The material structure described by Li3FeO4 is Caswellsilverite-like structured and crystallizes in the monoclinic Cm space group. There are eight inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(12), one O(5), two equivalent O(2), and two equivalent O(4) atoms to form LiO6 octahedra that share  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, and edges with four equivalent Li(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the second Li site, Li(2) is bonded to one O(11), one O(6), two equivalent O(2), and two equivalent O(4) atoms to form LiO6 octahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, and edges with four equivalent Li(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. In the third Li site, Li(3) is bonded to one O(7), one O(9), two equivalent O(1), and two equivalent O(3) atoms to form LiO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, and edges with four equivalent Li(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. In the fourth Li site, Li(4) is bonded to one O(10), one O(8), two equivalent O(1), and two equivalent O(3) atoms to form LiO6 octahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, and edges with four equivalent Li(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. In the fifth Li site, Li(5) is bonded to one O(1), one O(10), one O(4), one O(5), one O(6), and one O(9) atom to form LiO6 octahedra that share corners with three equivalent Li(7)O6 octahedra, corners with three equivalent Li(8)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(7)O6 octahedra,  an edgeedge with one Li(8)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-11°. In the sixth Li site, Li(6) is bonded to one O(11), one O(12), one O(2), one O(3), one O(7), and one O(8) atom to form LiO6 octahedra that share corners with three equivalent Li(7)O6 octahedra, corners with three equivalent Li(8)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(7)O6 octahedra,  an edgeedge with one Li(8)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-11°. In the seventh Li site, Li(7) is bonded to one O(1), one O(10), one O(3), one O(7), one O(8), and one O(9) atom to form LiO6 octahedra that share corners with three equivalent Li(5)O6 octahedra, corners with three equivalent Li(6)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, and edges with two equivalent Li(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-11°. In the eighth Li site, Li(8) is bonded to one O(11), one O(12), one O(2), one O(4), one O(5), and one O(6) atom to form LiO6 octahedra that share corners with three equivalent Li(5)O6 octahedra, corners with three equivalent Li(6)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, and edges with two equivalent Li(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-11°. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(10), one O(6), two equivalent O(1), and two equivalent O(4) atoms to form FeO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra,  a cornercorner with one Li(4)O6 octahedra, corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(3)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra, edges with two equivalent Li(7)O6 octahedra, edges with two equivalent Li(8)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and edges with four equivalent Li(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-3°. In the second Fe site, Fe(2) is bonded to one O(11), one O(7), two equivalent O(2), and two equivalent O(3) atoms to form FeO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra,  a cornercorner with one Li(3)O6 octahedra, corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(4)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra, edges with two equivalent Li(7)O6 octahedra, edges with two equivalent Li(8)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and edges with four equivalent