The compound described by Li4Cr3AlO8 is alpha Po-derived structured and crystallizes in the triclinic P-1 space group. There are six inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(2), one O(3), one O(5), one O(7), and one O(8) atom to form LiO6 octahedra that share corners with three equivalent Cr(3)O6 octahedra, corners with three equivalent Al(1)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Al(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-8°. In the second Li site, Li(2) is bonded to one O(1), one O(2), one O(4), one O(5), one O(6), and one O(7) atom to form LiO6 octahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, and edges with two equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-8°. In the third Li site, Li(3) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(6) atoms to form LiO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with four equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-9°. In the fourth Li site, Li(4) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(8) atoms to form LiO6 octahedra that share corners with two equivalent Al(1)O6 octahedra, corners with four equivalent Cr(3)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. In the fifth Li site, Li(5) is bonded to two equivalent O(3), two equivalent O(5), and two equivalent O(6) atoms to form LiO6 octahedra that share corners with two equivalent Cr(3)O6 octahedra, corners with four equivalent Al(1)O6 octahedra, edges with two 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 Al(1)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-8°. In the sixth Li site, Li(6) is bonded to two equivalent O(4), two equivalent O(7), and two equivalent O(8) atoms to form LiO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with four equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles are 5°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(1), one O(2), one O(7), one O(8), and two equivalent O(4) atoms to form CrO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra, corners with two equivalent Li(6)O6 octahedra, corners with three equivalent Li(2)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Al(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, and edges with three equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-8°. In the second Cr site, Cr(2) is bonded to one O(1), one O(3), one O(5), one O(7), and two equivalent O(6) atoms to form CrO6 octahedra that share  a cornercorner with one Li(6)O6 octahedra, corners with two equivalent Li(3)O6 octahedra, corners with three equivalent Li(2)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, and edges with three equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-9°. In the third Cr site, Cr(3) is bonded to one O(2), one O(4), one O(5), one O(7), and two equivalent O(8) atoms to form CrO6 octahedra that share  a cornercorner with one Li(5)O6 octahedra, corners with two equivalent Li(4)O6 octahedra, corners with three equivalent Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Al(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, and edges with three equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-8°. Al(1) is bonded to one O(1), one O(2), one O(5), one O(6), and two equivalent O(3) atoms to form AlO6 octahedra that share  a cornercorner with one Li(4)O6 octahedra, corners with two equivalent Li(5)O6 octahedra, corners with three equivalent Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Al(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, and edges with three equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-7°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Li(2), one