The structure described by HfZrO4 is Fluorite-derived structured and crystallizes in the cubic P2_13 space group. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a body-centered cubic geometry to one O(1), one O(2), one O(5), one O(8), two equivalent O(3), and two equivalent O(6) atoms. In the second Hf site, Hf(2) is bonded in a body-centered cubic geometry to one O(5), one O(8), three equivalent O(1), and three equivalent O(2) atoms. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded in a body-centered cubic geometry to one O(1), one O(2), one O(4), one O(7), two equivalent O(3), and two equivalent O(6) atoms. In the second Zr site, Zr(2) is bonded in a body-centered cubic geometry to one O(4), one O(7), three equivalent O(1), and three equivalent O(2) atoms. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Hf(1), one Hf(2), one Zr(1), and one Zr(2) atom to form OHf2Zr2 tetrahedra that share corners with two equivalent O(2)Hf2Zr2 tetrahedra, corners with two equivalent O(3)Hf2Zr2 tetrahedra, corners with two equivalent O(5)Hf4 tetrahedra, corners with two equivalent O(4)Zr4 tetrahedra, corners with four equivalent O(1)Hf2Zr2 tetrahedra, corners with four equivalent O(6)Hf2Zr2 tetrahedra,  an edgeedge with one O(3)Hf2Zr2 tetrahedra,  an edgeedge with one O(8)Hf4 tetrahedra,  an edgeedge with one O(7)Zr4 tetrahedra, and edges with three equivalent O(2)Hf2Zr2 tetrahedra. In the second O site, O(2) is bonded to one Hf(1), one Hf(2), one Zr(1), and one Zr(2) atom to form OHf2Zr2 tetrahedra that share corners with two equivalent O(1)Hf2Zr2 tetrahedra, corners with two equivalent O(6)Hf2Zr2 tetrahedra, corners with two equivalent O(8)Hf4 tetrahedra, corners with two equivalent O(7)Zr4 tetrahedra, corners with four equivalent O(2)Hf2Zr2 tetrahedra, corners with four equivalent O(3)Hf2Zr2 tetrahedra,  an edgeedge with one O(6)Hf2Zr2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra,  an edgeedge with one O(4)Zr4 tetrahedra, and edges with three equivalent O(1)Hf2Zr2 tetrahedra. In the third O site, O(3) is bonded to two equivalent Hf(1) and two equivalent Zr(1) atoms to form OHf2Zr2 tetrahedra that share corners with two equivalent O(1)Hf2Zr2 tetrahedra, corners with two equivalent O(6)Hf2Zr2 tetrahedra, corners with two equivalent O(8)Hf4 tetrahedra, corners with two equivalent O(7)Zr4 tetrahedra, corners with four equivalent O(2)Hf2Zr2 tetrahedra, corners with four equivalent O(3)Hf2Zr2 tetrahedra,  an edgeedge with one O(1)Hf2Zr2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra,  an edgeedge with one O(4)Zr4 tetrahedra, and edges with three equivalent O(6)Hf2Zr2 tetrahedra. In the fourth O site, O(4) is bonded to one Zr(2) and three equivalent Zr(1) atoms to form OZr4 tetrahedra that share corners with four equivalent O(7)Zr4 tetrahedra, corners with six equivalent O(1)Hf2Zr2 tetrahedra, corners with six equivalent O(6)Hf2Zr2 tetrahedra, edges with three equivalent O(2)Hf2Zr2 tetrahedra, and edges with three equivalent O(3)Hf2Zr2 tetrahedra. In the fifth O site, O(5) is bonded to one Hf(2) and three equivalent Hf(1) atoms to form OHf4 tetrahedra that share corners with four equivalent O(8)Hf4 tetrahedra, corners with six equivalent O(1)Hf2Zr2 tetrahedra, corners with six equivalent O(6)Hf2Zr2 tetrahedra, edges with three equivalent O(2)Hf2Zr2 tetrahedra, and edges with three equivalent O(3)Hf2Zr2 tetrahedra. In the sixth O site, O(6) is bonded to two equivalent Hf(1) and two equivalent Zr(1) atoms to form OHf2Zr2 tetrahedra that share corners with two equivalent O(2)Hf2Zr2 tetrahedra, corners with two equivalent O(3)Hf2Zr2 tetrahedra, corners with two equivalent O(5)Hf4 tetrahedra, corners with two equivalent O(4)Zr4 tetrahedra, corners with four equivalent O(1)Hf2Zr2 tetrahedra, corners with four equivalent O(6)Hf2Zr2 tetrahedra,  an edgeedge with one O(2)Hf2Zr2 tetrahedra,  an edgeedge with one O(8)Hf4 tetrahedra,  an edgeedge with one O(7)Zr4 tetrahedra, and edges with three equivalent O(3)Hf2Zr2 tetrahedra. In the seventh O