The material structure described by Na4V3O8 crystallizes in the monoclinic P2_1/m space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded in a 6-coordinate geometry to one O(4), one O(6), one O(7), and three equivalent O(3) atoms. In the second Na site, Na(2) is bonded to one O(2), one O(3), one O(5), one O(7), and two equivalent O(4) atoms to form distorted NaO6 octahedra that share corners with two equivalent Na(2)O6 octahedra, corners with two equivalent V(2)O6 octahedra,  an edgeedge with one V(1)O6 octahedra, edges with two equivalent V(2)O6 octahedra, and edges with two equivalent V(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-29°. In the third Na site, Na(3) is bonded in a 6-coordinate geometry to one O(1), one O(2), one O(5), and three equivalent O(8) atoms. In the fourth Na site, Na(4) is bonded in a 6-coordinate geometry to one O(2), one O(3), one O(5), one O(7), and two equivalent O(6) atoms. There are three inequivalent V sites. In the first V site, V(1) is bonded to one O(2), one O(5), one O(8), and three equivalent O(1) atoms to form distorted VO6 octahedra that share corners with two equivalent V(1)O6 octahedra,  an edgeedge with one Na(2)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with three equivalent V(3)O6 octahedra. The corner-sharing octahedral tilt angles are 19°. In the second V site, V(2) is bonded to one O(3), one O(4), one O(6), and three equivalent O(7) atoms to form distorted VO6 octahedra that share corners with two equivalent Na(2)O6 octahedra, corners with two equivalent V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-14°. In the third V site, V(3) is bonded to one O(1), one O(4), one O(6), one O(8), and two equivalent O(5) atoms to form VO6 octahedra that share corners with two equivalent V(3)O6 octahedra,  an edgeedge with one V(2)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, and edges with three equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles are 14°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Na(3), one V(3), and three equivalent V(1) atoms to form distorted ONaV4 square pyramids that share  a cornercorner with one O(4)Na3V2 square pyramid,  a cornercorner with one O(6)Na3V2 square pyramid,  a cornercorner with one O(8)Na3V2 square pyramid, corners with two equivalent O(1)NaV4 square pyramids, edges with three equivalent O(5)Na3V3 octahedra, edges with two equivalent O(1)NaV4 square pyramids, and edges with three equivalent O(8)Na3V2 square pyramids. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Na(2), one Na(3), one Na(4), and one V(1) atom. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Na(2), one Na(4), three equivalent Na(1), and one V(2) atom. In the fourth O site, O(4) is bonded to one Na(1), two equivalent Na(2), one V(2), and one V(3) atom to form distorted ONa3V2 square pyramids that share corners with two equivalent O(7)Na3V3 octahedra,  a cornercorner with one O(6)Na3V2 square pyramid,  a cornercorner with one O(8)Na3V2 square pyramid,  a cornercorner with one O(1)NaV4 square pyramid, corners with two equivalent O(4)Na3V2 square pyramids, edges with two equivalent O(5)Na3V3 octahedra, edges with two equivalent O(7)Na3V3 octahedra, and  an edgeedge with one O(6)Na3V2 square pyramid. The corner-sharing octahedral tilt angles range from 10-15°. In the fifth O site, O(5) is bonded to one Na(2), one Na(3), one Na(4), one V(1), and two equivalent V(3) atoms to form distorted ONa3V3 octahedra that share corners with two equivalent O(5)Na3V3 octahedra, corners with two equivalent O(8)Na3V2 square pyramids,  an edgeedge with one O(7)Na3V3 octahedra, edges with two equivalent O(4)Na3V2 square pyramids, edges with two equivalent O(6)Na3V2 square pyramids, edges with two equivalent O(8)Na3V2 square pyramids, and edges with three equivalent O(1)NaV4 square pyramids. The corner-sharing octahedral tilt angles are 14°. In the sixth O site, O(6) is bonded to one Na(1), two equivalent Na(4), one V(2), and one V(3) atom to form distorted ONa3V2 square pyramids that share  a cornercorner with one O(4)Na3V2 square pyramid,  a cornercorner with one O(8)Na3V2 square pyramid,  a cornercorner with one O(1)NaV4 square pyramid, corners with two equivalent O(6)Na3V2 square pyramids, edges with two equivalent O(5)Na3V3 octahedra, edges with three equivalent O(7)Na3V3 octahedra, and  an edgeedge with one O(4)Na3V2 square pyramid. In the seventh O site, O(7) is bonded to one Na(1), one Na(2), one Na(4), and three equivalent V(2) atoms to form ONa3V3 octahedra that share corners with two equivalent O(7)Na3V3 octahedra, corners with two equivalent O(4)Na3V2 square pyramids,  an edgeedge