Li(3), one Cr(1), one Cr(2), and one Al(1) atom to form OLi3AlCr2 octahedra that share  a cornercorner with one O(1)Li3AlCr2 octahedra,  a cornercorner with one O(4)Li3Cr3 octahedra, corners with two equivalent O(6)Li3AlCr2 octahedra, corners with two equivalent O(7)Li3Cr3 octahedra,  an edgeedge with one O(4)Li3Cr3 octahedra,  an edgeedge with one O(7)Li3Cr3 octahedra,  an edgeedge with one O(8)Li3Cr3 octahedra, edges with two equivalent O(2)Li3AlCr2 octahedra, edges with two equivalent O(5)Li3AlCr2 octahedra, edges with two equivalent O(6)Li3AlCr2 octahedra, and edges with three equivalent O(3)Li3Al2Cr octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the second O site, O(2) is bonded to one Li(1), one Li(2), one Li(4), one Cr(1), one Cr(3), and one Al(1) atom to form OLi3AlCr2 octahedra that share  a cornercorner with one O(3)Li3Al2Cr octahedra,  a cornercorner with one O(2)Li3AlCr2 octahedra, corners with two equivalent O(5)Li3AlCr2 octahedra, corners with two equivalent O(8)Li3Cr3 octahedra,  an edgeedge with one O(3)Li3Al2Cr octahedra,  an edgeedge with one O(5)Li3AlCr2 octahedra,  an edgeedge with one O(6)Li3AlCr2 octahedra, edges with two equivalent O(1)Li3AlCr2 octahedra, edges with two equivalent O(7)Li3Cr3 octahedra, edges with two equivalent O(8)Li3Cr3 octahedra, and edges with three equivalent O(4)Li3Cr3 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the third O site, O(3) is bonded to one Li(1), one Li(3), one Li(5), one Cr(2), and two equivalent Al(1) atoms to form OLi3Al2Cr octahedra that share  a cornercorner with one O(2)Li3AlCr2 octahedra,  a cornercorner with one O(8)Li3Cr3 octahedra, corners with two equivalent O(3)Li3Al2Cr octahedra, corners with two equivalent O(5)Li3AlCr2 octahedra,  an edgeedge with one O(3)Li3Al2Cr octahedra,  an edgeedge with one O(2)Li3AlCr2 octahedra,  an edgeedge with one O(7)Li3Cr3 octahedra, edges with two equivalent O(5)Li3AlCr2 octahedra, edges with three equivalent O(1)Li3AlCr2 octahedra, and edges with four equivalent O(6)Li3AlCr2 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the fourth O site, O(4) is bonded to one Li(2), one Li(4), one Li(6), one Cr(3), and two equivalent Cr(1) atoms to form OLi3Cr3 octahedra that share  a cornercorner with one O(1)Li3AlCr2 octahedra,  a cornercorner with one O(6)Li3AlCr2 octahedra, corners with two equivalent O(4)Li3Cr3 octahedra, corners with two equivalent O(7)Li3Cr3 octahedra,  an edgeedge with one O(1)Li3AlCr2 octahedra,  an edgeedge with one O(5)Li3AlCr2 octahedra,  an edgeedge with one O(4)Li3Cr3 octahedra, edges with two equivalent O(7)Li3Cr3 octahedra, edges with three equivalent O(2)Li3AlCr2 octahedra, and edges with four equivalent O(8)Li3Cr3 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the fifth O site, O(5) is bonded to one Li(1), one Li(2), one Li(5), one Cr(2), one Cr(3), and one Al(1) atom to form OLi3AlCr2 octahedra that share  a cornercorner with one O(5)Li3AlCr2 octahedra,  a cornercorner with one O(8)Li3Cr3 octahedra, corners with two equivalent O(3)Li3Al2Cr octahedra, corners with two equivalent O(2)Li3AlCr2 octahedra,  an edgeedge with one O(2)Li3AlCr2 octahedra,  an edgeedge with one O(4)Li3Cr3 octahedra,  an edgeedge with one O(8)Li3Cr3 octahedra, edges with two equivalent O(3)Li3Al2Cr octahedra, edges with two equivalent O(1)Li3AlCr2 octahedra, edges with two equivalent O(7)Li3Cr3 octahedra, and edges with three equivalent O(6)Li3AlCr2 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the sixth O site, O(6) is bonded to one Li(2), one Li(3), one Li(5), two