The structure described by Mg7Ag12Ga crystallizes in the trigonal R3m space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a body-centered cubic geometry to one Ag(3), one Ag(6), three equivalent Ag(1), and three equivalent Ag(8) atoms. In the second Mg site, Mg(2) is bonded in a distorted body-centered cubic geometry to one Ag(5), one Ag(7), three equivalent Ag(10), three equivalent Ag(11), three equivalent Ag(12), and three equivalent Ag(2) atoms. In the third Mg site, Mg(3) is bonded in a distorted body-centered cubic geometry to one Ag(2), one Ag(8), three equivalent Ag(12), three equivalent Ag(3), and three equivalent Ag(7) atoms. In the fourth Mg site, Mg(4) is bonded in a body-centered cubic geometry to one Ag(1), one Ag(9), three equivalent Ag(4), and three equivalent Ag(6) atoms. In the fifth Mg site, Mg(5) is bonded in a distorted body-centered cubic geometry to one Ag(10), one Ag(4), three equivalent Ag(11), three equivalent Ag(5), and three equivalent Ag(9) atoms. In the sixth Mg site, Mg(6) is bonded in a body-centered cubic geometry to one Ag(1), one Ag(7), three equivalent Ag(3), and three equivalent Ag(8) atoms. In the seventh Mg site, Mg(7) is bonded in a body-centered cubic geometry to one Ag(4), one Ag(8), three equivalent Ag(1), and three equivalent Ag(6) atoms. In the eighth Mg site, Mg(7) is bonded in a body-centered cubic geometry to one Ag(4), one Ag(8), three equivalent Ag(1), and three equivalent Ag(6) atoms. There are twelve inequivalent Ag sites. In the first Ag site, Ag(1) is bonded in a body-centered cubic geometry to one Mg(4), one Mg(6), three equivalent Mg(1), and three equivalent Mg(7) atoms. In the second Ag site, Ag(2) is bonded to one Mg(3), three equivalent Mg(2), one Ag(11), and three equivalent Ag(12) atoms to form a mixture of distorted corner, edge, and face-sharing AgMg4Ag4 tetrahedra. In the third Ag site, Ag(3) is bonded in a 7-coordinate geometry to one Mg(1), three equivalent Mg(3), three equivalent Mg(6), and one Ag(12) atom. In the fourth Ag site, Ag(4) is bonded in a body-centered cubic geometry to one Mg(5), one Mg(7), three equivalent Mg(4), and three equivalent Ga(1) atoms. In the fifth Ag site, Ag(5) is bonded in a 8-coordinate geometry to one Mg(2), three equivalent Mg(5), three equivalent Ag(11), and one Ga(1) atom. In the sixth Ag site, Ag(6) is bonded in a body-centered cubic geometry to one Mg(1), three equivalent Mg(4), three equivalent Mg(7), and one Ga(1) atom. In the seventh Ag site, Ag(7) is bonded in a 5-coordinate geometry to one Mg(2), one Mg(6), three equivalent Mg(3), and three equivalent Ag(12) atoms. In the eighth Ag site, Ag(8) is bonded in a body-centered cubic geometry to one Mg(3), one Mg(7), three equivalent Mg(1), and three equivalent Mg(6) atoms. In the ninth Ag site, Ag(9) is bonded in a 8-coordinate geometry to one Mg(4), three equivalent Mg(5), one Ag(11), and three equivalent Ga(1) atoms. In the tenth Ag site, Ag(10) is bonded to one Mg(5), three equivalent Mg(2), one Ag(12), and three equivalent Ag(11) atoms to form a mixture of distorted corner, edge, and face-sharing AgMg4Ag4 tetrahedra. In the eleventh Ag site, Ag(11) is bonded in a 14-coordinate geometry to three equivalent Mg(2), three equivalent Mg(5), one Ag(2), one Ag(9), three equivalent Ag(10), and three equivalent Ag(5) atoms. In the twelfth Ag site, Ag(12) is bonded in a 14-coordinate geometry to three equivalent Mg(2), three equivalent Mg(3), one Ag(10), one Ag(3), three equivalent Ag(2), and three equivalent Ag(7) atoms. Ga(1) is bonded in a distorted body-centered cubic geometry to one Ag(5), one Ag(6), three equivalent Ag(4), and three equivalent Ag(9) atoms. is represented by the CIF card [CIF]
