The compound described by 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 7-coordinate geometry to one O(8), two equivalent O(3), two equivalent O(4), and two equivalent O(7) atoms. In the second Ba site, Ba(2) is bonded in a 6-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 8-coordinate geometry to one O(16), one O(8), 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 to one O(14), one O(16), and two equivalent O(3) atoms to form distorted MgO4 trigonal pyramids that share  a cornercorner with one Tl(2)O6 octahedra and corners with two equivalent Mg(1)O4 trigonal pyramids. The corner-sharing octahedral tilt angles are 49°. There are eight inequivalent Tl sites. In the first Tl site, Tl(1) is bonded in a distorted trigonal non-coplanar geometry to one O(5) and two equivalent O(1) atoms. 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 TlO6 octahedra that share corners with two equivalent Tl(4)O6 octahedra,  a cornercorner with one Mg(1)O4 trigonal pyramid, edges with two equivalent Tl(2)O6 octahedra, and edges with two equivalent Tl(7)O6 octahedra. The corner-sharing octahedral tilt angles are 56°. 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 corner and edge-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles are 53°. 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 corner and edge-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles range from 49-56°. 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 corner and edge-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles range from 53-58°. In the sixth Tl site, Tl(6) is bonded to one O(10), one O(8), two equivalent O(12), and two equivalent O(7) atoms to form a mixture of corner and edge-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles are 49°. 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 a mixture of corner and edge-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles are 58°. In the eighth Tl site, Tl(8) is bonded in a 6-coordinate geometry to one O(12), one O(3), two equivalent O(14), and two equivalent O(16) atoms. 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 corner and edge-sharing OBa2Tl3 trigonal bipyramids. In the third O site, O(3) is bonded in a 2-coordinate geometry to two equivalent Ba(1), two equivalent Mg(1), and one Tl(8) atom. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to two equivalent Ba(1), one Tl(4), and two equivalent Tl(2) atoms. In the fifth O site, O(5) is bonded to two equivalent Ba(2), one Tl(1), and two equivalent Tl(3) atoms to form a mixture of distorted corner and edge-sharing OBa2Tl3 trigonal bipyramids. 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 a mixture of distorted corner and edge-sharing OBa2Tl3 square pyramids. In the seventh O site, O(7) is bonded to two equivalent Ba(1), one Tl(3), and two equivalent Tl(6) atoms to form a mixture of distorted corner and edge-sharing OBa2Tl3 trigonal bipyramids. In the eighth O site, O(8) is bonded to one Ba(1), one Ba(3), one Tl(6), and two equivalent Tl(4) atoms to form a mixture of distorted corner and edge-sharing OBa2Tl3 trigonal bipyramids. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Ba(4), one Tl(3), and two equivalent Tl(5) atoms. 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 a mixture of corner and edge-sharing OBa2Tl3 square pyramids. 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 in a 5-coordinate geometry to two equivalent Ba(4), one Mg(1), and two equivalent Tl(8) atoms. 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 corner and edge-sharing OBa2Tl3 trigonal bipyramids. In the sixteenth O site, O(16) is bonded in a 4-coordinate geometry to one Ba(3), one Mg(1), one Tl(2), and two equivalent Tl(8) atoms. is represented by the CIF file [CIF]
data_Ba4MgTl8O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.969
_cell_length_b   12.459
_cell_length_c   3.571
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   86.176
_symmetry_Int_Tables_number   1
_cell_volume   486.979
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ba  Ba0  1  0.264  0.328  0.750  1.0
  Ba  Ba1  1  0.266  0.871  0.250  1.0
  Ba  Ba2  1  0.732  0.133  0.750  1.0
  Ba  Ba3  1  0.772  0.656  0.250  1.0
  Mg  Mg4  1  0.025  0.449  0.750  1.0
  Tl  Tl5  1  0.122  0.645  0.750  1.0
  Tl  Tl6  1  0.068  0.113  0.750  1.0
  Tl  Tl7  1  0.447  0.624  0.250  1.0
  Tl  Tl8  1  0.428  0.104  0.250  1.0
  Tl  Tl9  1  0.590  0.888  0.750  1.0
  Tl  Tl10  1  0.558  0.395  0.750  1.0
  Tl  Tl11  1  0.932  0.899  0.250  1.0
  Tl  Tl12  1  0.864  0.360  0.250  1.0
  O  O13  1  0.021  0.740  0.250  1.0
  O  O14  1  0.090  0.938  0.750  1.0
  O  O15  1  0.093  0.421  0.250  1.0
  O  O16  1  0.210  0.158  0.250  1.0
  O  O17  1  0.329  0.701  0.750  1.0
  O  O18  1  0.397  0.982  0.750  1.0
  O  O19  1  0.419  0.438  0.250  1.0
  O  O20  1  0.476  0.217  0.750  1.0
  O  O21  1  0.554  0.779  0.250  1.0
  O  O22  1  0.585  0.571  0.750  1.0
  O  O23  1  0.618  0.017  0.250  1.0
  O  O24  1  0.677  0.312  0.250  1.0
  O  O25  1  0.798  0.842  0.750  1.0
  O  O26  1  0.852  0.493  0.750  1.0
  O  O27  1  0.914  0.077  0.250  1.0
  O  O28  1  0.961  0.277  0.750  1.0
[/CIF]
.
