The structure described by LiMg6Zr crystallizes in the orthorhombic Amm2 space group. Li(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Zr(1) atoms to form LiMg10Zr2 cuboctahedra that share corners with four equivalent Zr(1)Li2Mg10 cuboctahedra, corners with six equivalent Li(1)Mg10Zr2 cuboctahedra, corners with eight equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Zr(1)Li2Mg10 cuboctahedra, edges with four equivalent Mg(4)Li2Mg10 cuboctahedra, edges with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, edges with eight equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, faces with two equivalent Li(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Zr(1)Li2Mg10 cuboctahedra, faces with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Zr2 cuboctahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Li(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Zr(1) atoms to form distorted MgLi2Mg8Zr2 cuboctahedra that share corners with four equivalent Li(1)Mg10Zr2 cuboctahedra, corners with four equivalent Zr(1)Li2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Li(1)Mg10Zr2 cuboctahedra, edges with two equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Zr(1)Li2Mg10 cuboctahedra, edges with four equivalent Mg(4)Li2Mg10 cuboctahedra, edges with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent Li(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)Li2Mg10 cuboctahedra, faces with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, and faces with eight equivalent Mg(2)Li2Mg8Zr2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Li(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Zr(1) atoms to form distorted MgLi2Mg8Zr2 cuboctahedra that share corners with four equivalent Mg(4)Li2Mg10 cuboctahedra, corners with four equivalent Mg(3)Mg10Zr2 cuboctahedra, corners with ten equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(4)Li2Mg10 cuboctahedra, edges with two equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zr2 cuboctahedra, edges with four equivalent Li(1)Mg10Zr2 cuboctahedra, edges with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, edges with four equivalent Zr(1)Li2Mg10 cuboctahedra, faces with two equivalent Li(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)Li2Mg10 cuboctahedra, faces with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, and faces with eight equivalent Mg(1)Li2Mg8Zr2 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 Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Mg(4)Li2Mg10 cuboctahedra, corners with six equivalent Mg(3)Mg10Zr2 cuboctahedra, corners with eight equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(4)Li2Mg10 cuboctahedra, edges with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, edges with four equivalent Zr(1)Li2Mg10 cuboctahedra, edges with eight equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)Li2Mg10 cuboctahedra, faces with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, and faces with six equivalent Li(1)Mg10Zr2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Li(1), two equivalent Mg(3), four equivalent Mg(1), and four equivalent Mg(2) atoms to form distorted MgLi2Mg10 cuboctahedra that share corners with four equivalent Mg(3)Mg10Zr2 cuboctahedra, corners with six equivalent Mg(4)Li2Mg10 cuboctahedra, corners with eight equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zr2 cuboctahedra, edges with four equivalent Li(1)Mg10Zr2 cuboctahedra, edges with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, edges with eight equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, faces with two equivalent Li(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, and faces with six equivalent Zr(1)Li2Mg10 cuboctahedra. Zr(1) is bonded to two equivalent Li(1), two equivalent Mg(3), four equivalent Mg(1), and four equivalent Mg(2) atoms to form ZrLi2Mg10 cuboctahedra that share corners with four equivalent Li(1)Mg10Zr2 cuboctahedra, corners with six equivalent Zr(1)Li2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Li(1)Mg10Zr2 cuboctahedra, edges with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zr2 cuboctahedra, edges with eight equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, faces with two equivalent Li(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)Li2Mg10 cuboctahedra, faces with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, and faces with six equivalent Mg(4)Li2Mg10 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_LiMg6Zr
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.027
_cell_length_b   6.382
_cell_length_c   6.382
_cell_angle_alpha   119.156
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   178.842
_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
  Li  Li0  1  0.500  0.665  0.335  1.0
  Mg  Mg1  1  0.500  0.664  0.827  1.0
  Mg  Mg2  1  0.500  0.173  0.336  1.0
  Mg  Mg3  1  0.000  0.835  0.665  1.0
  Mg  Mg4  1  1.000  0.335  0.165  1.0
  Mg  Mg5  1  0.000  0.331  0.669  1.0
  Mg  Mg6  1  0.000  0.832  0.168  1.0
  Zr  Zr7  1  0.500  0.165  0.835  1.0
[/CIF]
.
