The material described by Li4Nb5Cr3O16 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(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Nb(3)O6 octahedra, and corners with four equivalent Nb(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-66°. 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 Nb(4)O6 octahedra, corners with three equivalent Nb(3)O6 octahedra,  an edgeedge with one Nb(2)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-64°. 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 tetrahedra that share  a cornercorner with one Nb(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Nb(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Nb(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-66°. 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 Nb(2)O6 octahedra, corners with two equivalent Nb(4)O6 octahedra, corners with three equivalent Nb(1)O6 octahedra, and corners with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-67°. There are four inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form distorted NbO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Nb(4)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Nb(2)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-54°. In the second Nb site, Nb(2) 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 Nb(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Nb(1)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 50°. In the third Nb site, Nb(3) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form distorted NbO6 octahedra that share corners with two equivalent Nb(2)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 Nb(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. In the fourth Nb site, Nb(4) 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 Nb(1)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 Nb(3)O6 octahedra, edges with two equivalent Nb(4)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-54°. 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 Nb(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Nb(1)O6 octahedra, edges with two equivalent Nb(2)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 51-53°. 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 Nb(1)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 Nb(3)O6 octahedra, edges with four equivalent Nb(4)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 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(1), one Nb(4), and one Cr(2) atom. In the second O site, O(2) is bonded to one Li(4), one Nb(1), and two equivalent Cr(1) atoms to form distorted OLiNbCr2 tetrahedra that share corners with two equivalent O(4)LiNbCr2 tetrahedra, corners with two equivalent O(6)LiNb2Cr trigonal pyramids, and edges with two equivalent O(6)LiNb2Cr trigonal pyramids. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Nb(2), and two equivalent Cr(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Nb(2), and two equivalent Cr(1) atoms to form OLiNbCr2 tetrahedra that share corners with two equivalent O(2)LiNbCr2 tetrahedra and corners with four equivalent O(6)LiNb2Cr trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Nb(4), and one Cr(2) atom to form corner-sharing OLiNb2Cr tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Nb(1), one Nb(2), and one Cr(1) atom to form distorted OLiNb2Cr trigonal pyramids that share  a cornercorner with one O(2)LiNbCr2 tetrahedra, corners with two equivalent O(4)LiNbCr2 tetrahedra,  a cornercorner with one O(6)LiNb2Cr trigonal pyramid,  an edgeedge with one O(2)LiNbCr2 tetrahedra, and  an edgeedge with one O(6)LiNb2Cr trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Nb(3), 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 Nb(1), and two equivalent Nb(4) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Nb(3), one Nb(4), and one Cr(2) atom to form a mixture of distorted edge and corner-sharing OLiNb2Cr tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent Nb(4), 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 Nb(2), one Nb(3), and one Cr(1) atom. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Nb(3), and two equivalent Nb(4) atoms. is represented by the CIF file [CIF]
data_Li4Nb5Cr3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.154
_cell_length_b   6.154
_cell_length_c   10.090
_cell_angle_alpha   89.500
_cell_angle_beta   89.500
_cell_angle_gamma   59.088
_symmetry_Int_Tables_number   1
_cell_volume   327.795
_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  0.672  0.672  0.910  1.0
  Li  Li1  1  0.006  0.006  0.989  1.0
  Li  Li2  1  0.998  0.998  0.491  1.0
  Li  Li3  1  0.336  0.336  0.395  1.0
  Nb  Nb4  1  0.655  0.655  0.492  1.0
  Nb  Nb5  1  0.829  0.829  0.224  1.0
  Nb  Nb6  1  0.333  0.333  0.999  1.0
  Nb  Nb7  1  0.630  0.185  0.716  1.0
  Nb  Nb8  1  0.185  0.630  0.716  1.0
  Cr  Cr9  1  0.831  0.339  0.210  1.0
  Cr  Cr10  1  0.339  0.831  0.210  1.0
  Cr  Cr11  1  0.164  0.164  0.709  1.0
  O  O12  1  0.817  0.334  0.590  1.0
  O  O13  1  0.527  0.527  0.358  1.0
  O  O14  1  0.675  0.675  0.109  1.0
  O  O15  1  0.999  0.999  0.306  1.0
  O  O16  1  1.000  1.000  0.804  1.0
  O  O17  1  0.334  0.817  0.590  1.0
  O  O18  1  0.969  0.529  0.341  1.0
  O  O19  1  0.529  0.969  0.341  1.0
  O  O20  1  0.173  0.173  0.082  1.0
  O  O21  1  0.830  0.830  0.592  1.0
  O  O22  1  0.496  0.046  0.848  1.0
  O  O23  1  0.046  0.496  0.848  1.0
  O  O24  1  0.318  0.318  0.588  1.0
  O  O25  1  0.665  0.158  0.098  1.0
  O  O26  1  0.491  0.491  0.854  1.0
  O  O27  1  0.158  0.665  0.098  1.0
[/CIF]
.
