The material described by Hf(Ni4Ga)3 is beta Cu3Ti-derived structured and crystallizes in the tetragonal P4/mmm space group. Hf(1) is bonded to four equivalent Ni(1) and eight equivalent Ni(4) atoms to form HfNi12 cuboctahedra that share corners with four equivalent Hf(1)Ni12 cuboctahedra, corners with eight equivalent Ga(1)Ni12 cuboctahedra, edges with eight equivalent Ni(2)Ga4Ni8 cuboctahedra, edges with sixteen equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra, faces with two equivalent Ga(1)Ni12 cuboctahedra, faces with four equivalent Hf(1)Ni12 cuboctahedra, and faces with eight equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra. There are six inequivalent Ni sites. In the first Ni site, Ni(1) is bonded in a distorted square co-planar geometry to four equivalent Hf(1) and eight equivalent Ni(4) atoms. In the second Ni site, Ni(2) is bonded to four equivalent Ni(4), four equivalent Ni(5), and four equivalent Ga(1) atoms to form NiGa4Ni8 cuboctahedra that share corners with four equivalent Ni(2)Ga4Ni8 cuboctahedra, corners with four equivalent Ni(3)Ga4Ni8 cuboctahedra, edges with four equivalent Hf(1)Ni12 cuboctahedra, edges with four equivalent Ga(2)Ni12 cuboctahedra, edges with eight equivalent Ni(5)Ga4Ni8 cuboctahedra, edges with eight equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra,  a faceface with one Ni(3)Ga4Ni8 cuboctahedra, faces with four equivalent Ni(2)Ga4Ni8 cuboctahedra, faces with four equivalent Ni(5)Ga4Ni8 cuboctahedra, faces with four equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra, and faces with four equivalent Ga(1)Ni12 cuboctahedra. In the third Ni site, Ni(3) is bonded to eight Ni(5,5) and four equivalent Ga(2) atoms to form NiGa4Ni8 cuboctahedra that share corners with four equivalent Ni(3)Ga4Ni8 cuboctahedra; corners with eight equivalent Ni(2)Ga4Ni8 cuboctahedra; edges with eight equivalent Ga(1)Ni12 cuboctahedra; edges with sixteen Ni(5,5)Ga4Ni8 cuboctahedra; faces with two equivalent Ni(2)Ga4Ni8 cuboctahedra; faces with four equivalent Ni(3)Ga4Ni8 cuboctahedra; faces with four equivalent Ga(2)Ni12 cuboctahedra; and faces with eight Ni(5,5)Ga4Ni8 cuboctahedra. In the fourth Ni site, Ni(4) is bonded to two equivalent Hf(1), two equivalent Ni(1), two equivalent Ni(2), four equivalent Ni(4), and two equivalent Ga(1) atoms to form distorted NiHf2Ga2Ni8 cuboctahedra that share corners with four equivalent Ni(5)Ga4Ni8 cuboctahedra, corners with eight equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra, edges with four equivalent Hf(1)Ni12 cuboctahedra, edges with four equivalent Ni(2)Ga4Ni8 cuboctahedra, edges with four equivalent Ni(5)Ga4Ni8 cuboctahedra, edges with four equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra, edges with four equivalent Ga(1)Ni12 cuboctahedra,  a faceface with one Ni(5)Ga4Ni8 cuboctahedra, faces with two equivalent Hf(1)Ni12 cuboctahedra, faces with two equivalent Ni(2)Ga4Ni8 cuboctahedra, faces with two equivalent Ga(1)Ni12 cuboctahedra, and faces with nine equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra. In the fifth Ni site, Ni(5) is bonded to two equivalent Ni(2), two equivalent Ni(3), four equivalent Ni(5), two equivalent Ga(1), and two equivalent Ga(2) atoms to form NiGa4Ni8 cuboctahedra that share corners with four equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra; corners with eight Ni(5,5)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(2)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(3)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(5)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra; edges with four