NaMg14LaO16 is Caswellsilverite-derived structured and crystallizes in the tetragonal P4/mmm space group. Na(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form NaO6 octahedra that share corners with two equivalent Na(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 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 Na(1)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent La(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 La(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. 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 Na(1)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, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. 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 Na(1)O6 octahedra,  an edgeedge with one La(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 2-12°. La(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form LaO6 octahedra that share corners with two equivalent La(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. 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 La(1) atom to form OLaMg5 octahedra that share corners with two equivalent O(2)NaMg5 octahedra, corners with four equivalent O(1)LaMg5 octahedra, edges with two equivalent O(4)La2Mg4 octahedra, edges with two equivalent O(1)LaMg5 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(2)NaMg5 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. In the second O site, O(2) is bonded to one Na(1), one Mg(1), two equivalent Mg(3), and two equivalent Mg(4) atoms to form ONaMg5 octahedra that share corners with two equivalent O(1)LaMg5 octahedra, corners with four equivalent O(2)NaMg5 octahedra, edges with two equivalent O(1)LaMg5 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(6)Na2Mg4 octahedra, edges with two equivalent O(2)NaMg5 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. 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(4)La2Mg4 octahedra,  an edgeedge with one O(6)Na2Mg4 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)LaMg5 octahedra, and edges with four equivalent O(2)NaMg5 octahedra. The corner-sharing octahedral tilt angles range from 4-10°. In the fourth O site, O(4) is bonded to four equivalent Mg(2) and two equivalent La(1) atoms to form OLa2Mg4 octahedra that share corners with two equivalent O(4)La2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)LaMg5 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(4)La2Mg4 octahedra, corners with two equivalent O(5)Mg6 octahedra, corners with two equivalent O(6)Na2Mg4 octahedra, edges with four equivalent O(1)LaMg5 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(2)NaMg5 octahedra. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to two equivalent Na(1) and four equivalent Mg(3) atoms to form ONa2Mg4 octahedra that share corners with two equivalent O(6)Na2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)NaMg5 octahedra. The corner-sharing octahedra are not tilted.
NaMg14LaO16 is Caswellsilverite-derived structured and crystallizes in the tetragonal P4/mmm space group. Na(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form NaO6 octahedra that share corners with two equivalent Na(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 Na(1)-O(6) bond lengths are 2.21 Å. All Na(1)-O(2) bond lengths are 2.29 Å. 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 Na(1)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent La(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 2.03 Å. Both Mg(1)-O(2) bond lengths are 2.08 Å. Both Mg(1)-O(5) bond lengths are 2.21 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 La(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. The Mg(2)-O(4) bond length is 2.36 Å. The Mg(2)-O(5) bond length is 2.02 Å. Both Mg(2)-O(1) bond lengths are 2.21 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 Na(1)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, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. The Mg(3)-O(5) bond length is 2.24 Å. The Mg(3)-O(6) bond length is 2.13 Å. Both Mg(3)-O(2) bond lengths are 2.21 Å. Both Mg(3)-O(3) bond lengths are 2.20 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 Na(1)O6 octahedra,  an edgeedge with one La(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 2-12°. Both Mg(4)-O(1) bond lengths are 2.30 Å. Both Mg(4)-O(2) bond lengths are 2.09 Å. Both Mg(4)-O(3) bond lengths are 2.21 Å. La(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form LaO6 octahedra that share corners with two equivalent La(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 La(1)-O(4) bond lengths are 2.21 Å. All La(1)-O(1) bond lengths are 2.34 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 La(1) atom to form OLaMg5 octahedra that share corners with two equivalent O(2)NaMg5 octahedra, corners with four equivalent O(1)LaMg5 octahedra, edges with two equivalent O(4)La2Mg4 octahedra, edges with two equivalent O(1)LaMg5 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(2)NaMg5 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. In the second O site, O(2) is bonded to one Na(1), one Mg(1), two equivalent Mg(3), and two equivalent Mg(4) atoms to form ONaMg5 octahedra that share corners with two equivalent O(1)LaMg5 octahedra, corners with four equivalent O(2)NaMg5 octahedra, edges with two equivalent O(1)LaMg5 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(6)Na2Mg4 octahedra, edges with two equivalent O(2)NaMg5 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. 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(4)La2Mg4 octahedra,  an edgeedge with one O(6)Na2Mg4 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)LaMg5 octahedra, and edges with four equivalent O(2)NaMg5 octahedra. The corner-sharing octahedral tilt angles range from 4-10°. In the fourth O site, O(4) is bonded to four equivalent Mg(2) and two equivalent La(1) atoms to form OLa2Mg4 octahedra that share corners with two equivalent O(4)La2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)LaMg5 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(4)La2Mg4 octahedra, corners with two equivalent O(5)Mg6 octahedra, corners with two equivalent O(6)Na2Mg4 octahedra, edges with four equivalent O(1)LaMg5 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(2)NaMg5 octahedra. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to two equivalent Na(1) and four equivalent Mg(3) atoms to form ONa2Mg4 octahedra that share corners with two equivalent O(6)Na2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)NaMg5 octahedra. The corner-sharing octahedra are not tilted.