The crystal structure described by Li4Cr3Mn3(CoO8)2 is Spinel-derived structured and crystallizes in the monoclinic Cm space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(12), one O(3), and two equivalent O(9) atoms to form LiO4 tetrahedra that share  a cornercorner with one Mn(1)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and corners with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-66°. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(5), one O(7), and two equivalent O(11) atoms. In the third Li site, Li(3) is bonded in a rectangular see-saw-like geometry to one O(4), one O(8), and two equivalent O(1) atoms. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), and two equivalent O(6) atoms to form LiO4 tetrahedra that share  a cornercorner with one Cr(2)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Co(1)O6 octahedra, and corners with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-67°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form CrO6 octahedra that share corners with two equivalent Co(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with two equivalent Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. In the second Cr site, Cr(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Co(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra, and edges with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Co(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. In the second Mn site, Mn(2) is bonded to one O(1), one O(10), one O(12), one O(5), one O(8), and one O(9) atom to form MnO6 octahedra that share corners with two equivalent Co(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-54°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Mn(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-54°. In the second Co site, Co(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-54°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(3), one Cr(2), one Mn(2), and one Co(1) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Cr(1), and one Co(1) atom to form distorted OLiCr2Co tetrahedra that share corners with two equivalent O(4)LiMnCr2 tetrahedra, corners with two equivalent O(6)LiMnCrCo tetrahedra, and edges with two equivalent O(6)LiMnCrCo tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Cr(1), and one Mn(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Cr(1), and one Mn(1) atom to form distorted OLiMnCr2 tetrahedra that share corners with two equivalent O(2)LiCr2Co tetrahedra and corners with four equivalent O(6)LiMnCrCo tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Cr(2), and two equivalent Mn(2) atoms to form distorted OLiMn2Cr tetrahedra that share corners with two equivalent O(12)LiMn2Co tetrahedra and corners with four equivalent O(9)LiMnCrCo tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Cr(1), one Mn(1), and one Co(1) atom to form distorted OLiMnCrCo tetrahedra that share  a cornercorner with one O(2)LiCr2Co tetrahedra,  a cornercorner with one O(6)LiMnCrCo tetrahedra, corners with two equivalent O(4)LiMnCr2 tetrahedra,  an edgeedge with one O(2)LiCr2Co tetrahedra, and  an edgeedge with one O(6)LiMnCrCo tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Cr(1), and one Co(2) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), two equivalent Mn(2), and one Co(1) atom. In the ninth O site, O(9) is bonded to one Li(1), one Cr(2), one Mn(2), and one Co(2) atom to form distorted OLiMnCrCo tetrahedra that share  a cornercorner with one O(12)LiMn2Co tetrahedra,  a cornercorner with one O(9)LiMnCrCo tetrahedra, corners with two equivalent O(5)LiMn2Cr tetrahedra,  an edgeedge with one O(12)LiMn2Co tetrahedra, and  an edgeedge with one O(9)LiMnCrCo tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Cr(2), and two equivalent Mn(2) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(1), one Mn(1), and one Co(2) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Mn(2), and one Co(2) atom to form distorted OLiMn2Co tetrahedra that share corners with two equivalent O(5)LiMn2Cr tetrahedra, corners with two equivalent O(9)LiMnCrCo tetrahedra, and edges with two equivalent O(9)LiMnCrCo tetrahedra. is represented by the CIF card [CIF]
data_Li4Mn3Cr3(CoO8)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.848
_cell_length_b   5.848
_cell_length_c   9.650
_cell_angle_alpha   89.480
_cell_angle_beta   89.480
_cell_angle_gamma   60.053
_symmetry_Int_Tables_number   1
_cell_volume   285.958
_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  0.332  0.332  0.104  1.0
  Li  Li1  1  0.996  0.996  0.003  1.0
  Li  Li2  1  0.997  0.997  0.503  1.0
  Li  Li3  1  0.668  0.668  0.604  1.0
  Mn  Mn4  1  0.170  0.170  0.785  1.0
  Mn  Mn5  1  0.831  0.336  0.286  1.0
  Mn  Mn6  1  0.336  0.831  0.286  1.0
  Cr  Cr7  1  0.664  0.171  0.786  1.0
  Cr  Cr8  1  0.171  0.664  0.786  1.0
  Cr  Cr9  1  0.830  0.830  0.286  1.0
  Co  Co10  1  0.332  0.332  0.506  1.0
  Co  Co11  1  0.666  0.666  0.007  1.0
  O  O12  1  0.682  0.154  0.394  1.0
  O  O13  1  0.485  0.485  0.675  1.0
  O  O14  1  0.328  0.328  0.894  1.0
  O  O15  1  0.006  0.006  0.687  1.0
  O  O16  1  0.004  0.004  0.188  1.0
  O  O17  1  0.154  0.682  0.394  1.0
  O  O18  1  0.485  0.038  0.670  1.0
  O  O19  1  0.038  0.485  0.670  1.0
  O  O20  1  0.839  0.839  0.891  1.0
  O  O21  1  0.157  0.157  0.395  1.0
  O  O22  1  0.967  0.518  0.173  1.0
  O  O23  1  0.518  0.967  0.173  1.0
  O  O24  1  0.660  0.660  0.392  1.0
  O  O25  1  0.839  0.314  0.895  1.0
  O  O26  1  0.519  0.519  0.168  1.0
  O  O27  1  0.314  0.839  0.895  1.0
[/CIF]
.
