The crystal structure described by MgCu3O4 crystallizes in the orthorhombic Pmm2 space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 20°. In the second Mg site, Mg(2) is bonded to two equivalent O(3), two equivalent O(4), and two equivalent O(7) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 19°. There are five inequivalent Cu sites. In the first Cu site, Cu(1) is bonded in a distorted rectangular see-saw-like geometry to one O(3), one O(5), and two equivalent O(1) atoms. In the second Cu site, Cu(2) is bonded in a distorted rectangular see-saw-like geometry to one O(4), one O(6), and two equivalent O(2) atoms. In the third Cu site, Cu(3) is bonded in a distorted rectangular see-saw-like geometry to one O(1), one O(7), and two equivalent O(3) atoms. In the fourth Cu site, Cu(4) is bonded in a distorted rectangular see-saw-like geometry to one O(2), one O(7), and two equivalent O(4) atoms. In the fifth Cu site, Cu(5) is bonded to two equivalent O(5) and four equivalent O(1) atoms to form a mixture of corner and edge-sharing CuO6 octahedra. The corner-sharing octahedral tilt angles are 24°. There are seven inequivalent O sites. In the first O site, O(1) is bonded to one Cu(3), two equivalent Cu(1), and two equivalent Cu(5) atoms to form distorted OCu5 square pyramids that share corners with six equivalent O(1)Cu5 square pyramids,  an edgeedge with one O(1)Cu5 square pyramid, and edges with two equivalent O(3)Mg2Cu3 square pyramids. In the second O site, O(2) is bonded to two equivalent Mg(1), one Cu(4), and two equivalent Cu(2) atoms to form a mixture of corner and edge-sharing OMg2Cu3 square pyramids. In the third O site, O(3) is bonded to two equivalent Mg(2), one Cu(1), and two equivalent Cu(3) atoms to form OMg2Cu3 square pyramids that share corners with two equivalent O(4)Mg2Cu3 square pyramids, corners with four equivalent O(3)Mg2Cu3 square pyramids,  an edgeedge with one O(4)Mg2Cu3 square pyramid, and edges with two equivalent O(1)Cu5 square pyramids. In the fourth O site, O(4) is bonded to two equivalent Mg(2), one Cu(2), and two equivalent Cu(4) atoms to form a mixture of corner and edge-sharing OMg2Cu3 square pyramids. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to two equivalent Cu(1) and two equivalent Cu(5) atoms. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to two equivalent Mg(1) and two equivalent Cu(2) atoms. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to two equivalent Mg(2), one Cu(3), and one Cu(4) atom. is represented by the CIF card [CIF]
data_MgCu3O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.239
_cell_length_b   4.029
_cell_length_c   18.655
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   243.462
_cell_formula_units_Z   3
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
  Mg  Mg0  1  0.640  0.500  0.500  1.0
  Mg  Mg1  1  0.360  0.000  0.750  1.0
  Mg  Mg2  1  0.360  0.000  0.250  1.0
  Cu  Cu3  1  0.182  0.000  0.917  1.0
  Cu  Cu4  1  0.177  0.000  0.418  1.0
  Cu  Cu5  1  0.182  0.000  0.083  1.0
  Cu  Cu6  1  0.177  0.000  0.582  1.0
  Cu  Cu7  1  0.813  0.500  0.833  1.0
  Cu  Cu8  1  0.822  0.500  0.332  1.0
  Cu  Cu9  1  0.822  0.500  0.668  1.0
  Cu  Cu10  1  0.813  0.500  0.167  1.0
  Cu  Cu11  1  0.652  0.500  0.000  1.0
  O  O12  1  0.133  0.500  0.920  1.0
  O  O13  1  0.127  0.500  0.423  1.0
  O  O14  1  0.133  0.500  0.080  1.0
  O  O15  1  0.127  0.500  0.577  1.0
  O  O16  1  0.880  0.000  0.828  1.0
  O  O17  1  0.872  0.000  0.328  1.0
  O  O18  1  0.872  0.000  0.672  1.0
  O  O19  1  0.880  0.000  0.172  1.0
  O  O20  1  0.521  0.000  0.000  1.0
  O  O21  1  0.530  0.000  0.500  1.0
  O  O22  1  0.463  0.500  0.749  1.0
  O  O23  1  0.463  0.500  0.251  1.0
[/CIF]
