The structure described by Li4V5Cr3O16 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 V(3)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent V(4)O6 octahedra, and corners with four equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-62°. In the second Li site, Li(2) is bonded to one O(5), one O(7), and two equivalent O(11) atoms to form distorted LiO4 tetrahedra that share  a cornercorner with one Cr(2)O6 octahedra, corners with two equivalent V(1)O6 octahedra, corners with three equivalent V(4)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. 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 V(1)O6 octahedra, corners with two equivalent V(3)O6 octahedra, corners with three equivalent V(2)O6 octahedra, and corners with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-62°. There are four inequivalent V sites. In the first V site, V(1) 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 VO6 octahedra that share corners with two equivalent V(2)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one V(4)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. In the second V site, V(2) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form VO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent V(1)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one V(3)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-54°. In the third V site, V(3) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form VO6 octahedra that share corners with two equivalent V(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one V(2)O6 octahedra, edges with four equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. In the fourth V site, V(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form VO6 octahedra that share corners with two equivalent V(3)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-52°. 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 V(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one V(2)O6 octahedra, edges with two equivalent V(3)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 50-52°. 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 V(2)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one V(4)O6 octahedra, and edges with four equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles are 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 V(1), one V(2), and one Cr(2) atom. In the second O site, O(2) is bonded to one Li(4), one V(2), and two equivalent Cr(1) atoms to form distorted corner-sharing OLiVCr2 tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one V(3), and two equivalent Cr(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one V(3), and two equivalent Cr(1) atoms to form corner-sharing OLiVCr2 tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), two equivalent V(1), and one Cr(2) atom to form distorted OLiV2Cr tetrahedra that share corners with two equivalent O(12)LiV3 tetrahedra and corners with four equivalent O(9)LiV2Cr tetrahedra. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Li(4), one V(2), one V(3), and one Cr(1) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one V(4), and two equivalent Cr(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one V(2), and two equivalent V(1) atoms. In the ninth O site, O(9) is bonded to one Li(1), one V(1), one V(4), and one Cr(2) atom to form distorted OLiV2Cr tetrahedra that share  a cornercorner with one O(9)LiV2Cr tetrahedra,  a cornercorner with one O(12)LiV3 tetrahedra, corners with two equivalent O(5)LiV2Cr tetrahedra,  an edgeedge with one O(9)LiV2Cr tetrahedra, and  an edgeedge with one O(12)LiV3 tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent V(1), and one Cr(2) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one V(3), one V(4), and one Cr(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one V(4), and two equivalent V(1) atoms to form a mixture of distorted corner and edge-sharing OLiV3 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4V5Cr3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.878
_cell_length_b   5.878
_cell_length_c   9.571
_cell_angle_alpha   89.230
_cell_angle_beta   89.230
_cell_angle_gamma   60.976
_symmetry_Int_Tables_number   1
_cell_volume   289.153
_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  0.667  0.667  0.896  1.0
  Li  Li1  1  0.999  0.999  0.998  1.0
  Li  Li2  1  0.999  0.999  0.494  1.0
  Li  Li3  1  0.335  0.335  0.392  1.0
  V  V4  1  0.661  0.165  0.715  1.0
  V  V5  1  0.663  0.663  0.486  1.0
  V  V6  1  0.826  0.826  0.217  1.0
  V  V7  1  0.335  0.335  0.992  1.0
  V  V8  1  0.165  0.661  0.715  1.0
  Cr  Cr9  1  0.826  0.341  0.212  1.0
  Cr  Cr10  1  0.341  0.826  0.212  1.0
  Cr  Cr11  1  0.169  0.169  0.713  1.0
  O  O12  1  0.827  0.322  0.604  1.0
  O  O13  1  0.519  0.519  0.337  1.0
  O  O14  1  0.677  0.677  0.103  1.0
  O  O15  1  0.995  0.995  0.306  1.0
  O  O16  1  0.997  0.997  0.813  1.0
  O  O17  1  0.322  0.827  0.604  1.0
  O  O18  1  0.963  0.523  0.340  1.0
  O  O19  1  0.523  0.963  0.340  1.0
  O  O20  1  0.173  0.173  0.091  1.0
  O  O21  1  0.834  0.834  0.608  1.0
  O  O22  1  0.487  0.040  0.839  1.0
  O  O23  1  0.040  0.487  0.839  1.0
  O  O24  1  0.339  0.339  0.604  1.0
  O  O25  1  0.665  0.169  0.095  1.0
  O  O26  1  0.478  0.478  0.844  1.0
  O  O27  1  0.169  0.665  0.095  1.0
[/CIF]
.
