The material structure described by Mg16Al12Ge crystallizes in the trigonal R3m space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 12-coordinate geometry to two equivalent Mg(2), four equivalent Mg(5), one Al(2), two equivalent Al(1), two equivalent Al(3), and one Ge(1) atom. In the second Mg site, Mg(2) is bonded in a 12-coordinate geometry to one Mg(3), two equivalent Mg(1), four equivalent Mg(5), one Al(1), and four equivalent Al(3) atoms. In the third Mg site, Mg(3) is bonded in a 10-coordinate geometry to one Mg(2), one Mg(4), two equivalent Mg(5), two equivalent Al(1), two equivalent Al(2), and two equivalent Al(3) atoms. In the fourth Mg site, Mg(4) is bonded in a 1-coordinate geometry to three equivalent Mg(3), three equivalent Al(1), three equivalent Al(2), six equivalent Al(3), and one Ge(1) atom. In the fifth Mg site, Mg(5) is bonded in a 12-coordinate geometry to one Mg(3), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(5), one Al(1), two equivalent Al(2), and two equivalent Al(3) atoms. There are three inequivalent Al sites. In the first Al site, Al(1) is bonded in a distorted q6 geometry to one Mg(2), one Mg(4), two equivalent Mg(1), two equivalent Mg(3), two equivalent Mg(5), one Al(2), and two equivalent Al(1) atoms. In the second Al site, Al(2) is bonded in a 11-coordinate geometry to one Mg(1), one Mg(4), two equivalent Mg(3), four equivalent Mg(5), one Al(1), and two equivalent Al(3) atoms. In the third Al site, Al(3) is bonded in a 11-coordinate geometry to one Mg(1), one Mg(3), one Mg(4), two equivalent Mg(2), two equivalent Mg(5), one Al(2), two equivalent Al(3), and one Ge(1) atom. Ge(1) is bonded in a 10-coordinate geometry to one Mg(4), three equivalent Mg(1), and six equivalent Al(3) atoms. is represented by the CIF file [CIF]
data_Mg16Al12Ge
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.090
_cell_length_b   9.090
_cell_length_c   9.090
_cell_angle_alpha   109.313
_cell_angle_beta   109.313
_cell_angle_gamma   109.313
_symmetry_Int_Tables_number   1
_cell_volume   581.585
_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  0.409  0.409  0.706  1.0
  Mg  Mg1  1  0.683  0.683  0.283  1.0
  Mg  Mg2  1  0.998  0.998  0.346  1.0
  Mg  Mg3  1  0.003  0.003  0.003  1.0
  Mg  Mg4  1  0.596  0.317  0.998  1.0
  Mg  Mg5  1  0.706  0.409  0.409  1.0
  Mg  Mg6  1  0.317  0.998  0.596  1.0
  Mg  Mg7  1  0.346  0.998  0.998  1.0
  Mg  Mg8  1  0.683  0.283  0.683  1.0
  Mg  Mg9  1  0.998  0.596  0.317  1.0
  Mg  Mg10  1  0.596  0.998  0.317  1.0
  Mg  Mg11  1  0.283  0.683  0.683  1.0
  Mg  Mg12  1  0.998  0.346  0.998  1.0
  Mg  Mg13  1  0.998  0.317  0.596  1.0
  Mg  Mg14  1  0.409  0.706  0.409  1.0
  Mg  Mg15  1  0.317  0.596  0.998  1.0
  Al  Al16  1  0.358  0.358  0.170  1.0
  Al  Al17  1  0.186  0.186  0.810  1.0
  Al  Al18  1  0.816  0.632  0.003  1.0
  Al  Al19  1  0.003  0.816  0.632  1.0
  Al  Al20  1  0.358  0.170  0.358  1.0
  Al  Al21  1  0.003  0.632  0.816  1.0
  Al  Al22  1  0.186  0.810  0.186  1.0
  Al  Al23  1  0.810  0.186  0.186  1.0
  Al  Al24  1  0.632  0.003  0.816  1.0
  Al  Al25  1  0.170  0.358  0.358  1.0
  Al  Al26  1  0.816  0.003  0.632  1.0
  Al  Al27  1  0.632  0.816  0.003  1.0
  Ge  Ge28  1  0.691  0.691  0.691  1.0
[/CIF]