The crystal structure described by Li4Cr3Mn3(CoO8)2 is Spinel-derived structured and crystallizes in the monoclinic Cm space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(12), one O(3), and two equivalent O(9) atoms to form LiO4 tetrahedra that share  a cornercorner with one Mn(1)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and corners with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-66°. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(5), one O(7), and two equivalent O(11) atoms. In the third Li site, Li(3) is bonded in a rectangular see-saw-like geometry to one O(4), one O(8), and two equivalent O(1) atoms. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), and two equivalent O(6) atoms to form LiO4 tetrahedra that share  a cornercorner with one Cr(2)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Co(1)O6 octahedra, and corners with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-67°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form CrO6 octahedra that share corners with two equivalent Co(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with two equivalent Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. In the second Cr site, Cr(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Co(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra, and edges with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Co(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. In the second Mn site, Mn(2) is bonded to one O(1), one O(10), one O(12), one O(5), one O(8), and one O(9) atom to form MnO6 octahedra that share corners with two equivalent Co(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-54°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Mn(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-54°. In the second Co site, Co(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-54°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(3), one Cr(2), one Mn(2), and one Co(1) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Cr(1), and one Co(1) atom to form distorted OLiCr2Co tetrahedra that share corners with two equivalent O(4)LiMnCr2 tetrahedra, corners with two equivalent O(6)LiMnCrCo tetrahedra, and edges with two equivalent O(6)LiMnCrCo tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Cr(1), and one Mn(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Cr(1), and one Mn(1) atom to form distorted OLiMnCr2 tetrahedra that share corners with two equivalent O(2)LiCr2Co tetrahedra and corners with four equivalent O(6)LiMnCrCo tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Cr(2), and two equivalent Mn(2) atoms to form distorted OLiMn2Cr tetrahedra that share corners with two equivalent O(12)LiMn2Co tetrahedra and corners with four equivalent O(9)LiMnCrCo tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Cr(1), one Mn(1), and one Co(1) atom to form distorted OLiMnCrCo tetrahedra that share  a cornercorner with one O(2)LiCr2Co tetrahedra,  a cornercorner with one O(6)LiMnCrCo tetrahedra, corners with two equivalent O(4)LiMnCr2 tetrahedra,  an edgeedge with one O(2)LiCr2Co tetrahedra, and  an edgeedge with one O(6)LiMnCrCo tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Cr(1), and one Co(2) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), two equivalent Mn(2), and one Co(1) atom. In the ninth O site, O(9) is bonded to one Li(1), one Cr(2), one Mn(2), and one Co(2) atom to form distorted OLiMnCrCo tetrahedra that share  a cornercorner with one O(12)LiMn2Co tetrahedra,  a cornercorner with one O(9)LiMnCrCo tetrahedra, corners with two equivalent O(5)LiMn2Cr tetrahedra,  an edgeedge with one O(12)LiMn2Co tetrahedra, and  an edgeedge with one O(9)LiMnCrCo tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Cr(2), and two equivalent Mn(2) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(1), one Mn(1), and one Co(2) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Mn(2), and one Co(2) atom to form distorted OLiMn2Co tetrahedra that share corners with two equivalent O(5)LiMn2Cr tetrahedra, corners with two equivalent O(9)LiMnCrCo tetrahedra, and edges with two equivalent O(9)LiMnCrCo tetrahedra. is represented by the CIF card [CIF]
data_Li4Mn3Cr3(CoO8)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.848
_cell_length_b   5.848
_cell_length_c   9.650
_cell_angle_alpha   89.480
_cell_angle_beta   89.480
_cell_angle_gamma   60.053
_symmetry_Int_Tables_number   1
_cell_volume   285.958
_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  0.332  0.332  0.104  1.0
  Li  Li1  1  0.996  0.996  0.003  1.0
  Li  Li2  1  0.997  0.997  0.503  1.0
  Li  Li3  1  0.668  0.668  0.604  1.0
  Mn  Mn4  1  0.170  0.170  0.785  1.0
  Mn  Mn5  1  0.831  0.336  0.286  1.0
  Mn  Mn6  1  0.336  0.831  0.286  1.0
  Cr  Cr7  1  0.664  0.171  0.786  1.0
  Cr  Cr8  1  0.171  0.664  0.786  1.0
  Cr  Cr9  1  0.830  0.830  0.286  1.0
  Co  Co10  1  0.332  0.332  0.506  1.0
  Co  Co11  1  0.666  0.666  0.007  1.0
  O  O12  1  0.682  0.154  0.394  1.0
  O  O13  1  0.485  0.485  0.675  1.0
  O  O14  1  0.328  0.328  0.894  1.0
  O  O15  1  0.006  0.006  0.687  1.0
  O  O16  1  0.004  0.004  0.188  1.0
  O  O17  1  0.154  0.682  0.394  1.0
  O  O18  1  0.485  0.038  0.670  1.0
  O  O19  1  0.038  0.485  0.670  1.0
  O  O20  1  0.839  0.839  0.891  1.0
  O  O21  1  0.157  0.157  0.395  1.0
  O  O22  1  0.967  0.518  0.173  1.0
  O  O23  1  0.518  0.967  0.173  1.0
  O  O24  1  0.660  0.660  0.392  1.0
  O  O25  1  0.839  0.314  0.895  1.0
  O  O26  1  0.519  0.519  0.168  1.0
  O  O27  1  0.314  0.839  0.895  1.0
[/CIF]
.