Li(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-3°. In the third Fe site, Fe(3) is bonded to one O(5), one O(9), two equivalent O(1), and two equivalent O(4) atoms to form FeO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Li(3)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Li(4)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra, edges with two equivalent Li(7)O6 octahedra, edges with two equivalent Li(8)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with four equivalent Li(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the fourth Fe site, Fe(4) is bonded to one O(12), one O(8), two equivalent O(2), and two equivalent O(3) atoms to form FeO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Li(4)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Li(3)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra, edges with two equivalent Li(7)O6 octahedra, edges with two equivalent Li(8)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with four equivalent Li(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Li(3), one Li(4), one Li(5), one Li(7), one Fe(1), and one Fe(3) atom to form OLi4Fe2 octahedra that share corners with three equivalent O(3)Li4Fe2 octahedra, corners with three equivalent O(4)Li4Fe2 octahedra,  an edgeedge with one O(3)Li4Fe2 octahedra,  an edgeedge with one O(4)Li4Fe2 octahedra,  an edgeedge with one O(5)Li5Fe octahedra,  an edgeedge with one O(6)Li5Fe octahedra,  an edgeedge with one O(7)Li5Fe octahedra,  an edgeedge with one O(8)Li5Fe octahedra, edges with two equivalent O(1)Li4Fe2 octahedra, edges with two equivalent O(10)Li5Fe octahedra, and edges with two equivalent O(9)Li5Fe octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the second O site, O(2) is bonded to one Li(1), one Li(2), one Li(6), one Li(8), one Fe(2), and one Fe(4) atom to form OLi4Fe2 octahedra that share corners with three equivalent O(3)Li4Fe2 octahedra, corners with three equivalent O(4)Li4Fe2 octahedra,  an edgeedge with one O(3)Li4Fe2 octahedra,  an edgeedge with one O(4)Li4Fe2 octahedra,  an edgeedge with one O(5)Li5Fe octahedra,  an edgeedge with one O(6)Li5Fe octahedra,  an edgeedge with one O(7)Li5Fe octahedra,  an edgeedge with one O(8)Li5Fe octahedra, edges with two equivalent O(2)Li4Fe2 octahedra, edges with two equivalent O(11)Li5Fe octahedra, and edges with two equivalent O(12)Li5Fe octahedra. The corner-sharing octahedral tilt angles range from 1-5°. In the third O site, O(3) is bonded to one Li(3), one Li(4), one Li(6), one Li(7), one Fe(2), and one Fe(4) atom to form OLi4Fe2 octahedra that share corners with three equivalent O(1)Li4Fe2 octahedra, corners with three equivalent O(2)Li4Fe2 octahedra,  an edgeedge with one O(1)Li4Fe2 octahedra,  an edgeedge with one O(2)Li4Fe2 octahedra,  an edgeedge with one O(10)Li5Fe octahedra,  an edgeedge with one O(11)Li5Fe octahedra,  an edgeedge with one O(12)Li5Fe octahedra,  an edgeedge with one O(9)Li5Fe octahedra, edges with two equivalent O(3)Li4Fe2 octahedra, edges with two equivalent O(7)Li5Fe octahedra, and edges with two equivalent O(8)Li5Fe octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the fourth O site, O(4) is bonded to one Li(1), one Li(2), one Li(5), one Li(8), one Fe(1), and one Fe(3) atom to form OLi4Fe2 octahedra that share corners with three equivalent O(1)Li4Fe2 octahedra, corners with three equivalent O(2)Li4Fe2 octahedra,  an edgeedge with one O(1)Li4Fe2 octahedra,  an edgeedge with one O(2)Li4Fe2 octahedra,  an edgeedge with one O(10)Li5Fe octahedra,  an edgeedge with one O(11)Li5Fe octahedra,  an edgeedge with one O(12)Li5Fe octahedra,  an edgeedge with one O(9)Li5Fe octahedra, edges with two equivalent O(4)Li4Fe2 octahedra, edges with two equivalent O(5)Li5Fe octahedra, and edges with two equivalent O(6)Li5Fe octahedra. The corner-sharing octahedral tilt angles range from 1-5°. In the