The crystal structure described by Li4Nb3Cr5O16 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 Nb(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 Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-63°. 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 in a distorted 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(3)O6 octahedra, corners with two equivalent Nb(1)O6 octahedra, corners with two equivalent Nb(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 49-63°. There are two inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form NbO6 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,  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 Nb site, Nb(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 NbO6 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 Nb(2)O6 octahedra, and edges with two equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. 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,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent Nb(1)O6 octahedra, and edges with two equivalent Cr(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 Nb(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Nb(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 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, and edges with four equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. 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 Nb(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 Nb(2)O6 octahedra. 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 Nb(2), one Cr(2), and one Cr(3) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Cr(2), and two equivalent Cr(1) atoms. In the third O site, O(3) is bonded to one Li(1), one Nb(1), and two equivalent Cr(1) atoms to form distorted corner-sharing OLiNbCr2 trigonal pyramids. In the fourth O site, O(4) is bonded to one Li(3), one Nb(1), and two equivalent Cr(1) atoms to form distorted OLiNbCr2 tetrahedra that share  a cornercorner with one O(8)LiNb2Cr trigonal pyramid and corners with three equivalent O(3)LiNbCr2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Nb(2), and one Cr(3) atom to form distorted OLiNb2Cr tetrahedra that share corners with four equivalent O(9)LiNbCr2 tetrahedra and  an edgeedge with one O(8)LiNb2Cr trigonal pyramid. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Nb(1), one Cr(1), and one Cr(2) atom. 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 to one Li(3), two equivalent Nb(2), and one Cr(2) atom to form distorted OLiNb2Cr trigonal pyramids that share  a cornercorner with one O(4)LiNbCr2 tetrahedra, corners with two equivalent O(9)LiNbCr2 tetrahedra, and  an edgeedge with one O(5)LiNb2Cr tetrahedra. In the ninth O site, O(9) is bonded to one Li(1), one Nb(2), one Cr(3), and one Cr(4) atom to form distorted OLiNbCr2 tetrahedra that share  a cornercorner with one O(9)LiNbCr2 tetrahedra, corners with two equivalent O(5)LiNb2Cr tetrahedra,  a cornercorner with one O(8)LiNb2Cr trigonal pyramid,  a cornercorner with one O(3)LiNbCr2 trigonal pyramid, and  an edgeedge with one O(9)LiNbCr2 tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent Nb(2), and one Cr(3) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Nb(1), one Cr(1), and one Cr(4) atom. In the twelfth O site, O(12) is bonded in a 4-coordinate geometry to one Li(1), two equivalent Nb(2), and one Cr(4) atom. is represented by the CIF card [CIF]
data_Li4Nb3Cr5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.021
_cell_length_b   6.021
_cell_length_c   9.763
_cell_angle_alpha   89.691
_cell_angle_beta   89.691
_cell_angle_gamma   59.498
_symmetry_Int_Tables_number   1
_cell_volume   304.908
_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  0.897  1.0
  Li  Li1  1  0.011  0.011  0.995  1.0
  Li  Li2  1  0.005  0.005  0.495  1.0
  Li  Li3  1  0.334  0.334  0.386  1.0
  Nb  Nb4  1  0.832  0.832  0.212  1.0
  Nb  Nb5  1  0.645  0.187  0.711  1.0
  Nb  Nb6  1  0.187  0.645  0.711  1.0
  Cr  Cr7  1  0.832  0.340  0.215  1.0
  Cr  Cr8  1  0.666  0.666  0.481  1.0
  Cr  Cr9  1  0.340  0.832  0.215  1.0
  Cr  Cr10  1  0.167  0.167  0.714  1.0
  Cr  Cr11  1  0.329  0.329  0.990  1.0
  O  O12  1  0.829  0.329  0.601  1.0
  O  O13  1  0.521  0.521  0.338  1.0
  O  O14  1  0.670  0.670  0.103  1.0
  O  O15  1  0.000  0.000  0.312  1.0
  O  O16  1  0.004  0.004  0.813  1.0
  O  O17  1  0.329  0.829  0.601  1.0
  O  O18  1  0.960  0.522  0.340  1.0
  O  O19  1  0.522  0.960  0.340  1.0
  O  O20  1  0.163  0.163  0.102  1.0
  O  O21  1  0.833  0.833  0.599  1.0
  O  O22  1  0.480  0.042  0.841  1.0
  O  O23  1  0.042  0.480  0.841  1.0
  O  O24  1  0.320  0.320  0.588  1.0
  O  O25  1  0.669  0.159  0.104  1.0
  O  O26  1  0.483  0.483  0.859  1.0
  O  O27  1  0.159  0.669  0.104  1.0
[/CIF]
.
