The material described by Mg16ZrAl12 is gamma-brass-derived structured and crystallizes in the trigonal R3m space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 11-coordinate geometry to one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Al(1), two equivalent Al(2), and two equivalent Al(3) atoms. In the second Mg site, Mg(2) is bonded in a 16-coordinate geometry to three equivalent Mg(1), one Zr(1), three equivalent Al(1), three equivalent Al(2), and six equivalent Al(3) atoms. In the third Mg site, Mg(3) is bonded in a 13-coordinate geometry to one Mg(1), two equivalent Mg(4), four equivalent Mg(5), one Zr(1), one Al(2), two equivalent Al(1), and two equivalent Al(3) atoms. In the fourth Mg site, Mg(4) is bonded in a 3-coordinate geometry to one Mg(1), two equivalent Mg(3), four equivalent Mg(5), one Al(1), and four equivalent Al(3) atoms. In the fifth Mg site, Mg(5) is bonded in a 12-coordinate geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(5), one Al(1), two equivalent Al(2), and two equivalent Al(3) atoms. Zr(1) is bonded in a 13-coordinate geometry to one Mg(2), three equivalent Mg(3), three equivalent Al(1), and six equivalent Al(3) atoms. There are three inequivalent Al sites. In the first Al site, Al(1) is bonded in a 12-coordinate geometry to one Mg(2), one Mg(4), two equivalent Mg(1), two equivalent Mg(3), two equivalent Mg(5), one Zr(1), 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(2), one Mg(3), two equivalent Mg(1), four equivalent Mg(5), one Al(1), and two equivalent Al(3) atoms. In the third Al site, Al(3) is bonded in a distorted q6 geometry to one Mg(1), one Mg(2), one Mg(3), two equivalent Mg(4), two equivalent Mg(5), one Zr(1), one Al(2), and two equivalent Al(3) atoms. is represented by the CIF file [CIF]
data_Mg16ZrAl12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.210
_cell_length_b   9.210
_cell_length_c   9.210
_cell_angle_alpha   110.434
_cell_angle_beta   110.434
_cell_angle_gamma   110.434
_symmetry_Int_Tables_number   1
_cell_volume   579.022
_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  0.005  0.005  0.345  1.0
  Mg  Mg1  1  0.997  0.997  0.997  1.0
  Mg  Mg2  1  0.395  0.395  0.721  1.0
  Mg  Mg3  1  0.685  0.685  0.280  1.0
  Mg  Mg4  1  0.606  0.311  0.999  1.0
  Mg  Mg5  1  0.311  0.999  0.606  1.0
  Mg  Mg6  1  0.721  0.395  0.395  1.0
  Mg  Mg7  1  0.345  0.005  0.005  1.0
  Mg  Mg8  1  0.999  0.606  0.311  1.0
  Mg  Mg9  1  0.685  0.280  0.685  1.0
  Mg  Mg10  1  0.280  0.685  0.685  1.0
  Mg  Mg11  1  0.606  0.999  0.311  1.0
  Mg  Mg12  1  0.005  0.345  0.005  1.0
  Mg  Mg13  1  0.395  0.721  0.395  1.0
  Mg  Mg14  1  0.999  0.311  0.606  1.0
  Mg  Mg15  1  0.311  0.606  0.999  1.0
  Zr  Zr16  1  0.629  0.629  0.629  1.0
  Al  Al17  1  0.374  0.374  0.194  1.0
  Al  Al18  1  0.191  0.191  0.825  1.0
  Al  Al19  1  0.812  0.634  0.993  1.0
  Al  Al20  1  0.993  0.812  0.634  1.0
  Al  Al21  1  0.374  0.194  0.374  1.0
  Al  Al22  1  0.993  0.634  0.812  1.0
  Al  Al23  1  0.191  0.825  0.191  1.0
  Al  Al24  1  0.825  0.191  0.191  1.0
  Al  Al25  1  0.634  0.993  0.812  1.0
  Al  Al26  1  0.194  0.374  0.374  1.0
  Al  Al27  1  0.812  0.993  0.634  1.0
  Al  Al28  1  0.634  0.812  0.993  1.0
[/CIF]
