The structure described by MgY2Cr3O9 crystallizes in the tetragonal P4/mmm space group. Mg(1) is bonded in a square co-planar geometry to four equivalent O(2) atoms. Y(1) is bonded to four equivalent O(1), four equivalent O(3), and four equivalent O(4) atoms to form distorted YO12 cuboctahedra that share corners with eight equivalent Y(1)O12 cuboctahedra, faces with five equivalent Y(1)O12 cuboctahedra, faces with four equivalent Cr(1)O6 octahedra, and faces with four equivalent Cr(2)O6 octahedra. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(1) and four equivalent O(3) atoms to form CrO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, and faces with eight equivalent Y(1)O12 cuboctahedra. The corner-sharing octahedra are not tilted. In the second Cr site, Cr(2) is bonded to one O(1), one O(2), and four equivalent O(4) atoms to form CrO6 octahedra that share  a cornercorner with one Cr(1)O6 octahedra, corners with five equivalent Cr(2)O6 octahedra, and faces with four equivalent Y(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-12°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to four equivalent Y(1), one Cr(1), and one Cr(2) atom. In the second O site, O(2) is bonded in a distorted linear geometry to four equivalent Mg(1) and two equivalent Cr(2) atoms. In the third O site, O(3) is bonded in a linear geometry to four equivalent Y(1) and two equivalent Cr(1) atoms. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to two equivalent Y(1) and two equivalent Cr(2) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Y2MgCr3O9
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.805
_cell_length_b   3.805
_cell_length_c   11.747
_cell_angle_alpha   90.002
_cell_angle_beta   89.994
_cell_angle_gamma   90.005
_symmetry_Int_Tables_number   1
_cell_volume   170.074
_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
  Y  Y0  1  1.000  0.000  0.982  1.0
  Y  Y1  1  0.000  1.000  0.351  1.0
  Mg  Mg2  1  1.000  0.000  0.667  1.0
  Cr  Cr3  1  0.500  0.500  0.167  1.0
  Cr  Cr4  1  0.500  0.500  0.502  1.0
  Cr  Cr5  1  0.500  0.500  0.832  1.0
  O  O6  1  0.500  0.500  0.002  1.0
  O  O7  1  0.500  0.500  0.331  1.0
  O  O8  1  0.500  0.500  0.667  1.0
  O  O9  1  0.500  0.000  0.167  1.0
  O  O10  1  0.500  1.000  0.485  1.0
  O  O11  1  0.500  0.000  0.848  1.0
  O  O12  1  1.000  0.500  0.167  1.0
  O  O13  1  1.000  0.500  0.485  1.0
  O  O14  1  0.000  0.500  0.848  1.0
[/CIF]
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The structure described by MgY2Cr3O9 crystallizes in the tetragonal P4/mmm space group. Mg(1) is bonded in a square co-planar geometry to four equivalent O(2) atoms. Y(1) is bonded to four equivalent O(1), four equivalent O(3), and four equivalent O(4) atoms to form distorted YO12 cuboctahedra that share corners with eight equivalent Y(1)O12 cuboctahedra, faces with five equivalent Y(1)O12 cuboctahedra, faces with four equivalent Cr(1)O6 octahedra, and faces with four equivalent Cr(2)O6 octahedra. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(1) and four equivalent O(3) atoms to form CrO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, and faces with eight equivalent Y(1)O12 cuboctahedra. The corner-sharing octahedra are not tilted. In the second Cr site, Cr(2) is bonded to one O(1), one O(2), and four equivalent O(4) atoms to form CrO6 octahedra that share  a cornercorner with one Cr(1)O6 octahedra, corners with five equivalent Cr(2)O6 octahedra, and faces with four equivalent Y(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-12°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to four equivalent Y(1), one Cr(1), and one Cr(2) atom. In the second O site, O(2) is bonded in a distorted linear geometry to four equivalent Mg(1) and two equivalent Cr(2) atoms. In the third O site, O(3) is bonded in a linear geometry to four equivalent Y(1) and two equivalent Cr(1) atoms. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to two equivalent Y(1) and two equivalent Cr(2) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Y2MgCr3O9
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.805
_cell_length_b   3.805
_cell_length_c   11.747
_cell_angle_alpha   90.002
_cell_angle_beta   89.994
_cell_angle_gamma   90.005
_symmetry_Int_Tables_number   1
_cell_volume   170.074
_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
  Y  Y0  1  1.000  0.000  0.982  1.0
  Y  Y1  1  0.000  1.000  0.351  1.0
  Mg  Mg2  1  1.000  0.000  0.667  1.0
  Cr  Cr3  1  0.500  0.500  0.167  1.0
  Cr  Cr4  1  0.500  0.500  0.502  1.0
  Cr  Cr5  1  0.500  0.500  0.832  1.0
  O  O6  1  0.500  0.500  0.002  1.0
  O  O7  1  0.500  0.500  0.331  1.0
  O  O8  1  0.500  0.500  0.667  1.0
  O  O9  1  0.500  0.000  0.167  1.0
  O  O10  1  0.500  1.000  0.485  1.0
  O  O11  1  0.500  0.000  0.848  1.0
  O  O12  1  1.000  0.500  0.167  1.0
  O  O13  1  1.000  0.500  0.485  1.0
  O  O14  1  0.000  0.500  0.848  1.0
[/CIF]
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