The crystal structure described by Li2MgCo13O28 crystallizes in the triclinic P1 space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(20), one O(25), one O(26), one O(3), one O(4), and one O(9) atom to form distorted LiO6 octahedra that share  a cornercorner with one Co(11)O6 octahedra,  a cornercorner with one Co(12)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(13)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, and  an edgeedge with one Co(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 14-19°. In the second Li site, Li(2) is bonded to one O(12), one O(14), one O(21), one O(22), one O(24), and one O(7) atom to form distorted LiO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Co(11)O6 octahedra,  a cornercorner with one Co(6)O6 octahedra,  a cornercorner with one Co(9)O6 octahedra, corners with two equivalent Co(2)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(12)O6 octahedra,  an edgeedge with one Co(13)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, and  an edgeedge with one Co(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 13-18°. Mg(1) is bonded to one O(13), one O(14), one O(15), one O(16), one O(20), and one O(9) atom to form MgO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra, corners with two equivalent Li(1)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra,  an edgeedge with one Co(8)O6 octahedra, and  an edgeedge with one Co(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 17-19°. There are thirteen inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(2), one O(23), one O(3), one O(4), one O(5), and one O(8) atom to form CoO6 octahedra that share  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Co(12)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, and  an edgeedge with one Co(6)O6 octahedra. In the second Co site, Co(2) is bonded to one O(24), one O(28), one O(3), one O(5), one O(6), and one O(7) atom to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(12)O6 octahedra,  an edgeedge with one Co(13)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and  an edgeedge with one Co(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 13-15°. In the third Co site, Co(3) is bonded to one O(1), one O(2), one O(23), one O(27), one O(28), and one O(6) atom to form edge-sharing CoO6 octahedra. In the fourth Co site, Co(4) is bonded to one O(10), one O(12), one O(2), one O(28), one O(4), and one O(7) atom to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, and  an edgeedge with one Co(7)O6 octahedra. The corner-sharing octahedral tilt angles are 17°. In the fifth Co site, Co(5) is bonded to one O(10), one O(14), one O(3), one O(7), one O(8), and one O(9) atom to form CoO6 octahedra that share  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, and  an edgeedge with one Co(7)O6 octahedra. In the sixth Co site, Co(6) is bonded to one O(11), one O(12), one O(13), one O(4), one O(8), and one O(9) atom to form CoO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, and  an edgeedge with one Co(8)O6 octahedra. The corner-sharing octahedral tilt angles are 17°. In the seventh Co site, Co(7) is bonded to one O(10), one O(11), one O(12), one O(14), one O(16), and one O(18) atom to form CoO6 octahedra that share  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra,  an edgeedge with one Co(8)O6 octahedra, and  an edgeedge with one Co(9)O6 octahedra. In the eighth Co site, Co(8) is bonded to one O(11), one O(13), one O(15), one O(17), one O(18), and one O(19) atom to form CoO6 octahedra that share  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(11)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, and  an edgeedge with one Co(9)O6 octahedra. In the ninth Co site, Co(9) is bonded to one O(16), one O(17), one O(18), one O(20), one O(21), and one O(25) atom to form CoO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(11)O6 octahedra,  an edgeedge with one Co(13)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, and  an edgeedge with one Co(8)O6 octahedra. The corner-sharing octahedral tilt angles are 15°. In the tenth Co site, Co(10) is bonded to one O(15), one O(19), one O(20), one O(21), one O(22), and one O(26) atom to form CoO6 octahedra that share  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(11)O6 octahedra,  an edgeedge with one Co(12)O6 octahedra,  an edgeedge with one