The material described by ZnCr2O4 is Spinel-like structured and crystallizes in the trigonal P3m1 space group. There are six inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form CrO6 octahedra that share  a cornercorner with one Cr(6)O4 tetrahedra,  a cornercorner with one Zn(2)O4 tetrahedra, corners with two equivalent Zn(1)O4 tetrahedra, corners with two equivalent Zn(5)O4 tetrahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. In the second Cr site, Cr(2) is bonded to one O(6), one O(9), two equivalent O(4), and two equivalent O(7) atoms to form CrO6 octahedra that share  a cornercorner with one Zn(4)O4 tetrahedra,  a cornercorner with one Zn(5)O4 tetrahedra, corners with two equivalent Zn(2)O4 tetrahedra, corners with two equivalent Zn(6)O4 tetrahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Cr(5)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. In the third Cr site, Cr(3) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form CrO6 octahedra that share corners with three equivalent Zn(2)O4 tetrahedra, corners with three equivalent Zn(5)O4 tetrahedra, edges with three equivalent Cr(1)O6 octahedra, and edges with three equivalent Cr(2)O6 octahedra. In the fourth Cr site, Cr(4) is bonded to one O(10), one O(12), two equivalent O(11), and two equivalent O(8) atoms to form CrO6 octahedra that share  a cornercorner with one Zn(1)O4 tetrahedra,  a cornercorner with one Zn(6)O4 tetrahedra, corners with two equivalent Cr(6)O4 tetrahedra, corners with two equivalent Zn(4)O4 tetrahedra,  an edgeedge with one Cr(5)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, and edges with four equivalent Cr(4)O6 octahedra. In the fifth Cr site, Cr(5) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form CrO6 octahedra that share corners with three equivalent Zn(4)O4 tetrahedra, corners with three equivalent Zn(6)O4 tetrahedra, edges with three equivalent Cr(2)O6 octahedra, and edges with three equivalent Cr(4)O6 octahedra. In the sixth Cr site, Cr(6) is bonded to one O(5) and three equivalent O(11) atoms to form CrO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Zn(3)O6 octahedra, and corners with six equivalent Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-61°. There are six inequivalent Zn sites. In the first Zn site, Zn(1) is bonded to one O(10) and three equivalent O(1) atoms to form ZnO4 tetrahedra that share corners with three equivalent Cr(4)O6 octahedra, corners with three equivalent Zn(3)O6 octahedra, and corners with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. In the second Zn site, Zn(2) is bonded to one O(2) and three equivalent O(4) atoms to form ZnO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(3)O6 octahedra, and corners with six equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the third Zn site, Zn(3) is bonded to three equivalent O(1) and three equivalent O(11) atoms to form ZnO6 octahedra that share corners with three equivalent Cr(6)O4 tetrahedra, corners with three equivalent Zn(1)O4 tetrahedra, edges with three equivalent Cr(1)O6 octahedra, and edges with three equivalent Cr(4)O6 octahedra. In the fourth Zn site, Zn(4) is bonded to one O(6) and three equivalent O(8) atoms to form ZnO4 tetrahedra that share corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Cr(5)O6 octahedra, and corners with six equivalent Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the fifth Zn site, Zn(5) is bonded to one O(9) and three equivalent O(3) atoms to form ZnO4 tetrahedra that share corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Cr(3)O6 