The material described by Li4Nb5Cr3O16 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(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Nb(3)O6 octahedra, and corners with four equivalent Nb(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-66°. 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 Nb(4)O6 octahedra, corners with three equivalent Nb(3)O6 octahedra,  an edgeedge with one Nb(2)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-64°. 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 tetrahedra that share  a cornercorner with one Nb(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Nb(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Nb(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-66°. 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 Nb(2)O6 octahedra, corners with two equivalent Nb(4)O6 octahedra, corners with three equivalent Nb(1)O6 octahedra, and corners with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-67°. There are four inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form distorted NbO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Nb(4)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Nb(2)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-54°. In the second Nb site, Nb(2) 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 Nb(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Nb(1)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 50°. In the third Nb site, Nb(3) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form distorted NbO6 octahedra that share corners with two equivalent Nb(2)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 Nb(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. In the fourth Nb site, Nb(4) 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 Nb(1)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 Nb(3)O6 octahedra, edges with two equivalent Nb(4)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-54°. 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 Nb(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Nb(1)O6 octahedra, edges with two equivalent Nb(2)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 51-53°. 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 Nb(1)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 Nb(3)O6 octahedra, edges with four equivalent Nb(4)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 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(1), one Nb(4), and one Cr(2) atom. In the second O site, O(2) is bonded to one Li(4), one Nb(1), and two equivalent Cr(1) atoms to form distorted OLiNbCr2 tetrahedra that share corners with two equivalent O(4)LiNbCr2 tetrahedra, corners with two equivalent O(6)LiNb2Cr trigonal pyramids, and edges with two equivalent O(6)LiNb2Cr trigonal pyramids. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Nb(2), and two equivalent Cr(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Nb(2), and two equivalent Cr(1) atoms to form OLiNbCr2 tetrahedra that share corners with two equivalent O(2)LiNbCr2 tetrahedra and corners with four equivalent O(6)LiNb2Cr trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Nb(4), and one Cr(2) atom to form corner-sharing OLiNb2Cr tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Nb(1), one Nb(2), and one Cr(1) atom to form distorted OLiNb2Cr trigonal pyramids that share  a cornercorner with one O(2)LiNbCr2 tetrahedra, corners with two equivalent O(4)LiNbCr2 tetrahedra,  a cornercorner with one O(6)LiNb2Cr trigonal pyramid,  an edgeedge with one O(2)LiNbCr2 tetrahedra, and  an edgeedge with one O(6)LiNb2Cr trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Nb(3), 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 Nb(1), and two equivalent Nb(4) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Nb(3), one Nb(4), and one Cr(2) atom to form a mixture of distorted edge and corner-sharing OLiNb2Cr tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent Nb(4), 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 Nb(2), one Nb(3), and one Cr(1) atom. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Nb(3), and two equivalent Nb(4) atoms. is represented by the CIF file [CIF]
data_Li4Nb5Cr3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.154
_cell_length_b   6.154
_cell_length_c   10.090
_cell_angle_alpha   89.500
_cell_angle_beta   89.500
_cell_angle_gamma   59.088
_symmetry_Int_Tables_number   1
_cell_volume   327.795
_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  0.672  0.672  0.910  1.0
  Li  Li1  1  0.006  0.006  0.989  1.0
  Li  Li2  1  0.998  0.998  0.491  1.0
  Li  Li3  1  0.336  0.336  0.395  1.0
  Nb  Nb4  1  0.655  0.655  0.492  1.0
  Nb  Nb5  1  0.829  0.829  0.224  1.0
  Nb  Nb6  1  0.333  0.333  0.999  1.0
  Nb  Nb7  1  0.630  0.185  0.716  1.0
  Nb  Nb8  1  0.185  0.630  0.716  1.0
  Cr  Cr9  1  0.831  0.339  0.210  1.0
  Cr  Cr10  1  0.339  0.831  0.210  1.0
  Cr  Cr11  1  0.164  0.164  0.709  1.0
  O  O12  1  0.817  0.334  0.590  1.0
  O  O13  1  0.527  0.527  0.358  1.0
  O  O14  1  0.675  0.675  0.109  1.0
  O  O15  1  0.999  0.999  0.306  1.0
  O  O16  1  1.000  1.000  0.804  1.0
  O  O17  1  0.334  0.817  0.590  1.0
  O  O18  1  0.969  0.529  0.341  1.0
  O  O19  1  0.529  0.969  0.341  1.0
  O  O20  1  0.173  0.173  0.082  1.0
  O  O21  1  0.830  0.830  0.592  1.0
  O  O22  1  0.496  0.046  0.848  1.0
  O  O23  1  0.046  0.496  0.848  1.0
  O  O24  1  0.318  0.318  0.588  1.0
  O  O25  1  0.665  0.158  0.098  1.0
  O  O26  1  0.491  0.491  0.854  1.0
  O  O27  1  0.158  0.665  0.098  1.0
[/CIF]
.