equivalent Cr(2), and one Al(1) atom to form OLi3AlCr2 octahedra that share  a cornercorner with one O(4)Li3Cr3 octahedra,  a cornercorner with one O(7)Li3Cr3 octahedra, corners with two equivalent O(1)Li3AlCr2 octahedra, corners with two equivalent O(6)Li3AlCr2 octahedra,  an edgeedge with one O(2)Li3AlCr2 octahedra,  an edgeedge with one O(6)Li3AlCr2 octahedra,  an edgeedge with one O(7)Li3Cr3 octahedra, edges with two equivalent O(1)Li3AlCr2 octahedra, edges with three equivalent O(5)Li3AlCr2 octahedra, and edges with four equivalent O(3)Li3Al2Cr octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the seventh O site, O(7) is bonded to one Li(1), one Li(2), one Li(6), one Cr(1), one Cr(2), and one Cr(3) atom to form OLi3Cr3 octahedra that share  a cornercorner with one O(6)Li3AlCr2 octahedra,  a cornercorner with one O(7)Li3Cr3 octahedra, corners with two equivalent O(1)Li3AlCr2 octahedra, corners with two equivalent O(4)Li3Cr3 octahedra,  an edgeedge with one O(3)Li3Al2Cr octahedra,  an edgeedge with one O(1)Li3AlCr2 octahedra,  an edgeedge with one O(6)Li3AlCr2 octahedra, edges with two equivalent O(2)Li3AlCr2 octahedra, edges with two equivalent O(5)Li3AlCr2 octahedra, edges with two equivalent O(4)Li3Cr3 octahedra, and edges with three equivalent O(8)Li3Cr3 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the eighth O site, O(8) is bonded to one Li(1), one Li(4), one Li(6), one Cr(1), and two equivalent Cr(3) atoms to form OLi3Cr3 octahedra that share  a cornercorner with one O(3)Li3Al2Cr octahedra,  a cornercorner with one O(5)Li3AlCr2 octahedra, corners with two equivalent O(2)Li3AlCr2 octahedra, corners with two equivalent O(8)Li3Cr3 octahedra,  an edgeedge with one O(1)Li3AlCr2 octahedra,  an edgeedge with one O(5)Li3AlCr2 octahedra,  an edgeedge with one O(8)Li3Cr3 octahedra, edges with two equivalent O(2)Li3AlCr2 octahedra, edges with three equivalent O(7)Li3Cr3 octahedra, and edges with four equivalent O(4)Li3Cr3 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. is represented by the CIF file [CIF]
data_Li4AlCr3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.109
_cell_length_b   5.866
_cell_length_c   10.158
_cell_angle_alpha   89.962
_cell_angle_beta   99.540
_cell_angle_gamma   106.670
_symmetry_Int_Tables_number   1
_cell_volume   287.262
_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
  Li  Li0  1  0.999  0.249  0.249  1.0
  Li  Li1  1  0.000  0.249  0.751  1.0
  Li  Li2  1  0.000  0.000  0.000  1.0
  Li  Li3  1  0.000  0.000  0.500  1.0
  Li  Li4  1  1.000  0.751  0.249  1.0
  Li  Li5  1  0.001  0.751  0.751  1.0
  Li  Li6  1  0.000  0.500  0.000  1.0
  Li  Li7  1  0.000  0.500  0.500  1.0
  Al  Al8  1  0.500  0.124  0.877  1.0
  Al  Al9  1  0.500  0.876  0.123  1.0
  Cr  Cr10  1  0.500  0.124  0.373  1.0
  Cr  Cr11  1  0.500  0.876  0.627  1.0
  Cr  Cr12  1  0.500  0.626  0.877  1.0
  Cr  Cr13  1  0.500  0.626  0.373  1.0
  Cr  Cr14  1  0.500  0.374  0.123  1.0
  Cr  Cr15  1  0.500  0.374  0.627  1.0
  O  O16  1  0.280  0.061  0.186  1.0
  O  O17  1  0.278  0.069  0.698  1.0
  O  O18  1  0.717  0.171  0.057  1.0
  O  O19  1  0.728  0.182  0.560  1.0
  O  O20  1  0.283  0.829  0.943  1.0
  O  O21  1  0.720  0.939  0.814  1.0
  O  O22  1  0.272  0.818  0.440  1.0
  O  O23  1  0.722  0.931  0.302  1.0
  O  O24  1  0.278  0.578  0.185  1.0
  O  O25  1  0.720  0.689  0.063  1.0
  O  O26  1  0.273  0.568  0.691  1.0
  O  O27  1  0.727  0.682  0.561  1.0
  O  O28  1  0.280  0.311  0.937  1.0
  O  O29  1  0.722  0.422  0.815  1.0
  O  O30  1  0.273  0.318  0.439  1.0
  O  O31  1  0.727  0.432  0.309  1.0
[/CIF]
.
