The structure described by Bi2MgO4 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(9) and three equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(5)O6 octahedra, corners with three equivalent Bi(5)O6 octahedra, and corners with six equivalent Bi(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-56°. In the second Mg site, Mg(2) is bonded to one O(2) and three equivalent O(3) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Bi(1)O6 octahedra, and corners with six equivalent Bi(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-58°. In the third Mg site, Mg(3) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Mg(2)O4 tetrahedra, corners with three equivalent Bi(4)O4 tetrahedra, edges with three equivalent Bi(1)O6 octahedra, and edges with three equivalent Bi(2)O6 octahedra. In the fourth Mg site, Mg(4) is bonded to one O(5) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Bi(2)O6 octahedra, corners with three equivalent Bi(3)O6 octahedra, and corners with six equivalent Bi(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-56°. In the fifth Mg site, Mg(5) 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 Bi(6)O4 tetrahedra, edges with three equivalent Bi(1)O6 octahedra, and edges with three equivalent Bi(5)O6 octahedra. In the sixth Mg site, Mg(6) is bonded to one O(12) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Bi(3)O6 octahedra, corners with three equivalent Bi(5)O6 octahedra, and corners with six equivalent Bi(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-56°. There are six inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one O(2), one O(6), two equivalent O(1), and two equivalent O(4) atoms to form BiO6 octahedra that share  a cornercorner with one Mg(2)O4 tetrahedra,  a cornercorner with one Bi(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Bi(4)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Mg(5)O6 octahedra, and edges with four equivalent Bi(1)O6 octahedra. In the second Bi site, Bi(2) is bonded to one O(10), one O(5), two equivalent O(3), and two equivalent O(8) atoms to form BiO6 octahedra that share  a cornercorner with one Mg(4)O4 tetrahedra,  a cornercorner with one Bi(4)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Bi(3)O6 octahedra, and edges with four equivalent Bi(2)O6 octahedra. In the third Bi site, Bi(3) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form BiO6 octahedra that share corners with three equivalent Mg(4)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Bi(2)O6 octahedra, and edges with three equivalent Bi(5)O6 octahedra. In the fourth Bi site, Bi(4) is bonded to one O(10) and three equivalent O(4) atoms to form BiO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Bi(2)O6 octahedra, and corners with six equivalent Bi(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-66°. In the fifth Bi site, Bi(5) is bonded to one O(12), one O(9), two equivalent O(11), and two equivalent O(7) atoms to form BiO6 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 Bi(6)O4 tetrahedra,  an edgeedge with one Mg(5)O6 octahedra,  an edgeedge with one Bi(3)O6 octahedra, and edges with four equivalent Bi(5)O6 octahedra. In the sixth Bi site, Bi(6) is bonded to one O(6) and three equivalent O(11) atoms to form BiO4 tetrahedra that share corners with three equivalent Mg(5)O6 octahedra, corners with three equivalent Bi(1)O6 octahedra, and corners with six equivalent Bi(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-65°. 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(5), and two equivalent Bi(1) atoms. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Mg(2) and three equivalent Bi(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Mg(3), and two equivalent Bi(2) atoms. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Mg(3), one Bi(4), and two equivalent Bi(1) atoms. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Mg(4) and three equivalent Bi(2) atoms. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Bi(6) and three equivalent Bi(1) atoms. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Mg(4), one Bi(3), and two equivalent Bi(5) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Mg(6), one Bi(3), and two equivalent Bi(2) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1) and three equivalent Bi(5) atoms. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Bi(4) and three equivalent Bi(2) atoms. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Mg(5), one Bi(6), and two equivalent Bi(5) atoms. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Mg(6) and three equivalent Bi(5) atoms. is represented by the CIF file [CIF]
