The material described by Mg6ZrBi crystallizes in the orthorhombic Amm2 space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 12-coordinate geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Zr(1)Mg10Bi2 cuboctahedra; corners with six equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with two equivalent Zr(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Bi(1)Mg10Zr2 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 Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. In the fourth 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 Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3,3,3); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with six equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; faces with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Zr(1)Mg10Bi2 cuboctahedra. In the sixth Mg site, Mg(1) is bonded in a 12-coordinate geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms. In the seventh 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 Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. In the eighth 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 Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. Zr(1) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3); and two equivalent Bi(1) atoms to form distorted ZrMg10Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zr2 cuboctahedra; corners with six equivalent Zr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Bi2 cuboctahedra. Bi(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3,3,3); and two equivalent Zr(1) atoms to form BiMg10Zr2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with six equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; faces with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Mg(2)Mg10Zr2 cuboctahedra. is represented by the CIF file [CIF]
data_Mg6ZrBi
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.131
_cell_length_b   6.438
_cell_length_c   6.438
_cell_angle_alpha   118.445
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   186.978
_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
  Bi  Bi0  1  0.500  0.332  0.668  1.0
  Mg  Mg1  1  1.000  0.680  0.840  1.0
  Mg  Mg2  1  1.000  0.160  0.320  1.0
  Mg  Mg3  1  0.000  0.664  0.336  1.0
  Mg  Mg4  1  0.500  0.831  0.665  1.0
  Mg  Mg5  1  0.500  0.335  0.169  1.0
  Mg  Mg6  1  0.500  0.834  0.166  1.0
  Zr  Zr7  1  0.000  0.164  0.836  1.0
[/CIF]
.
The material described by Mg6ZrBi crystallizes in the orthorhombic Amm2 space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 12-coordinate geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Zr(1)Mg10Bi2 cuboctahedra; corners with six equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with two equivalent Zr(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Bi(1)Mg10Zr2 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 Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. In the fourth 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 Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3,3,3); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with six equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; faces with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Zr(1)Mg10Bi2 cuboctahedra. In the sixth Mg site, Mg(1) is bonded in a 12-coordinate geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms. In the seventh 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 Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. In the eighth 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 Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. Zr(1) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3); and two equivalent Bi(1) atoms to form distorted ZrMg10Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zr2 cuboctahedra; corners with six equivalent Zr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Bi2 cuboctahedra. Bi(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3,3,3); and two equivalent Zr(1) atoms to form BiMg10Zr2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with six equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; faces with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Mg(2)Mg10Zr2 cuboctahedra. is represented by the CIF file [CIF]
data_Mg6ZrBi
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.131
_cell_length_b   6.438
_cell_length_c   6.438
_cell_angle_alpha   118.445
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   186.978
_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
  Bi  Bi0  1  0.500  0.332  0.668  1.0
  Mg  Mg1  1  1.000  0.680  0.840  1.0
  Mg  Mg2  1  1.000  0.160  0.320  1.0
  Mg  Mg3  1  0.000  0.664  0.336  1.0
  Mg  Mg4  1  0.500  0.831  0.665  1.0
  Mg  Mg5  1  0.500  0.335  0.169  1.0
  Mg  Mg6  1  0.500  0.834  0.166  1.0
  Zr  Zr7  1  0.000  0.164  0.836  1.0
[/CIF]
.