The compound described by Li4Cr3AlO8 is alpha Po-derived structured and crystallizes in the triclinic P-1 space group. There are six inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(2), one O(3), one O(5), one O(7), and one O(8) atom to form LiO6 octahedra that share corners with three equivalent Cr(3)O6 octahedra, corners with three equivalent Al(1)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Al(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-8°. In the second Li site, Li(2) is bonded to one O(1), one O(2), one O(4), one O(5), one O(6), and one O(7) atom to form LiO6 octahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, and edges with two equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-8°. In the third Li site, Li(3) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(6) atoms to form LiO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with four equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-9°. In the fourth Li site, Li(4) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(8) atoms to form LiO6 octahedra that share corners with two equivalent Al(1)O6 octahedra, corners with four equivalent Cr(3)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. In the fifth Li site, Li(5) is bonded to two equivalent O(3), two equivalent O(5), and two equivalent O(6) atoms to form LiO6 octahedra that share corners with two equivalent Cr(3)O6 octahedra, corners with four equivalent Al(1)O6 octahedra, edges with two 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 Al(1)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-8°. In the sixth Li site, Li(6) is bonded to two equivalent O(4), two equivalent O(7), and two equivalent O(8) atoms to form LiO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with four equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles are 5°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(1), one O(2), one O(7), one O(8), and two equivalent O(4) atoms to form CrO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra, corners with two equivalent Li(6)O6 octahedra, corners with three equivalent Li(2)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Al(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, and edges with three equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-8°. In the second Cr site, Cr(2) is bonded to one O(1), one O(3), one O(5), one O(7), and two equivalent O(6) atoms to form CrO6 octahedra that share  a cornercorner with one Li(6)O6 octahedra, corners with two equivalent Li(3)O6 octahedra, corners with three equivalent Li(2)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, and edges with three equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-9°. In the third Cr site, Cr(3) is bonded to one O(2), one O(4), one O(5), one O(7), and two equivalent O(8) atoms to form CrO6 octahedra that share  a cornercorner with one Li(5)O6 octahedra, corners with two equivalent Li(4)O6 octahedra, corners with three equivalent Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Al(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, and edges with three equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-8°. Al(1) is bonded to one O(1), one O(2), one O(5), one O(6), and two equivalent O(3) atoms to form AlO6 octahedra that share  a cornercorner with one Li(4)O6 octahedra, corners with two equivalent Li(5)O6 octahedra, corners with three equivalent Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Al(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, and edges with three equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-7°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Li(2), one