data_Mg7GaAg12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   19.325
_cell_length_b   19.325
_cell_length_c   19.325
_cell_angle_alpha   13.920
_cell_angle_beta   13.920
_cell_angle_gamma   13.920
_symmetry_Int_Tables_number   1
_cell_volume   363.467
_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  0.400  0.400  0.400  1.0
  Mg  Mg1  1  0.200  0.200  0.200  1.0
  Mg  Mg2  1  0.800  0.800  0.800  1.0
  Mg  Mg3  1  0.000  0.000  0.000  1.0
  Mg  Mg4  1  0.600  0.600  0.600  1.0
  Mg  Mg5  1  0.100  0.100  0.100  1.0
  Mg  Mg6  1  0.700  0.700  0.700  1.0
  Ga  Ga7  1  0.300  0.300  0.300  1.0
  Ag  Ag8  1  0.050  0.050  0.050  1.0
  Ag  Ag9  1  0.850  0.850  0.850  1.0
  Ag  Ag10  1  0.450  0.450  0.450  1.0
  Ag  Ag11  1  0.650  0.650  0.650  1.0
  Ag  Ag12  1  0.250  0.250  0.250  1.0
  Ag  Ag13  1  0.350  0.350  0.350  1.0
  Ag  Ag14  1  0.150  0.150  0.150  1.0
  Ag  Ag15  1  0.750  0.750  0.750  1.0
  Ag  Ag16  1  0.950  0.950  0.950  1.0
  Ag  Ag17  1  0.550  0.550  0.550  1.0
  Ag  Ag18  1  0.900  0.900  0.900  1.0
  Ag  Ag19  1  0.500  0.500  0.500  1.0
[/CIF]
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The structure described by Mg7Ag12Ga crystallizes in the trigonal R3m space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a body-centered cubic geometry to one Ag(3), one Ag(6), three equivalent Ag(1), and three equivalent Ag(8) atoms. In the second Mg site, Mg(2) is bonded in a distorted body-centered cubic geometry to one Ag(5), one Ag(7), three equivalent Ag(10), three equivalent Ag(11), three equivalent Ag(12), and three equivalent Ag(2) atoms. In the third Mg site, Mg(3) is bonded in a distorted body-centered cubic geometry to one Ag(2), one Ag(8), three equivalent Ag(12), three equivalent Ag(3), and three equivalent Ag(7) atoms. In the fourth Mg site, Mg(4) is bonded in a body-centered cubic geometry to one Ag(1), one Ag(9), three equivalent Ag(4), and three equivalent Ag(6) atoms. In the fifth Mg site, Mg(5) is bonded in a distorted body-centered cubic geometry to one Ag(10), one Ag(4), three equivalent Ag(11), three equivalent Ag(5), and three equivalent Ag(9) atoms. In the sixth Mg site, Mg(6) is bonded in a body-centered cubic geometry to one Ag(1), one Ag(7), three equivalent Ag(3), and three equivalent Ag(8) atoms. In the seventh Mg site, Mg(7) is bonded in a body-centered cubic geometry to one Ag(4), one Ag(8), three equivalent Ag(1), and three equivalent Ag(6) atoms. In the eighth Mg site, Mg(7) is bonded in a body-centered cubic geometry to one Ag(4), one Ag(8), three equivalent Ag(1), and three equivalent Ag(6) atoms. There are twelve inequivalent Ag sites. In the first Ag site, Ag(1) is bonded in a body-centered cubic geometry to one Mg(4), one Mg(6), three equivalent