The structure described by MgCuGa is Hexagonal Laves-derived structured and crystallizes in the orthorhombic Amm2 space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 16-coordinate geometry to one Mg(1), three equivalent Mg(2), three equivalent Cu(1), four equivalent Cu(2), one Ga(3), two equivalent Ga(1), and two equivalent Ga(2) atoms. In the second Mg site, Mg(2) is bonded in a 12-coordinate geometry to three equivalent Mg(1), two equivalent Cu(2), three equivalent Cu(1), one Ga(1), two equivalent Ga(3), and four equivalent Ga(2) atoms. There are two inequivalent Cu sites. In the first Cu site, Cu(1) is bonded to three equivalent Mg(1), three equivalent Mg(2), two equivalent Cu(2), one Ga(1), one Ga(3), and two equivalent Ga(2) atoms to form CuMg6Ga4Cu2 cuboctahedra that share corners with two equivalent Ga(1)Mg6Cu6 cuboctahedra, corners with two equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, corners with four equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, corners with four equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, edges with six equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, faces with two equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, faces with three equivalent Ga(1)Mg6Cu6 cuboctahedra, faces with three equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, faces with six equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, and faces with six equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra. In the second Cu site, Cu(2) is bonded to two equivalent Mg(2), four equivalent Mg(1), two equivalent Cu(1), two equivalent Cu(2), and two equivalent Ga(1) atoms to form CuMg6Ga2Cu4 cuboctahedra that share corners with four equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, corners with four equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, corners with four equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, corners with six equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, edges with two equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, edges with four equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, faces with two equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, faces with two equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, faces with four equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, faces with four equivalent Ga(1)Mg6Cu6 cuboctahedra, and faces with six equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra. There are three inequivalent Ga sites. In the first Ga site, Ga(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), two equivalent Cu(1), and four equivalent Cu(2) atoms to form GaMg6Cu6 cuboctahedra that share corners with two equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, corners with four equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, corners with four equivalent Ga(1)Mg6Cu6 cuboctahedra, corners with eight equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, edges with two equivalent Ga(1)Mg6Cu6 cuboctahedra, edges with four equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, faces with four equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, faces with six equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, and faces with eight equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra. In the second Ga site, Ga(2) is bonded to two equivalent Mg(1), four equivalent Mg(2), two equivalent Cu(1), two equivalent Ga(2), and two equivalent Ga(3) atoms to form GaMg6Ga4Cu2 cuboctahedra that share corners with four equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, corners with four equivalent Ga(1)Mg6Cu6 cuboctahedra, corners with four equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, corners with six equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, edges with two equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, edges with four equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, faces with two equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, faces with two equivalent Ga(1)Mg6Cu6 cuboctahedra, faces with four equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, faces with four equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, and faces with six equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra. In the third Ga site, Ga(3) is bonded to two equivalent Mg(1), four equivalent Mg(2), two equivalent Cu(1), and four equivalent Ga(2) atoms to form GaMg6Ga4Cu2 cuboctahedra that share corners with two equivalent Ga(1)Mg6Cu6 cuboctahedra, corners with four equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, corners with four equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, corners with eight equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, edges with two equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, edges with four equivalent Ga(1)Mg6Cu6 cuboctahedra, faces with four equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, faces with six equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, and faces with eight equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgGaCu
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.086
_cell_length_b   5.086
_cell_length_c   8.204
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.154
_symmetry_Int_Tables_number   1
_cell_volume   185.356
_cell_formula_units_Z   4
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  0.668  0.332  0.320  1.0
  Mg  Mg1  1  0.337  0.663  0.203  1.0
  Mg  Mg2  1  0.337  0.663  0.797  1.0
  Mg  Mg3  1  0.668  0.332  0.680  1.0
  Ga  Ga4  1  0.162  0.838  0.500  1.0
  Ga  Ga5  1  0.337  0.166  0.000  1.0
  Ga  Ga6  1  0.834  0.663  0.000  1.0
  Ga  Ga7  1  0.832  0.168  0.000  1.0
  Cu  Cu8  1  0.999  0.001  0.249  1.0
  Cu  Cu9  1  0.999  0.001  0.751  1.0
  Cu  Cu10  1  0.659  0.835  0.500  1.0
  Cu  Cu11  1  0.165  0.341  0.500  1.0
[/CIF]
