The compound described by Mg2Co9O13 crystallizes in the monoclinic C2/m space group. Mg(1) is bonded in a 6-coordinate geometry to two equivalent O(2), two equivalent O(4), and two equivalent O(5) atoms. There are five inequivalent Co sites. In the first Co site, Co(1) is bonded to two equivalent O(6) and four equivalent O(7) atoms to form a mixture of corner and edge-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles are 6°. In the second Co site, Co(2) is bonded to one O(4), two equivalent O(1), and three equivalent O(3) atoms to form a mixture of corner and edge-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. In the third Co site, Co(3) is bonded to one O(5), two equivalent O(6), and three equivalent O(7) atoms to form a mixture of corner and edge-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles range from 1-18°. In the fourth Co site, Co(4) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form a mixture of distorted corner and edge-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles range from 0-64°. In the fifth Co site, Co(5) is bonded to one O(2), one O(7), two equivalent O(5), and two equivalent O(6) atoms to form a mixture of distorted corner and edge-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles range from 1-64°. There are seven inequivalent O sites. In the first O site, O(7) is bonded to one Co(5), two equivalent Co(1), and three equivalent Co(3) atoms to form OCo6 octahedra that share corners with two equivalent O(7)Co6 octahedra, corners with two equivalent O(6)Co5 square pyramids,  a cornercorner with one O(2)Mg2Co2 tetrahedra,  a cornercorner with one O(5)Mg2Co3 trigonal bipyramid, edges with five equivalent O(7)Co6 octahedra, edges with five equivalent O(6)Co5 square pyramids, and edges with two equivalent O(5)Mg2Co3 trigonal bipyramids. The corner-sharing octahedra are not tilted. In the second O site, O(1) is bonded to two equivalent Co(4) and four equivalent Co(2) atoms to form OCo6 octahedra that share corners with four equivalent O(3)Co5 square pyramids, corners with two equivalent O(2)Mg2Co2 tetrahedra, edges with two equivalent O(1)Co6 octahedra, edges with six equivalent O(3)Co5 square pyramids, and edges with four equivalent O(4)Mg2Co3 trigonal bipyramids. In the third O site, O(2) is bonded to two equivalent Mg(1), one Co(4), and one Co(5) atom to form OMg2Co2 tetrahedra that share  a cornercorner with one O(1)Co6 octahedra,  a cornercorner with one O(7)Co6 octahedra, corners with two equivalent O(3)Co5 square pyramids, corners with two equivalent O(6)Co5 square pyramids, corners with two equivalent O(2)Mg2Co2 tetrahedra, corners with four equivalent O(4)Mg2Co3 trigonal bipyramids, corners with four equivalent O(5)Mg2Co3 trigonal bipyramids,  an edgeedge with one O(4)Mg2Co3 trigonal bipyramid, and  an edgeedge with one O(5)Mg2Co3 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 6-9°. In the fourth O site, O(3) is bonded to two equivalent Co(4) and three equivalent Co(2) atoms to form OCo5 square pyramids that share corners with two equivalent O(1)Co6 octahedra, corners with two equivalent O(2)Mg2Co2 tetrahedra, corners with five equivalent O(4)Mg2Co3 trigonal bipyramids, edges with three equivalent O(1)Co6 octahedra, edges with four equivalent O(3)Co5 square pyramids, and  an edgeedge with one O(4)Mg2Co3 trigonal bipyramid. The corner-sharing octahedral tilt angles are 4°. In the fifth O site, O(4) is bonded to two equivalent Mg(1), one Co(2), and two equivalent Co(4) atoms to form distorted OMg2Co3 trigonal bipyramids that share corners with five equivalent O(3)Co5 square pyramids, corners with four equivalent O(2)Mg2Co2 tetrahedra, corners with two equivalent O(5)Mg2Co3 trigonal bipyramids, edges with two equivalent O(1)Co6 octahedra,  an edgeedge with one O(3)Co5 square pyramid,  an edgeedge with one O(2)Mg2Co2 tetrahedra,  an edgeedge with one O(5)Mg2Co3 trigonal bipyramid, and edges with two equivalent O(4)Mg2Co3 trigonal bipyramids. In the sixth O site, O(5) is bonded to two equivalent Mg(1), one Co(3), and two equivalent Co(5) atoms to form distorted OMg2Co3 trigonal bipyramids that share  a cornercorner with one O(7)Co6 octahedra, corners with four equivalent O(6)Co5 square pyramids, corners with four equivalent O(2)Mg2Co2 tetrahedra, corners with two