equivalent Ga(1)Ni12 cuboctahedra; edges with four equivalent Ga(2)Ni12 cuboctahedra;  a faceface with one Ni(4)Hf2Ga2Ni8 cuboctahedra; faces with two equivalent Ni(2)Ga4Ni8 cuboctahedra; faces with two equivalent Ni(3)Ga4Ni8 cuboctahedra; faces with two equivalent Ga(1)Ni12 cuboctahedra; faces with two equivalent Ga(2)Ni12 cuboctahedra; and faces with nine Ni(5,5)Ga4Ni8 cuboctahedra. In the sixth Ni site, Ni(5) is bonded to two equivalent Ni(2), two equivalent Ni(3), four equivalent Ni(5), two equivalent Ga(1), and two equivalent Ga(2) atoms to form NiGa4Ni8 cuboctahedra that share corners with four equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra; corners with eight Ni(5,5)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(2)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(3)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(5)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra; edges with four equivalent Ga(1)Ni12 cuboctahedra; edges with four equivalent Ga(2)Ni12 cuboctahedra;  a faceface with one Ni(4)Hf2Ga2Ni8 cuboctahedra; faces with two equivalent Ni(2)Ga4Ni8 cuboctahedra; faces with two equivalent Ni(3)Ga4Ni8 cuboctahedra; faces with two equivalent Ga(1)Ni12 cuboctahedra; faces with two equivalent Ga(2)Ni12 cuboctahedra; and faces with nine Ni(5,5)Ga4Ni8 cuboctahedra. There are two inequivalent Ga sites. In the first Ga site, Ga(1) is bonded to four equivalent Ni(2), four equivalent Ni(4), and four equivalent Ni(5) atoms to form GaNi12 cuboctahedra that share corners with four equivalent Hf(1)Ni12 cuboctahedra, corners with four equivalent Ga(1)Ni12 cuboctahedra, corners with four equivalent Ga(2)Ni12 cuboctahedra, edges with four equivalent Ni(3)Ga4Ni8 cuboctahedra, edges with eight equivalent Ni(5)Ga4Ni8 cuboctahedra, edges with eight equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra,  a faceface with one Hf(1)Ni12 cuboctahedra,  a faceface with one Ga(2)Ni12 cuboctahedra, faces with four equivalent Ni(2)Ga4Ni8 cuboctahedra, faces with four equivalent Ni(5)Ga4Ni8 cuboctahedra, faces with four equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra, and faces with four equivalent Ga(1)Ni12 cuboctahedra. In the second Ga site, Ga(2) is bonded to four equivalent Ni(3) and eight Ni(5,5) atoms to form GaNi12 cuboctahedra that share corners with four equivalent Ga(2)Ni12 cuboctahedra; corners with eight equivalent Ga(1)Ni12 cuboctahedra; edges with eight equivalent Ni(2)Ga4Ni8 cuboctahedra; edges with sixteen Ni(5,5)Ga4Ni8 cuboctahedra; faces with two equivalent Ga(1)Ni12 cuboctahedra; faces with four equivalent Ni(3)Ga4Ni8 cuboctahedra; faces with four equivalent Ga(2)Ni12 cuboctahedra; and faces with eight Ni(5,5)Ga4Ni8 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Hf(GaNi4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.594
_cell_length_b   3.594
_cell_length_c   14.161
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   182.900
_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
  Ga  Ga1  1  0.000  0.000  0.256  1.0
  Ga  Ga2  1  0.000  0.000  0.500  1.0
  Ga  Ga3  1  0.000  0.000  0.744  1.0
  Ni  Ni4  1  0.500  0.500  0.000  1.0
  Ni  Ni5  1  0.500  0.500  0.255  1.0
  Ni  Ni6  1  0.500  0.500  0.500  1.0
  Ni  Ni7  1  0.500  0.500  0.745  1.0
  Ni  Ni8  1  0.500  0.000  0.133  1.0
  Ni  Ni9  1  0.500  0.000  0.377  1.0
  Ni  Ni10  1  0.500  0.000  0.623  1.0
  Ni  Ni11  1  0.500  0.000  0.867  1.0
  Ni  Ni12  1  0.000  0.500  0.133  1.0
  Ni  Ni13  1  0.000  0.500  0.377  1.0
  Ni  Ni14  1  0.000  0.500  0.623  1.0
  Ni  Ni15  1  0.000  0.500  0.867  1.0
[/CIF]
