The structure described by Mg14CuAl crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cu(1)Mg10Al2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Al(1)Mg10Cu2 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Al(1)Mg10Cu2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Cu(1)Mg10Al2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)Mg11Al cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Cu(1), and two equivalent Al(1) atoms to form distorted MgMg8Al2Cu2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with six equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, edges with two equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, edges with two equivalent Cu(1)Mg10Al2 cuboctahedra, edges with two equivalent Al(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, faces with two equivalent Cu(1)Mg10Al2 cuboctahedra, and faces with two equivalent Al(1)Mg10Cu2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, corners with four equivalent Cu(1)Mg10Al2 cuboctahedra, corners with four equivalent Al(1)Mg10Cu2 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with two equivalent Mg(3)Mg8Al2Cu2 cuboctahedra. In the fifth Mg site, Mg(5) is bonded in a 2-coordinate geometry to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(6), two equivalent Mg(7), one Cu(1), and one Al(1) atom. In the sixth Mg site, Mg(6) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Al(1) atom to form distorted MgMg11Al cuboctahedra that share corners with six equivalent Mg(6)Mg11Al cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Al(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Cu2 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Al(1)Mg10Cu2 cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with three equivalent Cu(1)Mg10Al2 cuboctahedra. In the seventh Mg site, Mg(7) is bonded in a distorted single-bond geometry to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Cu(1) atom. Cu(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Al(1) atoms to form CuMg10Al2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Cu(1)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Al(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Al(1)Mg10Cu2 cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, and faces with six equivalent Mg(6)Mg11Al cuboctahedra. Al(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Cu(1) atoms to form AlMg10Cu2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Al(1)Mg10Cu2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Cu(1)Mg10Al2 cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Cu(1)Mg10Al2 cuboctahedra, and faces with four equivalent Mg(3)Mg8Al2Cu2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14AlCu
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.222
_cell_length_b   6.237
_cell_length_c   10.216
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.082
_symmetry_Int_Tables_number   1
_cell_volume   343.092
_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  0.169  0.334  0.625  1.0
  Mg  Mg1  1  0.168  0.834  0.625  1.0
  Mg  Mg2  1  0.673  0.336  0.125  1.0
  Mg  Mg3  1  0.666  0.333  0.625  1.0
  Mg  Mg4  1  0.673  0.836  0.125  1.0
  Mg  Mg5  1  0.666  0.832  0.625  1.0
  Mg  Mg6  1  0.326  0.161  0.359  1.0
  Mg  Mg7  1  0.326  0.161  0.891  1.0
  Mg  Mg8  1  0.326  0.665  0.359  1.0
  Mg  Mg9  1  0.326  0.665  0.891  1.0
  Mg  Mg10  1  0.838  0.169  0.372  1.0
  Mg  Mg11  1  0.838  0.169  0.878  1.0
  Mg  Mg12  1  0.841  0.671  0.366  1.0
  Mg  Mg13  1  0.841  0.671  0.884  1.0
  Al  Al14  1  0.160  0.330  0.125  1.0
  Cu  Cu15  1  0.162  0.831  0.125  1.0
[/CIF]
.
The structure described by Mg14CuAl crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cu(1)Mg10Al2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Al(1)Mg10Cu2 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Al(1)Mg10Cu2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Cu(1)Mg10Al2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)Mg11Al cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Cu(1), and two equivalent Al(1) atoms to form distorted MgMg8Al2Cu2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with six equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, edges with two equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, edges with two equivalent Cu(1)Mg10Al2 cuboctahedra, edges with two equivalent Al(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, faces with two equivalent Cu(1)Mg10Al2 cuboctahedra, and faces with two equivalent Al(1)Mg10Cu2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, corners with four equivalent Cu(1)Mg10Al2 cuboctahedra, corners with four equivalent Al(1)Mg10Cu2 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with two equivalent Mg(3)Mg8Al2Cu2 cuboctahedra. In the fifth Mg site, Mg(5) is bonded in a 2-coordinate geometry to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(6), two equivalent Mg(7), one Cu(1), and one Al(1) atom. In the sixth Mg site, Mg(6) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Al(1) atom to form distorted MgMg11Al cuboctahedra that share corners with six equivalent Mg(6)Mg11Al cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Al(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Cu2 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Al(1)Mg10Cu2 cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with three equivalent Cu(1)Mg10Al2 cuboctahedra. In the seventh Mg site, Mg(7) is bonded in a distorted single-bond geometry to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Cu(1) atom. Cu(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Al(1) atoms to form CuMg10Al2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Cu(1)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Al(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Al(1)Mg10Cu2 cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, and faces with six equivalent Mg(6)Mg11Al cuboctahedra. Al(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Cu(1) atoms to form AlMg10Cu2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Al(1)Mg10Cu2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Cu(1)Mg10Al2 cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Cu2 cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Cu(1)Mg10Al2 cuboctahedra, and faces with four equivalent Mg(3)Mg8Al2Cu2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14AlCu
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.222
_cell_length_b   6.237
_cell_length_c   10.216
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.082
_symmetry_Int_Tables_number   1
_cell_volume   343.092
_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  0.169  0.334  0.625  1.0
  Mg  Mg1  1  0.168  0.834  0.625  1.0
  Mg  Mg2  1  0.673  0.336  0.125  1.0
  Mg  Mg3  1  0.666  0.333  0.625  1.0
  Mg  Mg4  1  0.673  0.836  0.125  1.0
  Mg  Mg5  1  0.666  0.832  0.625  1.0
  Mg  Mg6  1  0.326  0.161  0.359  1.0
  Mg  Mg7  1  0.326  0.161  0.891  1.0
  Mg  Mg8  1  0.326  0.665  0.359  1.0
  Mg  Mg9  1  0.326  0.665  0.891  1.0
  Mg  Mg10  1  0.838  0.169  0.372  1.0
  Mg  Mg11  1  0.838  0.169  0.878  1.0
  Mg  Mg12  1  0.841  0.671  0.366  1.0
  Mg  Mg13  1  0.841  0.671  0.884  1.0
  Al  Al14  1  0.160  0.330  0.125  1.0
  Cu  Cu15  1  0.162  0.831  0.125  1.0
[/CIF]
.