site, O(7) is bonded to one Zr(2) and three equivalent Zr(1) atoms to form OZr4 tetrahedra that share corners with four equivalent O(4)Zr4 tetrahedra, corners with six equivalent O(2)Hf2Zr2 tetrahedra, corners with six equivalent O(3)Hf2Zr2 tetrahedra, edges with three equivalent O(1)Hf2Zr2 tetrahedra, and edges with three equivalent O(6)Hf2Zr2 tetrahedra. In the eighth O site, O(8) is bonded to one Hf(2) and three equivalent Hf(1) atoms to form OHf4 tetrahedra that share corners with four equivalent O(5)Hf4 tetrahedra, corners with six equivalent O(2)Hf2Zr2 tetrahedra, corners with six equivalent O(3)Hf2Zr2 tetrahedra, edges with three equivalent O(1)Hf2Zr2 tetrahedra, and edges with three equivalent O(6)Hf2Zr2 tetrahedra. is represented by the CIF file [CIF]
data_HfZrO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.233
_cell_length_b   7.233
_cell_length_c   7.233
_cell_angle_alpha   60.000
_cell_angle_beta   60.000
_cell_angle_gamma   60.000
_symmetry_Int_Tables_number   1
_cell_volume   267.618
_cell_formula_units_Z   4
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  0.875  0.875  0.375  1.0
  Hf  Hf1  1  0.875  0.875  0.875  1.0
  Hf  Hf2  1  0.375  0.875  0.875  1.0
  Hf  Hf3  1  0.875  0.375  0.875  1.0
  O  O4  1  0.502  0.502  0.998  1.0
  O  O5  1  0.248  0.752  0.752  1.0
  O  O6  1  0.248  0.752  0.248  1.0
  O  O7  1  0.500  0.500  0.500  1.0
  O  O8  1  0.000  1.000  1.000  1.0
  O  O9  1  0.752  0.248  0.248  1.0
  O  O10  1  0.752  0.248  0.752  1.0
  O  O11  1  0.998  0.502  0.502  1.0
  O  O12  1  0.502  0.998  0.502  1.0
  O  O13  1  0.250  0.250  0.250  1.0
  O  O14  1  0.248  0.248  0.752  1.0
  O  O15  1  0.502  0.998  0.998  1.0
  O  O16  1  0.750  0.750  0.750  1.0
  O  O17  1  0.752  0.752  0.248  1.0
  O  O18  1  0.998  0.502  0.998  1.0
  O  O19  1  0.998  0.998  0.502  1.0
  Zr  Zr20  1  0.375  0.375  0.375  1.0
  Zr  Zr21  1  0.375  0.375  0.875  1.0
  Zr  Zr22  1  0.375  0.875  0.375  1.0
  Zr  Zr23  1  0.875  0.375  0.375  1.0
[/CIF]
.
The structure described by HfZrO4 is Fluorite-derived structured and crystallizes in the cubic P2_13 space group. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a body-centered cubic geometry to one O(1), one O(2), one O(5), one O(8), two equivalent O(3), and two equivalent O(6) atoms. In the second Hf site, Hf(2) is bonded in a body-centered cubic geometry to one O(5), one O(8), three equivalent O(1), and three equivalent O(2) atoms. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded in a body-centered cubic geometry to one O(1), one O(2), one O(4), one O(7), two equivalent O(3), and two equivalent O(6) atoms. In the second Zr site, Zr(2) is bonded in a body-centered cubic geometry to one O(4), one O(7), three equivalent O(1), and three equivalent O(2) atoms. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Hf(1), one Hf(2), one Zr(1), and one Zr(2) atom to form OHf2Zr2 tetrahedra that share corners with two equivalent O(2)Hf2Zr2 tetrahedra, corners with two equivalent O(3)Hf2Zr2 tetrahedra, corners with two equivalent O(5)Hf4 tetrahedra, corners with two equivalent O(4)Zr4 tetrahedra, corners with four equivalent O(1)Hf2Zr2 tetrahedra, corners with four equivalent O(6)Hf2Zr2 tetrahedra,  an edgeedge with one O(3)Hf2Zr2 tetrahedra,  an edgeedge with one O(8)Hf4 tetrahedra,  an edgeedge with one O(7)Zr4 tetrahedra, and edges with three equivalent O(2)Hf2Zr2 tetrahedra. In the second O site, O(2) is bonded to one Hf(1), one Hf(2), one Zr(1), and one Zr(2) atom to form OHf2Zr2 tetrahedra that share corners with two equivalent O(1)Hf2Zr2 tetrahedra, corners with two equivalent O(6)Hf2Zr2 tetrahedra, corners with two equivalent O(8)Hf4 tetrahedra, corners with two equivalent O(7)Zr4 tetrahedra, corners with four equivalent O(2)Hf2Zr2 tetrahedra, corners with four equivalent O(3)Hf2Zr2 tetrahedra,  an edgeedge with one O(6)Hf2Zr2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra,  an edgeedge with one O(4)Zr4 tetrahedra, and edges with three equivalent O(1)Hf2Zr2 