The crystal structure described by Li5Cr3MnO8 crystallizes in the hexagonal P6_3mc space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded in a 6-coordinate geometry to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms. In the second Li site, Li(2) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form LiO6 octahedra that share corners with three equivalent Mn(1)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, edges with six equivalent Cr(1)O6 octahedra, and  a faceface with one Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles are 11°. In the third Li site, Li(3) is bonded to one O(3) and three equivalent O(1) atoms to form distorted LiO4 tetrahedra that share corners with three equivalent Li(2)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra, and edges with three equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-61°. Cr(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form CrO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra,  a cornercorner with one Li(3)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with four equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. Mn(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form MnO6 octahedra that share corners with three equivalent Li(2)O6 octahedra, corners with six equivalent Cr(1)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, edges with three equivalent Cr(1)O6 octahedra, and  a faceface with one Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-51°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 7-coordinate geometry to one Li(2), one Li(3), two equivalent Li(1), two equivalent Cr(1), and one Mn(1) atom. In the second O site, O(2) is bonded to one Li(2), two equivalent Li(1), two equivalent Cr(1), and one Mn(1) atom to form OLi3MnCr2 octahedra that share edges with four equivalent O(2)Li3MnCr2 octahedra and edges with two equivalent O(4)Li3Cr3 pentagonal pyramids. In the third O site, O(3) is bonded in a 7-coordinate geometry to one Li(3), three equivalent Li(1), and three equivalent Cr(1) atoms. In the fourth O site, O(4) is bonded to three equivalent Li(1) and three equivalent Cr(1) atoms to form distorted edge-sharing OLi3Cr3 pentagonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li5MnCr3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.013
_cell_length_b   6.013
_cell_length_c   9.941
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   311.268
_cell_formula_units_Z   2
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  0.388  0.194  0.437  1.0
  Li  Li1  1  0.667  0.333  0.224  1.0
  Li  Li2  1  0.806  0.194  0.437  1.0
  Li  Li3  1  0.806  0.612  0.437  1.0
  Li  Li4  1  0.000  0.000  0.516  1.0
  Li  Li5  1  0.194  0.806  0.937  1.0
  Li  Li6  1  0.333  0.667  0.724  1.0
  Li  Li7  1  0.194  0.388  0.937  1.0
  Li  Li8  1  0.000  0.000  0.016  1.0
  Li  Li9  1  0.612  0.806  0.937  1.0
  Mn  Mn10  1  0.333  0.667  0.475  1.0
  Mn  Mn11  1  0.667  0.333  0.975  1.0
  Cr  Cr12  1  0.171  0.829  0.215  1.0
  Cr  Cr13  1  0.341  0.171  0.715  1.0
  Cr  Cr14  1  0.171  0.341  0.215  1.0
  Cr  Cr15  1  0.829  0.659  0.715  1.0
  Cr  Cr16  1  0.659  0.829  0.215  1.0
  Cr  Cr17  1  0.829  0.171  0.715  1.0
  O  O18  1  0.321  0.161  0.101  1.0
  O  O19  1  0.161  0.839  0.601  1.0
  O  O20  1  0.014  0.507  0.329  1.0
  O  O21  1  0.507  0.493  0.829  1.0
  O  O22  1  0.000  0.000  0.326  1.0
  O  O23  1  0.333  0.667  0.100  1.0
  O  O24  1  0.839  0.679  0.101  1.0
  O  O25  1  0.493  0.986  0.329  1.0
  O  O26  1  0.000  0.000  0.826  1.0
  O  O27  1  0.161  0.321  0.601  1.0
  O  O28  1  0.667  0.333  0.600  1.0
  O  O29  1  0.507  0.014  0.829  1.0
  O  O30  1  0.493  0.507  0.329  1.0
  O  O31  1  0.986  0.493  0.829  1.0
  O  O32  1  0.839  0.161  0.101  1.0
  O  O33  1  0.679  0.839  0.601  1.0
[/CIF]
