The compound described by Li21(FeO4)4 crystallizes in the monoclinic C2 space group. There are twelve inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(3), one O(4), and one O(7) atom to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Fe(1)O4 tetrahedra,  a cornercorner with one Fe(2)O4 tetrahedra, corners with two equivalent Li(12)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, corners with two equivalent Li(6)O4 tetrahedra, corners with two equivalent Li(7)O4 tetrahedra,  an edgeedge with one Li(10)O4 tetrahedra,  an edgeedge with one Li(3)O4 tetrahedra,  an edgeedge with one Li(5)O4 tetrahedra,  an edgeedge with one Fe(3)O4 tetrahedra, and  an edgeedge with one Li(8)O4 trigonal pyramid. In the second Li site, Li(2) is bonded to one O(2), one O(5), one O(6), and one O(8) atom to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Fe(1)O4 tetrahedra,  a cornercorner with one Fe(2)O4 tetrahedra, corners with two equivalent Li(11)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, corners with two equivalent Li(6)O4 tetrahedra, corners with two equivalent Li(7)O4 tetrahedra, corners with two equivalent Li(9)O4 tetrahedra,  an edgeedge with one Li(10)O4 tetrahedra,  an edgeedge with one Li(3)O4 tetrahedra,  an edgeedge with one Li(5)O4 tetrahedra,  an edgeedge with one Fe(3)O4 tetrahedra, and  an edgeedge with one Li(8)O4 trigonal pyramid. In the third Li site, Li(3) is bonded to one O(1), one O(4), one O(6), and one O(8) atom to form distorted LiO4 tetrahedra that share  a cornercorner with one Li(11)O4 tetrahedra,  a cornercorner with one Li(12)O4 tetrahedra,  a cornercorner with one Li(9)O4 tetrahedra, corners with two equivalent Li(10)O4 tetrahedra, corners with two equivalent Fe(1)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, corners with two equivalent Li(8)O4 trigonal pyramids,  an edgeedge with one Li(4)O4 tetrahedra,  an edgeedge with one Li(6)O4 tetrahedra,  an edgeedge with one Li(7)O4 tetrahedra,  an edgeedge with one Li(1)O4 trigonal pyramid, and  an edgeedge with one Li(2)O4 trigonal pyramid. In the fourth Li site, Li(4) is bonded to one O(2), one O(4), one O(6), and one O(7) atom to form LiO4 tetrahedra that share corners with two equivalent Li(7)O4 tetrahedra, corners with two equivalent Fe(1)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, corners with two equivalent Li(1)O4 trigonal pyramids, corners with two equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Li(11)O4 tetrahedra,  an edgeedge with one Li(3)O4 tetrahedra,  an edgeedge with one Li(5)O4 tetrahedra, and edges with two equivalent Li(8)O4 trigonal pyramids. In the fifth Li site, Li(5) is bonded to one O(2), one O(3), one O(5), and one O(7) atom to form distorted LiO4 tetrahedra that share  a cornercorner with one Li(11)O4 tetrahedra,  a cornercorner with one Li(12)O4 tetrahedra,  a cornercorner with one Li(9)O4 tetrahedra, corners with two equivalent Li(10)O4 tetrahedra, corners with two equivalent Fe(2)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, corners with two equivalent Li(8)O4 trigonal pyramids,  an edgeedge with one Li(4)O4 tetrahedra,  an edgeedge with one Li(6)O4 tetrahedra,  an edgeedge with one Li(7)O4 tetrahedra,  an edgeedge with one Li(1)O4 trigonal pyramid, and  an edgeedge with one Li(2)O4 trigonal pyramid. In the sixth Li site, Li(6) is bonded to one O(1), one O(3), one O(5), and one O(8) atom to form LiO4 tetrahedra that share corners with two equivalent Li(7)O4 tetrahedra, corners with two equivalent Fe(2)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, corners with two equivalent Li(1)O4 trigonal pyramids, corners with two equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Li(12)O4 tetrahedra,  an edgeedge with one Li(3)O4 tetrahedra,  an edgeedge with one Li(5)O4 tetrahedra,  an edgeedge with one Li(9)O4 tetrahedra, and edges with two equivalent Li(10)O4 tetrahedra. In the seventh Li site, Li(7) is bonded to one O(4), one O(5), one O(7), and one O(8) atom to form distorted LiO4 