tetrahedra. In the third O site, O(3) is bonded to two equivalent Hf(1) and two equivalent Zr(1) atoms to form OHf2Zr2 tetrahedra that share corners with two equivalent O(1)Hf2Zr2 tetrahedra, corners with two equivalent O(6)Hf2Zr2 tetrahedra, corners with two equivalent O(8)Hf4 tetrahedra, corners with two equivalent O(7)Zr4 tetrahedra, corners with four equivalent O(2)Hf2Zr2 tetrahedra, corners with four equivalent O(3)Hf2Zr2 tetrahedra,  an edgeedge with one O(1)Hf2Zr2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra,  an edgeedge with one O(4)Zr4 tetrahedra, and edges with three equivalent O(6)Hf2Zr2 tetrahedra. In the fourth O site, O(4) is bonded to one Zr(2) and three equivalent Zr(1) atoms to form OZr4 tetrahedra that share corners with four equivalent O(7)Zr4 tetrahedra, corners with six equivalent O(1)Hf2Zr2 tetrahedra, corners with six equivalent O(6)Hf2Zr2 tetrahedra, edges with three equivalent O(2)Hf2Zr2 tetrahedra, and edges with three equivalent O(3)Hf2Zr2 tetrahedra. In the fifth O site, O(5) is bonded to one Hf(2) and three equivalent Hf(1) atoms to form OHf4 tetrahedra that share corners with four equivalent O(8)Hf4 tetrahedra, corners with six equivalent O(1)Hf2Zr2 tetrahedra, corners with six equivalent O(6)Hf2Zr2 tetrahedra, edges with three equivalent O(2)Hf2Zr2 tetrahedra, and edges with three equivalent O(3)Hf2Zr2 tetrahedra. In the sixth O site, O(6) is bonded to two equivalent Hf(1) and two equivalent Zr(1) atoms to form OHf2Zr2 tetrahedra that share corners with two equivalent O(2)Hf2Zr2 tetrahedra, corners with two equivalent O(3)Hf2Zr2 tetrahedra, corners with two equivalent O(5)Hf4 tetrahedra, corners with two equivalent O(4)Zr4 tetrahedra, corners with four equivalent O(1)Hf2Zr2 tetrahedra, corners with four equivalent O(6)Hf2Zr2 tetrahedra,  an edgeedge with one O(2)Hf2Zr2 tetrahedra,  an edgeedge with one O(8)Hf4 tetrahedra,  an edgeedge with one O(7)Zr4 tetrahedra, and edges with three equivalent O(3)Hf2Zr2 tetrahedra. In the seventh O site, O(7) is bonded to one Zr(2) and three equivalent Zr(1) atoms to form OZr4 tetrahedra that share corners with four equivalent O(4)Zr4 tetrahedra, corners with six equivalent O(2)Hf2Zr2 tetrahedra, corners with six equivalent O(3)Hf2Zr2 tetrahedra, edges with three equivalent O(1)Hf2Zr2 tetrahedra, and edges with three equivalent O(6)Hf2Zr2 tetrahedra. In the eighth O site, O(8) is bonded to one Hf(2) and three equivalent Hf(1) atoms to form OHf4 tetrahedra that share corners with four equivalent O(5)Hf4 tetrahedra, corners with six equivalent O(2)Hf2Zr2 tetrahedra, corners with six equivalent O(3)Hf2Zr2 tetrahedra, edges with three equivalent O(1)Hf2Zr2 tetrahedra, and edges with three equivalent O(6)Hf2Zr2 tetrahedra. is represented by the CIF file [CIF]
data_HfZrO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.233
_cell_length_b   7.233
_cell_length_c   7.233
_cell_angle_alpha   60.000
_cell_angle_beta   60.000
_cell_angle_gamma   60.000
_symmetry_Int_Tables_number   1
_cell_volume   267.618
_cell_formula_units_Z   4
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  0.875  0.875  0.375  1.0
  Hf  Hf1  1  0.875  0.875  0.875  1.0
  Hf  Hf2  1  0.375  0.875  0.875  1.0
  Hf  Hf3  1  0.875  0.375  0.875  1.0
  O  O4  1  0.502  0.502  0.998  1.0
  O  O5  1  0.248  0.752  0.752  1.0
  O  O6  1  0.248  0.752  0.248  1.0
  O  O7  1  0.500  0.500  0.500  1.0
  O  O8  1  0.000  1.000  1.000  1.0
  O  O9  1  0.752  0.248  0.248  1.0
  O  O10  1  0.752  0.248  0.752  1.0
  O  O11  1  0.998  0.502  0.502  1.0
  O  O12  1  0.502  0.998  0.502  1.0
  O  O13  1  0.250  0.250  0.250  1.0
  O  O14  1  0.248  0.248  0.752  1.0
  O  O15  1  0.502  0.998  0.998  1.0
  O  O16  1  0.750  0.750  0.750  1.0
  O  O17  1  0.752  0.752  0.248  1.0
  O  O18  1  0.998  0.502  0.998  1.0
  O  O19  1  0.998  0.998  0.502  1.0
  Zr  Zr20  1  0.375  0.375  0.375  1.0
  Zr  Zr21  1  0.375  0.375  0.875  1.0
  Zr  Zr22  1  0.375  0.875  0.375  1.0
  Zr  Zr23  1  0.875  0.375  0.375  1.0
[/CIF]
.