The crystal structure described by Mg4Sc is alpha La-derived structured and crystallizes in the trigonal R-3m space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent Mg(2), six equivalent Mg(1), and three equivalent Sc(1) atoms to form MgMg9Sc3 cuboctahedra that share corners with three equivalent Mg(2)Mg12 cuboctahedra; corners with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; edges with six equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with nine Mg(2,2)Mg12 cuboctahedra; edges with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; faces with six equivalent Mg(2)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg9Sc3 cuboctahedra; and faces with six equivalent Sc(1)Mg6Sc6 cuboctahedra. In the second Mg site, Mg(2) is bonded to three equivalent Mg(1) and nine Mg(2,2) atoms to form MgMg12 cuboctahedra that share corners with three equivalent Mg(1)Mg9Sc3 cuboctahedra; corners with three equivalent Sc(1)Mg6Sc6 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with three equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; edges with twelve Mg(2,2)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg9Sc3 cuboctahedra; and faces with twelve Mg(2,2)Mg12 cuboctahedra. In the third Mg site, Mg(2) is bonded to three equivalent Mg(1) and nine Mg(2,2) atoms to form MgMg12 cuboctahedra that share corners with three equivalent Mg(1)Mg9Sc3 cuboctahedra; corners with three equivalent Sc(1)Mg6Sc6 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with three equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; edges with twelve Mg(2,2)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg9Sc3 cuboctahedra; and faces with twelve Mg(2,2)Mg12 cuboctahedra. In the fourth Mg site, Mg(2) is bonded to three equivalent Mg(1) and nine Mg(2,2) atoms to form MgMg12 cuboctahedra that share corners with three equivalent Mg(1)Mg9Sc3 cuboctahedra; corners with three equivalent Sc(1)Mg6Sc6 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with three equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; edges with twelve Mg(2,2)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg9Sc3 cuboctahedra; and faces with twelve Mg(2,2)Mg12 cuboctahedra. In the fifth Mg site, Mg(2) is bonded to three equivalent Mg(1) and nine Mg(2,2) atoms to form MgMg12 cuboctahedra that share corners with three equivalent Mg(1)Mg9Sc3 cuboctahedra; corners with three equivalent Sc(1)Mg6Sc6 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with three equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; edges with twelve Mg(2,2)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg9Sc3 cuboctahedra; and faces with twelve Mg(2,2)Mg12 cuboctahedra. In the sixth Mg site, Mg(2) is bonded to three equivalent Mg(1) and nine Mg(2,2) atoms to form MgMg12 cuboctahedra that share corners with three equivalent Mg(1)Mg9Sc3 cuboctahedra; corners with three equivalent Sc(1)Mg6Sc6 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with three equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; edges with twelve Mg(2,2)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg9Sc3 cuboctahedra; and faces with twelve Mg(2,2)Mg12 cuboctahedra. In the seventh Mg site, Mg(2) is bonded to three equivalent Mg(1) and nine Mg(2,2) atoms to form MgMg12 cuboctahedra that share corners with three equivalent Mg(1)Mg9Sc3 cuboctahedra; corners with three equivalent Sc(1)Mg6Sc6 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with three equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; edges with twelve Mg(2,2)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg9Sc3 cuboctahedra; and faces with twelve Mg(2,2)Mg12 cuboctahedra. Sc(1) is bonded to six equivalent Mg(1) and six equivalent Sc(1) atoms to form ScMg6Sc6 cuboctahedra that share corners with six Mg(2,2)Mg12 cuboctahedra; corners with six equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with six Mg(2,2)Mg12 cuboctahedra; edges with six equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with twelve equivalent Mg(1)Mg9Sc3 cuboctahedra; faces with six equivalent Sc(1)Mg6Sc6 cuboctahedra; and faces with twelve equivalent Mg(1)Mg9Sc3 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg4Sc
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   13.332
_cell_length_b   13.332
_cell_length_c   13.332
_cell_angle_alpha   13.788
_cell_angle_beta   13.788
_cell_angle_gamma   13.788
_symmetry_Int_Tables_number   1
_cell_volume   117.128
_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  0.600  0.600  0.600  1.0
  Mg  Mg1  1  0.200  0.200  0.200  1.0
  Mg  Mg2  1  0.800  0.800  0.800  1.0
  Mg  Mg3  1  0.400  0.400  0.400  1.0
  Sc  Sc4  1  0.000  0.000  0.000  1.0
[/CIF]