Li(3), one Cr(1), one Cr(2), and one Al(1) atom to form OLi3AlCr2 octahedra that share  a cornercorner with one O(1)Li3AlCr2 octahedra,  a cornercorner with one O(4)Li3Cr3 octahedra, corners with two equivalent O(6)Li3AlCr2 octahedra, corners with two equivalent O(7)Li3Cr3 octahedra,  an edgeedge with one O(4)Li3Cr3 octahedra,  an edgeedge with one O(7)Li3Cr3 octahedra,  an edgeedge with one O(8)Li3Cr3 octahedra, edges with two equivalent O(2)Li3AlCr2 octahedra, edges with two equivalent O(5)Li3AlCr2 octahedra, edges with two equivalent O(6)Li3AlCr2 octahedra, and edges with three equivalent O(3)Li3Al2Cr octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the second O site, O(2) is bonded to one Li(1), one Li(2), one Li(4), one Cr(1), one Cr(3), and one Al(1) atom to form OLi3AlCr2 octahedra that share  a cornercorner with one O(3)Li3Al2Cr octahedra,  a cornercorner with one O(2)Li3AlCr2 octahedra, corners with two equivalent O(5)Li3AlCr2 octahedra, corners with two equivalent O(8)Li3Cr3 octahedra,  an edgeedge with one O(3)Li3Al2Cr octahedra,  an edgeedge with one O(5)Li3AlCr2 octahedra,  an edgeedge with one O(6)Li3AlCr2 octahedra, edges with two equivalent O(1)Li3AlCr2 octahedra, edges with two equivalent O(7)Li3Cr3 octahedra, edges with two equivalent O(8)Li3Cr3 octahedra, and edges with three equivalent O(4)Li3Cr3 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the third O site, O(3) is bonded to one Li(1), one Li(3), one Li(5), one Cr(2), and two equivalent Al(1) atoms to form OLi3Al2Cr octahedra that share  a cornercorner with one O(2)Li3AlCr2 octahedra,  a cornercorner with one O(8)Li3Cr3 octahedra, corners with two equivalent O(3)Li3Al2Cr octahedra, corners with two equivalent O(5)Li3AlCr2 octahedra,  an edgeedge with one O(3)Li3Al2Cr octahedra,  an edgeedge with one O(2)Li3AlCr2 octahedra,  an edgeedge with one O(7)Li3Cr3 octahedra, edges with two equivalent O(5)Li3AlCr2 octahedra, edges with three equivalent O(1)Li3AlCr2 octahedra, and edges with four equivalent O(6)Li3AlCr2 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the fourth O site, O(4) is bonded to one Li(2), one Li(4), one Li(6), one Cr(3), and two equivalent Cr(1) atoms to form OLi3Cr3 octahedra that share  a cornercorner with one O(1)Li3AlCr2 octahedra,  a cornercorner with one O(6)Li3AlCr2 octahedra, corners with two equivalent O(4)Li3Cr3 octahedra, corners with two equivalent O(7)Li3Cr3 octahedra,  an edgeedge with one O(1)Li3AlCr2 octahedra,  an edgeedge with one O(5)Li3AlCr2 octahedra,  an edgeedge with one O(4)Li3Cr3 octahedra, edges with two equivalent O(7)Li3Cr3 octahedra, edges with three equivalent O(2)Li3AlCr2 octahedra, and edges with four equivalent O(8)Li3Cr3 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the fifth O site, O(5) is bonded to one Li(1), one Li(2), one Li(5), one Cr(2), one Cr(3), and one Al(1) atom to form OLi3AlCr2 octahedra that share  a cornercorner with one O(5)Li3AlCr2 octahedra,  a cornercorner with one O(8)Li3Cr3 octahedra, corners with two equivalent O(3)Li3Al2Cr octahedra, corners with two equivalent O(2)Li3AlCr2 octahedra,  an edgeedge with one O(2)Li3AlCr2 octahedra,  an edgeedge with one O(4)Li3Cr3 octahedra,  an edgeedge with one O(8)Li3Cr3 octahedra, edges with two equivalent O(3)Li3Al2Cr octahedra, edges with two equivalent O(1)Li3AlCr2 octahedra, edges with two equivalent O(7)Li3Cr3 octahedra, and edges with three equivalent O(6)Li3AlCr2 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the sixth O site, O(6) is bonded to one Li(2), one Li(3), one Li(5), two