octahedra, and corners with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the sixth Zn site, Zn(6) is bonded to one O(12) and three equivalent O(7) atoms to form ZnO4 tetrahedra that share corners with three equivalent Cr(4)O6 octahedra, corners with three equivalent Cr(5)O6 octahedra, and corners with six equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Cr(1), one Zn(1), and one Zn(3) atom to form distorted OZn2Cr2 trigonal pyramids that share  a cornercorner with one O(10)ZnCr3 trigonal pyramid, corners with two equivalent O(5)Cr4 trigonal pyramids, corners with two equivalent O(1)Zn2Cr2 trigonal pyramids, corners with four equivalent O(3)ZnCr3 trigonal pyramids,  an edgeedge with one O(2)ZnCr3 trigonal pyramid, and edges with two equivalent O(1)Zn2Cr2 trigonal pyramids. In the second O site, O(2) is bonded to three equivalent Cr(1) and one Zn(2) atom to form distorted OZnCr3 trigonal pyramids that share corners with three equivalent O(5)Cr4 trigonal pyramids, corners with three equivalent O(4)ZnCr3 trigonal pyramids, corners with six equivalent O(3)ZnCr3 trigonal pyramids, and edges with three equivalent O(1)Zn2Cr2 trigonal pyramids. In the third O site, O(3) is bonded to one Cr(3), two equivalent Cr(1), and one Zn(5) atom to form distorted OZnCr3 trigonal pyramids that share  a cornercorner with one O(9)ZnCr3 trigonal pyramid, corners with two equivalent O(2)ZnCr3 trigonal pyramids, corners with two equivalent O(3)ZnCr3 trigonal pyramids, corners with three equivalent O(4)ZnCr3 trigonal pyramids, corners with four equivalent O(1)Zn2Cr2 trigonal pyramids,  an edgeedge with one O(5)Cr4 trigonal pyramid, and edges with two equivalent O(3)ZnCr3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Cr(3), two equivalent Cr(2), and one Zn(2) atom to form a mixture of distorted corner and edge-sharing OZnCr3 trigonal pyramids. In the fifth O site, O(5) is bonded to one Cr(6) and three equivalent Cr(1) atoms to form distorted OCr4 trigonal pyramids that share corners with three equivalent O(2)ZnCr3 trigonal pyramids, corners with six equivalent O(1)Zn2Cr2 trigonal pyramids, and edges with three equivalent O(3)ZnCr3 trigonal pyramids. In the sixth O site, O(6) is bonded to three equivalent Cr(2) and one Zn(4) atom to form a mixture of distorted corner and edge-sharing OZnCr3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Cr(5), two equivalent Cr(2), and one Zn(6) atom to form a mixture of distorted corner and edge-sharing OZnCr3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Cr(5), two equivalent Cr(4), and one Zn(4) atom to form a mixture of distorted corner and edge-sharing OZnCr3 trigonal pyramids. In the ninth O site, O(9) is bonded to three equivalent Cr(2) and one Zn(5) atom to form a mixture of distorted corner and edge-sharing OZnCr3 trigonal pyramids. In the tenth O site, O(10) is bonded to three equivalent Cr(4) and one Zn(1) atom to form distorted OZnCr3 trigonal pyramids that share corners with three equivalent O(1)Zn2Cr2 trigonal pyramids, corners with three equivalent O(12)ZnCr3 trigonal pyramids, and edges with three equivalent O(8)ZnCr3 trigonal pyramids. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Cr(6), two equivalent Cr(4), and one Zn(3) atom. In the twelfth O site, O(12) is bonded to three equivalent Cr(4) and one Zn(6) atom to form distorted corner-sharing OZnCr3 trigonal pyramids. is represented by the CIF file [CIF]
data_ZnCr2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.997
_cell_length_b   5.997
_cell_length_c   14.739