with one O(5)Na3V3 octahedra, edges with two equivalent O(7)Na3V3 octahedra, edges with two equivalent O(4)Na3V2 square pyramids, and edges with three equivalent O(6)Na3V2 square pyramids. The corner-sharing octahedral tilt angles are 14°. In the eighth O site, O(8) is bonded to three equivalent Na(3), one V(1), and one V(3) atom to form distorted ONa3V2 square pyramids that share corners with two equivalent O(5)Na3V3 octahedra,  a cornercorner with one O(4)Na3V2 square pyramid,  a cornercorner with one O(6)Na3V2 square pyramid,  a cornercorner with one O(1)NaV4 square pyramid, corners with two equivalent O(8)Na3V2 square pyramids, edges with two equivalent O(5)Na3V3 octahedra, edges with two equivalent O(8)Na3V2 square pyramids, and edges with three equivalent O(1)NaV4 square pyramids. The corner-sharing octahedral tilt angles range from 5-17°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Na4V3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.260
_cell_length_b   6.894
_cell_length_c   12.215
_cell_angle_alpha   76.628
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   348.998
_cell_formula_units_Z   2
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  0.750  0.178  0.404  1.0
  Na  Na1  1  0.750  0.033  0.667  1.0
  Na  Na2  1  0.250  0.586  0.047  1.0
  Na  Na3  1  0.250  0.460  0.291  1.0
  Na  Na4  1  0.750  0.540  0.709  1.0
  Na  Na5  1  0.750  0.414  0.953  1.0
  Na  Na6  1  0.250  0.967  0.333  1.0
  Na  Na7  1  0.250  0.822  0.596  1.0
  V  V8  1  0.250  0.095  0.074  1.0
  V  V9  1  0.250  0.350  0.558  1.0
  V  V10  1  0.250  0.210  0.811  1.0
  V  V11  1  0.750  0.790  0.189  1.0
  V  V12  1  0.750  0.650  0.442  1.0
  V  V13  1  0.750  0.905  0.926  1.0
  O  O14  1  0.750  0.050  0.065  1.0
  O  O15  1  0.250  0.244  0.168  1.0
  O  O16  1  0.250  0.191  0.461  1.0
  O  O17  1  0.250  0.094  0.690  1.0
  O  O18  1  0.750  0.177  0.828  1.0
  O  O19  1  0.750  0.542  0.308  1.0
  O  O20  1  0.750  0.385  0.545  1.0
  O  O21  1  0.750  0.673  0.063  1.0
  O  O22  1  0.250  0.327  0.937  1.0
  O  O23  1  0.250  0.615  0.455  1.0
  O  O24  1  0.250  0.458  0.692  1.0
  O  O25  1  0.250  0.823  0.172  1.0
  O  O26  1  0.750  0.906  0.310  1.0
  O  O27  1  0.750  0.809  0.539  1.0
  O  O28  1  0.750  0.756  0.832  1.0
  O  O29  1  0.250  0.950  0.935  1.0
[/CIF]
.
The material structure described by Na4V3O8 crystallizes in the monoclinic P2_1/m space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded in a 6-coordinate geometry to one O(4), one O(6), one O(7), and three equivalent O(3) atoms. In the second Na site, Na(2) is bonded to one O(2), one O(3), one O(5), one O(7), and two equivalent O(4) atoms to form distorted NaO6 octahedra that share corners with two equivalent Na(2)O6 octahedra, corners with two equivalent V(2)O6 octahedra,  an edgeedge with one V(1)O6 octahedra, edges with two equivalent V(2)O6 octahedra, and edges with two equivalent V(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-29°. In the third Na site, Na(3) is bonded in a 6-coordinate geometry to one O(1), one O(2), one O(5), and three equivalent O(8) atoms. In the fourth Na site, Na(4) is bonded in a 6-coordinate geometry to one O(2), one O(3), one O(5), one O(7), and two equivalent O(6) atoms. There are three inequivalent V sites. In the first V site, V(1) is bonded to one O(2), one O(5), one O(8), and three equivalent O(1) atoms to form distorted VO6 octahedra that share corners with two equivalent V(1)O6 octahedra,  an edgeedge with one Na(2)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with three equivalent V(3)O6 octahedra. The corner-sharing octahedral tilt angles are 19°. In the second V site, V(2) is bonded to one O(3), one O(4), one O(6), and three equivalent O(7) atoms to form distorted VO6 octahedra that share corners with two equivalent Na(2)O6 octahedra, corners with two equivalent V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-14°. In the third V site, V(3) is bonded to one O(1), one O(4), one O(6), one O(8), and two equivalent O(5) atoms to form VO6 octahedra that share corners with two equivalent V(3)O6 octahedra,  an edgeedge with one V(2)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, and edges with three equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles are 14°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Na(3), one V(3), and three equivalent V(1) atoms to form distorted ONaV4 square pyramids that share  a cornercorner with one O(4)Na3V2 square pyramid,  a cornercorner with one O(6)Na3V2 square pyramid,  a cornercorner with one O(8)Na3V2 square pyramid, corners with two equivalent O(1)NaV4 square pyramids, edges with three equivalent O(5)Na3V3 octahedra, edges with two equivalent O(1)NaV4 square pyramids, and edges with three equivalent O(8)Na3V2 square pyramids. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Na(2), one Na(3), one Na(4), and one V(1) atom. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Na(2), one Na(4), three equivalent Na(1), and one V(2) atom. In the fourth O site, O(4) is bonded to one Na(1), two equivalent Na(2), one V(2), and one V(3) atom to form distorted ONa3V2 square pyramids that share corners with two equivalent O(7)Na3V3 octahedra,  a cornercorner with one O(6)Na3V2 square pyramid,  a cornercorner with one O(8)Na3V2 square pyramid,  a cornercorner with one O(1)NaV4 square pyramid, corners with two equivalent O(4)Na3V2 square pyramids, edges with two equivalent O(5)Na3V3 octahedra, edges with two equivalent O(7)Na3V3 octahedra, and  an edgeedge with one O(6)Na3V2 square pyramid. The corner-sharing octahedral tilt angles range from 10-15°. In the fifth O site, O(5) is bonded to one Na(2), one Na(3), one Na(4), one V(1), and two equivalent V(3) atoms to form distorted ONa3V3 octahedra that share corners with two equivalent O(5)Na3V3 octahedra, corners with two equivalent O(8)Na3V2 square pyramids,  an edgeedge with one O(7)Na3V3 octahedra, edges with two equivalent O(4)Na3V2 square pyramids, edges with two equivalent O(6)Na3V2 square pyramids, edges with two equivalent O(8)Na3V2 square pyramids, and edges with three equivalent O(1)NaV4 square pyramids. The corner-sharing octahedral tilt angles are 14°. In the sixth O site, O(6) is bonded to one Na(1), two equivalent Na(4), one V(2), and one V(3) atom to form distorted ONa3V2 square pyramids that share  a cornercorner with one O(4)Na3V2 square pyramid,  a cornercorner with one O(8)Na3V2 square pyramid,  a cornercorner with one O(1)NaV4 square pyramid, corners with two equivalent O(6)Na3V2 square pyramids, edges with two equivalent O(5)Na3V3 octahedra, edges with three equivalent O(7)Na3V3 octahedra, and  an edgeedge with one O(4)Na3V2 square pyramid. In the seventh O site, O(7) is bonded to one Na(1), one Na(2), one Na(4), and three equivalent V(2) atoms to form ONa3V3 octahedra that share corners with two equivalent O(7)Na3V3 octahedra, corners with two equivalent O(4)Na3V2 square pyramids,  an edgeedge with one O(5)Na3V3 octahedra, edges with two equivalent O(7)Na3V3 octahedra, edges with two equivalent O(4)Na3V2 square pyramids, and edges with three equivalent O(6)Na3V2 square pyramids. The corner-sharing octahedral tilt angles are 14°. In the eighth O site, O(8) is bonded to three equivalent Na(3), one V(1), and one V(3) atom to form distorted ONa3V2 square pyramids that share corners with two equivalent O(5)Na3V3 octahedra,  a cornercorner with one O(4)Na3V2 square pyramid,  a cornercorner with one O(6)Na3V2 square pyramid,  a cornercorner with one O(1)NaV4 square pyramid, corners with two equivalent O(8)Na3V2 square pyramids, edges with two equivalent O(5)Na3V3 octahedra, edges with two equivalent O(8)Na3V2 square pyramids, and edges with three equivalent O(1)NaV4 square pyramids. The corner-sharing octahedral tilt angles range from 5-17°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Na4V3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.260
_cell_length_b   6.894
_cell_length_c   12.215
_cell_angle_alpha   76.628
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   348.998
_cell_formula_units_Z   2
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  0.750  0.178  0.404  1.0
  Na  Na1  1  0.750  0.033  0.667  1.0
  Na  Na2  1  0.250  0.586  0.047  1.0
  Na  Na3  1  0.250  0.460  0.291  1.0
  Na  Na4  1  0.750  0.540  0.709  1.0
  Na  Na5  1  0.750  0.414  0.953  1.0
  Na  Na6  1  0.250  0.967  0.333  1.0
  Na  Na7  1  0.250  0.822  0.596  1.0
  V  V8  1  0.250  0.095  0.074  1.0
  V  V9  1  0.250  0.350  0.558  1.0
  V  V10  1  0.250  0.210  0.811  1.0
  V  V11  1  0.750  0.790  0.189  1.0
  V  V12  1  0.750  0.650  0.442  1.0
  V  V13  1  0.750  0.905  0.926  1.0
  O  O14  1  0.750  0.050  0.065  1.0
  O  O15  1  0.250  0.244  0.168  1.0
  O  O16  1  0.250  0.191  0.461  1.0
  O  O17  1  0.250  0.094  0.690  1.0
  O  O18  1  0.750  0.177  0.828  1.0
  O  O19  1  0.750  0.542  0.308  1.0
  O  O20  1  0.750  0.385  0.545  1.0
  O  O21  1  0.750  0.673  0.063  1.0
  O  O22  1  0.250  0.327  0.937  1.0
  O  O23  1  0.250  0.615  0.455  1.0
  O  O24  1  0.250  0.458  0.692  1.0
  O  O25  1  0.250  0.823  0.172  1.0
  O  O26  1  0.750  0.906  0.310  1.0
  O  O27  1  0.750  0.809  0.539  1.0
  O  O28  1  0.750  0.756  0.832  1.0
  O  O29  1  0.250  0.950  0.935  1.0
[/CIF]
.