tetrahedra that share  a cornercorner with one Fe(1)O4 tetrahedra,  a cornercorner with one Fe(2)O4 tetrahedra, corners with two equivalent Li(10)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, corners with two equivalent Li(6)O4 tetrahedra, corners with two equivalent Li(1)O4 trigonal pyramids, corners with two equivalent Li(2)O4 trigonal pyramids, corners with two equivalent Li(8)O4 trigonal pyramids,  an edgeedge with one Li(3)O4 tetrahedra,  an edgeedge with one Li(5)O4 tetrahedra,  an edgeedge with one Li(9)O4 tetrahedra, and  an edgeedge with one Fe(3)O4 tetrahedra. In the eighth Li site, Li(8) is bonded to one O(2), one O(4), one O(6), and one O(7) atom to form distorted LiO4 trigonal pyramids that share corners with two equivalent Li(11)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Li(7)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra,  an edgeedge with one Fe(1)O4 tetrahedra, edges with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Li(1)O4 trigonal pyramid, and  an edgeedge with one Li(2)O4 trigonal pyramid. In the ninth Li site, Li(9) is bonded to two equivalent O(5) and two equivalent O(8) atoms to form distorted LiO4 tetrahedra that share corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, corners with four equivalent Li(10)O4 tetrahedra, corners with four equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Fe(2)O4 tetrahedra, edges with two equivalent Li(6)O4 tetrahedra, and edges with two equivalent Li(7)O4 tetrahedra. In the tenth Li site, Li(10) is bonded to one O(1), one O(3), one O(5), and one O(8) atom to form distorted LiO4 tetrahedra that share corners with two equivalent Li(12)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Li(7)O4 tetrahedra, corners with two equivalent Li(9)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra,  an edgeedge with one Fe(2)O4 tetrahedra, edges with two equivalent Li(6)O4 tetrahedra,  an edgeedge with one Li(1)O4 trigonal pyramid, and  an edgeedge with one Li(2)O4 trigonal pyramid. In the eleventh Li site, Li(11) is bonded to two equivalent O(2) and two equivalent O(6) atoms to form distorted LiO4 tetrahedra that share corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, corners with four equivalent Li(2)O4 trigonal pyramids, corners with four equivalent Li(8)O4 trigonal pyramids,  an edgeedge with one Fe(1)O4 tetrahedra, and edges with two equivalent Li(4)O4 tetrahedra. In the twelfth Li site, Li(12) is bonded to two equivalent O(1) and two equivalent O(3) atoms to form LiO4 tetrahedra that share corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, corners with four equivalent Li(10)O4 tetrahedra, corners with four equivalent Li(1)O4 trigonal pyramids,  an edgeedge with one Fe(2)O4 tetrahedra, and edges with two equivalent Li(6)O4 tetrahedra. There are three inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to two equivalent O(4) and two equivalent O(6) atoms to form FeO4 tetrahedra that share corners with two equivalent Li(7)O4 tetrahedra, corners with four equivalent Li(3)O4 tetrahedra, corners with four equivalent Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 trigonal pyramids, corners with two equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Li(11)O4 tetrahedra, and edges with two equivalent Li(8)O4 trigonal pyramids. In the second Fe site, Fe(2) is bonded to two equivalent O(3) and two equivalent O(5) atoms to form distorted FeO4 tetrahedra that share corners with two equivalent Li(7)O4 tetrahedra, corners with four equivalent Li(5)O4 tetrahedra, corners with four equivalent Li(6)O4 tetrahedra, corners with two equivalent Li(1)O4 trigonal pyramids, corners with two equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Li(12)O4 tetrahedra,  an edgeedge with one Li(9)O4 tetrahedra, and edges with two equivalent Li(10)O4 tetrahedra. In the third Fe site, Fe(3) is bonded to one O(1), one O(2), one O(7), and one O(8) atom to form FeO4 tetrahedra that share  a cornercorner with one Li(11)O4 tetrahedra,  a cornercorner with one Li(12)O4 tetrahedra,  a cornercorner with one Li(9)O4 tetrahedra, corners with two equivalent Li(10)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Li(6)O4 tetrahedra, corners with two equivalent Li(8)O4 trigonal pyramids,  an edgeedge with one Li(7)O4 tetrahedra,  an edgeedge with one Li(1)O4 trigonal pyramid, and  an edgeedge with one Li(2)O4 trigonal pyramid. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Li(10), one Li(12), one Li(3), one Li(6), and one Fe(3) atom to form distorted OLi5Fe octahedra that share  a cornercorner with one O(1)Li5Fe octahedra,  a cornercorner with one O(2)Li5Fe octahedra, corners with two equivalent O(8)Li6Fe pentagonal bipyramids,  a cornercorner with one O(3)Li5Fe pentagonal pyramid,  a cornercorner with one O(6)Li5Fe pentagonal pyramid,  an edgeedge with one O(4)Li5Fe octahedra,  an edgeedge with one O(5)Li6Fe pentagonal bipyramid,  an edgeedge with one O(8)Li6Fe pentagonal bipyramid,  an edgeedge with one O(7)Li5Fe pentagonal pyramid, and edges with two equivalent O(3)Li5Fe pentagonal pyramids. The corner-sharing octahedral tilt angles range from 64-67°. In the second O site, O(2) is bonded to one Li(11), one Li(2), one Li(4), one Li(5), one Li(8), and one Fe(3) atom to form distorted OLi5Fe octahedra that share  a cornercorner with one O(1)Li5Fe octahedra,  a cornercorner with one O(2)Li5Fe octahedra,  a cornercorner with one O(3)Li5Fe pentagonal pyramid,  a cornercorner with one O(6)Li5Fe pentagonal pyramid, corners with two equivalent O(7)Li5Fe pentagonal pyramids,  an edgeedge with one O(4)Li5Fe octahedra,  an edgeedge with one O(5)Li6Fe pentagonal bipyramid,  an edgeedge with one O(8)Li6Fe pentagonal bipyramid,  an edgeedge with one O(7)Li5Fe pentagonal pyramid, and edges with two equivalent O(6)Li5Fe pentagonal pyramids. The corner-sharing octahedral tilt angles range from 61-67°. In the third O site, O(3) is bonded to one Li(1), one Li(10), one Li(12), one Li(5), one Li(6), and one Fe(2) atom to form distorted OLi5Fe pentagonal pyramids that share  a cornercorner with one O(1)Li5Fe octahedra,  a cornercorner with one O(2)Li5Fe octahedra,  a cornercorner with one O(4)Li5Fe octahedra,  a cornercorner with one O(5)Li6Fe pentagonal bipyramid, edges with two equivalent O(1)Li5Fe octahedra,  an edgeedge with one O(8)Li6Fe pentagonal bipyramid, edges with two equivalent O(5)Li6Fe pentagonal bipyramids,  an edgeedge with one O(3)Li5Fe pentagonal pyramid, and  an edgeedge with one O(7)Li5Fe pentagonal pyramid. The corner-sharing octahedral tilt angles range from 39-64°. In the fourth O site, O(4) is bonded to one Li(1), one Li(3), one Li(4), one Li(7), one Li(8), and one Fe(1) atom to form distorted OLi5Fe octahedra that share  a cornercorner with one O(4)Li5Fe octahedra,  a cornercorner with one O(5)Li6Fe pentagonal bipyramid,  a cornercorner with one O(3)Li5Fe pentagonal pyramid,  a cornercorner with one O(6)Li5Fe pentagonal pyramid, corners with two equivalent O(7)Li5Fe pentagonal pyramids,  an edgeedge with one O(1)Li5Fe octahedra,  an edgeedge with one O(2)Li5Fe octahedra,  an edgeedge with one O(8)Li6Fe pentagonal bipyramid,  an edgeedge with one O(7)Li5Fe pentagonal pyramid, and edges with two equivalent O(6)Li5Fe pentagonal pyramids. The corner-sharing octahedral tilt angles are 68°. In the fifth O site, O(5) is bonded to one Li(10), one Li(2), one Li(5), one Li(6), one Li(7), one Li(9), and one Fe(2) atom to form distorted OLi6Fe pentagonal bipyramids that share  a cornercorner with one O(4)Li5Fe octahedra,  a cornercorner with one O(3)Li5Fe pentagonal pyramid,  a cornercorner with one O(6)Li5Fe pentagonal pyramid,  an edgeedge with one O(1)Li5Fe octahedra,  an edgeedge with one O(2)Li5Fe octahedra,  an edgeedge with one O(5)Li6Fe pentagonal bipyramid, edges with three equivalent O(8)Li6Fe pentagonal bipyramids,  an edgeedge with one O(7)Li5Fe pentagonal pyramid, and edges with two equivalent O(3)Li5Fe pentagonal pyramids. The corner-sharing octahedral tilt angles