The crystal structure described by Mg21Sm3Sb16 crystallizes in the trigonal P-3m1 space group. There are eleven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent Sb(5,6) atoms to form MgSb6 octahedra that share corners with three equivalent Mg(3)Sb4 tetrahedra, corners with three equivalent Mg(4)Sb4 tetrahedra, corners with three equivalent Mg(8)Sb4 tetrahedra, corners with three equivalent Mg(9)Sb4 tetrahedra, edges with six equivalent Mg(1)Sb6 octahedra, edges with three equivalent Mg(8)Sb4 tetrahedra, and edges with three equivalent Mg(9)Sb4 tetrahedra. In the second Mg site, Mg(2) is bonded to three equivalent Sb(7) and three equivalent Sb(8) atoms to form MgSb6 octahedra that share corners with three equivalent Mg(10)Sb4 tetrahedra, corners with three equivalent Mg(11)Sb4 tetrahedra, corners with three equivalent Mg(5)Sb4 tetrahedra, corners with three equivalent Mg(6)Sb4 tetrahedra, edges with six equivalent Mg(2)Sb6 octahedra, edges with three equivalent Mg(10)Sb4 tetrahedra, and edges with three equivalent Mg(11)Sb4 tetrahedra. In the third Mg site, Mg(3) is bonded to one Sb(5,6) and three equivalent Sb(1) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(3)Sb4 tetrahedra, edges with three equivalent Sm(1)Sb6 octahedra, and edges with three equivalent Mg(8)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 14-59°. In the fourth Mg site, Mg(4) is bonded to one Sb(5,6) and three equivalent Sb(2) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(2)Sb6 octahedra, corners with six equivalent Mg(4)Sb4 tetrahedra, edges with three equivalent Sm(2)Sb6 octahedra, and edges with three equivalent Mg(9)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 14-59°. In the fifth Mg site, Mg(5) is bonded to one Sb(7) and three equivalent Sb(3) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(5)Sb4 tetrahedra, edges with three equivalent Sm(1)Sb6 octahedra, and edges with three equivalent Mg(10)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 13-58°. In the sixth Mg site, Mg(6) is bonded to one Sb(8) and three equivalent Sb(4) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Mg(7)Sb6 octahedra, corners with six equivalent Mg(6)Sb4 tetrahedra, edges with three equivalent Mg(7)Sb6 octahedra, and edges with three equivalent Mg(11)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 12-60°. In the seventh Mg site, Mg(7) is bonded to six equivalent Sb(4) atoms to form MgSb6 octahedra that share corners with six equivalent Mg(11)Sb4 tetrahedra, corners with six equivalent Mg(6)Sb4 tetrahedra, edges with six equivalent Mg(7)Sb6 octahedra, and edges with six equivalent Mg(6)Sb4 tetrahedra. In the eighth Mg site, Mg(8) is bonded to one Sb(1) and three equivalent Sb(5,6) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(8)Sb4 tetrahedra, edges with three equivalent Mg(1)Sb6 octahedra, and edges with three equivalent Mg(3)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 12-56°. In the ninth Mg site, Mg(9) is bonded to one Sb(2) and three equivalent Sb(5,6) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(2)Sb6 octahedra, corners with six equivalent Mg(9)Sb4 tetrahedra, edges with three equivalent Mg(1)Sb6 octahedra, and edges with three equivalent Mg(4)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 12-56°. In the tenth Mg site, Mg(10) is bonded to one Sb(3) and three equivalent Sb(7) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(10)Sb4 tetrahedra, edges with three equivalent Mg(2)Sb6 octahedra, and edges with three equivalent Mg(5)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 13-56°. In the eleventh Mg site, Mg(11) is bonded to one Sb(4) and three equivalent Sb(8) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Mg(7)Sb6 octahedra, corners with six equivalent Mg(11)Sb4 tetrahedra, edges with three equivalent Mg(2)Sb6 octahedra, and edges with three equivalent Mg(6)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 9-57°. There are two