The material described by Mg5Sn crystallizes in the trigonal R32 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to four equivalent Mg(2), six equivalent Mg(1), and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with eighteen Mg(1,1,1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with eight equivalent Mg(2)Mg9Sn3 cuboctahedra; faces with four equivalent Sn(1)Mg12 cuboctahedra; faces with eight Mg(1,1)Mg10Sn2 cuboctahedra; and faces with eight equivalent Mg(2)Mg9Sn3 cuboctahedra. In the second Mg site, Mg(2) is bonded to three equivalent Mg(2); six Mg(1,1,1,1); and three equivalent Sn(1) atoms to form distorted MgMg9Sn3 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg9Sn3 cuboctahedra; edges with six equivalent Mg(2)Mg9Sn3 cuboctahedra; edges with twelve Mg(1,1,1,1)Mg10Sn2 cuboctahedra; faces with four equivalent Mg(2)Mg9Sn3 cuboctahedra; faces with four equivalent Sn(1)Mg12 cuboctahedra; and faces with twelve Mg(1,1,1,1)Mg10Sn2 cuboctahedra. In the third Mg site, Mg(1) is bonded to four equivalent Mg(2); six Mg(1,1); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with eighteen Mg(1,1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with eight equivalent Mg(2)Mg9Sn3 cuboctahedra; faces with four equivalent Sn(1)Mg12 cuboctahedra; faces with eight Mg(1,1,1,1)Mg10Sn2 cuboctahedra; and faces with eight equivalent Mg(2)Mg9Sn3 cuboctahedra. In the fourth Mg site, Mg(1) is bonded to four Mg(2,2); six Mg(1,1); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with eighteen Mg(1,1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with eight Mg(2,2)Mg9Sn3 cuboctahedra; faces with four equivalent Sn(1)Mg12 cuboctahedra; faces with eight Mg(1,1,1)Mg10Sn2 cuboctahedra; and faces with eight Mg(2,2)Mg9Sn3 cuboctahedra. In the fifth Mg site, Mg(1) is bonded to four Mg(2,2); six Mg(1,1); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with eighteen Mg(1,1,1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with eight Mg(2,2)Mg9Sn3 cuboctahedra; faces with four equivalent Sn(1)Mg12 cuboctahedra; faces with eight Mg(1,1,1)Mg10Sn2 cuboctahedra; and faces with eight Mg(2,2)Mg9Sn3 cuboctahedra. In the sixth Mg site, Mg(1) is bonded to four Mg(2,2); six Mg(1,1); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with eighteen Mg(1,1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with eight Mg(2,2)Mg9Sn3 cuboctahedra; faces with four equivalent Sn(1)Mg12 cuboctahedra; faces with eight Mg(1,1,1)Mg10Sn2 cuboctahedra; and faces with eight Mg(2,2)Mg9Sn3 cuboctahedra. In the seventh Mg site, Mg(2) is bonded to three equivalent Mg(2); six Mg(1,1,1,1); and three equivalent Sn(1) atoms to form distorted MgMg9Sn3 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg9Sn3 cuboctahedra; edges with six equivalent Mg(2)Mg9Sn3 cuboctahedra; edges with twelve Mg(1,1,1,1)Mg10Sn2 cuboctahedra; faces with four equivalent Mg(2)Mg9Sn3 cuboctahedra; faces with four equivalent Sn(1)Mg12 cuboctahedra; and faces with twelve Mg(1,1,1,1)Mg10Sn2 cuboctahedra. Sn(1) is bonded to six Mg(1,1,1,1) and six equivalent Mg(2) atoms to form SnMg12 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg9Sn3 cuboctahedra; edges with six equivalent Sn(1)Mg12 cuboctahedra; edges with twelve Mg(1,1,1,1)Mg10Sn2 cuboctahedra; faces with eight Mg(2,2)Mg9Sn3 cuboctahedra; and faces with twelve Mg(1,1,1,1)Mg10Sn2 cuboctahedra. is represented by the CIF card [CIF]
data_Mg5Sn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.081
_cell_length_b   6.081
_cell_length_c   6.081
_cell_angle_alpha   53.833
_cell_angle_beta   53.833
_cell_angle_gamma   53.833
_symmetry_Int_Tables_number   1
_cell_volume   136.058
_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
  Mg  Mg0  1  0.000  0.666  0.334  1.0
  Mg  Mg1  1  0.833  0.833  0.833  1.0
  Mg  Mg2  1  0.666  0.334  0.000  1.0
  Mg  Mg3  1  0.334  0.000  0.666  1.0
  Mg  Mg4  1  0.167  0.167  0.167  1.0
  Sn  Sn5  1  0.500  0.500  0.500  1.0
[/CIF]
