The material described by Hf3TiV8 is Hexagonal Laves-derived structured and crystallizes in the trigonal R3m space group. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 16-coordinate geometry to one Hf(3), three equivalent Hf(2), three equivalent V(1), three equivalent V(4), and six equivalent V(2) atoms. In the second Hf site, Hf(2) is bonded in a 16-coordinate geometry to three equivalent Hf(1), one Ti(1), three equivalent V(2), three equivalent V(4), and six equivalent V(1) atoms. In the third Hf site, Hf(3) is bonded in a 16-coordinate geometry to one Hf(1), three equivalent Ti(1), three equivalent V(1), three equivalent V(3), and six equivalent V(2) atoms. Ti(1) is bonded in a 16-coordinate geometry to one Hf(2), three equivalent Hf(3), three equivalent V(2), three equivalent V(3), and six equivalent V(1) atoms. There are four inequivalent V sites. In the first V site, V(1) is bonded to one Hf(1), one Hf(3), two equivalent Hf(2), two equivalent Ti(1), one V(3), one V(4), and four equivalent V(1) atoms to form VHf4Ti2V6 cuboctahedra that share corners with two equivalent V(3)Hf3Ti3V6 cuboctahedra, corners with two equivalent V(4)Hf6V6 cuboctahedra, corners with four equivalent V(1)Hf4Ti2V6 cuboctahedra, corners with ten equivalent V(2)Hf5TiV6 cuboctahedra, edges with two equivalent V(1)Hf4Ti2V6 cuboctahedra, edges with four equivalent V(2)Hf5TiV6 cuboctahedra, faces with three equivalent V(3)Hf3Ti3V6 cuboctahedra, faces with three equivalent V(4)Hf6V6 cuboctahedra, faces with four equivalent V(2)Hf5TiV6 cuboctahedra, and faces with eight equivalent V(1)Hf4Ti2V6 cuboctahedra. In the second V site, V(2) is bonded to one Hf(2), two equivalent Hf(1), two equivalent Hf(3), one Ti(1), one V(3), one V(4), and four equivalent V(2) atoms to form VHf5TiV6 cuboctahedra that share corners with two equivalent V(3)Hf3Ti3V6 cuboctahedra, corners with two equivalent V(4)Hf6V6 cuboctahedra, corners with four equivalent V(2)Hf5TiV6 cuboctahedra, corners with ten equivalent V(1)Hf4Ti2V6 cuboctahedra, edges with two equivalent V(2)Hf5TiV6 cuboctahedra, edges with four equivalent V(1)Hf4Ti2V6 cuboctahedra, faces with three equivalent V(3)Hf3Ti3V6 cuboctahedra, faces with three equivalent V(4)Hf6V6 cuboctahedra, faces with four equivalent V(1)Hf4Ti2V6 cuboctahedra, and faces with eight equivalent V(2)Hf5TiV6 cuboctahedra. In the third V site, V(3) is bonded to three equivalent Hf(3), three equivalent Ti(1), three equivalent V(1), and three equivalent V(2) atoms to form VHf3Ti3V6 cuboctahedra that share corners with six equivalent V(1)Hf4Ti2V6 cuboctahedra, corners with six equivalent V(2)Hf5TiV6 cuboctahedra, corners with six equivalent V(4)Hf6V6 cuboctahedra, edges with six equivalent V(3)Hf3Ti3V6 cuboctahedra, faces with nine equivalent V(1)Hf4Ti2V6 cuboctahedra, and faces with nine equivalent V(2)Hf5TiV6 cuboctahedra. In the fourth V site, V(4) is bonded to three equivalent Hf(1), three equivalent Hf(2), three equivalent V(1), and three equivalent V(2) atoms to form VHf6V6 cuboctahedra that share corners with six equivalent V(3)Hf3Ti3V6 cuboctahedra, corners with six equivalent V(1)Hf4Ti2V6 cuboctahedra, corners with six equivalent V(2)Hf5TiV6 cuboctahedra, edges with six equivalent V(4)Hf6V6 cuboctahedra, faces with nine equivalent V(1)Hf4Ti2V6 cuboctahedra, and faces with nine equivalent V(2)Hf5TiV6 cuboctahedra. is represented by the CIF file [CIF]
data_Hf3TiV8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.942
_cell_length_b   8.942
_cell_length_c   8.942
_cell_angle_alpha   33.346
_cell_angle_beta   33.346
_cell_angle_gamma   33.346
_symmetry_Int_Tables_number   1
_cell_volume   192.344
_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  0.625  0.625  0.625  1.0
  Hf  Hf1  1  0.002  0.002  0.002  1.0
  Hf  Hf2  1  0.499  0.499  0.499  1.0
  Ti  Ti3  1  0.125  0.125  0.125  1.0
  V  V4  1  0.563  0.066  0.563  1.0
  V  V5  1  0.061  0.560  0.061  1.0
  V  V6  1  0.066  0.563  0.563  1.0
  V  V7  1  0.560  0.061  0.061  1.0
  V  V8  1  0.812  0.812  0.812  1.0
  V  V9  1  0.313  0.313  0.313  1.0
  V  V10  1  0.563  0.563  0.066  1.0
  V  V11  1  0.061  0.061  0.560  1.0
[/CIF]
.
