The material structure described by MgAl10O16 is beta indium sulfide-derived structured and crystallizes in the trigonal R3m space group. Mg(1) is bonded to one O(5) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Al(2)O6 octahedra, corners with three equivalent Al(5)O6 octahedra, and corners with six equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-61°. There are six inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(3) and three equivalent O(2) atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-58°. In the second Al site, Al(2) is bonded to one O(5), one O(6), two equivalent O(1), and two equivalent O(2) atoms to form AlO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Al(6)O4 tetrahedra, corners with two equivalent Al(1)O4 tetrahedra, corners with two equivalent Al(3)O4 tetrahedra,  an edgeedge with one Al(5)O6 octahedra, and edges with four equivalent Al(2)O6 octahedra. In the third Al site, Al(3) is bonded to one O(8) and three equivalent O(1) atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedral tilt angles range from 55-60°. In the fourth Al site, Al(4) is bonded to one O(3), one O(8), two equivalent O(4), and two equivalent O(7) atoms to form AlO6 octahedra that share  a cornercorner with one Al(1)O4 tetrahedra,  a cornercorner with one Al(3)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Al(6)O4 tetrahedra,  an edgeedge with one Al(5)O6 octahedra, and edges with four equivalent Al(4)O6 octahedra. In the fifth Al site, Al(5) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form AlO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Al(3)O4 tetrahedra, edges with three equivalent Al(2)O6 octahedra, and edges with three equivalent Al(4)O6 octahedra. In the sixth Al site, Al(6) is bonded to one O(6) and three equivalent O(7) atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedral tilt angles range from 55-60°. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Al(3), one Al(5), and two equivalent Al(2) atoms. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Al(1) and two equivalent Al(2) atoms. In the third O site, O(3) is bonded to one Al(1) and three equivalent Al(4) atoms to form distorted edge-sharing OAl4 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(1), one Al(5), and two equivalent Al(4) atoms to form distorted OMgAl3 tetrahedra that share corners with two equivalent O(4)MgAl3 tetrahedra, edges with two equivalent O(4)MgAl3 tetrahedra, and  an edgeedge with one O(3)Al4 trigonal pyramid. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Mg(1) and three equivalent Al(2) atoms. In the sixth O site, O(6) is bonded in a distorted tetrahedral geometry to one Al(6) and three equivalent Al(2) atoms. In the seventh O site, O(7) is bonded in a trigonal planar geometry to one Al(6) and two equivalent Al(4) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Al(3) and three equivalent Al(4) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgAl10O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.706
_cell_length_b   9.706
_cell_length_c   9.706
_cell_angle_alpha   34.267
_cell_angle_beta   34.267
_cell_angle_gamma   34.267
_symmetry_Int_Tables_number   1
_cell_volume   258.544
_cell_formula_units_Z   1
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  0.810  0.810  0.810  1.0
  Al  Al1  1  0.310  0.310  0.310  1.0
  Al  Al2  1  0.243  0.760  0.760  1.0
  Al  Al3  1  0.189  0.189  0.189  1.0
  Al  Al4  1  0.760  0.243  0.760  1.0
  Al  Al5  1  0.246  0.246  0.749  1.0
  Al  Al6  1  0.760  0.760  0.243  1.0
  Al  Al7  1  0.246  0.749  0.246  1.0
  Al  Al8  1  0.749  0.246  0.246  1.0
  Al  Al9  1  0.498  0.498  0.498  1.0
  Al  Al10  1  0.692  0.692  0.692  1.0
  O  O11  1  0.388  0.388  0.851  1.0
  O  O12  1  0.388  0.851  0.388  1.0
  O  O13  1  0.120  0.120  0.618  1.0
  O  O14  1  0.120  0.618  0.120  1.0
  O  O15  1  0.618  0.120  0.120  1.0
  O  O16  1  0.375  0.375  0.375  1.0
  O  O17  1  0.163  0.601  0.601  1.0
  O  O18  1  0.883  0.883  0.883  1.0
  O  O19  1  0.623  0.623  0.623  1.0
  O  O20  1  0.851  0.388  0.388  1.0
  O  O21  1  0.378  0.882  0.882  1.0
  O  O22  1  0.123  0.123  0.123  1.0
  O  O23  1  0.882  0.882  0.378  1.0
  O  O24  1  0.882  0.378  0.882  1.0
  O  O25  1  0.601  0.163  0.601  1.0
  O  O26  1  0.601  0.601  0.163  1.0
[/CIF]
