The structure described by LiMg6Fe is beta Cu3Ti-derived structured and crystallizes in the orthorhombic Amm2 space group. Li(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Fe(1) atoms to form LiMg10Fe2 cuboctahedra that share corners with four equivalent Mg(4)Li2Mg10 cuboctahedra, corners with six equivalent Li(1)Mg10Fe2 cuboctahedra, edges with two equivalent Mg(4)Li2Mg10 cuboctahedra, edges with four equivalent Fe(1)Li2Mg10 cuboctahedra, faces with two equivalent Li(1)Mg10Fe2 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Fe(1)Li2Mg10 cuboctahedra, and faces with six equivalent Mg(2)Mg10Fe2 cuboctahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 4-coordinate geometry to two equivalent Li(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Fe(1) atoms. 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 Fe(1) atoms to form MgMg10Fe2 cuboctahedra that share corners with four equivalent Fe(1)Li2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg10Fe2 cuboctahedra, edges with two equivalent Fe(1)Li2Mg10 cuboctahedra, edges with four equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Fe2 cuboctahedra, faces with two equivalent Fe(1)Li2Mg10 cuboctahedra, and faces with six equivalent Li(1)Mg10Fe2 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Li(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Fe(1) atoms. In the fourth Mg site, Mg(4) is bonded to two equivalent Li(1), two equivalent Mg(2), four equivalent Mg(1), and four equivalent Mg(3) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Li(1)Mg10Fe2 cuboctahedra, corners with six equivalent Mg(4)Li2Mg10 cuboctahedra, edges with two equivalent Li(1)Mg10Fe2 cuboctahedra, edges with four equivalent Mg(2)Mg10Fe2 cuboctahedra, faces with two equivalent Li(1)Mg10Fe2 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Fe2 cuboctahedra, and faces with six equivalent Fe(1)Li2Mg10 cuboctahedra. Fe(1) is bonded to two equivalent Li(1), two equivalent Mg(2), four equivalent Mg(1), and four equivalent Mg(3) atoms to form FeLi2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg10Fe2 cuboctahedra, corners with six equivalent Fe(1)Li2Mg10 cuboctahedra, edges with two equivalent Mg(2)Mg10Fe2 cuboctahedra, edges with four equivalent Li(1)Mg10Fe2 cuboctahedra, faces with two equivalent Li(1)Mg10Fe2 cuboctahedra, faces with two equivalent Mg(2)Mg10Fe2 cuboctahedra, faces with two equivalent Fe(1)Li2Mg10 cuboctahedra, and faces with six equivalent Mg(4)Li2Mg10 cuboctahedra. is represented by the CIF file [CIF]
data_LiMg6Fe
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.057
_cell_length_b   6.057
_cell_length_c   4.912
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   117.696
_symmetry_Int_Tables_number   1
_cell_volume   159.592
_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  0.667  0.333  0.500  1.0
  Mg  Mg1  1  0.833  0.653  0.000  1.0
  Mg  Mg2  1  0.347  0.167  0.000  1.0
  Mg  Mg3  1  0.338  0.662  0.000  1.0
  Mg  Mg4  1  0.670  0.862  0.500  1.0
  Mg  Mg5  1  0.138  0.330  0.500  1.0
  Mg  Mg6  1  0.160  0.840  0.500  1.0
  Fe  Fe7  1  0.845  0.155  0.000  1.0
[/CIF]
.
The structure described by LiMg6Fe is beta Cu3Ti-derived structured and crystallizes in the orthorhombic Amm2 space group. Li(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Fe(1) atoms to form LiMg10Fe2 cuboctahedra that share corners with four equivalent Mg(4)Li2Mg10 cuboctahedra, corners with six equivalent Li(1)Mg10Fe2 cuboctahedra, edges with two equivalent Mg(4)Li2Mg10 cuboctahedra, edges with four equivalent Fe(1)Li2Mg10 cuboctahedra, faces with two equivalent Li(1)Mg10Fe2 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Fe(1)Li2Mg10 cuboctahedra, and faces with six equivalent Mg(2)Mg10Fe2 cuboctahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 4-coordinate geometry to two equivalent Li(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Fe(1) atoms. 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 Fe(1) atoms to form MgMg10Fe2 cuboctahedra that share corners with four equivalent Fe(1)Li2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg10Fe2 cuboctahedra, edges with two equivalent Fe(1)Li2Mg10 cuboctahedra, edges with four equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Fe2 cuboctahedra, faces with two equivalent Fe(1)Li2Mg10 cuboctahedra, and faces with six equivalent Li(1)Mg10Fe2 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Li(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Fe(1) atoms. In the fourth Mg site, Mg(4) is bonded to two equivalent Li(1), two equivalent Mg(2), four equivalent Mg(1), and four equivalent Mg(3) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Li(1)Mg10Fe2 cuboctahedra, corners with six equivalent Mg(4)Li2Mg10 cuboctahedra, edges with two equivalent Li(1)Mg10Fe2 cuboctahedra, edges with four equivalent Mg(2)Mg10Fe2 cuboctahedra, faces with two equivalent Li(1)Mg10Fe2 cuboctahedra, faces with two equivalent Mg(4)Li2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Fe2 cuboctahedra, and faces with six equivalent Fe(1)Li2Mg10 cuboctahedra. Fe(1) is bonded to two equivalent Li(1), two equivalent Mg(2), four equivalent Mg(1), and four equivalent Mg(3) atoms to form FeLi2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg10Fe2 cuboctahedra, corners with six equivalent Fe(1)Li2Mg10 cuboctahedra, edges with two equivalent Mg(2)Mg10Fe2 cuboctahedra, edges with four equivalent Li(1)Mg10Fe2 cuboctahedra, faces with two equivalent Li(1)Mg10Fe2 cuboctahedra, faces with two equivalent Mg(2)Mg10Fe2 cuboctahedra, faces with two equivalent Fe(1)Li2Mg10 cuboctahedra, and faces with six equivalent Mg(4)Li2Mg10 cuboctahedra. is represented by the CIF file [CIF]
data_LiMg6Fe
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.057
_cell_length_b   6.057
_cell_length_c   4.912
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   117.696
_symmetry_Int_Tables_number   1
_cell_volume   159.592
_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  0.667  0.333  0.500  1.0
  Mg  Mg1  1  0.833  0.653  0.000  1.0
  Mg  Mg2  1  0.347  0.167  0.000  1.0
  Mg  Mg3  1  0.338  0.662  0.000  1.0
  Mg  Mg4  1  0.670  0.862  0.500  1.0
  Mg  Mg5  1  0.138  0.330  0.500  1.0
  Mg  Mg6  1  0.160  0.840  0.500  1.0
  Fe  Fe7  1  0.845  0.155  0.000  1.0
[/CIF]
.