are 57°. In the sixth O site, O(6) is bonded to one Li(11), one Li(2), one Li(3), one Li(4), one Li(8), and one Fe(1) atom to form distorted OLi5Fe pentagonal pyramids that share  a cornercorner with one O(1)Li5Fe octahedra,  a cornercorner with one O(2)Li5Fe octahedra,  a cornercorner with one O(4)Li5Fe octahedra,  a cornercorner with one O(5)Li6Fe pentagonal bipyramid, edges with two equivalent O(2)Li5Fe octahedra, edges with two equivalent O(4)Li5Fe octahedra,  an edgeedge with one O(8)Li6Fe pentagonal bipyramid,  an edgeedge with one O(6)Li5Fe pentagonal pyramid, and  an edgeedge with one O(7)Li5Fe pentagonal pyramid. The corner-sharing octahedral tilt angles range from 49-63°. In the seventh O site, O(7) is bonded to one Li(1), one Li(4), one Li(5), one Li(7), one Li(8), and one Fe(3) atom to form distorted OLi5Fe pentagonal pyramids that share corners with two equivalent O(2)Li5Fe octahedra, corners with two equivalent O(4)Li5Fe octahedra,  an edgeedge with one O(1)Li5Fe octahedra,  an edgeedge with one O(2)Li5Fe octahedra,  an edgeedge with one O(4)Li5Fe octahedra,  an edgeedge with one O(5)Li6Fe pentagonal bipyramid,  an edgeedge with one O(8)Li6Fe pentagonal bipyramid,  an edgeedge with one O(3)Li5Fe pentagonal pyramid, and  an edgeedge with one O(6)Li5Fe pentagonal pyramid. The corner-sharing octahedral tilt angles range from 42-60°. In the eighth O site, O(8) is bonded to one Li(10), one Li(2), one Li(3), one Li(6), one Li(7), one Li(9), and one Fe(3) atom to form distorted OLi6Fe pentagonal bipyramids that share corners with two equivalent O(1)Li5Fe octahedra,  a cornercorner with one O(8)Li6Fe pentagonal bipyramid,  an edgeedge with one O(1)Li5Fe octahedra,  an edgeedge with one O(2)Li5Fe octahedra,  an edgeedge with one O(4)Li5Fe octahedra, edges with three equivalent O(5)Li6Fe pentagonal bipyramids,  an edgeedge with one O(3)Li5Fe pentagonal pyramid,  an edgeedge with one O(6)Li5Fe pentagonal pyramid, and  an edgeedge with one O(7)Li5Fe pentagonal pyramid. The corner-sharing octahedral tilt angles range from 48-63°. is represented by the CIF card [CIF]
data_Li21(FeO4)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.547
_cell_length_b   6.547
_cell_length_c   9.496
_cell_angle_alpha   89.905
_cell_angle_beta   89.905
_cell_angle_gamma   92.414
_symmetry_Int_Tables_number   1
_cell_volume   406.604
_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  0.464  0.950  0.763  1.0
  Li  Li1  1  0.456  0.956  0.255  1.0
  Li  Li2  1  0.281  0.273  0.722  1.0
  Li  Li3  1  0.224  0.220  0.473  1.0
  Li  Li4  1  0.278  0.276  0.221  1.0
  Li  Li5  1  0.250  0.244  0.971  1.0
  Li  Li6  1  0.044  0.544  0.745  1.0
  Li  Li7  1  0.050  0.536  0.237  1.0
  Li  Li8  1  0.019  0.974  0.739  1.0
  Li  Li9  1  0.026  0.981  0.261  1.0
  Li  Li10  1  0.965  0.456  0.490  1.0
  Li  Li11  1  0.971  0.029  0.000  1.0
  Li  Li12  1  0.969  0.465  0.992  1.0
  Li  Li13  1  0.780  0.776  0.527  1.0
  Li  Li14  1  0.724  0.722  0.779  1.0
  Li  Li15  1  0.756  0.750  0.029  1.0
  Li  Li16  1  0.727  0.719  0.278  1.0
  Li  Li17  1  0.544  0.035  0.510  1.0
  Li  Li18  1  0.535  0.031  0.008  1.0
  Li  Li19  1  0.523  0.477  0.500  1.0
  Li  Li20  1  0.516  0.484  0.000  1.0
  Fe  Fe21  1  0.246  0.754  0.500  1.0
  Fe  Fe22  1  0.247  0.753  0.000  1.0
  Fe  Fe23  1  0.744  0.255  0.748  1.0
  Fe  Fe24  1  0.745  0.256  0.252  1.0
  O  O25  1  0.502  0.239  0.862  1.0
  O  O26  1  0.500  0.234  0.364  1.0
  O  O27  1  0.235  0.479  0.089  1.0
  O  O28  1  0.263  0.997  0.614  1.0
  O  O29  1  0.245  0.020  0.115  1.0
  O  O30  1  0.235  0.488  0.588  1.0
  O  O31  1  0.007  0.265  0.340  1.0
  O  O32  1  0.006  0.251  0.847  1.0
  O  O33  1  0.003  0.737  0.386  1.0
  O  O34  1  0.980  0.755  0.885  1.0
  O  O35  1  0.749  0.994  0.153  1.0
  O  O36  1  0.735  0.993  0.660  1.0
  O  O37  1  0.766  0.500  0.636  1.0
  O  O38  1  0.761  0.498  0.138  1.0
  O  O39  1  0.512  0.765  0.412  1.0
  O  O40  1  0.521  0.765  0.911  1.0
[/CIF]
.
