The material structure described by Mg14CoAl 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 Mg(1,1); four Mg(3,3); and two equivalent Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Co(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Co2 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; and faces with four Mg(1,1)Mg10Al2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Co(1) atoms to form distorted MgMg10Co2 cuboctahedra that share corners with four equivalent Al(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Co2 cuboctahedra; corners with eight Mg(1,1)Mg10Al2 cuboctahedra; edges with two equivalent Co(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Co2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Co(1)Mg12 cuboctahedra; and faces with four equivalent Mg(2)Mg10Co2 cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Co(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Co2 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; and faces with four Mg(1,1)Mg10Al2 cuboctahedra. In the fourth Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four equivalent Mg(3); and two equivalent Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Co(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Co2 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; and faces with four Mg(1,1)Mg10Al2 cuboctahedra. In the fifth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one Co(1); and one Al(1) atom. In the sixth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Co(1); and one Al(1) atom. In the seventh Mg site, Mg(4) is bonded to three Mg(1,1,1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; edges with six Mg(1,1,1)Mg10Al2 cuboctahedra; edges with six equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(1,1,1)Mg10Al2 cuboctahedra; faces with three equivalent Mg(2)Mg10Co2 cuboctahedra; faces with three equivalent Co(1)Mg12 cuboctahedra; and faces with three equivalent Al(1)Mg12 cuboctahedra. Co(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form CoMg12 cuboctahedra that share corners with six equivalent Co(1)Mg12 cuboctahedra; corners with twelve Mg(1,1,1)Mg10Al2 cuboctahedra; edges with six equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Co2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Al(1) is bonded to six Mg(1,1,1) and six Mg(3,3) atoms to form AlMg12 cuboctahedra that share corners with six equivalent Al(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Co2 cuboctahedra; edges with six Mg(1,1,1)Mg10Al2 cuboctahedra; faces with two equivalent Co(1)Mg12 cuboctahedra; faces with six Mg(1,1,1)Mg10Al2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_Mg14AlCo
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.263
_cell_length_b   6.263
_cell_length_c   9.842
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   334.344
_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  0.168  0.834  0.125  1.0
  Mg  Mg1  1  0.163  0.831  0.625  1.0
  Mg  Mg2  1  0.666  0.332  0.125  1.0
  Mg  Mg3  1  0.669  0.337  0.625  1.0
  Mg  Mg4  1  0.666  0.834  0.125  1.0
  Mg  Mg5  1  0.669  0.831  0.625  1.0
  Mg  Mg6  1  0.325  0.175  0.385  1.0
  Mg  Mg7  1  0.325  0.175  0.865  1.0
  Mg  Mg8  1  0.325  0.650  0.385  1.0
  Mg  Mg9  1  0.325  0.650  0.865  1.0
  Mg  Mg10  1  0.850  0.175  0.385  1.0
  Mg  Mg11  1  0.850  0.175  0.865  1.0
  Mg  Mg12  1  0.833  0.667  0.373  1.0
  Mg  Mg13  1  0.833  0.667  0.877  1.0
  Al  Al14  1  0.167  0.333  0.125  1.0
  Co  Co15  1  0.167  0.333  0.625  1.0
[/CIF]
.
The material structure described by Mg14CoAl 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 Mg(1,1); four Mg(3,3); and two equivalent Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Co(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Co2 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; and faces with four Mg(1,1)Mg10Al2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Co(1) atoms to form distorted MgMg10Co2 cuboctahedra that share corners with four equivalent Al(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Co2 cuboctahedra; corners with eight Mg(1,1)Mg10Al2 cuboctahedra; edges with two equivalent Co(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Co2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Co(1)Mg12 cuboctahedra; and faces with four equivalent Mg(2)Mg10Co2 cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Co(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Co2 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; and faces with four Mg(1,1)Mg10Al2 cuboctahedra. In the fourth Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four equivalent Mg(3); and two equivalent Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Co(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Co2 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; and faces with four Mg(1,1)Mg10Al2 cuboctahedra. In the fifth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one Co(1); and one Al(1) atom. In the sixth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Co(1); and one Al(1) atom. In the seventh Mg site, Mg(4) is bonded to three Mg(1,1,1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; edges with six Mg(1,1,1)Mg10Al2 cuboctahedra; edges with six equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(1,1,1)Mg10Al2 cuboctahedra; faces with three equivalent Mg(2)Mg10Co2 cuboctahedra; faces with three equivalent Co(1)Mg12 cuboctahedra; and faces with three equivalent Al(1)Mg12 cuboctahedra. Co(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form CoMg12 cuboctahedra that share corners with six equivalent Co(1)Mg12 cuboctahedra; corners with twelve Mg(1,1,1)Mg10Al2 cuboctahedra; edges with six equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Co2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Al(1) is bonded to six Mg(1,1,1) and six Mg(3,3) atoms to form AlMg12 cuboctahedra that share corners with six equivalent Al(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Co2 cuboctahedra; edges with six Mg(1,1,1)Mg10Al2 cuboctahedra; faces with two equivalent Co(1)Mg12 cuboctahedra; faces with six Mg(1,1,1)Mg10Al2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_Mg14AlCo
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.263
_cell_length_b   6.263
_cell_length_c   9.842
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   334.344
_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  0.168  0.834  0.125  1.0
  Mg  Mg1  1  0.163  0.831  0.625  1.0
  Mg  Mg2  1  0.666  0.332  0.125  1.0
  Mg  Mg3  1  0.669  0.337  0.625  1.0
  Mg  Mg4  1  0.666  0.834  0.125  1.0
  Mg  Mg5  1  0.669  0.831  0.625  1.0
  Mg  Mg6  1  0.325  0.175  0.385  1.0
  Mg  Mg7  1  0.325  0.175  0.865  1.0
  Mg  Mg8  1  0.325  0.650  0.385  1.0
  Mg  Mg9  1  0.325  0.650  0.865  1.0
  Mg  Mg10  1  0.850  0.175  0.385  1.0
  Mg  Mg11  1  0.850  0.175  0.865  1.0
  Mg  Mg12  1  0.833  0.667  0.373  1.0
  Mg  Mg13  1  0.833  0.667  0.877  1.0
  Al  Al14  1  0.167  0.333  0.125  1.0
  Co  Co15  1  0.167  0.333  0.625  1.0
[/CIF]
.