The compound described by BaCr10O15 crystallizes in the orthorhombic Cmce space group. Ba(1) is bonded to two equivalent O(2), two equivalent O(6), four equivalent O(3), and four equivalent O(5) atoms to form BaO12 cuboctahedra that share corners with eight equivalent Cr(1)O6 octahedra, corners with eight equivalent Cr(2)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, edges with four equivalent Cr(2)O6 octahedra, faces with two equivalent Cr(3)O6 octahedra, and faces with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 18-50°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(4), one O(6), two equivalent O(3), and two equivalent O(5) atoms to form CrO6 octahedra that share corners with two equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with two equivalent Cr(3)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra, edges with three equivalent Cr(2)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-51°. In the second Cr site, Cr(2) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form CrO6 octahedra that share corners with two equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one Cr(3)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra,  an edgeedge with one Ba(1)O12 cuboctahedra, edges with two equivalent Cr(2)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, and edges with three equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-62°. In the third Cr site, Cr(3) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(5) atoms to form CrO6 octahedra that share  a cornercorner with one Cr(3)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra,  an edgeedge with one Ba(1)O12 cuboctahedra, edges with two equivalent Cr(1)O6 octahedra, edges with four equivalent Cr(2)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-56°. There are six inequivalent O sites. In the first O site, O(6) is bonded to one Ba(1), two equivalent Cr(1), and two equivalent Cr(2) atoms to form distorted OBaCr4 trigonal bipyramids that share corners with four equivalent O(2)BaCr3 tetrahedra,  a cornercorner with one O(6)BaCr4 trigonal bipyramid, corners with two equivalent O(3)BaCr4 trigonal pyramids,  an edgeedge with one O(1)Cr6 octahedra, and edges with four equivalent O(3)BaCr4 trigonal pyramids. In the second O site, O(1) is bonded to two equivalent Cr(3) and four equivalent Cr(2) atoms to form OCr6 octahedra that share corners with two equivalent O(2)BaCr3 tetrahedra, edges with two equivalent O(2)BaCr3 tetrahedra, edges with two equivalent O(6)BaCr4 trigonal bipyramids, and edges with four equivalent O(3)BaCr4 trigonal pyramids. In the third O site, O(2) is bonded to one Ba(1), one Cr(3), and two equivalent Cr(2) atoms to form distorted OBaCr3 tetrahedra that share  a cornercorner with one O(1)Cr6 octahedra,  a cornercorner with one O(2)BaCr3 tetrahedra, corners with four equivalent O(6)BaCr4 trigonal bipyramids, corners with four equivalent O(3)BaCr4 trigonal pyramids,  an edgeedge with one O(1)Cr6 octahedra, and edges with two equivalent O(3)BaCr4 trigonal pyramids. The corner-sharing octahedral tilt angles are 5°. In the fourth O site, O(3) is bonded to one Ba(1), one Cr(2), one Cr(3), and two equivalent Cr(1) atoms to form distorted OBaCr4 trigonal pyramids that share corners with two equivalent O(2)BaCr3 tetrahedra,  a cornercorner with one O(6)BaCr4 trigonal bipyramid, corners with two equivalent O(3)BaCr4 trigonal pyramids,  an edgeedge with one O(1)Cr6 octahedra,  an edgeedge with one O(2)BaCr3 tetrahedra, edges with two equivalent O(6)BaCr4 trigonal bipyramids, and edges with two equivalent O(3)BaCr4 trigonal pyramids. In the fifth O site, O(4) is bonded in a distorted see-saw-like geometry to two equivalent Cr(1) and two equivalent Cr(2) atoms. In the sixth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one Cr(2), one Cr(3), and two equivalent Cr(1) atoms. is represented by the CIF card [CIF]
data_BaCr10O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.856
_cell_length_b   7.856
_cell_length_c   9.628
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   96.602
_symmetry_Int_Tables_number   1
_cell_volume   590.288
