The crystal structure described by Li4Cr5Co3O16 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 Co(1)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(3)O6 octahedra, corners with three equivalent Cr(4)O6 octahedra, and corners with four equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. In the second Li site, Li(2) is bonded in a distorted 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 to one O(4), one O(8), and two equivalent O(1) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Co(1)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-64°. 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(3)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and corners with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-62°. There are four 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 Cr(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the second Cr site, Cr(2) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Cr(3)O6 octahedra, corners with four equivalent Co(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the third Cr site, Cr(3) 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 Cr(2)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(4)O6 octahedra, edges with four equivalent Co(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. In the fourth Cr site, Cr(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(3)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent Cr(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Cr(2)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. In the second Co site, Co(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 CoO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(4)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 51-52°. 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 Cr(3), and one Co(2) atom. In the second O site, O(2) is bonded to one Li(4), one Cr(2), and two equivalent Cr(1) atoms to form distorted OLiCr3 tetrahedra that share corners with two equivalent O(4)LiCr2Co tetrahedra, corners with two equivalent O(6)LiCr2Co tetrahedra,  a cornercorner with one O(10)LiCrCo2 trigonal pyramid, and edges with two equivalent O(6)LiCr2Co tetrahedra. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), two equivalent Cr(1), and one Co(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Cr(1), and one Co(1) atom to form OLiCr2Co tetrahedra that share corners with two equivalent O(2)LiCr3 tetrahedra and corners with four equivalent O(6)LiCr2Co tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Cr(3), and two equivalent Co(2) atoms to form OLiCrCo2 tetrahedra that share corners with two equivalent O(12)LiCrCo2 tetrahedra, corners with four equivalent O(9)LiCr2Co tetrahedra, and corners with three equivalent O(10)LiCrCo2 trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Cr(1), one Cr(2), and one Co(1) atom to form distorted OLiCr2Co tetrahedra that share  a cornercorner with one O(6)LiCr2Co tetrahedra,  a cornercorner with one O(2)LiCr3 tetrahedra, corners with two equivalent O(4)LiCr2Co tetrahedra,  a cornercorner with one O(10)LiCrCo2 trigonal pyramid,  an edgeedge with one O(6)LiCr2Co tetrahedra, and  an edgeedge with one O(2)LiCr3 tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(4), and two equivalent Cr(1) atoms. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one Cr(2), and two equivalent Co(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Cr(3), one Cr(4), and one Co(2) atom to form distorted OLiCr2Co tetrahedra that share  a cornercorner with one O(9)LiCr2Co tetrahedra,  a cornercorner with one O(12)LiCrCo2 tetrahedra, corners with two equivalent O(5)LiCrCo2 tetrahedra,  an edgeedge with one O(9)LiCr2Co tetrahedra,  an edgeedge with one O(12)LiCrCo2 tetrahedra, and  an edgeedge with one O(10)LiCrCo2 trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(4), one Cr(3), and two equivalent Co(2) atoms to form distorted OLiCrCo2 trigonal pyramids that share  a cornercorner with one O(2)LiCr3 tetrahedra, corners with two equivalent