equivalent Cr(2), and one Al(1) atom to form OLi3AlCr2 octahedra that share  a cornercorner with one O(4)Li3Cr3 octahedra,  a cornercorner with one O(7)Li3Cr3 octahedra, corners with two equivalent O(1)Li3AlCr2 octahedra, corners with two equivalent O(6)Li3AlCr2 octahedra,  an edgeedge with one O(2)Li3AlCr2 octahedra,  an edgeedge with one O(6)Li3AlCr2 octahedra,  an edgeedge with one O(7)Li3Cr3 octahedra, edges with two equivalent O(1)Li3AlCr2 octahedra, edges with three equivalent O(5)Li3AlCr2 octahedra, and edges with four equivalent O(3)Li3Al2Cr octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the seventh O site, O(7) is bonded to one Li(1), one Li(2), one Li(6), one Cr(1), one Cr(2), and one Cr(3) atom to form OLi3Cr3 octahedra that share  a cornercorner with one O(6)Li3AlCr2 octahedra,  a cornercorner with one O(7)Li3Cr3 octahedra, corners with two equivalent O(1)Li3AlCr2 octahedra, corners with two equivalent O(4)Li3Cr3 octahedra,  an edgeedge with one O(3)Li3Al2Cr octahedra,  an edgeedge with one O(1)Li3AlCr2 octahedra,  an edgeedge with one O(6)Li3AlCr2 octahedra, edges with two equivalent O(2)Li3AlCr2 octahedra, edges with two equivalent O(5)Li3AlCr2 octahedra, edges with two equivalent O(4)Li3Cr3 octahedra, and edges with three equivalent O(8)Li3Cr3 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the eighth O site, O(8) is bonded to one Li(1), one Li(4), one Li(6), one Cr(1), and two equivalent Cr(3) atoms to form OLi3Cr3 octahedra that share  a cornercorner with one O(3)Li3Al2Cr octahedra,  a cornercorner with one O(5)Li3AlCr2 octahedra, corners with two equivalent O(2)Li3AlCr2 octahedra, corners with two equivalent O(8)Li3Cr3 octahedra,  an edgeedge with one O(1)Li3AlCr2 octahedra,  an edgeedge with one O(5)Li3AlCr2 octahedra,  an edgeedge with one O(8)Li3Cr3 octahedra, edges with two equivalent O(2)Li3AlCr2 octahedra, edges with three equivalent O(7)Li3Cr3 octahedra, and edges with four equivalent O(4)Li3Cr3 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. is represented by the CIF file [CIF]
data_Li4AlCr3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.109
_cell_length_b   5.866
_cell_length_c   10.158
_cell_angle_alpha   89.962
_cell_angle_beta   99.540
_cell_angle_gamma   106.670
_symmetry_Int_Tables_number   1
_cell_volume   287.262
_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
  Li  Li0  1  0.999  0.249  0.249  1.0
  Li  Li1  1  0.000  0.249  0.751  1.0
  Li  Li2  1  0.000  0.000  0.000  1.0
  Li  Li3  1  0.000  0.000  0.500  1.0
  Li  Li4  1  1.000  0.751  0.249  1.0
  Li  Li5  1  0.001  0.751  0.751  1.0
  Li  Li6  1  0.000  0.500  0.000  1.0
  Li  Li7  1  0.000  0.500  0.500  1.0
  Al  Al8  1  0.500  0.124  0.877  1.0
  Al  Al9  1  0.500  0.876  0.123  1.0
  Cr  Cr10  1  0.500  0.124  0.373  1.0
  Cr  Cr11  1  0.500  0.876  0.627  1.0
  Cr  Cr12  1  0.500  0.626  0.877  1.0
  Cr  Cr13  1  0.500  0.626  0.373  1.0
  Cr  Cr14  1  0.500  0.374  0.123  1.0
  Cr  Cr15  1  0.500  0.374  0.627  1.0
  O  O16  1  0.280  0.061  0.186  1.0
  O  O17  1  0.278  0.069  0.698  1.0
  O  O18  1  0.717  0.171  0.057  1.0
  O  O19  1  0.728  0.182  0.560  1.0
  O  O20  1  0.283  0.829  0.943  1.0
  O  O21  1  0.720  0.939  0.814  1.0
  O  O22  1  0.272  0.818  0.440  1.0
  O  O23  1  0.722  0.931  0.302  1.0
  O  O24  1  0.278  0.578  0.185  1.0
  O  O25  1  0.720  0.689  0.063  1.0
  O  O26  1  0.273  0.568  0.691  1.0
  O  O27  1  0.727  0.682  0.561  1.0
  O  O28  1  0.280  0.311  0.937  1.0
  O  O29  1  0.722  0.422  0.815  1.0
  O  O30  1  0.273  0.318  0.439  1.0
  O  O31  1  0.727  0.432  0.309  1.0
[/CIF]
.