The compound described by Mg2Zr14O5 crystallizes in the trigonal R3m space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent Mg(1), three equivalent Zr(1), and three equivalent Zr(3) atoms to form MgMg6Zr6 cuboctahedra that share corners with six equivalent Mg(1)Mg6Zr6 cuboctahedra, corners with three equivalent O(5)Zr4 trigonal pyramids, edges with six equivalent Mg(1)Mg6Zr6 cuboctahedra, edges with three equivalent O(5)Zr4 trigonal pyramids, and faces with six equivalent Mg(1)Mg6Zr6 cuboctahedra. In the second Mg site, Mg(2) is bonded to six equivalent Mg(2), three equivalent Zr(10), and three equivalent Zr(12) atoms to form MgMg6Zr6 cuboctahedra that share corners with three equivalent Zr(8)Zr12 cuboctahedra, corners with six equivalent Mg(2)Mg6Zr6 cuboctahedra, edges with three equivalent Zr(8)Zr12 cuboctahedra, edges with six equivalent Mg(2)Mg6Zr6 cuboctahedra, edges with six equivalent Zr(10)Mg3Zr9 cuboctahedra, faces with six equivalent Mg(2)Mg6Zr6 cuboctahedra, and faces with six equivalent Zr(10)Mg3Zr9 cuboctahedra. There are nineteen inequivalent Zr sites. In the first Zr site, Zr(1) is bonded in a 3-coordinate geometry to three equivalent Mg(1) and three equivalent O(5) atoms. In the second Zr site, Zr(2) is bonded in a distorted T-shaped geometry to three equivalent Zr(5) and three equivalent O(1) atoms. In the third Zr site, Zr(3) is bonded in a single-bond geometry to three equivalent Mg(1) and one O(1) atom. In the fourth Zr site, Zr(4) is bonded to three equivalent Zr(5), three equivalent Zr(6), and six equivalent Zr(4) atoms to form a mixture of edge, corner, and face-sharing ZrZr12 cuboctahedra. In the fifth Zr site, Zr(5) is bonded to three equivalent Zr(2), three equivalent Zr(4), and six equivalent Zr(5) atoms to form a mixture of edge, corner, and face-sharing ZrZr12 cuboctahedra. In the sixth Zr site, Zr(6) is bonded to three equivalent Zr(4), three equivalent Zr(7), and six equivalent Zr(6) atoms to form a mixture of edge, corner, and face-sharing ZrZr12 cuboctahedra. In the seventh Zr site, Zr(7) is bonded to three equivalent Zr(6), three equivalent Zr(9), and six equivalent Zr(7) atoms to form a mixture of edge, corner, and face-sharing ZrZr12 cuboctahedra. In the eighth Zr site, Zr(8) is bonded to three equivalent Zr(10), three equivalent Zr(9), and six equivalent Zr(8) atoms to form ZrZr12 cuboctahedra that share corners with three equivalent Mg(2)Mg6Zr6 cuboctahedra, corners with three equivalent Zr(7)Zr12 cuboctahedra, corners with six equivalent Zr(8)Zr12 cuboctahedra, edges with three equivalent Mg(2)Mg6Zr6 cuboctahedra, edges with three equivalent Zr(7)Zr12 cuboctahedra, edges with six equivalent Zr(10)Mg3Zr9 cuboctahedra, edges with six equivalent Zr(8)Zr12 cuboctahedra, edges with six equivalent Zr(9)Zr12 cuboctahedra, faces with six equivalent Zr(10)Mg3Zr9 cuboctahedra, faces with six equivalent Zr(8)Zr12 cuboctahedra, and faces with six equivalent Zr(9)Zr12 cuboctahedra. In the ninth Zr site, Zr(9) is bonded to three equivalent Zr(7), three equivalent Zr(8), and six equivalent Zr(9) atoms to form ZrZr12 