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   459.010
_cell_formula_units_Z   6
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
  Zn  Zn0  1  0.333  0.667  0.953  1.0
  Zn  Zn1  1  0.000  0.000  0.625  1.0
  Zn  Zn2  1  0.000  0.000  0.997  1.0
  Zn  Zn3  1  0.667  0.333  0.293  1.0
  Zn  Zn4  1  0.333  0.667  0.710  1.0
  Zn  Zn5  1  0.000  0.000  0.375  1.0
  Cr  Cr6  1  0.834  0.668  0.833  1.0
  Cr  Cr7  1  0.332  0.166  0.833  1.0
  Cr  Cr8  1  0.500  0.000  0.500  1.0
  Cr  Cr9  1  0.834  0.166  0.833  1.0
  Cr  Cr10  1  0.667  0.333  0.667  1.0
  Cr  Cr11  1  1.000  0.500  0.500  1.0
  Cr  Cr12  1  0.168  0.335  0.168  1.0
  Cr  Cr13  1  0.500  0.500  0.500  1.0
  Cr  Cr14  1  0.168  0.832  0.168  1.0
  Cr  Cr15  1  0.333  0.667  0.334  1.0
  Cr  Cr16  1  0.665  0.832  0.168  1.0
  Cr  Cr17  1  0.667  0.333  0.044  1.0
  O  O18  1  0.690  0.845  0.909  1.0
  O  O19  1  0.000  0.000  0.761  1.0
  O  O20  1  0.155  0.845  0.909  1.0
  O  O21  1  0.155  0.310  0.909  1.0
  O  O22  1  0.516  0.032  0.753  1.0
  O  O23  1  0.364  0.182  0.579  1.0
  O  O24  1  0.516  0.484  0.753  1.0
  O  O25  1  0.667  0.333  0.907  1.0
  O  O26  1  0.818  0.182  0.579  1.0
  O  O27  1  0.667  0.333  0.428  1.0
  O  O28  1  0.968  0.484  0.753  1.0
  O  O29  1  0.818  0.636  0.579  1.0
  O  O30  1  0.182  0.364  0.420  1.0
  O  O31  1  0.031  0.516  0.247  1.0
  O  O32  1  0.182  0.818  0.420  1.0
  O  O33  1  0.333  0.667  0.572  1.0
  O  O34  1  0.333  0.667  0.095  1.0
  O  O35  1  0.484  0.516  0.247  1.0
  O  O36  1  0.636  0.818  0.420  1.0
  O  O37  1  0.484  0.969  0.247  1.0
  O  O38  1  0.840  0.680  0.092  1.0
  O  O39  1  0.000  0.000  0.238  1.0
  O  O40  1  0.840  0.160  0.092  1.0
  O  O41  1  0.320  0.160  0.092  1.0
[/CIF]
.
The material described by ZnCr2O4 is Spinel-like structured and crystallizes in the trigonal P3m1 space group. There are six inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form CrO6 octahedra that share  a cornercorner with one Cr(6)O4 tetrahedra,  a cornercorner with one Zn(2)O4 tetrahedra, corners with two equivalent Zn(1)O4 tetrahedra, corners with two equivalent Zn(5)O4 tetrahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. In the second Cr site, Cr(2) is bonded to one O(6), one O(9), two equivalent O(4), and two equivalent O(7) atoms to form CrO6 octahedra that share  a cornercorner with one Zn(4)O4 tetrahedra,  a cornercorner with one Zn(5)O4 tetrahedra, corners with two equivalent Zn(2)O4 tetrahedra, corners with two equivalent Zn(6)O4 tetrahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Cr(5)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. In the third Cr site, Cr(3) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form CrO6 octahedra that share corners with three equivalent Zn(2)O4 tetrahedra, corners with three equivalent Zn(5)O4 tetrahedra, edges with three equivalent Cr(1)O6 octahedra, and edges with three equivalent Cr(2)O6 octahedra. In the fourth Cr site, Cr(4) is bonded to one O(10), one O(12), two equivalent O(11), and two equivalent O(8) atoms to form CrO6 octahedra that share  a cornercorner with one Zn(1)O4 tetrahedra,  a cornercorner with one Zn(6)O4 tetrahedra, corners with two equivalent Cr(6)O4 tetrahedra, corners with two equivalent Zn(4)O4 tetrahedra,  an edgeedge with one Cr(5)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, and edges with four equivalent Cr(4)O6 octahedra. In the fifth Cr site, Cr(5) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form CrO6 octahedra that share