The compound described by PrHfO4 crystallizes in the cubic P2_13 space group. There are two inequivalent Pr sites. In the first Pr site, Pr(1) is bonded in a body-centered cubic geometry to one O(1), one O(2), one O(4), one O(8), two equivalent O(3), and two equivalent O(6) atoms. In the second Pr site, Pr(2) is bonded in a body-centered cubic geometry to one O(4), one O(8), three equivalent O(1), and three equivalent O(2) atoms. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 8-coordinate geometry to one O(1), one O(2), one O(5), one O(7), two equivalent O(3), and two equivalent O(6) atoms. In the second Hf site, Hf(2) is bonded in a distorted body-centered cubic geometry to one O(5), 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 Pr(1), one Pr(2), one Hf(1), and one Hf(2) atom to form distorted OPr2Hf2 tetrahedra that share corners with two equivalent O(5)Hf4 tetrahedra, corners with two equivalent O(2)Pr2Hf2 tetrahedra, corners with two equivalent O(3)Pr2Hf2 tetrahedra, corners with two equivalent O(4)Pr4 tetrahedra, corners with four equivalent O(1)Pr2Hf2 tetrahedra, corners with four equivalent O(6)Pr2Hf2 tetrahedra,  an edgeedge with one O(7)Hf4 tetrahedra,  an edgeedge with one O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(8)Pr4 tetrahedra, and edges with three equivalent O(2)Pr2Hf2 tetrahedra. In the second O site, O(2) is bonded to one Pr(1), one Pr(2), one Hf(1), and one Hf(2) atom to form distorted OPr2Hf2 tetrahedra that share corners with two equivalent O(7)Hf4 tetrahedra, corners with two equivalent O(1)Pr2Hf2 tetrahedra, corners with two equivalent O(6)Pr2Hf2 tetrahedra, corners with two equivalent O(8)Pr4 tetrahedra, corners with four equivalent O(2)Pr2Hf2 tetrahedra, corners with four equivalent O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra,  an edgeedge with one O(6)Pr2Hf2 tetrahedra,  an edgeedge with one O(4)Pr4 tetrahedra, and edges with three equivalent O(1)Pr2Hf2 tetrahedra. In the third O site, O(3) is bonded to two equivalent Pr(1) and two equivalent Hf(1) atoms to form OPr2Hf2 tetrahedra that share corners with two equivalent O(7)Hf4 tetrahedra, corners with two equivalent O(1)Pr2Hf2 tetrahedra, corners with two equivalent O(6)Pr2Hf2 tetrahedra, corners with two equivalent O(8)Pr4 tetrahedra, corners with four equivalent O(2)Pr2Hf2 tetrahedra, corners with four equivalent O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra,  an edgeedge with one O(1)Pr2Hf2 tetrahedra,  an edgeedge with one O(4)Pr4 tetrahedra, and edges with three equivalent O(6)Pr2Hf2 tetrahedra. In the fourth O site, O(4) is bonded to one Pr(2) and three equivalent Pr(1) atoms to form OPr4 tetrahedra that share corners with four equivalent O(8)Pr4 tetrahedra, corners with six equivalent O(1)Pr2Hf2 tetrahedra, corners with six equivalent O(6)Pr2Hf2 tetrahedra, edges with three equivalent O(2)Pr2Hf2 tetrahedra, and edges with three equivalent O(3)Pr2Hf2 tetrahedra. In the fifth O site, O(5) is bonded to one Hf(2) and three equivalent Hf(1) atoms to form distorted OHf4 tetrahedra that share corners with four equivalent O(7)Hf4 tetrahedra, corners with six equivalent O(1)Pr2Hf2 tetrahedra, corners with six equivalent O(6)Pr2Hf2 tetrahedra, edges with three equivalent O(2)Pr2Hf2 tetrahedra, and edges with three equivalent O(3)Pr2Hf2 tetrahedra. In the sixth O site, O(6) is bonded