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The crystal structure described by Li5Cr3MnO8 crystallizes in the hexagonal P6_3mc space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded in a 6-coordinate geometry to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms. In the second Li site, Li(2) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form LiO6 octahedra that share corners with three equivalent Mn(1)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, edges with six equivalent Cr(1)O6 octahedra, and  a faceface with one Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles are 11°. In the third Li site, Li(3) is bonded to one O(3) and three equivalent O(1) atoms to form distorted LiO4 tetrahedra that share corners with three equivalent Li(2)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra, and edges with three equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-61°. Cr(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form CrO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra,  a cornercorner with one Li(3)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with four equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. Mn(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form MnO6 octahedra that share corners with three equivalent Li(2)O6 octahedra, corners with six equivalent Cr(1)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, edges with three equivalent Cr(1)O6 octahedra, and  a faceface with one Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-51°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 7-coordinate geometry to one Li(2), one Li(3), two equivalent Li(1), two equivalent Cr(1), and one Mn(1) atom. In the second O site, O(2) is bonded to one Li(2), two equivalent Li(1), two equivalent Cr(1), and one Mn(1) atom to form OLi3MnCr2 octahedra that share edges with four equivalent O(2)Li3MnCr2 octahedra and edges with two equivalent O(4)Li3Cr3 pentagonal pyramids. In the third O site, O(3) is bonded in a 7-coordinate geometry to one Li(3), three equivalent Li(1), and three equivalent Cr(1) atoms. In the fourth O site, O(4) is bonded to three equivalent Li(1) and three equivalent Cr(1) atoms to form distorted edge-sharing OLi3Cr3 pentagonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li5MnCr3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.013
_cell_length_b   6.013
_cell_length_c   9.941
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   311.268
_cell_formula_units_Z   2
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  0.388  0.194  0.437  1.0
  Li  Li1  1  0.667  0.333  0.224  1.0
  Li  Li2  1  0.806  0.194  0.437  1.0
  Li  Li3  1  0.806  0.612  0.437  1.0
  Li  Li4  1  0.000  0.000  0.516  1.0
  Li  Li5  1  0.194  0.806  0.937  1.0
  Li  Li6  1  0.333  0.667  0.724  1.0
  Li  Li7  1  0.194  0.388  0.937  1.0
  Li  Li8  1  0.000  0.000  0.016  1.0
  Li  Li9  1  0.612  0.806  0.937  1.0
  Mn  Mn10  1  0.333  0.667  0.475  1.0
  Mn  Mn11  1  0.667  0.333  0.975  1.0
  Cr  Cr12  1  0.171  0.829  0.215  1.0
  Cr  Cr13  1  0.341  0.171  0.715  1.0
  Cr  Cr14  1  0.171  0.341  0.215  1.0
  Cr  Cr15  1  0.829  0.659  0.715  1.0
  Cr  Cr16  1  0.659  0.829  0.215  1.0
  Cr  Cr17  1  0.829  0.171  0.715  1.0
  O  O18  1  0.321  0.161  0.101  1.0
  O  O19  1  0.161  0.839  0.601  1.0
  O  O20  1  0.014  0.507  0.329  1.0
  O  O21  1  0.507  0.493  0.829  1.0
  O  O22  1  0.000  0.000  0.326  1.0
  O  O23  1  0.333  0.667  0.100  1.0
  O  O24  1  0.839  0.679  0.101  1.0
  O  O25  1  0.493  0.986  0.329  1.0
  O  O26  1  0.000  0.000  0.826  1.0
  O  O27  1  0.161  0.321  0.601  1.0
  O  O28  1  0.667  0.333  0.600  1.0
  O  O29  1  0.507  0.014  0.829  1.0
  O  O30  1  0.493  0.507  0.329  1.0
  O  O31  1  0.986  0.493  0.829  1.0
  O  O32  1  0.839  0.161  0.101  1.0
  O  O33  1  0.679  0.839  0.601  1.0
[/CIF]
.