corners with three equivalent Zn(4)O4 tetrahedra, corners with three equivalent Zn(6)O4 tetrahedra, edges with three equivalent Cr(2)O6 octahedra, and edges with three equivalent Cr(4)O6 octahedra. In the sixth Cr site, Cr(6) is bonded to one O(5) and three equivalent O(11) atoms to form CrO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Zn(3)O6 octahedra, and corners with six equivalent Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-61°. There are six inequivalent Zn sites. In the first Zn site, Zn(1) is bonded to one O(10) and three equivalent O(1) atoms to form ZnO4 tetrahedra that share corners with three equivalent Cr(4)O6 octahedra, corners with three equivalent Zn(3)O6 octahedra, and corners with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. In the second Zn site, Zn(2) is bonded to one O(2) and three equivalent O(4) atoms to form ZnO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(3)O6 octahedra, and corners with six equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the third Zn site, Zn(3) is bonded to three equivalent O(1) and three equivalent O(11) atoms to form ZnO6 octahedra that share corners with three equivalent Cr(6)O4 tetrahedra, corners with three equivalent Zn(1)O4 tetrahedra, edges with three equivalent Cr(1)O6 octahedra, and edges with three equivalent Cr(4)O6 octahedra. In the fourth Zn site, Zn(4) is bonded to one O(6) and three equivalent O(8) atoms to form ZnO4 tetrahedra that share corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Cr(5)O6 octahedra, and corners with six equivalent Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the fifth Zn site, Zn(5) is bonded to one O(9) and three equivalent O(3) atoms to form ZnO4 tetrahedra that share corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Cr(3)O6 octahedra, and corners with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the sixth Zn site, Zn(6) is bonded to one O(12) and three equivalent O(7) atoms to form ZnO4 tetrahedra that share corners with three equivalent Cr(4)O6 octahedra, corners with three equivalent Cr(5)O6 octahedra, and corners with six equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Cr(1), one Zn(1), and one Zn(3) atom to form distorted OZn2Cr2 trigonal pyramids that share  a cornercorner with one O(10)ZnCr3 trigonal pyramid, corners with two equivalent O(5)Cr4 trigonal pyramids, corners with two equivalent O(1)Zn2Cr2 trigonal pyramids, corners with four equivalent O(3)ZnCr3 trigonal pyramids,  an edgeedge with one O(2)ZnCr3 trigonal pyramid, and edges with two equivalent O(1)Zn2Cr2 trigonal pyramids. In the second O site, O(2) is bonded to three equivalent Cr(1) and one Zn(2) atom to form distorted OZnCr3 trigonal pyramids that share corners with three equivalent O(5)Cr4 trigonal pyramids, corners with three equivalent O(4)ZnCr3 trigonal pyramids, corners with six equivalent O(3)ZnCr3 trigonal pyramids, and edges with three equivalent O(1)Zn2Cr2 trigonal pyramids. In the third O site, O(3) is bonded to one Cr(3), two equivalent Cr(1), and one Zn(5) atom to form distorted OZnCr3 trigonal pyramids that share  a cornercorner with one O(9)ZnCr3 trigonal pyramid, corners with two equivalent O(2)ZnCr3 trigonal pyramids, corners with two equivalent O(3)ZnCr3 trigonal pyramids, corners with three equivalent O(4)ZnCr3 trigonal pyramids, corners with four equivalent O(1)Zn2Cr2 trigonal pyramids,  an edgeedge with one O(5)Cr4 trigonal pyramid, and edges with two equivalent O(3)ZnCr3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Cr(3), two equivalent