The structure described by MgCu2O4 is Spinel-like structured and crystallizes in the trigonal P3m1 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(10) and three equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Cu(4)O6 octahedra, and corners with six equivalent Cu(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-60°. In the second Mg site, Mg(2) is bonded to one O(2) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Cu(1)O6 octahedra, corners with three equivalent Cu(3)O6 octahedra, and corners with six equivalent Cu(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. In the third Mg site, Mg(3) is bonded to three equivalent O(1) and three equivalent O(11) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cu(6)O4 tetrahedra, edges with three equivalent Cu(1)O6 octahedra, and edges with three equivalent Cu(4)O6 octahedra. In the fourth Mg site, Mg(4) is bonded to one O(6) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Cu(2)O6 octahedra, corners with three equivalent Cu(5)O6 octahedra, and corners with six equivalent Cu(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-60°. In the fifth Mg site, Mg(5) is bonded to one O(9) and three equivalent O(3) atoms to form MgO4 tetrahedra that share corners with three equivalent Cu(2)O6 octahedra, corners with three equivalent Cu(3)O6 octahedra, and corners with six equivalent Cu(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-60°. In the sixth Mg site, Mg(6) is bonded to one O(12) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Cu(4)O6 octahedra, corners with three equivalent Cu(5)O6 octahedra, and corners with six equivalent Cu(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. There are six inequivalent Cu sites. In the first Cu site, Cu(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form CuO6 octahedra that share  a cornercorner with one Mg(2)O4 tetrahedra,  a cornercorner with one Cu(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(5)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Cu(3)O6 octahedra, and edges with four equivalent Cu(1)O6 octahedra. In the second Cu site, Cu(2) is bonded to one O(6), one O(9), two equivalent O(4), and two equivalent O(7) atoms to form CuO6 octahedra that share  a cornercorner with one Mg(4)O4 tetrahedra,  a cornercorner with one Mg(5)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Cu(3)O6 octahedra,  an edgeedge with one Cu(5)O6 octahedra, and edges with four equivalent Cu(2)O6 octahedra. In the third Cu site, Cu(3) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form CuO6 octahedra that share corners with three equivalent Mg(2)O4 tetrahedra, corners with three equivalent Mg(5)O4 tetrahedra, edges with three equivalent Cu(1)O6 octahedra, and edges with three equivalent Cu(2)O6 octahedra. In the fourth Cu site, Cu(4) is bonded to one O(10), one O(12), two equivalent O(11), and two equivalent O(8) atoms to form CuO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(6)O4 tetrahedra, corners with two equivalent Mg(4)O4 tetrahedra, corners with two equivalent Cu(6)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Cu(5)O6 octahedra, and edges with four equivalent Cu(4)O6 octahedra. In the fifth Cu site, Cu(5) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form CuO6 octahedra that share corners with three equivalent Mg(4)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Cu(2)O6 octahedra, and edges with three equivalent Cu(4)O6 octahedra. In the sixth Cu site, Cu(6) is bonded to one O(5) and three equivalent O(11) atoms to form CuO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Cu(1)O6 octahedra, and corners with six equivalent Cu(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-60°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Mg(3), and two equivalent Cu(1) atoms. In the second O site, O(2) is bonded to one Mg(2) and three equivalent Cu(1) atoms to form distorted corner-sharing OMgCu3 trigonal pyramids. In the third O site, O(3) is bonded to one Mg(5), one Cu(3), and two equivalent Cu(1) atoms to form a mixture of distorted corner and edge-sharing OMgCu3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(2), one Cu(3), and two equivalent Cu(2) atoms to form a mixture of distorted corner and edge-sharing OMgCu3 trigonal pyramids. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Cu(6) and three equivalent Cu(1) atoms. In the sixth O site, O(6) is bonded to one Mg(4) and three equivalent Cu(2) atoms to form a mixture of distorted corner and edge-sharing OMgCu3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(6), one Cu(5), and two equivalent Cu(2) atoms to form a mixture of distorted corner and edge-sharing OMgCu3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Mg(4), one Cu(5), and two equivalent Cu(4) atoms to form a mixture of distorted corner and edge-sharing OMgCu3 trigonal pyramids. In the ninth O site, O(9) is bonded to one Mg(5) and three equivalent Cu(2) atoms to form a mixture of distorted corner and edge-sharing OMgCu3 trigonal pyramids. In the tenth O site, O(10) is bonded to one Mg(1) and three equivalent Cu(4) atoms to form a mixture of distorted corner and edge-sharing OMgCu3 trigonal pyramids. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Mg(3), one Cu(6), and two equivalent Cu(4) atoms. In the twelfth O site, O(12) is bonded to one Mg(6) and three equivalent Cu(4) atoms to form distorted corner-sharing OMgCu3 trigonal pyramids. is represented by the CIF file [CIF]