O(6)LiCr2Co tetrahedra, corners with three equivalent O(5)LiCrCo2 tetrahedra,  an edgeedge with one O(12)LiCrCo2 tetrahedra, and edges with two equivalent O(9)LiCr2Co tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(1), one Cr(4), and one Co(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Cr(4), and two equivalent Co(2) atoms to form distorted OLiCrCo2 tetrahedra that share corners with two equivalent O(9)LiCr2Co tetrahedra, corners with two equivalent O(5)LiCrCo2 tetrahedra, edges with two equivalent O(9)LiCr2Co tetrahedra, and  an edgeedge with one O(10)LiCrCo2 trigonal pyramid. is represented by the CIF card [CIF]
data_Li4Cr5Co3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.705
_cell_length_b   5.705
_cell_length_c   9.313
_cell_angle_alpha   89.870
_cell_angle_beta   89.870
_cell_angle_gamma   60.442
_symmetry_Int_Tables_number   1
_cell_volume   263.680
_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  0.330  0.330  0.110  1.0
  Li  Li1  1  0.007  0.007  0.004  1.0
  Li  Li2  1  0.006  0.006  0.502  1.0
  Li  Li3  1  0.664  0.664  0.605  1.0
  Cr  Cr4  1  0.171  0.656  0.788  1.0
  Cr  Cr5  1  0.332  0.332  0.508  1.0
  Cr  Cr6  1  0.656  0.171  0.788  1.0
  Cr  Cr7  1  0.828  0.828  0.289  1.0
  Cr  Cr8  1  0.665  0.665  0.013  1.0
  Co  Co9  1  0.172  0.172  0.787  1.0
  Co  Co10  1  0.341  0.831  0.287  1.0
  Co  Co11  1  0.831  0.341  0.287  1.0
  O  O12  1  0.165  0.667  0.398  1.0
  O  O13  1  0.478  0.478  0.658  1.0
  O  O14  1  0.333  0.333  0.900  1.0
  O  O15  1  0.002  0.002  0.693  1.0
  O  O16  1  0.002  0.002  0.194  1.0
  O  O17  1  0.667  0.165  0.398  1.0
  O  O18  1  0.042  0.478  0.658  1.0
  O  O19  1  0.478  0.042  0.658  1.0
  O  O20  1  0.833  0.833  0.898  1.0
  O  O21  1  0.169  0.169  0.396  1.0
  O  O22  1  0.520  0.956  0.159  1.0
  O  O23  1  0.956  0.520  0.159  1.0
  O  O24  1  0.664  0.664  0.396  1.0
  O  O25  1  0.334  0.831  0.898  1.0
  O  O26  1  0.521  0.521  0.164  1.0
  O  O27  1  0.831  0.334  0.898  1.0
[/CIF]
.
The crystal structure described by Li4Cr5Co3O16 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 Co(1)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(3)O6 octahedra, corners with three equivalent Cr(4)O6 octahedra, and corners with four equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. In the second Li site, Li(2) is bonded in a distorted 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 to one O(4), one O(8), and two equivalent O(1) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Co(1)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-64°. 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(3)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and corners with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-62°. There are four 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 Cr(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the second Cr site, Cr(2) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Cr(3)O6 octahedra, corners with four equivalent Co(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the third Cr site, Cr(3) 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 Cr(2)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(4)O6 octahedra, edges with four equivalent Co(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. In the fourth Cr site, Cr(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(3)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent Cr(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Cr(2)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. In the second Co site, Co(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 CoO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(4)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 51-52°. 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 Cr(3), and one Co(2) atom. In the second O site, O(2) is bonded to one Li(4), one Cr(2), and two equivalent Cr(1) atoms to form distorted OLiCr3 tetrahedra that share corners with two equivalent O(4)LiCr2Co tetrahedra, corners with two equivalent O(6)LiCr2Co tetrahedra,  a cornercorner with one O(10)LiCrCo2 trigonal pyramid, and edges with two equivalent O(6)LiCr2Co tetrahedra. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), two equivalent Cr(1), and one Co(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Cr(1), and one Co(1) atom to form OLiCr2Co tetrahedra that share corners with two equivalent O(2)LiCr3 tetrahedra and corners with four equivalent O(6)LiCr2Co tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Cr(3), and two equivalent Co(2) atoms to form OLiCrCo2 tetrahedra that share corners with two equivalent O(12)LiCrCo2 tetrahedra, corners with four equivalent O(9)LiCr2Co tetrahedra, and corners with three equivalent O(10)LiCrCo2 trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Cr(1), one Cr(2), and one Co(1) atom to form distorted OLiCr2Co tetrahedra that share  a cornercorner with one O(6)LiCr2Co tetrahedra,  a cornercorner with one O(2)LiCr3 tetrahedra, corners with two equivalent O(4)LiCr2Co tetrahedra,  a cornercorner with one O(10)LiCrCo2 trigonal pyramid,  an edgeedge with one O(6)LiCr2Co tetrahedra, and  an edgeedge with one O(2)LiCr3 tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(4), and two equivalent Cr(1) atoms. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one Cr(2), and two equivalent Co(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Cr(3), one Cr(4), and one Co(2) atom to form distorted OLiCr2Co tetrahedra that share  a cornercorner with one O(9)LiCr2Co tetrahedra,  a cornercorner with one O(12)LiCrCo2 tetrahedra, corners with two equivalent O(5)LiCrCo2 tetrahedra,  an edgeedge with one O(9)LiCr2Co tetrahedra,  an edgeedge with one O(12)LiCrCo2 tetrahedra, and  an edgeedge with one O(10)LiCrCo2 trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(4), one Cr(3), and two equivalent Co(2) atoms to form distorted OLiCrCo2 trigonal pyramids that share  a cornercorner with one O(2)LiCr3 tetrahedra, corners with two equivalent O(6)LiCr2Co tetrahedra, corners with three equivalent O(5)LiCrCo2 tetrahedra,  an edgeedge with one O(12)LiCrCo2 tetrahedra, and edges with two equivalent O(9)LiCr2Co tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(1), one Cr(4), and one Co(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Cr(4), and two equivalent Co(2) atoms to form distorted OLiCrCo2 tetrahedra that share corners with two equivalent O(9)LiCr2Co tetrahedra, corners with two equivalent O(5)LiCrCo2 tetrahedra, edges with two equivalent O(9)LiCr2Co tetrahedra, and  an edgeedge with one O(10)LiCrCo2 trigonal pyramid. is represented by the CIF card [CIF]
data_Li4Cr5Co3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.705
_cell_length_b   5.705
_cell_length_c   9.313
_cell_angle_alpha   89.870
_cell_angle_beta   89.870
_cell_angle_gamma   60.442
_symmetry_Int_Tables_number   1
_cell_volume   263.680
_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  0.330  0.330  0.110  1.0
  Li  Li1  1  0.007  0.007  0.004  1.0
  Li  Li2  1  0.006  0.006  0.502  1.0
  Li  Li3  1  0.664  0.664  0.605  1.0
  Cr  Cr4  1  0.171  0.656  0.788  1.0
  Cr  Cr5  1  0.332  0.332  0.508  1.0
  Cr  Cr6  1  0.656  0.171  0.788  1.0
  Cr  Cr7  1  0.828  0.828  0.289  1.0
  Cr  Cr8  1  0.665  0.665  0.013  1.0
  Co  Co9  1  0.172  0.172  0.787  1.0
  Co  Co10  1  0.341  0.831  0.287  1.0
  Co  Co11  1  0.831  0.341  0.287  1.0
  O  O12  1  0.165  0.667  0.398  1.0
  O  O13  1  0.478  0.478  0.658  1.0
  O  O14  1  0.333  0.333  0.900  1.0
  O  O15  1  0.002  0.002  0.693  1.0
  O  O16  1  0.002  0.002  0.194  1.0
  O  O17  1  0.667  0.165  0.398  1.0
  O  O18  1  0.042  0.478  0.658  1.0
  O  O19  1  0.478  0.042  0.658  1.0
  O  O20  1  0.833  0.833  0.898  1.0
  O  O21  1  0.169  0.169  0.396  1.0
  O  O22  1  0.520  0.956  0.159  1.0
  O  O23  1  0.956  0.520  0.159  1.0
  O  O24  1  0.664  0.664  0.396  1.0
  O  O25  1  0.334  0.831  0.898  1.0
  O  O26  1  0.521  0.521  0.164  1.0
  O  O27  1  0.831  0.334  0.898  1.0
[/CIF]
.