The material structure described by MgCr6O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(10), one O(12), one O(13), and one O(7) atom to form MgO4 tetrahedra that share  a cornercorner with one Cr(4)O4 tetrahedra,  a cornercorner with one Cr(5)O4 tetrahedra, corners with two equivalent Cr(3)O4 tetrahedra, and  an edgeedge with one Cr(6)O6 octahedra. There are six inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(15), one O(16), one O(2), one O(3), one O(5), and one O(6) atom to form corner-sharing CrO6 octahedra. In the second Cr site, Cr(2) is bonded to one O(14), one O(2), one O(4), and one O(8) atom to form corner-sharing CrO4 tetrahedra. The corner-sharing octahedral tilt angles range from 38-41°. In the third Cr site, Cr(3) is bonded to one O(1), one O(13), one O(3), and one O(7) atom to form CrO4 tetrahedra that share  a cornercorner with one Cr(1)O6 octahedra, corners with two equivalent Cr(6)O6 octahedra, and corners with two equivalent Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 37-44°. In the fourth Cr site, Cr(4) is bonded to one O(10), one O(15), one O(5), and one O(9) atom to form CrO4 tetrahedra that share  a cornercorner with one Cr(6)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, and  a cornercorner with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 38-43°. In the fifth Cr site, Cr(5) is bonded to one O(11), one O(12), one O(16), and one O(6) atom to form CrO4 tetrahedra that share  a cornercorner with one Cr(6)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, and  a cornercorner with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 33-41°. In the sixth Cr site, Cr(6) is bonded to one O(11), one O(13), one O(14), one O(7), one O(8), and one O(9) atom to form CrO6 octahedra that share  a cornercorner with one Cr(4)O4 tetrahedra,  a cornercorner with one Cr(5)O4 tetrahedra, corners with two equivalent Cr(2)O4 tetrahedra, corners with two equivalent Cr(3)O4 tetrahedra, and  an edgeedge with one Mg(1)O4 tetrahedra. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a single-bond geometry to one Cr(3) atom. In the second O site, O(2) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(2) atom. In the third O site, O(3) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(3) atom. In the fourth O site, O(4) is bonded in a single-bond geometry to one Cr(2) atom. In the fifth O site, O(5) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(4) atom. In the sixth O site, O(6) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(5) atom. In the seventh O site, O(7) is bonded in a distorted trigonal planar geometry to one Mg(1), one Cr(3), and one Cr(6) atom. In the eighth O site, O(8) is bonded in a bent 150 degrees geometry to one Cr(2) and one Cr(6) atom. In the ninth O site, O(9) is bonded in a bent 150 degrees geometry to one Cr(4) and one Cr(6) atom. In the tenth O site, O(10) is bonded in a linear geometry to one Mg(1) and one Cr(4) atom. In the eleventh O site, O(11) is bonded in a bent 150 degrees geometry to one Cr(5) and one Cr(6) atom. In the twelfth O site, O(12) is bonded in a bent 120 degrees geometry to one Mg(1) and one Cr(5) atom. In the thirteenth O site, O(13) is bonded in a distorted trigonal planar geometry to one Mg(1), one Cr(3), and one Cr(6) atom. In the fourteenth O site, O(14) is bonded in a bent 150 degrees geometry to one Cr(2) and one Cr(6) atom. In the fifteenth O site, O(15) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(4) atom. In the sixteenth O site, O(16) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(5) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgCr6O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.531
_cell_length_b   8.319
_cell_length_c   7.478
_cell_angle_alpha   91.146
_cell_angle_beta   90.315
_cell_angle_gamma   90.021
_symmetry_Int_Tables_number   1
_cell_volume   343.997
_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  0.506  0.473  0.879  1.0
  Cr  Cr1  1  0.000  0.995  0.003  1.0
  Cr  Cr2  1  0.998  0.683  0.298  1.0
  Cr  Cr3  1  0.003  0.317  0.697  1.0
  Cr  Cr4  1  0.503  0.173  0.204  1.0
  Cr  Cr5  1  0.498  0.828  0.799  1.0
  Cr  Cr6  1  0.500  0.504  0.484  1.0
  O  O7  1  0.002  0.192  0.535  1.0
  O  O8  1  0.998  0.776  0.097  1.0
  O  O9  1  0.003  0.223  0.891  1.0
  O  O10  1  0.998  0.813  0.457  1.0
  O  O11  1  0.256  0.058  0.181  1.0
  O  O12  1  0.248  0.939  0.819  1.0
  O  O13  1  0.260  0.436  0.684  1.0
  O  O14  1  0.245  0.563  0.316  1.0
  O  O15  1  0.501  0.274  0.400  1.0
  O  O16  1  0.502  0.302  0.043  1.0
  O  O17  1  0.500  0.723  0.606  1.0
  O  O18  1  0.500  0.697  0.962  1.0
  O  O19  1  0.747  0.437  0.683  1.0
  O  O20  1  0.749  0.564  0.313  1.0
  O  O21  1  0.753  0.062  0.184  1.0
  O  O22  1  0.742  0.944  0.822  1.0
[/CIF]
.
