The compound described by Li3Cr4O8 crystallizes in the monoclinic C2/m space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form LiO6 octahedra that share corners with three equivalent Cr(4)O6 octahedra, corners with three equivalent Cr(6)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, edges with two equivalent Cr(5)O6 octahedra, and edges with four equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-10°. In the second Li site, Li(2) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form LiO6 octahedra that share corners with three equivalent Cr(3)O6 octahedra, corners with three equivalent Cr(5)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Cr(4)O6 octahedra,  an edgeedge with one Cr(5)O6 octahedra,  an edgeedge with one Cr(6)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, and edges with two equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-10°. There are six inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(5) and four equivalent O(3) atoms to form CrO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Cr(4)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Cr(5)O6 octahedra. In the second Cr site, Cr(2) is bonded to two equivalent O(6) and four equivalent O(4) atoms to form CrO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Cr(6)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Cr(3)O6 octahedra. In the third Cr site, Cr(3) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with six equivalent Li(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, and edges with two equivalent Cr(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-10°. In the fourth Cr site, Cr(4) is bonded to two equivalent O(1) and four equivalent O(3) atoms to form CrO6 octahedra that share corners with six equivalent Li(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Cr(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-10°. In the fifth Cr site, Cr(5) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(5) atoms to form CrO6 octahedra that share corners with six equivalent Li(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Cr(4)O6 octahedra, and edges with two equivalent Cr(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-9°. In the sixth Cr site, Cr(6) is bonded to two equivalent O(2) and four equivalent O(4) atoms to form CrO6 octahedra that share corners with six equivalent Li(1)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-9°. There are six inequivalent O sites. In the first O site, O(3) is bonded to one Li(1), one Li(2), one Cr(1), one Cr(4), and one Cr(5) atom to form OLi2Cr3 square pyramids that share  a cornercorner with one O(5)Li2Cr3 square pyramid,  a cornercorner with one O(6)Li2Cr3 square pyramid, corners with three equivalent O(4)Li2Cr3 square pyramids, corners with four equivalent O(3)Li2Cr3 square pyramids,  an edgeedge with one O(2)Li3Cr3 octahedra, edges with three equivalent O(1)Li3Cr3 octahedra, edges with two equivalent O(3)Li2Cr3 square pyramids, and edges with two equivalent O(5)Li2Cr3 square pyramids. In the second O site, O(4) is bonded to one Li(1), one Li(2), one Cr(2), one Cr(3), and one Cr(6) atom to form OLi2Cr3 square pyramids that share  a cornercorner with one O(5)Li2Cr3 square pyramid,  a cornercorner with one O(6)Li2Cr3 square pyramid, corners with three equivalent O(3)Li2Cr3 square pyramids, corners with four equivalent O(4)Li2Cr3 square pyramids,  an edgeedge with one O(1)Li3Cr3 octahedra, edges with three equivalent O(2)Li3Cr3 octahedra, edges with two equivalent O(4)Li2Cr3 square pyramids, and edges with two equivalent O(6)Li2Cr3 square pyramids. In the third O site, O(5) is bonded to two equivalent Li(2), one Cr(1), and two equivalent Cr(5) atoms to form OLi2Cr3 square pyramids that share corners with two equivalent O(3)Li2Cr3 square pyramids, corners with two equivalent O(4)Li2Cr3 square pyramids, corners with two equivalent O(6)Li2Cr3 square pyramids, corners with three equivalent O(5)Li2Cr3 square pyramids,  an edgeedge with one O(2)Li3Cr3 octahedra, edges with three equivalent O(1)Li3Cr3 octahedra, and edges with four equivalent O(3)Li2Cr3 square pyramids. In the fourth O site, O(6) is bonded to two equivalent Li(2), one Cr(2), and two equivalent Cr(3) atoms to form OLi2Cr3 square pyramids that share corners with two equivalent O(3)Li2Cr3 square pyramids, corners with two equivalent O(4)Li2Cr3 square pyramids, corners