The material described by Mg14AlB crystallizes in the hexagonal P-6m2 space group. There are six 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 distorted MgMg10Al2 cuboctahedra that share corners with six equivalent Mg(1)Mg10Al2 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; edges with eight Mg(3,3)Mg10AlB cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Al2 cuboctahedra; and faces with ten Mg(3,3)Mg10AlB cuboctahedra. In the second Mg site, Mg(2) is bonded in a 10-coordinate geometry to two equivalent Mg(4) and four Mg(3,3) atoms. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Al(1) atoms to form distorted MgMg10Al2 cuboctahedra that share corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10AlB cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Al2 cuboctahedra; and faces with ten Mg(3,3)Mg10AlB cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Al(1); and one B(1) atom to form distorted MgMg10AlB cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10AlB cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Al2 cuboctahedra; edges with four Mg(3,3)Mg10AlB cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Mg10Al2 cuboctahedra; and faces with six Mg(3,3)Mg10AlB cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Al(1), and one B(1) atom to form distorted MgMg10AlB cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10AlB cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10AlB cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Mg10Al2 cuboctahedra; and faces with six Mg(3,3)Mg10AlB cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three Mg(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; corners with twelve Mg(3,3)Mg10AlB cuboctahedra; edges with six Mg(1,1)Mg10Al2 cuboctahedra; edges with six Mg(3,3)Mg10AlB cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(1,1)Mg10Al2 cuboctahedra; faces with three equivalent Al(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10AlB cuboctahedra. Al(1) is bonded to six Mg(1,1) and six Mg(3,3) atoms to form AlMg12 cuboctahedra that share corners with six equivalent Al(1)Mg12 cuboctahedra; edges with six Mg(1,1)Mg10Al2 cuboctahedra; edges with twelve Mg(3,3)Mg10AlB cuboctahedra; faces with six Mg(1,1)Mg10Al2 cuboctahedra; faces with six Mg(3,3)Mg10AlB cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. B(1) is bonded in a 6-coordinate geometry to six Mg(3,3) atoms. is represented by the CIF file [CIF]
data_Mg14AlB
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.237
_cell_length_b   6.237
_cell_length_c   10.172
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   342.716
_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  0.165  0.832  0.625  1.0
  Mg  Mg2  1  0.666  0.332  0.125  1.0
  Mg  Mg3  1  0.668  0.335  0.625  1.0
  Mg  Mg4  1  0.666  0.834  0.125  1.0
  Mg  Mg5  1  0.668  0.832  0.625  1.0
  Mg  Mg6  1  0.328  0.172  0.381  1.0
  Mg  Mg7  1  0.328  0.172  0.869  1.0
  Mg  Mg8  1  0.328  0.657  0.381  1.0
  Mg  Mg9  1  0.328  0.657  0.869  1.0
  Mg  Mg10  1  0.843  0.172  0.381  1.0
  Mg  Mg11  1  0.843  0.172  0.869  1.0
  Mg  Mg12  1  0.833  0.667  0.374  1.0
  Mg  Mg13  1  0.833  0.667  0.876  1.0
  Al  Al14  1  0.167  0.333  0.125  1.0
  B  B15  1  0.167  0.333  0.625  1.0
[/CIF]
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The material described by Mg14AlB crystallizes in the hexagonal P-6m2 space group. There are six 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 distorted MgMg10Al2 cuboctahedra that share corners with six equivalent Mg(1)Mg10Al2 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; edges with eight Mg(3,3)Mg10AlB cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Al2 cuboctahedra; and faces with ten Mg(3,3)Mg10AlB cuboctahedra. In the second Mg site, Mg(2) is bonded in a 10-coordinate geometry to two equivalent Mg(4) and four Mg(3,3) atoms. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Al(1) atoms to form distorted MgMg10Al2 cuboctahedra that share corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10AlB cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Al2 cuboctahedra; and faces with ten Mg(3,3)Mg10AlB cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Al(1); and one B(1) atom to form distorted MgMg10AlB cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10AlB cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Al2 cuboctahedra; edges with four Mg(3,3)Mg10AlB cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Mg10Al2 cuboctahedra; and faces with six Mg(3,3)Mg10AlB cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Al(1), and one B(1) atom to form distorted MgMg10AlB cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10AlB cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10AlB cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Mg10Al2 cuboctahedra; and faces with six Mg(3,3)Mg10AlB cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three Mg(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; corners with twelve Mg(3,3)Mg10AlB cuboctahedra; edges with six Mg(1,1)Mg10Al2 cuboctahedra; edges with six Mg(3,3)Mg10AlB cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(1,1)Mg10Al2 cuboctahedra; faces with three equivalent Al(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10AlB cuboctahedra. Al(1) is bonded to six Mg(1,1) and six Mg(3,3) atoms to form AlMg12 cuboctahedra that share corners with six equivalent Al(1)Mg12 cuboctahedra; edges with six Mg(1,1)Mg10Al2 cuboctahedra; edges with twelve Mg(3,3)Mg10AlB cuboctahedra; faces with six Mg(1,1)Mg10Al2 cuboctahedra; faces with six Mg(3,3)Mg10AlB cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. B(1) is bonded in a 6-coordinate geometry to six Mg(3,3) atoms. is represented by the CIF file [CIF]
data_Mg14AlB
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.237
_cell_length_b   6.237
_cell_length_c   10.172
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   342.716
_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  0.165  0.832  0.625  1.0
  Mg  Mg2  1  0.666  0.332  0.125  1.0
  Mg  Mg3  1  0.668  0.335  0.625  1.0
  Mg  Mg4  1  0.666  0.834  0.125  1.0
  Mg  Mg5  1  0.668  0.832  0.625  1.0
  Mg  Mg6  1  0.328  0.172  0.381  1.0
  Mg  Mg7  1  0.328  0.172  0.869  1.0
  Mg  Mg8  1  0.328  0.657  0.381  1.0
  Mg  Mg9  1  0.328  0.657  0.869  1.0
  Mg  Mg10  1  0.843  0.172  0.381  1.0
  Mg  Mg11  1  0.843  0.172  0.869  1.0
  Mg  Mg12  1  0.833  0.667  0.374  1.0
  Mg  Mg13  1  0.833  0.667  0.876  1.0
  Al  Al14  1  0.167  0.333  0.125  1.0
  B  B15  1  0.167  0.333  0.625  1.0
[/CIF]
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