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The material described by Mg5Sn crystallizes in the trigonal R32 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to four equivalent Mg(2), six equivalent Mg(1), and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with eighteen Mg(1,1,1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with eight equivalent Mg(2)Mg9Sn3 cuboctahedra; faces with four equivalent Sn(1)Mg12 cuboctahedra; faces with eight Mg(1,1)Mg10Sn2 cuboctahedra; and faces with eight equivalent Mg(2)Mg9Sn3 cuboctahedra. In the second Mg site, Mg(2) is bonded to three equivalent Mg(2); six Mg(1,1,1,1); and three equivalent Sn(1) atoms to form distorted MgMg9Sn3 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg9Sn3 cuboctahedra; edges with six equivalent Mg(2)Mg9Sn3 cuboctahedra; edges with twelve Mg(1,1,1,1)Mg10Sn2 cuboctahedra; faces with four equivalent Mg(2)Mg9Sn3 cuboctahedra; faces with four equivalent Sn(1)Mg12 cuboctahedra; and faces with twelve Mg(1,1,1,1)Mg10Sn2 cuboctahedra. In the third Mg site, Mg(1) is bonded to four equivalent Mg(2); six Mg(1,1); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with eighteen Mg(1,1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with eight equivalent Mg(2)Mg9Sn3 cuboctahedra; faces with four equivalent Sn(1)Mg12 cuboctahedra; faces with eight Mg(1,1,1,1)Mg10Sn2 cuboctahedra; and faces with eight equivalent Mg(2)Mg9Sn3 cuboctahedra. In the fourth Mg site, Mg(1) is bonded to four Mg(2,2); six Mg(1,1); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with eighteen Mg(1,1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with eight Mg(2,2)Mg9Sn3 cuboctahedra; faces with four equivalent Sn(1)Mg12 cuboctahedra; faces with eight Mg(1,1,1)Mg10Sn2 cuboctahedra; and faces with eight Mg(2,2)Mg9Sn3 cuboctahedra. In the fifth Mg site, Mg(1) is bonded to four Mg(2,2); six Mg(1,1); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with eighteen Mg(1,1,1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with eight Mg(2,2)Mg9Sn3 cuboctahedra; faces with four equivalent Sn(1)Mg12 cuboctahedra; faces with eight Mg(1,1,1)Mg10Sn2 cuboctahedra; and faces with eight Mg(2,2)Mg9Sn3 cuboctahedra. In the sixth Mg site, Mg(1) is bonded to four Mg(2,2); six Mg(1,1); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with eighteen Mg(1,1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with eight Mg(2,2)Mg9Sn3 cuboctahedra; faces with four equivalent Sn(1)Mg12 cuboctahedra; faces with eight Mg(1,1,1)Mg10Sn2 cuboctahedra; and faces with eight Mg(2,2)Mg9Sn3 cuboctahedra. In the seventh Mg site, Mg(2) is bonded to three equivalent Mg(2); six Mg(1,1,1,1); and three equivalent Sn(1) atoms to form distorted MgMg9Sn3 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg9Sn3 cuboctahedra; edges with six equivalent Mg(2)Mg9Sn3 cuboctahedra; edges with twelve Mg(1,1,1,1)Mg10Sn2 cuboctahedra; faces with four equivalent Mg(2)Mg9Sn3 cuboctahedra; faces with four equivalent Sn(1)Mg12 cuboctahedra; and faces with twelve Mg(1,1,1,1)Mg10Sn2 cuboctahedra. Sn(1) is bonded to six Mg(1,1,1,1) and six equivalent Mg(2) atoms to form SnMg12 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg9Sn3 cuboctahedra; edges with six equivalent Sn(1)Mg12 cuboctahedra; edges with twelve Mg(1,1,1,1)Mg10Sn2 cuboctahedra; faces with eight Mg(2,2)Mg9Sn3 cuboctahedra; and faces with twelve Mg(1,1,1,1)Mg10Sn2 cuboctahedra. is represented by the CIF card [CIF]
data_Mg5Sn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.081
_cell_length_b   6.081
_cell_length_c   6.081
_cell_angle_alpha   53.833
_cell_angle_beta   53.833
_cell_angle_gamma   53.833
_symmetry_Int_Tables_number   1
_cell_volume   136.058
_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
  Mg  Mg0  1  0.000  0.666  0.334  1.0
  Mg  Mg1  1  0.833  0.833  0.833  1.0
  Mg  Mg2  1  0.666  0.334  0.000  1.0
  Mg  Mg3  1  0.334  0.000  0.666  1.0
  Mg  Mg4  1  0.167  0.167  0.167  1.0
  Sn  Sn5  1  0.500  0.500  0.500  1.0
[/CIF]
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