The structure described by MgAl2O4 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(2)O6 octahedra, corners with three equivalent Al(4)O6 octahedra, and corners with six equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-61°. In the second Mg site, Mg(2) 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 Al(6)O4 tetrahedra, edges with three equivalent Al(1)O6 octahedra, and edges with three equivalent Al(4)O6 octahedra. In the third Mg site, Mg(3) is bonded to one O(2) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(4)O6 octahedra, corners with three equivalent Al(1)O6 octahedra, and corners with six equivalent Al(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. In the fourth Mg site, Mg(4) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Mg(3)O4 tetrahedra, corners with three equivalent Al(5)O4 tetrahedra, edges with three equivalent Al(1)O6 octahedra, and edges with three equivalent Al(2)O6 octahedra. In the fifth Mg site, Mg(5) is bonded to one O(6) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Al(2)O6 octahedra, corners with three equivalent Al(3)O6 octahedra, and corners with six equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. 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 Al(3)O6 octahedra, corners with three equivalent Al(4)O6 octahedra, and corners with six equivalent Al(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-61°. There are six inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form AlO6 octahedra that share  a cornercorner with one Mg(3)O4 tetrahedra,  a cornercorner with one Al(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Al(5)O4 tetrahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Mg(4)O6 octahedra, and edges with four equivalent Al(1)O6 octahedra. In the second Al site, Al(2) is bonded to one O(6), one O(9), two equivalent O(4), and two equivalent O(8) atoms to form AlO6 octahedra that share  a cornercorner with one Mg(5)O4 tetrahedra,  a cornercorner with one Al(5)O4 tetrahedra, corners with two equivalent Mg(3)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Mg(4)O6 octahedra,  an edgeedge with one Al(3)O6 octahedra, and edges with four equivalent Al(2)O6 octahedra. In the third Al site, Al(3) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form AlO6 octahedra that share corners with three equivalent Mg(5)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Al(2)O6 octahedra, and edges with three equivalent Al(4)O6 octahedra. In the fourth Al site, Al(4) is bonded to one O(10), one O(12), two equivalent O(11), and two equivalent O(7) atoms to form AlO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(6)O4 tetrahedra, corners with two equivalent Mg(5)O4 tetrahedra, corners with two equivalent Al(6)O4 tetrahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Al(3)O6 octahedra, and edges with four equivalent Al(4)O6 octahedra. In the fifth Al site, Al(5) is bonded to one O(9) and three equivalent O(3) atoms to form AlO4 tetrahedra that share corners with three equivalent Mg(4)O6 octahedra, corners with three equivalent Al(2)O6 octahedra, and corners with six equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-60°. In the sixth Al site, Al(6) is bonded to one O(5) and three equivalent O(11) atoms to form AlO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra, corners with three equivalent Al(1)O6 octahedra, and corners with six equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-61°. 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(2), and two equivalent Al(1) atoms. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Mg(3) and three equivalent Al(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Mg(4), one Al(5), and two equivalent Al(1) atoms. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(3), one Mg(4), and two equivalent Al(2) atoms. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Al(6) and three equivalent Al(1) atoms. In the sixth O site, O(6) is bonded to one Mg(5) and three equivalent Al(2) atoms to form distorted corner-sharing OMgAl3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(5), one Al(3), and two equivalent Al(4) atoms to form a mixture of distorted corner and edge-sharing OMgAl3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Mg(6), one Al(3), and two equivalent Al(2) atoms to form a mixture of distorted corner and edge-sharing OMgAl3 tetrahedra. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Al(5) and three equivalent Al(2) atoms. In the tenth O site, O(10) is bonded to one Mg(1) and three equivalent Al(4) atoms to form a mixture of distorted corner and edge-sharing OMgAl3 trigonal pyramids. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Al(6), and two equivalent Al(4) atoms. In the twelfth O site, O(12) is bonded to one Mg(6) and three equivalent Al(4) atoms to form corner-sharing OMgAl3 tetrahedra. is represented by the CIF file [CIF]
