The compound described by BaMg14Hf crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(6); four Mg(3,3,3); four equivalent Mg(5); and two equivalent Hf(1) atoms to form BaHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Ba(1)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra; edges with four Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(6)BaMg11 cuboctahedra; edges with eight Mg(5,5)BaHfMg10 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra; faces with four Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(5)BaHfMg10 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)Ba2Mg10 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)BaMg11 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)BaHfMg10 cuboctahedra; faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four equivalent Mg(5)BaHfMg10 cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. 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 four equivalent Ba(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)BaHfMg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra; faces with four equivalent Mg(5)BaHfMg10 cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)BaMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Hf(1) atoms to form distorted MgBa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(5)BaHfMg10 cuboctahedra; edges with four equivalent Mg(6)BaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra; and faces with eight Mg(5,5)BaHfMg10 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; corners with four equivalent Hf(1)Ba2Mg10 cuboctahedra; corners with six equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)BaHfMg10 cuboctahedra; edges with four equivalent Mg(6)BaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with eight Mg(5,5)BaHfMg10 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Hf(1) atoms to form distorted MgBa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(5)BaHfMg10 cuboctahedra; edges with four equivalent Mg(6)BaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra; and faces with eight equivalent Mg(5)BaHfMg10 cuboctahedra. In the sixth Mg site, Mg(5) is bonded to one Ba(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgBaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)BaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5)BaHfMg10 cuboctahedra; edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)BaHfMg10 cuboctahedra; edges with two equivalent Mg(6)BaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)BaHfMg10 cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the seventh Mg site, Mg(6) is bonded to one Ba(1); one Mg(1); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(7); and four Mg(5,5) atoms to form distorted MgBaMg11 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with six equivalent Mg(6)BaMg11 cuboctahedra; corners with eight Mg(5,5)BaHfMg10 cuboctahedra; edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; edges with four Mg(5,5)BaHfMg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra;  a faceface with one Ba(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two Mg(3,3)Ba2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Hf(1)Ba2Mg10 cuboctahedra; and faces with four Mg(5,5)BaHfMg10 cuboctahedra. In the eighth Mg site, Mg(7) is bonded to one Mg(2); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(6); four Mg(5,5); and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(6)BaMg11 cuboctahedra; corners with six equivalent Mg(7)HfMg11 cuboctahedra; corners with eight Mg(5,5)BaHfMg10 cuboctahedra; edges with two equivalent Mg(6)BaMg11 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra; edges with four Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; edges with four Mg(5,5)BaHfMg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ba2Mg10 cuboctahedra; faces with two Mg(3,3)Ba2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; and faces with four Mg(5,5)BaHfMg10 cuboctahedra. In the ninth Mg site, Mg(3) is bonded to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Hf(1) atoms to form distorted MgBa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(5)BaHfMg10 cuboctahedra; edges with four equivalent Mg(6)BaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra; and faces with eight Mg(5,5)BaHfMg10 cuboctahedra. In the tenth Mg site, Mg(5) is bonded to one Ba(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgBaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)BaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5)BaHfMg10 cuboctahedra; edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)BaHfMg10 cuboctahedra; edges with two equivalent Mg(6)BaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3)Ba2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)BaHfMg10 cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. Hf(1) is bonded to two equivalent Ba(1); two equivalent Mg(7); four Mg(3,3,3); and four equivalent Mg(5) atoms to form distorted HfBa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Hf(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra; edges with four Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with eight Mg(5,5)BaHfMg10 cuboctahedra; faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(5)BaHfMg10 cuboctahedra; and faces with six equivalent Mg(6)BaMg11 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_BaHfMg14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.590
_cell_length_b   6.601
_cell_length_c   10.484
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.051
_symmetry_Int_Tables_number   1
_cell_volume   394.765
_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
  Ba  Ba0  1  0.163  0.332  0.125  1.0
  Hf  Hf1  1  0.187  0.844  0.125  1.0
  Mg  Mg2  1  0.168  0.334  0.625  1.0
  Mg  Mg3  1  0.164  0.832  0.625  1.0
  Mg  Mg4  1  0.664  0.331  0.125  1.0
  Mg  Mg5  1  0.667  0.337  0.625  1.0
  Mg  Mg6  1  0.664  0.833  0.125  1.0
  Mg  Mg7  1  0.667  0.830  0.625  1.0
  Mg  Mg8  1  0.336  0.156  0.386  1.0
  Mg  Mg9  1  0.336  0.156  0.864  1.0
  Mg  Mg10  1  0.336  0.680  0.386  1.0
  Mg  Mg11  1  0.336  0.680  0.864  1.0
  Mg  Mg12  1  0.819  0.159  0.390  1.0
  Mg  Mg13  1  0.819  0.159  0.860  1.0
  Mg  Mg14  1  0.838  0.669  0.370  1.0
  Mg  Mg15  1  0.838  0.669  0.880  1.0
[/CIF]
.
