The material structure described by Fe3O4 is Spinel-derived structured and crystallizes in the triclinic P1 space group. There are twelve inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(10), one O(14), one O(2), one O(4), one O(6), and one O(8) atom to form FeO6 octahedra that share  a cornercorner with one Fe(6)O4 tetrahedra,  a cornercorner with one Fe(8)O4 tetrahedra, corners with two equivalent Fe(7)O4 tetrahedra, corners with two equivalent Fe(9)O4 tetrahedra,  an edgeedge with one Fe(11)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Fe(12)O6 octahedra, and edges with two equivalent Fe(5)O6 octahedra. In the second Fe site, Fe(2) is bonded to one O(12), one O(15), one O(2), one O(3), one O(8), and one O(9) atom to form FeO6 octahedra that share corners with three equivalent Fe(7)O4 tetrahedra, corners with three equivalent Fe(8)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(10)O6 octahedra,  an edgeedge with one Fe(12)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, and  an edgeedge with one Fe(5)O6 octahedra. In the third Fe site, Fe(3) is bonded to one O(1), one O(11), one O(13), one O(15), one O(3), and one O(5) atom to form FeO6 octahedra that share  a cornercorner with one Fe(7)O4 tetrahedra,  a cornercorner with one Fe(9)O4 tetrahedra, corners with two equivalent Fe(6)O4 tetrahedra, corners with two equivalent Fe(8)O4 tetrahedra,  an edgeedge with one Fe(11)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Fe(10)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. In the fourth Fe site, Fe(4) is bonded to one O(11), one O(13), one O(15), one O(5), one O(7), and one O(9) atom to form FeO6 octahedra that share  a cornercorner with one Fe(7)O4 tetrahedra,  a cornercorner with one Fe(9)O4 tetrahedra, corners with two equivalent Fe(6)O4 tetrahedra, corners with two equivalent Fe(8)O4 tetrahedra,  an edgeedge with one Fe(11)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Fe(10)O6 octahedra, and edges with two equivalent Fe(3)O6 octahedra. In the fifth Fe site, Fe(5) is bonded to one O(10), one O(12), one O(14), one O(16), one O(6), and one O(8) atom to form FeO6 octahedra that share  a cornercorner with one Fe(6)O4 tetrahedra,  a cornercorner with one Fe(8)O4 tetrahedra, corners with two equivalent Fe(7)O4 tetrahedra, corners with two equivalent Fe(9)O4 tetrahedra,  an edgeedge with one Fe(11)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(12)O6 octahedra. In the sixth Fe site, Fe(6) is bonded to one O(1), one O(11), one O(14), and one O(7) atom to form corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 52-60°. In the seventh Fe site, Fe(7) is bonded to one O(12), one O(13), one O(2), and one O(8) atom to form corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-59°. In the eighth Fe site, Fe(8) is bonded to one O(15), one O(3), one O(6), and one O(9) atom to form corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-60°. In the ninth Fe site, Fe(9) is bonded to one O(10), one O(16), one O(4), and one O(5) atom to form corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-61°. In the tenth Fe site, Fe(10) is bonded to one O(1), one O(13), one O(3), one O(5), one O(7), and one O(9) atom to form FeO6 octahedra that share  a cornercorner with one Fe(7)O4 tetrahedra,  a cornercorner with one Fe(9)O4 tetrahedra, corners with two equivalent Fe(6)O4 tetrahedra, corners with two equivalent Fe(8)O4 tetrahedra,  an edgeedge with one Fe(11)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. In the eleventh Fe site, Fe(11) is bonded to one O(1), one O(10), one O(11), one O(16), one O(4), and one O(7) atom to form FeO6 octahedra that share corners with three equivalent Fe(6)O4 tetrahedra, corners with three equivalent