_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  0.000  0.000  0.500  1.0
  Ba  Ba1  1  0.500  0.500  0.000  1.0
  Cr  Cr2  1  0.418  0.907  0.115  1.0
  Cr  Cr3  1  0.082  0.593  0.615  1.0
  Cr  Cr4  1  0.407  0.918  0.385  1.0
  Cr  Cr5  1  0.093  0.582  0.885  1.0
  Cr  Cr6  1  0.582  0.093  0.885  1.0
  Cr  Cr7  1  0.918  0.407  0.385  1.0
  Cr  Cr8  1  0.593  0.082  0.615  1.0
  Cr  Cr9  1  0.907  0.418  0.115  1.0
  Cr  Cr10  1  0.788  0.043  0.143  1.0
  Cr  Cr11  1  0.712  0.457  0.643  1.0
  Cr  Cr12  1  0.543  0.288  0.357  1.0
  Cr  Cr13  1  0.957  0.211  0.857  1.0
  Cr  Cr14  1  0.211  0.957  0.857  1.0
  Cr  Cr15  1  0.288  0.543  0.357  1.0
  Cr  Cr16  1  0.457  0.712  0.643  1.0
  Cr  Cr17  1  0.043  0.788  0.143  1.0
  Cr  Cr18  1  0.817  0.817  0.865  1.0
  Cr  Cr19  1  0.683  0.683  0.365  1.0
  Cr  Cr20  1  0.317  0.317  0.635  1.0
  Cr  Cr21  1  0.183  0.183  0.135  1.0
  O  O22  1  0.500  0.500  0.500  1.0
  O  O23  1  0.000  0.000  0.000  1.0
  O  O24  1  0.145  0.145  0.740  1.0
  O  O25  1  0.355  0.355  0.240  1.0
  O  O26  1  0.645  0.645  0.760  1.0
  O  O27  1  0.855  0.855  0.260  1.0
  O  O28  1  0.223  0.959  0.240  1.0
  O  O29  1  0.277  0.541  0.740  1.0
  O  O30  1  0.459  0.723  0.260  1.0
  O  O31  1  0.041  0.777  0.760  1.0
  O  O32  1  0.777  0.041  0.760  1.0
  O  O33  1  0.723  0.459  0.260  1.0
  O  O34  1  0.541  0.277  0.740  1.0
  O  O35  1  0.959  0.223  0.240  1.0
  O  O36  1  0.565  0.065  0.250  1.0
  O  O37  1  0.935  0.435  0.750  1.0
  O  O38  1  0.435  0.935  0.750  1.0
  O  O39  1  0.065  0.565  0.250  1.0
  O  O40  1  0.365  0.104  0.995  1.0
  O  O41  1  0.135  0.396  0.495  1.0
  O  O42  1  0.604  0.865  0.505  1.0
  O  O43  1  0.896  0.635  0.005  1.0
  O  O44  1  0.756  0.244  0.000  1.0
  O  O45  1  0.744  0.256  0.500  1.0
  O  O46  1  0.244  0.756  0.000  1.0
  O  O47  1  0.256  0.744  0.500  1.0
  O  O48  1  0.104  0.365  0.995  1.0
  O  O49  1  0.396  0.135  0.495  1.0
  O  O50  1  0.865  0.604  0.505  1.0
  O  O51  1  0.635  0.896  0.005  1.0
[/CIF]
.
The compound described by BaCr10O15 crystallizes in the orthorhombic Cmce space group. Ba(1) is bonded to two equivalent O(2), two equivalent O(6), four equivalent O(3), and four equivalent O(5) atoms to form BaO12 cuboctahedra that share corners with eight equivalent Cr(1)O6 octahedra, corners with eight equivalent Cr(2)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, edges with four equivalent Cr(2)O6 octahedra, faces with two equivalent Cr(3)O6 octahedra, and faces with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 18-50°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(4), one O(6), two equivalent O(3), and two equivalent O(5) atoms to form CrO6 octahedra that share corners with two equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with two equivalent Cr(3)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra, edges with three equivalent Cr(2)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-51°. In the second Cr site, Cr(2) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form CrO6 octahedra that share corners with two equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one Cr(3)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra,  an edgeedge with one Ba(1)O12 cuboctahedra, edges with two equivalent Cr(2)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, and edges with three equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-62°. In the third Cr site, Cr(3) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(5) atoms to form CrO6 octahedra that share  a cornercorner with one Cr(3)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra,  an edgeedge with one Ba(1)O12 cuboctahedra, edges with two equivalent Cr(1)O6 octahedra, edges with four equivalent Cr(2)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-56°. There are six inequivalent O sites. In the first O site, O(6) is bonded to one Ba(1), two equivalent Cr(1), and two equivalent Cr(2) atoms to form distorted OBaCr4 trigonal bipyramids that share corners with four equivalent O(2)BaCr3 tetrahedra,  a cornercorner with