The material described by Hf3TiV8 is Hexagonal Laves-derived structured and crystallizes in the trigonal R3m space group. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 16-coordinate geometry to one Hf(3), three equivalent Hf(2), three equivalent V(1), three equivalent V(4), and six equivalent V(2) atoms. In the second Hf site, Hf(2) is bonded in a 16-coordinate geometry to three equivalent Hf(1), one Ti(1), three equivalent V(2), three equivalent V(4), and six equivalent V(1) atoms. In the third Hf site, Hf(3) is bonded in a 16-coordinate geometry to one Hf(1), three equivalent Ti(1), three equivalent V(1), three equivalent V(3), and six equivalent V(2) atoms. Ti(1) is bonded in a 16-coordinate geometry to one Hf(2), three equivalent Hf(3), three equivalent V(2), three equivalent V(3), and six equivalent V(1) atoms. There are four inequivalent V sites. In the first V site, V(1) is bonded to one Hf(1), one Hf(3), two equivalent Hf(2), two equivalent Ti(1), one V(3), one V(4), and four equivalent V(1) atoms to form VHf4Ti2V6 cuboctahedra that share corners with two equivalent V(3)Hf3Ti3V6 cuboctahedra, corners with two equivalent V(4)Hf6V6 cuboctahedra, corners with four equivalent V(1)Hf4Ti2V6 cuboctahedra, corners with ten equivalent V(2)Hf5TiV6 cuboctahedra, edges with two equivalent V(1)Hf4Ti2V6 cuboctahedra, edges with four equivalent V(2)Hf5TiV6 cuboctahedra, faces with three equivalent V(3)Hf3Ti3V6 cuboctahedra, faces with three equivalent V(4)Hf6V6 cuboctahedra, faces with four equivalent V(2)Hf5TiV6 cuboctahedra, and faces with eight equivalent V(1)Hf4Ti2V6 cuboctahedra. In the second V site, V(2) is bonded to one Hf(2), two equivalent Hf(1), two equivalent Hf(3), one Ti(1), one V(3), one V(4), and four equivalent V(2) atoms to form VHf5TiV6 cuboctahedra that share corners with two equivalent V(3)Hf3Ti3V6 cuboctahedra, corners with two equivalent V(4)Hf6V6 cuboctahedra, corners with four equivalent V(2)Hf5TiV6 cuboctahedra, corners with ten equivalent V(1)Hf4Ti2V6 cuboctahedra, edges with two equivalent V(2)Hf5TiV6 cuboctahedra, edges with four equivalent V(1)Hf4Ti2V6 cuboctahedra, faces with three equivalent V(3)Hf3Ti3V6 cuboctahedra, faces with three equivalent V(4)Hf6V6 cuboctahedra, faces with four equivalent V(1)Hf4Ti2V6 cuboctahedra, and faces with eight equivalent V(2)Hf5TiV6 cuboctahedra. In the third V site, V(3) is bonded to three equivalent Hf(3), three equivalent Ti(1), three equivalent V(1), and three equivalent V(2) atoms to form VHf3Ti3V6 cuboctahedra that share corners with six equivalent V(1)Hf4Ti2V6 cuboctahedra, corners with six equivalent V(2)Hf5TiV6 cuboctahedra, corners with six equivalent V(4)Hf6V6 cuboctahedra, edges with six equivalent V(3)Hf3Ti3V6 cuboctahedra, faces with nine equivalent V(1)Hf4Ti2V6 cuboctahedra, and faces with nine equivalent V(2)Hf5TiV6 cuboctahedra. In the fourth V site, V(4) is bonded to three equivalent Hf(1), three equivalent Hf(2), three equivalent V(1), and three equivalent V(2) atoms to form VHf6V6 cuboctahedra that share corners with six equivalent V(3)Hf3Ti3V6 cuboctahedra, corners with six equivalent V(1)Hf4Ti2V6 cuboctahedra, corners with six equivalent V(2)Hf5TiV6 cuboctahedra, edges with six equivalent V(4)Hf6V6 cuboctahedra, faces with nine equivalent V(1)Hf4Ti2V6 cuboctahedra, and faces with nine equivalent V(2)Hf5TiV6 cuboctahedra. is represented by the CIF file [CIF]
data_Hf3TiV8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.942
_cell_length_b   8.942
_cell_length_c   8.942
_cell_angle_alpha   33.346
_cell_angle_beta   33.346
_cell_angle_gamma   33.346
_symmetry_Int_Tables_number   1
_cell_volume   192.344
_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  0.625  0.625  0.625  1.0
  Hf  Hf1  1  0.002  0.002  0.002  1.0
  Hf  Hf2  1  0.499  0.499  0.499  1.0
  Ti  Ti3  1  0.125  0.125  0.125  1.0
  V  V4  1  0.563  0.066  0.563  1.0
  V  V5  1  0.061  0.560  0.061  1.0
  V  V6  1  0.066  0.563  0.563  1.0
  V  V7  1  0.560  0.061  0.061  1.0
  V  V8  1  0.812  0.812  0.812  1.0
  V  V9  1  0.313  0.313  0.313  1.0
  V  V10  1  0.563  0.563  0.066  1.0
  V  V11  1  0.061  0.061  0.560  1.0
[/CIF]
.