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The material described by Mg16ZrAl12 is gamma-brass-derived structured and crystallizes in the trigonal R3m space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 11-coordinate geometry to one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Al(1), two equivalent Al(2), and two equivalent Al(3) atoms. In the second Mg site, Mg(2) is bonded in a 16-coordinate geometry to three equivalent Mg(1), one Zr(1), three equivalent Al(1), three equivalent Al(2), and six equivalent Al(3) atoms. In the third Mg site, Mg(3) is bonded in a 13-coordinate geometry to one Mg(1), two equivalent Mg(4), four equivalent Mg(5), one Zr(1), one Al(2), two equivalent Al(1), and two equivalent Al(3) atoms. In the fourth Mg site, Mg(4) is bonded in a 3-coordinate geometry to one Mg(1), two equivalent Mg(3), four equivalent Mg(5), one Al(1), and four equivalent Al(3) atoms. In the fifth Mg site, Mg(5) is bonded in a 12-coordinate geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(5), one Al(1), two equivalent Al(2), and two equivalent Al(3) atoms. Zr(1) is bonded in a 13-coordinate geometry to one Mg(2), three equivalent Mg(3), three equivalent Al(1), and six equivalent Al(3) atoms. There are three inequivalent Al sites. In the first Al site, Al(1) is bonded in a 12-coordinate geometry to one Mg(2), one Mg(4), two equivalent Mg(1), two equivalent Mg(3), two equivalent Mg(5), one Zr(1), 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(2), one Mg(3), two equivalent Mg(1), four equivalent Mg(5), one Al(1), and two equivalent Al(3) atoms. In the third Al site, Al(3) is bonded in a distorted q6 geometry to one Mg(1), one Mg(2), one Mg(3), two equivalent Mg(4), two equivalent Mg(5), one Zr(1), one Al(2), and two equivalent Al(3) atoms. is represented by the CIF file [CIF]
data_Mg16ZrAl12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.210
_cell_length_b   9.210
_cell_length_c   9.210
_cell_angle_alpha   110.434
_cell_angle_beta   110.434
_cell_angle_gamma   110.434
_symmetry_Int_Tables_number   1
_cell_volume   579.022
_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  0.005  0.005  0.345  1.0
  Mg  Mg1  1  0.997  0.997  0.997  1.0
  Mg  Mg2  1  0.395  0.395  0.721  1.0
  Mg  Mg3  1  0.685  0.685  0.280  1.0
  Mg  Mg4  1  0.606  0.311  0.999  1.0
  Mg  Mg5  1  0.311  0.999  0.606  1.0
  Mg  Mg6  1  0.721  0.395  0.395  1.0
  Mg  Mg7  1  0.345  0.005  0.005  1.0
  Mg  Mg8  1  0.999  0.606  0.311  1.0
  Mg  Mg9  1  0.685  0.280  0.685  1.0
  Mg  Mg10  1  0.280  0.685  0.685  1.0
  Mg  Mg11  1  0.606  0.999  0.311  1.0
  Mg  Mg12  1  0.005  0.345  0.005  1.0
  Mg  Mg13  1  0.395  0.721  0.395  1.0
  Mg  Mg14  1  0.999  0.311  0.606  1.0
  Mg  Mg15  1  0.311  0.606  0.999  1.0
  Zr  Zr16  1  0.629  0.629  0.629  1.0
  Al  Al17  1  0.374  0.374  0.194  1.0
  Al  Al18  1  0.191  0.191  0.825  1.0
  Al  Al19  1  0.812  0.634  0.993  1.0
  Al  Al20  1  0.993  0.812  0.634  1.0
  Al  Al21  1  0.374  0.194  0.374  1.0
  Al  Al22  1  0.993  0.634  0.812  1.0
  Al  Al23  1  0.191  0.825  0.191  1.0
  Al  Al24  1  0.825  0.191  0.191  1.0
  Al  Al25  1  0.634  0.993  0.812  1.0
  Al  Al26  1  0.194  0.374  0.374  1.0
  Al  Al27  1  0.812  0.993  0.634  1.0
  Al  Al28  1  0.634  0.812  0.993  1.0
[/CIF]
.