The compound described by Li21(FeO4)4 crystallizes in the monoclinic C2 space group. There are twelve inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(3), one O(4), and one O(7) atom to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Fe(1)O4 tetrahedra,  a cornercorner with one Fe(2)O4 tetrahedra, corners with two equivalent Li(12)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, corners with two equivalent Li(6)O4 tetrahedra, corners with two equivalent Li(7)O4 tetrahedra,  an edgeedge with one Li(10)O4 tetrahedra,  an edgeedge with one Li(3)O4 tetrahedra,  an edgeedge with one Li(5)O4 tetrahedra,  an edgeedge with one Fe(3)O4 tetrahedra, and  an edgeedge with one Li(8)O4 trigonal pyramid. In the second Li site, Li(2) is bonded to one O(2), one O(5), one O(6), and one O(8) atom to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Fe(1)O4 tetrahedra,  a cornercorner with one Fe(2)O4 tetrahedra, corners with two equivalent Li(11)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, corners with two equivalent Li(6)O4 tetrahedra, corners with two equivalent Li(7)O4 tetrahedra, corners with two equivalent Li(9)O4 tetrahedra,  an edgeedge with one Li(10)O4 tetrahedra,  an edgeedge with one Li(3)O4 tetrahedra,  an edgeedge with one Li(5)O4 tetrahedra,  an edgeedge with one Fe(3)O4 tetrahedra, and  an edgeedge with one Li(8)O4 trigonal pyramid. In the third Li site, Li(3) is bonded to one O(1), one O(4), one O(6), and one O(8) atom to form distorted LiO4 tetrahedra that share  a cornercorner with one Li(11)O4 tetrahedra,  a cornercorner with one Li(12)O4 tetrahedra,  a cornercorner with one Li(9)O4 tetrahedra, corners with two equivalent Li(10)O4 tetrahedra, corners with two equivalent Fe(1)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, corners with two equivalent Li(8)O4 trigonal pyramids,  an edgeedge with one Li(4)O4 tetrahedra,  an edgeedge with one Li(6)O4 tetrahedra,  an edgeedge with one Li(7)O4 tetrahedra,  an edgeedge with one Li(1)O4 trigonal pyramid, and  an edgeedge with one Li(2)O4 trigonal pyramid. In the fourth Li site, Li(4) is bonded to one O(2), one O(4), one O(6), and one O(7) atom to form LiO4 tetrahedra that share corners with two equivalent Li(7)O4 tetrahedra, corners with two equivalent Fe(1)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, corners with two equivalent Li(1)O4 trigonal pyramids, corners with two equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Li(11)O4 tetrahedra,  an edgeedge with one Li(3)O4 tetrahedra,  an edgeedge with one Li(5)O4 tetrahedra, and edges with two equivalent Li(8)O4 trigonal pyramids. In the fifth Li site, Li(5) is bonded to one O(2), one O(3), one O(5), and one O(7) atom to form distorted LiO4 tetrahedra that share  a cornercorner with one Li(11)O4 tetrahedra,  a cornercorner with one Li(12)O4 tetrahedra,  a cornercorner with one Li(9)O4 tetrahedra, corners with two equivalent Li(10)O4 tetrahedra, corners with two equivalent Fe(2)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, corners with two equivalent Li(8)O4 trigonal pyramids,  an edgeedge with one Li(4)O4 tetrahedra,  an edgeedge with one Li(6)O4 tetrahedra,  an edgeedge with one Li(7)O4 tetrahedra,  an edgeedge with one Li(1)O4 trigonal pyramid, and  an edgeedge with one Li(2)O4 trigonal pyramid. In the sixth Li site, Li(6) is bonded to one O(1), one O(3), one O(5), and one O(8) atom to form LiO4 tetrahedra that share corners with two equivalent Li(7)O4 tetrahedra, corners with two equivalent Fe(2)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, corners with two equivalent Li(1)O4 trigonal pyramids, corners with two equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Li(12)O4 tetrahedra,  an edgeedge with one Li(3)O4 tetrahedra,  an edgeedge with one Li(5)O4 tetrahedra,  an edgeedge with one Li(9)O4 tetrahedra, and edges with two equivalent Li(10)O4 tetrahedra. In the seventh Li site, Li(7) is bonded to one O(4), one O(5), one O(7), and one O(8) atom to form distorted LiO4 