inequivalent Sm sites. In the first Sm site, Sm(1) is bonded to three equivalent Sb(1) and three equivalent Sb(3) atoms to form SmSb6 octahedra that share corners with three equivalent Mg(10)Sb4 tetrahedra, corners with three equivalent Mg(3)Sb4 tetrahedra, corners with three equivalent Mg(5)Sb4 tetrahedra, corners with three equivalent Mg(8)Sb4 tetrahedra, edges with six equivalent Sm(1)Sb6 octahedra, edges with three equivalent Mg(3)Sb4 tetrahedra, and edges with three equivalent Mg(5)Sb4 tetrahedra. In the second Sm site, Sm(2) is bonded to six equivalent Sb(2) atoms to form SmSb6 octahedra that share corners with six equivalent Mg(4)Sb4 tetrahedra, corners with six equivalent Mg(9)Sb4 tetrahedra, edges with six equivalent Sm(2)Sb6 octahedra, and edges with six equivalent Mg(4)Sb4 tetrahedra. There are seven inequivalent Sb sites. In the first Sb site, Sb(1) is bonded to one Mg(8), three equivalent Mg(3), and three equivalent Sm(1) atoms to form a mixture of distorted edge and corner-sharing SbSm3Mg4 pentagonal bipyramids. In the second Sb site, Sb(2) is bonded to one Mg(9), three equivalent Mg(4), and three equivalent Sm(2) atoms to form a mixture of distorted edge and corner-sharing SbSm3Mg4 pentagonal bipyramids. In the third Sb site, Sb(3) is bonded to one Mg(10), three equivalent Mg(5), and three equivalent Sm(1) atoms to form a mixture of distorted edge and corner-sharing SbSm3Mg4 pentagonal bipyramids. In the fourth Sb site, Sb(4) is bonded to one Mg(11), three equivalent Mg(6), and three equivalent Mg(7) atoms to form a mixture of distorted edge and corner-sharing SbMg7 pentagonal bipyramids. In the fifth Sb site, Sb(5,6) is bonded in a 7-coordinate geometry to one Mg(3), three equivalent Mg(1), and three equivalent Mg(8) atoms. In the sixth Sb site, Sb(7) is bonded in a 7-coordinate geometry to one Mg(5), three equivalent Mg(10), and three equivalent Mg(2) atoms. In the seventh Sb site, Sb(8) is bonded to one Mg(6), three equivalent Mg(11), and three equivalent Mg(2) atoms to form distorted edge-sharing SbMg7 pentagonal bipyramids. is represented by the CIF card [CIF]
data_Sm3Mg21Sb16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.657
_cell_length_b   4.657
_cell_length_c   58.304
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   1095.187
_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
  Sm  Sm0  1  0.000  0.000  0.250  1.0
  Sm  Sm1  1  0.000  0.000  0.000  1.0
  Sm  Sm2  1  0.000  0.000  0.750  1.0
  Mg  Mg3  1  0.000  0.000  0.125  1.0
  Mg  Mg4  1  0.000  0.000  0.875  1.0
  Mg  Mg5  1  0.000  0.000  0.624  1.0
  Mg  Mg6  1  0.000  0.000  0.376  1.0
  Mg  Mg7  1  0.333  0.667  0.202  1.0
  Mg  Mg8  1  0.333  0.667  0.952  1.0
  Mg  Mg9  1  0.333  0.667  0.702  1.0
  Mg  Mg10  1  0.333  0.667  0.453  1.0
  Mg  Mg11  1  0.667  0.333  0.048  1.0
  Mg  Mg12  1  0.667  0.333  0.798  1.0
  Mg  Mg13  1  0.667  0.333  0.547  1.0
  Mg  Mg14  1  0.667  0.333  0.298  1.0
  Mg  Mg15  1  0.000  0.000  0.500  1.0
  Mg  Mg16  1  0.667  0.333  0.168  1.0
  Mg  Mg17  1  0.667  0.333  0.918  1.0
  Mg  Mg18  1  0.667  0.333  0.668  1.0
  Mg  Mg19  1  0.667  0.333  0.419  1.0
  Mg  Mg20  1  0.333  0.667  0.082  1.0
  Mg  Mg21  1  0.333  0.667  0.832  1.0
  Mg  Mg22  1  0.333  0.667  0.581  1.0
  Mg  Mg23  1  0.333  0.667  0.332  1.0
  Sb  Sb24  1  0.667  0.333  0.219  1.0
  Sb  Sb25  1  0.667  0.333  0.969  1.0
  Sb  Sb26  1  0.667  0.333  0.719  1.0
  Sb  Sb27  1  0.667  0.333  0.470  1.0
  Sb  Sb28  1  0.333  0.667  0.031  1.0
  Sb  Sb29  1  0.333  0.667  0.781  1.0
  Sb  Sb30  1  0.333  0.667  0.530  1.0
  Sb  Sb31  1  0.333  0.667  0.281  1.0
  Sb  Sb32  1  0.333  0.667  0.152  1.0
  Sb  Sb33  1  0.333  0.667  0.902  1.0
  Sb  Sb34  1  0.333  0.667  0.653  1.0
  Sb  Sb35  1  0.333  0.667  0.402  1.0
  Sb  Sb36  1  0.667  0.333  0.098  1.0
  Sb  Sb37  1  0.667  0.333  0.848  1.0
  Sb  Sb38  1  0.667  0.333  0.598  1.0
  Sb  Sb39  1  0.667  0.333  0.347  1.0
[/CIF]
.
