The crystal structure described by MgLu2S4 is Spinel-like structured and crystallizes in the orthorhombic Pnma space group. Mg(1) is bonded to one S(2), one S(3), and two equivalent S(1) atoms to form MgS4 tetrahedra that share corners with two equivalent Lu(1)S6 octahedra, corners with four equivalent Lu(2)S6 octahedra,  an edgeedge with one Lu(2)S6 octahedra, and edges with two equivalent Lu(1)S6 octahedra. The corner-sharing octahedral tilt angles range from 61-67°. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to two equivalent S(1), two equivalent S(2), and two equivalent S(3) atoms to form LuS6 octahedra that share corners with four equivalent Lu(2)S6 octahedra, corners with two equivalent Mg(1)S4 tetrahedra, edges with two equivalent Lu(1)S6 octahedra, edges with two equivalent Lu(2)S6 octahedra, and edges with two equivalent Mg(1)S4 tetrahedra. The corner-sharing octahedral tilt angles range from 50-54°. In the second Lu site, Lu(2) is bonded to one S(2), one S(3), and four equivalent S(1) atoms to form LuS6 octahedra that share corners with four equivalent Lu(1)S6 octahedra, corners with four equivalent Lu(2)S6 octahedra, corners with four equivalent Mg(1)S4 tetrahedra, edges with two equivalent Lu(1)S6 octahedra, and  an edgeedge with one Mg(1)S4 tetrahedra. The corner-sharing octahedral tilt angles range from 47-54°. There are three inequivalent S sites. In the first S site, S(1) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Lu(1), and two equivalent Lu(2) atoms. In the second S site, S(2) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Lu(2), and two equivalent Lu(1) atoms. In the third S site, S(3) is bonded to one Mg(1), one Lu(2), and two equivalent Lu(1) atoms to form distorted corner-sharing SLu3Mg tetrahedra. is represented by the CIF card [CIF]
data_Lu2MgS4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   13.300
_cell_length_b   7.752
_cell_length_c   6.444
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   664.414
_cell_formula_units_Z   4
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
  Lu  Lu0  1  0.000  0.000  0.500  1.0
  Lu  Lu1  1  0.500  0.000  0.000  1.0
  Lu  Lu2  1  0.500  0.500  0.000  1.0
  Lu  Lu3  1  0.000  0.500  0.500  1.0
  Lu  Lu4  1  0.232  0.750  0.001  1.0
  Lu  Lu5  1  0.768  0.250  0.999  1.0
  Lu  Lu6  1  0.268  0.250  0.501  1.0
  Lu  Lu7  1  0.732  0.750  0.499  1.0
  Mg  Mg8  1  0.092  0.250  0.930  1.0
  Mg  Mg9  1  0.908  0.750  0.070  1.0
  Mg  Mg10  1  0.408  0.750  0.430  1.0
  Mg  Mg11  1  0.592  0.250  0.570  1.0
  S  S12  1  0.168  0.006  0.745  1.0
  S  S13  1  0.832  0.994  0.255  1.0
  S  S14  1  0.332  0.994  0.245  1.0
  S  S15  1  0.668  0.006  0.755  1.0
  S  S16  1  0.668  0.494  0.755  1.0
  S  S17  1  0.332  0.506  0.245  1.0
  S  S18  1  0.832  0.506  0.255  1.0
  S  S19  1  0.168  0.494  0.745  1.0
  S  S20  1  0.072  0.750  0.249  1.0
  S  S21  1  0.928  0.250  0.751  1.0
  S  S22  1  0.428  0.250  0.749  1.0
  S  S23  1  0.572  0.750  0.251  1.0
  S  S24  1  0.092  0.250  0.301  1.0
  S  S25  1  0.908  0.750  0.699  1.0
  S  S26  1  0.408  0.750  0.801  1.0
  S  S27  1  0.592  0.250  0.199  1.0
[/CIF]
