The structure described by Mg15Ti crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six Mg(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)Mg10Ti2 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; edges with twelve Mg(4,4)Mg11Ti cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with six Mg(4,4)Mg11Ti cuboctahedra; faces with six Mg(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 equivalent Mg(4), and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Ti cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Ti2 cuboctahedra; and faces with ten Mg(4,4)Mg11Ti cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(5), four equivalent Mg(3), and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Ti cuboctahedra; faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four equivalent Mg(3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Ti 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 Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ti2 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)Mg11Ti cuboctahedra; faces with two equivalent Mg(2)Mg10Ti2 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)Mg11Ti cuboctahedra. In the fifth 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 Ti(1) atom to form distorted MgMg11Ti cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Ti cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with four Mg(4,4)Mg11Ti cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Ti cuboctahedra. In the sixth Mg site, Mg(4) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(5), four equivalent Mg(4), and one Ti(1) atom to form distorted MgMg11Ti cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Ti cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg11Ti cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Ti cuboctahedra. In the seventh Mg site, Mg(5) is bonded to three equivalent Mg(2); three Mg(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)Mg11Ti cuboctahedra; edges with six equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with six Mg(4,4)Mg11Ti cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3)Mg12 cuboctahedra; faces with three equivalent Ti(1)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Ti cuboctahedra. Ti(1) is bonded to six equivalent Mg(2) and six Mg(4,4) atoms to form TiMg12 cuboctahedra that share corners with six equivalent Ti(1)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with twelve Mg(4,4)Mg11Ti cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with six Mg(4,4)Mg11Ti cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg15Ti
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.383
_cell_length_b   6.383
_cell_length_c   10.144
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   357.899
_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  0.003  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  0.997  0.500  1.0
  Mg  Mg6  1  0.500  1.000  0.000  1.0
  Mg  Mg7  1  0.164  0.327  0.254  1.0
  Mg  Mg8  1  0.164  0.327  0.746  1.0
  Mg  Mg9  1  0.164  0.837  0.254  1.0
  Mg  Mg10  1  0.164  0.837  0.746  1.0
  Mg  Mg11  1  0.673  0.837  0.254  1.0
  Mg  Mg12  1  0.673  0.837  0.746  1.0
  Mg  Mg13  1  0.667  0.333  0.250  1.0
  Mg  Mg14  1  0.667  0.333  0.750  1.0
  Ti  Ti15  1  0.000  0.000  0.500  1.0
[/CIF]
.
The structure described by Mg15Ti crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six Mg(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)Mg10Ti2 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; edges with twelve Mg(4,4)Mg11Ti cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with six Mg(4,4)Mg11Ti cuboctahedra; faces with six Mg(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 equivalent Mg(4), and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Ti cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Ti2 cuboctahedra; and faces with ten Mg(4,4)Mg11Ti cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(5), four equivalent Mg(3), and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Ti cuboctahedra; faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four equivalent Mg(3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Ti 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 Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ti2 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)Mg11Ti cuboctahedra; faces with two equivalent Mg(2)Mg10Ti2 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)Mg11Ti cuboctahedra. In the fifth 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 Ti(1) atom to form distorted MgMg11Ti cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Ti cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with four Mg(4,4)Mg11Ti cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Ti cuboctahedra. In the sixth Mg site, Mg(4) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(5), four equivalent Mg(4), and one Ti(1) atom to form distorted MgMg11Ti cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Ti cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg11Ti cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Ti cuboctahedra. In the seventh Mg site, Mg(5) is bonded to three equivalent Mg(2); three Mg(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)Mg11Ti cuboctahedra; edges with six equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with six Mg(4,4)Mg11Ti cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3)Mg12 cuboctahedra; faces with three equivalent Ti(1)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Ti cuboctahedra. Ti(1) is bonded to six equivalent Mg(2) and six Mg(4,4) atoms to form TiMg12 cuboctahedra that share corners with six equivalent Ti(1)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with twelve Mg(4,4)Mg11Ti cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with six Mg(4,4)Mg11Ti cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg15Ti
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.383
_cell_length_b   6.383
_cell_length_c   10.144
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   357.899
_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  0.003  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  0.997  0.500  1.0
  Mg  Mg6  1  0.500  1.000  0.000  1.0
  Mg  Mg7  1  0.164  0.327  0.254  1.0
  Mg  Mg8  1  0.164  0.327  0.746  1.0
  Mg  Mg9  1  0.164  0.837  0.254  1.0
  Mg  Mg10  1  0.164  0.837  0.746  1.0
  Mg  Mg11  1  0.673  0.837  0.254  1.0
  Mg  Mg12  1  0.673  0.837  0.746  1.0
  Mg  Mg13  1  0.667  0.333  0.250  1.0
  Mg  Mg14  1  0.667  0.333  0.750  1.0
  Ti  Ti15  1  0.000  0.000  0.500  1.0
[/CIF]
.