The crystal structure described by Mg21Sm3Sb16 crystallizes in the trigonal P-3m1 space group. There are eleven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent Sb(5,6) atoms to form MgSb6 octahedra that share corners with three equivalent Mg(3)Sb4 tetrahedra, corners with three equivalent Mg(4)Sb4 tetrahedra, corners with three equivalent Mg(8)Sb4 tetrahedra, corners with three equivalent Mg(9)Sb4 tetrahedra, edges with six equivalent Mg(1)Sb6 octahedra, edges with three equivalent Mg(8)Sb4 tetrahedra, and edges with three equivalent Mg(9)Sb4 tetrahedra. In the second Mg site, Mg(2) is bonded to three equivalent Sb(7) and three equivalent Sb(8) atoms to form MgSb6 octahedra that share corners with three equivalent Mg(10)Sb4 tetrahedra, corners with three equivalent Mg(11)Sb4 tetrahedra, corners with three equivalent Mg(5)Sb4 tetrahedra, corners with three equivalent Mg(6)Sb4 tetrahedra, edges with six equivalent Mg(2)Sb6 octahedra, edges with three equivalent Mg(10)Sb4 tetrahedra, and edges with three equivalent Mg(11)Sb4 tetrahedra. In the third Mg site, Mg(3) is bonded to one Sb(5,6) and three equivalent Sb(1) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(3)Sb4 tetrahedra, edges with three equivalent Sm(1)Sb6 octahedra, and edges with three equivalent Mg(8)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 14-59°. In the fourth Mg site, Mg(4) is bonded to one Sb(5,6) and three equivalent Sb(2) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(2)Sb6 octahedra, corners with six equivalent Mg(4)Sb4 tetrahedra, edges with three equivalent Sm(2)Sb6 octahedra, and edges with three equivalent Mg(9)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 14-59°. In the fifth Mg site, Mg(5) is bonded to one Sb(7) and three equivalent Sb(3) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(5)Sb4 tetrahedra, edges with three equivalent Sm(1)Sb6 octahedra, and edges with three equivalent Mg(10)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 13-58°. In the sixth Mg site, Mg(6) is bonded to one Sb(8) and three equivalent Sb(4) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Mg(7)Sb6 octahedra, corners with six equivalent Mg(6)Sb4 tetrahedra, edges with three equivalent Mg(7)Sb6 octahedra, and edges with three equivalent Mg(11)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 12-60°. In the seventh Mg site, Mg(7) is bonded to six equivalent Sb(4) atoms to form MgSb6 octahedra that share corners with six equivalent Mg(11)Sb4 tetrahedra, corners with six equivalent Mg(6)Sb4 tetrahedra, edges with six equivalent Mg(7)Sb6 octahedra, and edges with six equivalent Mg(6)Sb4 tetrahedra. In the eighth Mg site, Mg(8) is bonded to one Sb(1) and three equivalent Sb(5,6) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(8)Sb4 tetrahedra, edges with three equivalent Mg(1)Sb6 octahedra, and edges with three equivalent Mg(3)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 12-56°. In the ninth Mg site, Mg(9) is bonded to one Sb(2) and three equivalent Sb(5,6) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(2)Sb6 octahedra, corners with six equivalent Mg(9)Sb4 tetrahedra, edges with three equivalent Mg(1)Sb6 octahedra, and edges with three equivalent Mg(4)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 12-56°. In the tenth Mg site, Mg(10) is bonded to one Sb(3) and three equivalent Sb(7) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(10)Sb4 tetrahedra, edges with three equivalent Mg(2)Sb6 octahedra, and edges with three equivalent Mg(5)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 13-56°. In the eleventh Mg site, Mg(11) is bonded to one Sb(4) and three equivalent Sb(8) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Mg(7)Sb6 octahedra, corners with six equivalent Mg(11)Sb4 tetrahedra, edges with three equivalent Mg(2)Sb6 octahedra, and edges with three equivalent Mg(6)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 9-57°. There are two