The material described by Ba4CaZr5O15 crystallizes in the tetragonal I-42m space group. There are five inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to two equivalent O(1), two equivalent O(2), two equivalent O(3), two equivalent O(5), and four equivalent O(6) atoms to form BaO12 cuboctahedra that share corners with four equivalent Ba(1)O12 cuboctahedra, corners with four equivalent Ba(2)O12 cuboctahedra, corners with four equivalent Ba(3)O12 cuboctahedra,  a faceface with one Ba(5)O12 cuboctahedra, faces with four equivalent Ba(4)O12 cuboctahedra, faces with four equivalent Zr(1)O6 octahedra, and faces with four equivalent Zr(2)O6 octahedra. In the second Ba site, Ba(2) is bonded to four equivalent O(1), four equivalent O(2), and four equivalent O(7) atoms to form BaO12 cuboctahedra that share corners with four equivalent Ba(2)O12 cuboctahedra, corners with eight equivalent Ba(1)O12 cuboctahedra, faces with two equivalent Ba(4)O12 cuboctahedra, faces with four equivalent Ba(5)O12 cuboctahedra, and faces with eight equivalent Zr(1)O6 octahedra. In the third Ba site, Ba(3) is bonded to two equivalent O(3), two equivalent O(5), four equivalent O(4), and four equivalent O(8) atoms to form BaO12 cuboctahedra that share corners with four equivalent Ba(1)O12 cuboctahedra, corners with eight equivalent Ba(3)O12 cuboctahedra,  a faceface with one Ba(4)O12 cuboctahedra, faces with four equivalent Zr(2)O6 octahedra, and faces with four equivalent Zr(3)O6 octahedra. In the fourth Ba site, Ba(4) is bonded to two equivalent O(1), two equivalent O(2), two equivalent O(3), two equivalent O(5), and four equivalent O(6) atoms to form distorted BaO12 cuboctahedra that share corners with four equivalent Ba(4)O12 cuboctahedra, corners with four equivalent Ba(5)O12 cuboctahedra,  a faceface with one Ba(2)O12 cuboctahedra,  a faceface with one Ba(3)O12 cuboctahedra, faces with four equivalent Ba(1)O12 cuboctahedra, faces with four equivalent Zr(1)O6 octahedra, and faces with four equivalent Zr(2)O6 octahedra. In the fifth Ba site, Ba(5) is bonded to four equivalent O(1), four equivalent O(2), and four equivalent O(7) atoms to form BaO12 cuboctahedra that share corners with four equivalent Ba(5)O12 cuboctahedra, corners with eight equivalent Ba(4)O12 cuboctahedra, faces with two equivalent Ba(1)O12 cuboctahedra, faces with four equivalent Ba(2)O12 cuboctahedra, and faces with eight equivalent Zr(1)O6 octahedra. There are two inequivalent Ca sites. In the first Ca site, Ca(1) is bonded in a 8-coordinate geometry to two equivalent O(4), two equivalent O(5), and four equivalent O(8) atoms. In the second Ca site, Ca(1) is bonded in a 8-coordinate geometry to two equivalent O(4), two equivalent O(5), and four equivalent O(8) atoms. There are three inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to one O(6), one O(7), two equivalent O(1), and two equivalent O(2) atoms to form ZrO6 octahedra that share  a cornercorner with one Zr(2)O6 octahedra, corners with five equivalent Zr(1)O6 octahedra, faces with two equivalent Ba(1)O12 cuboctahedra, faces with two equivalent Ba(2)O12 cuboctahedra, faces with two equivalent Ba(4)O12 cuboctahedra, and faces with two equivalent Ba(5)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-10°. In the second Zr site, Zr(2) is bonded to one O(6), one O(8), two equivalent O(3), and two equivalent O(5) atoms to form ZrO6 octahedra that share  a cornercorner with one Zr(1)O6 octahedra,  a cornercorner with one Zr(3)O6 octahedra, corners with four equivalent Zr(2)O6 octahedra, faces with two equivalent Ba(1)O12 cuboctahedra, faces with two equivalent Ba(3)O12 cuboctahedra, and faces with two equivalent Ba(4)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-19°. In the third Zr site, Zr(3) is bonded to two equivalent O(8) and four equivalent O(4) atoms to form ZrO6 octahedra that share corners with two equivalent Zr(2)O6 octahedra, corners with four equivalent Zr(3)O6 octahedra, and faces with four equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-24°. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), one Ba(5), and two equivalent Zr(1) atoms. In the second O site, O(2) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), one Ba(5), and two equivalent Zr(1) atoms. In the third O site, O(3) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(3), one Ba(4), and two equivalent Zr(2) atoms. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to two equivalent Ba(3), one Ca(1), and two equivalent Zr(3) atoms. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one Ba(1), one Ba(3), one Ba(4), one Ca(1), and two equivalent Zr(2) atoms. In the sixth O site, O(6) is bonded to two equivalent Ba(1), two equivalent Ba(4), one Zr(1), and one Zr(2) atom to form a mixture of distorted corner and edge-sharing OBa4Zr2 octahedra. The corner-sharing octahedral tilt angles are 1°. In the seventh O site, O(7) is bonded in a distorted linear geometry to two equivalent Ba(2), two equivalent Ba(5), and two equivalent Zr(1) atoms. In the eighth O site, O(8) is bonded in a distorted linear geometry to two equivalent Ba(3), two equivalent Ca(1), one Zr(2), and one Zr(3) atom. is represented by the CIF file [CIF]
data_Ba4CaZr5O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   21.661
_cell_length_b   21.661
_cell_length_c   21.661
_cell_angle_alpha   164.180
_cell_angle_beta   164.180
_cell_angle_gamma   22.445
_symmetry_Int_Tables_number   1
_cell_volume   755.225
_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  0.101  0.101  0.000  1.0
  Ba  Ba1  1  0.500  0.500  0.000  1.0
  Ba  Ba2  1  0.899  0.899  0.000  1.0
  Ba  Ba3  1  0.299  0.299  0.000  1.0
  Ba  Ba4  1  0.701  0.701  0.000  1.0
  Ba  Ba5  1  0.600  0.600  0.000  1.0
  Ba  Ba6  1  0.000  0.000  0.000  1.0
  Ba  Ba7  1  0.400  0.400  0.000  1.0
  Ca  Ca8  1  0.801  0.801  0.000  1.0
  Ca  Ca9  1  0.199  0.199  0.000  1.0
  Zr  Zr10  1  0.050  0.550  0.500  1.0
  Zr  Zr11  1  0.450  0.950  0.500  1.0
  Zr  Zr12  1  0.849  0.349  0.500  1.0
  Zr  Zr13  1  0.250  0.750  0.500  1.0
  Zr  Zr14  1  0.651  0.151  0.500  1.0
  Zr  Zr15  1  0.151  0.651  0.500  1.0
  Zr  Zr16  1  0.550  0.050  0.500  1.0
  Zr  Zr17  1  0.950  0.450  0.500  1.0
  Zr  Zr18  1  0.349  0.849  0.500  1.0
  Zr  Zr19  1  0.750  0.250  0.500  1.0
  O  O20  1  0.323  0.778  0.000  1.0
  O  O21  1  0.722  0.178  0.000  1.0
  O  O22  1  0.132  0.567  0.000  1.0
  O  O23  1  0.554  0.955  0.000  1.0
  O  O24  1  0.944  0.365  0.000  1.0
  O  O25  1  0.778  0.323  0.000  1.0
  O  O26  1  0.178  0.722  0.000  1.0
  O  O27  1  0.567  0.132  0.000  1.0
  O  O28  1  0.955  0.554  0.000  1.0
  O  O29  1  0.365  0.944  0.000  1.0
  O  O30  1  0.868  0.868  0.435  1.0
  O  O31  1  0.278  0.278  0.456  1.0
  O  O32  1  0.677  0.677  0.455  1.0
  O  O33  1  0.056  0.056  0.422  1.0
  O  O34  1  0.446  0.446  0.401  1.0
  O  O35  1  0.433  0.433  0.565  1.0
  O  O36  1  0.822  0.822  0.544  1.0
  O  O37  1  0.222  0.222  0.545  1.0
  O  O38  1  0.635  0.635  0.578  1.0
  O  O39  1  0.045  0.045  0.599  1.0
  O  O40  1  0.601  0.101  0.500  1.0
  O  O41  1  0.000  0.500  0.500  1.0
  O  O42  1  0.399  0.899  0.500  1.0
  O  O43  1  0.799  0.299  0.500  1.0
  O  O44  1  0.201  0.701  0.500  1.0
  O  O45  1  0.101  0.601  0.500  1.0
  O  O46  1  0.500  0.000  0.500  1.0
  O  O47  1  0.899  0.399  0.500  1.0
  O  O48  1  0.299  0.799  0.500  1.0
  O  O49  1  0.701  0.201  0.500  1.0
[/CIF]
.