fifth O site, O(5) is bonded to one Li(1), two equivalent Li(5), two equivalent Li(8), and one Fe(3) atom to form OLi5Fe octahedra that share  a cornercorner with one O(12)Li5Fe octahedra,  a cornercorner with one O(9)Li5Fe octahedra, corners with two equivalent O(10)Li5Fe octahedra, corners with two equivalent O(11)Li5Fe octahedra,  an edgeedge with one O(12)Li5Fe octahedra,  an edgeedge with one O(9)Li5Fe octahedra, edges with two equivalent O(1)Li4Fe2 octahedra, edges with two equivalent O(2)Li4Fe2 octahedra, edges with two equivalent O(6)Li5Fe octahedra, and edges with four equivalent O(4)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the sixth O site, O(6) is bonded to one Li(2), two equivalent Li(5), two equivalent Li(8), and one Fe(1) atom to form OLi5Fe octahedra that share  a cornercorner with one O(10)Li5Fe octahedra,  a cornercorner with one O(11)Li5Fe octahedra, corners with two equivalent O(12)Li5Fe octahedra, corners with two equivalent O(9)Li5Fe octahedra,  an edgeedge with one O(10)Li5Fe octahedra,  an edgeedge with one O(11)Li5Fe octahedra, edges with two equivalent O(1)Li4Fe2 octahedra, edges with two equivalent O(2)Li4Fe2 octahedra, edges with two equivalent O(5)Li5Fe octahedra, and edges with four equivalent O(4)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the seventh O site, O(7) is bonded to one Li(3), two equivalent Li(6), two equivalent Li(7), and one Fe(2) atom to form OLi5Fe octahedra that share  a cornercorner with one O(11)Li5Fe octahedra,  a cornercorner with one O(9)Li5Fe octahedra, corners with two equivalent O(10)Li5Fe octahedra, corners with two equivalent O(12)Li5Fe octahedra,  an edgeedge with one O(11)Li5Fe octahedra,  an edgeedge with one O(9)Li5Fe octahedra, edges with two equivalent O(1)Li4Fe2 octahedra, edges with two equivalent O(2)Li4Fe2 octahedra, edges with two equivalent O(8)Li5Fe octahedra, and edges with four equivalent O(3)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the eighth O site, O(8) is bonded to one Li(4), two equivalent Li(6), two equivalent Li(7), and one Fe(4) atom to form OLi5Fe octahedra that share  a cornercorner with one O(10)Li5Fe octahedra,  a cornercorner with one O(12)Li5Fe octahedra, corners with two equivalent O(11)Li5Fe octahedra, corners with two equivalent O(9)Li5Fe octahedra,  an edgeedge with one O(10)Li5Fe octahedra,  an edgeedge with one O(12)Li5Fe octahedra, edges with two equivalent O(1)Li4Fe2 octahedra, edges with two equivalent O(2)Li4Fe2 octahedra, edges with two equivalent O(7)Li5Fe octahedra, and edges with four equivalent O(3)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the ninth O site, O(9) is bonded to one Li(3), two equivalent Li(5), two equivalent Li(7), and one Fe(3) atom to form OLi5Fe octahedra that share  a cornercorner with one O(5)Li5Fe octahedra,  a cornercorner with one O(7)Li5Fe octahedra, corners with two equivalent O(6)Li5Fe octahedra, corners with two equivalent O(8)Li5Fe octahedra,  an edgeedge with one O(5)Li5Fe octahedra,  an edgeedge with one O(7)Li5Fe octahedra, edges with two equivalent O(3)Li4Fe2 octahedra, edges with two equivalent O(4)Li4Fe2 octahedra, edges with two equivalent O(10)Li5Fe octahedra, and edges with four equivalent O(1)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the tenth O site, O(10) is bonded to one Li(4), two equivalent Li(5), two equivalent Li(7), and one Fe(1) atom to form OLi5Fe octahedra that share  a cornercorner with one O(6)Li5Fe octahedra,  a cornercorner with one O(8)Li5Fe octahedra, corners with two equivalent O(5)Li5Fe octahedra, corners with two equivalent O(7)Li5Fe octahedra,  an edgeedge with one O(6)Li5Fe octahedra,  an edgeedge with one O(8)Li5Fe octahedra, edges with two equivalent O(3)Li4Fe2 octahedra, edges with two equivalent O(4)Li4Fe2 octahedra, edges with two equivalent O(9)Li5Fe octahedra, and edges with four