The material described by Mg6CrZn crystallizes in the orthorhombic Amm2 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Cr(1), and two equivalent Zn(1) atoms to form MgMg8Zn2Cr2 cuboctahedra that share corners with four equivalent Cr(1)Mg10Zn2 cuboctahedra, corners with four equivalent Zn(1)Mg10Cr2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, edges with two equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, edges with two equivalent Cr(1)Mg10Zn2 cuboctahedra, edges with two equivalent Zn(1)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, and faces with eight equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Cr(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cr2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cr2 cuboctahedra, corners with four equivalent Mg(3)Mg10Zn2 cuboctahedra, corners with ten equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, edges with two equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zn2 cuboctahedra, edges with two equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, edges with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, edges with four equivalent Cr(1)Mg10Zn2 cuboctahedra, edges with four equivalent Zn(1)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Zn(1) atoms to form distorted MgMg10Zn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cr2 cuboctahedra, corners with six equivalent Mg(3)Mg10Zn2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, edges with two equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, edges with four equivalent Zn(1)Mg10Cr2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, faces with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, and faces with six equivalent Cr(1)Mg10Zn2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Cr(1) atoms to form distorted MgMg10Cr2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Zn2 cuboctahedra, corners with six equivalent Mg(4)Mg10Cr2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, edges with four equivalent Cr(1)Mg10Zn2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Zn2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, faces with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, and faces with six equivalent Zn(1)Mg10Cr2 cuboctahedra. Cr(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Zn(1) atoms to form CrMg10Zn2 cuboctahedra that share corners with four equivalent Zn(1)Mg10Cr2 cuboctahedra, corners with six equivalent Cr(1)Mg10Zn2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, edges with two equivalent Zn(1)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Cr(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, faces with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Zn2 cuboctahedra. Zn(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Cr(1) atoms to form ZnMg10Cr2 cuboctahedra that share corners with four equivalent Cr(1)Mg10Zn2 cuboctahedra, corners with six equivalent Zn(1)Mg10Cr2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, edges with two equivalent Cr(1)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, faces with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Cr2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg6ZnCr
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.966
_cell_length_b   6.168
_cell_length_c   6.189
_cell_angle_alpha   119.886
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   164.368
_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
  Cr  Cr0  1  0.500  0.667  0.335  1.0
  Mg  Mg1  1  0.500  0.669  0.834  1.0
  Mg  Mg2  1  0.500  0.165  0.834  1.0
  Mg  Mg3  1  1.000  0.835  0.173  1.0
  Mg  Mg4  1  0.000  0.338  0.173  1.0
  Mg  Mg5  1  0.000  0.331  0.661  1.0
  Mg  Mg6  1  0.000  0.829  0.659  1.0
  Zn  Zn7  1  0.500  0.166  0.332  1.0
[/CIF]
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The material described by Mg6CrZn crystallizes in the orthorhombic Amm2 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Cr(1), and two equivalent Zn(1) atoms to form MgMg8Zn2Cr2 cuboctahedra that share corners with four equivalent Cr(1)Mg10Zn2 cuboctahedra, corners with four equivalent Zn(1)Mg10Cr2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, edges with two equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, edges with two equivalent Cr(1)Mg10Zn2 cuboctahedra, edges with two equivalent Zn(1)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, and faces with eight equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Cr(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cr2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cr2 cuboctahedra, corners with four equivalent Mg(3)Mg10Zn2 cuboctahedra, corners with ten equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, edges with two equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zn2 cuboctahedra, edges with two equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, edges with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, edges with four equivalent Cr(1)Mg10Zn2 cuboctahedra, edges with four equivalent Zn(1)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Zn(1) atoms to form distorted MgMg10Zn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cr2 cuboctahedra, corners with six equivalent Mg(3)Mg10Zn2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, edges with two equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, edges with four equivalent Zn(1)Mg10Cr2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, faces with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, and faces with six equivalent Cr(1)Mg10Zn2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Cr(1) atoms to form distorted MgMg10Cr2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Zn2 cuboctahedra, corners with six equivalent Mg(4)Mg10Cr2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, edges with four equivalent Cr(1)Mg10Zn2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Zn2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, faces with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, and faces with six equivalent Zn(1)Mg10Cr2 cuboctahedra. Cr(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Zn(1) atoms to form CrMg10Zn2 cuboctahedra that share corners with four equivalent Zn(1)Mg10Cr2 cuboctahedra, corners with six equivalent Cr(1)Mg10Zn2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, edges with two equivalent Zn(1)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Cr(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, faces with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Zn2 cuboctahedra. Zn(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Cr(1) atoms to form ZnMg10Cr2 cuboctahedra that share corners with four equivalent Cr(1)Mg10Zn2 cuboctahedra, corners with six equivalent Zn(1)Mg10Cr2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, edges with two equivalent Cr(1)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cr2 cuboctahedra, faces with four equivalent Mg(2)Mg8Zn2Cr2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Cr2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg6ZnCr
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.966
_cell_length_b   6.168
_cell_length_c   6.189
_cell_angle_alpha   119.886
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   164.368
_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
  Cr  Cr0  1  0.500  0.667  0.335  1.0
  Mg  Mg1  1  0.500  0.669  0.834  1.0
  Mg  Mg2  1  0.500  0.165  0.834  1.0
  Mg  Mg3  1  1.000  0.835  0.173  1.0
  Mg  Mg4  1  0.000  0.338  0.173  1.0
  Mg  Mg5  1  0.000  0.331  0.661  1.0
  Mg  Mg6  1  0.000  0.829  0.659  1.0
  Zn  Zn7  1  0.500  0.166  0.332  1.0
[/CIF]
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