The crystal structure described by Li4Zr3O8 crystallizes in the orthorhombic C222 space group. There are three 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 Zr(2)O6 octahedra, corners with four equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Zr(1)O6 octahedra, and edges with four equivalent Zr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-10°. In the second Li site, Li(2) is bonded to two equivalent O(2) and four equivalent O(1) atoms to form LiO6 octahedra that share corners with four equivalent Li(3)O6 octahedra, edges with two equivalent Zr(1)O6 octahedra, edges with four equivalent Li(1)O6 octahedra, and edges with four equivalent Zr(2)O6 octahedra. The corner-sharing octahedral tilt angles are 12°. In the third Li site, Li(3) is bonded to two equivalent O(3) and four equivalent O(1) atoms to form LiO6 octahedra that share corners with two equivalent Zr(1)O6 octahedra, corners with four equivalent Li(2)O6 octahedra, edges with two equivalent Zr(1)O6 octahedra, edges with four equivalent Li(1)O6 octahedra, and edges with four equivalent Zr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to two equivalent O(3) and four equivalent O(1) atoms to form ZrO6 octahedra that share corners with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with four equivalent Li(1)O6 octahedra, and edges with four equivalent Zr(2)O6 octahedra. The corner-sharing octahedra are not tilted. In the second Zr site, Zr(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form ZrO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with four equivalent Zr(2)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Zr(1)O6 octahedra, and edges with four equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-10°. There are three inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Li(2), one Li(3), one Zr(1), and one Zr(2) atom to form OLi3Zr2 square pyramids that share corners with two equivalent O(2)Li3Zr2 square pyramids, corners with seven equivalent O(1)Li3Zr2 square pyramids, edges with four equivalent O(3)Li3Zr3 octahedra, edges with two equivalent O(1)Li3Zr2 square pyramids, and edges with two equivalent O(2)Li3Zr2 square pyramids. In the second O site, O(2) is bonded to one Li(2), two equivalent Li(1), and two equivalent Zr(2) atoms to form OLi3Zr2 square pyramids that share corners with four equivalent O(3)Li3Zr3 octahedra,  a cornercorner with one O(2)Li3Zr2 square pyramid, corners with four equivalent O(1)Li3Zr2 square pyramids, edges with two equivalent O(3)Li3Zr3 octahedra, edges with two equivalent O(2)Li3Zr2 square pyramids, and edges with four equivalent O(1)Li3Zr2 square pyramids. The corner-sharing octahedral tilt angles range from 2-7°. In the third O site, O(3) is bonded to one Li(3), two equivalent Li(1), one Zr(1), and two equivalent Zr(2) atoms to form OLi3Zr3 octahedra that share corners with two equivalent O(3)Li3Zr3 octahedra, corners with four equivalent O(2)Li3Zr2 square pyramids, edges with two equivalent O(3)Li3Zr3 octahedra, edges with two equivalent O(2)Li3Zr2 square pyramids, and edges with eight equivalent O(1)Li3Zr2 square pyramids. The corner-sharing octahedra are not tilted. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Zr3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.465
_cell_length_b   5.465
_cell_length_c   6.216
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   111.564
_symmetry_Int_Tables_number   1
_cell_volume   172.669
_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  0.500  0.000  0.755  1.0
  Li  Li1  1  0.000  0.500  0.245  1.0
  Li  Li2  1  0.000  0.000  0.500  1.0
  Li  Li3  1  0.500  0.500  0.000  1.0
  Zr  Zr4  1  0.000  0.000  0.000  1.0
  Zr  Zr5  1  0.000  0.500  0.723  1.0
  Zr  Zr6  1  0.500  0.000  0.277  1.0
  O  O7  1  0.736  0.781  0.232  1.0
  O  O8  1  0.219  0.264  0.768  1.0
  O  O9  1  0.767  0.233  0.500  1.0
  O  O10  1  0.241  0.759  0.000  1.0
  O  O11  1  0.759  0.241  0.000  1.0
  O  O12  1  0.233  0.767  0.500  1.0
  O  O13  1  0.781  0.736  0.768  1.0
  O  O14  1  0.264  0.219  0.232  1.0
[/CIF]