equivalent O(1)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the eleventh O site, O(11) is bonded to one Li(2), two equivalent Li(6), two equivalent Li(8), and one Fe(2) atom to form OLi5Fe octahedra that share  a cornercorner with one O(6)Li5Fe octahedra,  a cornercorner with one O(7)Li5Fe octahedra, corners with two equivalent O(5)Li5Fe octahedra, corners with two equivalent O(8)Li5Fe octahedra,  an edgeedge with one O(6)Li5Fe octahedra,  an edgeedge with one O(7)Li5Fe octahedra, edges with two equivalent O(3)Li4Fe2 octahedra, edges with two equivalent O(4)Li4Fe2 octahedra, edges with two equivalent O(12)Li5Fe octahedra, and edges with four equivalent O(2)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Li(6), two equivalent Li(8), and one Fe(4) atom to form OLi5Fe octahedra that share  a cornercorner with one O(5)Li5Fe octahedra,  a cornercorner with one O(8)Li5Fe octahedra, corners with two equivalent O(6)Li5Fe octahedra, corners with two equivalent O(7)Li5Fe octahedra,  an edgeedge with one O(5)Li5Fe octahedra,  an edgeedge with one O(8)Li5Fe octahedra, edges with two equivalent O(3)Li4Fe2 octahedra, edges with two equivalent O(4)Li4Fe2 octahedra, edges with two equivalent O(11)Li5Fe octahedra, and edges with four equivalent O(2)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li3FeO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   2.921
_cell_length_b   5.008
_cell_length_c   5.017
_cell_angle_alpha   71.693
_cell_angle_beta   90.006
_cell_angle_gamma   90.067
_symmetry_Int_Tables_number   1
_cell_volume   69.656
_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
  Fe  Fe0  1  0.507  0.002  0.499  1.0
  Li  Li1  1  0.507  0.500  0.997  1.0
  Li  Li2  1  0.006  0.002  1.000  1.0
  Li  Li3  1  0.006  0.503  0.498  1.0
  O  O4  1  0.007  0.773  0.728  1.0
  O  O5  1  0.007  0.231  0.270  1.0
  O  O6  1  0.507  0.230  0.727  1.0
  O  O7  1  0.506  0.774  0.272  1.0
[/CIF]
.
The material structure described by Li3FeO4 is Caswellsilverite-like structured and crystallizes in the monoclinic Cm space group. There are eight inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(12), one O(5), two equivalent O(2), and two equivalent O(4) atoms to form LiO6 octahedra that share  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, and edges with four equivalent Li(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the second Li site, Li(2) is bonded to one O(11), one O(6), two equivalent O(2), and two equivalent O(4) atoms to form LiO6 octahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, and edges with four equivalent Li(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. In the third Li site, Li(3) is bonded to one O(7), one O(9), two equivalent O(1), and two equivalent O(3) atoms to form LiO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, and edges with four equivalent Li(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. In the fourth Li site, Li(4) is bonded to one O(10), one O(8), two equivalent O(1), and two equivalent O(3) atoms to form LiO6 octahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, and edges with four equivalent Li(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. In the fifth Li site, Li(5) is bonded to one O(1), one O(10), one O(4), one O(5), one O(6), and one O(9) atom to form LiO6 octahedra that share corners with three equivalent Li(7)O6 octahedra, corners with three equivalent Li(8)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(7)O6 octahedra,  an edgeedge with one Li(8)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-11°. In the sixth Li site, Li(6) is bonded to one O(11), one O(12), one O(2), one O(3), one O(7), and one O(8) atom to form LiO6 octahedra that share corners with three equivalent Li(7)O6 octahedra, corners with three equivalent Li(8)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(7)O6 