The material described by Mg14YGa crystallizes in the hexagonal P-6m2 space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Y(1) atoms to form MgY2Mg10 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Y2Mg10 cuboctahedra, corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with two equivalent Y(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(1)Y2Mg10 cuboctahedra, edges with eight equivalent Mg(3)YMg10Ga cuboctahedra, faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Y(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Y2Mg10 cuboctahedra, and faces with ten equivalent Mg(3)YMg10Ga cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(2), four equivalent Mg(3), and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Y(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Y2Mg10 cuboctahedra, edges with two equivalent Ga(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)YMg10Ga cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(1)Y2Mg10 cuboctahedra, faces with two equivalent Ga(1)Mg12 cuboctahedra, faces with four equivalent Mg(2)Mg10Ga2 cuboctahedra, and faces with ten equivalent Mg(3)YMg10Ga cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four equivalent Mg(3); and two equivalent Y(1) atoms to form MgY2Mg10 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Y2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with two equivalent Y(1)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four Mg(1,1)Y2Mg10 cuboctahedra; edges with eight equivalent Mg(3)YMg10Ga cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Y(1)Mg12 cuboctahedra; faces with four Mg(1,1)Y2Mg10 cuboctahedra; and faces with ten equivalent Mg(3)YMg10Ga cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one Y(1); and one Ga(1) atom to form distorted MgYMg10Ga cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen equivalent Mg(3)YMg10Ga cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Y(1)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with four Mg(1,1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(3)YMg10Ga cuboctahedra;  a faceface with one Y(1)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with five Mg(1,1)Y2Mg10 cuboctahedra; and faces with six equivalent Mg(3)YMg10Ga cuboctahedra. In the fifth Mg site, Mg(4) is bonded to three Mg(1,1); three equivalent Mg(2); and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)YMg10Ga cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with six Mg(1,1)Y2Mg10 cuboctahedra; edges with six equivalent Mg(3)YMg10Ga cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with three Mg(1,1)Y2Mg10 cuboctahedra; faces with three equivalent Y(1)Mg12 cuboctahedra; faces with three equivalent Ga(1)Mg12 cuboctahedra; and faces with six equivalent Mg(3)YMg10Ga cuboctahedra. Y(1) is bonded to six Mg(1,1) and six equivalent Mg(3) atoms to form YMg12 cuboctahedra that share corners with six equivalent Y(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with six Mg(1,1)Y2Mg10 cuboctahedra; edges with twelve equivalent Mg(3)YMg10Ga cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; faces with six Mg(1,1)Y2Mg10 cuboctahedra; and faces with six equivalent Mg(3)YMg10Ga cuboctahedra. Ga(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form GaMg12 cuboctahedra that share corners with six equivalent Ga(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Y2Mg10 cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with twelve equivalent Mg(3)YMg10Ga cuboctahedra; faces with two equivalent Y(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(3)YMg10Ga cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_YMg14Ga
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.429
_cell_length_b   6.429
_cell_length_c   10.366
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   371.027
_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
  Y  Y0  1  0.167  0.333  0.125  1.0
  Mg  Mg1  1  0.179  0.840  0.125  1.0
  Mg  Mg2  1  0.162  0.831  0.625  1.0
  Mg  Mg3  1  0.660  0.321  0.125  1.0
  Mg  Mg4  1  0.669  0.338  0.625  1.0
  Mg  Mg5  1  0.660  0.840  0.125  1.0
  Mg  Mg6  1  0.669  0.831  0.625  1.0
  Mg  Mg7  1  0.332  0.168  0.384  1.0
  Mg  Mg8  1  0.332  0.168  0.866  1.0
  Mg  Mg9  1  0.332  0.664  0.384  1.0
  Mg  Mg10  1  0.332  0.664  0.866  1.0
  Mg  Mg11  1  0.836  0.168  0.384  1.0
  Mg  Mg12  1  0.836  0.168  0.866  1.0
  Mg  Mg13  1  0.833  0.667  0.366  1.0
  Mg  Mg14  1  0.833  0.667  0.884  1.0
  Ga  Ga15  1  0.167  0.333  0.625  1.0
[/CIF]