data_MgAl2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.763
_cell_length_b   5.763
_cell_length_c   14.185
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   408.043
_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  0.999  1.0
  Mg  Mg2  1  0.000  0.000  0.621  1.0
  Mg  Mg3  1  0.667  0.333  0.664  1.0
  Mg  Mg4  1  0.667  0.333  0.291  1.0
  Mg  Mg5  1  0.000  0.000  0.378  1.0
  Al  Al6  1  0.838  0.162  0.834  1.0
  Al  Al7  1  0.503  0.006  0.500  1.0
  Al  Al8  1  0.324  0.162  0.834  1.0
  Al  Al9  1  0.503  0.497  0.500  1.0
  Al  Al10  1  0.994  0.497  0.500  1.0
  Al  Al11  1  0.838  0.676  0.834  1.0
  Al  Al12  1  0.333  0.667  0.335  1.0
  Al  Al13  1  0.169  0.831  0.168  1.0
  Al  Al14  1  0.333  0.667  0.714  1.0
  Al  Al15  1  0.662  0.831  0.168  1.0
  Al  Al16  1  0.169  0.338  0.168  1.0
  Al  Al17  1  0.667  0.333  0.043  1.0
  O  O18  1  0.694  0.847  0.906  1.0
  O  O19  1  0.000  0.000  0.760  1.0
  O  O20  1  0.153  0.847  0.906  1.0
  O  O21  1  0.153  0.306  0.906  1.0
  O  O22  1  0.507  0.014  0.758  1.0
  O  O23  1  0.359  0.179  0.570  1.0
  O  O24  1  0.667  0.333  0.912  1.0
  O  O25  1  0.507  0.493  0.758  1.0
  O  O26  1  0.667  0.333  0.427  1.0
  O  O27  1  0.821  0.179  0.570  1.0
  O  O28  1  0.986  0.493  0.758  1.0
  O  O29  1  0.821  0.641  0.570  1.0
  O  O30  1  0.038  0.519  0.246  1.0
  O  O31  1  0.187  0.374  0.422  1.0
  O  O32  1  0.333  0.667  0.583  1.0
  O  O33  1  0.481  0.519  0.246  1.0
  O  O34  1  0.187  0.813  0.422  1.0
  O  O35  1  0.333  0.667  0.096  1.0
  O  O36  1  0.481  0.962  0.246  1.0
  O  O37  1  0.626  0.813  0.422  1.0
  O  O38  1  0.836  0.673  0.091  1.0
  O  O39  1  0.000  0.000  0.233  1.0
  O  O40  1  0.836  0.164  0.091  1.0
  O  O41  1  0.327  0.164  0.091  1.0
[/CIF]
.
The structure described by MgAl2O4 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(2)O6 octahedra, corners with three equivalent Al(4)O6 octahedra, and corners with six equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-61°. In the second Mg site, Mg(2) 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 Al(6)O4 tetrahedra, edges with three equivalent Al(1)O6 octahedra, and edges with three equivalent Al(4)O6 octahedra. In the third Mg site, Mg(3) is bonded to one O(2) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(4)O6 octahedra, corners with three equivalent Al(1)O6 octahedra, and corners with six equivalent Al(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. In the fourth Mg site, Mg(4) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Mg(3)O4 tetrahedra, corners with three equivalent Al(5)O4 tetrahedra, edges with three equivalent Al(1)O6 octahedra, and edges with three equivalent Al(2)O6 octahedra. In the fifth Mg site, Mg(5) is bonded to one O(6) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Al(2)O6 octahedra, corners with three equivalent Al(3)O6 octahedra, and corners with six equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. 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 Al(3)O6 octahedra, corners with three equivalent Al(4)O6 octahedra, and corners with six equivalent Al(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-61°. There are six inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form AlO6 octahedra that share  a cornercorner with one Mg(3)O4 tetrahedra,  a cornercorner with one Al(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Al(5)O4 tetrahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Mg(4)O6 octahedra, and edges with four equivalent Al(1)O6 octahedra. In the second Al site, Al(2) is bonded to one O(6), one O(9), two equivalent O(4), and two equivalent O(8) atoms to form AlO6 octahedra that share  a cornercorner with one Mg(5)O4 tetrahedra,  a cornercorner with one Al(5)O4 tetrahedra, corners with two equivalent Mg(3)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Mg(4)O6 octahedra,  an edgeedge with one Al(3)O6 octahedra, and edges with four equivalent Al(2)O6 octahedra. In the third Al