cuboctahedra that share corners with three equivalent Zr(10)Mg3Zr9 cuboctahedra, corners with three equivalent Zr(6)Zr12 cuboctahedra, corners with six equivalent Zr(9)Zr12 cuboctahedra, edges with three equivalent Zr(10)Mg3Zr9 cuboctahedra, edges with three equivalent Zr(6)Zr12 cuboctahedra, edges with six equivalent Zr(7)Zr12 cuboctahedra, edges with six equivalent Zr(8)Zr12 cuboctahedra, edges with six equivalent Zr(9)Zr12 cuboctahedra, faces with six equivalent Zr(7)Zr12 cuboctahedra, faces with six equivalent Zr(8)Zr12 cuboctahedra, and faces with six equivalent Zr(9)Zr12 cuboctahedra. In the tenth Zr site, Zr(10) is bonded to three equivalent Mg(2), three equivalent Zr(8), and six equivalent Zr(10) atoms to form ZrMg3Zr9 cuboctahedra that share corners with three equivalent Zr(9)Zr12 cuboctahedra, corners with six equivalent Zr(10)Mg3Zr9 cuboctahedra, edges with three equivalent Zr(9)Zr12 cuboctahedra, edges with six equivalent Mg(2)Mg6Zr6 cuboctahedra, edges with six equivalent Zr(10)Mg3Zr9 cuboctahedra, edges with six equivalent Zr(8)Zr12 cuboctahedra, faces with six equivalent Mg(2)Mg6Zr6 cuboctahedra, faces with six equivalent Zr(10)Mg3Zr9 cuboctahedra, and faces with six equivalent Zr(8)Zr12 cuboctahedra. In the eleventh Zr site, Zr(11) is bonded in a rectangular see-saw-like geometry to one O(3) and three equivalent O(2) atoms. In the twelfth Zr site, Zr(12) is bonded in a single-bond geometry to three equivalent Mg(2) and one O(2) atom. In the thirteenth Zr site, Zr(13) is bonded in a rectangular see-saw-like geometry to one O(4) and three equivalent O(3) atoms. In the fourteenth Zr site, Zr(14) is bonded in a distorted rectangular see-saw-like geometry to one O(5) and three equivalent O(4) atoms. In the fifteenth Zr site, Zr(8) is bonded to three equivalent Zr(10), three equivalent Zr(9), and six equivalent Zr(8) atoms to form ZrZr12 cuboctahedra that share corners with three equivalent Mg(2)Mg6Zr6 cuboctahedra, corners with three equivalent Zr(7)Zr12 cuboctahedra, corners with six equivalent Zr(8)Zr12 cuboctahedra, edges with three equivalent Mg(2)Mg6Zr6 cuboctahedra, edges with three equivalent Zr(7)Zr12 cuboctahedra, edges with six equivalent Zr(10)Mg3Zr9 cuboctahedra, edges with six equivalent Zr(8)Zr12 cuboctahedra, edges with six equivalent Zr(9)Zr12 cuboctahedra, faces with six equivalent Zr(10)Mg3Zr9 cuboctahedra, faces with six equivalent Zr(8)Zr12 cuboctahedra, and faces with six equivalent Zr(9)Zr12 cuboctahedra. In the sixteenth Zr site, Zr(4) is bonded to three equivalent Zr(5), three equivalent Zr(6), and six equivalent Zr(4) atoms to form a mixture of edge, corner, and face-sharing ZrZr12 cuboctahedra. In the seventeenth Zr site, Zr(6) is bonded to three equivalent Zr(4), three equivalent Zr(7), and six equivalent Zr(6) atoms to form a mixture of edge, corner, and face-sharing ZrZr12 cuboctahedra. In the eighteenth Zr site, Zr(8) is bonded to three equivalent Zr(10), three equivalent Zr(9), and six equivalent Zr(8) atoms to form ZrZr12 cuboctahedra that share corners with three equivalent Mg(2)Mg6Zr6 cuboctahedra, corners with