The crystal structure described by MgYb2Ti2O6 crystallizes in the trigonal R3 space group. Mg(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form distorted MgO6 octahedra that share corners with three equivalent Ti(2)O6 octahedra, corners with six equivalent Yb(1)O6 octahedra, edges with three equivalent Ti(1)O6 octahedra, and  a faceface with one Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 29-59°. There are two inequivalent Yb sites. In the first Yb site, Yb(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form YbO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with six equivalent Mg(1)O6 octahedra, edges with three equivalent Ti(2)O6 octahedra, and  a faceface with one Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 29-59°. In the second Yb site, Yb(2) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(2) atoms. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form TiO6 octahedra that share corners with three equivalent Yb(1)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, edges with three equivalent Mg(1)O6 octahedra,  a faceface with one Yb(1)O6 octahedra, and  a faceface with one Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 31-47°. In the second Ti site, Ti(2) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form TiO6 octahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra, edges with three equivalent Yb(1)O6 octahedra,  a faceface with one Mg(1)O6 octahedra, and  a faceface with one Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 31-48°. There are two inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to one Mg(1), one Yb(1), one Yb(2), one Ti(1), and one Ti(2) atom. In the second O site, O(2) is bonded to one Mg(1), one Yb(1), one Yb(2), one Ti(1), and one Ti(2) atom to form a mixture of distorted edge and corner-sharing OYb2MgTi2 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Yb2MgTi2O6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.937
_cell_length_b   5.941
_cell_length_c   5.943
_cell_angle_alpha   54.675
_cell_angle_beta   54.716
_cell_angle_gamma   54.706
_symmetry_Int_Tables_number   1
_cell_volume   129.908
_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
  Yb  Yb0  1  0.333  0.333  0.332  1.0
  Yb  Yb1  1  0.531  0.531  0.531  1.0
  Mg  Mg2  1  0.804  0.805  0.803  1.0
  Ti  Ti3  1  0.150  0.151  0.150  1.0
  Ti  Ti4  1  0.989  0.989  0.988  1.0
  O  O5  1  0.078  0.775  0.381  1.0
  O  O6  1  0.382  0.079  0.774  1.0
  O  O7  1  0.775  0.383  0.076  1.0
  O  O8  1  0.165  0.582  0.959  1.0
  O  O9  1  0.582  0.959  0.164  1.0
  O  O10  1  0.959  0.164  0.581  1.0
[/CIF]
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The crystal structure described by MgYb2Ti2O6 crystallizes in the trigonal R3 space group. Mg(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form distorted MgO6 octahedra that share corners with three equivalent Ti(2)O6 octahedra, corners with six equivalent Yb(1)O6 octahedra, edges with three equivalent Ti(1)O6 octahedra, and  a faceface with one Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 29-59°. There are two inequivalent Yb sites. In the first Yb site, Yb(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form YbO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with six equivalent Mg(1)O6 octahedra, edges with three equivalent Ti(2)O6 octahedra, and  a faceface with one Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 29-59°. In the second Yb site, Yb(2) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(2) atoms. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form TiO6 octahedra that share corners with three equivalent Yb(1)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, edges with three equivalent Mg(1)O6 octahedra,  a faceface with one Yb(1)O6 octahedra, and  a faceface with one Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 31-47°. In the second Ti site, Ti(2) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form TiO6 octahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra, edges with three equivalent Yb(1)O6 octahedra,  a faceface with one Mg(1)O6 octahedra, and  a faceface with one Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 31-48°. There are two inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to one Mg(1), one Yb(1), one Yb(2), one Ti(1), and one Ti(2) atom. In the second O site, O(2) is bonded to one Mg(1), one Yb(1), one Yb(2), one Ti(1), and one Ti(2) atom to form a mixture of distorted edge and corner-sharing OYb2MgTi2 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Yb2MgTi2O6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.937
_cell_length_b   5.941
_cell_length_c   5.943
_cell_angle_alpha   54.675
_cell_angle_beta   54.716
_cell_angle_gamma   54.706
_symmetry_Int_Tables_number   1
_cell_volume   129.908
_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
  Yb  Yb0  1  0.333  0.333  0.332  1.0
  Yb  Yb1  1  0.531  0.531  0.531  1.0
  Mg  Mg2  1  0.804  0.805  0.803  1.0
  Ti  Ti3  1  0.150  0.151  0.150  1.0
  Ti  Ti4  1  0.989  0.989  0.988  1.0
  O  O5  1  0.078  0.775  0.381  1.0
  O  O6  1  0.382  0.079  0.774  1.0
  O  O7  1  0.775  0.383  0.076  1.0
  O  O8  1  0.165  0.582  0.959  1.0
  O  O9  1  0.582  0.959  0.164  1.0
  O  O10  1  0.959  0.164  0.581  1.0
[/CIF]
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