data_Mg(BiO2)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.891
_cell_length_b   6.891
_cell_length_c   16.363
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   672.828
_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  0.000  0.000  0.958  1.0
  Mg  Mg1  1  0.667  0.333  0.622  1.0
  Mg  Mg2  1  0.333  0.667  0.668  1.0
  Mg  Mg3  1  0.333  0.667  0.292  1.0
  Mg  Mg4  1  0.667  0.333  0.998  1.0
  Mg  Mg5  1  0.667  0.333  0.375  1.0
  Bi  Bi6  1  0.995  0.497  0.834  1.0
  Bi  Bi7  1  0.503  0.497  0.834  1.0
  Bi  Bi8  1  0.659  0.829  0.504  1.0
  Bi  Bi9  1  0.503  0.005  0.834  1.0
  Bi  Bi10  1  0.171  0.829  0.504  1.0
  Bi  Bi11  1  0.000  0.000  0.335  1.0
  Bi  Bi12  1  0.000  0.000  0.718  1.0
  Bi  Bi13  1  0.336  0.168  0.166  1.0
  Bi  Bi14  1  0.171  0.341  0.504  1.0
  Bi  Bi15  1  0.832  0.168  0.166  1.0
  Bi  Bi16  1  0.832  0.664  0.166  1.0
  Bi  Bi17  1  0.333  0.667  0.050  1.0
  O  O18  1  0.343  0.172  0.919  1.0
  O  O19  1  0.667  0.333  0.748  1.0
  O  O20  1  0.828  0.172  0.919  1.0
  O  O21  1  0.828  0.657  0.919  1.0
  O  O22  1  0.019  0.509  0.588  1.0
  O  O23  1  0.188  0.377  0.745  1.0
  O  O24  1  0.333  0.667  0.420  1.0
  O  O25  1  0.188  0.812  0.745  1.0
  O  O26  1  0.333  0.667  0.917  1.0
  O  O27  1  0.491  0.509  0.588  1.0
  O  O28  1  0.491  0.981  0.588  1.0
  O  O29  1  0.623  0.812  0.745  1.0
  O  O30  1  0.655  0.827  0.247  1.0
  O  O31  1  0.833  0.665  0.415  1.0
  O  O32  1  0.833  0.167  0.415  1.0
  O  O33  1  0.000  0.000  0.082  1.0
  O  O34  1  0.000  0.000  0.586  1.0
  O  O35  1  0.173  0.827  0.247  1.0
  O  O36  1  0.173  0.345  0.247  1.0
  O  O37  1  0.335  0.167  0.415  1.0
  O  O38  1  0.523  0.046  0.076  1.0
  O  O39  1  0.523  0.477  0.076  1.0
  O  O40  1  0.667  0.333  0.249  1.0
  O  O41  1  0.954  0.477  0.076  1.0
[/CIF]
.
The structure described by Bi2MgO4 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(9) and three equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(5)O6 octahedra, corners with three equivalent Bi(5)O6 octahedra, and corners with six equivalent Bi(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-56°. In the second Mg site, Mg(2) is bonded to one O(2) and three equivalent O(3) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Bi(1)O6 octahedra, and corners with six equivalent Bi(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-58°. In the third Mg site, Mg(3) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Mg(2)O4 tetrahedra, corners with three equivalent Bi(4)O4 tetrahedra, edges with three equivalent Bi(1)O6 octahedra, and edges with three equivalent Bi(2)O6 octahedra. In the fourth Mg site, Mg(4) is bonded to one O(5) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Bi(2)O6 octahedra, corners with three equivalent Bi(3)O6 octahedra, and corners with six equivalent Bi(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-56°. In the fifth Mg site, Mg(5) 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 Bi(6)O4 tetrahedra, edges with three equivalent Bi(1)O6 octahedra, and edges with three equivalent Bi(5)O6 octahedra. In the sixth Mg site, Mg(6) is bonded to one O(12) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Bi(3)O6 octahedra, corners with three equivalent Bi(5)O6 octahedra, and corners with six equivalent Bi(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-56°. There are six inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one O(2), one O(6), two equivalent O(1), and two equivalent O(4) atoms to form BiO6 octahedra that share  a cornercorner with one Mg(2)O4 tetrahedra,  a cornercorner with one Bi(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Bi(4)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Mg(5)O6 octahedra, and edges with four equivalent Bi(1)O6 octahedra. In the second Bi site, Bi(2) is bonded to one O(10), one O(5), two equivalent O(3), and two equivalent O(8) atoms to form BiO6 octahedra that share  a cornercorner with one Mg(4)O4 tetrahedra,  a