Ba4MgTl8O16 crystallizes in the monoclinic Pm space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 6-coordinate geometry to one O(16), one O(8), two equivalent O(3), and two equivalent O(4) atoms. In the second Ba site, Ba(2) is bonded in a 7-coordinate geometry to one O(1), two equivalent O(2), two equivalent O(5), and two equivalent O(6) atoms. In the third Ba site, Ba(3) is bonded in a 7-coordinate geometry to one O(16), two equivalent O(11), two equivalent O(12), and two equivalent O(15) atoms. In the fourth Ba site, Ba(4) is bonded in a 8-coordinate geometry to one O(1), one O(9), two equivalent O(10), two equivalent O(13), and two equivalent O(14) atoms. Mg(1) is bonded in a trigonal non-coplanar geometry to one O(5) and two equivalent O(7) atoms. There are eight inequivalent Tl sites. In the first Tl site, Tl(1) is bonded to one O(14), two equivalent O(1), and two equivalent O(3) atoms to form distorted TlO5 square pyramids that share corners with two equivalent Tl(7)O6 octahedra, edges with two equivalent Tl(8)O6 octahedra, and edges with two equivalent Tl(1)O5 square pyramids. The corner-sharing octahedral tilt angles are 52°. In the second Tl site, Tl(2) is bonded to one O(16), one O(2), two equivalent O(15), and two equivalent O(4) atoms to form a mixture of edge and corner-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles range from 51-57°. In the third Tl site, Tl(3) is bonded to one O(7), one O(9), two equivalent O(10), and two equivalent O(5) atoms to form a mixture of edge and corner-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles are 55°. In the fourth Tl site, Tl(4) is bonded to one O(11), one O(4), two equivalent O(6), and two equivalent O(8) atoms to form a mixture of edge and corner-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles are 57°. In the fifth Tl site, Tl(5) is bonded to one O(13), one O(6), two equivalent O(11), and two equivalent O(9) atoms to form a mixture of edge and corner-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles range from 55-62°. In the sixth Tl site, Tl(6) is bonded in a 3-coordinate geometry to one O(10) and two equivalent O(12) atoms. In the seventh Tl site, Tl(7) is bonded to one O(1), one O(15), two equivalent O(13), and two equivalent O(2) atoms to form TlO6 octahedra that share corners with two equivalent Tl(5)O6 octahedra, corners with two equivalent Tl(1)O5 square pyramids, edges with two equivalent Tl(2)O6 octahedra, and edges with two equivalent Tl(7)O6 octahedra. The corner-sharing octahedral tilt angles are 62°. In the eighth Tl site, Tl(8) is bonded to one O(12), one O(3), two equivalent O(14), and two equivalent O(16) atoms to form TlO6 octahedra that share corners with two equivalent Tl(2)O6 octahedra, edges with two equivalent Tl(8)O6 octahedra, and edges with two equivalent Tl(1)O5 square pyramids. The corner-sharing octahedral tilt angles are 51°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to one Ba(2), one Ba(4), one Tl(7), and two equivalent Tl(1) atoms. In the second O site, O(2) is bonded to two equivalent Ba(2), one Tl(2), and two equivalent Tl(7) atoms to form a mixture of distorted edge and corner-sharing OBa2Tl3 trigonal bipyramids. In the third O site, O(3) is bonded to two equivalent Ba(1), one Tl(8), and two equivalent Tl(1) atoms to form a mixture of edge and corner-sharing OBa2Tl3 square pyramids. In the fourth O site, O(4) is bonded to two equivalent Ba(1), one Tl(4), and two equivalent Tl(2) atoms to form a mixture of distorted edge and corner-sharing OBa2Tl3 trigonal bipyramids. In the fifth O site, O(5) is bonded in a 5-coordinate geometry to two equivalent Ba(2), one Mg(1), and two equivalent Tl(3) atoms. In the sixth O site, O(6) is bonded to two equivalent Ba(2), one Tl(5), and two equivalent Tl(4) atoms to form distorted OBa2Tl3 trigonal bipyramids that share corners with two equivalent O(9)BaTl3 tetrahedra, corners with two equivalent O(2)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(4)Ba2Tl3 trigonal bipyramids,  an edgeedge with one O(2)Ba2Tl3 trigonal bipyramid, edges with two equivalent O(11)Ba2Tl3 trigonal bipyramids, and edges with two equivalent O(6)Ba2Tl3 trigonal bipyramids. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to two equivalent Mg(1) and one Tl(3) atom. In the eighth O site, O(8) is bonded in a distorted trigonal non-coplanar geometry to one Ba(1) and two equivalent Tl(4) atoms. In the ninth O site, O(9) is bonded to one Ba(4), one Tl(3), and two equivalent Tl(5) atoms to form distorted OBaTl3 tetrahedra that share corners with two equivalent O(14)Ba2Tl3 square pyramids, corners with two equivalent O(9)BaTl3 tetrahedra, corners with two equivalent O(11)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(6)Ba2Tl3 trigonal bipyramids, and  an edgeedge with one O(11)Ba2Tl3 trigonal bipyramid. In the tenth O site, O(10) is bonded in a 5-coordinate geometry to two equivalent Ba(4), one Tl(6), and two equivalent Tl(3) atoms. In the eleventh O site, O(11) is bonded to two equivalent Ba(3), one Tl(4), and two equivalent Tl(5) atoms to form distorted OBa2Tl3 trigonal bipyramids that share corners with two equivalent O(9)BaTl3 tetrahedra,  a cornercorner with one O(4)Ba2Tl3 trigonal bipyramid, corners with two equivalent O(15)Ba2Tl3 trigonal bipyramids,  an edgeedge with one O(9)BaTl3 tetrahedra,  an edgeedge with one O(15)Ba2Tl3 trigonal bipyramid, edges with two equivalent O(11)Ba2Tl3 trigonal bipyramids, and edges with two equivalent O(6)Ba2Tl3 trigonal bipyramids. In the twelfth O site, O(12) is bonded in a 5-coordinate geometry to two equivalent Ba(3), one Tl(8), and two equivalent Tl(6) atoms. In the thirteenth O site, O(13) is bonded in a 5-coordinate geometry to two equivalent Ba(4), one Tl(5), and two equivalent Tl(7) atoms. In the fourteenth O site, O(14) is bonded to two equivalent Ba(4), one Tl(1), and two equivalent Tl(8) atoms to form OBa2Tl3 square pyramids that share corners with two equivalent O(9)BaTl3 tetrahedra, edges with two equivalent O(14)Ba2Tl3 square pyramids, and edges with two equivalent O(3)Ba2Tl3 square pyramids. In the fifteenth O site, O(15) is bonded to two equivalent Ba(3), one Tl(7), and two equivalent Tl(2) atoms to form a mixture of distorted edge and corner-sharing OBa2Tl3 trigonal bipyramids. In the sixteenth O site, O(16) is bonded in a 5-coordinate geometry to one Ba(1), one Ba(3), one Tl(2), and two equivalent Tl(8) atoms.
Ba4MgTl8O16 crystallizes in the monoclinic Pm space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 6-coordinate geometry to one O(16), one O(8), two equivalent O(3), and two equivalent O(4) atoms. The Ba(1)-O(16) bond length is 2.71 Å. The Ba(1)-O(8) bond length is 2.64 Å. Both Ba(1)-O(3) bond lengths are 2.99 Å. Both Ba(1)-O(4) bond lengths are 2.74 Å. In the second Ba site, Ba(2) is bonded in a 7-coordinate geometry to one O(1), two equivalent O(2), two equivalent O(5), and two equivalent O(6) atoms. The Ba(2)-O(1) bond length is 3.28 Å. Both Ba(2)-O(2) bond lengths are 2.75 Å. Both Ba(2)-O(5) bond lengths are 2.75 Å. Both Ba(2)-O(6) bond lengths are 2.77 Å. In the third Ba site, Ba(3) is bonded in a 7-coordinate geometry to one O(16), two equivalent O(11), two equivalent O(12), and two equivalent O(15) atoms. The Ba(3)-O(16) bond length is 3.19 Å. Both Ba(3)-O(11) bond lengths are 2.79 Å. Both Ba(3)-O(12) bond lengths are 2.67 Å. Both