to two equivalent Pr(1) and two equivalent Hf(1) atoms to form distorted OPr2Hf2 tetrahedra that share corners with two equivalent O(5)Hf4 tetrahedra, corners with two equivalent O(2)Pr2Hf2 tetrahedra, corners with two equivalent O(3)Pr2Hf2 tetrahedra, corners with two equivalent O(4)Pr4 tetrahedra, corners with four equivalent O(1)Pr2Hf2 tetrahedra, corners with four equivalent O(6)Pr2Hf2 tetrahedra,  an edgeedge with one O(7)Hf4 tetrahedra,  an edgeedge with one O(2)Pr2Hf2 tetrahedra,  an edgeedge with one O(8)Pr4 tetrahedra, and edges with three equivalent O(3)Pr2Hf2 tetrahedra. In the seventh O site, O(7) 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)Pr2Hf2 tetrahedra, corners with six equivalent O(3)Pr2Hf2 tetrahedra, edges with three equivalent O(1)Pr2Hf2 tetrahedra, and edges with three equivalent O(6)Pr2Hf2 tetrahedra. In the eighth O site, O(8) is bonded to one Pr(2) and three equivalent Pr(1) atoms to form OPr4 tetrahedra that share corners with four equivalent O(4)Pr4 tetrahedra, corners with six equivalent O(2)Pr2Hf2 tetrahedra, corners with six equivalent O(3)Pr2Hf2 tetrahedra, edges with three equivalent O(1)Pr2Hf2 tetrahedra, and edges with three equivalent O(6)Pr2Hf2 tetrahedra. is represented by the CIF file [CIF]
data_PrHfO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.656
_cell_length_b   7.656
_cell_length_c   10.827
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   634.648
_cell_formula_units_Z   8
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  0.264  0.498  0.882  1.0
  Hf  Hf1  1  0.741  0.498  0.880  1.0
  Hf  Hf2  1  0.002  0.759  0.620  1.0
  Hf  Hf3  1  0.002  0.236  0.618  1.0
  Hf  Hf4  1  0.236  0.002  0.382  1.0
  Hf  Hf5  1  0.759  0.002  0.380  1.0
  Hf  Hf6  1  0.498  0.741  0.120  1.0
  Hf  Hf7  1  0.498  0.264  0.118  1.0
  O  O8  1  0.002  0.503  0.963  1.0
  O  O9  1  0.726  0.277  0.999  1.0
  O  O10  1  0.270  0.270  0.000  1.0
  O  O11  1  0.997  0.997  0.000  1.0
  O  O12  1  0.490  0.490  0.000  1.0
  O  O13  1  0.277  0.726  0.001  1.0
  O  O14  1  0.718  0.718  1.000  1.0
  O  O15  1  0.210  0.290  0.750  1.0
  O  O16  1  0.216  0.709  0.751  1.0
  O  O17  1  0.993  0.507  0.750  1.0
  O  O18  1  0.503  0.497  0.776  1.0
  O  O19  1  0.785  0.715  0.750  1.0
  O  O20  1  0.499  0.001  0.750  1.0
  O  O21  1  0.003  0.997  0.724  1.0
  O  O22  1  0.791  0.284  0.749  1.0
  O  O23  1  0.997  0.498  0.537  1.0
  O  O24  1  0.503  0.503  0.500  1.0
  O  O25  1  0.010  0.010  0.500  1.0
  O  O26  1  0.774  0.223  0.499  1.0
  O  O27  1  0.782  0.782  0.500  1.0
  O  O28  1  0.230  0.230  0.500  1.0
  O  O29  1  0.223  0.774  0.501  1.0
  O  O30  1  0.498  0.997  0.463  1.0
  O  O31  1  0.290  0.210  0.250  1.0
  O  O32  1  0.284  0.791  0.251  1.0
  O  O33  1  0.507  0.993  0.250  1.0
  O  O34  1  0.997  0.003  0.276  1.0
  O  O35  1  0.715  0.785  0.250  1.0
  O  O36  1  0.001  0.499  0.250  1.0
  O  O37  1  0.497  0.503  0.224  1.0
  O  O38  1  0.709  0.216  0.249  1.0
  O  O39  1  0.503  0.002  0.037  1.0
  Pr  Pr40  1  0.246  0.999  0.876  1.0
  Pr  Pr41  1  0.751  0.999  0.876  1.0
  Pr  Pr42  1  0.501  0.749  0.624  1.0
  Pr  Pr43  1  0.501  0.254  0.624  1.0
  Pr  Pr44  1  0.254  0.501  0.376  1.0
  Pr  Pr45  1  0.749  0.501  0.376  1.0
  Pr  Pr46  1  0.999  0.751  0.124  1.0
  Pr  Pr47  1  0.999  0.246  0.124  1.0
[/CIF]
.