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The structure described by MgCuGa is Hexagonal Laves-derived structured and crystallizes in the orthorhombic Amm2 space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 16-coordinate geometry to one Mg(1), three equivalent Mg(2), three equivalent Cu(1), four equivalent Cu(2), one Ga(3), two equivalent Ga(1), and two equivalent Ga(2) atoms. In the second Mg site, Mg(2) is bonded in a 12-coordinate geometry to three equivalent Mg(1), two equivalent Cu(2), three equivalent Cu(1), one Ga(1), two equivalent Ga(3), and four equivalent Ga(2) atoms. There are two inequivalent Cu sites. In the first Cu site, Cu(1) is bonded to three equivalent Mg(1), three equivalent Mg(2), two equivalent Cu(2), one Ga(1), one Ga(3), and two equivalent Ga(2) atoms to form CuMg6Ga4Cu2 cuboctahedra that share corners with two equivalent Ga(1)Mg6Cu6 cuboctahedra, corners with two equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, corners with four equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, corners with four equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, edges with six equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, faces with two equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, faces with three equivalent Ga(1)Mg6Cu6 cuboctahedra, faces with three equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, faces with six equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, and faces with six equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra. In the second Cu site, Cu(2) is bonded to two equivalent Mg(2), four equivalent Mg(1), two equivalent Cu(1), two equivalent Cu(2), and two equivalent Ga(1) atoms to form CuMg6Ga2Cu4 cuboctahedra that share corners with four equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, corners with four equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, corners with four equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, corners with six equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, edges with two equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, edges with four equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, faces with two equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, faces with two equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, faces with four equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, faces with four equivalent Ga(1)Mg6Cu6 cuboctahedra, and faces with six equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra. There are three inequivalent Ga sites. In the first Ga site, Ga(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), two equivalent Cu(1), and four equivalent Cu(2) atoms to form GaMg6Cu6 cuboctahedra that share corners with two equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, corners with four equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, corners with four equivalent Ga(1)Mg6Cu6 cuboctahedra, corners with eight equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, edges with two equivalent Ga(1)Mg6Cu6 cuboctahedra, edges with four equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, faces with four equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, faces with six equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, and faces with eight equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra. In the second Ga site, Ga(2) is bonded to two equivalent Mg(1), four equivalent Mg(2), two equivalent Cu(1), two equivalent Ga(2), and two equivalent Ga(3) atoms to form GaMg6Ga4Cu2 cuboctahedra that share corners with four equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, corners with four equivalent Ga(1)Mg6Cu6 cuboctahedra, corners with four equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, corners with six equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, edges with two equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, edges with four equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, faces with two equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, faces with two equivalent Ga(1)Mg6Cu6 cuboctahedra, faces with four equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra, faces with four equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, and faces with six equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra. In the third Ga site, Ga(3) is bonded to two equivalent Mg(1), four equivalent Mg(2), two equivalent Cu(1), and four equivalent Ga(2) atoms to form GaMg6Ga4Cu2 cuboctahedra that share corners with two equivalent Ga(1)Mg6Cu6 cuboctahedra, corners with four equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, corners with four equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, corners with eight equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, edges with two equivalent Ga(3)Mg6Ga4Cu2 cuboctahedra, edges with four equivalent Ga(1)Mg6Cu6 cuboctahedra, faces with four equivalent Cu(2)Mg6Ga2Cu4 cuboctahedra, faces with six equivalent Cu(1)Mg6Ga4Cu2 cuboctahedra, and faces with eight equivalent Ga(2)Mg6Ga4Cu2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgGaCu
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.086
_cell_length_b   5.086
_cell_length_c   8.204
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.154
_symmetry_Int_Tables_number   1
_cell_volume   185.356
_cell_formula_units_Z   4
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  0.668  0.332  0.320  1.0
  Mg  Mg1  1  0.337  0.663  0.203  1.0
  Mg  Mg2  1  0.337  0.663  0.797  1.0
  Mg  Mg3  1  0.668  0.332  0.680  1.0
  Ga  Ga4  1  0.162  0.838  0.500  1.0
  Ga  Ga5  1  0.337  0.166  0.000  1.0
  Ga  Ga6  1  0.834  0.663  0.000  1.0
  Ga  Ga7  1  0.832  0.168  0.000  1.0
  Cu  Cu8  1  0.999  0.001  0.249  1.0
  Cu  Cu9  1  0.999  0.001  0.751  1.0
  Cu  Cu10  1  0.659  0.835  0.500  1.0
  Cu  Cu11  1  0.165  0.341  0.500  1.0
[/CIF]
.