The material structure described by MgCe5 crystallizes in the trigonal R32 space group. Mg(1) is bonded to six Ce(1,1) and six equivalent Ce(2) atoms to form MgCe12 cuboctahedra that share corners with six equivalent Mg(1)Ce12 cuboctahedra; corners with twelve Ce(2,2)Ce9Mg3 cuboctahedra; edges with six equivalent Mg(1)Ce12 cuboctahedra; edges with twelve Ce(1,1)Ce10Mg2 cuboctahedra; faces with eight Ce(2,2)Ce9Mg3 cuboctahedra; and faces with twelve Ce(1,1)Ce10Mg2 cuboctahedra. There are five inequivalent Ce sites. In the first Ce site, Ce(1) is bonded to two equivalent Mg(1), four equivalent Ce(2), and six equivalent Ce(1) atoms to form CeCe10Mg2 cuboctahedra that share corners with eighteen equivalent Ce(1)Ce10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ce12 cuboctahedra; edges with six equivalent Ce(1)Ce10Mg2 cuboctahedra; edges with eight equivalent Ce(2)Ce9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ce12 cuboctahedra; faces with eight Ce(1,1)Ce10Mg2 cuboctahedra; and faces with eight equivalent Ce(2)Ce9Mg3 cuboctahedra. In the second Ce site, Ce(2) is bonded to three equivalent Mg(1); three equivalent Ce(2); and six Ce(1,1) atoms to form CeCe9Mg3 cuboctahedra that share corners with six equivalent Mg(1)Ce12 cuboctahedra; corners with twelve Ce(2,2,2)Ce9Mg3 cuboctahedra; edges with six equivalent Ce(2)Ce9Mg3 cuboctahedra; edges with twelve Ce(1,1)Ce10Mg2 cuboctahedra; faces with four equivalent Mg(1)Ce12 cuboctahedra; faces with four equivalent Ce(2)Ce9Mg3 cuboctahedra; and faces with twelve Ce(1,1)Ce10Mg2 cuboctahedra. In the third Ce site, Ce(2) is bonded to three equivalent Mg(1); three equivalent Ce(2); and six Ce(1,1) atoms to form CeCe9Mg3 cuboctahedra that share corners with six equivalent Mg(1)Ce12 cuboctahedra; corners with twelve Ce(2,2)Ce9Mg3 cuboctahedra; edges with six equivalent Ce(2)Ce9Mg3 cuboctahedra; edges with twelve Ce(1,1)Ce10Mg2 cuboctahedra; faces with four equivalent Mg(1)Ce12 cuboctahedra; faces with four Ce(2,2)Ce9Mg3 cuboctahedra; and faces with twelve Ce(1,1)Ce10Mg2 cuboctahedra. In the fourth Ce site, Ce(1) is bonded to two equivalent Mg(1); four Ce(2,2,2); and six equivalent Ce(1) atoms to form CeCe10Mg2 cuboctahedra that share corners with eighteen equivalent Ce(1)Ce10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ce12 cuboctahedra; edges with six equivalent Ce(1)Ce10Mg2 cuboctahedra; edges with eight Ce(2,2,2)Ce9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ce12 cuboctahedra; faces with eight Ce(1,1)Ce10Mg2 cuboctahedra; and faces with eight Ce(2,2,2)Ce9Mg3 cuboctahedra. In the fifth Ce site, Ce(2) is bonded to three equivalent Mg(1); three equivalent Ce(2); and six Ce(1,1) atoms to form CeCe9Mg3 cuboctahedra that share corners with six equivalent Mg(1)Ce12 cuboctahedra; corners with twelve Ce(2,2)Ce9Mg3 cuboctahedra; edges with six equivalent Ce(2)Ce9Mg3 cuboctahedra; edges with twelve Ce(1,1)Ce10Mg2 cuboctahedra; faces with four equivalent Mg(1)Ce12 cuboctahedra; faces with four Ce(2,2)Ce9Mg3 cuboctahedra; and faces with twelve Ce(1,1)Ce10Mg2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ce5Mg
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.472
_cell_length_b   6.472
_cell_length_c   6.472
_cell_angle_alpha   53.635
_cell_angle_beta   53.635
_cell_angle_gamma   53.635
_symmetry_Int_Tables_number   1
_cell_volume   163.156
_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
  Ce  Ce0  1  0.000  0.672  0.328  1.0
  Ce  Ce1  1  0.168  0.168  0.168  1.0
  Ce  Ce2  1  0.328  0.000  0.672  1.0
  Ce  Ce3  1  0.672  0.328  0.000  1.0
  Ce  Ce4  1  0.832  0.832  0.832  1.0
  Mg  Mg5  1  0.500  0.500  0.500  1.0
[/CIF]
