The material structure described by Li4Nb3Cr2Fe3O16 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 Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and corners with four equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-62°. 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 Fe(2)O6 octahedra, corners with two equivalent Nb(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra,  an edgeedge with one Nb(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-70°. 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 Nb(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-68°. 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 Fe(2)O6 octahedra, corners with two equivalent Nb(1)O6 octahedra, corners with two equivalent Nb(2)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra, and corners with four equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-66°. 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(2)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(1)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 49°. 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(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 Cr(2)O6 octahedra, edges with two equivalent Nb(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 50°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) 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 Fe(2)O6 octahedra, corners with four equivalent Nb(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Nb(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-52°. In the second Cr site, Cr(2) 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 Fe(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-52°. There are two inequivalent Fe sites. In the first Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Cr(2)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(1)O6 octahedra, edges with two equivalent Nb(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the second Fe site, Fe(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form FeO6 octahedra that share corners with two equivalent Cr(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 Cr(2)O6 octahedra, edges with four equivalent Nb(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. 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(2), one Cr(1), and one Fe(2) atom. In the second O site, O(2) is bonded to one Li(4), one Cr(1), and two equivalent Fe(1) atoms to form a mixture of distorted edge and corner-sharing OLiCrFe2 tetrahedra. In the third O site, O(3) is bonded to one Li(1), one Nb(1), and two equivalent Fe(1) atoms to form distorted OLiNbFe2 trigonal pyramids that share  a cornercorner with one O(12)LiNb2Cr tetrahedra, corners with two equivalent O(9)LiNbCrFe tetrahedra, corners with three equivalent O(4)LiNbFe2 tetrahedra, and  an edgeedge with one O(2)LiCrFe2 tetrahedra. In the fourth O site, O(4) is bonded to one Li(3), one Nb(1), and two equivalent Fe(1) atoms to form distorted OLiNbFe2 tetrahedra that share corners with two equivalent O(2)LiCrFe2 tetrahedra and corners with three equivalent O(3)LiNbFe2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Nb(2), and one Fe(2) atom to form distorted OLiNb2Fe tetrahedra that share corners with two equivalent O(12)LiNb2Cr tetrahedra and corners with four equivalent O(9)LiNbCrFe tetrahedra. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Li(4), one Nb(1), one Cr(1), and one Fe(1) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(2), and two equivalent Fe(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), two equivalent Nb(2), and one Cr(1) atom. In the ninth O site, O(9) is bonded to one Li(1), one Nb(2), one Cr(2), and one Fe(2) atom to form distorted OLiNbCrFe tetrahedra that share  a cornercorner with one O(12)LiNb2Cr tetrahedra,  a cornercorner with one O(9)LiNbCrFe tetrahedra, corners with two equivalent O(5)LiNb2Fe tetrahedra,  a cornercorner with one O(3)LiNbFe2 trigonal pyramid,  an edgeedge with one O(12)LiNb2Cr tetrahedra, and  an edgeedge with one O(9)LiNbCrFe 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 Fe(2) 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(2), and one Fe(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Nb(2), and one Cr(2) atom to form distorted OLiNb2Cr tetrahedra that share corners with two equivalent O(5)LiNb2Fe tetrahedra, corners with two equivalent O(9)LiNbCrFe tetrahedra,  a cornercorner with one O(3)LiNbFe2 trigonal pyramid, and edges with two equivalent O(9)LiNbCrFe tetrahedra. is represented by the CIF file [CIF]
data_Li4Nb3Cr2Fe3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.073
_cell_length_b   6.073
_cell_length_c   9.762
_cell_angle_alpha   88.620
_cell_angle_beta   88.620
_cell_angle_gamma   59.971
_symmetry_Int_Tables_number   1
_cell_volume   311.536
_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  0.334  0.334  0.098  1.0
  Li  Li1  1  0.991  0.991  0.999  1.0
  Li  Li2  1  0.983  0.983  0.513  1.0
  Li  Li3  1  0.665  0.665  0.615  1.0
  Nb  Nb4  1  0.173  0.173  0.789  1.0
  Nb  Nb5  1  0.339  0.839  0.288  1.0
  Nb  Nb6  1  0.839  0.339  0.288  1.0
  Cr  Cr7  1  0.343  0.343  0.523  1.0
  Cr  Cr8  1  0.673  0.673  0.009  1.0
  Fe  Fe9  1  0.167  0.663  0.786  1.0
  Fe  Fe10  1  0.663  0.167  0.786  1.0
  Fe  Fe11  1  0.830  0.830  0.283  1.0
  O  O12  1  0.178  0.675  0.401  1.0
  O  O13  1  0.478  0.478  0.658  1.0
  O  O14  1  0.332  0.332  0.899  1.0
  O  O15  1  0.005  0.005  0.694  1.0
  O  O16  1  0.008  0.008  0.184  1.0
  O  O17  1  0.675  0.178  0.401  1.0
  O  O18  1  0.044  0.474  0.651  1.0
  O  O19  1  0.474  0.044  0.651  1.0
  O  O20  1  0.835  0.835  0.899  1.0
  O  O21  1  0.169  0.169  0.397  1.0
  O  O22  1  0.519  0.960  0.154  1.0
  O  O23  1  0.960  0.519  0.154  1.0
  O  O24  1  0.660  0.660  0.404  1.0
  O  O25  1  0.339  0.847  0.902  1.0
  O  O26  1  0.522  0.522  0.162  1.0
  O  O27  1  0.847  0.339  0.902  1.0
[/CIF]
.