data_Mg(CuO2)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.931
_cell_length_b   5.931
_cell_length_c   14.474
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   440.886
_cell_formula_units_Z   6
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  0.333  0.667  0.955  1.0
  Mg  Mg1  1  0.000  0.000  0.624  1.0
  Mg  Mg2  1  0.000  0.000  0.998  1.0
  Mg  Mg3  1  0.667  0.333  0.289  1.0
  Mg  Mg4  1  0.333  0.667  0.711  1.0
  Mg  Mg5  1  0.000  0.000  0.374  1.0
  Cu  Cu6  1  0.834  0.667  0.834  1.0
  Cu  Cu7  1  0.333  0.166  0.834  1.0
  Cu  Cu8  1  0.500  0.000  0.500  1.0
  Cu  Cu9  1  0.834  0.166  0.834  1.0
  Cu  Cu10  1  0.667  0.333  0.667  1.0
  Cu  Cu11  1  1.000  0.500  0.500  1.0
  Cu  Cu12  1  0.167  0.334  0.166  1.0
  Cu  Cu13  1  0.500  0.500  0.500  1.0
  Cu  Cu14  1  0.167  0.833  0.166  1.0
  Cu  Cu15  1  0.333  0.667  0.335  1.0
  Cu  Cu16  1  0.666  0.833  0.166  1.0
  Cu  Cu17  1  0.667  0.333  0.044  1.0
  O  O18  1  0.693  0.846  0.908  1.0
  O  O19  1  0.000  0.000  0.759  1.0
  O  O20  1  0.154  0.846  0.908  1.0
  O  O21  1  0.154  0.307  0.908  1.0
  O  O22  1  0.517  0.035  0.756  1.0
  O  O23  1  0.364  0.182  0.580  1.0
  O  O24  1  0.517  0.483  0.756  1.0
  O  O25  1  0.667  0.333  0.912  1.0
  O  O26  1  0.818  0.182  0.580  1.0
  O  O27  1  0.667  0.333  0.427  1.0
  O  O28  1  0.965  0.483  0.756  1.0
  O  O29  1  0.818  0.636  0.580  1.0
  O  O30  1  0.181  0.363  0.420  1.0
  O  O31  1  0.034  0.517  0.247  1.0
  O  O32  1  0.181  0.819  0.420  1.0
  O  O33  1  0.333  0.667  0.574  1.0
  O  O34  1  0.333  0.667  0.093  1.0
  O  O35  1  0.483  0.517  0.247  1.0
  O  O36  1  0.637  0.819  0.420  1.0
  O  O37  1  0.483  0.966  0.247  1.0
  O  O38  1  0.844  0.687  0.090  1.0
  O  O39  1  0.000  0.000  0.237  1.0
  O  O40  1  0.844  0.156  0.090  1.0
  O  O41  1  0.313  0.156  0.090  1.0
[/CIF]
.
The structure described by MgCu2O4 is Spinel-like structured and crystallizes in the trigonal P3m1 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(10) and three equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Cu(4)O6 octahedra, and corners with six equivalent Cu(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-60°. In the second Mg site, Mg(2) is bonded to one O(2) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Cu(1)O6 octahedra, corners with three equivalent Cu(3)O6 octahedra, and corners with six equivalent Cu(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. In the third Mg site, Mg(3) is bonded to three equivalent O(1) and three equivalent O(11) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cu(6)O4 tetrahedra, edges with three equivalent Cu(1)O6 octahedra, and edges with three equivalent Cu(4)O6 octahedra. In the fourth Mg site, Mg(4) is bonded to one O(6) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Cu(2)O6 octahedra, corners with three equivalent Cu(5)O6 octahedra, and corners with six equivalent Cu(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-60°. In the fifth Mg site, Mg(5) is bonded to one O(9) and three equivalent O(3) atoms to form MgO4 tetrahedra that share corners with three equivalent Cu(2)O6 octahedra, corners with three equivalent Cu(3)O6 octahedra, and corners with six equivalent Cu(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-60°. In the sixth Mg site, Mg(6) is bonded to one O(12) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Cu(4)O6 octahedra, corners with three equivalent Cu(5)O6 octahedra, and corners with six equivalent Cu(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. There are six inequivalent Cu sites. In the first Cu site, Cu(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form CuO6 octahedra that share  a cornercorner with one Mg(2)O4 tetrahedra,  a cornercorner with one Cu(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(5)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Cu(3)O6 octahedra, and edges with four equivalent Cu(1)O6 octahedra. In the second Cu site, Cu(2) is bonded to one O(6), one O(9), two equivalent O(4), and two equivalent O(7) atoms to form CuO6 octahedra that share  a cornercorner with one Mg(4)O4 tetrahedra,  a cornercorner with one Mg(5)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Cu(3)O6 octahedra,  an edgeedge with one Cu(5)O6 octahedra, and edges with four