The compound described by Ba4Mg(RhO3)4 crystallizes in the trigonal P3m1 space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(3), three equivalent O(4), and six equivalent O(1) atoms to form distorted BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra,  a faceface with one Rh(2)O6 octahedra,  a faceface with one Rh(3)O6 octahedra, faces with three equivalent Rh(1)O6 octahedra, and faces with three equivalent Rh(4)O6 octahedra. In the second Ba site, Ba(2) is bonded in a 10-coordinate geometry to one Mg(1), three equivalent O(3), and six equivalent O(2) atoms. In the third Ba site, Ba(3) is bonded in a distorted q6 geometry to three equivalent O(1) and six equivalent O(3) atoms. In the fourth Ba site, Ba(4) is bonded in a distorted q6 geometry to three equivalent O(1) and six equivalent O(4) atoms. Mg(1) is bonded in a 3-coordinate geometry to one Ba(2) and three equivalent O(4) atoms. There are four inequivalent Rh sites. In the first Rh site, Rh(1) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form distorted RhO6 octahedra that share corners with three equivalent Rh(3)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and  a faceface with one Rh(4)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. In the second Rh site, Rh(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form RhO6 octahedra that share corners with three equivalent Rh(4)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Rh(3)O6 octahedra. The corner-sharing octahedral tilt angles are 10°. In the third Rh site, Rh(3) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form RhO6 octahedra that share corners with three equivalent Rh(1)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Rh(2)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. In the fourth Rh site, Rh(4) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form RhO6 octahedra that share corners with three equivalent Rh(2)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and  a faceface with one Rh(1)O6 octahedra. The corner-sharing octahedral tilt angles are 10°. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Ba(3), one Ba(4), two equivalent Ba(1), one Rh(1), and one Rh(4) atom to form a mixture of distorted corner, edge, and face-sharing OBa4Rh2 octahedra. The corner-sharing octahedral tilt angles range from 6-62°. In the second O site, O(2) is bonded in a distorted L-shaped geometry to two equivalent Ba(2), one Rh(2), and one Rh(3) atom. In the third O site, O(3) is bonded to one Ba(1), one Ba(2), two equivalent Ba(3), one Rh(2), and one Rh(4) atom to form a mixture of distorted corner, edge, and face-sharing OBa4Rh2 octahedra. The corner-sharing octahedral tilt angles range from 10-62°. In the fourth O site, O(4) is bonded in a 6-coordinate geometry to one Ba(1), two equivalent Ba(4), one Mg(1), one Rh(1), and one Rh(3) atom. is represented by the CIF card [CIF]
data_Ba4Mg(RhO3)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.772
_cell_length_b   5.772
_cell_length_c   10.842
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   312.851
_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  0.667  0.333  0.735  1.0
  Ba  Ba1  1  0.333  0.667  0.333  1.0
  Ba  Ba2  1  0.000  0.000  0.539  1.0
  Ba  Ba3  1  0.000  0.000  0.959  1.0
  Mg  Mg4  1  0.333  0.667  0.083  1.0
  Rh  Rh5  1  0.333  0.667  0.860  1.0
  Rh  Rh6  1  0.667  0.333  0.377  1.0
  Rh  Rh7  1  0.667  0.333  0.115  1.0
  Rh  Rh8  1  0.333  0.667  0.609  1.0
  O  O9  1  0.182  0.363  0.738  1.0
  O  O10  1  0.812  0.188  0.247  1.0
  O  O11  1  0.377  0.188  0.247  1.0
  O  O12  1  0.637  0.818  0.738  1.0
  O  O13  1  0.182  0.818  0.738  1.0
  O  O14  1  0.812  0.623  0.247  1.0
  O  O15  1  0.507  0.015  0.508  1.0
  O  O16  1  0.498  0.502  0.994  1.0
  O  O17  1  0.498  0.997  0.994  1.0
  O  O18  1  0.507  0.493  0.508  1.0
  O  O19  1  0.985  0.493  0.508  1.0
  O  O20  1  0.003  0.502  0.994  1.0
[/CIF]