inequivalent Sm sites. In the first Sm site, Sm(1) is bonded to three equivalent Sb(1) and three equivalent Sb(3) atoms to form SmSb6 octahedra that share corners with three equivalent Mg(10)Sb4 tetrahedra, corners with three equivalent Mg(3)Sb4 tetrahedra, corners with three equivalent Mg(5)Sb4 tetrahedra, corners with three equivalent Mg(8)Sb4 tetrahedra, edges with six equivalent Sm(1)Sb6 octahedra, edges with three equivalent Mg(3)Sb4 tetrahedra, and edges with three equivalent Mg(5)Sb4 tetrahedra. In the second Sm site, Sm(2) is bonded to six equivalent Sb(2) atoms to form SmSb6 octahedra that share corners with six equivalent Mg(4)Sb4 tetrahedra, corners with six equivalent Mg(9)Sb4 tetrahedra, edges with six equivalent Sm(2)Sb6 octahedra, and edges with six equivalent Mg(4)Sb4 tetrahedra. There are seven inequivalent Sb sites. In the first Sb site, Sb(1) is bonded to one Mg(8), three equivalent Mg(3), and three equivalent Sm(1) atoms to form a mixture of distorted edge and corner-sharing SbSm3Mg4 pentagonal bipyramids. In the second Sb site, Sb(2) is bonded to one Mg(9), three equivalent Mg(4), and three equivalent Sm(2) atoms to form a mixture of distorted edge and corner-sharing SbSm3Mg4 pentagonal bipyramids. In the third Sb site, Sb(3) is bonded to one Mg(10), three equivalent Mg(5), and three equivalent Sm(1) atoms to form a mixture of distorted edge and corner-sharing SbSm3Mg4 pentagonal bipyramids. In the fourth Sb site, Sb(4) is bonded to one Mg(11), three equivalent Mg(6), and three equivalent Mg(7) atoms to form a mixture of distorted edge and corner-sharing SbMg7 pentagonal bipyramids. In the fifth Sb site, Sb(5,6) is bonded in a 7-coordinate geometry to one Mg(3), three equivalent Mg(1), and three equivalent Mg(8) atoms. In the sixth Sb site, Sb(7) is bonded in a 7-coordinate geometry to one Mg(5), three equivalent Mg(10), and three equivalent Mg(2) atoms. In the seventh Sb site, Sb(8) is bonded to one Mg(6), three equivalent Mg(11), and three equivalent Mg(2) atoms to form distorted edge-sharing SbMg7 pentagonal bipyramids. is represented by the CIF card [CIF]
data_Sm3Mg21Sb16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.657
_cell_length_b   4.657
_cell_length_c   58.304
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   1095.187
_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
  Sm  Sm0  1  0.000  0.000  0.250  1.0
  Sm  Sm1  1  0.000  0.000  0.000  1.0
  Sm  Sm2  1  0.000  0.000  0.750  1.0
  Mg  Mg3  1  0.000  0.000  0.125  1.0
  Mg  Mg4  1  0.000  0.000  0.875  1.0
  Mg  Mg5  1  0.000  0.000  0.624  1.0
  Mg  Mg6  1  0.000  0.000  0.376  1.0
  Mg  Mg7  1  0.333  0.667  0.202  1.0
  Mg  Mg8  1  0.333  0.667  0.952  1.0
  Mg  Mg9  1  0.333  0.667  0.702  1.0
  Mg  Mg10  1  0.333  0.667  0.453  1.0
  Mg  Mg11  1  0.667  0.333  0.048  1.0
  Mg  Mg12  1  0.667  0.333  0.798  1.0
  Mg  Mg13  1  0.667  0.333  0.547  1.0
  Mg  Mg14  1  0.667  0.333  0.298  1.0
  Mg  Mg15  1  0.000  0.000  0.500  1.0
  Mg  Mg16  1  0.667  0.333  0.168  1.0
  Mg  Mg17  1  0.667  0.333  0.918  1.0
  Mg  Mg18  1  0.667  0.333  0.668  1.0
  Mg  Mg19  1  0.667  0.333  0.419  1.0
  Mg  Mg20  1  0.333  0.667  0.082  1.0
  Mg  Mg21  1  0.333  0.667  0.832  1.0
  Mg  Mg22  1  0.333  0.667  0.581  1.0
  Mg  Mg23  1  0.333  0.667  0.332  1.0
  Sb  Sb24  1  0.667  0.333  0.219  1.0
  Sb  Sb25  1  0.667  0.333  0.969  1.0
  Sb  Sb26  1  0.667  0.333  0.719  1.0
  Sb  Sb27  1  0.667  0.333  0.470  1.0
  Sb  Sb28  1  0.333  0.667  0.031  1.0
  Sb  Sb29  1  0.333  0.667  0.781  1.0
  Sb  Sb30  1  0.333  0.667  0.530  1.0
  Sb  Sb31  1  0.333  0.667  0.281  1.0
  Sb  Sb32  1  0.333  0.667  0.152  1.0
  Sb  Sb33  1  0.333  0.667  0.902  1.0
  Sb  Sb34  1  0.333  0.667  0.653  1.0
  Sb  Sb35  1  0.333  0.667  0.402  1.0
  Sb  Sb36  1  0.667  0.333  0.098  1.0
  Sb  Sb37  1  0.667  0.333  0.848  1.0
  Sb  Sb38  1  0.667  0.333  0.598  1.0
  Sb  Sb39  1  0.667  0.333  0.347  1.0
[/CIF]
.