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The crystal structure described by MgLu2S4 is Spinel-like structured and crystallizes in the orthorhombic Pnma space group. Mg(1) is bonded to one S(2), one S(3), and two equivalent S(1) atoms to form MgS4 tetrahedra that share corners with two equivalent Lu(1)S6 octahedra, corners with four equivalent Lu(2)S6 octahedra,  an edgeedge with one Lu(2)S6 octahedra, and edges with two equivalent Lu(1)S6 octahedra. The corner-sharing octahedral tilt angles range from 61-67°. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to two equivalent S(1), two equivalent S(2), and two equivalent S(3) atoms to form LuS6 octahedra that share corners with four equivalent Lu(2)S6 octahedra, corners with two equivalent Mg(1)S4 tetrahedra, edges with two equivalent Lu(1)S6 octahedra, edges with two equivalent Lu(2)S6 octahedra, and edges with two equivalent Mg(1)S4 tetrahedra. The corner-sharing octahedral tilt angles range from 50-54°. In the second Lu site, Lu(2) is bonded to one S(2), one S(3), and four equivalent S(1) atoms to form LuS6 octahedra that share corners with four equivalent Lu(1)S6 octahedra, corners with four equivalent Lu(2)S6 octahedra, corners with four equivalent Mg(1)S4 tetrahedra, edges with two equivalent Lu(1)S6 octahedra, and  an edgeedge with one Mg(1)S4 tetrahedra. The corner-sharing octahedral tilt angles range from 47-54°. There are three inequivalent S sites. In the first S site, S(1) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Lu(1), and two equivalent Lu(2) atoms. In the second S site, S(2) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Lu(2), and two equivalent Lu(1) atoms. In the third S site, S(3) is bonded to one Mg(1), one Lu(2), and two equivalent Lu(1) atoms to form distorted corner-sharing SLu3Mg tetrahedra. is represented by the CIF card [CIF]
data_Lu2MgS4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   13.300
_cell_length_b   7.752
_cell_length_c   6.444
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   664.414
_cell_formula_units_Z   4
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
  Lu  Lu0  1  0.000  0.000  0.500  1.0
  Lu  Lu1  1  0.500  0.000  0.000  1.0
  Lu  Lu2  1  0.500  0.500  0.000  1.0
  Lu  Lu3  1  0.000  0.500  0.500  1.0
  Lu  Lu4  1  0.232  0.750  0.001  1.0
  Lu  Lu5  1  0.768  0.250  0.999  1.0
  Lu  Lu6  1  0.268  0.250  0.501  1.0
  Lu  Lu7  1  0.732  0.750  0.499  1.0
  Mg  Mg8  1  0.092  0.250  0.930  1.0
  Mg  Mg9  1  0.908  0.750  0.070  1.0
  Mg  Mg10  1  0.408  0.750  0.430  1.0
  Mg  Mg11  1  0.592  0.250  0.570  1.0
  S  S12  1  0.168  0.006  0.745  1.0
  S  S13  1  0.832  0.994  0.255  1.0
  S  S14  1  0.332  0.994  0.245  1.0
  S  S15  1  0.668  0.006  0.755  1.0
  S  S16  1  0.668  0.494  0.755  1.0
  S  S17  1  0.332  0.506  0.245  1.0
  S  S18  1  0.832  0.506  0.255  1.0
  S  S19  1  0.168  0.494  0.745  1.0
  S  S20  1  0.072  0.750  0.249  1.0
  S  S21  1  0.928  0.250  0.751  1.0
  S  S22  1  0.428  0.250  0.749  1.0
  S  S23  1  0.572  0.750  0.251  1.0
  S  S24  1  0.092  0.250  0.301  1.0
  S  S25  1  0.908  0.750  0.699  1.0
  S  S26  1  0.408  0.750  0.801  1.0
  S  S27  1  0.592  0.250  0.199  1.0
[/CIF]
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