The material described by Mg6TiGa is beta-derived structured and crystallizes in the orthorhombic Amm2 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ti(1), and two equivalent Ga(1) atoms to form distorted MgMg8Ti2Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Ti2 cuboctahedra, corners with four equivalent Ti(1)Mg10Ga2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg10Ti2 cuboctahedra, edges with two equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Ti(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, edges with four equivalent Ga(1)Mg10Ti2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, and faces with eight equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Ti(1)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Ti(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, and faces with six equivalent Ga(1)Mg10Ti2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ti(1), and two equivalent Ga(1) atoms to form distorted MgMg8Ti2Ga2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with four equivalent Ga(1)Mg10Ti2 cuboctahedra, corners with ten equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with two equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, edges with four equivalent Ti(1)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Ti2 cuboctahedra, corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra, faces with two equivalent Ga(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, and faces with six equivalent Ti(1)Mg10Ga2 cuboctahedra. Ti(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ga(1) atoms to form TiMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Ti2 cuboctahedra, corners with six equivalent Ti(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, edges with four equivalent Ga(1)Mg10Ti2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra. Ga(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ti(1) atoms to form distorted GaMg10Ti2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with six equivalent Ga(1)Mg10Ti2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, edges with four equivalent Ti(1)Mg10Ga2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ti(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, and faces with six equivalent Mg(2)Mg10Ti2 cuboctahedra. is represented by the CIF file [CIF]
data_Mg6TiGa
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.840
_cell_length_b   6.298
_cell_length_c   6.298
_cell_angle_alpha   119.849
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   166.499
_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
  Ga  Ga0  1  0.500  0.683  0.317  1.0
  Mg  Mg1  1  1.000  0.828  0.664  1.0
  Mg  Mg2  1  1.000  0.336  0.172  1.0
  Mg  Mg3  1  0.000  0.333  0.667  1.0
  Mg  Mg4  1  0.500  0.670  0.841  1.0
  Mg  Mg5  1  0.500  0.159  0.330  1.0
  Mg  Mg6  1  0.500  0.167  0.833  1.0
  Ti  Ti7  1  0.000  0.824  0.176  1.0
[/CIF]
.
The material described by Mg6TiGa is beta-derived structured and crystallizes in the orthorhombic Amm2 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ti(1), and two equivalent Ga(1) atoms to form distorted MgMg8Ti2Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Ti2 cuboctahedra, corners with four equivalent Ti(1)Mg10Ga2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg10Ti2 cuboctahedra, edges with two equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Ti(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, edges with four equivalent Ga(1)Mg10Ti2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, and faces with eight equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Ti(1)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Ti(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, and faces with six equivalent Ga(1)Mg10Ti2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ti(1), and two equivalent Ga(1) atoms to form distorted MgMg8Ti2Ga2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with four equivalent Ga(1)Mg10Ti2 cuboctahedra, corners with ten equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with two equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, edges with four equivalent Ti(1)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Ti2 cuboctahedra, corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra, faces with two equivalent Ga(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, and faces with six equivalent Ti(1)Mg10Ga2 cuboctahedra. Ti(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ga(1) atoms to form TiMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Ti2 cuboctahedra, corners with six equivalent Ti(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, edges with four equivalent Ga(1)Mg10Ti2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra. Ga(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ti(1) atoms to form distorted GaMg10Ti2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with six equivalent Ga(1)Mg10Ti2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, edges with four equivalent Ti(1)Mg10Ga2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ti(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Ti2Ga2 cuboctahedra, and faces with six equivalent Mg(2)Mg10Ti2 cuboctahedra. is represented by the CIF file [CIF]
data_Mg6TiGa
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.840
_cell_length_b   6.298
_cell_length_c   6.298
_cell_angle_alpha   119.849
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   166.499
_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
  Ga  Ga0  1  0.500  0.683  0.317  1.0
  Mg  Mg1  1  1.000  0.828  0.664  1.0
  Mg  Mg2  1  1.000  0.336  0.172  1.0
  Mg  Mg3  1  0.000  0.333  0.667  1.0
  Mg  Mg4  1  0.500  0.670  0.841  1.0
  Mg  Mg5  1  0.500  0.159  0.330  1.0
  Mg  Mg6  1  0.500  0.167  0.833  1.0
  Ti  Ti7  1  0.000  0.824  0.176  1.0
[/CIF]
.