The structure described by MgLu2Se4 crystallizes in the orthorhombic Pnma space group. Mg(1) is bonded to two equivalent Se(3), two equivalent Se(4), and three equivalent Se(1) atoms to form distorted MgSe7 pentagonal bipyramids that share corners with four equivalent Lu(1)Se6 octahedra, corners with four equivalent Lu(2)Se6 octahedra,  an edgeedge with one Lu(1)Se6 octahedra, edges with four equivalent Lu(2)Se6 octahedra, edges with two equivalent Mg(1)Se7 pentagonal bipyramids, and faces with two equivalent Mg(1)Se7 pentagonal bipyramids. The corner-sharing octahedral tilt angles range from 10-65°. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one Se(3), two equivalent Se(4), and three equivalent Se(2) atoms to form LuSe6 octahedra that share corners with three equivalent Lu(2)Se6 octahedra, corners with four equivalent Mg(1)Se7 pentagonal bipyramids, edges with two equivalent Lu(2)Se6 octahedra, edges with four equivalent Lu(1)Se6 octahedra, and  an edgeedge with one Mg(1)Se7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 50-60°. In the second Lu site, Lu(2) is bonded to one Se(2), one Se(4), two equivalent Se(1), and two equivalent Se(3) atoms to form LuSe6 octahedra that share corners with three equivalent Lu(1)Se6 octahedra, corners with four equivalent Mg(1)Se7 pentagonal bipyramids, edges with two equivalent Lu(1)Se6 octahedra, edges with two equivalent Lu(2)Se6 octahedra, and edges with four equivalent Mg(1)Se7 pentagonal bipyramids. The corner-sharing octahedral tilt angles range from 50-60°. There are four inequivalent Se sites. In the first Se site, Se(1) is bonded to three equivalent Mg(1) and two equivalent Lu(2) atoms to form SeLu2Mg3 square pyramids that share corners with two equivalent Se(4)Lu3Mg2 square pyramids, corners with six equivalent Se(3)Lu3Mg2 trigonal bipyramids, edges with three equivalent Se(4)Lu3Mg2 square pyramids, edges with four equivalent Se(1)Lu2Mg3 square pyramids, and edges with two equivalent Se(3)Lu3Mg2 trigonal bipyramids. In the second Se site, Se(2) is bonded in a rectangular see-saw-like geometry to one Lu(2) and three equivalent Lu(1) atoms. In the third Se site, Se(3) is bonded to two equivalent Mg(1), one Lu(1), and two equivalent Lu(2) atoms to form distorted SeLu3Mg2 trigonal bipyramids that share corners with two equivalent Se(4)Lu3Mg2 square pyramids, corners with six equivalent Se(1)Lu2Mg3 square pyramids, edges with two equivalent Se(1)Lu2Mg3 square pyramids, edges with three equivalent Se(4)Lu3Mg2 square pyramids, and edges with two equivalent Se(3)Lu3Mg2 trigonal bipyramids. In the fourth Se site, Se(4) is bonded to two equivalent Mg(1), one Lu(2), and two equivalent Lu(1) atoms to form SeLu3Mg2 square pyramids that share corners with two equivalent Se(1)Lu2Mg3 square pyramids, corners with two equivalent Se(3)Lu3Mg2 trigonal bipyramids, edges with two equivalent Se(4)Lu3Mg2 square pyramids, edges with three equivalent Se(1)Lu2Mg3 square pyramids, and edges with three equivalent Se(3)Lu3Mg2 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Lu2MgSe4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.918
_cell_length_b   12.999
_cell_length_c   13.607
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   693.022
_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  0.110  0.081  1.0
  Lu  Lu1  1  0.750  0.890  0.919  1.0
  Lu  Lu2  1  0.750  0.390  0.581  1.0
  Lu  Lu3  1  0.250  0.610  0.419  1.0
  Lu  Lu4  1  0.250  0.145  0.703  1.0
  Lu  Lu5  1  0.750  0.855  0.297  1.0
  Lu  Lu6  1  0.750  0.355  0.203  1.0
  Lu  Lu7  1  0.250  0.645  0.797  1.0
  Mg  Mg8  1  0.750  0.126  0.424  1.0
  Mg  Mg9  1  0.250  0.874  0.576  1.0
  Mg  Mg10  1  0.250  0.374  0.924  1.0
  Mg  Mg11  1  0.750  0.626  0.076  1.0
  Se  Se12  1  0.750  0.023  0.610  1.0
  Se  Se13  1  0.250  0.977  0.390  1.0
  Se  Se14  1  0.250  0.477  0.110  1.0
  Se  Se15  1  0.750  0.523  0.890  1.0
  Se  Se16  1  0.250  0.035  0.881  1.0
  Se  Se17  1  0.750  0.965  0.119  1.0
  Se  Se18  1  0.750  0.465  0.381  1.0
  Se  Se19  1  0.250  0.535  0.619  1.0
  Se  Se20  1  0.250  0.215  0.263  1.0
  Se  Se21  1  0.750  0.785  0.737  1.0
  Se  Se22  1  0.750  0.285  0.763  1.0
  Se  Se23  1  0.250  0.715  0.237  1.0
  Se  Se24  1  0.750  0.250  0.020  1.0
  Se  Se25  1  0.250  0.750  0.980  1.0
  Se  Se26  1  0.250  0.250  0.520  1.0
  Se  Se27  1  0.750  0.750  0.480  1.0
[/CIF]