three equivalent Zr(7)Zr12 cuboctahedra, corners with six equivalent Zr(8)Zr12 cuboctahedra, edges with three equivalent Mg(2)Mg6Zr6 cuboctahedra, edges with three equivalent Zr(7)Zr12 cuboctahedra, edges with six equivalent Zr(10)Mg3Zr9 cuboctahedra, edges with six equivalent Zr(8)Zr12 cuboctahedra, edges with six equivalent Zr(9)Zr12 cuboctahedra, faces with six equivalent Zr(10)Mg3Zr9 cuboctahedra, faces with six equivalent Zr(8)Zr12 cuboctahedra, and faces with six equivalent Zr(9)Zr12 cuboctahedra. In the nineteenth Zr site, Zr(9) is bonded to three equivalent Zr(7), three equivalent Zr(8), and six equivalent Zr(9) atoms to form ZrZr12 cuboctahedra that share corners with three equivalent Zr(10)Mg3Zr9 cuboctahedra, corners with three equivalent Zr(6)Zr12 cuboctahedra, corners with six equivalent Zr(9)Zr12 cuboctahedra, edges with three equivalent Zr(10)Mg3Zr9 cuboctahedra, edges with three equivalent Zr(6)Zr12 cuboctahedra, edges with six equivalent Zr(7)Zr12 cuboctahedra, edges with six equivalent Zr(8)Zr12 cuboctahedra, edges with six equivalent Zr(9)Zr12 cuboctahedra, faces with six equivalent Zr(7)Zr12 cuboctahedra, faces with six equivalent Zr(8)Zr12 cuboctahedra, and faces with six equivalent Zr(9)Zr12 cuboctahedra. There are five inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Zr(3) and three equivalent Zr(2) atoms. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Zr(12) and three equivalent Zr(11) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Zr(11) and three equivalent Zr(13) atoms. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Zr(13) and three equivalent Zr(14) atoms. In the fifth O site, O(5) is bonded to one Zr(14) and three equivalent Zr(1) atoms to form distorted OZr4 trigonal pyramids that share corners with three equivalent Mg(1)Mg6Zr6 cuboctahedra, corners with six equivalent O(5)Zr4 trigonal pyramids, and edges with three equivalent Mg(1)Mg6Zr6 cuboctahedra. is represented by the CIF file [CIF]
data_Mg2Zr14O5
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.240
_cell_length_b   3.240
_cell_length_c   54.259
_cell_angle_alpha   61.462
_cell_angle_beta   61.462
_cell_angle_gamma   60.000
_symmetry_Int_Tables_number   1
_cell_volume   411.495
_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
  Mg  Mg0  1  0.924  0.924  0.077  1.0
  Mg  Mg1  1  0.108  0.108  0.667  1.0
  Zr  Zr2  1  0.888  0.888  0.021  1.0
  Zr  Zr3  1  0.893  0.893  0.208  1.0
  Zr  Zr4  1  0.946  0.946  0.135  1.0
  Zr  Zr5  1  0.951  0.951  0.322  1.0
  Zr  Zr6  1  0.927  0.927  0.264  1.0
  Zr  Zr7  1  0.979  0.979  0.379  1.0
  Zr  Zr8  1  0.002  0.002  0.437  1.0
  Zr  Zr9  1  0.053  0.053  0.553  1.0
  Zr  Zr10  1  0.024  0.024  0.495  1.0
  Zr  Zr11  1  0.090  0.090  0.608  1.0
  Zr  Zr12  1  0.060  0.060  0.801  1.0
  Zr  Zr13  1  0.126  0.126  0.726  1.0
  Zr  Zr14  1  0.995  0.995  0.876  1.0
  Zr  Zr15  1  0.932  0.932  0.950  1.0
  O  O16  1  0.705  0.705  0.180  1.0
  O  O17  1  0.885  0.885  0.772  1.0
  O  O18  1  0.818  0.818  0.847  1.0
  O  O19  1  0.754  0.754  0.921  1.0
  O  O20  1  0.690  0.690  0.996  1.0
[/CIF]
.