Ba(3)-O(15) bond lengths are 2.77 Å. In the fourth Ba site, Ba(4) is bonded in a 8-coordinate geometry to one O(1), one O(9), two equivalent O(10), two equivalent O(13), and two equivalent O(14) atoms. The Ba(4)-O(1) bond length is 2.99 Å. The Ba(4)-O(9) bond length is 2.77 Å. Both Ba(4)-O(10) bond lengths are 2.75 Å. Both Ba(4)-O(13) bond lengths are 2.91 Å. Both Ba(4)-O(14) bond lengths are 2.77 Å. Mg(1) is bonded in a trigonal non-coplanar geometry to one O(5) and two equivalent O(7) atoms. The Mg(1)-O(5) bond length is 1.94 Å. Both Mg(1)-O(7) bond lengths are 1.96 Å. There are eight inequivalent Tl sites. In the first Tl site, Tl(1) is bonded to one O(14), two equivalent O(1), and two equivalent O(3) atoms to form distorted TlO5 square pyramids that share corners with two equivalent Tl(7)O6 octahedra, edges with two equivalent Tl(8)O6 octahedra, and edges with two equivalent Tl(1)O5 square pyramids. The corner-sharing octahedral tilt angles are 52°. The Tl(1)-O(14) bond length is 2.22 Å. Both Tl(1)-O(1) bond lengths are 2.26 Å. Both Tl(1)-O(3) bond lengths are 2.38 Å. In the second Tl site, Tl(2) is bonded to one O(16), one O(2), two equivalent O(15), and two equivalent O(4) atoms to form a mixture of edge and corner-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles range from 51-57°. The Tl(2)-O(16) bond length is 2.36 Å. The Tl(2)-O(2) bond length is 2.28 Å. Both Tl(2)-O(15) bond lengths are 2.39 Å. Both Tl(2)-O(4) bond lengths are 2.38 Å. In the third Tl site, Tl(3) is bonded to one O(7), one O(9), two equivalent O(10), and two equivalent O(5) atoms to form a mixture of edge and corner-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles are 55°. The Tl(3)-O(7) bond length is 2.42 Å. The Tl(3)-O(9) bond length is 2.23 Å. Both Tl(3)-O(10) bond lengths are 2.28 Å. Both Tl(3)-O(5) bond lengths are 2.45 Å. In the fourth Tl site, Tl(4) is bonded to one O(11), one O(4), two equivalent O(6), and two equivalent O(8) atoms to form a mixture of edge and corner-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles are 57°. The Tl(4)-O(11) bond length is 2.42 Å. The Tl(4)-O(4) bond length is 2.63 Å. Both Tl(4)-O(6) bond lengths are 2.40 Å. Both Tl(4)-O(8) bond lengths are 2.23 Å. In the fifth Tl site, Tl(5) is bonded to one O(13), one O(6), two equivalent O(11), and two equivalent O(9) atoms to form a mixture of edge and corner-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles range from 55-62°. The Tl(5)-O(13) bond length is 2.64 Å. The Tl(5)-O(6) bond length is 2.40 Å. Both Tl(5)-O(11) bond lengths are 2.35 Å. Both Tl(5)-O(9) bond lengths are 2.23 Å. In the sixth Tl site, Tl(6) is bonded in a 3-coordinate geometry to one O(10) and two equivalent O(12) atoms. The Tl(6)-O(10) bond length is 2.67 Å. Both Tl(6)-O(12) bond lengths are 2.65 Å. In the seventh Tl site, Tl(7) is bonded to one O(1), one O(15), two equivalent O(13), and two equivalent O(2) atoms to form TlO6 octahedra that share corners with two equivalent Tl(5)O6 octahedra, corners with two equivalent Tl(1)O5 square pyramids, edges with two equivalent Tl(2)O6 octahedra, and edges with two equivalent Tl(7)O6 octahedra. The corner-sharing octahedral tilt angles are 62°. The Tl(7)-O(1) bond length is 2.45 Å. The Tl(7)-O(15) bond length is 2.28 Å. Both Tl(7)-O(13) bond lengths are 2.32 Å. Both Tl(7)-O(2) bond lengths are 2.43 Å. In the eighth Tl site, Tl(8) is bonded to one O(12), one O(3), two equivalent O(14), and two equivalent O(16) atoms to form TlO6 octahedra that share corners with two equivalent Tl(2)O6 octahedra, edges with two equivalent Tl(8)O6 octahedra, and edges with two equivalent Tl(1)O5 square pyramids. The corner-sharing octahedral tilt angles are 51°. The Tl(8)-O(12) bond length is 2.20 Å. The Tl(8)-O(3) bond length is 2.53 Å. Both Tl(8)-O(14) bond lengths are 2.47 Å. Both Tl(8)-O(16) bond lengths are 2.32 Å. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to one Ba(2), one Ba(4), one Tl(7), and two equivalent Tl(1) atoms. In the second O site, O(2) is bonded to two equivalent Ba(2), one Tl(2), and two equivalent Tl(7) atoms to form a mixture of distorted edge and corner-sharing OBa2Tl3 trigonal bipyramids. In the third O site, O(3) is bonded to two equivalent Ba(1), one Tl(8), and two equivalent Tl(1) atoms to form a mixture of edge and corner-sharing OBa2Tl3 square pyramids. In the fourth O site, O(4) is bonded to two equivalent Ba(1), one Tl(4), and two equivalent Tl(2) atoms to form a mixture of distorted edge and corner-sharing OBa2Tl3 trigonal bipyramids. In the fifth O site, O(5) is bonded in a 5-coordinate geometry to two equivalent Ba(2), one Mg(1), and two equivalent Tl(3) atoms. In the sixth O site, O(6) is bonded to two equivalent Ba(2), one Tl(5), and two equivalent Tl(4) atoms to form distorted OBa2Tl3 trigonal bipyramids that share corners with two equivalent O(9)BaTl3 tetrahedra, corners with two equivalent O(2)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(4)Ba2Tl3 trigonal bipyramids,  an edgeedge with one O(2)Ba2Tl3 trigonal bipyramid, edges with two equivalent O(11)Ba2Tl3 trigonal bipyramids, and edges with two equivalent O(6)Ba2Tl3 trigonal bipyramids. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to two equivalent Mg(1) and one Tl(3) atom. In the eighth O site, O(8) is bonded in a distorted trigonal non-coplanar geometry to one Ba(1) and two equivalent Tl(4) atoms. In the ninth O site, O(9) is bonded to one Ba(4), one Tl(3), and two equivalent Tl(5) atoms to form distorted OBaTl3 tetrahedra that share corners with two equivalent O(14)Ba2Tl3 square pyramids, corners with two equivalent O(9)BaTl3 tetrahedra, corners with two equivalent O(11)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(6)Ba2Tl3 trigonal bipyramids, and  an edgeedge with one O(11)Ba2Tl3 trigonal bipyramid. In the tenth O site, O(10) is bonded in a 5-coordinate geometry to two equivalent Ba(4), one Tl(6), and two equivalent Tl(3) atoms. In the eleventh O site, O(11) is bonded to two equivalent Ba(3), one Tl(4), and two equivalent Tl(5) atoms to form distorted OBa2Tl3 trigonal bipyramids that share corners with two equivalent O(9)BaTl3 tetrahedra,  a cornercorner with one O(4)Ba2Tl3 trigonal bipyramid, corners with two equivalent O(15)Ba2Tl3 trigonal bipyramids,  an edgeedge with one O(9)BaTl3 tetrahedra,  an edgeedge with one O(15)Ba2Tl3 trigonal bipyramid, edges with two equivalent O(11)Ba2Tl3 trigonal bipyramids, and edges with two equivalent O(6)Ba2Tl3 trigonal bipyramids. In the twelfth O site, O(12) is bonded in a 5-coordinate geometry to two equivalent Ba(3), one Tl(8), and two equivalent Tl(6) atoms. In the thirteenth O site, O(13) is bonded in a 5-coordinate geometry to two equivalent Ba(4), one Tl(5), and two equivalent Tl(7) atoms. In the fourteenth O site, O(14) is bonded to two equivalent Ba(4), one Tl(1), and two equivalent Tl(8) atoms to form OBa2Tl3 square pyramids that share corners with two equivalent O(9)BaTl3 tetrahedra, edges with two equivalent O(14)Ba2Tl3 square pyramids, and edges with two equivalent O(3)Ba2Tl3 square pyramids. In the fifteenth O site, O(15) is bonded to two equivalent Ba(3), one Tl(7), and two equivalent Tl(2) atoms to form a mixture of distorted edge and corner-sharing OBa2Tl3 trigonal bipyramids. In the sixteenth O site, O(16) is bonded in a 5-coordinate geometry to one Ba(1), one Ba(3), one Tl(2), and two equivalent Tl(8) atoms.