The compound described by Mg14ZrB crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; and faces with four Mg(1,1)Mg10Zr2 cuboctahedra. In the second Mg site, Mg(2) is bonded in a 10-coordinate geometry to two equivalent Mg(4); four equivalent Mg(2); and four Mg(3,3) atoms. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; and faces with four Mg(1,1)Mg10Zr2 cuboctahedra. In the fourth Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four equivalent Mg(3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; and faces with four Mg(1,1)Mg10Zr2 cuboctahedra. In the fifth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one Zr(1); and one B(1) atom. In the sixth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Zr(1); and one B(1) atom. In the seventh Mg site, Mg(4) is bonded to three Mg(1,1,1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; edges with six Mg(1,1,1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(1,1,1)Mg10Zr2 cuboctahedra; and faces with three equivalent Zr(1)Mg12 cuboctahedra. Zr(1) is bonded to six Mg(1,1,1) and six Mg(3,3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; edges with six Mg(1,1,1)Mg10Zr2 cuboctahedra; faces with six Mg(1,1,1)Mg10Zr2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. B(1) is bonded in a 6-coordinate geometry to six Mg(3,3) atoms. is represented by the CIF file [CIF]
data_Mg14ZrB
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.297
_cell_length_b   6.297
_cell_length_c   9.993
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   343.153
_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  0.324  0.176  0.386  1.0
  Mg  Mg7  1  0.324  0.176  0.864  1.0
  Mg  Mg8  1  0.324  0.647  0.386  1.0
  Mg  Mg9  1  0.324  0.647  0.864  1.0
  Mg  Mg10  1  0.853  0.176  0.386  1.0
  Mg  Mg11  1  0.853  0.176  0.864  1.0
  Mg  Mg12  1  0.833  0.667  0.366  1.0
  Mg  Mg13  1  0.833  0.667  0.884  1.0
  Zr  Zr14  1  0.167  0.333  0.125  1.0
  B  B15  1  0.167  0.333  0.625  1.0
[/CIF]
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The compound described by Mg14ZrB crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; and faces with four Mg(1,1)Mg10Zr2 cuboctahedra. In the second Mg site, Mg(2) is bonded in a 10-coordinate geometry to two equivalent Mg(4); four equivalent Mg(2); and four Mg(3,3) atoms. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; and faces with four Mg(1,1)Mg10Zr2 cuboctahedra. In the fourth Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four equivalent Mg(3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; and faces with four Mg(1,1)Mg10Zr2 cuboctahedra. In the fifth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one Zr(1); and one B(1) atom. In the sixth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Zr(1); and one B(1) atom. In the seventh Mg site, Mg(4) is bonded to three Mg(1,1,1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; edges with six Mg(1,1,1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(1,1,1)Mg10Zr2 cuboctahedra; and faces with three equivalent Zr(1)Mg12 cuboctahedra. Zr(1) is bonded to six Mg(1,1,1) and six Mg(3,3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; edges with six Mg(1,1,1)Mg10Zr2 cuboctahedra; faces with six Mg(1,1,1)Mg10Zr2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. B(1) is bonded in a 6-coordinate geometry to six Mg(3,3) atoms. is represented by the CIF file [CIF]
data_Mg14ZrB
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.297
_cell_length_b   6.297
_cell_length_c   9.993
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   343.153
_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  0.324  0.176  0.386  1.0
  Mg  Mg7  1  0.324  0.176  0.864  1.0
  Mg  Mg8  1  0.324  0.647  0.386  1.0
  Mg  Mg9  1  0.324  0.647  0.864  1.0
  Mg  Mg10  1  0.853  0.176  0.386  1.0
  Mg  Mg11  1  0.853  0.176  0.864  1.0
  Mg  Mg12  1  0.833  0.667  0.366  1.0
  Mg  Mg13  1  0.833  0.667  0.884  1.0
  Zr  Zr14  1  0.167  0.333  0.125  1.0
  B  B15  1  0.167  0.333  0.625  1.0
[/CIF]
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