tetrahedra that share  a cornercorner with one Fe(1)O4 tetrahedra,  a cornercorner with one Fe(2)O4 tetrahedra, corners with two equivalent Li(10)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, corners with two equivalent Li(6)O4 tetrahedra, corners with two equivalent Li(1)O4 trigonal pyramids, corners with two equivalent Li(2)O4 trigonal pyramids, corners with two equivalent Li(8)O4 trigonal pyramids,  an edgeedge with one Li(3)O4 tetrahedra,  an edgeedge with one Li(5)O4 tetrahedra,  an edgeedge with one Li(9)O4 tetrahedra, and  an edgeedge with one Fe(3)O4 tetrahedra. In the eighth Li site, Li(8) is bonded to one O(2), one O(4), one O(6), and one O(7) atom to form distorted LiO4 trigonal pyramids that share corners with two equivalent Li(11)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Li(7)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra,  an edgeedge with one Fe(1)O4 tetrahedra, edges with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Li(1)O4 trigonal pyramid, and  an edgeedge with one Li(2)O4 trigonal pyramid. In the ninth Li site, Li(9) is bonded to two equivalent O(5) and two equivalent O(8) atoms to form distorted LiO4 tetrahedra that share corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, corners with four equivalent Li(10)O4 tetrahedra, corners with four equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Fe(2)O4 tetrahedra, edges with two equivalent Li(6)O4 tetrahedra, and edges with two equivalent Li(7)O4 tetrahedra. In the tenth Li site, Li(10) is bonded to one O(1), one O(3), one O(5), and one O(8) atom to form distorted LiO4 tetrahedra that share corners with two equivalent Li(12)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Li(7)O4 tetrahedra, corners with two equivalent Li(9)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra,  an edgeedge with one Fe(2)O4 tetrahedra, edges with two equivalent Li(6)O4 tetrahedra,  an edgeedge with one Li(1)O4 trigonal pyramid, and  an edgeedge with one Li(2)O4 trigonal pyramid. In the eleventh Li site, Li(11) is bonded to two equivalent O(2) and two equivalent O(6) atoms to form distorted LiO4 tetrahedra that share corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, corners with four equivalent Li(2)O4 trigonal pyramids, corners with four equivalent Li(8)O4 trigonal pyramids,  an edgeedge with one Fe(1)O4 tetrahedra, and edges with two equivalent Li(4)O4 tetrahedra. In the twelfth Li site, Li(12) is bonded to two equivalent O(1) and two equivalent O(3) atoms to form LiO4 tetrahedra that share corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, corners with four equivalent Li(10)O4 tetrahedra, corners with four equivalent Li(1)O4 trigonal pyramids,  an edgeedge with one Fe(2)O4 tetrahedra, and edges with two equivalent Li(6)O4 tetrahedra. There are three inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to two equivalent O(4) and two equivalent O(6) atoms to form FeO4 tetrahedra that share corners with two equivalent Li(7)O4 tetrahedra, corners with four equivalent Li(3)O4 tetrahedra, corners with four equivalent Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 trigonal pyramids, corners with two equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Li(11)O4 tetrahedra, and edges with two equivalent Li(8)O4 trigonal pyramids. In the second Fe site, Fe(2) is bonded to two equivalent O(3) and two equivalent O(5) atoms to form distorted FeO4 tetrahedra that share corners with two equivalent Li(7)O4 tetrahedra, corners with four equivalent Li(5)O4 tetrahedra, corners with four equivalent Li(6)O4 tetrahedra, corners with two equivalent Li(1)O4 trigonal pyramids, corners with two equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Li(12)O4 tetrahedra,  an edgeedge with one Li(9)O4 tetrahedra, and edges with two equivalent Li(10)O4 tetrahedra. In the third Fe site, Fe(3) is bonded to one O(1), one O(2), one O(7), and one O(8) atom to form FeO4 tetrahedra that share  a cornercorner with one Li(11)O4 tetrahedra,  a cornercorner with one Li(12)O4 tetrahedra,  a cornercorner with one Li(9)O4 tetrahedra, corners with two equivalent Li(10)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Li(6)O4 tetrahedra, corners with two equivalent Li(8)O4 trigonal pyramids,  an edgeedge with one Li(7)O4 tetrahedra,  an edgeedge with one Li(1)O4 trigonal pyramid, and  an edgeedge with one Li(2)O4 trigonal pyramid. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Li(10), one Li(12), one Li(3), one Li(6), and one Fe(3) atom to form distorted OLi5Fe octahedra that share  a cornercorner with one O(1)Li5Fe octahedra,  a cornercorner with one O(2)Li5Fe octahedra, corners with two equivalent O(8)Li6Fe pentagonal bipyramids,  a cornercorner with one O(3)Li5Fe pentagonal pyramid,  a cornercorner with one O(6)Li5Fe pentagonal pyramid,  an edgeedge with one O(4)Li5Fe octahedra,  an edgeedge with one O(5)Li6Fe pentagonal bipyramid,  an edgeedge with one O(8)Li6Fe pentagonal bipyramid,  an edgeedge with one O(7)Li5Fe pentagonal pyramid, and edges with two equivalent O(3)Li5Fe pentagonal pyramids. The corner-sharing octahedral tilt angles range from 64-67°. In the second O site, O(2) is bonded to one Li(11), one Li(2), one Li(4), one Li(5), one Li(8), and one Fe(3) atom to form distorted OLi5Fe octahedra that share  a cornercorner with one O(1)Li5Fe octahedra,  a cornercorner with one O(2)Li5Fe octahedra,  a cornercorner with one O(3)Li5Fe pentagonal pyramid,  a cornercorner with one O(6)Li5Fe pentagonal pyramid, corners with two equivalent O(7)Li5Fe pentagonal pyramids,  an edgeedge with one O(4)Li5Fe octahedra,  an edgeedge with one O(5)Li6Fe pentagonal bipyramid,  an edgeedge with one O(8)Li6Fe pentagonal bipyramid,  an edgeedge with one O(7)Li5Fe pentagonal pyramid, and edges with two equivalent O(6)Li5Fe pentagonal pyramids. The corner-sharing octahedral tilt angles range from 61-67°. In the third O site, O(3) is bonded to one Li(1), one Li(10), one Li(12), one Li(5), one Li(6), and one Fe(2) atom to form distorted OLi5Fe pentagonal pyramids that share  a cornercorner with one O(1)Li5Fe octahedra,  a cornercorner with one O(2)Li5Fe octahedra,  a cornercorner with one O(4)Li5Fe octahedra,  a cornercorner with one O(5)Li6Fe pentagonal bipyramid, edges with two equivalent O(1)Li5Fe octahedra,  an edgeedge with one O(8)Li6Fe pentagonal bipyramid, edges with two equivalent O(5)Li6Fe pentagonal bipyramids,  an edgeedge with one O(3)Li5Fe pentagonal pyramid, and  an edgeedge with one O(7)Li5Fe pentagonal pyramid. The corner-sharing octahedral tilt angles range from 39-64°. In the fourth O site, O(4) is bonded to one Li(1), one Li(3), one Li(4), one Li(7), one Li(8), and one Fe(1) atom to form distorted OLi5Fe octahedra that share  a cornercorner with one O(4)Li5Fe octahedra,  a cornercorner with one O(5)Li6Fe pentagonal bipyramid,  a cornercorner with one O(3)Li5Fe pentagonal pyramid,  a cornercorner with one O(6)Li5Fe pentagonal pyramid, corners with two equivalent O(7)Li5Fe pentagonal pyramids,  an edgeedge with one O(1)Li5Fe octahedra,  an edgeedge with one O(2)Li5Fe octahedra,  an edgeedge with one O(8)Li6Fe pentagonal bipyramid,  an edgeedge with one O(7)Li5Fe pentagonal pyramid, and edges with two equivalent O(6)Li5Fe pentagonal pyramids. The corner-sharing octahedral tilt angles are 68°. In the fifth O site, O(5) is bonded to one Li(10), one Li(2), one Li(5), one Li(6), one Li(7), one Li(9), and one Fe(2) atom to form distorted OLi6Fe pentagonal bipyramids that share  a cornercorner with one O(4)Li5Fe octahedra,  a cornercorner with one O(3)Li5Fe pentagonal pyramid,  a cornercorner with one O(6)Li5Fe pentagonal pyramid,  an edgeedge with one O(1)Li5Fe octahedra,  an edgeedge with one O(2)Li5Fe octahedra,  an edgeedge with one O(5)Li6Fe pentagonal bipyramid, edges with three equivalent O(8)Li6Fe pentagonal bipyramids,  an edgeedge with one O(7)Li5Fe pentagonal pyramid, and edges with two equivalent O(3)Li5Fe pentagonal pyramids. The corner-sharing octahedral tilt angles