Cr(2), and one Zn(2) atom to form a mixture of distorted corner and edge-sharing OZnCr3 trigonal pyramids. In the fifth O site, O(5) is bonded to one Cr(6) and three equivalent Cr(1) atoms to form distorted OCr4 trigonal pyramids that share corners with three equivalent O(2)ZnCr3 trigonal pyramids, corners with six equivalent O(1)Zn2Cr2 trigonal pyramids, and edges with three equivalent O(3)ZnCr3 trigonal pyramids. In the sixth O site, O(6) is bonded to three equivalent Cr(2) and one Zn(4) atom to form a mixture of distorted corner and edge-sharing OZnCr3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Cr(5), two equivalent Cr(2), and one Zn(6) atom to form a mixture of distorted corner and edge-sharing OZnCr3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Cr(5), two equivalent Cr(4), and one Zn(4) atom to form a mixture of distorted corner and edge-sharing OZnCr3 trigonal pyramids. In the ninth O site, O(9) is bonded to three equivalent Cr(2) and one Zn(5) atom to form a mixture of distorted corner and edge-sharing OZnCr3 trigonal pyramids. In the tenth O site, O(10) is bonded to three equivalent Cr(4) and one Zn(1) atom to form distorted OZnCr3 trigonal pyramids that share corners with three equivalent O(1)Zn2Cr2 trigonal pyramids, corners with three equivalent O(12)ZnCr3 trigonal pyramids, and edges with three equivalent O(8)ZnCr3 trigonal pyramids. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Cr(6), two equivalent Cr(4), and one Zn(3) atom. In the twelfth O site, O(12) is bonded to three equivalent Cr(4) and one Zn(6) atom to form distorted corner-sharing OZnCr3 trigonal pyramids. is represented by the CIF file [CIF]
data_ZnCr2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.997
_cell_length_b   5.997
_cell_length_c   14.739
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   459.010
_cell_formula_units_Z   6
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
  Zn  Zn0  1  0.333  0.667  0.953  1.0
  Zn  Zn1  1  0.000  0.000  0.625  1.0
  Zn  Zn2  1  0.000  0.000  0.997  1.0
  Zn  Zn3  1  0.667  0.333  0.293  1.0
  Zn  Zn4  1  0.333  0.667  0.710  1.0
  Zn  Zn5  1  0.000  0.000  0.375  1.0
  Cr  Cr6  1  0.834  0.668  0.833  1.0
  Cr  Cr7  1  0.332  0.166  0.833  1.0
  Cr  Cr8  1  0.500  0.000  0.500  1.0
  Cr  Cr9  1  0.834  0.166  0.833  1.0
  Cr  Cr10  1  0.667  0.333  0.667  1.0
  Cr  Cr11  1  1.000  0.500  0.500  1.0
  Cr  Cr12  1  0.168  0.335  0.168  1.0
  Cr  Cr13  1  0.500  0.500  0.500  1.0
  Cr  Cr14  1  0.168  0.832  0.168  1.0
  Cr  Cr15  1  0.333  0.667  0.334  1.0
  Cr  Cr16  1  0.665  0.832  0.168  1.0
  Cr  Cr17  1  0.667  0.333  0.044  1.0
  O  O18  1  0.690  0.845  0.909  1.0
  O  O19  1  0.000  0.000  0.761  1.0
  O  O20  1  0.155  0.845  0.909  1.0
  O  O21  1  0.155  0.310  0.909  1.0
  O  O22  1  0.516  0.032  0.753  1.0
  O  O23  1  0.364  0.182  0.579  1.0
  O  O24  1  0.516  0.484  0.753  1.0
  O  O25  1  0.667  0.333  0.907  1.0
  O  O26  1  0.818  0.182  0.579  1.0
  O  O27  1  0.667  0.333  0.428  1.0
  O  O28  1  0.968  0.484  0.753  1.0
  O  O29  1  0.818  0.636  0.579  1.0
  O  O30  1  0.182  0.364  0.420  1.0
  O  O31  1  0.031  0.516  0.247  1.0
  O  O32  1  0.182  0.818  0.420  1.0
  O  O33  1  0.333  0.667  0.572  1.0
  O  O34  1  0.333  0.667  0.095  1.0
  O  O35  1  0.484  0.516  0.247  1.0
  O  O36  1  0.636  0.818  0.420  1.0
  O  O37  1  0.484  0.969  0.247  1.0
  O  O38  1  0.840  0.680  0.092  1.0
  O  O39  1  0.000  0.000  0.238  1.0
  O  O40  1  0.840  0.160  0.092  1.0
  O  O41  1  0.320  0.160  0.092  1.0
[/CIF]
.