The material described by Mg14HfC crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 10-coordinate geometry to two equivalent Mg(2), four equivalent Mg(4), and four equivalent Mg(5) atoms. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, and faces with two equivalent Mg(7)HfMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded in a single-bond geometry to two equivalent Mg(5), two equivalent Mg(7), and one C(1) atom. In the fourth Mg site, Mg(4) is bonded in a 10-coordinate geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), and two equivalent Mg(7) atoms. In the fifth Mg site, Mg(5) is bonded in a 11-coordinate geometry to one Mg(1), one Mg(2), one Mg(3), one Mg(4), one Mg(6), two equivalent Mg(5), two equivalent Mg(7), one Hf(1), and one C(1) atom. In the sixth Mg site, Mg(6) is bonded in a single-bond geometry to two equivalent Mg(5), two equivalent Mg(7), and one C(1) atom. In the seventh Mg site, Mg(7) is bonded to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with six equivalent Mg(7)HfMg11 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra, and faces with two equivalent Mg(7)HfMg11 cuboctahedra. Hf(1) is bonded in a 2-coordinate geometry to two equivalent Mg(7), four equivalent Mg(5), and two equivalent C(1) atoms. C(1) is bonded in a 4-coordinate geometry to two equivalent Mg(3), two equivalent Mg(6), four equivalent Mg(5), and two equivalent Hf(1) atoms. is represented by the CIF card [CIF]
data_HfMg14C
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.498
_cell_length_b   5.815
_cell_length_c   10.154
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   116.580
_symmetry_Int_Tables_number   1
_cell_volume   343.102
_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  0.099  0.800  0.125  1.0
  Mg  Mg1  1  0.134  0.317  0.625  1.0
  Mg  Mg2  1  0.154  0.827  0.625  1.0
  Mg  Mg3  1  0.578  0.303  0.125  1.0
  Mg  Mg4  1  0.649  0.322  0.625  1.0
  Mg  Mg5  1  0.578  0.775  0.125  1.0
  Mg  Mg6  1  0.649  0.827  0.625  1.0
  Mg  Mg7  1  0.338  0.164  0.373  1.0
  Mg  Mg8  1  0.338  0.164  0.877  1.0
  Mg  Mg9  1  0.338  0.673  0.373  1.0
  Mg  Mg10  1  0.338  0.673  0.877  1.0
  Mg  Mg11  1  0.939  0.220  0.272  1.0
  Mg  Mg12  1  0.939  0.220  0.978  1.0
  Mg  Mg13  1  0.835  0.668  0.376  1.0
  Mg  Mg14  1  0.835  0.668  0.874  1.0
  C  C15  1  0.259  0.379  0.125  1.0
[/CIF]
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The material described by Mg14HfC crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 10-coordinate geometry to two equivalent Mg(2), four equivalent Mg(4), and four equivalent Mg(5) atoms. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, and faces with two equivalent Mg(7)HfMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded in a single-bond geometry to two equivalent Mg(5), two equivalent Mg(7), and one C(1) atom. In the fourth Mg site, Mg(4) is bonded in a 10-coordinate geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), and two equivalent Mg(7) atoms. In the fifth Mg site, Mg(5) is bonded in a 11-coordinate geometry to one Mg(1), one Mg(2), one Mg(3), one Mg(4), one Mg(6), two equivalent Mg(5), two equivalent Mg(7), one Hf(1), and one C(1) atom. In the sixth Mg site, Mg(6) is bonded in a single-bond geometry to two equivalent Mg(5), two equivalent Mg(7), and one C(1) atom. In the seventh Mg site, Mg(7) is bonded to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with six equivalent Mg(7)HfMg11 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra, and faces with two equivalent Mg(7)HfMg11 cuboctahedra. Hf(1) is bonded in a 2-coordinate geometry to two equivalent Mg(7), four equivalent Mg(5), and two equivalent C(1) atoms. C(1) is bonded in a 4-coordinate geometry to two equivalent Mg(3), two equivalent Mg(6), four equivalent Mg(5), and two equivalent Hf(1) atoms. is represented by the CIF card [CIF]
data_HfMg14C
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.498
_cell_length_b   5.815
_cell_length_c   10.154
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   116.580
_symmetry_Int_Tables_number   1
_cell_volume   343.102
_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  0.099  0.800  0.125  1.0
  Mg  Mg1  1  0.134  0.317  0.625  1.0
  Mg  Mg2  1  0.154  0.827  0.625  1.0
  Mg  Mg3  1  0.578  0.303  0.125  1.0
  Mg  Mg4  1  0.649  0.322  0.625  1.0
  Mg  Mg5  1  0.578  0.775  0.125  1.0
  Mg  Mg6  1  0.649  0.827  0.625  1.0
  Mg  Mg7  1  0.338  0.164  0.373  1.0
  Mg  Mg8  1  0.338  0.164  0.877  1.0
  Mg  Mg9  1  0.338  0.673  0.373  1.0
  Mg  Mg10  1  0.338  0.673  0.877  1.0
  Mg  Mg11  1  0.939  0.220  0.272  1.0
  Mg  Mg12  1  0.939  0.220  0.978  1.0
  Mg  Mg13  1  0.835  0.668  0.376  1.0
  Mg  Mg14  1  0.835  0.668  0.874  1.0
  C  C15  1  0.259  0.379  0.125  1.0
[/CIF]
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