Fe(9)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(10)O6 octahedra,  an edgeedge with one Fe(12)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, and  an edgeedge with one Fe(5)O6 octahedra. In the twelfth Fe site, Fe(12) is bonded to one O(12), one O(14), one O(16), one O(2), one O(4), and one O(6) atom to form FeO6 octahedra that share  a cornercorner with one Fe(6)O4 tetrahedra,  a cornercorner with one Fe(8)O4 tetrahedra, corners with two equivalent Fe(7)O4 tetrahedra, corners with two equivalent Fe(9)O4 tetrahedra,  an edgeedge with one Fe(11)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(5)O6 octahedra. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Fe(10), one Fe(11), one Fe(3), and one Fe(6) atom. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(12), one Fe(2), and one Fe(7) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Fe(10), one Fe(2), one Fe(3), and one Fe(8) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(11), one Fe(12), and one Fe(9) atom. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Fe(10), one Fe(3), one Fe(4), and one Fe(9) atom. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(12), one Fe(5), and one Fe(8) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Fe(10), one Fe(11), one Fe(4), and one Fe(6) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(2), one Fe(5), and one Fe(7) atom. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Fe(10), one Fe(2), one Fe(4), and one Fe(8) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(11), one Fe(5), and one Fe(9) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Fe(11), one Fe(3), one Fe(4), and one Fe(6) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Fe(12), one Fe(2), one Fe(5), and one Fe(7) atom. In the thirteenth O site, O(13) is bonded in a rectangular see-saw-like geometry to one Fe(10), one Fe(3), one Fe(4), and one Fe(7) atom. In the fourteenth O site, O(14) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(12), one Fe(5), and one Fe(6) atom. In the fifteenth O site, O(15) is bonded in a rectangular see-saw-like geometry to one Fe(2), one Fe(3), one Fe(4), and one Fe(8) atom. In the sixteenth O site, O(16) is bonded in a rectangular see-saw-like geometry to one Fe(11), one Fe(12), one Fe(5), and one Fe(9) atom. is represented by the CIF card [CIF]
data_Fe3O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.072
_cell_length_b   6.091
_cell_length_c   10.501
_cell_angle_alpha   89.787
_cell_angle_beta   73.124
_cell_angle_gamma   59.575
_symmetry_Int_Tables_number   1
_cell_volume   315.581
_cell_formula_units_Z   4
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
  Fe  Fe0  1  0.500  0.750  0.751  1.0
  Fe  Fe1  1  0.501  0.001  0.497  1.0
  Fe  Fe2  1  0.001  0.750  0.249  1.0
  Fe  Fe3  1  0.501  0.747  0.247  1.0
  Fe  Fe4  1  0.500  0.252  0.752  1.0
  Fe  Fe5  1  0.131  0.188  0.063  1.0
  Fe  Fe6  1  0.131  0.688  0.563  1.0
  Fe  Fe7  1  0.870  0.313  0.437  1.0
  Fe  Fe8  1  0.869  0.811  0.937  1.0
  Fe  Fe9  1  0.500  0.251  0.249  1.0
  Fe  Fe10  1  0.499  0.499  0.002  1.0
  Fe  Fe11  1  0.999  0.250  0.750  1.0
  O  O12  1  0.256  0.380  0.126  1.0
  O  O13  1  0.268  0.878  0.626  1.0
  O  O14  1  0.737  0.119  0.382  1.0
  O  O15  1  0.739  0.624  0.867  1.0
  O  O16  1  0.746  0.865  0.131  1.0
  O  O17  1  0.728  0.388  0.634  1.0
  O  O18  1  0.741  0.391  0.132  1.0
  O  O19  1  0.729  0.883  0.628  1.0
  O  O20  1  0.264  0.107  0.380  1.0
  O  O21  1  0.265  0.620  0.862  1.0
  O  O22  1  0.259  0.871  0.132  1.0
  O  O23  1  0.272  0.354  0.623  1.0
  O  O24  1  0.252  0.636  0.371  1.0
  O  O25  1  0.273  0.112  0.864  1.0
  O  O26  1  0.730  0.644  0.378  1.0
  O  O27  1  0.741  0.129  0.867  1.0
[/CIF]
.
