The structure described by Li3BiO4 is Caswellsilverite-like structured and crystallizes in the tetragonal P4_2/mnm space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form LiO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with four equivalent Li(2)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra, edges with five equivalent Bi(1)O6 octahedra, and edges with six equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-11°. In the second Li site, Li(2) is bonded to one O(1), one O(3), and four equivalent O(2) atoms to form distorted LiO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Bi(1)O6 octahedra, edges with three equivalent Li(1)O6 octahedra, edges with three equivalent Bi(1)O6 octahedra, and edges with six equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-13°. Bi(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form BiO6 octahedra that share corners with two equivalent Bi(1)O6 octahedra, corners with four equivalent Li(2)O6 octahedra,  an edgeedge with one Bi(1)O6 octahedra, edges with five equivalent Li(1)O6 octahedra, and edges with six equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. There are three inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Li(1), two equivalent Li(2), and two equivalent Bi(1) atoms to form OLi4Bi2 octahedra that share corners with two equivalent O(1)Li4Bi2 octahedra, corners with four equivalent O(2)Li5Bi octahedra,  an edgeedge with one O(1)Li4Bi2 octahedra, edges with five equivalent O(3)Li4Bi2 octahedra, and edges with six equivalent O(2)Li5Bi octahedra. The corner-sharing octahedral tilt angles range from 3-11°. In the second O site, O(2) is bonded to one Li(1), four equivalent Li(2), and one Bi(1) atom to form OLi5Bi octahedra that share corners with two equivalent O(1)Li4Bi2 octahedra, corners with two equivalent O(3)Li4Bi2 octahedra, corners with two equivalent O(2)Li5Bi octahedra, edges with three equivalent O(1)Li4Bi2 octahedra, edges with three equivalent O(3)Li4Bi2 octahedra, and edges with six equivalent O(2)Li5Bi octahedra. The corner-sharing octahedral tilt angles range from 1-13°. In the third O site, O(3) is bonded to two equivalent Li(1), two equivalent Li(2), and two equivalent Bi(1) atoms to form OLi4Bi2 octahedra that share corners with two equivalent O(3)Li4Bi2 octahedra, corners with four equivalent O(2)Li5Bi octahedra,  an edgeedge with one O(3)Li4Bi2 octahedra, edges with five equivalent O(1)Li4Bi2 octahedra, and edges with six equivalent O(2)Li5Bi octahedra. The corner-sharing octahedral tilt angles range from 1-11°. is represented by the CIF file [CIF]
data_Li3BiO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.697
_cell_length_b   8.697
_cell_length_c   4.246
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   321.128
_cell_formula_units_Z   4
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  0.870  0.130  0.500  1.0
  Li  Li1  1  0.630  0.630  0.000  1.0
  Li  Li2  1  0.397  0.888  0.000  1.0
  Li  Li3  1  0.612  0.897  0.500  1.0
  Li  Li4  1  0.130  0.870  0.500  1.0
  Li  Li5  1  0.103  0.388  0.500  1.0
  Li  Li6  1  0.888  0.397  0.000  1.0
  Li  Li7  1  0.603  0.112  0.000  1.0
  Li  Li8  1  0.897  0.612  0.500  1.0
  Li  Li9  1  0.370  0.370  0.000  1.0
  Li  Li10  1  0.112  0.603  0.000  1.0
  Li  Li11  1  0.388  0.103  0.500  1.0
  Bi  Bi12  1  0.366  0.634  0.500  1.0
  Bi  Bi13  1  0.634  0.366  0.500  1.0
  Bi  Bi14  1  0.866  0.866  0.000  1.0
  Bi  Bi15  1  0.134  0.134  0.000  1.0
  O  O16  1  0.887  0.113  0.000  1.0
  O  O17  1  0.387  0.387  0.500  1.0
  O  O18  1  0.622  0.130  0.500  1.0
  O  O19  1  0.870  0.378  0.500  1.0
  O  O20  1  0.876  0.876  0.500  1.0
  O  O21  1  0.124  0.124  0.500  1.0
  O  O22  1  0.130  0.622  0.500  1.0
  O  O23  1  0.613  0.613  0.500  1.0
  O  O24  1  0.630  0.878  0.000  1.0
  O  O25  1  0.122  0.370  0.000  1.0
  O  O26  1  0.376  0.624  0.000  1.0
  O  O27  1  0.624  0.376  0.000  1.0
  O  O28  1  0.878  0.630  0.000  1.0
  O  O29  1  0.378  0.870  0.500  1.0
  O  O30  1  0.113  0.887  0.000  1.0
  O  O31  1  0.370  0.122  0.000  1.0
[/CIF]
.
