The crystal structure described by Mg3Hf is Copper-derived structured and crystallizes in the tetragonal I4/mmm space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to eight equivalent Mg(2) and four equivalent Hf(1) atoms to form MgHf4Mg8 cuboctahedra that share corners with four equivalent Mg(1)Hf4Mg8 cuboctahedra, corners with eight equivalent Hf(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Hf4Mg8 cuboctahedra, edges with sixteen equivalent Mg(2)Hf4Mg8 cuboctahedra, faces with four equivalent Mg(1)Hf4Mg8 cuboctahedra, faces with six equivalent Hf(1)Mg12 cuboctahedra, and faces with eight equivalent Mg(2)Hf4Mg8 cuboctahedra. In the second Mg site, Mg(2) is bonded to four equivalent Mg(1), four equivalent Mg(2), and four equivalent Hf(1) atoms to form MgHf4Mg8 cuboctahedra that share corners with twelve equivalent Mg(2)Hf4Mg8 cuboctahedra, edges with eight equivalent Mg(1)Hf4Mg8 cuboctahedra, edges with eight equivalent Mg(2)Hf4Mg8 cuboctahedra, edges with eight equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Hf4Mg8 cuboctahedra, faces with four equivalent Hf(1)Mg12 cuboctahedra, and faces with ten equivalent Mg(2)Hf4Mg8 cuboctahedra. Hf(1) is bonded to four equivalent Mg(1) and eight equivalent Mg(2) atoms to form HfMg12 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra, corners with eight equivalent Mg(1)Hf4Mg8 cuboctahedra, edges with eight equivalent Hf(1)Mg12 cuboctahedra, edges with sixteen equivalent Mg(2)Hf4Mg8 cuboctahedra, faces with four equivalent Hf(1)Mg12 cuboctahedra, faces with six equivalent Mg(1)Hf4Mg8 cuboctahedra, and faces with eight equivalent Mg(2)Hf4Mg8 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_HfMg3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.480
_cell_length_b   5.480
_cell_length_c   5.480
_cell_angle_alpha   132.054
_cell_angle_beta   132.054
_cell_angle_gamma   70.143
_symmetry_Int_Tables_number   1
_cell_volume   88.915
_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
  Hf  Hf0  1  0.000  0.000  0.000  1.0
  Mg  Mg1  1  0.500  0.500  0.000  1.0
  Mg  Mg2  1  0.250  0.750  0.500  1.0
  Mg  Mg3  1  0.750  0.250  0.500  1.0
[/CIF]
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The crystal structure described by Mg3Hf is Copper-derived structured and crystallizes in the tetragonal I4/mmm space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to eight equivalent Mg(2) and four equivalent Hf(1) atoms to form MgHf4Mg8 cuboctahedra that share corners with four equivalent Mg(1)Hf4Mg8 cuboctahedra, corners with eight equivalent Hf(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Hf4Mg8 cuboctahedra, edges with sixteen equivalent Mg(2)Hf4Mg8 cuboctahedra, faces with four equivalent Mg(1)Hf4Mg8 cuboctahedra, faces with six equivalent Hf(1)Mg12 cuboctahedra, and faces with eight equivalent Mg(2)Hf4Mg8 cuboctahedra. In the second Mg site, Mg(2) is bonded to four equivalent Mg(1), four equivalent Mg(2), and four equivalent Hf(1) atoms to form MgHf4Mg8 cuboctahedra that share corners with twelve equivalent Mg(2)Hf4Mg8 cuboctahedra, edges with eight equivalent Mg(1)Hf4Mg8 cuboctahedra, edges with eight equivalent Mg(2)Hf4Mg8 cuboctahedra, edges with eight equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Hf4Mg8 cuboctahedra, faces with four equivalent Hf(1)Mg12 cuboctahedra, and faces with ten equivalent Mg(2)Hf4Mg8 cuboctahedra. Hf(1) is bonded to four equivalent Mg(1) and eight equivalent Mg(2) atoms to form HfMg12 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra, corners with eight equivalent Mg(1)Hf4Mg8 cuboctahedra, edges with eight equivalent Hf(1)Mg12 cuboctahedra, edges with sixteen equivalent Mg(2)Hf4Mg8 cuboctahedra, faces with four equivalent Hf(1)Mg12 cuboctahedra, faces with six equivalent Mg(1)Hf4Mg8 cuboctahedra, and faces with eight equivalent Mg(2)Hf4Mg8 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_HfMg3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.480
_cell_length_b   5.480
_cell_length_c   5.480
_cell_angle_alpha   132.054
_cell_angle_beta   132.054
_cell_angle_gamma   70.143
_symmetry_Int_Tables_number   1
_cell_volume   88.915
_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
  Hf  Hf0  1  0.000  0.000  0.000  1.0
  Mg  Mg1  1  0.500  0.500  0.000  1.0
  Mg  Mg2  1  0.250  0.750  0.500  1.0
  Mg  Mg3  1  0.750  0.250  0.500  1.0
[/CIF]
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