cornercorner with one Bi(4)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Bi(3)O6 octahedra, and edges with four equivalent Bi(2)O6 octahedra. In the third Bi site, Bi(3) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form BiO6 octahedra that share corners with three equivalent Mg(4)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Bi(2)O6 octahedra, and edges with three equivalent Bi(5)O6 octahedra. In the fourth Bi site, Bi(4) is bonded to one O(10) and three equivalent O(4) atoms to form BiO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Bi(2)O6 octahedra, and corners with six equivalent Bi(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-66°. In the fifth Bi site, Bi(5) is bonded to one O(12), one O(9), two equivalent O(11), and two equivalent O(7) atoms to form BiO6 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 Bi(6)O4 tetrahedra,  an edgeedge with one Mg(5)O6 octahedra,  an edgeedge with one Bi(3)O6 octahedra, and edges with four equivalent Bi(5)O6 octahedra. In the sixth Bi site, Bi(6) is bonded to one O(6) and three equivalent O(11) atoms to form BiO4 tetrahedra that share corners with three equivalent Mg(5)O6 octahedra, corners with three equivalent Bi(1)O6 octahedra, and corners with six equivalent Bi(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-65°. 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(5), and two equivalent Bi(1) atoms. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Mg(2) and three equivalent Bi(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Mg(3), and two equivalent Bi(2) atoms. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Mg(3), one Bi(4), and two equivalent Bi(1) atoms. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Mg(4) and three equivalent Bi(2) atoms. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Bi(6) and three equivalent Bi(1) atoms. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Mg(4), one Bi(3), and two equivalent Bi(5) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Mg(6), one Bi(3), and two equivalent Bi(2) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1) and three equivalent Bi(5) atoms. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Bi(4) and three equivalent Bi(2) atoms. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Mg(5), one Bi(6), and two equivalent Bi(5) atoms. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Mg(6) and three equivalent Bi(5) atoms. is represented by the CIF file [CIF]
data_Mg(BiO2)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.891
_cell_length_b   6.891
_cell_length_c   16.363
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   672.828
_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  0.000  0.000  0.958  1.0
  Mg  Mg1  1  0.667  0.333  0.622  1.0
  Mg  Mg2  1  0.333  0.667  0.668  1.0
  Mg  Mg3  1  0.333  0.667  0.292  1.0
  Mg  Mg4  1  0.667  0.333  0.998  1.0
  Mg  Mg5  1  0.667  0.333  0.375  1.0
  Bi  Bi6  1  0.995  0.497  0.834  1.0
  Bi  Bi7  1  0.503  0.497  0.834  1.0
  Bi  Bi8  1  0.659  0.829  0.504  1.0
  Bi  Bi9  1  0.503  0.005  0.834  1.0
  Bi  Bi10  1  0.171  0.829  0.504  1.0
  Bi  Bi11  1  0.000  0.000  0.335  1.0
  Bi  Bi12  1  0.000  0.000  0.718  1.0
  Bi  Bi13  1  0.336  0.168  0.166  1.0
  Bi  Bi14  1  0.171  0.341  0.504  1.0
  Bi  Bi15  1  0.832  0.168  0.166  1.0
  Bi  Bi16  1  0.832  0.664  0.166  1.0
  Bi  Bi17  1  0.333  0.667  0.050  1.0
  O  O18  1  0.343  0.172  0.919  1.0
  O  O19  1  0.667  0.333  0.748  1.0
  O  O20  1  0.828  0.172  0.919  1.0
  O  O21  1  0.828  0.657  0.919  1.0
  O  O22  1  0.019  0.509  0.588  1.0
  O  O23  1  0.188  0.377  0.745  1.0
  O  O24  1  0.333  0.667  0.420  1.0
  O  O25  1  0.188  0.812  0.745  1.0
  O  O26  1  0.333  0.667  0.917  1.0
  O  O27  1  0.491  0.509  0.588  1.0
  O  O28  1  0.491  0.981  0.588  1.0
  O  O29  1  0.623  0.812  0.745  1.0
  O  O30  1  0.655  0.827  0.247  1.0
  O  O31  1  0.833  0.665  0.415  1.0
  O  O32  1  0.833  0.167  0.415  1.0
  O  O33  1  0.000  0.000  0.082  1.0
  O  O34  1  0.000  0.000  0.586  1.0
  O  O35  1  0.173  0.827  0.247  1.0
  O  O36  1  0.173  0.345  0.247  1.0
  O  O37  1  0.335  0.167  0.415  1.0
  O  O38  1  0.523  0.046  0.076  1.0
  O  O39  1  0.523  0.477  0.076  1.0
  O  O40  1  0.667  0.333  0.249  1.0
  O  O41  1  0.954  0.477  0.076  1.0
[/CIF]
.