The crystal structure described by Ba6Lu2Al4O15 crystallizes in the monoclinic P2/c space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 10-coordinate geometry to one O(5), one O(6), one O(7), two equivalent O(2), two equivalent O(4), and three equivalent O(8) atoms. In the second Ba site, Ba(2) is bonded in a 9-coordinate geometry to one O(1), one O(5), one O(6), two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms. In the third Ba site, Ba(3) is bonded in a 8-coordinate geometry to two equivalent O(1), two equivalent O(3), two equivalent O(6), and two equivalent O(7) atoms. In the fourth Ba site, Ba(4) is bonded in a 8-coordinate geometry to two equivalent O(5), two equivalent O(6), two equivalent O(7), and two equivalent O(8) atoms. Lu(1) is bonded to one O(2), one O(3), one O(4), one O(6), one O(7), and one O(8) atom to form LuO6 octahedra that share corners with two equivalent Al(2)O4 tetrahedra and corners with four equivalent Al(1)O4 tetrahedra. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(2), one O(3), one O(4), and one O(8) atom to form AlO4 tetrahedra that share corners with four equivalent Lu(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-36°. In the second Al site, Al(2) is bonded to one O(1), one O(5), one O(6), and one O(7) atom to form AlO4 tetrahedra that share corners with two equivalent Lu(1)O6 octahedra and  a cornercorner with one Al(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 7-30°. There are eight inequivalent O sites. In the first O site, O(4) is bonded in a 6-coordinate geometry to two equivalent Ba(1), two equivalent Ba(2), one Lu(1), and one Al(1) atom. In the second O site, O(5) is bonded in a 4-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), and one Al(2) atom. In the third O site, O(6) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Lu(1), and one Al(2) atom. In the fourth O site, O(7) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(3), one Ba(4), one Lu(1), and one Al(2) atom. In the fifth O site, O(8) is bonded in a 2-coordinate geometry to one Ba(4), three equivalent Ba(1), one Lu(1), and one Al(1) atom. In the sixth O site, O(1) is bonded in a distorted linear geometry to two equivalent Ba(2), two equivalent Ba(3), and two equivalent Al(2) atoms. In the seventh O site, O(2) is bonded in a 6-coordinate geometry to two equivalent Ba(1), two equivalent Ba(2), one Lu(1), and one Al(1) atom. In the eighth O site, O(3) is bonded in a 5-coordinate geometry to one Ba(3), two equivalent Ba(2), one Lu(1), and one Al(1) atom. is represented by the CIF card [CIF]
data_Ba6Lu2Al4O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.907
_cell_length_b   7.895
_cell_length_c   18.375
_cell_angle_alpha   88.401
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   856.551
_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
  Ba  Ba0  1  0.756  0.501  0.080  1.0
  Ba  Ba1  1  0.244  0.499  0.920  1.0
  Ba  Ba2  1  0.756  0.499  0.420  1.0
  Ba  Ba3  1  0.244  0.501  0.580  1.0
  Ba  Ba4  1  0.747  0.971  0.089  1.0
  Ba  Ba5  1  0.253  0.029  0.911  1.0
  Ba  Ba6  1  0.747  0.029  0.411  1.0
  Ba  Ba7  1  0.253  0.971  0.589  1.0
  Ba  Ba8  1  0.721  0.000  0.750  1.0
  Ba  Ba9  1  0.279  0.000  0.250  1.0
  Ba  Ba10  1  0.673  0.500  0.750  1.0