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The material described by Hf(Ni4Ga)3 is beta Cu3Ti-derived structured and crystallizes in the tetragonal P4/mmm space group. Hf(1) is bonded to four equivalent Ni(1) and eight equivalent Ni(4) atoms to form HfNi12 cuboctahedra that share corners with four equivalent Hf(1)Ni12 cuboctahedra, corners with eight equivalent Ga(1)Ni12 cuboctahedra, edges with eight equivalent Ni(2)Ga4Ni8 cuboctahedra, edges with sixteen equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra, faces with two equivalent Ga(1)Ni12 cuboctahedra, faces with four equivalent Hf(1)Ni12 cuboctahedra, and faces with eight equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra. There are six inequivalent Ni sites. In the first Ni site, Ni(1) is bonded in a distorted square co-planar geometry to four equivalent Hf(1) and eight equivalent Ni(4) atoms. In the second Ni site, Ni(2) is bonded to four equivalent Ni(4), four equivalent Ni(5), and four equivalent Ga(1) atoms to form NiGa4Ni8 cuboctahedra that share corners with four equivalent Ni(2)Ga4Ni8 cuboctahedra, corners with four equivalent Ni(3)Ga4Ni8 cuboctahedra, edges with four equivalent Hf(1)Ni12 cuboctahedra, edges with four equivalent Ga(2)Ni12 cuboctahedra, edges with eight equivalent Ni(5)Ga4Ni8 cuboctahedra, edges with eight equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra,  a faceface with one Ni(3)Ga4Ni8 cuboctahedra, faces with four equivalent Ni(2)Ga4Ni8 cuboctahedra, faces with four equivalent Ni(5)Ga4Ni8 cuboctahedra, faces with four equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra, and faces with four equivalent Ga(1)Ni12 cuboctahedra. In the third Ni site, Ni(3) is bonded to eight Ni(5,5) and four equivalent Ga(2) atoms to form NiGa4Ni8 cuboctahedra that share corners with four equivalent Ni(3)Ga4Ni8 cuboctahedra; corners with eight equivalent Ni(2)Ga4Ni8 cuboctahedra; edges with eight equivalent Ga(1)Ni12 cuboctahedra; edges with sixteen Ni(5,5)Ga4Ni8 cuboctahedra; faces with two equivalent Ni(2)Ga4Ni8 cuboctahedra; faces with four equivalent Ni(3)Ga4Ni8 cuboctahedra; faces with four equivalent Ga(2)Ni12 cuboctahedra; and faces with eight Ni(5,5)Ga4Ni8 cuboctahedra. In the fourth Ni site, Ni(4) is bonded to two equivalent Hf(1), two equivalent Ni(1), two equivalent Ni(2), four equivalent Ni(4), and two equivalent Ga(1) atoms to form distorted NiHf2Ga2Ni8 cuboctahedra that share corners with four equivalent Ni(5)Ga4Ni8 cuboctahedra, corners with eight equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra, edges with four equivalent Hf(1)Ni12 cuboctahedra, edges with four equivalent Ni(2)Ga4Ni8 cuboctahedra, edges with four equivalent Ni(5)Ga4Ni8 cuboctahedra, edges with four equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra, edges with four equivalent Ga(1)Ni12 cuboctahedra,  a faceface with one Ni(5)Ga4Ni8 cuboctahedra, faces with two equivalent Hf(1)Ni12 cuboctahedra, faces with two equivalent Ni(2)Ga4Ni8 cuboctahedra, faces with two equivalent Ga(1)Ni12 cuboctahedra, and faces with nine equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra. In the fifth Ni site, Ni(5) is bonded to two equivalent Ni(2), two equivalent Ni(3), four equivalent Ni(5), two equivalent Ga(1), and two equivalent Ga(2) atoms to form NiGa4Ni8 cuboctahedra that share corners with four equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra; corners with eight Ni(5,5)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(2)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(3)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(5)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra; edges