The compound described by 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 7-coordinate geometry to one O(8), two equivalent O(3), two equivalent O(4), and two equivalent O(7) atoms. In the second Ba site, Ba(2) is bonded in a 6-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 8-coordinate geometry to one O(16), one O(8), 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 to one O(14), one O(16), and two equivalent O(3) atoms to form distorted MgO4 trigonal pyramids that share  a cornercorner with one Tl(2)O6 octahedra and corners with two equivalent Mg(1)O4 trigonal pyramids. The corner-sharing octahedral tilt angles are 49°. There are eight inequivalent Tl sites. In the first Tl site, Tl(1) is bonded in a distorted trigonal non-coplanar geometry to one O(5) and two equivalent O(1) atoms. 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 TlO6 octahedra that share corners with two equivalent Tl(4)O6 octahedra,  a cornercorner with one Mg(1)O4 trigonal pyramid, edges with two equivalent Tl(2)O6 octahedra, and edges with two equivalent Tl(7)O6 octahedra. The corner-sharing octahedral tilt angles are 56°. 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 corner and edge-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles are 53°. 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 corner and edge-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles range from 49-56°. 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 corner and edge-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles range from 53-58°. In the sixth Tl site, Tl(6) is bonded to one O(10), one O(8), two equivalent O(12), and two equivalent O(7) atoms to form a mixture of corner and edge-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles are 49°. 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 a mixture of corner and edge-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles are 58°. In the eighth Tl site, Tl(8) is bonded in a 6-coordinate geometry to one O(12), one O(3), two equivalent O(14), and two equivalent O(16) atoms. 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 corner and edge-sharing OBa2Tl3 trigonal bipyramids. In the third O site, O(3) is bonded in a 2-coordinate geometry to two equivalent Ba(1), two equivalent Mg(1), and one Tl(8) atom. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to two equivalent Ba(1), one Tl(4), and two equivalent Tl(2) atoms. In the fifth O site, O(5) is bonded to two equivalent Ba(2), one Tl(1), and two equivalent Tl(3) atoms to form a mixture of distorted corner and edge-sharing OBa2Tl3 trigonal bipyramids. 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 a mixture of distorted corner and edge-sharing OBa2Tl3 square pyramids. In the seventh O site, O(7) is bonded to two equivalent Ba(1), one Tl(3), and two equivalent Tl(6) atoms to form a mixture of distorted corner and edge-sharing OBa2Tl3 trigonal bipyramids. In the eighth O site, O(8) is bonded to one Ba(1), one Ba(3), one Tl(6), and two equivalent Tl(4) atoms to form a mixture of distorted corner and edge-sharing OBa2Tl3 trigonal bipyramids. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Ba(4), one Tl(3), and two equivalent Tl(5) atoms. 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 a mixture of corner and edge-sharing OBa2Tl3 square pyramids. 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 in a 5-coordinate geometry to two equivalent Ba(4), one Mg(1), and two equivalent Tl(8) atoms. 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 corner and edge-sharing OBa2Tl3 trigonal bipyramids. In the sixteenth O site, O(16) is bonded in a 4-coordinate geometry to one Ba(3), one Mg(1), one Tl(2), and two equivalent Tl(8) atoms. is represented by the CIF file [CIF]
data_Ba4MgTl8O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.969
_cell_length_b   12.459
_cell_length_c   3.571
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   86.176
_symmetry_Int_Tables_number   1
_cell_volume   486.979
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ba  Ba0  1  0.264  0.328  0.750  1.0
  Ba  Ba1  1  0.266  0.871  0.250  1.0
  Ba  Ba2  1  0.732  0.133  0.750  1.0
  Ba  Ba3  1  0.772  0.656  0.250  1.0
  Mg  Mg4  1  0.025  0.449  0.750  1.0
  Tl  Tl5  1  0.122  0.645  0.750  1.0
  Tl  Tl6  1  0.068  0.113  0.750  1.0
  Tl  Tl7  1  0.447  0.624  0.250  1.0
  Tl  Tl8  1  0.428  0.104  0.250  1.0
  Tl  Tl9  1  0.590  0.888  0.750  1.0
  Tl  Tl10  1  0.558  0.395  0.750  1.0
  Tl  Tl11  1  0.932  0.899  0.250  1.0
  Tl  Tl12  1  0.864  0.360  0.250  1.0
  O  O13  1  0.021  0.740  0.250  1.0
  O  O14  1  0.090  0.938  0.750  1.0
  O  O15  1  0.093  0.421  0.250  1.0
  O  O16  1  0.210  0.158  0.250  1.0
  O  O17  1  0.329  0.701  0.750  1.0
  O  O18  1  0.397  0.982  0.750  1.0
  O  O19  1  0.419  0.438  0.250  1.0
  O  O20  1  0.476  0.217  0.750  1.0
  O  O21  1  0.554  0.779  0.250  1.0
  O  O22  1  0.585  0.571  0.750  1.0
  O  O23  1  0.618  0.017  0.250  1.0
  O  O24  1  0.677  0.312  0.250  1.0
  O  O25  1  0.798  0.842  0.750  1.0
  O  O26  1  0.852  0.493  0.750  1.0
  O  O27  1  0.914  0.077  0.250  1.0
  O  O28  1  0.961  0.277  0.750  1.0
[/CIF]
.