The compound described by PrHfO4 crystallizes in the cubic P2_13 space group. There are two inequivalent Pr sites. In the first Pr site, Pr(1) is bonded in a body-centered cubic geometry to one O(1), one O(2), one O(4), one O(8), two equivalent O(3), and two equivalent O(6) atoms. In the second Pr site, Pr(2) is bonded in a body-centered cubic geometry to one O(4), one O(8), three equivalent O(1), and three equivalent O(2) atoms. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 8-coordinate geometry to one O(1), one O(2), one O(5), one O(7), two equivalent O(3), and two equivalent O(6) atoms. In the second Hf site, Hf(2) is bonded in a distorted body-centered cubic geometry to one O(5), 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 Pr(1), one Pr(2), one Hf(1), and one Hf(2) atom to form distorted OPr2Hf2 tetrahedra that share corners with two equivalent O(5)Hf4 tetrahedra, corners with two equivalent O(2)Pr2Hf2 tetrahedra, corners with two equivalent O(3)Pr2Hf2 tetrahedra, corners with two equivalent O(4)Pr4 tetrahedra, corners with four equivalent O(1)Pr2Hf2 tetrahedra, corners with four equivalent O(6)Pr2Hf2 tetrahedra,  an edgeedge with one O(7)Hf4 tetrahedra,  an edgeedge with one O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(8)Pr4 tetrahedra, and edges with three equivalent O(2)Pr2Hf2 tetrahedra. In the second O site, O(2) is bonded to one Pr(1), one Pr(2), one Hf(1), and one Hf(2) atom to form distorted OPr2Hf2 tetrahedra that share corners with two equivalent O(7)Hf4 tetrahedra, corners with two equivalent O(1)Pr2Hf2 tetrahedra, corners with two equivalent O(6)Pr2Hf2 tetrahedra, corners with two equivalent O(8)Pr4 tetrahedra, corners with four equivalent O(2)Pr2Hf2 tetrahedra, corners with four equivalent O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra,  an edgeedge with one O(6)Pr2Hf2 tetrahedra,  an edgeedge with one O(4)Pr4 tetrahedra, and edges with three equivalent O(1)Pr2Hf2 tetrahedra. In the third O site, O(3) is bonded to two equivalent Pr(1) and two equivalent Hf(1) atoms to form OPr2Hf2 tetrahedra that share corners with two equivalent O(7)Hf4 tetrahedra, corners with two equivalent O(1)Pr2Hf2 tetrahedra, corners with two equivalent O(6)Pr2Hf2 tetrahedra, corners with two equivalent O(8)Pr4 tetrahedra, corners with four equivalent O(2)Pr2Hf2 tetrahedra, corners with four equivalent O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra,  an edgeedge with one O(1)Pr2Hf2 tetrahedra,  an edgeedge with one O(4)Pr4 tetrahedra, and edges with three equivalent O(6)Pr2Hf2 tetrahedra. In the fourth O site, O(4) is bonded to one Pr(2) and three equivalent Pr(1) atoms to form OPr4 tetrahedra that share corners with four equivalent O(8)Pr4 tetrahedra, corners with six equivalent O(1)Pr2Hf2 tetrahedra, corners with six equivalent O(6)Pr2Hf2 tetrahedra, edges with three equivalent O(2)Pr2Hf2 tetrahedra, and edges with three equivalent O(3)Pr2Hf2 tetrahedra. In the fifth O site, O(5) is bonded to one Hf(2) and three equivalent