with four equivalent O(11)HfMg5 octahedra,  an edgeedge with one O(1)HfMg5 octahedra,  an edgeedge with one O(3)HfMg5 octahedra,  an edgeedge with one O(2)LiMg5 octahedra, edges with two equivalent O(9)Hf2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with two equivalent O(8)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 1-7°.