  Ba  Ba11  1  0.327  0.500  0.250  1.0
  Lu  Lu12  1  0.744  0.751  0.910  1.0
  Lu  Lu13  1  0.256  0.249  0.090  1.0
  Lu  Lu14  1  0.744  0.249  0.590  1.0
  Lu  Lu15  1  0.256  0.751  0.410  1.0
  Al  Al16  1  0.752  0.753  0.555  1.0
  Al  Al17  1  0.248  0.247  0.445  1.0
  Al  Al18  1  0.752  0.247  0.945  1.0
  Al  Al19  1  0.248  0.753  0.055  1.0
  Al  Al20  1  0.772  0.779  0.268  1.0
  Al  Al21  1  0.228  0.221  0.732  1.0
  Al  Al22  1  0.772  0.221  0.232  1.0
  Al  Al23  1  0.228  0.779  0.768  1.0
  O  O24  1  0.210  0.000  0.750  1.0
  O  O25  1  0.790  0.000  0.250  1.0
  O  O26  1  0.493  0.763  0.998  1.0
  O  O27  1  0.507  0.237  0.002  1.0
  O  O28  1  0.493  0.237  0.502  1.0
  O  O29  1  0.507  0.763  0.498  1.0
  O  O30  1  0.757  0.948  0.604  1.0
  O  O31  1  0.243  0.052  0.396  1.0
  O  O32  1  0.757  0.052  0.896  1.0
  O  O33  1  0.243  0.948  0.104  1.0
  O  O34  1  0.002  0.762  0.996  1.0
  O  O35  1  0.998  0.238  0.004  1.0
  O  O36  1  0.002  0.238  0.504  1.0
  O  O37  1  0.998  0.762  0.496  1.0
  O  O38  1  0.313  0.691  0.687  1.0
  O  O39  1  0.687  0.309  0.313  1.0
  O  O40  1  0.313  0.309  0.813  1.0
  O  O41  1  0.687  0.691  0.187  1.0
  O  O42  1  0.454  0.753  0.834  1.0
  O  O43  1  0.546  0.247  0.166  1.0
  O  O44  1  0.454  0.247  0.666  1.0
  O  O45  1  0.546  0.753  0.334  1.0
  O  O46  1  0.967  0.733  0.814  1.0
  O  O47  1  0.033  0.267  0.186  1.0
  O  O48  1  0.967  0.267  0.686  1.0
  O  O49  1  0.033  0.733  0.314  1.0
  O  O50  1  0.754  0.538  0.591  1.0
  O  O51  1  0.246  0.462  0.409  1.0
  O  O52  1  0.754  0.462  0.909  1.0
  O  O53  1  0.246  0.538  0.091  1.0
[/CIF]
.
The crystal structure described by Ba6Lu2Al4O15 crystallizes in the monoclinic P2/c space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 10-coordinate geometry to one O(5), one O(6), one O(7), two equivalent O(2), two equivalent O(4), and three equivalent O(8) atoms. In the second Ba site, Ba(2) is bonded in a 9-coordinate geometry to one O(1), one O(5), one O(6), two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms. In the third Ba site, Ba(3) is bonded in a 8-coordinate geometry to two equivalent O(1), two equivalent O(3), two equivalent O(6), and two equivalent O(7) atoms. In the fourth Ba site, Ba(4) is bonded in a 8-coordinate geometry to two equivalent O(5), two equivalent O(6), two equivalent O(7), and two equivalent O(8) atoms. Lu(1) is bonded to one O(2), one O(3), one O(4), one O(6), one O(7), and one O(8) atom to form LuO6 octahedra that share corners with two equivalent Al(2)O4 tetrahedra and corners with four equivalent Al(1)O4 tetrahedra. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(2), one O(3), one O(4), and one O(8) atom to form AlO4 tetrahedra that share corners with four equivalent Lu(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-36°. In the second Al site, Al(2) is bonded to one O(1), one O(5), one O(6), and one O(7) atom to form AlO4 tetrahedra that share corners with two equivalent Lu(1)O6 octahedra and  a cornercorner with one Al(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 7-30°. There are eight inequivalent O sites. In the first O site, O(4) is bonded in a 6-coordinate geometry to two equivalent Ba(1), two equivalent Ba(2), one Lu(1), and one Al(1) atom. In the