Co(13)O6 octahedra,  an edgeedge with one Co(8)O6 octahedra, and  an edgeedge with one Co(9)O6 octahedra. In the eleventh Co site, Co(11) is bonded to one O(1), one O(17), one O(19), one O(22), one O(25), and one O(27) atom to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Li(2)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(12)O6 octahedra,  an edgeedge with one Co(13)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(8)O6 octahedra, and  an edgeedge with one Co(9)O6 octahedra. The corner-sharing octahedral tilt angles are 15°. In the twelfth Co site, Co(12) is bonded to one O(1), one O(22), one O(23), one O(24), one O(26), and one O(5) atom to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(11)O6 octahedra,  an edgeedge with one Co(13)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, and  an edgeedge with one Co(3)O6 octahedra. The corner-sharing octahedral tilt angles are 15°. In the thirteenth Co site, Co(13) is bonded to one O(21), one O(24), one O(25), one O(26), one O(27), and one O(6) atom to form CoO6 octahedra that share  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(11)O6 octahedra,  an edgeedge with one Co(12)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and  an edgeedge with one Co(9)O6 octahedra. There are twenty-eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Co(11), one Co(12), and one Co(3) atom. In the second O site, O(2) is bonded in a distorted T-shaped geometry to one Co(1), one Co(3), and one Co(4) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(1), one Co(2), and one Co(5) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(1), one Co(4), and one Co(6) atom. In the fifth O site, O(5) is bonded in a distorted T-shaped geometry to one Co(1), one Co(12), and one Co(2) atom. In the sixth O site, O(6) is bonded in a distorted T-shaped geometry to one Co(13), one Co(2), and one Co(3) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(2), one Co(4), and one Co(5) atom. In the eighth O site, O(8) is bonded in a distorted T-shaped geometry to one Co(1), one Co(5), and one Co(6) atom. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mg(1), one Co(5), and one Co(6) atom. In the tenth O site, O(10) is bonded in a distorted T-shaped geometry to one Co(4), one Co(5), and one Co(7) atom. In the eleventh O site, O(11) is bonded in a distorted T-shaped geometry to one Co(6), one Co(7), and one Co(8) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(4), one Co(6), and one Co(7) atom. In the thirteenth O site, O(13) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Co(6), and one Co(8) atom. In the fourteenth O site, O(14) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mg(1), one Co(5), and one Co(7) atom. In the fifteenth O site, O(15) is bonded in a distorted T-shaped geometry to one Mg(1), one Co(10), and one Co(8) atom. In the sixteenth O site, O(16) is bonded in a distorted T-shaped geometry to one Mg(1), one Co(7), and one Co(9) atom. In the seventeenth O site, O(17) is bonded in a distorted trigonal non-coplanar geometry to one Co(11), one Co(8), and one Co(9) atom. In the eighteenth O site, O(18) is bonded in a distorted T-shaped geometry to one Co(7), one Co(8), and one Co(9) atom. In the nineteenth O site, O(19) is bonded in a distorted T-shaped geometry to one Co(10), one Co(11), and one Co(8) atom. In the twentieth O site, O(20) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mg(1), one Co(10), and one Co(9) atom. In the twenty-first O site, O(21) is bonded in a see-saw-like geometry to one Li(2), one Co(10), one Co(13), and one Co(9) atom. In the twenty-second O site, O(22) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(10), one Co(11), and one Co(12) atom. In the twenty-third O site, O(23) is bonded in a distorted T-shaped geometry to one Co(1), one Co(12), and one Co(3) atom. In the twenty-fourth O site, O(24) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(12), one Co(13), and one Co(2) atom. In the twenty-fifth O site, O(25) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(11), one Co(13), and one Co(9) atom. In the twenty-sixth O site, O(26) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(10), one Co(12), and one Co(13) atom. In the twenty-seventh O site, O(27) is bonded in a distorted T-shaped geometry to one Co(11), one Co(13), and one Co(3) atom. In the twenty-eighth O site, O(28) is bonded in a distorted T-shaped geometry to one Co(2), one Co(3), and one Co(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li2MgCo13O28