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The crystal structure described by Li4Zr3O8 crystallizes in the orthorhombic C222 space group. There are three 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 Zr(2)O6 octahedra, corners with four equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Zr(1)O6 octahedra, and edges with four equivalent Zr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-10°. In the second Li site, Li(2) is bonded to two equivalent O(2) and four equivalent O(1) atoms to form LiO6 octahedra that share corners with four equivalent Li(3)O6 octahedra, edges with two equivalent Zr(1)O6 octahedra, edges with four equivalent Li(1)O6 octahedra, and edges with four equivalent Zr(2)O6 octahedra. The corner-sharing octahedral tilt angles are 12°. In the third Li site, Li(3) is bonded to two equivalent O(3) and four equivalent O(1) atoms to form LiO6 octahedra that share corners with two equivalent Zr(1)O6 octahedra, corners with four equivalent Li(2)O6 octahedra, edges with two equivalent Zr(1)O6 octahedra, edges with four equivalent Li(1)O6 octahedra, and edges with four equivalent Zr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to two equivalent O(3) and four equivalent O(1) atoms to form ZrO6 octahedra that share corners with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with four equivalent Li(1)O6 octahedra, and edges with four equivalent Zr(2)O6 octahedra. The corner-sharing octahedra are not tilted. In the second Zr site, Zr(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form ZrO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with four equivalent Zr(2)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Zr(1)O6 octahedra, and edges with four equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-10°. There are three inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Li(2), one Li(3), one Zr(1), and one Zr(2) atom to form OLi3Zr2 square pyramids that share corners with two equivalent O(2)Li3Zr2 square pyramids, corners with seven equivalent O(1)Li3Zr2 square pyramids, edges with four equivalent O(3)Li3Zr3 octahedra, edges with two equivalent O(1)Li3Zr2 square pyramids, and edges with two equivalent O(2)Li3Zr2 square pyramids. In the second O site, O(2) is bonded to one Li(2), two equivalent Li(1), and two equivalent Zr(2) atoms to form OLi3Zr2 square pyramids that share corners with four equivalent O(3)Li3Zr3 octahedra,  a cornercorner with one O(2)Li3Zr2 square pyramid, corners with four equivalent O(1)Li3Zr2 square pyramids, edges with two equivalent O(3)Li3Zr3 octahedra, edges with two equivalent O(2)Li3Zr2 square pyramids, and edges with four equivalent O(1)Li3Zr2 square pyramids. The corner-sharing octahedral tilt angles range from 2-7°. In the third O site, O(3) is bonded to one Li(3), two equivalent Li(1), one Zr(1), and two equivalent Zr(2) atoms to form OLi3Zr3 octahedra that share corners with two equivalent O(3)Li3Zr3 octahedra, corners with four equivalent O(2)Li3Zr2 square pyramids, edges with two equivalent O(3)Li3Zr3 octahedra, edges with two equivalent O(2)Li3Zr2 square pyramids, and edges with eight equivalent O(1)Li3Zr2 square pyramids. The corner-sharing octahedra are not tilted. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Zr3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.465
_cell_length_b   5.465
_cell_length_c   6.216
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   111.564
_symmetry_Int_Tables_number   1
_cell_volume   172.669
_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  0.500  0.000  0.755  1.0
  Li  Li1  1  0.000  0.500  0.245  1.0
  Li  Li2  1  0.000  0.000  0.500  1.0
  Li  Li3  1  0.500  0.500  0.000  1.0
  Zr  Zr4  1  0.000  0.000  0.000  1.0
  Zr  Zr5  1  0.000  0.500  0.723  1.0
  Zr  Zr6  1  0.500  0.000  0.277  1.0
  O  O7  1  0.736  0.781  0.232  1.0
  O  O8  1  0.219  0.264  0.768  1.0
  O  O9  1  0.767  0.233  0.500  1.0
  O  O10  1  0.241  0.759  0.000  1.0
  O  O11  1  0.759  0.241  0.000  1.0
  O  O12  1  0.233  0.767  0.500  1.0
  O  O13  1  0.781  0.736  0.768  1.0
  O  O14  1  0.264  0.219  0.232  1.0
[/CIF]
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