second O site, O(5) is bonded in a 4-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), and one Al(2) atom. In the third O site, O(6) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Lu(1), and one Al(2) atom. In the fourth O site, O(7) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(3), one Ba(4), one Lu(1), and one Al(2) atom. In the fifth O site, O(8) is bonded in a 2-coordinate geometry to one Ba(4), three equivalent Ba(1), one Lu(1), and one Al(1) atom. In the sixth O site, O(1) is bonded in a distorted linear geometry to two equivalent Ba(2), two equivalent Ba(3), and two equivalent Al(2) atoms. In the seventh O site, O(2) is bonded in a 6-coordinate geometry to two equivalent Ba(1), two equivalent Ba(2), one Lu(1), and one Al(1) atom. In the eighth O site, O(3) is bonded in a 5-coordinate geometry to one Ba(3), two equivalent Ba(2), one Lu(1), and one Al(1) atom. is represented by the CIF card [CIF]
data_Ba6Lu2Al4O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.907
_cell_length_b   7.895
_cell_length_c   18.375
_cell_angle_alpha   88.401
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   856.551
_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
  Ba  Ba0  1  0.756  0.501  0.080  1.0
  Ba  Ba1  1  0.244  0.499  0.920  1.0
  Ba  Ba2  1  0.756  0.499  0.420  1.0
  Ba  Ba3  1  0.244  0.501  0.580  1.0
  Ba  Ba4  1  0.747  0.971  0.089  1.0
  Ba  Ba5  1  0.253  0.029  0.911  1.0
  Ba  Ba6  1  0.747  0.029  0.411  1.0
  Ba  Ba7  1  0.253  0.971  0.589  1.0
  Ba  Ba8  1  0.721  0.000  0.750  1.0
  Ba  Ba9  1  0.279  0.000  0.250  1.0
  Ba  Ba10  1  0.673  0.500  0.750  1.0
  Ba  Ba11  1  0.327  0.500  0.250  1.0
  Lu  Lu12  1  0.744  0.751  0.910  1.0
  Lu  Lu13  1  0.256  0.249  0.090  1.0
  Lu  Lu14  1  0.744  0.249  0.590  1.0
  Lu  Lu15  1  0.256  0.751  0.410  1.0
  Al  Al16  1  0.752  0.753  0.555  1.0
  Al  Al17  1  0.248  0.247  0.445  1.0
  Al  Al18  1  0.752  0.247  0.945  1.0
  Al  Al19  1  0.248  0.753  0.055  1.0
  Al  Al20  1  0.772  0.779  0.268  1.0
  Al  Al21  1  0.228  0.221  0.732  1.0
  Al  Al22  1  0.772  0.221  0.232  1.0
  Al  Al23  1  0.228  0.779  0.768  1.0
  O  O24  1  0.210  0.000  0.750  1.0
  O  O25  1  0.790  0.000  0.250  1.0
  O  O26  1  0.493  0.763  0.998  1.0
  O  O27  1  0.507  0.237  0.002  1.0
  O  O28  1  0.493  0.237  0.502  1.0
  O  O29  1  0.507  0.763  0.498  1.0
  O  O30  1  0.757  0.948  0.604  1.0
  O  O31  1  0.243  0.052  0.396  1.0
  O  O32  1  0.757  0.052  0.896  1.0
  O  O33  1  0.243  0.948  0.104  1.0
  O  O34  1  0.002  0.762  0.996  1.0
  O  O35  1  0.998  0.238  0.004  1.0
  O  O36  1  0.002  0.238  0.504  1.0
  O  O37  1  0.998  0.762  0.496  1.0
  O  O38  1  0.313  0.691  0.687  1.0
  O  O39  1  0.687  0.309  0.313  1.0
  O  O40  1  0.313  0.309  0.813  1.0
  O  O41  1  0.687  0.691  0.187  1.0
  O  O42  1  0.454  0.753  0.834  1.0
  O  O43  1  0.546  0.247  0.166  1.0
  O  O44  1  0.454  0.247  0.666  1.0
  O  O45  1  0.546  0.753  0.334  1.0
  O  O46  1  0.967  0.733  0.814  1.0
  O  O47  1  0.033  0.267  0.186  1.0
  O  O48  1  0.967  0.267  0.686  1.0
  O  O49  1  0.033  0.733  0.314  1.0
  O  O50  1  0.754  0.538  0.591  1.0
  O  O51  1  0.246  0.462  0.409  1.0
  O  O52  1  0.754  0.462  0.909  1.0
  O  O53  1  0.246  0.538  0.091  1.0
[/CIF]
.