The crystal structure described by MgLu2S4 crystallizes in the orthorhombic Pnma space group. Mg(1) is bonded to two equivalent S(4) and three equivalent S(1) atoms to form MgS5 square pyramids that share corners with two equivalent Lu(1)S6 octahedra, corners with two equivalent Lu(2)S6 octahedra,  an edgeedge with one Lu(1)S6 octahedra, edges with three equivalent Lu(2)S6 octahedra, and edges with four equivalent Mg(1)S5 square pyramids. The corner-sharing octahedral tilt angles range from 6-9°. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one S(3), two equivalent S(4), and three equivalent S(2) atoms to form LuS6 octahedra that share corners with three equivalent Lu(2)S6 octahedra, corners with two equivalent Mg(1)S5 square pyramids, edges with two equivalent Lu(2)S6 octahedra, edges with four equivalent Lu(1)S6 octahedra, and  an edgeedge with one Mg(1)S5 square pyramid. The corner-sharing octahedral tilt angles range from 54-59°. In the second Lu site, Lu(2) is bonded to one S(2), one S(4), two equivalent S(1), and two equivalent S(3) atoms to form LuS6 octahedra that share corners with three equivalent Lu(1)S6 octahedra, corners with two equivalent Mg(1)S5 square pyramids, edges with two equivalent Lu(1)S6 octahedra, edges with two equivalent Lu(2)S6 octahedra, and edges with three equivalent Mg(1)S5 square pyramids. The corner-sharing octahedral tilt angles range from 54-59°. There are four inequivalent S sites. In the first S site, S(1) is bonded to three equivalent Mg(1) and two equivalent Lu(2) atoms to form SLu2Mg3 square pyramids that share corners with two equivalent S(4)Lu3Mg2 square pyramids, edges with three equivalent S(4)Lu3Mg2 square pyramids, and edges with four equivalent S(1)Lu2Mg3 square pyramids. In the second S site, S(2) is bonded in a rectangular see-saw-like geometry to one Lu(2) and three equivalent Lu(1) atoms. In the third S site, S(3) is bonded in a distorted T-shaped geometry to one Lu(1) and two equivalent Lu(2) atoms. In the fourth S site, S(4) is bonded to two equivalent Mg(1), one Lu(2), and two equivalent Lu(1) atoms to form SLu3Mg2 square pyramids that share corners with two equivalent S(1)Lu2Mg3 square pyramids, edges with two equivalent S(4)Lu3Mg2 square pyramids, and edges with three equivalent S(1)Lu2Mg3 square pyramids. is represented by the CIF file [CIF]
data_Lu2MgS4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.785
_cell_length_b   12.472
_cell_length_c   13.106
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   618.672
_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  0.250  0.114  0.077  1.0
  Lu  Lu1  1  0.750  0.886  0.923  1.0
  Lu  Lu2  1  0.750  0.386  0.577  1.0
  Lu  Lu3  1  0.250  0.614  0.423  1.0
  Lu  Lu4  1  0.250  0.143  0.704  1.0
  Lu  Lu5  1  0.750  0.857  0.296  1.0
  Lu  Lu6  1  0.750  0.357  0.204  1.0
  Lu  Lu7  1  0.250  0.643  0.796  1.0
  Mg  Mg8  1  0.750  0.117  0.440  1.0
  Mg  Mg9  1  0.250  0.883  0.560  1.0
  Mg  Mg10  1  0.250  0.383  0.940  1.0
  Mg  Mg11  1  0.750  0.617  0.060  1.0
  S  S12  1  0.750  0.016  0.615  1.0
  S  S13  1  0.250  0.984  0.385  1.0
  S  S14  1  0.250  0.484  0.115  1.0
  S  S15  1  0.750  0.516  0.885  1.0
  S  S16  1  0.250  0.029  0.882  1.0
  S  S17  1  0.750  0.971  0.118  1.0
  S  S18  1  0.750  0.471  0.382  1.0
  S  S19  1  0.250  0.529  0.618  1.0
  S  S20  1  0.250  0.222  0.254  1.0
  S  S21  1  0.750  0.778  0.746  1.0
  S  S22  1  0.750  0.278  0.754  1.0
  S  S23  1  0.250  0.722  0.246  1.0
  S  S24  1  0.750  0.256  0.017  1.0
  S  S25  1  0.250  0.744  0.983  1.0
  S  S26  1  0.250  0.244  0.517  1.0
  S  S27  1  0.750  0.756  0.483  1.0
[/CIF]