octahedra,  an edgeedge with one Li(8)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-11°. In the seventh Li site, Li(7) is bonded to one O(1), one O(10), one O(3), one O(7), one O(8), and one O(9) atom to form LiO6 octahedra that share corners with three equivalent Li(5)O6 octahedra, corners with three equivalent Li(6)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, and edges with two equivalent Li(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-11°. In the eighth Li site, Li(8) is bonded to one O(11), one O(12), one O(2), one O(4), one O(5), and one O(6) atom to form LiO6 octahedra that share corners with three equivalent Li(5)O6 octahedra, corners with three equivalent Li(6)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, and edges with two equivalent Li(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-11°. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(10), one O(6), two equivalent O(1), and two equivalent O(4) atoms to form FeO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra,  a cornercorner with one Li(4)O6 octahedra, corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(3)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra, edges with two equivalent Li(7)O6 octahedra, edges with two equivalent Li(8)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and edges with four equivalent Li(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-3°. In the second Fe site, Fe(2) is bonded to one O(11), one O(7), two equivalent O(2), and two equivalent O(3) atoms to form FeO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra,  a cornercorner with one Li(3)O6 octahedra, corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(4)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra, edges with two equivalent Li(7)O6 octahedra, edges with two equivalent Li(8)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and edges with four equivalent Li(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-3°. In the third Fe site, Fe(3) is bonded to one O(5), one O(9), two equivalent O(1), and two equivalent O(4) atoms to form FeO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Li(3)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Li(4)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra, edges with two equivalent Li(7)O6 octahedra, edges with two equivalent Li(8)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with four equivalent Li(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the fourth Fe site, Fe(4) is bonded to one O(12), one O(8), two equivalent O(2), and two equivalent O(3) atoms to form FeO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Li(4)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Li(3)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra, edges with two equivalent Li(7)O6 octahedra, edges with two equivalent Li(8)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with four equivalent Li(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Li(3), one Li(4), one Li(5), one Li(7), one Fe(1), and one Fe(3) atom to form OLi4Fe2 octahedra that share corners with three equivalent O(3)Li4Fe2 octahedra, corners with three equivalent O(4)Li4Fe2 octahedra,  an edgeedge with one O(3)Li4Fe2 octahedra,  an edgeedge with one O(4)Li4Fe2 octahedra,  an edgeedge with one O(5)Li5Fe octahedra,  an edgeedge with one O(6)Li5Fe octahedra,  an edgeedge with one O(7)Li5Fe octahedra,  an edgeedge with one O(8)Li5Fe octahedra, edges with two equivalent O(1)Li4Fe2 octahedra, edges with two equivalent O(10)Li5Fe octahedra, and edges with two equivalent O(9)Li5Fe octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the second O site, O(2) is bonded to one Li(1), one Li(2), one Li(6), one Li(8), one Fe(2), and one Fe(4) atom to form OLi4Fe2 octahedra that share corners with three equivalent O(3)Li4Fe2 octahedra, corners with three equivalent