The structure described by LiFeSiO4 crystallizes in the trigonal P31c space group. Li(1) is bonded to one O(1), one O(2), one O(3), and one O(5) atom to form distorted LiO4 tetrahedra that share  a cornercorner with one Si(1)O4 tetrahedra,  a cornercorner with one Si(3)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Si(2)O4 tetrahedra, and corners with three equivalent Fe(1)O5 trigonal bipyramids. Fe(1) is bonded to one O(1), one O(2), one O(3), one O(4), and one O(6) atom to form distorted FeO5 trigonal bipyramids that share  a cornercorner with one Si(2)O4 tetrahedra, corners with two equivalent Si(1)O4 tetrahedra, corners with two equivalent Si(3)O4 tetrahedra, corners with three equivalent Li(1)O4 tetrahedra, and edges with two equivalent Fe(1)O5 trigonal bipyramids. There are three inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(4) and three equivalent O(2) atoms to form SiO4 tetrahedra that share corners with three equivalent Li(1)O4 tetrahedra and corners with six equivalent Fe(1)O5 trigonal bipyramids. In the second Si site, Si(2) is bonded to one O(5) and three equivalent O(1) atoms to form SiO4 tetrahedra that share corners with six equivalent Li(1)O4 tetrahedra and corners with three equivalent Fe(1)O5 trigonal bipyramids. In the third Si site, Si(3) is bonded to one O(6) and three equivalent O(3) atoms to form SiO4 tetrahedra that share corners with three equivalent Li(1)O4 tetrahedra and corners with six equivalent Fe(1)O5 trigonal bipyramids. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Li(1), one Fe(1), and one Si(2) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Li(1), one Fe(1), and one Si(1) atom. In the third O site, O(3) is bonded in a trigonal planar geometry to one Li(1), one Fe(1), and one Si(3) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to three equivalent Fe(1) and one Si(1) atom. In the fifth O site, O(5) is bonded in a tetrahedral geometry to three equivalent Li(1) and one Si(2) atom. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to three equivalent Fe(1) and one Si(3) atom. is represented by the CIF card [CIF]
data_LiFeSiO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.499
_cell_length_b   7.499
_cell_length_c   9.622
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   468.674
_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
  Li  Li0  1  0.205  0.947  0.252  1.0
  Li  Li1  1  0.053  0.257  0.252  1.0
  Li  Li2  1  0.257  0.053  0.752  1.0
  Li  Li3  1  0.743  0.795  0.252  1.0
  Li  Li4  1  0.795  0.743  0.752  1.0
  Li  Li5  1  0.947  0.205  0.752  1.0
  Fe  Fe6  1  0.059  0.601  0.472  1.0
  Fe  Fe7  1  0.542  0.941  0.472  1.0
  Fe  Fe8  1  0.399  0.458  0.472  1.0
  Fe  Fe9  1  0.458  0.399  0.972  1.0
  Fe  Fe10  1  0.601  0.059  0.972  1.0
  Fe  Fe11  1  0.941  0.542  0.972  1.0
  Si  Si12  1  0.333  0.667  0.169  1.0
  Si  Si13  1  0.000  0.000  0.006  1.0
  Si  Si14  1  0.000  0.000  0.506  1.0
  Si  Si15  1  0.333  0.667  0.777  1.0
  Si  Si16  1  0.667  0.333  0.669  1.0
  Si  Si17  1  0.667  0.333  0.277  1.0
  O  O18  1  0.110  0.872  0.442  1.0
  O  O19  1  0.138  0.689  0.117  1.0
  O  O20  1  0.406  0.901  0.829  1.0
  O  O21  1  0.099  0.505  0.829  1.0
  O  O22  1  0.311  0.449  0.117  1.0
  O  O23  1  0.333  0.667  0.345  1.0
  O  O24  1  0.000  0.000  0.173  1.0
  O  O25  1  0.000  0.000  0.673  1.0
  O  O26  1  0.333  0.667  0.600  1.0
  O  O27  1  0.128  0.238  0.442  1.0
  O  O28  1  0.551  0.862  0.117  1.0
  O  O29  1  0.238  0.128  0.942  1.0
  O  O30  1  0.495  0.594  0.829  1.0
  O  O31  1  0.762  0.890  0.442  1.0
  O  O32  1  0.449  0.311  0.617  1.0
  O  O33  1  0.505  0.099  0.329  1.0
  O  O34  1  0.594  0.495  0.329  1.0
  O  O35  1  0.862  0.551  0.617  1.0
  O  O36  1  0.667  0.333  0.845  1.0
  O  O37  1  0.667  0.333  0.100  1.0
  O  O38  1  0.890  0.762  0.942  1.0
  O  O39  1  0.689  0.138  0.617  1.0
  O  O40  1  0.901  0.406  0.329  1.0
  O  O41  1  0.872  0.110  0.942  1.0
[/CIF]
.