with four equivalent Ga(1)Ni12 cuboctahedra; edges with four equivalent Ga(2)Ni12 cuboctahedra;  a faceface with one Ni(4)Hf2Ga2Ni8 cuboctahedra; faces with two equivalent Ni(2)Ga4Ni8 cuboctahedra; faces with two equivalent Ni(3)Ga4Ni8 cuboctahedra; faces with two equivalent Ga(1)Ni12 cuboctahedra; faces with two equivalent Ga(2)Ni12 cuboctahedra; and faces with nine Ni(5,5)Ga4Ni8 cuboctahedra. In the sixth Ni site, Ni(5) is bonded to two equivalent Ni(2), two equivalent Ni(3), four equivalent Ni(5), two equivalent Ga(1), and two equivalent Ga(2) atoms to form NiGa4Ni8 cuboctahedra that share corners with four equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra; corners with eight Ni(5,5)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(2)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(3)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(5)Ga4Ni8 cuboctahedra; edges with four equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra; edges with four equivalent Ga(1)Ni12 cuboctahedra; edges with four equivalent Ga(2)Ni12 cuboctahedra;  a faceface with one Ni(4)Hf2Ga2Ni8 cuboctahedra; faces with two equivalent Ni(2)Ga4Ni8 cuboctahedra; faces with two equivalent Ni(3)Ga4Ni8 cuboctahedra; faces with two equivalent Ga(1)Ni12 cuboctahedra; faces with two equivalent Ga(2)Ni12 cuboctahedra; and faces with nine Ni(5,5)Ga4Ni8 cuboctahedra. There are two inequivalent Ga sites. In the first Ga site, Ga(1) is bonded to four equivalent Ni(2), four equivalent Ni(4), and four equivalent Ni(5) atoms to form GaNi12 cuboctahedra that share corners with four equivalent Hf(1)Ni12 cuboctahedra, corners with four equivalent Ga(1)Ni12 cuboctahedra, corners with four equivalent Ga(2)Ni12 cuboctahedra, edges with four equivalent Ni(3)Ga4Ni8 cuboctahedra, edges with eight equivalent Ni(5)Ga4Ni8 cuboctahedra, edges with eight equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra,  a faceface with one Hf(1)Ni12 cuboctahedra,  a faceface with one Ga(2)Ni12 cuboctahedra, faces with four equivalent Ni(2)Ga4Ni8 cuboctahedra, faces with four equivalent Ni(5)Ga4Ni8 cuboctahedra, faces with four equivalent Ni(4)Hf2Ga2Ni8 cuboctahedra, and faces with four equivalent Ga(1)Ni12 cuboctahedra. In the second Ga site, Ga(2) is bonded to four equivalent Ni(3) and eight Ni(5,5) atoms to form GaNi12 cuboctahedra that share corners with four equivalent Ga(2)Ni12 cuboctahedra; corners with eight equivalent Ga(1)Ni12 cuboctahedra; edges with eight equivalent Ni(2)Ga4Ni8 cuboctahedra; edges with sixteen Ni(5,5)Ga4Ni8 cuboctahedra; faces with two equivalent Ga(1)Ni12 cuboctahedra; faces with four equivalent Ni(3)Ga4Ni8 cuboctahedra; faces with four equivalent Ga(2)Ni12 cuboctahedra; and faces with eight Ni(5,5)Ga4Ni8 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Hf(GaNi4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.594
_cell_length_b   3.594
_cell_length_c   14.161
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   182.900
_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
  Ga  Ga1  1  0.000  0.000  0.256  1.0
  Ga  Ga2  1  0.000  0.000  0.500  1.0
  Ga  Ga3  1  0.000  0.000  0.744  1.0
  Ni  Ni4  1  0.500  0.500  0.000  1.0
  Ni  Ni5  1  0.500  0.500  0.255  1.0
  Ni  Ni6  1  0.500  0.500  0.500  1.0
  Ni  Ni7  1  0.500  0.500  0.745  1.0
  Ni  Ni8  1  0.500  0.000  0.133  1.0
  Ni  Ni9  1  0.500  0.000  0.377  1.0
  Ni  Ni10  1  0.500  0.000  0.623  1.0
  Ni  Ni11  1  0.500  0.000  0.867  1.0
  Ni  Ni12  1  0.000  0.500  0.133  1.0
  Ni  Ni13  1  0.000  0.500  0.377  1.0
  Ni  Ni14  1  0.000  0.500  0.623  1.0
  Ni  Ni15  1  0.000  0.500  0.867  1.0
[/CIF]
.