are 57°. In the sixth O site, O(6) is bonded to one Li(11), one Li(2), one Li(3), one Li(4), one Li(8), and one Fe(1) atom to form distorted OLi5Fe pentagonal pyramids that share  a cornercorner with one O(1)Li5Fe octahedra,  a cornercorner with one O(2)Li5Fe octahedra,  a cornercorner with one O(4)Li5Fe octahedra,  a cornercorner with one O(5)Li6Fe pentagonal bipyramid, edges with two equivalent O(2)Li5Fe octahedra, edges with two equivalent O(4)Li5Fe octahedra,  an edgeedge with one O(8)Li6Fe pentagonal bipyramid,  an edgeedge with one O(6)Li5Fe pentagonal pyramid, and  an edgeedge with one O(7)Li5Fe pentagonal pyramid. The corner-sharing octahedral tilt angles range from 49-63°. In the seventh O site, O(7) is bonded to one Li(1), one Li(4), one Li(5), one Li(7), one Li(8), and one Fe(3) atom to form distorted OLi5Fe pentagonal pyramids that share corners with two equivalent O(2)Li5Fe octahedra, corners with two equivalent O(4)Li5Fe octahedra,  an edgeedge with one O(1)Li5Fe octahedra,  an edgeedge with one O(2)Li5Fe octahedra,  an edgeedge with one O(4)Li5Fe octahedra,  an edgeedge with one O(5)Li6Fe pentagonal bipyramid,  an edgeedge with one O(8)Li6Fe pentagonal bipyramid,  an edgeedge with one O(3)Li5Fe pentagonal pyramid, and  an edgeedge with one O(6)Li5Fe pentagonal pyramid. The corner-sharing octahedral tilt angles range from 42-60°. In the eighth O site, O(8) is bonded to one Li(10), one Li(2), one Li(3), one Li(6), one Li(7), one Li(9), and one Fe(3) atom to form distorted OLi6Fe pentagonal bipyramids that share corners with two equivalent O(1)Li5Fe octahedra,  a cornercorner with one O(8)Li6Fe pentagonal bipyramid,  an edgeedge with one O(1)Li5Fe octahedra,  an edgeedge with one O(2)Li5Fe octahedra,  an edgeedge with one O(4)Li5Fe octahedra, edges with three equivalent O(5)Li6Fe pentagonal bipyramids,  an edgeedge with one O(3)Li5Fe pentagonal pyramid,  an edgeedge with one O(6)Li5Fe pentagonal pyramid, and  an edgeedge with one O(7)Li5Fe pentagonal pyramid. The corner-sharing octahedral tilt angles range from 48-63°. is represented by the CIF card [CIF]
data_Li21(FeO4)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.547
_cell_length_b   6.547
_cell_length_c   9.496
_cell_angle_alpha   89.905
_cell_angle_beta   89.905
_cell_angle_gamma   92.414
_symmetry_Int_Tables_number   1
_cell_volume   406.604
_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  0.464  0.950  0.763  1.0
  Li  Li1  1  0.456  0.956  0.255  1.0
  Li  Li2  1  0.281  0.273  0.722  1.0
  Li  Li3  1  0.224  0.220  0.473  1.0
  Li  Li4  1  0.278  0.276  0.221  1.0
  Li  Li5  1  0.250  0.244  0.971  1.0
  Li  Li6  1  0.044  0.544  0.745  1.0
  Li  Li7  1  0.050  0.536  0.237  1.0
  Li  Li8  1  0.019  0.974  0.739  1.0
  Li  Li9  1  0.026  0.981  0.261  1.0
  Li  Li10  1  0.965  0.456  0.490  1.0
  Li  Li11  1  0.971  0.029  0.000  1.0
  Li  Li12  1  0.969  0.465  0.992  1.0
  Li  Li13  1  0.780  0.776  0.527  1.0
  Li  Li14  1  0.724  0.722  0.779  1.0
  Li  Li15  1  0.756  0.750  0.029  1.0
  Li  Li16  1  0.727  0.719  0.278  1.0
  Li  Li17  1  0.544  0.035  0.510  1.0
  Li  Li18  1  0.535  0.031  0.008  1.0
  Li  Li19  1  0.523  0.477  0.500  1.0
  Li  Li20  1  0.516  0.484  0.000  1.0
  Fe  Fe21  1  0.246  0.754  0.500  1.0
  Fe  Fe22  1  0.247  0.753  0.000  1.0
  Fe  Fe23  1  0.744  0.255  0.748  1.0
  Fe  Fe24  1  0.745  0.256  0.252  1.0
  O  O25  1  0.502  0.239  0.862  1.0
  O  O26  1  0.500  0.234  0.364  1.0
  O  O27  1  0.235  0.479  0.089  1.0
  O  O28  1  0.263  0.997  0.614  1.0
  O  O29  1  0.245  0.020  0.115  1.0
  O  O30  1  0.235  0.488  0.588  1.0
  O  O31  1  0.007  0.265  0.340  1.0
  O  O32  1  0.006  0.251  0.847  1.0
  O  O33  1  0.003  0.737  0.386  1.0
  O  O34  1  0.980  0.755  0.885  1.0
  O  O35  1  0.749  0.994  0.153  1.0
  O  O36  1  0.735  0.993  0.660  1.0
  O  O37  1  0.766  0.500  0.636  1.0
  O  O38  1  0.761  0.498  0.138  1.0
  O  O39  1  0.512  0.765  0.412  1.0
  O  O40  1  0.521  0.765  0.911  1.0
[/CIF]
.