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The material structure described by MgCe5 crystallizes in the trigonal R32 space group. Mg(1) is bonded to six Ce(1,1) and six equivalent Ce(2) atoms to form MgCe12 cuboctahedra that share corners with six equivalent Mg(1)Ce12 cuboctahedra; corners with twelve Ce(2,2)Ce9Mg3 cuboctahedra; edges with six equivalent Mg(1)Ce12 cuboctahedra; edges with twelve Ce(1,1)Ce10Mg2 cuboctahedra; faces with eight Ce(2,2)Ce9Mg3 cuboctahedra; and faces with twelve Ce(1,1)Ce10Mg2 cuboctahedra. There are five inequivalent Ce sites. In the first Ce site, Ce(1) is bonded to two equivalent Mg(1), four equivalent Ce(2), and six equivalent Ce(1) atoms to form CeCe10Mg2 cuboctahedra that share corners with eighteen equivalent Ce(1)Ce10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ce12 cuboctahedra; edges with six equivalent Ce(1)Ce10Mg2 cuboctahedra; edges with eight equivalent Ce(2)Ce9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ce12 cuboctahedra; faces with eight Ce(1,1)Ce10Mg2 cuboctahedra; and faces with eight equivalent Ce(2)Ce9Mg3 cuboctahedra. In the second Ce site, Ce(2) is bonded to three equivalent Mg(1); three equivalent Ce(2); and six Ce(1,1) atoms to form CeCe9Mg3 cuboctahedra that share corners with six equivalent Mg(1)Ce12 cuboctahedra; corners with twelve Ce(2,2,2)Ce9Mg3 cuboctahedra; edges with six equivalent Ce(2)Ce9Mg3 cuboctahedra; edges with twelve Ce(1,1)Ce10Mg2 cuboctahedra; faces with four equivalent Mg(1)Ce12 cuboctahedra; faces with four equivalent Ce(2)Ce9Mg3 cuboctahedra; and faces with twelve Ce(1,1)Ce10Mg2 cuboctahedra. In the third Ce site, Ce(2) is bonded to three equivalent Mg(1); three equivalent Ce(2); and six Ce(1,1) atoms to form CeCe9Mg3 cuboctahedra that share corners with six equivalent Mg(1)Ce12 cuboctahedra; corners with twelve Ce(2,2)Ce9Mg3 cuboctahedra; edges with six equivalent Ce(2)Ce9Mg3 cuboctahedra; edges with twelve Ce(1,1)Ce10Mg2 cuboctahedra; faces with four equivalent Mg(1)Ce12 cuboctahedra; faces with four Ce(2,2)Ce9Mg3 cuboctahedra; and faces with twelve Ce(1,1)Ce10Mg2 cuboctahedra. In the fourth Ce site, Ce(1) is bonded to two equivalent Mg(1); four Ce(2,2,2); and six equivalent Ce(1) atoms to form CeCe10Mg2 cuboctahedra that share corners with eighteen equivalent Ce(1)Ce10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ce12 cuboctahedra; edges with six equivalent Ce(1)Ce10Mg2 cuboctahedra; edges with eight Ce(2,2,2)Ce9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ce12 cuboctahedra; faces with eight Ce(1,1)Ce10Mg2 cuboctahedra; and faces with eight Ce(2,2,2)Ce9Mg3 cuboctahedra. In the fifth Ce site, Ce(2) is bonded to three equivalent Mg(1); three equivalent Ce(2); and six Ce(1,1) atoms to form CeCe9Mg3 cuboctahedra that share corners with six equivalent Mg(1)Ce12 cuboctahedra; corners with twelve Ce(2,2)Ce9Mg3 cuboctahedra; edges with six equivalent Ce(2)Ce9Mg3 cuboctahedra; edges with twelve Ce(1,1)Ce10Mg2 cuboctahedra; faces with four equivalent Mg(1)Ce12 cuboctahedra; faces with four Ce(2,2)Ce9Mg3 cuboctahedra; and faces with twelve Ce(1,1)Ce10Mg2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ce5Mg
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.472
_cell_length_b   6.472
_cell_length_c   6.472
_cell_angle_alpha   53.635
_cell_angle_beta   53.635
_cell_angle_gamma   53.635
_symmetry_Int_Tables_number   1
_cell_volume   163.156
_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
  Ce  Ce0  1  0.000  0.672  0.328  1.0
  Ce  Ce1  1  0.168  0.168  0.168  1.0
  Ce  Ce2  1  0.328  0.000  0.672  1.0
  Ce  Ce3  1  0.672  0.328  0.000  1.0
  Ce  Ce4  1  0.832  0.832  0.832  1.0
  Mg  Mg5  1  0.500  0.500  0.500  1.0
[/CIF]
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