The compound described by Mg6CrMn is beta Cu3Ti-derived structured and 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 Mn(1) atoms to form distorted MgMg8Mn2Cr2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Mn2 cuboctahedra, corners with four equivalent Mn(1)Mg10Cr2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Mg(2)Mg10Mn2 cuboctahedra, edges with two equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Mn(1)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, edges with four equivalent Cr(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(2)Mg10Mn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, and faces with eight equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Mn(1) atoms to form MgMg10Mn2 cuboctahedra that share corners with four equivalent Mn(1)Mg10Cr2 cuboctahedra, corners with six equivalent Mg(2)Mg10Mn2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Mn(1)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(2)Mg10Mn2 cuboctahedra, faces with two equivalent Mn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, faces with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, and faces with six equivalent Cr(1)Mg10Mn2 cuboctahedra. In the third Mg site, Mg(3) 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 Mn(1) atoms to form distorted MgMg8Mn2Cr2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cr2 cuboctahedra, corners with four equivalent Cr(1)Mg10Mn2 cuboctahedra, corners with ten equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with two equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Cr(1)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(2)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, edges with four equivalent Mn(1)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(2)Mg10Mn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Cr(1) atoms to form MgMg10Cr2 cuboctahedra that share corners with four equivalent Cr(1)Mg10Mn2 cuboctahedra, corners with six equivalent Mg(4)Mg10Cr2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Cr(1)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(2)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(2)Mg10Mn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Mn2 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, faces with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, and faces with six equivalent Mn(1)Mg10Cr2 cuboctahedra. Cr(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Mn(1) atoms to form CrMg10Mn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cr2 cuboctahedra, corners with six equivalent Cr(1)Mg10Mn2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, edges with four equivalent Mn(1)Mg10Cr2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Cr(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, faces with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, and faces with six equivalent Mg(2)Mg10Mn2 cuboctahedra. Mn(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Cr(1) atoms to form MnMg10Cr2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Mn2 cuboctahedra, corners with six equivalent Mn(1)Mg10Cr2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Mg(2)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, edges with four equivalent Cr(1)Mg10Mn2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, faces with two equivalent Mg(2)Mg10Mn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, faces with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Cr2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg6MnCr
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.955
_cell_length_b   6.149
_cell_length_c   6.175
_cell_angle_alpha   119.865
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   163.153
_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  0.333  1.0
  Mg  Mg1  1  0.000  0.345  0.173  1.0
  Mg  Mg2  1  1.000  0.829  0.173  1.0
  Mg  Mg3  1  1.000  0.333  0.666  1.0
  Mg  Mg4  1  0.500  0.155  0.827  1.0
  Mg  Mg5  1  0.500  0.672  0.827  1.0
  Mg  Mg6  1  0.500  0.167  0.334  1.0
  Mn  Mn7  1  1.000  0.833  0.667  1.0
[/CIF]
.
The compound described by Mg6CrMn is beta Cu3Ti-derived structured and 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 Mn(1) atoms to form distorted MgMg8Mn2Cr2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Mn2 cuboctahedra, corners with four equivalent Mn(1)Mg10Cr2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Mg(2)Mg10Mn2 cuboctahedra, edges with two equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Mn(1)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, edges with four equivalent Cr(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(2)Mg10Mn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, and faces with eight equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Mn(1) atoms to form MgMg10Mn2 cuboctahedra that share corners with four equivalent Mn(1)Mg10Cr2 cuboctahedra, corners with six equivalent Mg(2)Mg10Mn2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Mn(1)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(2)Mg10Mn2 cuboctahedra, faces with two equivalent Mn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, faces with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, and faces with six equivalent Cr(1)Mg10Mn2 cuboctahedra. In the third Mg site, Mg(3) 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 Mn(1) atoms to form distorted MgMg8Mn2Cr2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cr2 cuboctahedra, corners with four equivalent Cr(1)Mg10Mn2 cuboctahedra, corners with ten equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with two equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Cr(1)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(2)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, edges with four equivalent Mn(1)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(2)Mg10Mn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Cr(1) atoms to form MgMg10Cr2 cuboctahedra that share corners with four equivalent Cr(1)Mg10Mn2 cuboctahedra, corners with six equivalent Mg(4)Mg10Cr2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Cr(1)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(2)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Mg(2)Mg10Mn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Mn2 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, faces with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, and faces with six equivalent Mn(1)Mg10Cr2 cuboctahedra. Cr(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Mn(1) atoms to form CrMg10Mn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cr2 cuboctahedra, corners with six equivalent Cr(1)Mg10Mn2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Mg(4)Mg10Cr2 cuboctahedra, edges with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, edges with four equivalent Mn(1)Mg10Cr2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cr2 cuboctahedra, faces with two equivalent Cr(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, faces with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, and faces with six equivalent Mg(2)Mg10Mn2 cuboctahedra. Mn(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Cr(1) atoms to form MnMg10Cr2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Mn2 cuboctahedra, corners with six equivalent Mn(1)Mg10Cr2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, edges with two equivalent Mg(2)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, edges with four equivalent Cr(1)Mg10Mn2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, faces with two equivalent Mg(2)Mg10Mn2 cuboctahedra, faces with two equivalent Cr(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mn(1)Mg10Cr2 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn2Cr2 cuboctahedra, faces with four equivalent Mg(3)Mg8Mn2Cr2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Cr2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg6MnCr
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.955
_cell_length_b   6.149
_cell_length_c   6.175
_cell_angle_alpha   119.865
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   163.153
_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  0.333  1.0
  Mg  Mg1  1  0.000  0.345  0.173  1.0
  Mg  Mg2  1  1.000  0.829  0.173  1.0
  Mg  Mg3  1  1.000  0.333  0.666  1.0
  Mg  Mg4  1  0.500  0.155  0.827  1.0
  Mg  Mg5  1  0.500  0.672  0.827  1.0
  Mg  Mg6  1  0.500  0.167  0.334  1.0
  Mn  Mn7  1  1.000  0.833  0.667  1.0
[/CIF]
.