The structure described by LiMg6Zr crystallizes in the orthorhombic Amm2 space group. Li(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Zr(1) atoms to form LiMg10Zr2 cuboctahedra that share corners with four equivalent Zr(1)Li2Mg10 cuboctahedra, corners with six equivalent Li(1)Mg10Zr2 cuboctahedra, corners with eight equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Zr(1)Li2Mg10 cuboctahedra, edges with four equivalent Mg(4)Li2Mg10 cuboctahedra, edges with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, edges with eight equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, faces with two equivalent Li(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Zr(1)Li2Mg10 cuboctahedra, faces with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Zr2 cuboctahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Li(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Zr(1) atoms to form distorted MgLi2Mg8Zr2 cuboctahedra that share corners with four equivalent Li(1)Mg10Zr2 cuboctahedra, corners with four equivalent Zr(1)Li2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Li(1)Mg10Zr2 cuboctahedra, edges with two equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Zr(1)Li2Mg10 cuboctahedra, edges with four equivalent Mg(4)Li2Mg10 cuboctahedra, edges with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent Li(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)Li2Mg10 cuboctahedra, faces with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, and faces with eight equivalent Mg(2)Li2Mg8Zr2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Li(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Zr(1) atoms to form distorted MgLi2Mg8Zr2 cuboctahedra that share corners with four equivalent Mg(4)Li2Mg10 cuboctahedra, corners with four equivalent Mg(3)Mg10Zr2 cuboctahedra, corners with ten equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(4)Li2Mg10 cuboctahedra, edges with two equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zr2 cuboctahedra, edges with four equivalent Li(1)Mg10Zr2 cuboctahedra, edges with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, edges with four equivalent Zr(1)Li2Mg10 cuboctahedra, faces with two equivalent Li(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)Li2Mg10 cuboctahedra, faces with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, and faces with eight equivalent Mg(1)Li2Mg8Zr2 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 Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Mg(4)Li2Mg10 cuboctahedra, corners with six equivalent Mg(3)Mg10Zr2 cuboctahedra, corners with eight equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(4)Li2Mg10 cuboctahedra, edges with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, edges with four equivalent Zr(1)Li2Mg10 cuboctahedra, edges with eight equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)Li2Mg10 cuboctahedra, faces with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, and faces with six equivalent Li(1)Mg10Zr2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Li(1), two equivalent Mg(3), four equivalent Mg(1), and four equivalent Mg(2) atoms to form distorted MgLi2Mg10 cuboctahedra that share corners with four equivalent Mg(3)Mg10Zr2 cuboctahedra, corners with six equivalent Mg(4)Li2Mg10 cuboctahedra, corners with eight equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zr2 cuboctahedra, edges with four equivalent Li(1)Mg10Zr2 cuboctahedra, edges with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, edges with eight equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, faces with two equivalent Li(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, and faces with six equivalent Zr(1)Li2Mg10 cuboctahedra. Zr(1) is bonded to two equivalent Li(1), two equivalent Mg(3), four equivalent Mg(1), and four equivalent Mg(2) atoms to form ZrLi2Mg10 cuboctahedra that share corners with four equivalent Li(1)Mg10Zr2 cuboctahedra, corners with six equivalent Zr(1)Li2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, edges with two equivalent Li(1)Mg10Zr2 cuboctahedra, edges with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zr2 cuboctahedra, edges with eight equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, faces with two equivalent Li(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)Li2Mg10 cuboctahedra, faces with four equivalent Mg(1)Li2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)Li2Mg8Zr2 cuboctahedra, and faces with six equivalent Mg(4)Li2Mg10 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_LiMg6Zr
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.027
_cell_length_b   6.382
_cell_length_c   6.382
_cell_angle_alpha   119.156
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   178.842
_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
  Li  Li0  1  0.500  0.665  0.335  1.0
  Mg  Mg1  1  0.500  0.664  0.827  1.0
  Mg  Mg2  1  0.500  0.173  0.336  1.0
  Mg  Mg3  1  0.000  0.835  0.665  1.0
  Mg  Mg4  1  1.000  0.335  0.165  1.0
  Mg  Mg5  1  0.000  0.331  0.669  1.0
  Mg  Mg6  1  0.000  0.832  0.168  1.0
  Zr  Zr7  1  0.500  0.165  0.835  1.0
[/CIF]
.