The structure described by Li4V5Cr3O16 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 V(3)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent V(4)O6 octahedra, and corners with four equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-62°. In the second Li site, Li(2) is bonded to one O(5), one O(7), and two equivalent O(11) atoms to form distorted LiO4 tetrahedra that share  a cornercorner with one Cr(2)O6 octahedra, corners with two equivalent V(1)O6 octahedra, corners with three equivalent V(4)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. 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 V(1)O6 octahedra, corners with two equivalent V(3)O6 octahedra, corners with three equivalent V(2)O6 octahedra, and corners with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-62°. There are four inequivalent V sites. In the first V site, V(1) 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 VO6 octahedra that share corners with two equivalent V(2)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one V(4)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. In the second V site, V(2) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form VO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent V(1)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one V(3)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-54°. In the third V site, V(3) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form VO6 octahedra that share corners with two equivalent V(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one V(2)O6 octahedra, edges with four equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. In the fourth V site, V(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form VO6 octahedra that share corners with two equivalent V(3)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-52°. 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 V(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one V(2)O6 octahedra, edges with two equivalent V(3)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 50-52°. 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 V(2)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one V(4)O6 octahedra, and edges with four equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles are 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 V(1), one V(2), and one Cr(2) atom. In the second O site, O(2) is bonded to one Li(4), one V(2), and two equivalent Cr(1) atoms to form distorted corner-sharing OLiVCr2 tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one V(3), and two equivalent Cr(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one V(3), and two equivalent Cr(1) atoms to form corner-sharing OLiVCr2 tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), two equivalent V(1), and one Cr(2) atom to form distorted OLiV2Cr tetrahedra that share corners with two equivalent O(12)LiV3 tetrahedra and corners with four equivalent O(9)LiV2Cr tetrahedra. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Li(4), one V(2), one V(3), and one Cr(1) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one V(4), and two equivalent Cr(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one V(2), and two equivalent V(1) atoms. In the ninth O site, O(9) is bonded to one Li(1), one V(1), one V(4), and one Cr(2) atom to form distorted OLiV2Cr tetrahedra that share  a cornercorner with one O(9)LiV2Cr tetrahedra,  a cornercorner with one O(12)LiV3 tetrahedra, corners with two equivalent O(5)LiV2Cr tetrahedra,  an edgeedge with one O(9)LiV2Cr tetrahedra, and  an edgeedge with one O(12)LiV3 tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent V(1), and one Cr(2) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one V(3), one V(4), and one Cr(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one V(4), and two equivalent V(1) atoms to form a mixture of distorted corner and edge-sharing OLiV3 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4V5Cr3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.878
_cell_length_b   5.878
_cell_length_c   9.571
_cell_angle_alpha   89.230
_cell_angle_beta   89.230
_cell_angle_gamma   60.976
_symmetry_Int_Tables_number   1
_cell_volume   289.153
_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  0.667  0.667  0.896  1.0
  Li  Li1  1  0.999  0.999  0.998  1.0
  Li  Li2  1  0.999  0.999  0.494  1.0
  Li  Li3  1  0.335  0.335  0.392  1.0
  V  V4  1  0.661  0.165  0.715  1.0
  V  V5  1  0.663  0.663  0.486  1.0
  V  V6  1  0.826  0.826  0.217  1.0
  V  V7  1  0.335  0.335  0.992  1.0
  V  V8  1  0.165  0.661  0.715  1.0
  Cr  Cr9  1  0.826  0.341  0.212  1.0
  Cr  Cr10  1  0.341  0.826  0.212  1.0
  Cr  Cr11  1  0.169  0.169  0.713  1.0
  O  O12  1  0.827  0.322  0.604  1.0
  O  O13  1  0.519  0.519  0.337  1.0
  O  O14  1  0.677  0.677  0.103  1.0
  O  O15  1  0.995  0.995  0.306  1.0
  O  O16  1  0.997  0.997  0.813  1.0
  O  O17  1  0.322  0.827  0.604  1.0
  O  O18  1  0.963  0.523  0.340  1.0
  O  O19  1  0.523  0.963  0.340  1.0
  O  O20  1  0.173  0.173  0.091  1.0
  O  O21  1  0.834  0.834  0.608  1.0
  O  O22  1  0.487  0.040  0.839  1.0
  O  O23  1  0.040  0.487  0.839  1.0
  O  O24  1  0.339  0.339  0.604  1.0
  O  O25  1  0.665  0.169  0.095  1.0
  O  O26  1  0.478  0.478  0.844  1.0
  O  O27  1  0.169  0.665  0.095  1.0
[/CIF]
.