site, Al(3) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form AlO6 octahedra that share corners with three equivalent Mg(5)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Al(2)O6 octahedra, and edges with three equivalent Al(4)O6 octahedra. In the fourth Al site, Al(4) is bonded to one O(10), one O(12), two equivalent O(11), and two equivalent O(7) atoms to form AlO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(6)O4 tetrahedra, corners with two equivalent Mg(5)O4 tetrahedra, corners with two equivalent Al(6)O4 tetrahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Al(3)O6 octahedra, and edges with four equivalent Al(4)O6 octahedra. In the fifth Al site, Al(5) is bonded to one O(9) and three equivalent O(3) atoms to form AlO4 tetrahedra that share corners with three equivalent Mg(4)O6 octahedra, corners with three equivalent Al(2)O6 octahedra, and corners with six equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-60°. In the sixth Al site, Al(6) is bonded to one O(5) and three equivalent O(11) atoms to form AlO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra, corners with three equivalent Al(1)O6 octahedra, and corners with six equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-61°. 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(2), and two equivalent Al(1) atoms. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Mg(3) and three equivalent Al(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Mg(4), one Al(5), and two equivalent Al(1) atoms. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(3), one Mg(4), and two equivalent Al(2) atoms. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Al(6) and three equivalent Al(1) atoms. In the sixth O site, O(6) is bonded to one Mg(5) and three equivalent Al(2) atoms to form distorted corner-sharing OMgAl3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(5), one Al(3), and two equivalent Al(4) atoms to form a mixture of distorted corner and edge-sharing OMgAl3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Mg(6), one Al(3), and two equivalent Al(2) atoms to form a mixture of distorted corner and edge-sharing OMgAl3 tetrahedra. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Al(5) and three equivalent Al(2) atoms. In the tenth O site, O(10) is bonded to one Mg(1) and three equivalent Al(4) atoms to form a mixture of distorted corner and edge-sharing OMgAl3 trigonal pyramids. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Al(6), and two equivalent Al(4) atoms. In the twelfth O site, O(12) is bonded to one Mg(6) and three equivalent Al(4) atoms to form corner-sharing OMgAl3 tetrahedra. is represented by the CIF file [CIF]
data_MgAl2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.763
_cell_length_b   5.763
_cell_length_c   14.185
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   408.043
_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  0.999  1.0
  Mg  Mg2  1  0.000  0.000  0.621  1.0
  Mg  Mg3  1  0.667  0.333  0.664  1.0
  Mg  Mg4  1  0.667  0.333  0.291  1.0
  Mg  Mg5  1  0.000  0.000  0.378  1.0
  Al  Al6  1  0.838  0.162  0.834  1.0
  Al  Al7  1  0.503  0.006  0.500  1.0
  Al  Al8  1  0.324  0.162  0.834  1.0
  Al  Al9  1  0.503  0.497  0.500  1.0
  Al  Al10  1  0.994  0.497  0.500  1.0
  Al  Al11  1  0.838  0.676  0.834  1.0
  Al  Al12  1  0.333  0.667  0.335  1.0
  Al  Al13  1  0.169  0.831  0.168  1.0
  Al  Al14  1  0.333  0.667  0.714  1.0
  Al  Al15  1  0.662  0.831  0.168  1.0
  Al  Al16  1  0.169  0.338  0.168  1.0
  Al  Al17  1  0.667  0.333  0.043  1.0
  O  O18  1  0.694  0.847  0.906  1.0
  O  O19  1  0.000  0.000  0.760  1.0
  O  O20  1  0.153  0.847  0.906  1.0
  O  O21  1  0.153  0.306  0.906  1.0
  O  O22  1  0.507  0.014  0.758  1.0
  O  O23  1  0.359  0.179  0.570  1.0
  O  O24  1  0.667  0.333  0.912  1.0
  O  O25  1  0.507  0.493  0.758  1.0
  O  O26  1  0.667  0.333  0.427  1.0
  O  O27  1  0.821  0.179  0.570  1.0
  O  O28  1  0.986  0.493  0.758  1.0
  O  O29  1  0.821  0.641  0.570  1.0
  O  O30  1  0.038  0.519  0.246  1.0
  O  O31  1  0.187  0.374  0.422  1.0
  O  O32  1  0.333  0.667  0.583  1.0
  O  O33  1  0.481  0.519  0.246  1.0
  O  O34  1  0.187  0.813  0.422  1.0
  O  O35  1  0.333  0.667  0.096  1.0
  O  O36  1  0.481  0.962  0.246  1.0
  O  O37  1  0.626  0.813  0.422  1.0
  O  O38  1  0.836  0.673  0.091  1.0
  O  O39  1  0.000  0.000  0.233  1.0
  O  O40  1  0.836  0.164  0.091  1.0
  O  O41  1  0.327  0.164  0.091  1.0
[/CIF]
.