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The crystal structure described by MgLu2S4 crystallizes in the orthorhombic Pnma space group. Mg(1) is bonded to two equivalent S(4) and three equivalent S(1) atoms to form MgS5 square pyramids that share corners with two equivalent Lu(1)S6 octahedra, corners with two equivalent Lu(2)S6 octahedra,  an edgeedge with one Lu(1)S6 octahedra, edges with three equivalent Lu(2)S6 octahedra, and edges with four equivalent Mg(1)S5 square pyramids. The corner-sharing octahedral tilt angles range from 6-9°. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one S(3), two equivalent S(4), and three equivalent S(2) atoms to form LuS6 octahedra that share corners with three equivalent Lu(2)S6 octahedra, corners with two equivalent Mg(1)S5 square pyramids, edges with two equivalent Lu(2)S6 octahedra, edges with four equivalent Lu(1)S6 octahedra, and  an edgeedge with one Mg(1)S5 square pyramid. The corner-sharing octahedral tilt angles range from 54-59°. In the second Lu site, Lu(2) is bonded to one S(2), one S(4), two equivalent S(1), and two equivalent S(3) atoms to form LuS6 octahedra that share corners with three equivalent Lu(1)S6 octahedra, corners with two equivalent Mg(1)S5 square pyramids, edges with two equivalent Lu(1)S6 octahedra, edges with two equivalent Lu(2)S6 octahedra, and edges with three equivalent Mg(1)S5 square pyramids. The corner-sharing octahedral tilt angles range from 54-59°. There are four inequivalent S sites. In the first S site, S(1) is bonded to three equivalent Mg(1) and two equivalent Lu(2) atoms to form SLu2Mg3 square pyramids that share corners with two equivalent S(4)Lu3Mg2 square pyramids, edges with three equivalent S(4)Lu3Mg2 square pyramids, and edges with four equivalent S(1)Lu2Mg3 square pyramids. In the second S site, S(2) is bonded in a rectangular see-saw-like geometry to one Lu(2) and three equivalent Lu(1) atoms. In the third S site, S(3) is bonded in a distorted T-shaped geometry to one Lu(1) and two equivalent Lu(2) atoms. In the fourth S site, S(4) is bonded to two equivalent Mg(1), one Lu(2), and two equivalent Lu(1) atoms to form SLu3Mg2 square pyramids that share corners with two equivalent S(1)Lu2Mg3 square pyramids, edges with two equivalent S(4)Lu3Mg2 square pyramids, and edges with three equivalent S(1)Lu2Mg3 square pyramids. is represented by the CIF file [CIF]
data_Lu2MgS4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.785
_cell_length_b   12.472
_cell_length_c   13.106
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   618.672
_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  0.250  0.114  0.077  1.0
  Lu  Lu1  1  0.750  0.886  0.923  1.0
  Lu  Lu2  1  0.750  0.386  0.577  1.0
  Lu  Lu3  1  0.250  0.614  0.423  1.0
  Lu  Lu4  1  0.250  0.143  0.704  1.0
  Lu  Lu5  1  0.750  0.857  0.296  1.0
  Lu  Lu6  1  0.750  0.357  0.204  1.0
  Lu  Lu7  1  0.250  0.643  0.796  1.0
  Mg  Mg8  1  0.750  0.117  0.440  1.0
  Mg  Mg9  1  0.250  0.883  0.560  1.0
  Mg  Mg10  1  0.250  0.383  0.940  1.0
  Mg  Mg11  1  0.750  0.617  0.060  1.0
  S  S12  1  0.750  0.016  0.615  1.0
  S  S13  1  0.250  0.984  0.385  1.0
  S  S14  1  0.250  0.484  0.115  1.0
  S  S15  1  0.750  0.516  0.885  1.0
  S  S16  1  0.250  0.029  0.882  1.0
  S  S17  1  0.750  0.971  0.118  1.0
  S  S18  1  0.750  0.471  0.382  1.0
  S  S19  1  0.250  0.529  0.618  1.0
  S  S20  1  0.250  0.222  0.254  1.0
  S  S21  1  0.750  0.778  0.746  1.0
  S  S22  1  0.750  0.278  0.754  1.0
  S  S23  1  0.250  0.722  0.246  1.0
  S  S24  1  0.750  0.256  0.017  1.0
  S  S25  1  0.250  0.744  0.983  1.0
  S  S26  1  0.250  0.244  0.517  1.0
  S  S27  1  0.750  0.756  0.483  1.0
[/CIF]
.