The compound described by Mg2Zr14O5 crystallizes in the trigonal R3m space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent Mg(1), three equivalent Zr(1), and three equivalent Zr(3) atoms to form MgMg6Zr6 cuboctahedra that share corners with six equivalent Mg(1)Mg6Zr6 cuboctahedra, corners with three equivalent O(5)Zr4 trigonal pyramids, edges with six equivalent Mg(1)Mg6Zr6 cuboctahedra, edges with three equivalent O(5)Zr4 trigonal pyramids, and faces with six equivalent Mg(1)Mg6Zr6 cuboctahedra. In the second Mg site, Mg(2) is bonded to six equivalent Mg(2), three equivalent Zr(10), and three equivalent Zr(12) atoms to form MgMg6Zr6 cuboctahedra that share corners with three equivalent Zr(8)Zr12 cuboctahedra, corners with six equivalent Mg(2)Mg6Zr6 cuboctahedra, edges with three equivalent Zr(8)Zr12 cuboctahedra, edges with six equivalent Mg(2)Mg6Zr6 cuboctahedra, edges with six equivalent Zr(10)Mg3Zr9 cuboctahedra, faces with six equivalent Mg(2)Mg6Zr6 cuboctahedra, and faces with six equivalent Zr(10)Mg3Zr9 cuboctahedra. There are nineteen inequivalent Zr sites. In the first Zr site, Zr(1) is bonded in a 3-coordinate geometry to three equivalent Mg(1) and three equivalent O(5) atoms. In the second Zr site, Zr(2) is bonded in a distorted T-shaped geometry to three equivalent Zr(5) and three equivalent O(1) atoms. In the third Zr site, Zr(3) is bonded in a single-bond geometry to three equivalent Mg(1) and one O(1) atom. In the fourth Zr site, Zr(4) is bonded to three equivalent Zr(5), three equivalent Zr(6), and six equivalent Zr(4) atoms to form a mixture of edge, corner, and face-sharing ZrZr12 cuboctahedra. In the fifth Zr site, Zr(5) is bonded to three equivalent Zr(2), three equivalent Zr(4), and six equivalent Zr(5) atoms to form a mixture of edge, corner, and face-sharing ZrZr12 cuboctahedra. In the sixth Zr site, Zr(6) is bonded to three equivalent Zr(4), three equivalent Zr(7), and six equivalent Zr(6) atoms to form a mixture of edge, corner, and face-sharing ZrZr12 cuboctahedra. In the seventh Zr site, Zr(7) is bonded to three equivalent Zr(6), three equivalent Zr(9), and six equivalent Zr(7) atoms to form a mixture of edge, corner, and face-sharing ZrZr12 cuboctahedra. In the eighth Zr site, Zr(8) is bonded to three equivalent Zr(10), three equivalent Zr(9), and six equivalent Zr(8) atoms to form ZrZr12 cuboctahedra that share corners with three equivalent Mg(2)Mg6Zr6 cuboctahedra, corners with three equivalent Zr(7)Zr12 cuboctahedra, corners with six equivalent Zr(8)Zr12 cuboctahedra, edges with three equivalent Mg(2)Mg6Zr6 cuboctahedra, edges with three equivalent Zr(7)Zr12 cuboctahedra, edges with six equivalent Zr(10)Mg3Zr9 cuboctahedra, edges with six equivalent Zr(8)Zr12 cuboctahedra, edges with six equivalent Zr(9)Zr12 cuboctahedra, faces with six equivalent Zr(10)Mg3Zr9 cuboctahedra, faces with six equivalent Zr(8)Zr12 cuboctahedra, and faces with six equivalent Zr(9)Zr12 cuboctahedra. In the ninth Zr site, Zr(9) is bonded to three equivalent Zr(7), three equivalent Zr(8), and six equivalent Zr(9) atoms to form ZrZr12 