O(4)Li4Fe2 octahedra,  an edgeedge with one O(3)Li4Fe2 octahedra,  an edgeedge with one O(4)Li4Fe2 octahedra,  an edgeedge with one O(5)Li5Fe octahedra,  an edgeedge with one O(6)Li5Fe octahedra,  an edgeedge with one O(7)Li5Fe octahedra,  an edgeedge with one O(8)Li5Fe octahedra, edges with two equivalent O(2)Li4Fe2 octahedra, edges with two equivalent O(11)Li5Fe octahedra, and edges with two equivalent O(12)Li5Fe octahedra. The corner-sharing octahedral tilt angles range from 1-5°. In the third O site, O(3) is bonded to one Li(3), one Li(4), one Li(6), one Li(7), one Fe(2), and one Fe(4) atom to form OLi4Fe2 octahedra that share corners with three equivalent O(1)Li4Fe2 octahedra, corners with three equivalent O(2)Li4Fe2 octahedra,  an edgeedge with one O(1)Li4Fe2 octahedra,  an edgeedge with one O(2)Li4Fe2 octahedra,  an edgeedge with one O(10)Li5Fe octahedra,  an edgeedge with one O(11)Li5Fe octahedra,  an edgeedge with one O(12)Li5Fe octahedra,  an edgeedge with one O(9)Li5Fe octahedra, edges with two equivalent O(3)Li4Fe2 octahedra, edges with two equivalent O(7)Li5Fe octahedra, and edges with two equivalent O(8)Li5Fe octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the fourth O site, O(4) is bonded to one Li(1), one Li(2), one Li(5), one Li(8), one Fe(1), and one Fe(3) atom to form OLi4Fe2 octahedra that share corners with three equivalent O(1)Li4Fe2 octahedra, corners with three equivalent O(2)Li4Fe2 octahedra,  an edgeedge with one O(1)Li4Fe2 octahedra,  an edgeedge with one O(2)Li4Fe2 octahedra,  an edgeedge with one O(10)Li5Fe octahedra,  an edgeedge with one O(11)Li5Fe octahedra,  an edgeedge with one O(12)Li5Fe octahedra,  an edgeedge with one O(9)Li5Fe octahedra, edges with two equivalent O(4)Li4Fe2 octahedra, edges with two equivalent O(5)Li5Fe octahedra, and edges with two equivalent O(6)Li5Fe octahedra. The corner-sharing octahedral tilt angles range from 1-5°. In the fifth O site, O(5) is bonded to one Li(1), two equivalent Li(5), two equivalent Li(8), and one Fe(3) atom to form OLi5Fe octahedra that share  a cornercorner with one O(12)Li5Fe octahedra,  a cornercorner with one O(9)Li5Fe octahedra, corners with two equivalent O(10)Li5Fe octahedra, corners with two equivalent O(11)Li5Fe octahedra,  an edgeedge with one O(12)Li5Fe octahedra,  an edgeedge with one O(9)Li5Fe octahedra, edges with two equivalent O(1)Li4Fe2 octahedra, edges with two equivalent O(2)Li4Fe2 octahedra, edges with two equivalent O(6)Li5Fe octahedra, and edges with four equivalent O(4)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the sixth O site, O(6) is bonded to one Li(2), two equivalent Li(5), two equivalent Li(8), and one Fe(1) atom to form OLi5Fe octahedra that share  a cornercorner with one O(10)Li5Fe octahedra,  a cornercorner with one O(11)Li5Fe octahedra, corners with two equivalent O(12)Li5Fe octahedra, corners with two equivalent O(9)Li5Fe octahedra,  an edgeedge with one O(10)Li5Fe octahedra,  an edgeedge with one O(11)Li5Fe octahedra, edges with two equivalent O(1)Li4Fe2 octahedra, edges with two equivalent O(2)Li4Fe2 octahedra, edges with two equivalent O(5)Li5Fe octahedra, and edges with four equivalent O(4)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the seventh O site, O(7) is bonded to one Li(3), two equivalent Li(6), two equivalent Li(7), and one Fe(2) atom to form OLi5Fe octahedra that share  a cornercorner with one O(11)Li5Fe octahedra,  a cornercorner with one O(9)Li5Fe octahedra, corners with two equivalent O(10)Li5Fe octahedra, corners with two equivalent O(12)Li5Fe octahedra,  an edgeedge with one O(11)Li5Fe octahedra,  an edgeedge with one O(9)Li5Fe octahedra, edges with two equivalent O(1)Li4Fe2 octahedra, edges with two equivalent O(2)Li4Fe2 octahedra, edges with two equivalent O(8)Li5Fe octahedra, and edges with four equivalent