The material structure described by MgCr6O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(10), one O(12), one O(13), and one O(7) atom to form MgO4 tetrahedra that share  a cornercorner with one Cr(4)O4 tetrahedra,  a cornercorner with one Cr(5)O4 tetrahedra, corners with two equivalent Cr(3)O4 tetrahedra, and  an edgeedge with one Cr(6)O6 octahedra. There are six inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(15), one O(16), one O(2), one O(3), one O(5), and one O(6) atom to form corner-sharing CrO6 octahedra. In the second Cr site, Cr(2) is bonded to one O(14), one O(2), one O(4), and one O(8) atom to form corner-sharing CrO4 tetrahedra. The corner-sharing octahedral tilt angles range from 38-41°. In the third Cr site, Cr(3) is bonded to one O(1), one O(13), one O(3), and one O(7) atom to form CrO4 tetrahedra that share  a cornercorner with one Cr(1)O6 octahedra, corners with two equivalent Cr(6)O6 octahedra, and corners with two equivalent Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 37-44°. In the fourth Cr site, Cr(4) is bonded to one O(10), one O(15), one O(5), and one O(9) atom to form CrO4 tetrahedra that share  a cornercorner with one Cr(6)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, and  a cornercorner with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 38-43°. In the fifth Cr site, Cr(5) is bonded to one O(11), one O(12), one O(16), and one O(6) atom to form CrO4 tetrahedra that share  a cornercorner with one Cr(6)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, and  a cornercorner with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 33-41°. In the sixth Cr site, Cr(6) is bonded to one O(11), one O(13), one O(14), one O(7), one O(8), and one O(9) atom to form CrO6 octahedra that share  a cornercorner with one Cr(4)O4 tetrahedra,  a cornercorner with one Cr(5)O4 tetrahedra, corners with two equivalent Cr(2)O4 tetrahedra, corners with two equivalent Cr(3)O4 tetrahedra, and  an edgeedge with one Mg(1)O4 tetrahedra. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a single-bond geometry to one Cr(3) atom. In the second O site, O(2) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(2) atom. In the third O site, O(3) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(3) atom. In the fourth O site, O(4) is bonded in a single-bond geometry to one Cr(2) atom. In the fifth O site, O(5) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(4) atom. In the sixth O site, O(6) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(5) atom. In the seventh O site, O(7) is bonded in a distorted trigonal planar geometry to one Mg(1), one Cr(3), and one Cr(6) atom. In the eighth O site, O(8) is bonded in a bent 150 degrees geometry to one Cr(2) and one Cr(6) atom. In the ninth O site, O(9) is bonded in a bent 150 degrees geometry to one Cr(4) and one Cr(6) atom. In the tenth O site, O(10) is bonded in a linear geometry to one Mg(1) and one Cr(4) atom. In the eleventh O site, O(11) is bonded in a bent 150 degrees geometry to one Cr(5) and one Cr(6) atom. In the twelfth O site, O(12) is bonded in a bent 120 degrees geometry to one Mg(1) and one Cr(5) atom. In the thirteenth O site, O(13) is bonded in a distorted trigonal planar geometry to one Mg(1), one Cr(3), and one Cr(6) atom. In the fourteenth O site, O(14) is bonded in a bent 150 degrees geometry to one Cr(2) and one Cr(6) atom. In the fifteenth O site, O(15) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(4) atom. In the sixteenth O site, O(16) is bonded in a bent 150 degrees geometry to one Cr(1) and one Cr(5) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgCr6O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.531
_cell_length_b   8.319
_cell_length_c   7.478
_cell_angle_alpha   91.146
_cell_angle_beta   90.315
_cell_angle_gamma   90.021
_symmetry_Int_Tables_number   1
_cell_volume   343.997
_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  0.506  0.473  0.879  1.0
  Cr  Cr1  1  0.000  0.995  0.003  1.0
  Cr  Cr2  1  0.998  0.683  0.298  1.0
  Cr  Cr3  1  0.003  0.317  0.697  1.0
  Cr  Cr4  1  0.503  0.173  0.204  1.0
  Cr  Cr5  1  0.498  0.828  0.799  1.0
  Cr  Cr6  1  0.500  0.504  0.484  1.0
  O  O7  1  0.002  0.192  0.535  1.0
  O  O8  1  0.998  0.776  0.097  1.0
  O  O9  1  0.003  0.223  0.891  1.0
  O  O10  1  0.998  0.813  0.457  1.0
  O  O11  1  0.256  0.058  0.181  1.0
  O  O12  1  0.248  0.939  0.819  1.0
  O  O13  1  0.260  0.436  0.684  1.0
  O  O14  1  0.245  0.563  0.316  1.0
  O  O15  1  0.501  0.274  0.400  1.0
  O  O16  1  0.502  0.302  0.043  1.0
  O  O17  1  0.500  0.723  0.606  1.0
  O  O18  1  0.500  0.697  0.962  1.0
  O  O19  1  0.747  0.437  0.683  1.0
  O  O20  1  0.749  0.564  0.313  1.0
  O  O21  1  0.753  0.062  0.184  1.0
  O  O22  1  0.742  0.944  0.822  1.0
[/CIF]
.