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The structure described by MgLu2Se4 crystallizes in the orthorhombic Pnma space group. Mg(1) is bonded to two equivalent Se(3), two equivalent Se(4), and three equivalent Se(1) atoms to form distorted MgSe7 pentagonal bipyramids that share corners with four equivalent Lu(1)Se6 octahedra, corners with four equivalent Lu(2)Se6 octahedra,  an edgeedge with one Lu(1)Se6 octahedra, edges with four equivalent Lu(2)Se6 octahedra, edges with two equivalent Mg(1)Se7 pentagonal bipyramids, and faces with two equivalent Mg(1)Se7 pentagonal bipyramids. The corner-sharing octahedral tilt angles range from 10-65°. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one Se(3), two equivalent Se(4), and three equivalent Se(2) atoms to form LuSe6 octahedra that share corners with three equivalent Lu(2)Se6 octahedra, corners with four equivalent Mg(1)Se7 pentagonal bipyramids, edges with two equivalent Lu(2)Se6 octahedra, edges with four equivalent Lu(1)Se6 octahedra, and  an edgeedge with one Mg(1)Se7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 50-60°. In the second Lu site, Lu(2) is bonded to one Se(2), one Se(4), two equivalent Se(1), and two equivalent Se(3) atoms to form LuSe6 octahedra that share corners with three equivalent Lu(1)Se6 octahedra, corners with four equivalent Mg(1)Se7 pentagonal bipyramids, edges with two equivalent Lu(1)Se6 octahedra, edges with two equivalent Lu(2)Se6 octahedra, and edges with four equivalent Mg(1)Se7 pentagonal bipyramids. The corner-sharing octahedral tilt angles range from 50-60°. There are four inequivalent Se sites. In the first Se site, Se(1) is bonded to three equivalent Mg(1) and two equivalent Lu(2) atoms to form SeLu2Mg3 square pyramids that share corners with two equivalent Se(4)Lu3Mg2 square pyramids, corners with six equivalent Se(3)Lu3Mg2 trigonal bipyramids, edges with three equivalent Se(4)Lu3Mg2 square pyramids, edges with four equivalent Se(1)Lu2Mg3 square pyramids, and edges with two equivalent Se(3)Lu3Mg2 trigonal bipyramids. In the second Se site, Se(2) is bonded in a rectangular see-saw-like geometry to one Lu(2) and three equivalent Lu(1) atoms. In the third Se site, Se(3) is bonded to two equivalent Mg(1), one Lu(1), and two equivalent Lu(2) atoms to form distorted SeLu3Mg2 trigonal bipyramids that share corners with two equivalent Se(4)Lu3Mg2 square pyramids, corners with six equivalent Se(1)Lu2Mg3 square pyramids, edges with two equivalent Se(1)Lu2Mg3 square pyramids, edges with three equivalent Se(4)Lu3Mg2 square pyramids, and edges with two equivalent Se(3)Lu3Mg2 trigonal bipyramids. In the fourth Se site, Se(4) is bonded to two equivalent Mg(1), one Lu(2), and two equivalent Lu(1) atoms to form SeLu3Mg2 square pyramids that share corners with two equivalent Se(1)Lu2Mg3 square pyramids, corners with two equivalent Se(3)Lu3Mg2 trigonal bipyramids, edges with two equivalent Se(4)Lu3Mg2 square pyramids, edges with three equivalent Se(1)Lu2Mg3 square pyramids, and edges with three equivalent Se(3)Lu3Mg2 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Lu2MgSe4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.918
_cell_length_b   12.999
_cell_length_c   13.607
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   693.022
_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  0.110  0.081  1.0
  Lu  Lu1  1  0.750  0.890  0.919  1.0
  Lu  Lu2  1  0.750  0.390  0.581  1.0
  Lu  Lu3  1  0.250  0.610  0.419  1.0
  Lu  Lu4  1  0.250  0.145  0.703  1.0
  Lu  Lu5  1  0.750  0.855  0.297  1.0
  Lu  Lu6  1  0.750  0.355  0.203  1.0
  Lu  Lu7  1  0.250  0.645  0.797  1.0
  Mg  Mg8  1  0.750  0.126  0.424  1.0
  Mg  Mg9  1  0.250  0.874  0.576  1.0
  Mg  Mg10  1  0.250  0.374  0.924  1.0
  Mg  Mg11  1  0.750  0.626  0.076  1.0
  Se  Se12  1  0.750  0.023  0.610  1.0
  Se  Se13  1  0.250  0.977  0.390  1.0
  Se  Se14  1  0.250  0.477  0.110  1.0
  Se  Se15  1  0.750  0.523  0.890  1.0
  Se  Se16  1  0.250  0.035  0.881  1.0
  Se  Se17  1  0.750  0.965  0.119  1.0
  Se  Se18  1  0.750  0.465  0.381  1.0
  Se  Se19  1  0.250  0.535  0.619  1.0
  Se  Se20  1  0.250  0.215  0.263  1.0
  Se  Se21  1  0.750  0.785  0.737  1.0
  Se  Se22  1  0.750  0.285  0.763  1.0
  Se  Se23  1  0.250  0.715  0.237  1.0
  Se  Se24  1  0.750  0.250  0.020  1.0
  Se  Se25  1  0.250  0.750  0.980  1.0
  Se  Se26  1  0.250  0.250  0.520  1.0
  Se  Se27  1  0.750  0.750  0.480  1.0
[/CIF]
.