The crystal structure described by Ba2Cr3AlO8 crystallizes in the tetragonal P4/mmm space group. Ba(1) is bonded to four equivalent O(1), four equivalent O(2), and four equivalent O(3) atoms to form distorted BaO12 cuboctahedra that share corners with eight equivalent Ba(1)O12 cuboctahedra, faces with five equivalent Ba(1)O12 cuboctahedra, faces with four equivalent Cr(2)O6 octahedra, and faces with four equivalent Cr(1)O5 trigonal bipyramids. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(3) and four equivalent O(1) atoms to form distorted CrO5 trigonal bipyramids that share  a cornercorner with one Cr(2)O6 octahedra, corners with four equivalent Cr(1)O5 trigonal bipyramids, and faces with four equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedra are not tilted. In the second Cr site, Cr(2) is bonded to two equivalent O(3) and four equivalent O(2) atoms to form CrO6 octahedra that share corners with four equivalent Cr(2)O6 octahedra, corners with two equivalent Cr(1)O5 trigonal bipyramids, and faces with eight equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedra are not tilted. Al(1) is bonded in a body-centered cubic geometry to eight equivalent O(1) atoms. There are three inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to two equivalent Ba(1), two equivalent Cr(1), and two equivalent Al(1) atoms. In the second O site, O(2) is bonded to four equivalent Ba(1) and two equivalent Cr(2) atoms to form a mixture of distorted edge, corner, and face-sharing OBa4Cr2 octahedra. The corner-sharing octahedral tilt angles range from 0-56°. In the third O site, O(3) is bonded to four equivalent Ba(1), one Cr(1), and one Cr(2) atom to form a mixture of distorted edge, corner, and face-sharing OBa4Cr2 octahedra. The corner-sharing octahedral tilt angles range from 0-56°. is represented by the CIF card [CIF]
data_Ba2AlCr3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.897
_cell_length_b   3.897
_cell_length_c   11.647
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   176.880
_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
  Ba  Ba0  1  0.500  0.500  0.167  1.0
  Ba  Ba1  1  0.500  0.500  0.833  1.0
  Al  Al2  1  0.500  0.500  0.500  1.0
  Cr  Cr3  1  0.000  0.000  0.353  1.0
  Cr  Cr4  1  0.000  0.000  0.000  1.0
  Cr  Cr5  1  0.000  0.000  0.647  1.0
  O  O6  1  0.000  0.500  0.392  1.0
  O  O7  1  0.500  0.000  0.392  1.0
  O  O8  1  0.500  0.000  0.000  1.0
  O  O9  1  0.000  0.000  0.189  1.0
  O  O10  1  0.000  0.500  0.608  1.0
  O  O11  1  0.500  0.000  0.608  1.0
  O  O12  1  0.000  0.000  0.811  1.0
  O  O13  1  0.000  0.500  0.000  1.0
[/CIF]
.
The crystal structure described by Ba2Cr3AlO8 crystallizes in the tetragonal P4/mmm space group. Ba(1) is bonded to four equivalent O(1), four equivalent O(2), and four equivalent O(3) atoms to form distorted BaO12 cuboctahedra that share corners with eight equivalent Ba(1)O12 cuboctahedra, faces with five equivalent Ba(1)O12 cuboctahedra, faces with four equivalent Cr(2)O6 octahedra, and faces with four equivalent Cr(1)O5 trigonal bipyramids. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(3) and four equivalent O(1) atoms to form distorted CrO5 trigonal bipyramids that share  a cornercorner with one Cr(2)O6 octahedra, corners with four equivalent Cr(1)O5 trigonal bipyramids, and faces with four equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedra are not tilted. In the second Cr site, Cr(2) is bonded to two equivalent O(3) and four equivalent O(2) atoms to form CrO6 octahedra that share corners with four equivalent Cr(2)O6 octahedra, corners with two equivalent Cr(1)O5 trigonal bipyramids, and faces with eight equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedra are not tilted. Al(1) is bonded in a body-centered cubic geometry to eight equivalent O(1) atoms. There are three inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to two equivalent Ba(1), two equivalent Cr(1), and two equivalent Al(1) atoms. In the second O site, O(2) is bonded to four equivalent Ba(1) and two equivalent Cr(2) atoms to form a mixture of distorted edge, corner, and face-sharing OBa4Cr2 octahedra. The corner-sharing octahedral tilt angles range from 0-56°. In the third O site, O(3) is bonded to four equivalent Ba(1), one Cr(1), and one Cr(2) atom to form a mixture of distorted edge, corner, and face-sharing OBa4Cr2 octahedra. The corner-sharing octahedral tilt angles range from 0-56°. is represented by the CIF card [CIF]
data_Ba2AlCr3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.897
_cell_length_b   3.897
_cell_length_c   11.647
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   176.880
_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
  Ba  Ba0  1  0.500  0.500  0.167  1.0
  Ba  Ba1  1  0.500  0.500  0.833  1.0
  Al  Al2  1  0.500  0.500  0.500  1.0
  Cr  Cr3  1  0.000  0.000  0.353  1.0
  Cr  Cr4  1  0.000  0.000  0.000  1.0
  Cr  Cr5  1  0.000  0.000  0.647  1.0
  O  O6  1  0.000  0.500  0.392  1.0
  O  O7  1  0.500  0.000  0.392  1.0
  O  O8  1  0.500  0.000  0.000  1.0
  O  O9  1  0.000  0.000  0.189  1.0
  O  O10  1  0.000  0.500  0.608  1.0
  O  O11  1  0.500  0.000  0.608  1.0
  O  O12  1  0.000  0.000  0.811  1.0
  O  O13  1  0.000  0.500  0.000  1.0
[/CIF]
.