The structure described by Li4Mg crystallizes in the trigonal R-3m space group. There are six inequivalent Li sites. In the first Li site, Li(1) is bonded to three equivalent Li(2), six equivalent Li(1), and three equivalent Mg(1) atoms to form LiLi9Mg3 cuboctahedra that share corners with three equivalent Li(2)Li12 cuboctahedra; corners with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with six equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine Li(2,2)Li12 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; faces with six equivalent Li(2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with six equivalent Mg(1)Li6Mg6 cuboctahedra. In the second Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. In the third Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. In the fourth Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. In the fifth Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. In the sixth Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. Mg(1) is bonded to six equivalent Li(1) and six equivalent Mg(1) atoms to form MgLi6Mg6 cuboctahedra that share corners with six Li(2,2)Li12 cuboctahedra; corners with six equivalent Mg(1)Li6Mg6 cuboctahedra; edges with six Li(2,2)Li12 cuboctahedra; edges with six equivalent Mg(1)Li6Mg6 cuboctahedra; edges with twelve equivalent Li(1)Li9Mg3 cuboctahedra; faces with six equivalent Mg(1)Li6Mg6 cuboctahedra; and faces with twelve equivalent Li(1)Li9Mg3 cuboctahedra. is represented by the CIF file [CIF]
data_Li4Mg
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   12.884
_cell_length_b   12.884
_cell_length_c   12.884
_cell_angle_alpha   13.674
_cell_angle_beta   13.674
_cell_angle_gamma   13.674
_symmetry_Int_Tables_number   1
_cell_volume   103.989
_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  0.600  0.600  0.600  1.0
  Li  Li1  1  0.200  0.200  0.200  1.0
  Li  Li2  1  0.800  0.800  0.800  1.0
  Li  Li3  1  0.400  0.400  0.400  1.0
  Mg  Mg4  1  0.000  0.000  0.000  1.0
[/CIF]
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The structure described by Li4Mg crystallizes in the trigonal R-3m space group. There are six inequivalent Li sites. In the first Li site, Li(1) is bonded to three equivalent Li(2), six equivalent Li(1), and three equivalent Mg(1) atoms to form LiLi9Mg3 cuboctahedra that share corners with three equivalent Li(2)Li12 cuboctahedra; corners with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with six equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine Li(2,2)Li12 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; faces with six equivalent Li(2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with six equivalent Mg(1)Li6Mg6 cuboctahedra. In the second Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. In the third Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. In the fourth Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. In the fifth Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. In the sixth Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. Mg(1) is bonded to six equivalent Li(1) and six equivalent Mg(1) atoms to form MgLi6Mg6 cuboctahedra that share corners with six Li(2,2)Li12 cuboctahedra; corners with six equivalent Mg(1)Li6Mg6 cuboctahedra; edges with six Li(2,2)Li12 cuboctahedra; edges with six equivalent Mg(1)Li6Mg6 cuboctahedra; edges with twelve equivalent Li(1)Li9Mg3 cuboctahedra; faces with six equivalent Mg(1)Li6Mg6 cuboctahedra; and faces with twelve equivalent Li(1)Li9Mg3 cuboctahedra. is represented by the CIF file [CIF]
data_Li4Mg
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   12.884
_cell_length_b   12.884
_cell_length_c   12.884
_cell_angle_alpha   13.674
_cell_angle_beta   13.674
_cell_angle_gamma   13.674
_symmetry_Int_Tables_number   1
_cell_volume   103.989
_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  0.600  0.600  0.600  1.0
  Li  Li1  1  0.200  0.200  0.200  1.0
  Li  Li2  1  0.800  0.800  0.800  1.0
  Li  Li3  1  0.400  0.400  0.400  1.0
  Mg  Mg4  1  0.000  0.000  0.000  1.0
[/CIF]
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