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The crystal structure described by MgCu3O4 crystallizes in the orthorhombic Pmm2 space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 20°. In the second Mg site, Mg(2) is bonded to two equivalent O(3), two equivalent O(4), and two equivalent O(7) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 19°. There are five inequivalent Cu sites. In the first Cu site, Cu(1) is bonded in a distorted rectangular see-saw-like geometry to one O(3), one O(5), and two equivalent O(1) atoms. In the second Cu site, Cu(2) is bonded in a distorted rectangular see-saw-like geometry to one O(4), one O(6), and two equivalent O(2) atoms. In the third Cu site, Cu(3) is bonded in a distorted rectangular see-saw-like geometry to one O(1), one O(7), and two equivalent O(3) atoms. In the fourth Cu site, Cu(4) is bonded in a distorted rectangular see-saw-like geometry to one O(2), one O(7), and two equivalent O(4) atoms. In the fifth Cu site, Cu(5) is bonded to two equivalent O(5) and four equivalent O(1) atoms to form a mixture of corner and edge-sharing CuO6 octahedra. The corner-sharing octahedral tilt angles are 24°. There are seven inequivalent O sites. In the first O site, O(1) is bonded to one Cu(3), two equivalent Cu(1), and two equivalent Cu(5) atoms to form distorted OCu5 square pyramids that share corners with six equivalent O(1)Cu5 square pyramids,  an edgeedge with one O(1)Cu5 square pyramid, and edges with two equivalent O(3)Mg2Cu3 square pyramids. In the second O site, O(2) is bonded to two equivalent Mg(1), one Cu(4), and two equivalent Cu(2) atoms to form a mixture of corner and edge-sharing OMg2Cu3 square pyramids. In the third O site, O(3) is bonded to two equivalent Mg(2), one Cu(1), and two equivalent Cu(3) atoms to form OMg2Cu3 square pyramids that share corners with two equivalent O(4)Mg2Cu3 square pyramids, corners with four equivalent O(3)Mg2Cu3 square pyramids,  an edgeedge with one O(4)Mg2Cu3 square pyramid, and edges with two equivalent O(1)Cu5 square pyramids. In the fourth O site, O(4) is bonded to two equivalent Mg(2), one Cu(2), and two equivalent Cu(4) atoms to form a mixture of corner and edge-sharing OMg2Cu3 square pyramids. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to two equivalent Cu(1) and two equivalent Cu(5) atoms. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to two equivalent Mg(1) and two equivalent Cu(2) atoms. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to two equivalent Mg(2), one Cu(3), and one Cu(4) atom. is represented by the CIF card [CIF]
data_MgCu3O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.239
_cell_length_b   4.029
_cell_length_c   18.655
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   243.462
_cell_formula_units_Z   3
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
  Mg  Mg0  1  0.640  0.500  0.500  1.0
  Mg  Mg1  1  0.360  0.000  0.750  1.0
  Mg  Mg2  1  0.360  0.000  0.250  1.0
  Cu  Cu3  1  0.182  0.000  0.917  1.0
  Cu  Cu4  1  0.177  0.000  0.418  1.0
  Cu  Cu5  1  0.182  0.000  0.083  1.0
  Cu  Cu6  1  0.177  0.000  0.582  1.0
  Cu  Cu7  1  0.813  0.500  0.833  1.0
  Cu  Cu8  1  0.822  0.500  0.332  1.0
  Cu  Cu9  1  0.822  0.500  0.668  1.0
  Cu  Cu10  1  0.813  0.500  0.167  1.0
  Cu  Cu11  1  0.652  0.500  0.000  1.0
  O  O12  1  0.133  0.500  0.920  1.0
  O  O13  1  0.127  0.500  0.423  1.0
  O  O14  1  0.133  0.500  0.080  1.0
  O  O15  1  0.127  0.500  0.577  1.0
  O  O16  1  0.880  0.000  0.828  1.0
  O  O17  1  0.872  0.000  0.328  1.0
  O  O18  1  0.872  0.000  0.672  1.0
  O  O19  1  0.880  0.000  0.172  1.0
  O  O20  1  0.521  0.000  0.000  1.0
  O  O21  1  0.530  0.000  0.500  1.0
  O  O22  1  0.463  0.500  0.749  1.0
  O  O23  1  0.463  0.500  0.251  1.0
[/CIF]
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