with two equivalent O(5)Li2Cr3 square pyramids, corners with three equivalent O(6)Li2Cr3 square pyramids,  an edgeedge with one O(1)Li3Cr3 octahedra, edges with three equivalent O(2)Li3Cr3 octahedra, and edges with four equivalent O(4)Li2Cr3 square pyramids. In the fifth O site, O(1) is bonded to one Li(1), two equivalent Li(2), one Cr(4), and two equivalent Cr(5) atoms to form OLi3Cr3 octahedra that share corners with three equivalent O(1)Li3Cr3 octahedra, corners with three equivalent O(2)Li3Cr3 octahedra,  an edgeedge with one O(6)Li2Cr3 square pyramid, edges with two equivalent O(4)Li2Cr3 square pyramids, edges with three equivalent O(5)Li2Cr3 square pyramids, and edges with six equivalent O(3)Li2Cr3 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. In the sixth O site, O(2) is bonded to one Li(1), two equivalent Li(2), one Cr(6), and two equivalent Cr(3) atoms to form OLi3Cr3 octahedra that share corners with three equivalent O(1)Li3Cr3 octahedra, corners with three equivalent O(2)Li3Cr3 octahedra,  an edgeedge with one O(5)Li2Cr3 square pyramid, edges with two equivalent O(3)Li2Cr3 square pyramids, edges with three equivalent O(6)Li2Cr3 square pyramids, and edges with six equivalent O(4)Li2Cr3 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. is represented by the CIF file [CIF]
data_Li3Cr4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.893
_cell_length_b   5.893
_cell_length_c   5.960
_cell_angle_alpha   60.518
_cell_angle_beta   60.522
_cell_angle_gamma   60.312
_symmetry_Int_Tables_number   1
_cell_volume   147.829
_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
  Cr  Cr0  1  0.500  0.500  0.500  1.0
  Cr  Cr1  1  0.000  0.500  0.500  1.0
  Cr  Cr2  1  0.500  0.000  0.500  1.0
  Cr  Cr3  1  1.000  1.000  0.500  1.0
  Li  Li4  1  0.500  0.500  0.000  1.0
  Li  Li5  1  0.000  0.500  1.000  1.0
  Li  Li6  1  0.500  1.000  1.000  1.0
  O  O7  1  0.758  0.758  0.724  1.0
  O  O8  1  0.242  0.242  0.276  1.0
  O  O9  1  0.268  0.747  0.716  1.0
  O  O10  1  0.747  0.268  0.716  1.0
  O  O11  1  0.269  0.269  0.714  1.0
  O  O12  1  0.731  0.731  0.286  1.0
  O  O13  1  0.253  0.732  0.284  1.0
  O  O14  1  0.732  0.253  0.284  1.0
[/CIF]
.
The compound described by Li3Cr4O8 crystallizes in the monoclinic C2/m space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form LiO6 octahedra that share corners with three equivalent Cr(4)O6 octahedra, corners with three equivalent Cr(6)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, edges with two equivalent Cr(5)O6 octahedra, and edges with four equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-10°. In the second Li site, Li(2) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form LiO6 octahedra that share corners with three equivalent Cr(3)O6 octahedra, corners with three equivalent Cr(5)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Cr(4)O6 octahedra,  an edgeedge with one Cr(5)O6 octahedra,  an edgeedge with one Cr(6)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, and edges with two equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-10°. There are six inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(5) and four equivalent O(3) atoms to form CrO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Cr(4)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Cr(5)O6 octahedra. In the second Cr site, Cr(2) is bonded to two equivalent O(6) and four equivalent O(4) atoms to form CrO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Cr(6)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Cr(3)O6 octahedra. In the third Cr site, Cr(3) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with six equivalent Li(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, and edges with two equivalent Cr(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-10°. In the fourth Cr site, Cr(4) is bonded to two equivalent O(1) and four equivalent O(3) atoms to form CrO6 octahedra that share corners with six equivalent Li(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Cr(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-10°. In the fifth Cr site, Cr(5) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(5) atoms to form CrO6 octahedra that share corners with six equivalent Li(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Cr(4)O6 octahedra, and edges with two equivalent Cr(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-9°. In