The structure described by Mg14TiZn crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent Zn(1) atoms to form MgMg10Zn2 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zn2 cuboctahedra; corners with eight Mg(2,2)Mg10Ti2 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10TiZn cuboctahedra; faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiZn cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four Mg(3,3); and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10TiZn cuboctahedra; faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiZn cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four equivalent Mg(3); and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10TiZn cuboctahedra; faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiZn cuboctahedra. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four Mg(3,3); and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10TiZn cuboctahedra; faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiZn cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four Mg(3,3); one Ti(1); and one Zn(1) atom to form distorted MgMg10TiZn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiZn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four Mg(3,3)Mg10TiZn cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2,2)Mg10Ti2 cuboctahedra; faces with five equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six Mg(3,3)Mg10TiZn cuboctahedra. In the sixth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); one Ti(1); and one Zn(1) atom to form distorted MgMg10TiZn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiZn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Mg10TiZn cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2,2)Mg10Ti2 cuboctahedra; faces with five equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six Mg(3,3)Mg10TiZn cuboctahedra. In the seventh Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2,2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg10TiZn cuboctahedra; edges with six Mg(2,2,2)Mg10Ti2 cuboctahedra; edges with six Mg(3,3)Mg10TiZn cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2,2)Mg10Ti2 cuboctahedra; faces with three equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with three equivalent Ti(1)Mg12 cuboctahedra; faces with three equivalent Zn(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10TiZn cuboctahedra. Ti(1) is bonded to six Mg(2,2,2) and six Mg(3,3) atoms to form TiMg12 cuboctahedra that share corners with six equivalent Ti(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with six Mg(2,2,2)Mg10Ti2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiZn cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with six Mg(2,2,2)Mg10Ti2 cuboctahedra; faces with six Mg(3,3)Mg10TiZn cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Zn(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form ZnMg12 cuboctahedra that share corners with six equivalent Zn(1)Mg12 cuboctahedra; corners with twelve Mg(2,2,2)Mg10Ti2 cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiZn cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with six Mg(3,3)Mg10TiZn cuboctahedra; faces with six equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14TiZn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.328
_cell_length_b   6.328
_cell_length_c   10.031
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   347.903
_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  0.165  0.832  0.125  1.0
  Mg  Mg1  1  0.171  0.836  0.625  1.0
  Mg  Mg2  1  0.668  0.335  0.125  1.0
  Mg  Mg3  1  0.664  0.329  0.625  1.0
  Mg  Mg4  1  0.668  0.832  0.125  1.0
  Mg  Mg5  1  0.664  0.836  0.625  1.0
  Mg  Mg6  1  0.328  0.172  0.374  1.0
  Mg  Mg7  1  0.328  0.172  0.876  1.0
  Mg  Mg8  1  0.328  0.657  0.374  1.0
  Mg  Mg9  1  0.328  0.657  0.876  1.0
  Mg  Mg10  1  0.843  0.172  0.374  1.0
  Mg  Mg11  1  0.843  0.172  0.876  1.0
  Mg  Mg12  1  0.833  0.667  0.377  1.0
  Mg  Mg13  1  0.833  0.667  0.873  1.0
  Ti  Ti14  1  0.167  0.333  0.625  1.0
  Zn  Zn15  1  0.167  0.333  0.125  1.0
[/CIF]
.
The structure described by Mg14TiZn crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent Zn(1) atoms to form MgMg10Zn2 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zn2 cuboctahedra; corners with eight Mg(2,2)Mg10Ti2 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10TiZn cuboctahedra; faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiZn cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four Mg(3,3); and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10TiZn cuboctahedra; faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiZn cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four equivalent Mg(3); and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10TiZn cuboctahedra; faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiZn cuboctahedra. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four Mg(3,3); and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10TiZn cuboctahedra; faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiZn cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four Mg(3,3); one Ti(1); and one Zn(1) atom to form distorted MgMg10TiZn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiZn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four Mg(3,3)Mg10TiZn cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2,2)Mg10Ti2 cuboctahedra; faces with five equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six Mg(3,3)Mg10TiZn cuboctahedra. In the sixth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); one Ti(1); and one Zn(1) atom to form distorted MgMg10TiZn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiZn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Mg10TiZn cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2,2)Mg10Ti2 cuboctahedra; faces with five equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six Mg(3,3)Mg10TiZn cuboctahedra. In the seventh Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2,2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg10TiZn cuboctahedra; edges with six Mg(2,2,2)Mg10Ti2 cuboctahedra; edges with six Mg(3,3)Mg10TiZn cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2,2)Mg10Ti2 cuboctahedra; faces with three equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with three equivalent Ti(1)Mg12 cuboctahedra; faces with three equivalent Zn(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10TiZn cuboctahedra. Ti(1) is bonded to six Mg(2,2,2) and six Mg(3,3) atoms to form TiMg12 cuboctahedra that share corners with six equivalent Ti(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with six Mg(2,2,2)Mg10Ti2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiZn cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with six Mg(2,2,2)Mg10Ti2 cuboctahedra; faces with six Mg(3,3)Mg10TiZn cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Zn(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form ZnMg12 cuboctahedra that share corners with six equivalent Zn(1)Mg12 cuboctahedra; corners with twelve Mg(2,2,2)Mg10Ti2 cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiZn cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with six Mg(3,3)Mg10TiZn cuboctahedra; faces with six equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14TiZn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.328
_cell_length_b   6.328
_cell_length_c   10.031
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   347.903
_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  0.165  0.832  0.125  1.0
  Mg  Mg1  1  0.171  0.836  0.625  1.0
  Mg  Mg2  1  0.668  0.335  0.125  1.0
  Mg  Mg3  1  0.664  0.329  0.625  1.0
  Mg  Mg4  1  0.668  0.832  0.125  1.0
  Mg  Mg5  1  0.664  0.836  0.625  1.0
  Mg  Mg6  1  0.328  0.172  0.374  1.0
  Mg  Mg7  1  0.328  0.172  0.876  1.0
  Mg  Mg8  1  0.328  0.657  0.374  1.0
  Mg  Mg9  1  0.328  0.657  0.876  1.0
  Mg  Mg10  1  0.843  0.172  0.374  1.0
  Mg  Mg11  1  0.843  0.172  0.876  1.0
  Mg  Mg12  1  0.833  0.667  0.377  1.0
  Mg  Mg13  1  0.833  0.667  0.873  1.0
  Ti  Ti14  1  0.167  0.333  0.625  1.0
  Zn  Zn15  1  0.167  0.333  0.125  1.0
[/CIF]
.