The crystal structure described by MgGd6WO12 crystallizes in the trigonal R3 space group. Mg(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form MgO6 octahedra that share  a faceface with one W(1)O6 octahedra. There are two inequivalent Gd sites. In the first Gd site, Gd(1) is bonded in a 7-coordinate geometry to one O(2), two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms. In the second Gd site, Gd(2) is bonded in a 7-coordinate geometry to one O(1), two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms. W(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form WO6 octahedra that share  a faceface with one Mg(1)O6 octahedra. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Gd(2), two equivalent Gd(1), and one W(1) atom to form distorted OGd3W trigonal pyramids that share corners with two equivalent O(3)Gd4Mg square pyramids, corners with six equivalent O(4)Gd4 tetrahedra, corners with four equivalent O(1)Gd3W trigonal pyramids, and edges with two equivalent O(3)Gd4Mg square pyramids. In the second O site, O(2) is bonded in a 5-coordinate geometry to one Mg(1), one Gd(1), two equivalent Gd(2), and one W(1) atom. In the third O site, O(3) is bonded to one Mg(1), two equivalent Gd(1), and two equivalent Gd(2) atoms to form distorted OGd4Mg square pyramids that share corners with two equivalent O(3)Gd4Mg square pyramids, corners with two equivalent O(4)Gd4 tetrahedra, corners with two equivalent O(1)Gd3W trigonal pyramids, edges with two equivalent O(3)Gd4Mg square pyramids, edges with three equivalent O(4)Gd4 tetrahedra, and edges with two equivalent O(1)Gd3W trigonal pyramids. In the fourth O site, O(4) is bonded to two equivalent Gd(1) and two equivalent Gd(2) atoms to form OGd4 tetrahedra that share corners with two equivalent O(3)Gd4Mg square pyramids, corners with four equivalent O(4)Gd4 tetrahedra, corners with six equivalent O(1)Gd3W trigonal pyramids, and edges with three equivalent O(3)Gd4Mg square pyramids. is represented by the CIF file [CIF]
data_Gd6MgWO12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.643
_cell_length_b   6.643
_cell_length_c   6.643
_cell_angle_alpha   99.486
_cell_angle_beta   99.486
_cell_angle_gamma   99.486
_symmetry_Int_Tables_number   1
_cell_volume   279.555
_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
  Gd  Gd0  1  0.396  0.860  0.674  1.0
  Gd  Gd1  1  0.300  0.653  0.133  1.0
  Gd  Gd2  1  0.133  0.300  0.653  1.0
  Gd  Gd3  1  0.860  0.674  0.396  1.0
  Gd  Gd4  1  0.674  0.396  0.860  1.0
  Gd  Gd5  1  0.653  0.133  0.300  1.0
  Mg  Mg6  1  0.271  0.271  0.271  1.0
  W  W7  1  0.984  0.984  0.984  1.0
  O  O8  1  0.052  0.921  0.687  1.0
  O  O9  1  0.304  0.985  0.090  1.0
  O  O10  1  0.190  0.555  0.418  1.0
  O  O11  1  0.580  0.829  0.408  1.0
  O  O12  1  0.090  0.304  0.985  1.0
  O  O13  1  0.408  0.580  0.829  1.0
  O  O14  1  0.555  0.418  0.190  1.0
  O  O15  1  0.921  0.687  0.052  1.0
  O  O16  1  0.418  0.190  0.555  1.0
  O  O17  1  0.829  0.408  0.580  1.0
  O  O18  1  0.687  0.052  0.921  1.0
  O  O19  1  0.985  0.090  0.304  1.0
[/CIF]
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The crystal structure described by MgGd6WO12 crystallizes in the trigonal R3 space group. Mg(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form MgO6 octahedra that share  a faceface with one W(1)O6 octahedra. There are two inequivalent Gd sites. In the first Gd site, Gd(1) is bonded in a 7-coordinate geometry to one O(2), two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms. In the second Gd site, Gd(2) is bonded in a 7-coordinate geometry to one O(1), two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms. W(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form WO6 octahedra that share  a faceface with one Mg(1)O6 octahedra. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Gd(2), two equivalent Gd(1), and one W(1) atom to form distorted OGd3W trigonal pyramids that share corners with two equivalent O(3)Gd4Mg square pyramids, corners with six equivalent O(4)Gd4 tetrahedra, corners with four equivalent O(1)Gd3W trigonal pyramids, and edges with two equivalent O(3)Gd4Mg square pyramids. In the second O site, O(2) is bonded in a 5-coordinate geometry to one Mg(1), one Gd(1), two equivalent Gd(2), and one W(1) atom. In the third O site, O(3) is bonded to one Mg(1), two equivalent Gd(1), and two equivalent Gd(2) atoms to form distorted OGd4Mg square pyramids that share corners with two equivalent O(3)Gd4Mg square pyramids, corners with two equivalent O(4)Gd4 tetrahedra, corners with two equivalent O(1)Gd3W trigonal pyramids, edges with two equivalent O(3)Gd4Mg square pyramids, edges with three equivalent O(4)Gd4 tetrahedra, and edges with two equivalent O(1)Gd3W trigonal pyramids. In the fourth O site, O(4) is bonded to two equivalent Gd(1) and two equivalent Gd(2) atoms to form OGd4 tetrahedra that share corners with two equivalent O(3)Gd4Mg square pyramids, corners with four equivalent O(4)Gd4 tetrahedra, corners with six equivalent O(1)Gd3W trigonal pyramids, and edges with three equivalent O(3)Gd4Mg square pyramids. is represented by the CIF file [CIF]
data_Gd6MgWO12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.643
_cell_length_b   6.643
_cell_length_c   6.643
_cell_angle_alpha   99.486
_cell_angle_beta   99.486
_cell_angle_gamma   99.486
_symmetry_Int_Tables_number   1
_cell_volume   279.555
_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
  Gd  Gd0  1  0.396  0.860  0.674  1.0
  Gd  Gd1  1  0.300  0.653  0.133  1.0
  Gd  Gd2  1  0.133  0.300  0.653  1.0
  Gd  Gd3  1  0.860  0.674  0.396  1.0
  Gd  Gd4  1  0.674  0.396  0.860  1.0
  Gd  Gd5  1  0.653  0.133  0.300  1.0
  Mg  Mg6  1  0.271  0.271  0.271  1.0
  W  W7  1  0.984  0.984  0.984  1.0
  O  O8  1  0.052  0.921  0.687  1.0
  O  O9  1  0.304  0.985  0.090  1.0
  O  O10  1  0.190  0.555  0.418  1.0
  O  O11  1  0.580  0.829  0.408  1.0
  O  O12  1  0.090  0.304  0.985  1.0
  O  O13  1  0.408  0.580  0.829  1.0
  O  O14  1  0.555  0.418  0.190  1.0
  O  O15  1  0.921  0.687  0.052  1.0
  O  O16  1  0.418  0.190  0.555  1.0
  O  O17  1  0.829  0.408  0.580  1.0
  O  O18  1  0.687  0.052  0.921  1.0
  O  O19  1  0.985  0.090  0.304  1.0
[/CIF]
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