The crystal structure described by Li4Nb3Cr5O16 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 Nb(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 Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-63°. 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 in a distorted 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(3)O6 octahedra, corners with two equivalent Nb(1)O6 octahedra, corners with two equivalent Nb(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 49-63°. There are two inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form NbO6 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,  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 Nb site, Nb(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 NbO6 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 Nb(2)O6 octahedra, and edges with two equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. 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,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent Nb(1)O6 octahedra, and edges with two equivalent Cr(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 Nb(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Nb(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 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, and edges with four equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. 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 Nb(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 Nb(2)O6 octahedra. 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 Nb(2), one Cr(2), and one Cr(3) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Cr(2), and two equivalent Cr(1) atoms. In the third O site, O(3) is bonded to one Li(1), one Nb(1), and two equivalent Cr(1) atoms to form distorted corner-sharing OLiNbCr2 trigonal pyramids. In the fourth O site, O(4) is bonded to one Li(3), one Nb(1), and two equivalent Cr(1) atoms to form distorted OLiNbCr2 tetrahedra that share  a cornercorner with one O(8)LiNb2Cr trigonal pyramid and corners with three equivalent O(3)LiNbCr2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Nb(2), and one Cr(3) atom to form distorted OLiNb2Cr tetrahedra that share corners with four equivalent O(9)LiNbCr2 tetrahedra and  an edgeedge with one O(8)LiNb2Cr trigonal pyramid. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Nb(1), one Cr(1), and one Cr(2) atom. 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 to one Li(3), two equivalent Nb(2), and one Cr(2) atom to form distorted OLiNb2Cr trigonal pyramids that share  a cornercorner with one O(4)LiNbCr2 tetrahedra, corners with two equivalent O(9)LiNbCr2 tetrahedra, and  an edgeedge with one O(5)LiNb2Cr tetrahedra. In the ninth O site, O(9) is bonded to one Li(1), one Nb(2), one Cr(3), and one Cr(4) atom to form distorted OLiNbCr2 tetrahedra that share  a cornercorner with one O(9)LiNbCr2 tetrahedra, corners with two equivalent O(5)LiNb2Cr tetrahedra,  a cornercorner with one O(8)LiNb2Cr trigonal pyramid,  a cornercorner with one O(3)LiNbCr2 trigonal pyramid, and  an edgeedge with one O(9)LiNbCr2 tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent Nb(2), and one Cr(3) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Nb(1), one Cr(1), and one Cr(4) atom. In the twelfth O site, O(12) is bonded in a 4-coordinate geometry to one Li(1), two equivalent Nb(2), and one Cr(4) atom. is represented by the CIF card [CIF]
data_Li4Nb3Cr5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.021
_cell_length_b   6.021
_cell_length_c   9.763
_cell_angle_alpha   89.691
_cell_angle_beta   89.691
_cell_angle_gamma   59.498
_symmetry_Int_Tables_number   1
_cell_volume   304.908
_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  0.897  1.0
  Li  Li1  1  0.011  0.011  0.995  1.0
  Li  Li2  1  0.005  0.005  0.495  1.0
  Li  Li3  1  0.334  0.334  0.386  1.0
  Nb  Nb4  1  0.832  0.832  0.212  1.0
  Nb  Nb5  1  0.645  0.187  0.711  1.0
  Nb  Nb6  1  0.187  0.645  0.711  1.0
  Cr  Cr7  1  0.832  0.340  0.215  1.0
  Cr  Cr8  1  0.666  0.666  0.481  1.0
  Cr  Cr9  1  0.340  0.832  0.215  1.0
  Cr  Cr10  1  0.167  0.167  0.714  1.0
  Cr  Cr11  1  0.329  0.329  0.990  1.0
  O  O12  1  0.829  0.329  0.601  1.0
  O  O13  1  0.521  0.521  0.338  1.0
  O  O14  1  0.670  0.670  0.103  1.0
  O  O15  1  0.000  0.000  0.312  1.0
  O  O16  1  0.004  0.004  0.813  1.0
  O  O17  1  0.329  0.829  0.601  1.0
  O  O18  1  0.960  0.522  0.340  1.0
  O  O19  1  0.522  0.960  0.340  1.0
  O  O20  1  0.163  0.163  0.102  1.0
  O  O21  1  0.833  0.833  0.599  1.0
  O  O22  1  0.480  0.042  0.841  1.0
  O  O23  1  0.042  0.480  0.841  1.0
  O  O24  1  0.320  0.320  0.588  1.0
  O  O25  1  0.669  0.159  0.104  1.0
  O  O26  1  0.483  0.483  0.859  1.0
  O  O27  1  0.159  0.669  0.104  1.0
[/CIF]
.