Mg(1), and three equivalent Mg(7) atoms. In the second Ag site, Ag(2) is bonded to one Mg(3), three equivalent Mg(2), one Ag(11), and three equivalent Ag(12) atoms to form a mixture of distorted corner, edge, and face-sharing AgMg4Ag4 tetrahedra. In the third Ag site, Ag(3) is bonded in a 7-coordinate geometry to one Mg(1), three equivalent Mg(3), three equivalent Mg(6), and one Ag(12) atom. In the fourth Ag site, Ag(4) is bonded in a body-centered cubic geometry to one Mg(5), one Mg(7), three equivalent Mg(4), and three equivalent Ga(1) atoms. In the fifth Ag site, Ag(5) is bonded in a 8-coordinate geometry to one Mg(2), three equivalent Mg(5), three equivalent Ag(11), and one Ga(1) atom. In the sixth Ag site, Ag(6) is bonded in a body-centered cubic geometry to one Mg(1), three equivalent Mg(4), three equivalent Mg(7), and one Ga(1) atom. In the seventh Ag site, Ag(7) is bonded in a 5-coordinate geometry to one Mg(2), one Mg(6), three equivalent Mg(3), and three equivalent Ag(12) atoms. In the eighth Ag site, Ag(8) is bonded in a body-centered cubic geometry to one Mg(3), one Mg(7), three equivalent Mg(1), and three equivalent Mg(6) atoms. In the ninth Ag site, Ag(9) is bonded in a 8-coordinate geometry to one Mg(4), three equivalent Mg(5), one Ag(11), and three equivalent Ga(1) atoms. In the tenth Ag site, Ag(10) is bonded to one Mg(5), three equivalent Mg(2), one Ag(12), and three equivalent Ag(11) atoms to form a mixture of distorted corner, edge, and face-sharing AgMg4Ag4 tetrahedra. In the eleventh Ag site, Ag(11) is bonded in a 14-coordinate geometry to three equivalent Mg(2), three equivalent Mg(5), one Ag(2), one Ag(9), three equivalent Ag(10), and three equivalent Ag(5) atoms. In the twelfth Ag site, Ag(12) is bonded in a 14-coordinate geometry to three equivalent Mg(2), three equivalent Mg(3), one Ag(10), one Ag(3), three equivalent Ag(2), and three equivalent Ag(7) atoms. Ga(1) is bonded in a distorted body-centered cubic geometry to one Ag(5), one Ag(6), three equivalent Ag(4), and three equivalent Ag(9) atoms. is represented by the CIF card [CIF]
data_Mg7GaAg12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   19.325
_cell_length_b   19.325
_cell_length_c   19.325
_cell_angle_alpha   13.920
_cell_angle_beta   13.920
_cell_angle_gamma   13.920
_symmetry_Int_Tables_number   1
_cell_volume   363.467
_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  0.400  0.400  0.400  1.0
  Mg  Mg1  1  0.200  0.200  0.200  1.0
  Mg  Mg2  1  0.800  0.800  0.800  1.0
  Mg  Mg3  1  0.000  0.000  0.000  1.0
  Mg  Mg4  1  0.600  0.600  0.600  1.0
  Mg  Mg5  1  0.100  0.100  0.100  1.0
  Mg  Mg6  1  0.700  0.700  0.700  1.0
  Ga  Ga7  1  0.300  0.300  0.300  1.0
  Ag  Ag8  1  0.050  0.050  0.050  1.0
  Ag  Ag9  1  0.850  0.850  0.850  1.0
  Ag  Ag10  1  0.450  0.450  0.450  1.0
  Ag  Ag11  1  0.650  0.650  0.650  1.0
  Ag  Ag12  1  0.250  0.250  0.250  1.0
  Ag  Ag13  1  0.350  0.350  0.350  1.0
  Ag  Ag14  1  0.150  0.150  0.150  1.0
  Ag  Ag15  1  0.750  0.750  0.750  1.0
  Ag  Ag16  1  0.950  0.950  0.950  1.0
  Ag  Ag17  1  0.550  0.550  0.550  1.0
  Ag  Ag18  1  0.900  0.900  0.900  1.0
  Ag  Ag19  1  0.500  0.500  0.500  1.0
[/CIF]
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