The structure described by LiFeSiO4 crystallizes in the trigonal P31c space group. Li(1) is bonded to one O(1), one O(2), one O(3), and one O(5) atom to form distorted LiO4 tetrahedra that share  a cornercorner with one Si(1)O4 tetrahedra,  a cornercorner with one Si(3)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Si(2)O4 tetrahedra, and corners with three equivalent Fe(1)O5 trigonal bipyramids. Fe(1) is bonded to one O(1), one O(2), one O(3), one O(4), and one O(6) atom to form distorted FeO5 trigonal bipyramids that share  a cornercorner with one Si(2)O4 tetrahedra, corners with two equivalent Si(1)O4 tetrahedra, corners with two equivalent Si(3)O4 tetrahedra, corners with three equivalent Li(1)O4 tetrahedra, and edges with two equivalent Fe(1)O5 trigonal bipyramids. There are three inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(4) and three equivalent O(2) atoms to form SiO4 tetrahedra that share corners with three equivalent Li(1)O4 tetrahedra and corners with six equivalent Fe(1)O5 trigonal bipyramids. In the second Si site, Si(2) is bonded to one O(5) and three equivalent O(1) atoms to form SiO4 tetrahedra that share corners with six equivalent Li(1)O4 tetrahedra and corners with three equivalent Fe(1)O5 trigonal bipyramids. In the third Si site, Si(3) is bonded to one O(6) and three equivalent O(3) atoms to form SiO4 tetrahedra that share corners with three equivalent Li(1)O4 tetrahedra and corners with six equivalent Fe(1)O5 trigonal bipyramids. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Li(1), one Fe(1), and one Si(2) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Li(1), one Fe(1), and one Si(1) atom. In the third O site, O(3) is bonded in a trigonal planar geometry to one Li(1), one Fe(1), and one Si(3) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to three equivalent Fe(1) and one Si(1) atom. In the fifth O site, O(5) is bonded in a tetrahedral geometry to three equivalent Li(1) and one Si(2) atom. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to three equivalent Fe(1) and one Si(3) atom. is represented by the CIF card [CIF]
data_LiFeSiO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.499
_cell_length_b   7.499
_cell_length_c   9.622
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   468.674
_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
  Li  Li0  1  0.205  0.947  0.252  1.0
  Li  Li1  1  0.053  0.257  0.252  1.0
  Li  Li2  1  0.257  0.053  0.752  1.0
  Li  Li3  1  0.743  0.795  0.252  1.0
  Li  Li4  1  0.795  0.743  0.752  1.0
  Li  Li5  1  0.947  0.205  0.752  1.0
  Fe  Fe6  1  0.059  0.601  0.472  1.0
  Fe  Fe7  1  0.542  0.941  0.472  1.0
  Fe  Fe8  1  0.399  0.458  0.472  1.0
  Fe  Fe9  1  0.458  0.399  0.972  1.0
  Fe  Fe10  1  0.601  0.059  0.972  1.0
  Fe  Fe11  1  0.941  0.542  0.972  1.0
  Si  Si12  1  0.333  0.667  0.169  1.0
  Si  Si13  1  0.000  0.000  0.006  1.0
  Si  Si14  1  0.000  0.000  0.506  1.0
  Si  Si15  1  0.333  0.667  0.777  1.0
  Si  Si16  1  0.667  0.333  0.669  1.0
  Si  Si17  1  0.667  0.333  0.277  1.0
  O  O18  1  0.110  0.872  0.442  1.0
  O  O19  1  0.138  0.689  0.117  1.0
  O  O20  1  0.406  0.901  0.829  1.0
  O  O21  1  0.099  0.505  0.829  1.0
  O  O22  1  0.311  0.449  0.117  1.0
  O  O23  1  0.333  0.667  0.345  1.0
  O  O24  1  0.000  0.000  0.173  1.0
  O  O25  1  0.000  0.000  0.673  1.0
  O  O26  1  0.333  0.667  0.600  1.0
  O  O27  1  0.128  0.238  0.442  1.0
  O  O28  1  0.551  0.862  0.117  1.0
  O  O29  1  0.238  0.128  0.942  1.0
  O  O30  1  0.495  0.594  0.829  1.0
  O  O31  1  0.762  0.890  0.442  1.0
  O  O32  1  0.449  0.311  0.617  1.0
  O  O33  1  0.505  0.099  0.329  1.0
  O  O34  1  0.594  0.495  0.329  1.0
  O  O35  1  0.862  0.551  0.617  1.0
  O  O36  1  0.667  0.333  0.845  1.0
  O  O37  1  0.667  0.333  0.100  1.0
  O  O38  1  0.890  0.762  0.942  1.0
  O  O39  1  0.689  0.138  0.617  1.0
  O  O40  1  0.901  0.406  0.329  1.0
  O  O41  1  0.872  0.110  0.942  1.0
[/CIF]
.