The material described by LiV2CrO6 is Corundum-derived structured and 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(4), one O(6), two equivalent O(3), and two equivalent O(5) atoms to form LiO6 octahedra that share  a cornercorner with one V(2)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra, corners with four equivalent V(1)O6 octahedra, edges with two equivalent V(1)O6 octahedra, edges with two equivalent V(2)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-16°. In the second Li site, Li(2) is bonded to two equivalent O(2) and four equivalent O(1) atoms to form LiO6 octahedra that share corners with two equivalent V(2)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with four equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-12°. There are two inequivalent V sites. In the first V site, V(1) is bonded to one O(1), one O(2), one O(4), one O(5), and two equivalent O(3) atoms to form VO6 octahedra that share corners with two equivalent Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles are 10°. In the second V site, V(2) is bonded to one O(2), one O(6), two equivalent O(3), and two equivalent O(5) atoms to form VO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Li(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with four equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-11°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(1), two equivalent O(5), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Li(2)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles are 12°. In the second Cr site, Cr(2) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form CrO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with four equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles are 16°. There are six inequivalent O sites. In the first O site, O(6) is bonded in a rectangular see-saw-like geometry to one Li(1), one V(2), and two equivalent Cr(1) atoms. In the second O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(2), one V(1), one Cr(1), and one Cr(2) atom. In the third O site, O(2) is bonded in a rectangular see-saw-like geometry to one Li(2), one V(2), and two equivalent V(1) atoms. In the fourth O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one V(2), and two equivalent V(1) atoms. In the fifth O site, O(4) is bonded in a see-saw-like geometry to one Li(1), two equivalent V(1), and one Cr(2) atom. In the sixth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Li(1), one V(1), one V(2), and one Cr(1) atom. is represented by the CIF file [CIF]
data_LiV2CrO6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.940
_cell_length_b   7.940
_cell_length_c   6.066
_cell_angle_alpha   77.670
_cell_angle_beta   77.670
_cell_angle_gamma   68.106
_symmetry_Int_Tables_number   1
_cell_volume   342.882
_cell_formula_units_Z   3
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  0.330  0.330  0.343  1.0
  Li  Li1  1  0.000  0.000  0.000  1.0
  Li  Li2  1  0.670  0.670  0.657  1.0
  V  V3  1  0.005  0.665  0.832  1.0
  V  V4  1  0.335  0.995  0.168  1.0
  V  V5  1  0.340  0.340  0.834  1.0
  V  V6  1  0.665  0.005  0.832  1.0
  V  V7  1  0.660  0.660  0.166  1.0
  V  V8  1  0.995  0.335  0.168  1.0
  Cr  Cr9  1  0.328  0.672  0.500  1.0
  Cr  Cr10  1  0.672  0.328  0.500  1.0
  Cr  Cr11  1  0.000  0.000  0.500  1.0
  O  O12  1  0.177  0.852  0.267  1.0
  O  O13  1  0.179  0.179  0.947  1.0
  O  O14  1  0.511  0.842  0.942  1.0
  O  O15  1  0.148  0.823  0.733  1.0
  O  O16  1  0.163  0.163  0.374  1.0
  O  O17  1  0.493  0.824  0.385  1.0
  O  O18  1  0.158  0.489  0.058  1.0
  O  O19  1  0.489  0.158  0.058  1.0
  O  O20  1  0.821  0.821  0.053  1.0
  O  O21  1  0.176  0.507  0.615  1.0
  O  O22  1  0.507  0.176  0.615  1.0
  O  O23  1  0.837  0.837  0.626  1.0
  O  O24  1  0.513  0.513  0.272  1.0
  O  O25  1  0.852  0.177  0.267  1.0
  O  O26  1  0.842  0.511  0.942  1.0
  O  O27  1  0.487  0.487  0.728  1.0
  O  O28  1  0.823  0.148  0.733  1.0
  O  O29  1  0.824  0.493  0.385  1.0
[/CIF]
.