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.552
_cell_length_b   8.233
_cell_length_c   8.705
_cell_angle_alpha   100.213
_cell_angle_beta   104.410
_cell_angle_gamma   105.292
_symmetry_Int_Tables_number   1
_cell_volume   488.229
_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
  Li  Li0  1  0.504  0.001  0.500  1.0
  Li  Li1  1  0.352  0.568  0.925  1.0
  Mg  Mg2  1  0.502  0.504  0.505  1.0
  Co  Co3  1  0.717  0.150  0.863  1.0
  Co  Co4  1  0.356  0.068  0.928  1.0
  Co  Co5  1  0.001  0.001  0.001  1.0
  Co  Co6  1  0.067  0.205  0.779  1.0
  Co  Co7  1  0.427  0.283  0.715  1.0
  Co  Co8  1  0.790  0.362  0.648  1.0
  Co  Co9  1  0.137  0.421  0.565  1.0
  Co  Co10  1  0.860  0.574  0.429  1.0
  Co  Co11  1  0.210  0.636  0.350  1.0
  Co  Co12  1  0.574  0.715  0.285  1.0
  Co  Co13  1  0.930  0.789  0.216  1.0
  Co  Co14  1  0.647  0.937  0.078  1.0
  Co  Co15  1  0.285  0.856  0.141  1.0
  O  O16  1  0.914  0.009  0.188  1.0
  O  O17  1  0.986  0.218  0.970  1.0
  O  O18  1  0.449  0.066  0.743  1.0
  O  O19  1  0.795  0.135  0.672  1.0
  O  O20  1  0.623  0.151  0.046  1.0
  O  O21  1  0.269  0.074  0.113  1.0
  O  O22  1  0.334  0.287  0.898  1.0
  O  O23  1  0.699  0.364  0.835  1.0
  O  O24  1  0.523  0.266  0.539  1.0
  O  O25  1  0.155  0.200  0.597  1.0
  O  O26  1  0.872  0.352  0.456  1.0
  O  O27  1  0.060  0.428  0.759  1.0
  O  O28  1  0.790  0.576  0.620  1.0
  O  O29  1  0.398  0.496  0.699  1.0
  O  O30  1  0.600  0.507  0.306  1.0
  O  O31  1  0.213  0.422  0.378  1.0
  O  O32  1  0.944  0.571  0.240  1.0
  O  O33  1  0.127  0.643  0.539  1.0
  O  O34  1  0.844  0.796  0.400  1.0
  O  O35  1  0.476  0.737  0.461  1.0
  O  O36  1  0.303  0.636  0.159  1.0
  O  O37  1  0.659  0.716  0.098  1.0
  O  O38  1  0.731  0.929  0.891  1.0
  O  O39  1  0.377  0.849  0.957  1.0
  O  O40  1  0.201  0.863  0.327  1.0
  O  O41  1  0.552  0.937  0.261  1.0
  O  O42  1  0.016  0.782  0.029  1.0
  O  O43  1  0.088  0.990  0.814  1.0
[/CIF]
.
The crystal structure described by Li2MgCo13O28 crystallizes in the triclinic P1 space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(20), one O(25), one O(26), one O(3), one O(4), and one O(9) atom to form distorted LiO6 octahedra that share  a cornercorner with one Co(11)O6 octahedra,  a cornercorner with one Co(12)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(13)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, and  an edgeedge with one Co(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 14-19°. In the second Li site, Li(2) is bonded to one O(12), one O(14), one O(21), one O(22), one O(24), and one O(7) atom to form distorted LiO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Co(11)O6 octahedra,  a cornercorner with one Co(6)O6 octahedra,  a cornercorner with one Co(9)O6 octahedra, corners with two equivalent Co(2)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(12)O6 octahedra,  an edgeedge with one Co(13)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, and  an edgeedge with one Co(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 13-18°. Mg(1) is bonded to one O(13), one O(14), one O(15), one O(16), one O(20), and one O(9) atom to form MgO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra, corners with two equivalent Li(1)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra,  an edgeedge with one Co(8)O6 octahedra, and  an edgeedge with one Co(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 17-19°. There are thirteen inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(2), one O(23), one O(3), one O(4), one O(5), and one O(8) atom to form CoO6 octahedra that share  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Co(12)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, and  an edgeedge with one Co(6)O6 octahedra. In the second Co site, Co(2) is bonded to one O(24), one O(28), one O(3), one O(5), one O(6), and one O(7) atom to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(12)O6 octahedra,  an edgeedge with one Co(13)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and  an edgeedge with one Co(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 13-15°. In the third Co site, Co(3) is bonded to one O(1), one O(2), one