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The material structure described by MgAl10O16 is beta indium sulfide-derived structured and crystallizes in the trigonal R3m space group. Mg(1) is bonded to one O(5) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Al(2)O6 octahedra, corners with three equivalent Al(5)O6 octahedra, and corners with six equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-61°. There are six inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(3) and three equivalent O(2) atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-58°. In the second Al site, Al(2) is bonded to one O(5), one O(6), two equivalent O(1), and two equivalent O(2) atoms to form AlO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Al(6)O4 tetrahedra, corners with two equivalent Al(1)O4 tetrahedra, corners with two equivalent Al(3)O4 tetrahedra,  an edgeedge with one Al(5)O6 octahedra, and edges with four equivalent Al(2)O6 octahedra. In the third Al site, Al(3) is bonded to one O(8) and three equivalent O(1) atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedral tilt angles range from 55-60°. In the fourth Al site, Al(4) is bonded to one O(3), one O(8), two equivalent O(4), and two equivalent O(7) atoms to form AlO6 octahedra that share  a cornercorner with one Al(1)O4 tetrahedra,  a cornercorner with one Al(3)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Al(6)O4 tetrahedra,  an edgeedge with one Al(5)O6 octahedra, and edges with four equivalent Al(4)O6 octahedra. In the fifth Al site, Al(5) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form AlO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Al(3)O4 tetrahedra, edges with three equivalent Al(2)O6 octahedra, and edges with three equivalent Al(4)O6 octahedra. In the sixth Al site, Al(6) is bonded to one O(6) and three equivalent O(7) atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedral tilt angles range from 55-60°. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Al(3), one Al(5), and two equivalent Al(2) atoms. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Al(1) and two equivalent Al(2) atoms. In the third O site, O(3) is bonded to one Al(1) and three equivalent Al(4) atoms to form distorted edge-sharing OAl4 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(1), one Al(5), and two equivalent Al(4) atoms to form distorted OMgAl3 tetrahedra that share corners with two equivalent O(4)MgAl3 tetrahedra, edges with two equivalent O(4)MgAl3 tetrahedra, and  an edgeedge with one O(3)Al4 trigonal pyramid. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Mg(1) and three equivalent Al(2) atoms. In the sixth O site, O(6) is bonded in a distorted tetrahedral geometry to one Al(6) and three equivalent Al(2) atoms. In the seventh O site, O(7) is bonded in a trigonal planar geometry to one Al(6) and two equivalent Al(4) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Al(3) and three equivalent Al(4) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgAl10O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.706
_cell_length_b   9.706
_cell_length_c   9.706
_cell_angle_alpha   34.267
_cell_angle_beta   34.267
_cell_angle_gamma   34.267
_symmetry_Int_Tables_number   1
_cell_volume   258.544
_cell_formula_units_Z   1
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  0.810  0.810  0.810  1.0
  Al  Al1  1  0.310  0.310  0.310  1.0
  Al  Al2  1  0.243  0.760  0.760  1.0
  Al  Al3  1  0.189  0.189  0.189  1.0
  Al  Al4  1  0.760  0.243  0.760  1.0
  Al  Al5  1  0.246  0.246  0.749  1.0
  Al  Al6  1  0.760  0.760  0.243  1.0
  Al  Al7  1  0.246  0.749  0.246  1.0
  Al  Al8  1  0.749  0.246  0.246  1.0
  Al  Al9  1  0.498  0.498  0.498  1.0
  Al  Al10  1  0.692  0.692  0.692  1.0
  O  O11  1  0.388  0.388  0.851  1.0
  O  O12  1  0.388  0.851  0.388  1.0
  O  O13  1  0.120  0.120  0.618  1.0
  O  O14  1  0.120  0.618  0.120  1.0
  O  O15  1  0.618  0.120  0.120  1.0
  O  O16  1  0.375  0.375  0.375  1.0
  O  O17  1  0.163  0.601  0.601  1.0
  O  O18  1  0.883  0.883  0.883  1.0
  O  O19  1  0.623  0.623  0.623  1.0
  O  O20  1  0.851  0.388  0.388  1.0
  O  O21  1  0.378  0.882  0.882  1.0
  O  O22  1  0.123  0.123  0.123  1.0
  O  O23  1  0.882  0.882  0.378  1.0
  O  O24  1  0.882  0.378  0.882  1.0
  O  O25  1  0.601  0.163  0.601  1.0
  O  O26  1  0.601  0.601  0.163  1.0
[/CIF]
.