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The crystal structure described by Mg4Sc is alpha La-derived structured and crystallizes in the trigonal R-3m space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent Mg(2), six equivalent Mg(1), and three equivalent Sc(1) atoms to form MgMg9Sc3 cuboctahedra that share corners with three equivalent Mg(2)Mg12 cuboctahedra; corners with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; edges with six equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with nine Mg(2,2)Mg12 cuboctahedra; edges with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; faces with six equivalent Mg(2)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg9Sc3 cuboctahedra; and faces with six equivalent Sc(1)Mg6Sc6 cuboctahedra. In the second Mg site, Mg(2) is bonded to three equivalent Mg(1) and nine Mg(2,2) atoms to form MgMg12 cuboctahedra that share corners with three equivalent Mg(1)Mg9Sc3 cuboctahedra; corners with three equivalent Sc(1)Mg6Sc6 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with three equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; edges with twelve Mg(2,2)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg9Sc3 cuboctahedra; and faces with twelve Mg(2,2)Mg12 cuboctahedra. In the third Mg site, Mg(2) is bonded to three equivalent Mg(1) and nine Mg(2,2) atoms to form MgMg12 cuboctahedra that share corners with three equivalent Mg(1)Mg9Sc3 cuboctahedra; corners with three equivalent Sc(1)Mg6Sc6 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with three equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; edges with twelve Mg(2,2)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg9Sc3 cuboctahedra; and faces with twelve Mg(2,2)Mg12 cuboctahedra. In the fourth Mg site, Mg(2) is bonded to three equivalent Mg(1) and nine Mg(2,2) atoms to form MgMg12 cuboctahedra that share corners with three equivalent Mg(1)Mg9Sc3 cuboctahedra; corners with three equivalent Sc(1)Mg6Sc6 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with three equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; edges with twelve Mg(2,2)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg9Sc3 cuboctahedra; and faces with twelve Mg(2,2)Mg12 cuboctahedra. In the fifth Mg site, Mg(2) is bonded to three equivalent Mg(1) and nine Mg(2,2) atoms to form MgMg12 cuboctahedra that share corners with three equivalent Mg(1)Mg9Sc3 cuboctahedra; corners with three equivalent Sc(1)Mg6Sc6 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with three equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; edges with twelve Mg(2,2)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg9Sc3 cuboctahedra; and faces with twelve Mg(2,2)Mg12 cuboctahedra. In the sixth Mg site, Mg(2) is bonded to three equivalent Mg(1) and nine Mg(2,2) atoms to form MgMg12 cuboctahedra that share corners with three equivalent Mg(1)Mg9Sc3 cuboctahedra; corners with three equivalent Sc(1)Mg6Sc6 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with three equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; edges with twelve Mg(2,2)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg9Sc3 cuboctahedra; and faces with twelve Mg(2,2)Mg12 cuboctahedra. In the seventh Mg site, Mg(2) is bonded to three equivalent Mg(1) and nine Mg(2,2) atoms to form MgMg12 cuboctahedra that share corners with three equivalent Mg(1)Mg9Sc3 cuboctahedra; corners with three equivalent Sc(1)Mg6Sc6 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with three equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with nine equivalent Mg(1)Mg9Sc3 cuboctahedra; edges with twelve Mg(2,2)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg9Sc3 cuboctahedra; and faces with twelve Mg(2,2)Mg12 cuboctahedra. Sc(1) is bonded to six equivalent Mg(1) and six equivalent Sc(1) atoms to form ScMg6Sc6 cuboctahedra that share corners with six Mg(2,2)Mg12 cuboctahedra; corners with six equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with six Mg(2,2)Mg12 cuboctahedra; edges with six equivalent Sc(1)Mg6Sc6 cuboctahedra; edges with twelve equivalent Mg(1)Mg9Sc3 cuboctahedra; faces with six equivalent Sc(1)Mg6Sc6 cuboctahedra; and faces with twelve equivalent Mg(1)Mg9Sc3 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg4Sc
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   13.332
_cell_length_b   13.332
_cell_length_c   13.332
_cell_angle_alpha   13.788
_cell_angle_beta   13.788
_cell_angle_gamma   13.788
_symmetry_Int_Tables_number   1
_cell_volume   117.128
_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  0.600  0.600  0.600  1.0
  Mg  Mg1  1  0.200  0.200  0.200  1.0
  Mg  Mg2  1  0.800  0.800  0.800  1.0
  Mg  Mg3  1  0.400  0.400  0.400  1.0
  Sc  Sc4  1  0.000  0.000  0.000  1.0
[/CIF]
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