The compound described by Mg14ZrFe crystallizes in the hexagonal P-6m2 space group. There are four 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 Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Fe(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra, corners with eight equivalent Mg(2)Mg10Fe2 cuboctahedra, edges with two equivalent Zr(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg10Fe2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Zr(1)Mg12 cuboctahedra, and faces with four equivalent Mg(1)Mg10Zr2 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 Fe(1) atoms to form distorted MgMg10Fe2 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Mg10Fe2 cuboctahedra, corners with eight equivalent Mg(1)Mg10Zr2 cuboctahedra, edges with two equivalent Fe(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Mg10Fe2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Fe(1)Mg12 cuboctahedra, and faces with four equivalent Mg(2)Mg10Fe2 cuboctahedra. In the third Mg site, Mg(3) is bonded in a distorted single-bond geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), one Zr(1), and one Fe(1) atom. In the fourth Mg site, Mg(4) is bonded to three equivalent Mg(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, edges with six equivalent Mg(2)Mg10Fe2 cuboctahedra, edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg10Fe2 cuboctahedra, faces with three equivalent Mg(1)Mg10Zr2 cuboctahedra, faces with three equivalent Zr(1)Mg12 cuboctahedra, and faces with three equivalent Fe(1)Mg12 cuboctahedra. Zr(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(2)Mg10Fe2 cuboctahedra, edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra, faces with two equivalent Fe(1)Mg12 cuboctahedra, faces with six equivalent Mg(1)Mg10Zr2 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. Fe(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form FeMg12 cuboctahedra that share corners with six equivalent Fe(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(1)Mg10Zr2 cuboctahedra, edges with six equivalent Mg(2)Mg10Fe2 cuboctahedra, faces with two equivalent Zr(1)Mg12 cuboctahedra, faces with six equivalent Mg(2)Mg10Fe2 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14ZrFe
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.272
_cell_length_b   6.272
_cell_length_c   10.024
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   341.520
_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  0.177  0.839  0.125  1.0
  Mg  Mg1  1  0.162  0.831  0.625  1.0
  Mg  Mg2  1  0.661  0.323  0.125  1.0
  Mg  Mg3  1  0.669  0.338  0.625  1.0
  Mg  Mg4  1  0.661  0.839  0.125  1.0
  Mg  Mg5  1  0.669  0.831  0.625  1.0
  Mg  Mg6  1  0.325  0.175  0.389  1.0
  Mg  Mg7  1  0.325  0.175  0.861  1.0
  Mg  Mg8  1  0.325  0.650  0.389  1.0
  Mg  Mg9  1  0.325  0.650  0.861  1.0
  Mg  Mg10  1  0.850  0.175  0.389  1.0
  Mg  Mg11  1  0.850  0.175  0.861  1.0
  Mg  Mg12  1  0.833  0.667  0.365  1.0
  Mg  Mg13  1  0.833  0.667  0.885  1.0
  Zr  Zr14  1  0.167  0.333  0.125  1.0
  Fe  Fe15  1  0.167  0.333  0.625  1.0
[/CIF]
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The compound described by Mg14ZrFe crystallizes in the hexagonal P-6m2 space group. There are four 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 Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Fe(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra, corners with eight equivalent Mg(2)Mg10Fe2 cuboctahedra, edges with two equivalent Zr(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg10Fe2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Zr(1)Mg12 cuboctahedra, and faces with four equivalent Mg(1)Mg10Zr2 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 Fe(1) atoms to form distorted MgMg10Fe2 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Mg10Fe2 cuboctahedra, corners with eight equivalent Mg(1)Mg10Zr2 cuboctahedra, edges with two equivalent Fe(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Mg10Fe2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Fe(1)Mg12 cuboctahedra, and faces with four equivalent Mg(2)Mg10Fe2 cuboctahedra. In the third Mg site, Mg(3) is bonded in a distorted single-bond geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), one Zr(1), and one Fe(1) atom. In the fourth Mg site, Mg(4) is bonded to three equivalent Mg(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, edges with six equivalent Mg(2)Mg10Fe2 cuboctahedra, edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg10Fe2 cuboctahedra, faces with three equivalent Mg(1)Mg10Zr2 cuboctahedra, faces with three equivalent Zr(1)Mg12 cuboctahedra, and faces with three equivalent Fe(1)Mg12 cuboctahedra. Zr(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(2)Mg10Fe2 cuboctahedra, edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra, faces with two equivalent Fe(1)Mg12 cuboctahedra, faces with six equivalent Mg(1)Mg10Zr2 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. Fe(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form FeMg12 cuboctahedra that share corners with six equivalent Fe(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(1)Mg10Zr2 cuboctahedra, edges with six equivalent Mg(2)Mg10Fe2 cuboctahedra, faces with two equivalent Zr(1)Mg12 cuboctahedra, faces with six equivalent Mg(2)Mg10Fe2 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14ZrFe
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.272
_cell_length_b   6.272
_cell_length_c   10.024
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   341.520
_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  0.177  0.839  0.125  1.0
  Mg  Mg1  1  0.162  0.831  0.625  1.0
  Mg  Mg2  1  0.661  0.323  0.125  1.0
  Mg  Mg3  1  0.669  0.338  0.625  1.0
  Mg  Mg4  1  0.661  0.839  0.125  1.0
  Mg  Mg5  1  0.669  0.831  0.625  1.0
  Mg  Mg6  1  0.325  0.175  0.389  1.0
  Mg  Mg7  1  0.325  0.175  0.861  1.0
  Mg  Mg8  1  0.325  0.650  0.389  1.0
  Mg  Mg9  1  0.325  0.650  0.861  1.0
  Mg  Mg10  1  0.850  0.175  0.389  1.0
  Mg  Mg11  1  0.850  0.175  0.861  1.0
  Mg  Mg12  1  0.833  0.667  0.365  1.0
  Mg  Mg13  1  0.833  0.667  0.885  1.0
  Zr  Zr14  1  0.167  0.333  0.125  1.0
  Fe  Fe15  1  0.167  0.333  0.625  1.0
[/CIF]
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