cuboctahedra that share corners with three equivalent Zr(10)Mg3Zr9 cuboctahedra, corners with three equivalent Zr(6)Zr12 cuboctahedra, corners with six equivalent Zr(9)Zr12 cuboctahedra, edges with three equivalent Zr(10)Mg3Zr9 cuboctahedra, edges with three equivalent Zr(6)Zr12 cuboctahedra, edges with six equivalent Zr(7)Zr12 cuboctahedra, edges with six equivalent Zr(8)Zr12 cuboctahedra, edges with six equivalent Zr(9)Zr12 cuboctahedra, faces with six equivalent Zr(7)Zr12 cuboctahedra, faces with six equivalent Zr(8)Zr12 cuboctahedra, and faces with six equivalent Zr(9)Zr12 cuboctahedra. In the tenth Zr site, Zr(10) is bonded to three equivalent Mg(2), three equivalent Zr(8), and six equivalent Zr(10) atoms to form ZrMg3Zr9 cuboctahedra that share corners with three equivalent Zr(9)Zr12 cuboctahedra, corners with six equivalent Zr(10)Mg3Zr9 cuboctahedra, edges with three equivalent Zr(9)Zr12 cuboctahedra, edges with six equivalent Mg(2)Mg6Zr6 cuboctahedra, edges with six equivalent Zr(10)Mg3Zr9 cuboctahedra, edges with six equivalent Zr(8)Zr12 cuboctahedra, faces with six equivalent Mg(2)Mg6Zr6 cuboctahedra, faces with six equivalent Zr(10)Mg3Zr9 cuboctahedra, and faces with six equivalent Zr(8)Zr12 cuboctahedra. In the eleventh Zr site, Zr(11) is bonded in a rectangular see-saw-like geometry to one O(3) and three equivalent O(2) atoms. In the twelfth Zr site, Zr(12) is bonded in a single-bond geometry to three equivalent Mg(2) and one O(2) atom. In the thirteenth Zr site, Zr(13) is bonded in a rectangular see-saw-like geometry to one O(4) and three equivalent O(3) atoms. In the fourteenth Zr site, Zr(14) is bonded in a distorted rectangular see-saw-like geometry to one O(5) and three equivalent O(4) atoms. In the fifteenth Zr site, Zr(8) is bonded to three equivalent Zr(10), three equivalent Zr(9), and six equivalent Zr(8) atoms to form ZrZr12 cuboctahedra that share corners with three equivalent Mg(2)Mg6Zr6 cuboctahedra, corners with three equivalent Zr(7)Zr12 cuboctahedra, corners with six equivalent Zr(8)Zr12 cuboctahedra, edges with three equivalent Mg(2)Mg6Zr6 cuboctahedra, edges with three equivalent Zr(7)Zr12 cuboctahedra, edges with six equivalent Zr(10)Mg3Zr9 cuboctahedra, edges with six equivalent Zr(8)Zr12 cuboctahedra, edges with six equivalent Zr(9)Zr12 cuboctahedra, faces with six equivalent Zr(10)Mg3Zr9 cuboctahedra, faces with six equivalent Zr(8)Zr12 cuboctahedra, and faces with six equivalent Zr(9)Zr12 cuboctahedra. In the sixteenth Zr site, Zr(4) is bonded to three equivalent Zr(5), three equivalent Zr(6), and six equivalent Zr(4) atoms to form a mixture of edge, corner, and face-sharing ZrZr12 cuboctahedra. In the seventeenth Zr site, Zr(6) is bonded to three equivalent Zr(4), three equivalent Zr(7), and six equivalent Zr(6) atoms to form a mixture of edge, corner, and face-sharing ZrZr12 cuboctahedra. In the eighteenth Zr site, Zr(8) is bonded to three equivalent Zr(10), three equivalent Zr(9), and six equivalent Zr(8) atoms to form ZrZr12 cuboctahedra that share corners with three equivalent Mg(2)Mg6Zr6 cuboctahedra, corners with