equivalent Cu(2)O6 octahedra. In the third Cu site, Cu(3) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form CuO6 octahedra that share corners with three equivalent Mg(2)O4 tetrahedra, corners with three equivalent Mg(5)O4 tetrahedra, edges with three equivalent Cu(1)O6 octahedra, and edges with three equivalent Cu(2)O6 octahedra. In the fourth Cu site, Cu(4) is bonded to one O(10), one O(12), two equivalent O(11), and two equivalent O(8) atoms to form CuO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(6)O4 tetrahedra, corners with two equivalent Mg(4)O4 tetrahedra, corners with two equivalent Cu(6)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Cu(5)O6 octahedra, and edges with four equivalent Cu(4)O6 octahedra. In the fifth Cu site, Cu(5) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form CuO6 octahedra that share corners with three equivalent Mg(4)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Cu(2)O6 octahedra, and edges with three equivalent Cu(4)O6 octahedra. In the sixth Cu site, Cu(6) is bonded to one O(5) and three equivalent O(11) atoms to form CuO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Cu(1)O6 octahedra, and corners with six equivalent Cu(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-60°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Mg(3), and two equivalent Cu(1) atoms. In the second O site, O(2) is bonded to one Mg(2) and three equivalent Cu(1) atoms to form distorted corner-sharing OMgCu3 trigonal pyramids. In the third O site, O(3) is bonded to one Mg(5), one Cu(3), and two equivalent Cu(1) atoms to form a mixture of distorted corner and edge-sharing OMgCu3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(2), one Cu(3), and two equivalent Cu(2) atoms to form a mixture of distorted corner and edge-sharing OMgCu3 trigonal pyramids. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Cu(6) and three equivalent Cu(1) atoms. In the sixth O site, O(6) is bonded to one Mg(4) and three equivalent Cu(2) atoms to form a mixture of distorted corner and edge-sharing OMgCu3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(6), one Cu(5), and two equivalent Cu(2) atoms to form a mixture of distorted corner and edge-sharing OMgCu3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Mg(4), one Cu(5), and two equivalent Cu(4) atoms to form a mixture of distorted corner and edge-sharing OMgCu3 trigonal pyramids. In the ninth O site, O(9) is bonded to one Mg(5) and three equivalent Cu(2) atoms to form a mixture of distorted corner and edge-sharing OMgCu3 trigonal pyramids. In the tenth O site, O(10) is bonded to one Mg(1) and three equivalent Cu(4) atoms to form a mixture of distorted corner and edge-sharing OMgCu3 trigonal pyramids. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Mg(3), one Cu(6), and two equivalent Cu(4) atoms. In the twelfth O site, O(12) is bonded to one Mg(6) and three equivalent Cu(4) atoms to form distorted corner-sharing OMgCu3 trigonal pyramids. is represented by the CIF file [CIF]
data_Mg(CuO2)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.931
_cell_length_b   5.931
_cell_length_c   14.474
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   440.886
_cell_formula_units_Z   6
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  0.333  0.667  0.955  1.0
  Mg  Mg1  1  0.000  0.000  0.624  1.0
  Mg  Mg2  1  0.000  0.000  0.998  1.0
  Mg  Mg3  1  0.667  0.333  0.289  1.0
  Mg  Mg4  1  0.333  0.667  0.711  1.0
  Mg  Mg5  1  0.000  0.000  0.374  1.0
  Cu  Cu6  1  0.834  0.667  0.834  1.0
  Cu  Cu7  1  0.333  0.166  0.834  1.0
  Cu  Cu8  1  0.500  0.000  0.500  1.0
  Cu  Cu9  1  0.834  0.166  0.834  1.0
  Cu  Cu10  1  0.667  0.333  0.667  1.0
  Cu  Cu11  1  1.000  0.500  0.500  1.0
  Cu  Cu12  1  0.167  0.334  0.166  1.0
  Cu  Cu13  1  0.500  0.500  0.500  1.0
  Cu  Cu14  1  0.167  0.833  0.166  1.0
  Cu  Cu15  1  0.333  0.667  0.335  1.0
  Cu  Cu16  1  0.666  0.833  0.166  1.0
  Cu  Cu17  1  0.667  0.333  0.044  1.0
  O  O18  1  0.693  0.846  0.908  1.0
  O  O19  1  0.000  0.000  0.759  1.0
  O  O20  1  0.154  0.846  0.908  1.0
  O  O21  1  0.154  0.307  0.908  1.0
  O  O22  1  0.517  0.035  0.756  1.0
  O  O23  1  0.364  0.182  0.580  1.0
  O  O24  1  0.517  0.483  0.756  1.0
  O  O25  1  0.667  0.333  0.912  1.0
  O  O26  1  0.818  0.182  0.580  1.0
  O  O27  1  0.667  0.333  0.427  1.0
  O  O28  1  0.965  0.483  0.756  1.0
  O  O29  1  0.818  0.636  0.580  1.0
  O  O30  1  0.181  0.363  0.420  1.0
  O  O31  1  0.034  0.517  0.247  1.0
  O  O32  1  0.181  0.819  0.420  1.0
  O  O33  1  0.333  0.667  0.574  1.0
  O  O34  1  0.333  0.667  0.093  1.0
  O  O35  1  0.483  0.517  0.247  1.0
  O  O36  1  0.637  0.819  0.420  1.0
  O  O37  1  0.483  0.966  0.247  1.0
  O  O38  1  0.844  0.687  0.090  1.0
  O  O39  1  0.000  0.000  0.237  1.0
  O  O40  1  0.844  0.156  0.090  1.0
  O  O41  1  0.313  0.156  0.090  1.0
[/CIF]
.