The material structure described by Fe3O4 is Spinel-derived structured and crystallizes in the triclinic P1 space group. There are twelve inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(10), one O(14), one O(2), one O(4), one O(6), and one O(8) atom to form FeO6 octahedra that share  a cornercorner with one Fe(6)O4 tetrahedra,  a cornercorner with one Fe(8)O4 tetrahedra, corners with two equivalent Fe(7)O4 tetrahedra, corners with two equivalent Fe(9)O4 tetrahedra,  an edgeedge with one Fe(11)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Fe(12)O6 octahedra, and edges with two equivalent Fe(5)O6 octahedra. In the second Fe site, Fe(2) is bonded to one O(12), one O(15), one O(2), one O(3), one O(8), and one O(9) atom to form FeO6 octahedra that share corners with three equivalent Fe(7)O4 tetrahedra, corners with three equivalent Fe(8)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(10)O6 octahedra,  an edgeedge with one Fe(12)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, and  an edgeedge with one Fe(5)O6 octahedra. In the third Fe site, Fe(3) is bonded to one O(1), one O(11), one O(13), one O(15), one O(3), and one O(5) atom to form FeO6 octahedra that share  a cornercorner with one Fe(7)O4 tetrahedra,  a cornercorner with one Fe(9)O4 tetrahedra, corners with two equivalent Fe(6)O4 tetrahedra, corners with two equivalent Fe(8)O4 tetrahedra,  an edgeedge with one Fe(11)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Fe(10)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. In the fourth Fe site, Fe(4) is bonded to one O(11), one O(13), one O(15), one O(5), one O(7), and one O(9) atom to form FeO6 octahedra that share  a cornercorner with one Fe(7)O4 tetrahedra,  a cornercorner with one Fe(9)O4 tetrahedra, corners with two equivalent Fe(6)O4 tetrahedra, corners with two equivalent Fe(8)O4 tetrahedra,  an edgeedge with one Fe(11)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Fe(10)O6 octahedra, and edges with two equivalent Fe(3)O6 octahedra. In the fifth Fe site, Fe(5) is bonded to one O(10), one O(12), one O(14), one O(16), one O(6), and one O(8) atom to form FeO6 octahedra that share  a cornercorner with one Fe(6)O4 tetrahedra,  a cornercorner with one Fe(8)O4 tetrahedra, corners with two equivalent Fe(7)O4 tetrahedra, corners with two equivalent Fe(9)O4 tetrahedra,  an edgeedge with one Fe(11)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(12)O6 octahedra. In the sixth Fe site, Fe(6) is bonded to one O(1), one O(11), one O(14), and one O(7) atom to form corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 52-60°. In the seventh Fe site, Fe(7) is bonded to one O(12), one O(13), one O(2), and one O(8) atom to form corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-59°. In the eighth Fe site, Fe(8) is bonded to one O(15), one O(3), one O(6), and one O(9) atom to form corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-60°. In the ninth Fe site, Fe(9) is bonded to one O(10), one O(16), one O(4), and one O(5) atom to form corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-61°. In the tenth Fe site, Fe(10) is bonded to one O(1), one O(13), one O(3), one O(5), one O(7), and one O(9) atom to form FeO6 octahedra that share  a cornercorner with one Fe(7)O4 tetrahedra,  a cornercorner with one Fe(9)O4 tetrahedra, corners with two equivalent Fe(6)O4 tetrahedra, corners with two equivalent Fe(8)O4 tetrahedra,  an edgeedge with one Fe(11)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. In the eleventh Fe site, Fe(11) is bonded to one O(1), one O(10), one O(11), one O(16), one O(4), and one O(7) atom to form FeO6 octahedra that share corners with three equivalent Fe(6)O4 tetrahedra, corners with three equivalent