O(3)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the eighth O site, O(8) is bonded to one Li(4), two equivalent Li(6), two equivalent Li(7), and one Fe(4) atom to form OLi5Fe octahedra that share  a cornercorner with one O(10)Li5Fe octahedra,  a cornercorner with one O(12)Li5Fe octahedra, corners with two equivalent O(11)Li5Fe octahedra, corners with two equivalent O(9)Li5Fe octahedra,  an edgeedge with one O(10)Li5Fe octahedra,  an edgeedge with one O(12)Li5Fe octahedra, edges with two equivalent O(1)Li4Fe2 octahedra, edges with two equivalent O(2)Li4Fe2 octahedra, edges with two equivalent O(7)Li5Fe octahedra, and edges with four equivalent O(3)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the ninth O site, O(9) is bonded to one Li(3), two equivalent Li(5), two equivalent Li(7), and one Fe(3) atom to form OLi5Fe octahedra that share  a cornercorner with one O(5)Li5Fe octahedra,  a cornercorner with one O(7)Li5Fe octahedra, corners with two equivalent O(6)Li5Fe octahedra, corners with two equivalent O(8)Li5Fe octahedra,  an edgeedge with one O(5)Li5Fe octahedra,  an edgeedge with one O(7)Li5Fe octahedra, edges with two equivalent O(3)Li4Fe2 octahedra, edges with two equivalent O(4)Li4Fe2 octahedra, edges with two equivalent O(10)Li5Fe octahedra, and edges with four equivalent O(1)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the tenth O site, O(10) is bonded to one Li(4), two equivalent Li(5), two equivalent Li(7), and one Fe(1) atom to form OLi5Fe octahedra that share  a cornercorner with one O(6)Li5Fe octahedra,  a cornercorner with one O(8)Li5Fe octahedra, corners with two equivalent O(5)Li5Fe octahedra, corners with two equivalent O(7)Li5Fe octahedra,  an edgeedge with one O(6)Li5Fe octahedra,  an edgeedge with one O(8)Li5Fe octahedra, edges with two equivalent O(3)Li4Fe2 octahedra, edges with two equivalent O(4)Li4Fe2 octahedra, edges with two equivalent O(9)Li5Fe octahedra, and edges with four equivalent O(1)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the eleventh O site, O(11) is bonded to one Li(2), two equivalent Li(6), two equivalent Li(8), and one Fe(2) atom to form OLi5Fe octahedra that share  a cornercorner with one O(6)Li5Fe octahedra,  a cornercorner with one O(7)Li5Fe octahedra, corners with two equivalent O(5)Li5Fe octahedra, corners with two equivalent O(8)Li5Fe octahedra,  an edgeedge with one O(6)Li5Fe octahedra,  an edgeedge with one O(7)Li5Fe octahedra, edges with two equivalent O(3)Li4Fe2 octahedra, edges with two equivalent O(4)Li4Fe2 octahedra, edges with two equivalent O(12)Li5Fe octahedra, and edges with four equivalent O(2)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Li(6), two equivalent Li(8), and one Fe(4) atom to form OLi5Fe octahedra that share  a cornercorner with one O(5)Li5Fe octahedra,  a cornercorner with one O(8)Li5Fe octahedra, corners with two equivalent O(6)Li5Fe octahedra, corners with two equivalent O(7)Li5Fe octahedra,  an edgeedge with one O(5)Li5Fe octahedra,  an edgeedge with one O(8)Li5Fe octahedra, edges with two equivalent O(3)Li4Fe2 octahedra, edges with two equivalent O(4)Li4Fe2 octahedra, edges with two equivalent O(11)Li5Fe octahedra, and edges with four equivalent O(2)Li4Fe2 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li3FeO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   2.921
_cell_length_b   5.008
_cell_length_c   5.017
_cell_angle_alpha   71.693
_cell_angle_beta   90.006
_cell_angle_gamma   90.067
_symmetry_Int_Tables_number   1
_cell_volume   69.656
_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
  Fe  Fe0  1  0.507  0.002  0.499  1.0
  Li  Li1  1  0.507  0.500  0.997  1.0
  Li  Li2  1  0.006  0.002  1.000  1.0
  Li  Li3  1  0.006  0.503  0.498  1.0
  O  O4  1  0.007  0.773  0.728  1.0
  O  O5  1  0.007  0.231  0.270  1.0
  O  O6  1  0.507  0.230  0.727  1.0
  O  O7  1  0.506  0.774  0.272  1.0
[/CIF]
.