The material described by Ba4CaZr5O15 crystallizes in the tetragonal I-42m space group. There are five inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to two equivalent O(1), two equivalent O(2), two equivalent O(3), two equivalent O(5), and four equivalent O(6) atoms to form BaO12 cuboctahedra that share corners with four equivalent Ba(1)O12 cuboctahedra, corners with four equivalent Ba(2)O12 cuboctahedra, corners with four equivalent Ba(3)O12 cuboctahedra,  a faceface with one Ba(5)O12 cuboctahedra, faces with four equivalent Ba(4)O12 cuboctahedra, faces with four equivalent Zr(1)O6 octahedra, and faces with four equivalent Zr(2)O6 octahedra. In the second Ba site, Ba(2) is bonded to four equivalent O(1), four equivalent O(2), and four equivalent O(7) atoms to form BaO12 cuboctahedra that share corners with four equivalent Ba(2)O12 cuboctahedra, corners with eight equivalent Ba(1)O12 cuboctahedra, faces with two equivalent Ba(4)O12 cuboctahedra, faces with four equivalent Ba(5)O12 cuboctahedra, and faces with eight equivalent Zr(1)O6 octahedra. In the third Ba site, Ba(3) is bonded to two equivalent O(3), two equivalent O(5), four equivalent O(4), and four equivalent O(8) atoms to form BaO12 cuboctahedra that share corners with four equivalent Ba(1)O12 cuboctahedra, corners with eight equivalent Ba(3)O12 cuboctahedra,  a faceface with one Ba(4)O12 cuboctahedra, faces with four equivalent Zr(2)O6 octahedra, and faces with four equivalent Zr(3)O6 octahedra. In the fourth Ba site, Ba(4) is bonded to two equivalent O(1), two equivalent O(2), two equivalent O(3), two equivalent O(5), and four equivalent O(6) atoms to form distorted BaO12 cuboctahedra that share corners with four equivalent Ba(4)O12 cuboctahedra, corners with four equivalent Ba(5)O12 cuboctahedra,  a faceface with one Ba(2)O12 cuboctahedra,  a faceface with one Ba(3)O12 cuboctahedra, faces with four equivalent Ba(1)O12 cuboctahedra, faces with four equivalent Zr(1)O6 octahedra, and faces with four equivalent Zr(2)O6 octahedra. In the fifth Ba site, Ba(5) is bonded to four equivalent O(1), four equivalent O(2), and four equivalent O(7) atoms to form BaO12 cuboctahedra that share corners with four equivalent Ba(5)O12 cuboctahedra, corners with eight equivalent Ba(4)O12 cuboctahedra, faces with two equivalent Ba(1)O12 cuboctahedra, faces with four equivalent Ba(2)O12 cuboctahedra, and faces with eight equivalent Zr(1)O6 octahedra. There are two inequivalent Ca sites. In the first Ca site, Ca(1) is bonded in a 8-coordinate geometry to two equivalent O(4), two equivalent O(5), and four equivalent O(8) atoms. In the second Ca site, Ca(1) is bonded in a 8-coordinate geometry to two equivalent O(4), two equivalent O(5), and four equivalent O(8) atoms. There are three inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to one O(6), one O(7), two equivalent O(1), and two equivalent O(2) atoms to form ZrO6 octahedra that share  a cornercorner with one Zr(2)O6 octahedra, corners with five equivalent Zr(1)O6 octahedra, faces with two equivalent Ba(1)O12 cuboctahedra, faces with two equivalent Ba(2)O12 cuboctahedra, faces with two equivalent Ba(4)O12 cuboctahedra, and faces with two equivalent Ba(5)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-10°. In the second Zr site, Zr(2) is bonded to one O(6), one O(8), two equivalent O(3), and two equivalent O(5) atoms to form ZrO6 octahedra that share  a cornercorner with one Zr(1)O6 octahedra,  a cornercorner with one Zr(3)O6 octahedra, corners with four equivalent Zr(2)O6 octahedra, faces with two equivalent Ba(1)O12 cuboctahedra, faces with two equivalent Ba(3)O12 cuboctahedra, and faces with two equivalent Ba(4)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-19°. In the third Zr site, Zr(3) is bonded to two equivalent O(8) and four equivalent O(4) atoms to form ZrO6 octahedra that share corners with two equivalent Zr(2)O6 octahedra, corners with four equivalent Zr(3)O6 octahedra, and faces with four equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-24°. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), one Ba(5), and two equivalent Zr(1) atoms. In the second O site, O(2) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), one Ba(5), and two equivalent Zr(1) atoms. In the third O site, O(3) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(3), one Ba(4), and two equivalent Zr(2) atoms. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to two equivalent Ba(3), one Ca(1), and two equivalent Zr(3) atoms. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one Ba(1), one Ba(3), one Ba(4), one Ca(1), and two equivalent Zr(2) atoms. In the sixth O site, O(6) is bonded to two equivalent Ba(1), two equivalent Ba(4), one Zr(1), and one Zr(2) atom to form a mixture of distorted corner and edge-sharing OBa4Zr2 octahedra. The corner-sharing octahedral tilt angles are 1°. In the seventh O site, O(7) is bonded in a distorted linear geometry to two equivalent Ba(2), two equivalent Ba(5), and two equivalent Zr(1) atoms. In the eighth O site, O(8) is bonded in a distorted linear geometry to two equivalent Ba(3), two equivalent Ca(1), one Zr(2), and one Zr(3) atom. is represented by the CIF file [CIF]
data_Ba4CaZr5O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   21.661
_cell_length_b   21.661
_cell_length_c   21.661
_cell_angle_alpha   164.180
_cell_angle_beta   164.180
_cell_angle_gamma   22.445
_symmetry_Int_Tables_number   1
_cell_volume   755.225
_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  0.101  0.101  0.000  1.0
  Ba  Ba1  1  0.500  0.500  0.000  1.0
  Ba  Ba2  1  0.899  0.899  0.000  1.0
  Ba  Ba3  1  0.299  0.299  0.000  1.0
  Ba  Ba4  1  0.701  0.701  0.000  1.0
  Ba  Ba5  1  0.600  0.600  0.000  1.0
  Ba  Ba6  1  0.000  0.000  0.000  1.0
  Ba  Ba7  1  0.400  0.400  0.000  1.0
  Ca  Ca8  1  0.801  0.801  0.000  1.0
  Ca  Ca9  1  0.199  0.199  0.000  1.0
  Zr  Zr10  1  0.050  0.550  0.500  1.0
  Zr  Zr11  1  0.450  0.950  0.500  1.0
  Zr  Zr12  1  0.849  0.349  0.500  1.0
  Zr  Zr13  1  0.250  0.750  0.500  1.0
  Zr  Zr14  1  0.651  0.151  0.500  1.0
  Zr  Zr15  1  0.151  0.651  0.500  1.0
  Zr  Zr16  1  0.550  0.050  0.500  1.0
  Zr  Zr17  1  0.950  0.450  0.500  1.0
  Zr  Zr18  1  0.349  0.849  0.500  1.0
  Zr  Zr19  1  0.750  0.250  0.500  1.0
  O  O20  1  0.323  0.778  0.000  1.0
  O  O21  1  0.722  0.178  0.000  1.0
  O  O22  1  0.132  0.567  0.000  1.0
  O  O23  1  0.554  0.955  0.000  1.0
  O  O24  1  0.944  0.365  0.000  1.0
  O  O25  1  0.778  0.323  0.000  1.0
  O  O26  1  0.178  0.722  0.000  1.0
  O  O27  1  0.567  0.132  0.000  1.0
  O  O28  1  0.955  0.554  0.000  1.0
  O  O29  1  0.365  0.944  0.000  1.0
  O  O30  1  0.868  0.868  0.435  1.0
  O  O31  1  0.278  0.278  0.456  1.0
  O  O32  1  0.677  0.677  0.455  1.0
  O  O33  1  0.056  0.056  0.422  1.0
  O  O34  1  0.446  0.446  0.401  1.0
  O  O35  1  0.433  0.433  0.565  1.0
  O  O36  1  0.822  0.822  0.544  1.0
  O  O37  1  0.222  0.222  0.545  1.0
  O  O38  1  0.635  0.635  0.578  1.0
  O  O39  1  0.045  0.045  0.599  1.0
  O  O40  1  0.601  0.101  0.500  1.0
  O  O41  1  0.000  0.500  0.500  1.0
  O  O42  1  0.399  0.899  0.500  1.0
  O  O43  1  0.799  0.299  0.500  1.0
  O  O44  1  0.201  0.701  0.500  1.0
  O  O45  1  0.101  0.601  0.500  1.0
  O  O46  1  0.500  0.000  0.500  1.0
  O  O47  1  0.899  0.399  0.500  1.0
  O  O48  1  0.299  0.799  0.500  1.0
  O  O49  1  0.701  0.201  0.500  1.0
[/CIF]
.