Fe(9)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(10)O6 octahedra,  an edgeedge with one Fe(12)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, and  an edgeedge with one Fe(5)O6 octahedra. In the twelfth Fe site, Fe(12) is bonded to one O(12), one O(14), one O(16), one O(2), one O(4), and one O(6) atom to form FeO6 octahedra that share  a cornercorner with one Fe(6)O4 tetrahedra,  a cornercorner with one Fe(8)O4 tetrahedra, corners with two equivalent Fe(7)O4 tetrahedra, corners with two equivalent Fe(9)O4 tetrahedra,  an edgeedge with one Fe(11)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(5)O6 octahedra. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Fe(10), one Fe(11), one Fe(3), and one Fe(6) atom. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(12), one Fe(2), and one Fe(7) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Fe(10), one Fe(2), one Fe(3), and one Fe(8) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(11), one Fe(12), and one Fe(9) atom. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Fe(10), one Fe(3), one Fe(4), and one Fe(9) atom. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(12), one Fe(5), and one Fe(8) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Fe(10), one Fe(11), one Fe(4), and one Fe(6) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(2), one Fe(5), and one Fe(7) atom. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Fe(10), one Fe(2), one Fe(4), and one Fe(8) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(11), one Fe(5), and one Fe(9) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Fe(11), one Fe(3), one Fe(4), and one Fe(6) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Fe(12), one Fe(2), one Fe(5), and one Fe(7) atom. In the thirteenth O site, O(13) is bonded in a rectangular see-saw-like geometry to one Fe(10), one Fe(3), one Fe(4), and one Fe(7) atom. In the fourteenth O site, O(14) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(12), one Fe(5), and one Fe(6) atom. In the fifteenth O site, O(15) is bonded in a rectangular see-saw-like geometry to one Fe(2), one Fe(3), one Fe(4), and one Fe(8) atom. In the sixteenth O site, O(16) is bonded in a rectangular see-saw-like geometry to one Fe(11), one Fe(12), one Fe(5), and one Fe(9) atom. is represented by the CIF card [CIF]
data_Fe3O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.072
_cell_length_b   6.091
_cell_length_c   10.501
_cell_angle_alpha   89.787
_cell_angle_beta   73.124
_cell_angle_gamma   59.575
_symmetry_Int_Tables_number   1
_cell_volume   315.581
_cell_formula_units_Z   4
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
  Fe  Fe0  1  0.500  0.750  0.751  1.0
  Fe  Fe1  1  0.501  0.001  0.497  1.0
  Fe  Fe2  1  0.001  0.750  0.249  1.0
  Fe  Fe3  1  0.501  0.747  0.247  1.0
  Fe  Fe4  1  0.500  0.252  0.752  1.0
  Fe  Fe5  1  0.131  0.188  0.063  1.0
  Fe  Fe6  1  0.131  0.688  0.563  1.0
  Fe  Fe7  1  0.870  0.313  0.437  1.0
  Fe  Fe8  1  0.869  0.811  0.937  1.0
  Fe  Fe9  1  0.500  0.251  0.249  1.0
  Fe  Fe10  1  0.499  0.499  0.002  1.0
  Fe  Fe11  1  0.999  0.250  0.750  1.0
  O  O12  1  0.256  0.380  0.126  1.0
  O  O13  1  0.268  0.878  0.626  1.0
  O  O14  1  0.737  0.119  0.382  1.0
  O  O15  1  0.739  0.624  0.867  1.0
  O  O16  1  0.746  0.865  0.131  1.0
  O  O17  1  0.728  0.388  0.634  1.0
  O  O18  1  0.741  0.391  0.132  1.0
  O  O19  1  0.729  0.883  0.628  1.0
  O  O20  1  0.264  0.107  0.380  1.0
  O  O21  1  0.265  0.620  0.862  1.0
  O  O22  1  0.259  0.871  0.132  1.0
  O  O23  1  0.272  0.354  0.623  1.0
  O  O24  1  0.252  0.636  0.371  1.0
  O  O25  1  0.273  0.112  0.864  1.0
  O  O26  1  0.730  0.644  0.378  1.0
  O  O27  1  0.741  0.129  0.867  1.0
[/CIF]
.