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The compound described by Ba4Mg(RhO3)4 crystallizes in the trigonal P3m1 space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(3), three equivalent O(4), and six equivalent O(1) atoms to form distorted BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra,  a faceface with one Rh(2)O6 octahedra,  a faceface with one Rh(3)O6 octahedra, faces with three equivalent Rh(1)O6 octahedra, and faces with three equivalent Rh(4)O6 octahedra. In the second Ba site, Ba(2) is bonded in a 10-coordinate geometry to one Mg(1), three equivalent O(3), and six equivalent O(2) atoms. In the third Ba site, Ba(3) is bonded in a distorted q6 geometry to three equivalent O(1) and six equivalent O(3) atoms. In the fourth Ba site, Ba(4) is bonded in a distorted q6 geometry to three equivalent O(1) and six equivalent O(4) atoms. Mg(1) is bonded in a 3-coordinate geometry to one Ba(2) and three equivalent O(4) atoms. There are four inequivalent Rh sites. In the first Rh site, Rh(1) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form distorted RhO6 octahedra that share corners with three equivalent Rh(3)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and  a faceface with one Rh(4)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. In the second Rh site, Rh(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form RhO6 octahedra that share corners with three equivalent Rh(4)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Rh(3)O6 octahedra. The corner-sharing octahedral tilt angles are 10°. In the third Rh site, Rh(3) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form RhO6 octahedra that share corners with three equivalent Rh(1)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Rh(2)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. In the fourth Rh site, Rh(4) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form RhO6 octahedra that share corners with three equivalent Rh(2)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and  a faceface with one Rh(1)O6 octahedra. The corner-sharing octahedral tilt angles are 10°. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Ba(3), one Ba(4), two equivalent Ba(1), one Rh(1), and one Rh(4) atom to form a mixture of distorted corner, edge, and face-sharing OBa4Rh2 octahedra. The corner-sharing octahedral tilt angles range from 6-62°. In the second O site, O(2) is bonded in a distorted L-shaped geometry to two equivalent Ba(2), one Rh(2), and one Rh(3) atom. In the third O site, O(3) is bonded to one Ba(1), one Ba(2), two equivalent Ba(3), one Rh(2), and one Rh(4) atom to form a mixture of distorted corner, edge, and face-sharing OBa4Rh2 octahedra. The corner-sharing octahedral tilt angles range from 10-62°. In the fourth O site, O(4) is bonded in a 6-coordinate geometry to one Ba(1), two equivalent Ba(4), one Mg(1), one Rh(1), and one Rh(3) atom. is represented by the CIF card [CIF]
data_Ba4Mg(RhO3)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.772
_cell_length_b   5.772
_cell_length_c   10.842
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   312.851
_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  0.667  0.333  0.735  1.0
  Ba  Ba1  1  0.333  0.667  0.333  1.0
  Ba  Ba2  1  0.000  0.000  0.539  1.0
  Ba  Ba3  1  0.000  0.000  0.959  1.0
  Mg  Mg4  1  0.333  0.667  0.083  1.0
  Rh  Rh5  1  0.333  0.667  0.860  1.0
  Rh  Rh6  1  0.667  0.333  0.377  1.0
  Rh  Rh7  1  0.667  0.333  0.115  1.0
  Rh  Rh8  1  0.333  0.667  0.609  1.0
  O  O9  1  0.182  0.363  0.738  1.0
  O  O10  1  0.812  0.188  0.247  1.0
  O  O11  1  0.377  0.188  0.247  1.0
  O  O12  1  0.637  0.818  0.738  1.0
  O  O13  1  0.182  0.818  0.738  1.0
  O  O14  1  0.812  0.623  0.247  1.0
  O  O15  1  0.507  0.015  0.508  1.0
  O  O16  1  0.498  0.502  0.994  1.0
  O  O17  1  0.498  0.997  0.994  1.0
  O  O18  1  0.507  0.493  0.508  1.0
  O  O19  1  0.985  0.493  0.508  1.0
  O  O20  1  0.003  0.502  0.994  1.0
[/CIF]
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