The structure described by Li3BiO4 is Caswellsilverite-like structured and crystallizes in the tetragonal P4_2/mnm space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form LiO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with four equivalent Li(2)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra, edges with five equivalent Bi(1)O6 octahedra, and edges with six equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-11°. In the second Li site, Li(2) is bonded to one O(1), one O(3), and four equivalent O(2) atoms to form distorted LiO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Bi(1)O6 octahedra, edges with three equivalent Li(1)O6 octahedra, edges with three equivalent Bi(1)O6 octahedra, and edges with six equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-13°. Bi(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form BiO6 octahedra that share corners with two equivalent Bi(1)O6 octahedra, corners with four equivalent Li(2)O6 octahedra,  an edgeedge with one Bi(1)O6 octahedra, edges with five equivalent Li(1)O6 octahedra, and edges with six equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. There are three inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Li(1), two equivalent Li(2), and two equivalent Bi(1) atoms to form OLi4Bi2 octahedra that share corners with two equivalent O(1)Li4Bi2 octahedra, corners with four equivalent O(2)Li5Bi octahedra,  an edgeedge with one O(1)Li4Bi2 octahedra, edges with five equivalent O(3)Li4Bi2 octahedra, and edges with six equivalent O(2)Li5Bi octahedra. The corner-sharing octahedral tilt angles range from 3-11°. In the second O site, O(2) is bonded to one Li(1), four equivalent Li(2), and one Bi(1) atom to form OLi5Bi octahedra that share corners with two equivalent O(1)Li4Bi2 octahedra, corners with two equivalent O(3)Li4Bi2 octahedra, corners with two equivalent O(2)Li5Bi octahedra, edges with three equivalent O(1)Li4Bi2 octahedra, edges with three equivalent O(3)Li4Bi2 octahedra, and edges with six equivalent O(2)Li5Bi octahedra. The corner-sharing octahedral tilt angles range from 1-13°. In the third O site, O(3) is bonded to two equivalent Li(1), two equivalent Li(2), and two equivalent Bi(1) atoms to form OLi4Bi2 octahedra that share corners with two equivalent O(3)Li4Bi2 octahedra, corners with four equivalent O(2)Li5Bi octahedra,  an edgeedge with one O(3)Li4Bi2 octahedra, edges with five equivalent O(1)Li4Bi2 octahedra, and edges with six equivalent O(2)Li5Bi octahedra. The corner-sharing octahedral tilt angles range from 1-11°. is represented by the CIF file [CIF]
data_Li3BiO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.697
_cell_length_b   8.697
_cell_length_c   4.246
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   321.128
_cell_formula_units_Z   4
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  0.870  0.130  0.500  1.0
  Li  Li1  1  0.630  0.630  0.000  1.0
  Li  Li2  1  0.397  0.888  0.000  1.0
  Li  Li3  1  0.612  0.897  0.500  1.0
  Li  Li4  1  0.130  0.870  0.500  1.0
  Li  Li5  1  0.103  0.388  0.500  1.0
  Li  Li6  1  0.888  0.397  0.000  1.0
  Li  Li7  1  0.603  0.112  0.000  1.0
  Li  Li8  1  0.897  0.612  0.500  1.0
  Li  Li9  1  0.370  0.370  0.000  1.0
  Li  Li10  1  0.112  0.603  0.000  1.0
  Li  Li11  1  0.388  0.103  0.500  1.0
  Bi  Bi12  1  0.366  0.634  0.500  1.0
  Bi  Bi13  1  0.634  0.366  0.500  1.0
  Bi  Bi14  1  0.866  0.866  0.000  1.0
  Bi  Bi15  1  0.134  0.134  0.000  1.0
  O  O16  1  0.887  0.113  0.000  1.0
  O  O17  1  0.387  0.387  0.500  1.0
  O  O18  1  0.622  0.130  0.500  1.0
  O  O19  1  0.870  0.378  0.500  1.0
  O  O20  1  0.876  0.876  0.500  1.0
  O  O21  1  0.124  0.124  0.500  1.0
  O  O22  1  0.130  0.622  0.500  1.0
  O  O23  1  0.613  0.613  0.500  1.0
  O  O24  1  0.630  0.878  0.000  1.0
  O  O25  1  0.122  0.370  0.000  1.0
  O  O26  1  0.376  0.624  0.000  1.0
  O  O27  1  0.624  0.376  0.000  1.0
  O  O28  1  0.878  0.630  0.000  1.0
  O  O29  1  0.378  0.870  0.500  1.0
  O  O30  1  0.113  0.887  0.000  1.0
  O  O31  1  0.370  0.122  0.000  1.0
[/CIF]
.