The crystal structure described by NaV5O8 crystallizes in the monoclinic C2 space group. Na(1) is bonded to two equivalent O(2) and four equivalent O(1) atoms to form NaO6 octahedra that share corners with two equivalent V(2)O6 octahedra, corners with four equivalent V(1)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, and edges with six equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-24°. There are three inequivalent V sites. In the first V site, V(1) is bonded to one O(4), two equivalent O(2), and three equivalent O(1) atoms to form VO6 octahedra that share  a cornercorner with one V(3)O6 octahedra, corners with two equivalent Na(1)O6 octahedra, edges with two equivalent V(2)O6 octahedra, edges with three equivalent Na(1)O6 octahedra, and edges with four equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-23°. In the second V site, V(2) is bonded to one O(2), two equivalent O(4), and three equivalent O(3) atoms to form VO6 octahedra that share  a cornercorner with one Na(1)O6 octahedra, corners with two equivalent V(3)O6 octahedra, edges with two equivalent V(1)O6 octahedra, edges with three equivalent V(3)O6 octahedra, and edges with four equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-24°. In the third V site, V(3) is bonded to two equivalent O(4) and four equivalent O(3) atoms to form a mixture of edge and corner-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 9-23°. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Na(1) and three equivalent V(1) atoms to form a mixture of edge and corner-sharing ONa2V3 square pyramids. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Na(1), one V(2), and two equivalent V(1) atoms. In the third O site, O(3) is bonded to two equivalent V(3) and three equivalent V(2) atoms to form a mixture of edge and corner-sharing OV5 square pyramids. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one V(1), one V(3), and two equivalent V(2) atoms. is represented by the CIF file [CIF]
data_NaV5O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.519
_cell_length_b   5.519
_cell_length_c   10.639
_cell_angle_alpha   77.536
_cell_angle_beta   77.536
_cell_angle_gamma   31.576
_symmetry_Int_Tables_number   1
_cell_volume   165.365
_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
  Na  Na0  1  0.509  0.491  0.000  1.0
  V  V1  1  0.281  0.245  0.873  1.0
  V  V2  1  0.267  0.262  0.368  1.0
  V  V3  1  0.506  0.494  0.500  1.0
  V  V4  1  0.755  0.719  0.127  1.0
  V  V5  1  0.738  0.733  0.632  1.0
  O  O6  1  0.158  0.131  0.064  1.0
  O  O7  1  0.327  0.350  0.184  1.0
  O  O8  1  0.138  0.119  0.551  1.0
  O  O9  1  0.359  0.337  0.670  1.0
  O  O10  1  0.650  0.673  0.816  1.0
  O  O11  1  0.663  0.641  0.330  1.0
  O  O12  1  0.869  0.842  0.936  1.0
  O  O13  1  0.881  0.862  0.449  1.0
[/CIF]
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The crystal structure described by NaV5O8 crystallizes in the monoclinic C2 space group. Na(1) is bonded to two equivalent O(2) and four equivalent O(1) atoms to form NaO6 octahedra that share corners with two equivalent V(2)O6 octahedra, corners with four equivalent V(1)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, and edges with six equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-24°. There are three inequivalent V sites. In the first V site, V(1) is bonded to one O(4), two equivalent O(2), and three equivalent O(1) atoms to form VO6 octahedra that share  a cornercorner with one V(3)O6 octahedra, corners with two equivalent Na(1)O6 octahedra, edges with two equivalent V(2)O6 octahedra, edges with three equivalent Na(1)O6 octahedra, and edges with four equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-23°. In the second V site, V(2) is bonded to one O(2), two equivalent O(4), and three equivalent O(3) atoms to form VO6 octahedra that share  a cornercorner with one Na(1)O6 octahedra, corners with two equivalent V(3)O6 octahedra, edges with two equivalent V(1)O6 octahedra, edges with three equivalent V(3)O6 octahedra, and edges with four equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-24°. In the third V site, V(3) is bonded to two equivalent O(4) and four equivalent O(3) atoms to form a mixture of edge and corner-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 9-23°. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Na(1) and three equivalent V(1) atoms to form a mixture of edge and corner-sharing ONa2V3 square pyramids. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Na(1), one V(2), and two equivalent V(1) atoms. In the third O site, O(3) is bonded to two equivalent V(3) and three equivalent V(2) atoms to form a mixture of edge and corner-sharing OV5 square pyramids. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one V(1), one V(3), and two equivalent V(2) atoms. is represented by the CIF file [CIF]
data_NaV5O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.519
_cell_length_b   5.519
_cell_length_c   10.639
_cell_angle_alpha   77.536
_cell_angle_beta   77.536
_cell_angle_gamma   31.576
_symmetry_Int_Tables_number   1
_cell_volume   165.365
_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
  Na  Na0  1  0.509  0.491  0.000  1.0
  V  V1  1  0.281  0.245  0.873  1.0
  V  V2  1  0.267  0.262  0.368  1.0
  V  V3  1  0.506  0.494  0.500  1.0
  V  V4  1  0.755  0.719  0.127  1.0
  V  V5  1  0.738  0.733  0.632  1.0
  O  O6  1  0.158  0.131  0.064  1.0
  O  O7  1  0.327  0.350  0.184  1.0
  O  O8  1  0.138  0.119  0.551  1.0
  O  O9  1  0.359  0.337  0.670  1.0
  O  O10  1  0.650  0.673  0.816  1.0
  O  O11  1  0.663  0.641  0.330  1.0
  O  O12  1  0.869  0.842  0.936  1.0
  O  O13  1  0.881  0.862  0.449  1.0
[/CIF]
.