The material structure described by Mg15Nb crystallizes in the hexagonal P-6m2 space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six Mg(3,3,3) and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with six Mg(3,3,3)Mg12 cuboctahedra; edges with twelve Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Nb(1)Mg12 cuboctahedra; faces with six Mg(4,4)Mg11Nb cuboctahedra; faces with six Mg(3,3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5); four equivalent Mg(2); four Mg(4,4); and two equivalent Nb(1) atoms to form MgMg10Nb2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Nb2 cuboctahedra; corners with eight Mg(3,3)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Nb(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Nb2 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Nb(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Nb(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Nb cuboctahedra; faces with two equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Nb(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. In the sixth Mg site, Mg(4) is bonded to one Mg(1); two equivalent Mg(2); two Mg(3,3); two equivalent Mg(5); four Mg(4,4); and one Nb(1) atom to form distorted MgMg11Nb cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Nb cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with four Mg(4,4)Mg11Nb cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Nb(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with five Mg(3,3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Nb cuboctahedra. In the seventh Mg site, Mg(4) is bonded to one Mg(1); two equivalent Mg(2); two Mg(3,3); two equivalent Mg(5); four equivalent Mg(4); and one Nb(1) atom to form distorted MgMg11Nb cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Nb cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with four equivalent Mg(4)Mg11Nb cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Nb(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with five Mg(3,3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Nb cuboctahedra. In the eighth Mg site, Mg(5) is bonded to three equivalent Mg(2); three Mg(3,3,3); and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve Mg(4,4)Mg11Nb cuboctahedra; edges with six equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with six Mg(4,4)Mg11Nb cuboctahedra; edges with six Mg(3,3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3,3)Mg12 cuboctahedra; faces with three equivalent Nb(1)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Nb cuboctahedra. Nb(1) is bonded to six equivalent Mg(2) and six Mg(4,4) atoms to form NbMg12 cuboctahedra that share corners with six equivalent Nb(1)Mg12 cuboctahedra; corners with twelve Mg(3,3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with twelve Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with six Mg(4,4)Mg11Nb cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. is represented by the CIF card [CIF]
data_Mg15Nb
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.354
_cell_length_b   6.354
_cell_length_c   10.108
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   353.406
_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  0.000  0.000  1.0
  Mg  Mg1  1  0.002  0.501  0.500  1.0
  Mg  Mg2  1  0.000  0.500  0.000  1.0
  Mg  Mg3  1  0.499  0.501  0.500  1.0
  Mg  Mg4  1  0.500  0.500  0.000  1.0
  Mg  Mg5  1  0.499  0.998  0.500  1.0
  Mg  Mg6  1  0.500  1.000  0.000  1.0
  Mg  Mg7  1  0.162  0.325  0.255  1.0
  Mg  Mg8  1  0.162  0.325  0.745  1.0
  Mg  Mg9  1  0.162  0.838  0.255  1.0
  Mg  Mg10  1  0.162  0.838  0.745  1.0
  Mg  Mg11  1  0.675  0.838  0.255  1.0
  Mg  Mg12  1  0.675  0.838  0.745  1.0
  Mg  Mg13  1  0.667  0.333  0.250  1.0
  Mg  Mg14  1  0.667  0.333  0.750  1.0
  Nb  Nb15  1  0.000  0.000  0.500  1.0
[/CIF]
.
The material structure described by Mg15Nb crystallizes in the hexagonal P-6m2 space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six Mg(3,3,3) and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with six Mg(3,3,3)Mg12 cuboctahedra; edges with twelve Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Nb(1)Mg12 cuboctahedra; faces with six Mg(4,4)Mg11Nb cuboctahedra; faces with six Mg(3,3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5); four equivalent Mg(2); four Mg(4,4); and two equivalent Nb(1) atoms to form MgMg10Nb2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Nb2 cuboctahedra; corners with eight Mg(3,3)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Nb(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Nb2 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Nb(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Nb(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Nb cuboctahedra; faces with two equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Nb(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. In the sixth Mg site, Mg(4) is bonded to one Mg(1); two equivalent Mg(2); two Mg(3,3); two equivalent Mg(5); four Mg(4,4); and one Nb(1) atom to form distorted MgMg11Nb cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Nb cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with four Mg(4,4)Mg11Nb cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Nb(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with five Mg(3,3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Nb cuboctahedra. In the seventh Mg site, Mg(4) is bonded to one Mg(1); two equivalent Mg(2); two Mg(3,3); two equivalent Mg(5); four equivalent Mg(4); and one Nb(1) atom to form distorted MgMg11Nb cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Nb cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with four equivalent Mg(4)Mg11Nb cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Nb(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with five Mg(3,3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Nb cuboctahedra. In the eighth Mg site, Mg(5) is bonded to three equivalent Mg(2); three Mg(3,3,3); and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve Mg(4,4)Mg11Nb cuboctahedra; edges with six equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with six Mg(4,4)Mg11Nb cuboctahedra; edges with six Mg(3,3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3,3)Mg12 cuboctahedra; faces with three equivalent Nb(1)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Nb cuboctahedra. Nb(1) is bonded to six equivalent Mg(2) and six Mg(4,4) atoms to form NbMg12 cuboctahedra that share corners with six equivalent Nb(1)Mg12 cuboctahedra; corners with twelve Mg(3,3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with twelve Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with six Mg(4,4)Mg11Nb cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. is represented by the CIF card [CIF]
data_Mg15Nb
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.354
_cell_length_b   6.354
_cell_length_c   10.108
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   353.406
_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  0.000  0.000  1.0
  Mg  Mg1  1  0.002  0.501  0.500  1.0
  Mg  Mg2  1  0.000  0.500  0.000  1.0
  Mg  Mg3  1  0.499  0.501  0.500  1.0
  Mg  Mg4  1  0.500  0.500  0.000  1.0
  Mg  Mg5  1  0.499  0.998  0.500  1.0
  Mg  Mg6  1  0.500  1.000  0.000  1.0
  Mg  Mg7  1  0.162  0.325  0.255  1.0
  Mg  Mg8  1  0.162  0.325  0.745  1.0
  Mg  Mg9  1  0.162  0.838  0.255  1.0
  Mg  Mg10  1  0.162  0.838  0.745  1.0
  Mg  Mg11  1  0.675  0.838  0.255  1.0
  Mg  Mg12  1  0.675  0.838  0.745  1.0
  Mg  Mg13  1  0.667  0.333  0.250  1.0
  Mg  Mg14  1  0.667  0.333  0.750  1.0
  Nb  Nb15  1  0.000  0.000  0.500  1.0
[/CIF]
.