Mg14YHfO16 is alpha Po-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 Y(1)O6 octahedra, corners with two equivalent Hf(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 Y(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 Hf(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. 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 Y(1)O6 octahedra,  an edgeedge with one Hf(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 1-9°. Y(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form YO6 octahedra that share corners with two equivalent Y(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. Hf(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form HfO6 octahedra that share corners with two equivalent Hf(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 Y(1) atom to form OYMg5 octahedra that share corners with two equivalent O(2)HfMg5 octahedra, corners with four equivalent O(1)YMg5 octahedra, edges with two equivalent O(2)HfMg5 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(4)Y2Mg4 octahedra, edges with two equivalent O(1)YMg5 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(1)YMg5 octahedra, corners with four equivalent O(2)HfMg5 octahedra, edges with two equivalent O(6)Hf2Mg4 octahedra, edges with two equivalent O(2)HfMg5 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(1)YMg5 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. 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)Hf2Mg4 octahedra,  an edgeedge with one O(4)Y2Mg4 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)HfMg5 octahedra, and edges with four equivalent O(1)YMg5 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. In the fourth O site, O(4) is bonded to four equivalent Mg(2) and two equivalent Y(1) atoms to form OY2Mg4 octahedra that share corners with two equivalent O(4)Y2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)YMg5 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)Hf2Mg4 octahedra, corners with two equivalent O(5)Mg6 octahedra, corners with two equivalent O(4)Y2Mg4 octahedra, edges with four equivalent O(2)HfMg5 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(1)YMg5 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 Hf(1) atoms to form OHf2Mg4 octahedra that share corners with two equivalent O(6)Hf2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)HfMg5 octahedra. The corner-sharing octahedra are not tilted.
Mg14YHfO16 is alpha Po-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 Y(1)O6 octahedra, corners with two equivalent Hf(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 2.13 Å. Both Mg(1)-O(2) bond lengths are 2.08 Å. Both Mg(1)-O(5) bond lengths are 2.19 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 Y(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 2.31 Å. The Mg(2)-O(5) bond length is 2.09 Å. Both Mg(2)-O(1) bond lengths are 2.19 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 Hf(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. The Mg(3)-O(5) bond length is 2.16 Å. The Mg(3)-O(6) bond length is 2.24 Å. Both Mg(3)-O(2) bond lengths are 2.19 Å. Both Mg(3)-O(3) bond lengths are 2.22 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 Y(1)O6 octahedra,  an edgeedge with one Hf(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 1-9°. Both Mg(4)-O(1) bond lengths are 2.25 Å. Both Mg(4)-O(2) bond lengths are 2.15 Å. Both Mg(4)-O(3) bond lengths are 2.19 Å. Y(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form YO6 octahedra that share corners with two equivalent Y(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 Y(1)-O(4) bond lengths are 2.19 Å. All Y(1)-O(1) bond lengths are 2.27 Å. Hf(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form HfO6 octahedra that share corners with two equivalent Hf(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 Hf(1)-O(6) bond lengths are 2.19 Å. All Hf(1)-O(2) bond lengths are 2.31 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 Y(1) atom to form OYMg5 octahedra that share corners with two equivalent O(2)HfMg5 octahedra, corners with four equivalent O(1)YMg5 octahedra, edges with two equivalent O(2)HfMg5 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(4)Y2Mg4 octahedra, edges with two equivalent O(1)YMg5 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(1)YMg5 octahedra, corners with four equivalent O(2)HfMg5 octahedra, edges with two equivalent O(6)Hf2Mg4 octahedra, edges with two equivalent O(2)HfMg5 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(1)YMg5 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. 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)Hf2Mg4 octahedra,  an edgeedge with one O(4)Y2Mg4 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)HfMg5 octahedra, and edges with four equivalent O(1)YMg5 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. In the fourth O site, O(4) is bonded to four equivalent Mg(2) and two equivalent Y(1) atoms to form OY2Mg4 octahedra that share corners with two equivalent O(4)Y2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)YMg5 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)Hf2Mg4 octahedra, corners with two equivalent O(5)Mg6 octahedra, corners with two equivalent O(4)Y2Mg4 octahedra, edges with four equivalent O(2)HfMg5 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(1)YMg5 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 Hf(1) atoms to form OHf2Mg4 octahedra that share corners with two equivalent O(6)Hf2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)HfMg5 octahedra. The corner-sharing octahedra are not tilted.