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The material described by Mg14YGa crystallizes in the hexagonal P-6m2 space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Y(1) atoms to form MgY2Mg10 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Y2Mg10 cuboctahedra, corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with two equivalent Y(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(1)Y2Mg10 cuboctahedra, edges with eight equivalent Mg(3)YMg10Ga cuboctahedra, faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Y(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Y2Mg10 cuboctahedra, and faces with ten equivalent Mg(3)YMg10Ga cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(2), four equivalent Mg(3), and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Y(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Y2Mg10 cuboctahedra, edges with two equivalent Ga(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)YMg10Ga cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(1)Y2Mg10 cuboctahedra, faces with two equivalent Ga(1)Mg12 cuboctahedra, faces with four equivalent Mg(2)Mg10Ga2 cuboctahedra, and faces with ten equivalent Mg(3)YMg10Ga cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four equivalent Mg(3); and two equivalent Y(1) atoms to form MgY2Mg10 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Y2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with two equivalent Y(1)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four Mg(1,1)Y2Mg10 cuboctahedra; edges with eight equivalent Mg(3)YMg10Ga cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Y(1)Mg12 cuboctahedra; faces with four Mg(1,1)Y2Mg10 cuboctahedra; and faces with ten equivalent Mg(3)YMg10Ga cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one Y(1); and one Ga(1) atom to form distorted MgYMg10Ga cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen equivalent Mg(3)YMg10Ga cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Y(1)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with four Mg(1,1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(3)YMg10Ga cuboctahedra;  a faceface with one Y(1)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with five Mg(1,1)Y2Mg10 cuboctahedra; and faces with six equivalent Mg(3)YMg10Ga cuboctahedra. In the fifth Mg site, Mg(4) is bonded to three Mg(1,1); three equivalent Mg(2); and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)YMg10Ga cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with six Mg(1,1)Y2Mg10 cuboctahedra; edges with six equivalent Mg(3)YMg10Ga cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with three Mg(1,1)Y2Mg10 cuboctahedra; faces with three equivalent Y(1)Mg12 cuboctahedra; faces with three equivalent Ga(1)Mg12 cuboctahedra; and faces with six equivalent Mg(3)YMg10Ga cuboctahedra. Y(1) is bonded to six Mg(1,1) and six equivalent Mg(3) atoms to form YMg12 cuboctahedra that share corners with six equivalent Y(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with six Mg(1,1)Y2Mg10 cuboctahedra; edges with twelve equivalent Mg(3)YMg10Ga cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; faces with six Mg(1,1)Y2Mg10 cuboctahedra; and faces with six equivalent Mg(3)YMg10Ga cuboctahedra. Ga(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form GaMg12 cuboctahedra that share corners with six equivalent Ga(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Y2Mg10 cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with twelve equivalent Mg(3)YMg10Ga cuboctahedra; faces with two equivalent Y(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(3)YMg10Ga cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_YMg14Ga
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.429
_cell_length_b   6.429
_cell_length_c   10.366
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   371.027
_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
  Y  Y0  1  0.167  0.333  0.125  1.0
  Mg  Mg1  1  0.179  0.840  0.125  1.0
  Mg  Mg2  1  0.162  0.831  0.625  1.0
  Mg  Mg3  1  0.660  0.321  0.125  1.0
  Mg  Mg4  1  0.669  0.338  0.625  1.0
  Mg  Mg5  1  0.660  0.840  0.125  1.0
  Mg  Mg6  1  0.669  0.831  0.625  1.0
  Mg  Mg7  1  0.332  0.168  0.384  1.0
  Mg  Mg8  1  0.332  0.168  0.866  1.0
  Mg  Mg9  1  0.332  0.664  0.384  1.0
  Mg  Mg10  1  0.332  0.664  0.866  1.0
  Mg  Mg11  1  0.836  0.168  0.384  1.0
  Mg  Mg12  1  0.836  0.168  0.866  1.0
  Mg  Mg13  1  0.833  0.667  0.366  1.0
  Mg  Mg14  1  0.833  0.667  0.884  1.0
  Ga  Ga15  1  0.167  0.333  0.625  1.0
[/CIF]
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