The material described by LiV2CrO6 is Corundum-derived structured and 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(4), one O(6), two equivalent O(3), and two equivalent O(5) atoms to form LiO6 octahedra that share  a cornercorner with one V(2)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra, corners with four equivalent V(1)O6 octahedra, edges with two equivalent V(1)O6 octahedra, edges with two equivalent V(2)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-16°. In the second Li site, Li(2) is bonded to two equivalent O(2) and four equivalent O(1) atoms to form LiO6 octahedra that share corners with two equivalent V(2)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with four equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-12°. There are two inequivalent V sites. In the first V site, V(1) is bonded to one O(1), one O(2), one O(4), one O(5), and two equivalent O(3) atoms to form VO6 octahedra that share corners with two equivalent Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles are 10°. In the second V site, V(2) is bonded to one O(2), one O(6), two equivalent O(3), and two equivalent O(5) atoms to form VO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Li(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with four equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-11°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(1), two equivalent O(5), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Li(2)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles are 12°. In the second Cr site, Cr(2) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form CrO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with four equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles are 16°. There are six inequivalent O sites. In the first O site, O(6) is bonded in a rectangular see-saw-like geometry to one Li(1), one V(2), and two equivalent Cr(1) atoms. In the second O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(2), one V(1), one Cr(1), and one Cr(2) atom. In the third O site, O(2) is bonded in a rectangular see-saw-like geometry to one Li(2), one V(2), and two equivalent V(1) atoms. In the fourth O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one V(2), and two equivalent V(1) atoms. In the fifth O site, O(4) is bonded in a see-saw-like geometry to one Li(1), two equivalent V(1), and one Cr(2) atom. In the sixth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Li(1), one V(1), one V(2), and one Cr(1) atom. is represented by the CIF file [CIF]
data_LiV2CrO6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.940
_cell_length_b   7.940
_cell_length_c   6.066
_cell_angle_alpha   77.670
_cell_angle_beta   77.670
_cell_angle_gamma   68.106
_symmetry_Int_Tables_number   1
_cell_volume   342.882
_cell_formula_units_Z   3
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  0.330  0.330  0.343  1.0
  Li  Li1  1  0.000  0.000  0.000  1.0
  Li  Li2  1  0.670  0.670  0.657  1.0
  V  V3  1  0.005  0.665  0.832  1.0
  V  V4  1  0.335  0.995  0.168  1.0
  V  V5  1  0.340  0.340  0.834  1.0
  V  V6  1  0.665  0.005  0.832  1.0
  V  V7  1  0.660  0.660  0.166  1.0
  V  V8  1  0.995  0.335  0.168  1.0
  Cr  Cr9  1  0.328  0.672  0.500  1.0
  Cr  Cr10  1  0.672  0.328  0.500  1.0
  Cr  Cr11  1  0.000  0.000  0.500  1.0
  O  O12  1  0.177  0.852  0.267  1.0
  O  O13  1  0.179  0.179  0.947  1.0
  O  O14  1  0.511  0.842  0.942  1.0
  O  O15  1  0.148  0.823  0.733  1.0
  O  O16  1  0.163  0.163  0.374  1.0
  O  O17  1  0.493  0.824  0.385  1.0
  O  O18  1  0.158  0.489  0.058  1.0
  O  O19  1  0.489  0.158  0.058  1.0
  O  O20  1  0.821  0.821  0.053  1.0
  O  O21  1  0.176  0.507  0.615  1.0
  O  O22  1  0.507  0.176  0.615  1.0
  O  O23  1  0.837  0.837  0.626  1.0
  O  O24  1  0.513  0.513  0.272  1.0
  O  O25  1  0.852  0.177  0.267  1.0
  O  O26  1  0.842  0.511  0.942  1.0
  O  O27  1  0.487  0.487  0.728  1.0
  O  O28  1  0.823  0.148  0.733  1.0
  O  O29  1  0.824  0.493  0.385  1.0
[/CIF]
.