equivalent O(4)Mg2Co3 trigonal bipyramids, edges with two equivalent O(7)Co6 octahedra,  an edgeedge with one O(6)Co5 square pyramid,  an edgeedge with one O(2)Mg2Co2 tetrahedra,  an edgeedge with one O(4)Mg2Co3 trigonal bipyramid, and edges with two equivalent O(5)Mg2Co3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 2°. In the seventh O site, O(6) is bonded to one Co(1), two equivalent Co(3), and two equivalent Co(5) atoms to form OCo5 square pyramids that share corners with two equivalent O(7)Co6 octahedra,  a cornercorner with one O(6)Co5 square pyramid, corners with two equivalent O(2)Mg2Co2 tetrahedra, corners with four equivalent O(5)Mg2Co3 trigonal bipyramids, edges with five equivalent O(7)Co6 octahedra, edges with two equivalent O(6)Co5 square pyramids, and  an edgeedge with one O(5)Mg2Co3 trigonal bipyramid. The corner-sharing octahedral tilt angles are 10°. is represented by the CIF file [CIF]
data_Mg2Co9O13
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.174
_cell_length_b   5.174
_cell_length_c   16.600
_cell_angle_alpha   81.831
_cell_angle_beta   81.831
_cell_angle_gamma   32.866
_symmetry_Int_Tables_number   1
_cell_volume   238.544
_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  0.790  0.790  0.227  1.0
  Mg  Mg1  1  0.210  0.210  0.773  1.0
  Co  Co2  1  0.500  0.500  0.500  1.0
  Co  Co3  1  0.354  0.354  0.040  1.0
  Co  Co4  1  0.646  0.646  0.960  1.0
  Co  Co5  1  0.247  0.247  0.417  1.0
  Co  Co6  1  0.753  0.753  0.583  1.0
  Co  Co7  1  0.066  0.066  0.128  1.0
  Co  Co8  1  0.934  0.934  0.872  1.0
  Co  Co9  1  0.002  0.002  0.329  1.0
  Co  Co10  1  0.998  0.998  0.671  1.0
  O  O11  1  0.000  0.000  0.000  1.0
  O  O12  1  0.139  0.139  0.224  1.0
  O  O13  1  0.861  0.861  0.776  1.0
  O  O14  1  0.698  0.698  0.073  1.0
  O  O15  1  0.302  0.302  0.927  1.0
  O  O16  1  0.421  0.421  0.147  1.0
  O  O17  1  0.579  0.579  0.853  1.0
  O  O18  1  0.363  0.363  0.307  1.0
  O  O19  1  0.637  0.637  0.693  1.0
  O  O20  1  0.606  0.606  0.391  1.0
  O  O21  1  0.394  0.394  0.609  1.0
  O  O22  1  0.872  0.872  0.465  1.0
  O  O23  1  0.128  0.128  0.535  1.0
[/CIF]
.
The compound described by Mg2Co9O13 crystallizes in the monoclinic C2/m space group. Mg(1) is bonded in a 6-coordinate geometry to two equivalent O(2), two equivalent O(4), and two equivalent O(5) atoms. There are five inequivalent Co sites. In the first Co site, Co(1) is bonded to two equivalent O(6) and four equivalent O(7) atoms to form a mixture of corner and edge-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles are 6°. In the second Co site, Co(2) is bonded to one O(4), two equivalent O(1), and three equivalent O(3) atoms to form a mixture of corner and edge-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. In the third Co site, Co(3) is bonded to one O(5), two equivalent O(6), and three equivalent O(7) atoms to form a mixture of corner and edge-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles range from 1-18°. In the fourth Co site, Co(4) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form a mixture of distorted corner and edge-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles range from 0-64°. In the fifth Co site, Co(5) is bonded to one O(2), one O(7), two equivalent O(5), and two equivalent O(6) atoms to form a mixture of distorted corner and edge-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles range from 1-64°. There are seven inequivalent O sites. In the first O site, O(7) is bonded to one Co(5), two equivalent Co(1), and three equivalent Co(3) atoms to form OCo6 octahedra that share corners with two equivalent O(7)Co6 octahedra, corners with two equivalent O(6)Co5 square pyramids,  a cornercorner with one O(2)Mg2Co2 tetrahedra,  a cornercorner with one O(5)Mg2Co3 trigonal bipyramid, edges with five equivalent O(7)Co6 octahedra, edges with five equivalent O(6)Co5 square pyramids, and edges with two equivalent O(5)Mg2Co3 trigonal bipyramids. The corner-sharing octahedra are not tilted. In the second O site, O(1) is bonded to two equivalent Co(4) and four equivalent Co(2) atoms to form OCo6 octahedra that share corners with four equivalent O(3)Co5 square pyramids, corners with two equivalent O(2)Mg2Co2 tetrahedra, edges with two equivalent O(1)Co6 octahedra, edges