one O(6)BaCr4 trigonal bipyramid, corners with two equivalent O(3)BaCr4 trigonal pyramids,  an edgeedge with one O(1)Cr6 octahedra, and edges with four equivalent O(3)BaCr4 trigonal pyramids. In the second O site, O(1) is bonded to two equivalent Cr(3) and four equivalent Cr(2) atoms to form OCr6 octahedra that share corners with two equivalent O(2)BaCr3 tetrahedra, edges with two equivalent O(2)BaCr3 tetrahedra, edges with two equivalent O(6)BaCr4 trigonal bipyramids, and edges with four equivalent O(3)BaCr4 trigonal pyramids. In the third O site, O(2) is bonded to one Ba(1), one Cr(3), and two equivalent Cr(2) atoms to form distorted OBaCr3 tetrahedra that share  a cornercorner with one O(1)Cr6 octahedra,  a cornercorner with one O(2)BaCr3 tetrahedra, corners with four equivalent O(6)BaCr4 trigonal bipyramids, corners with four equivalent O(3)BaCr4 trigonal pyramids,  an edgeedge with one O(1)Cr6 octahedra, and edges with two equivalent O(3)BaCr4 trigonal pyramids. The corner-sharing octahedral tilt angles are 5°. In the fourth O site, O(3) is bonded to one Ba(1), one Cr(2), one Cr(3), and two equivalent Cr(1) atoms to form distorted OBaCr4 trigonal pyramids that share corners with two equivalent O(2)BaCr3 tetrahedra,  a cornercorner with one O(6)BaCr4 trigonal bipyramid, corners with two equivalent O(3)BaCr4 trigonal pyramids,  an edgeedge with one O(1)Cr6 octahedra,  an edgeedge with one O(2)BaCr3 tetrahedra, edges with two equivalent O(6)BaCr4 trigonal bipyramids, and edges with two equivalent O(3)BaCr4 trigonal pyramids. In the fifth O site, O(4) is bonded in a distorted see-saw-like geometry to two equivalent Cr(1) and two equivalent Cr(2) atoms. In the sixth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one Cr(2), one Cr(3), and two equivalent Cr(1) atoms. is represented by the CIF card [CIF]
data_BaCr10O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.856
_cell_length_b   7.856
_cell_length_c   9.628
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   96.602
_symmetry_Int_Tables_number   1
_cell_volume   590.288
_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  0.000  0.000  0.500  1.0
  Ba  Ba1  1  0.500  0.500  0.000  1.0
  Cr  Cr2  1  0.418  0.907  0.115  1.0
  Cr  Cr3  1  0.082  0.593  0.615  1.0
  Cr  Cr4  1  0.407  0.918  0.385  1.0
  Cr  Cr5  1  0.093  0.582  0.885  1.0
  Cr  Cr6  1  0.582  0.093  0.885  1.0
  Cr  Cr7  1  0.918  0.407  0.385  1.0
  Cr  Cr8  1  0.593  0.082  0.615  1.0
  Cr  Cr9  1  0.907  0.418  0.115  1.0
  Cr  Cr10  1  0.788  0.043  0.143  1.0
  Cr  Cr11  1  0.712  0.457  0.643  1.0
  Cr  Cr12  1  0.543  0.288  0.357  1.0
  Cr  Cr13  1  0.957  0.211  0.857  1.0
  Cr  Cr14  1  0.211  0.957  0.857  1.0
  Cr  Cr15  1  0.288  0.543  0.357  1.0
  Cr  Cr16  1  0.457  0.712  0.643  1.0
  Cr  Cr17  1  0.043  0.788  0.143  1.0
  Cr  Cr18  1  0.817  0.817  0.865  1.0
  Cr  Cr19  1  0.683  0.683  0.365  1.0
  Cr  Cr20  1  0.317  0.317  0.635  1.0
  Cr  Cr21  1  0.183  0.183  0.135  1.0
  O  O22  1  0.500  0.500  0.500  1.0
  O  O23  1  0.000  0.000  0.000  1.0
  O  O24  1  0.145  0.145  0.740  1.0
  O  O25  1  0.355  0.355  0.240  1.0
  O  O26  1  0.645  0.645  0.760  1.0
  O  O27  1  0.855  0.855  0.260  1.0
  O  O28  1  0.223  0.959  0.240  1.0
  O  O29  1  0.277  0.541  0.740  1.0
  O  O30  1  0.459  0.723  0.260  1.0
  O  O31  1  0.041  0.777  0.760  1.0
  O  O32  1  0.777  0.041  0.760  1.0
  O  O33  1  0.723  0.459  0.260  1.0
  O  O34  1  0.541  0.277  0.740  1.0
  O  O35  1  0.959  0.223  0.240  1.0
  O  O36  1  0.565  0.065  0.250  1.0
  O  O37  1  0.935  0.435  0.750  1.0
  O  O38  1  0.435  0.935  0.750  1.0
  O  O39  1  0.065  0.565  0.250  1.0
  O  O40  1  0.365  0.104  0.995  1.0
  O  O41  1  0.135  0.396  0.495  1.0
  O  O42  1  0.604  0.865  0.505  1.0
  O  O43  1  0.896  0.635  0.005  1.0
  O  O44  1  0.756  0.244  0.000  1.0
  O  O45  1  0.744  0.256  0.500  1.0
  O  O46  1  0.244  0.756  0.000  1.0
  O  O47  1  0.256  0.744  0.500  1.0
  O  O48  1  0.104  0.365  0.995  1.0
  O  O49  1  0.396  0.135  0.495  1.0
  O  O50  1  0.865  0.604  0.505  1.0
  O  O51  1  0.635  0.896  0.005  1.0
[/CIF]
.