The compound described by BaMg14Hf crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(6); four Mg(3,3,3); four equivalent Mg(5); and two equivalent Hf(1) atoms to form BaHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Ba(1)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra; edges with four Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(6)BaMg11 cuboctahedra; edges with eight Mg(5,5)BaHfMg10 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra; faces with four Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(5)BaHfMg10 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)Ba2Mg10 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)BaMg11 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)BaHfMg10 cuboctahedra; faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four equivalent Mg(5)BaHfMg10 cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. 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 four equivalent Ba(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)BaHfMg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra; faces with four equivalent Mg(5)BaHfMg10 cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)BaMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Hf(1) atoms to form distorted MgBa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(5)BaHfMg10 cuboctahedra; edges with four equivalent Mg(6)BaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra; and faces with eight Mg(5,5)BaHfMg10 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; corners with four equivalent Hf(1)Ba2Mg10 cuboctahedra; corners with six equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)BaHfMg10 cuboctahedra; edges with four equivalent Mg(6)BaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with eight Mg(5,5)BaHfMg10 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Hf(1) atoms to form distorted MgBa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(5)BaHfMg10 cuboctahedra; edges with four equivalent Mg(6)BaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra; and faces with eight equivalent Mg(5)BaHfMg10 cuboctahedra. In the sixth Mg site, Mg(5) is bonded to one Ba(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgBaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)BaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5)BaHfMg10 cuboctahedra; edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)BaHfMg10 cuboctahedra; edges with two equivalent Mg(6)BaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)BaHfMg10 cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the seventh Mg site, Mg(6) is bonded to one Ba(1); one Mg(1); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(7); and four Mg(5,5) atoms to form distorted MgBaMg11 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with six equivalent Mg(6)BaMg11 cuboctahedra; corners with eight Mg(5,5)BaHfMg10 cuboctahedra; edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; edges with four Mg(5,5)BaHfMg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra;  a faceface with one Ba(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two Mg(3,3)Ba2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Hf(1)Ba2Mg10 cuboctahedra; and faces with four Mg(5,5)BaHfMg10 cuboctahedra. In the eighth Mg site, Mg(7) is bonded to one Mg(2); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(6); four Mg(5,5); and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(6)BaMg11 cuboctahedra; corners with six equivalent Mg(7)HfMg11 cuboctahedra; corners with eight Mg(5,5)BaHfMg10 cuboctahedra; edges with two equivalent Mg(6)BaMg11 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra; edges with four Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; edges with four Mg(5,5)BaHfMg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ba2Mg10 cuboctahedra; faces with two Mg(3,3)Ba2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; and faces with four Mg(5,5)BaHfMg10 cuboctahedra. In the ninth Mg site, Mg(3) is bonded to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Hf(1) atoms to form distorted MgBa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(5)BaHfMg10 cuboctahedra; edges with four equivalent Mg(6)BaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra; and faces with eight Mg(5,5)BaHfMg10 cuboctahedra. In the tenth Mg site, Mg(5) is bonded to one Ba(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgBaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)BaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5)BaHfMg10 cuboctahedra; edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)BaHfMg10 cuboctahedra; edges with two equivalent Mg(6)BaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(6)BaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3)Ba2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)BaHfMg10 cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. Hf(1) is bonded to two equivalent Ba(1); two equivalent Mg(7); four Mg(3,3,3); and four equivalent Mg(5) atoms to form distorted HfBa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Hf(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra; edges with four Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with eight Mg(5,5)BaHfMg10 cuboctahedra; faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(3,3,3)Ba2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(5)BaHfMg10 cuboctahedra; and faces with six equivalent Mg(6)BaMg11 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_BaHfMg14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.590
_cell_length_b   6.601
_cell_length_c   10.484
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.051
_symmetry_Int_Tables_number   1
_cell_volume   394.765
_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
  Ba  Ba0  1  0.163  0.332  0.125  1.0
  Hf  Hf1  1  0.187  0.844  0.125  1.0
  Mg  Mg2  1  0.168  0.334  0.625  1.0
  Mg  Mg3  1  0.164  0.832  0.625  1.0
  Mg  Mg4  1  0.664  0.331  0.125  1.0
  Mg  Mg5  1  0.667  0.337  0.625  1.0
  Mg  Mg6  1  0.664  0.833  0.125  1.0
  Mg  Mg7  1  0.667  0.830  0.625  1.0
  Mg  Mg8  1  0.336  0.156  0.386  1.0
  Mg  Mg9  1  0.336  0.156  0.864  1.0
  Mg  Mg10  1  0.336  0.680  0.386  1.0
  Mg  Mg11  1  0.336  0.680  0.864  1.0
  Mg  Mg12  1  0.819  0.159  0.390  1.0
  Mg  Mg13  1  0.819  0.159  0.860  1.0
  Mg  Mg14  1  0.838  0.669  0.370  1.0
  Mg  Mg15  1  0.838  0.669  0.880  1.0
[/CIF]
.