O(23), one O(27), one O(28), and one O(6) atom to form edge-sharing CoO6 octahedra. In the fourth Co site, Co(4) is bonded to one O(10), one O(12), one O(2), one O(28), one O(4), and one O(7) atom to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, and  an edgeedge with one Co(7)O6 octahedra. The corner-sharing octahedral tilt angles are 17°. In the fifth Co site, Co(5) is bonded to one O(10), one O(14), one O(3), one O(7), one O(8), and one O(9) atom to form CoO6 octahedra that share  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, and  an edgeedge with one Co(7)O6 octahedra. In the sixth Co site, Co(6) is bonded to one O(11), one O(12), one O(13), one O(4), one O(8), and one O(9) atom to form CoO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, and  an edgeedge with one Co(8)O6 octahedra. The corner-sharing octahedral tilt angles are 17°. In the seventh Co site, Co(7) is bonded to one O(10), one O(11), one O(12), one O(14), one O(16), and one O(18) atom to form CoO6 octahedra that share  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra,  an edgeedge with one Co(8)O6 octahedra, and  an edgeedge with one Co(9)O6 octahedra. In the eighth Co site, Co(8) is bonded to one O(11), one O(13), one O(15), one O(17), one O(18), and one O(19) atom to form CoO6 octahedra that share  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(11)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, and  an edgeedge with one Co(9)O6 octahedra. In the ninth Co site, Co(9) is bonded to one O(16), one O(17), one O(18), one O(20), one O(21), and one O(25) atom to form CoO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(11)O6 octahedra,  an edgeedge with one Co(13)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, and  an edgeedge with one Co(8)O6 octahedra. The corner-sharing octahedral tilt angles are 15°. In the tenth Co site, Co(10) is bonded to one O(15), one O(19), one O(20), one O(21), one O(22), and one O(26) atom to form CoO6 octahedra that share  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(11)O6 octahedra,  an edgeedge with one Co(12)O6 octahedra,  an edgeedge with one Co(13)O6 octahedra,  an edgeedge with one Co(8)O6 octahedra, and  an edgeedge with one Co(9)O6 octahedra. In the eleventh Co site, Co(11) is bonded to one O(1), one O(17), one O(19), one O(22), one O(25), and one O(27) atom to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Li(2)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(12)O6 octahedra,  an edgeedge with one Co(13)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(8)O6 octahedra, and  an edgeedge with one Co(9)O6 octahedra. The corner-sharing octahedral tilt angles are 15°. In the twelfth Co site, Co(12) is bonded to one O(1), one O(22), one O(23), one O(24), one O(26), and one O(5) atom to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(11)O6 octahedra,  an edgeedge with one Co(13)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, and  an edgeedge with one Co(3)O6 octahedra. The corner-sharing octahedral tilt angles are 15°. In the thirteenth Co site, Co(13) is bonded to one O(21), one O(24), one O(25), one O(26), one O(27), and one O(6) atom to form CoO6 octahedra that share  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Co(10)O6 octahedra,  an edgeedge with one Co(11)O6 octahedra,  an edgeedge with one Co(12)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and  an edgeedge with one Co(9)O6 octahedra. There are twenty-eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Co(11), one Co(12), and one Co(3) atom. In the second O site, O(2) is bonded in a distorted T-shaped geometry to one Co(1), one Co(3), and one Co(4) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(1), one Co(2), and one Co(5) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(1), one Co(4), and one Co(6) atom. In the fifth O site, O(5) is bonded in a distorted T-shaped geometry to one Co(1), one Co(12), and one Co(2) atom. In the sixth O site, O(6) is bonded in a distorted T-shaped geometry to one Co(13), one Co(2), and one Co(3) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(2), one Co(4), and one Co(5) atom. In the eighth O site, O(8) is bonded in a distorted T-shaped geometry to one Co(1), one Co(5), and one Co(6) atom. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mg(1), one Co(5), and one Co(6) atom. In the tenth O site, O(10) is bonded in a distorted T-shaped geometry to one Co(4), one Co(5), and one Co(7) atom. In the eleventh O site, O(11) is bonded in a distorted T-shaped geometry to one Co(6), one Co(7), and one Co(8) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(4), one Co(6), and one Co(7) atom. In the thirteenth O site, O(13) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Co(6), and one Co(8) atom. In the fourteenth O site, O(14) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mg(1), one Co(5), and one Co(7) atom. In the fifteenth O site, O(15) is bonded in a distorted T-shaped geometry to one Mg(1), one Co(10), and one Co(8) atom. In the sixteenth O site, O(16) is bonded in a distorted T-shaped geometry to one Mg(1), one Co(7), and one Co(9) atom. In the seventeenth O site, O(17) is bonded in a distorted trigonal non-coplanar geometry to one Co(11), one Co(8), and one Co(9) atom. In the eighteenth O site, O(18) is bonded in a distorted T-shaped geometry to one Co(7), one Co(8), and one Co(9) atom. In the nineteenth O site, O(19) is bonded in a distorted T-shaped geometry to one Co(10), one Co(11), and one Co(8) atom. In the twentieth O site, O(20) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mg(1), one Co(10), and one Co(9) atom. In the twenty-first O site, O(21) is bonded in a see-saw-like geometry to one Li(2), one Co(10), one Co(13), and one Co(9) atom. In the twenty-second O site, O(22) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(10), one Co(11), and one Co(12) atom. In the twenty-third O site, O(23) is bonded in a distorted T-shaped geometry to one Co(1), one Co(12), and one Co(3) atom. In the twenty-fourth O site, O(24) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(12), one Co(13), and one Co(2) atom. In the twenty-fifth O site, O(25) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(11), one Co(13), and one Co(9) atom. In the twenty-sixth O site, O(26) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(10), one Co(12), and one Co(13) atom. In the twenty-seventh O site, O(27) is bonded in a distorted T-shaped geometry to one Co(11), one Co(13), and one Co(3) atom. In the twenty-eighth O site, O(28) is bonded in a distorted T-shaped geometry to one Co(2), one Co(3), and one Co(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li2MgCo13O28
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.552
_cell_length_b   8.233
_cell_length_c   8.705
_cell_angle_alpha   100.213
_cell_angle_beta   104.410
_cell_angle_gamma   105.292
_symmetry_Int_Tables_number   1
_cell_volume   488.229
_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
  Li  Li0  1  0.504  0.001  0.500  1.0
  Li  Li1  1  0.352  0.568  0.925  1.0
  Mg  Mg2  1  0.502  0.504  0.505  1.0
  Co  Co3  1  0.717  0.150  0.863  1.0
  Co  Co4  1  0.356  0.068  0.928  1.0
  Co  Co5  1  0.001  0.001  0.001  1.0
  Co  Co6  1  0.067  0.205  0.779  1.0
  Co  Co7  1  0.427  0.283  0.715  1.0
  Co  Co8  1  0.790  0.362  0.648  1.0
  Co  Co9  1  0.137  0.421  0.565  1.0
  Co  Co10  1  0.860  0.574  0.429  1.0
  Co  Co11  1  0.210  0.636  0.350  1.0
  Co  Co12  1  0.574  0.715  0.285  1.0
  Co  Co13  1  0.930  0.789  0.216  1.0
  Co  Co14  1  0.647  0.937  0.078  1.0
  Co  Co15  1  0.285  0.856  0.141  1.0
  O  O16  1  0.914  0.009  0.188  1.0
  O  O17  1  0.986  0.218  0.970  1.0
  O  O18  1  0.449  0.066  0.743  1.0
  O  O19  1  0.795  0.135  0.672  1.0
  O  O20  1  0.623  0.151  0.046  1.0
  O  O21  1  0.269  0.074  0.113  1.0
  O  O22  1  0.334  0.287  0.898  1.0
  O  O23  1  0.699  0.364  0.835  1.0
  O  O24  1  0.523  0.266  0.539  1.0
  O  O25  1  0.155  0.200  0.597  1.0
  O  O26  1  0.872  0.352  0.456  1.0
  O  O27  1  0.060  0.428  0.759  1.0
  O  O28  1  0.790  0.576  0.620  1.0
  O  O29  1  0.398  0.496  0.699  1.0
  O  O30  1  0.600  0.507  0.306  1.0
  O  O31  1  0.213  0.422  0.378  1.0
  O  O32  1  0.944  0.571  0.240  1.0
  O  O33  1  0.127  0.643  0.539  1.0
  O  O34  1  0.844  0.796  0.400  1.0
  O  O35  1  0.476  0.737  0.461  1.0
  O  O36  1  0.303  0.636  0.159  1.0
  O  O37  1  0.659  0.716  0.098  1.0
  O  O38  1  0.731  0.929  0.891  1.0
  O  O39  1  0.377  0.849  0.957  1.0
  O  O40  1  0.201  0.863  0.327  1.0
  O  O41  1  0.552  0.937  0.261  1.0
  O  O42  1  0.016  0.782  0.029  1.0
  O  O43  1  0.088  0.990  0.814  1.0
[/CIF]
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