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The material structure described by Mg16Al12Ge crystallizes in the trigonal R3m space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 12-coordinate geometry to two equivalent Mg(2), four equivalent Mg(5), one Al(2), two equivalent Al(1), two equivalent Al(3), and one Ge(1) atom. In the second Mg site, Mg(2) is bonded in a 12-coordinate geometry to one Mg(3), two equivalent Mg(1), four equivalent Mg(5), one Al(1), and four equivalent Al(3) atoms. In the third Mg site, Mg(3) is bonded in a 10-coordinate geometry to one Mg(2), one Mg(4), two equivalent Mg(5), two equivalent Al(1), two equivalent Al(2), and two equivalent Al(3) atoms. In the fourth Mg site, Mg(4) is bonded in a 1-coordinate geometry to three equivalent Mg(3), three equivalent Al(1), three equivalent Al(2), six equivalent Al(3), and one Ge(1) atom. In the fifth Mg site, Mg(5) is bonded in a 12-coordinate geometry to one Mg(3), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(5), one Al(1), two equivalent Al(2), and two equivalent Al(3) atoms. There are three inequivalent Al sites. In the first Al site, Al(1) is bonded in a distorted q6 geometry to one Mg(2), one Mg(4), two equivalent Mg(1), two equivalent Mg(3), two equivalent Mg(5), one Al(2), and two equivalent Al(1) atoms. In the second Al site, Al(2) is bonded in a 11-coordinate geometry to one Mg(1), one Mg(4), two equivalent Mg(3), four equivalent Mg(5), one Al(1), and two equivalent Al(3) atoms. In the third Al site, Al(3) is bonded in a 11-coordinate geometry to one Mg(1), one Mg(3), one Mg(4), two equivalent Mg(2), two equivalent Mg(5), one Al(2), two equivalent Al(3), and one Ge(1) atom. Ge(1) is bonded in a 10-coordinate geometry to one Mg(4), three equivalent Mg(1), and six equivalent Al(3) atoms. is represented by the CIF file [CIF]
data_Mg16Al12Ge
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.090
_cell_length_b   9.090
_cell_length_c   9.090
_cell_angle_alpha   109.313
_cell_angle_beta   109.313
_cell_angle_gamma   109.313
_symmetry_Int_Tables_number   1
_cell_volume   581.585
_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  0.409  0.409  0.706  1.0
  Mg  Mg1  1  0.683  0.683  0.283  1.0
  Mg  Mg2  1  0.998  0.998  0.346  1.0
  Mg  Mg3  1  0.003  0.003  0.003  1.0
  Mg  Mg4  1  0.596  0.317  0.998  1.0
  Mg  Mg5  1  0.706  0.409  0.409  1.0
  Mg  Mg6  1  0.317  0.998  0.596  1.0
  Mg  Mg7  1  0.346  0.998  0.998  1.0
  Mg  Mg8  1  0.683  0.283  0.683  1.0
  Mg  Mg9  1  0.998  0.596  0.317  1.0
  Mg  Mg10  1  0.596  0.998  0.317  1.0
  Mg  Mg11  1  0.283  0.683  0.683  1.0
  Mg  Mg12  1  0.998  0.346  0.998  1.0
  Mg  Mg13  1  0.998  0.317  0.596  1.0
  Mg  Mg14  1  0.409  0.706  0.409  1.0
  Mg  Mg15  1  0.317  0.596  0.998  1.0
  Al  Al16  1  0.358  0.358  0.170  1.0
  Al  Al17  1  0.186  0.186  0.810  1.0
  Al  Al18  1  0.816  0.632  0.003  1.0
  Al  Al19  1  0.003  0.816  0.632  1.0
  Al  Al20  1  0.358  0.170  0.358  1.0
  Al  Al21  1  0.003  0.632  0.816  1.0
  Al  Al22  1  0.186  0.810  0.186  1.0
  Al  Al23  1  0.810  0.186  0.186  1.0
  Al  Al24  1  0.632  0.003  0.816  1.0
  Al  Al25  1  0.170  0.358  0.358  1.0
  Al  Al26  1  0.816  0.003  0.632  1.0
  Al  Al27  1  0.632  0.816  0.003  1.0
  Ge  Ge28  1  0.691  0.691  0.691  1.0
[/CIF]
.