three equivalent Zr(7)Zr12 cuboctahedra, corners with six equivalent Zr(8)Zr12 cuboctahedra, edges with three equivalent Mg(2)Mg6Zr6 cuboctahedra, edges with three equivalent Zr(7)Zr12 cuboctahedra, edges with six equivalent Zr(10)Mg3Zr9 cuboctahedra, edges with six equivalent Zr(8)Zr12 cuboctahedra, edges with six equivalent Zr(9)Zr12 cuboctahedra, faces with six equivalent Zr(10)Mg3Zr9 cuboctahedra, faces with six equivalent Zr(8)Zr12 cuboctahedra, and faces with six equivalent Zr(9)Zr12 cuboctahedra. In the nineteenth Zr site, Zr(9) is bonded to three equivalent Zr(7), three equivalent Zr(8), and six equivalent Zr(9) atoms to form ZrZr12 cuboctahedra that share corners with three equivalent Zr(10)Mg3Zr9 cuboctahedra, corners with three equivalent Zr(6)Zr12 cuboctahedra, corners with six equivalent Zr(9)Zr12 cuboctahedra, edges with three equivalent Zr(10)Mg3Zr9 cuboctahedra, edges with three equivalent Zr(6)Zr12 cuboctahedra, edges with six equivalent Zr(7)Zr12 cuboctahedra, edges with six equivalent Zr(8)Zr12 cuboctahedra, edges with six equivalent Zr(9)Zr12 cuboctahedra, faces with six equivalent Zr(7)Zr12 cuboctahedra, faces with six equivalent Zr(8)Zr12 cuboctahedra, and faces with six equivalent Zr(9)Zr12 cuboctahedra. There are five inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Zr(3) and three equivalent Zr(2) atoms. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Zr(12) and three equivalent Zr(11) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Zr(11) and three equivalent Zr(13) atoms. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Zr(13) and three equivalent Zr(14) atoms. In the fifth O site, O(5) is bonded to one Zr(14) and three equivalent Zr(1) atoms to form distorted OZr4 trigonal pyramids that share corners with three equivalent Mg(1)Mg6Zr6 cuboctahedra, corners with six equivalent O(5)Zr4 trigonal pyramids, and edges with three equivalent Mg(1)Mg6Zr6 cuboctahedra. is represented by the CIF file [CIF]
data_Mg2Zr14O5
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.240
_cell_length_b   3.240
_cell_length_c   54.259
_cell_angle_alpha   61.462
_cell_angle_beta   61.462
_cell_angle_gamma   60.000
_symmetry_Int_Tables_number   1
_cell_volume   411.495
_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
  Mg  Mg0  1  0.924  0.924  0.077  1.0
  Mg  Mg1  1  0.108  0.108  0.667  1.0
  Zr  Zr2  1  0.888  0.888  0.021  1.0
  Zr  Zr3  1  0.893  0.893  0.208  1.0
  Zr  Zr4  1  0.946  0.946  0.135  1.0
  Zr  Zr5  1  0.951  0.951  0.322  1.0
  Zr  Zr6  1  0.927  0.927  0.264  1.0
  Zr  Zr7  1  0.979  0.979  0.379  1.0
  Zr  Zr8  1  0.002  0.002  0.437  1.0
  Zr  Zr9  1  0.053  0.053  0.553  1.0
  Zr  Zr10  1  0.024  0.024  0.495  1.0
  Zr  Zr11  1  0.090  0.090  0.608  1.0
  Zr  Zr12  1  0.060  0.060  0.801  1.0
  Zr  Zr13  1  0.126  0.126  0.726  1.0
  Zr  Zr14  1  0.995  0.995  0.876  1.0
  Zr  Zr15  1  0.932  0.932  0.950  1.0
  O  O16  1  0.705  0.705  0.180  1.0
  O  O17  1  0.885  0.885  0.772  1.0
  O  O18  1  0.818  0.818  0.847  1.0
  O  O19  1  0.754  0.754  0.921  1.0
  O  O20  1  0.690  0.690  0.996  1.0
[/CIF]
.