with six equivalent O(3)Co5 square pyramids, and edges with four equivalent O(4)Mg2Co3 trigonal bipyramids. In the third O site, O(2) is bonded to two equivalent Mg(1), one Co(4), and one Co(5) atom to form OMg2Co2 tetrahedra that share  a cornercorner with one O(1)Co6 octahedra,  a cornercorner with one O(7)Co6 octahedra, corners with two equivalent O(3)Co5 square pyramids, corners with two equivalent O(6)Co5 square pyramids, corners with two equivalent O(2)Mg2Co2 tetrahedra, corners with four equivalent O(4)Mg2Co3 trigonal bipyramids, corners with four equivalent O(5)Mg2Co3 trigonal bipyramids,  an edgeedge with one O(4)Mg2Co3 trigonal bipyramid, and  an edgeedge with one O(5)Mg2Co3 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 6-9°. In the fourth O site, O(3) is bonded to two equivalent Co(4) and three equivalent Co(2) atoms to form OCo5 square pyramids that share corners with two equivalent O(1)Co6 octahedra, corners with two equivalent O(2)Mg2Co2 tetrahedra, corners with five equivalent O(4)Mg2Co3 trigonal bipyramids, edges with three equivalent O(1)Co6 octahedra, edges with four equivalent O(3)Co5 square pyramids, and  an edgeedge with one O(4)Mg2Co3 trigonal bipyramid. The corner-sharing octahedral tilt angles are 4°. In the fifth O site, O(4) is bonded to two equivalent Mg(1), one Co(2), and two equivalent Co(4) atoms to form distorted OMg2Co3 trigonal bipyramids that share corners with five equivalent O(3)Co5 square pyramids, corners with four equivalent O(2)Mg2Co2 tetrahedra, corners with two equivalent O(5)Mg2Co3 trigonal bipyramids, edges with two equivalent O(1)Co6 octahedra,  an edgeedge with one O(3)Co5 square pyramid,  an edgeedge with one O(2)Mg2Co2 tetrahedra,  an edgeedge with one O(5)Mg2Co3 trigonal bipyramid, and edges with two equivalent O(4)Mg2Co3 trigonal bipyramids. In the sixth O site, O(5) is bonded to two equivalent Mg(1), one Co(3), and two equivalent Co(5) atoms to form distorted OMg2Co3 trigonal bipyramids that share  a cornercorner with one O(7)Co6 octahedra, corners with four equivalent O(6)Co5 square pyramids, corners with four equivalent O(2)Mg2Co2 tetrahedra, corners with two equivalent O(4)Mg2Co3 trigonal bipyramids, edges with two equivalent O(7)Co6 octahedra,  an edgeedge with one O(6)Co5 square pyramid,  an edgeedge with one O(2)Mg2Co2 tetrahedra,  an edgeedge with one O(4)Mg2Co3 trigonal bipyramid, and edges with two equivalent O(5)Mg2Co3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 2°. In the seventh O site, O(6) is bonded to one Co(1), two equivalent Co(3), and two equivalent Co(5) atoms to form OCo5 square pyramids that share corners with two equivalent O(7)Co6 octahedra,  a cornercorner with one O(6)Co5 square pyramid, corners with two equivalent O(2)Mg2Co2 tetrahedra, corners with four equivalent O(5)Mg2Co3 trigonal bipyramids, edges with five equivalent O(7)Co6 octahedra, edges with two equivalent O(6)Co5 square pyramids, and  an edgeedge with one O(5)Mg2Co3 trigonal bipyramid. The corner-sharing octahedral tilt angles are 10°. is represented by the CIF file [CIF]
data_Mg2Co9O13
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.174
_cell_length_b   5.174
_cell_length_c   16.600
_cell_angle_alpha   81.831
_cell_angle_beta   81.831
_cell_angle_gamma   32.866
_symmetry_Int_Tables_number   1
_cell_volume   238.544
_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  0.790  0.790  0.227  1.0
  Mg  Mg1  1  0.210  0.210  0.773  1.0
  Co  Co2  1  0.500  0.500  0.500  1.0
  Co  Co3  1  0.354  0.354  0.040  1.0
  Co  Co4  1  0.646  0.646  0.960  1.0
  Co  Co5  1  0.247  0.247  0.417  1.0
  Co  Co6  1  0.753  0.753  0.583  1.0
  Co  Co7  1  0.066  0.066  0.128  1.0
  Co  Co8  1  0.934  0.934  0.872  1.0
  Co  Co9  1  0.002  0.002  0.329  1.0
  Co  Co10  1  0.998  0.998  0.671  1.0
  O  O11  1  0.000  0.000  0.000  1.0
  O  O12  1  0.139  0.139  0.224  1.0
  O  O13  1  0.861  0.861  0.776  1.0
  O  O14  1  0.698  0.698  0.073  1.0
  O  O15  1  0.302  0.302  0.927  1.0
  O  O16  1  0.421  0.421  0.147  1.0
  O  O17  1  0.579  0.579  0.853  1.0
  O  O18  1  0.363  0.363  0.307  1.0
  O  O19  1  0.637  0.637  0.693  1.0
  O  O20  1  0.606  0.606  0.391  1.0
  O  O21  1  0.394  0.394  0.609  1.0
  O  O22  1  0.872  0.872  0.465  1.0
  O  O23  1  0.128  0.128  0.535  1.0
[/CIF]
.