The material structure described by Li4Nb3Cr2Fe3O16 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 Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and corners with four equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-62°. 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 Fe(2)O6 octahedra, corners with two equivalent Nb(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra,  an edgeedge with one Nb(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-70°. 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 Nb(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-68°. 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 Fe(2)O6 octahedra, corners with two equivalent Nb(1)O6 octahedra, corners with two equivalent Nb(2)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra, and corners with four equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-66°. 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(2)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(1)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 49°. 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(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 Cr(2)O6 octahedra, edges with two equivalent Nb(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 50°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) 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 Fe(2)O6 octahedra, corners with four equivalent Nb(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Nb(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-52°. In the second Cr site, Cr(2) 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 Fe(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-52°. There are two inequivalent Fe sites. In the first Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Cr(2)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(1)O6 octahedra, edges with two equivalent Nb(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the second Fe site, Fe(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form FeO6 octahedra that share corners with two equivalent Cr(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 Cr(2)O6 octahedra, edges with four equivalent Nb(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. 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(2), one Cr(1), and one Fe(2) atom. In the second O site, O(2) is bonded to one Li(4), one Cr(1), and two equivalent Fe(1) atoms to form a mixture of distorted edge and corner-sharing OLiCrFe2 tetrahedra. In the third O site, O(3) is bonded to one Li(1), one Nb(1), and two equivalent Fe(1) atoms to form distorted OLiNbFe2 trigonal pyramids that share  a cornercorner with one O(12)LiNb2Cr tetrahedra, corners with two equivalent O(9)LiNbCrFe tetrahedra, corners with three equivalent O(4)LiNbFe2 tetrahedra, and  an edgeedge with one O(2)LiCrFe2 tetrahedra. In the fourth O site, O(4) is bonded to one Li(3), one Nb(1), and two equivalent Fe(1) atoms to form distorted OLiNbFe2 tetrahedra that share corners with two equivalent O(2)LiCrFe2 tetrahedra and corners with three equivalent O(3)LiNbFe2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Nb(2), and one Fe(2) atom to form distorted OLiNb2Fe tetrahedra that share corners with two equivalent O(12)LiNb2Cr tetrahedra and corners with four equivalent O(9)LiNbCrFe tetrahedra. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Li(4), one Nb(1), one Cr(1), and one Fe(1) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(2), and two equivalent Fe(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), two equivalent Nb(2), and one Cr(1) atom. In the ninth O site, O(9) is bonded to one Li(1), one Nb(2), one Cr(2), and one Fe(2) atom to form distorted OLiNbCrFe tetrahedra that share  a cornercorner with one O(12)LiNb2Cr tetrahedra,  a cornercorner with one O(9)LiNbCrFe tetrahedra, corners with two equivalent O(5)LiNb2Fe tetrahedra,  a cornercorner with one O(3)LiNbFe2 trigonal pyramid,  an edgeedge with one O(12)LiNb2Cr tetrahedra, and  an edgeedge with one O(9)LiNbCrFe 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 Fe(2) 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(2), and one Fe(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Nb(2), and one Cr(2) atom to form distorted OLiNb2Cr tetrahedra that share corners with two equivalent O(5)LiNb2Fe tetrahedra, corners with two equivalent O(9)LiNbCrFe tetrahedra,  a cornercorner with one O(3)LiNbFe2 trigonal pyramid, and edges with two equivalent O(9)LiNbCrFe tetrahedra. is represented by the CIF file [CIF]
data_Li4Nb3Cr2Fe3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.073
_cell_length_b   6.073
_cell_length_c   9.762
_cell_angle_alpha   88.620
_cell_angle_beta   88.620
_cell_angle_gamma   59.971
_symmetry_Int_Tables_number   1
_cell_volume   311.536
_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  0.334  0.334  0.098  1.0
  Li  Li1  1  0.991  0.991  0.999  1.0
  Li  Li2  1  0.983  0.983  0.513  1.0
  Li  Li3  1  0.665  0.665  0.615  1.0
  Nb  Nb4  1  0.173  0.173  0.789  1.0
  Nb  Nb5  1  0.339  0.839  0.288  1.0
  Nb  Nb6  1  0.839  0.339  0.288  1.0
  Cr  Cr7  1  0.343  0.343  0.523  1.0
  Cr  Cr8  1  0.673  0.673  0.009  1.0
  Fe  Fe9  1  0.167  0.663  0.786  1.0
  Fe  Fe10  1  0.663  0.167  0.786  1.0
  Fe  Fe11  1  0.830  0.830  0.283  1.0
  O  O12  1  0.178  0.675  0.401  1.0
  O  O13  1  0.478  0.478  0.658  1.0
  O  O14  1  0.332  0.332  0.899  1.0
  O  O15  1  0.005  0.005  0.694  1.0
  O  O16  1  0.008  0.008  0.184  1.0
  O  O17  1  0.675  0.178  0.401  1.0
  O  O18  1  0.044  0.474  0.651  1.0
  O  O19  1  0.474  0.044  0.651  1.0
  O  O20  1  0.835  0.835  0.899  1.0
  O  O21  1  0.169  0.169  0.397  1.0
  O  O22  1  0.519  0.960  0.154  1.0
  O  O23  1  0.960  0.519  0.154  1.0
  O  O24  1  0.660  0.660  0.404  1.0
  O  O25  1  0.339  0.847  0.902  1.0
  O  O26  1  0.522  0.522  0.162  1.0
  O  O27  1  0.847  0.339  0.902  1.0
[/CIF]
.