the sixth Cr site, Cr(6) is bonded to two equivalent O(2) and four equivalent O(4) atoms to form CrO6 octahedra that share corners with six equivalent Li(1)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-9°. There are six inequivalent O sites. In the first O site, O(3) is bonded to one Li(1), one Li(2), one Cr(1), one Cr(4), and one Cr(5) atom to form OLi2Cr3 square pyramids that share  a cornercorner with one O(5)Li2Cr3 square pyramid,  a cornercorner with one O(6)Li2Cr3 square pyramid, corners with three equivalent O(4)Li2Cr3 square pyramids, corners with four equivalent O(3)Li2Cr3 square pyramids,  an edgeedge with one O(2)Li3Cr3 octahedra, edges with three equivalent O(1)Li3Cr3 octahedra, edges with two equivalent O(3)Li2Cr3 square pyramids, and edges with two equivalent O(5)Li2Cr3 square pyramids. In the second O site, O(4) is bonded to one Li(1), one Li(2), one Cr(2), one Cr(3), and one Cr(6) atom to form OLi2Cr3 square pyramids that share  a cornercorner with one O(5)Li2Cr3 square pyramid,  a cornercorner with one O(6)Li2Cr3 square pyramid, corners with three equivalent O(3)Li2Cr3 square pyramids, corners with four equivalent O(4)Li2Cr3 square pyramids,  an edgeedge with one O(1)Li3Cr3 octahedra, edges with three equivalent O(2)Li3Cr3 octahedra, edges with two equivalent O(4)Li2Cr3 square pyramids, and edges with two equivalent O(6)Li2Cr3 square pyramids. In the third O site, O(5) is bonded to two equivalent Li(2), one Cr(1), and two equivalent Cr(5) atoms to form OLi2Cr3 square pyramids that share corners with two equivalent O(3)Li2Cr3 square pyramids, corners with two equivalent O(4)Li2Cr3 square pyramids, corners with two equivalent O(6)Li2Cr3 square pyramids, corners with three equivalent O(5)Li2Cr3 square pyramids,  an edgeedge with one O(2)Li3Cr3 octahedra, edges with three equivalent O(1)Li3Cr3 octahedra, and edges with four equivalent O(3)Li2Cr3 square pyramids. In the fourth O site, O(6) is bonded to two equivalent Li(2), one Cr(2), and two equivalent Cr(3) atoms to form OLi2Cr3 square pyramids that share corners with two equivalent O(3)Li2Cr3 square pyramids, corners with two equivalent O(4)Li2Cr3 square pyramids, corners with two equivalent O(5)Li2Cr3 square pyramids, corners with three equivalent O(6)Li2Cr3 square pyramids,  an edgeedge with one O(1)Li3Cr3 octahedra, edges with three equivalent O(2)Li3Cr3 octahedra, and edges with four equivalent O(4)Li2Cr3 square pyramids. In the fifth O site, O(1) is bonded to one Li(1), two equivalent Li(2), one Cr(4), and two equivalent Cr(5) atoms to form OLi3Cr3 octahedra that share corners with three equivalent O(1)Li3Cr3 octahedra, corners with three equivalent O(2)Li3Cr3 octahedra,  an edgeedge with one O(6)Li2Cr3 square pyramid, edges with two equivalent O(4)Li2Cr3 square pyramids, edges with three equivalent O(5)Li2Cr3 square pyramids, and edges with six equivalent O(3)Li2Cr3 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. In the sixth O site, O(2) is bonded to one Li(1), two equivalent Li(2), one Cr(6), and two equivalent Cr(3) atoms to form OLi3Cr3 octahedra that share corners with three equivalent O(1)Li3Cr3 octahedra, corners with three equivalent O(2)Li3Cr3 octahedra,  an edgeedge with one O(5)Li2Cr3 square pyramid, edges with two equivalent O(3)Li2Cr3 square pyramids, edges with three equivalent O(6)Li2Cr3 square pyramids, and edges with six equivalent O(4)Li2Cr3 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. is represented by the CIF file [CIF]
data_Li3Cr4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.893
_cell_length_b   5.893
_cell_length_c   5.960
_cell_angle_alpha   60.518
_cell_angle_beta   60.522
_cell_angle_gamma   60.312
_symmetry_Int_Tables_number   1
_cell_volume   147.829
_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
  Cr  Cr0  1  0.500  0.500  0.500  1.0
  Cr  Cr1  1  0.000  0.500  0.500  1.0
  Cr  Cr2  1  0.500  0.000  0.500  1.0
  Cr  Cr3  1  1.000  1.000  0.500  1.0
  Li  Li4  1  0.500  0.500  0.000  1.0
  Li  Li5  1  0.000  0.500  1.000  1.0
  Li  Li6  1  0.500  1.000  1.000  1.0
  O  O7  1  0.758  0.758  0.724  1.0
  O  O8  1  0.242  0.242  0.276  1.0
  O  O9  1  0.268  0.747  0.716  1.0
  O  O10  1  0.747  0.268  0.716  1.0
  O  O11  1  0.269  0.269  0.714  1.0
  O  O12  1  0.731  0.731  0.286  1.0
  O  O13  1  0.253  0.732  0.284  1.0
  O  O14  1  0.732  0.253  0.284  1.0
[/CIF]
.