Hf(1) atoms to form distorted OHf4 tetrahedra that share corners with four equivalent O(7)Hf4 tetrahedra, corners with six equivalent O(1)Pr2Hf2 tetrahedra, corners with six equivalent O(6)Pr2Hf2 tetrahedra, edges with three equivalent O(2)Pr2Hf2 tetrahedra, and edges with three equivalent O(3)Pr2Hf2 tetrahedra. In the sixth O site, O(6) is bonded to two equivalent Pr(1) and two equivalent Hf(1) atoms to form distorted OPr2Hf2 tetrahedra that share corners with two equivalent O(5)Hf4 tetrahedra, corners with two equivalent O(2)Pr2Hf2 tetrahedra, corners with two equivalent O(3)Pr2Hf2 tetrahedra, corners with two equivalent O(4)Pr4 tetrahedra, corners with four equivalent O(1)Pr2Hf2 tetrahedra, corners with four equivalent O(6)Pr2Hf2 tetrahedra,  an edgeedge with one O(7)Hf4 tetrahedra,  an edgeedge with one O(2)Pr2Hf2 tetrahedra,  an edgeedge with one O(8)Pr4 tetrahedra, and edges with three equivalent O(3)Pr2Hf2 tetrahedra. In the seventh O site, O(7) 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)Pr2Hf2 tetrahedra, corners with six equivalent O(3)Pr2Hf2 tetrahedra, edges with three equivalent O(1)Pr2Hf2 tetrahedra, and edges with three equivalent O(6)Pr2Hf2 tetrahedra. In the eighth O site, O(8) is bonded to one Pr(2) and three equivalent Pr(1) atoms to form OPr4 tetrahedra that share corners with four equivalent O(4)Pr4 tetrahedra, corners with six equivalent O(2)Pr2Hf2 tetrahedra, corners with six equivalent O(3)Pr2Hf2 tetrahedra, edges with three equivalent O(1)Pr2Hf2 tetrahedra, and edges with three equivalent O(6)Pr2Hf2 tetrahedra. is represented by the CIF file [CIF]
data_PrHfO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.656
_cell_length_b   7.656
_cell_length_c   10.827
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   634.648
_cell_formula_units_Z   8
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  0.264  0.498  0.882  1.0
  Hf  Hf1  1  0.741  0.498  0.880  1.0
  Hf  Hf2  1  0.002  0.759  0.620  1.0
  Hf  Hf3  1  0.002  0.236  0.618  1.0
  Hf  Hf4  1  0.236  0.002  0.382  1.0
  Hf  Hf5  1  0.759  0.002  0.380  1.0
  Hf  Hf6  1  0.498  0.741  0.120  1.0
  Hf  Hf7  1  0.498  0.264  0.118  1.0
  O  O8  1  0.002  0.503  0.963  1.0
  O  O9  1  0.726  0.277  0.999  1.0
  O  O10  1  0.270  0.270  0.000  1.0
  O  O11  1  0.997  0.997  0.000  1.0
  O  O12  1  0.490  0.490  0.000  1.0
  O  O13  1  0.277  0.726  0.001  1.0
  O  O14  1  0.718  0.718  1.000  1.0
  O  O15  1  0.210  0.290  0.750  1.0
  O  O16  1  0.216  0.709  0.751  1.0
  O  O17  1  0.993  0.507  0.750  1.0
  O  O18  1  0.503  0.497  0.776  1.0
  O  O19  1  0.785  0.715  0.750  1.0
  O  O20  1  0.499  0.001  0.750  1.0
  O  O21  1  0.003  0.997  0.724  1.0
  O  O22  1  0.791  0.284  0.749  1.0
  O  O23  1  0.997  0.498  0.537  1.0
  O  O24  1  0.503  0.503  0.500  1.0
  O  O25  1  0.010  0.010  0.500  1.0
  O  O26  1  0.774  0.223  0.499  1.0
  O  O27  1  0.782  0.782  0.500  1.0
  O  O28  1  0.230  0.230  0.500  1.0
  O  O29  1  0.223  0.774  0.501  1.0
  O  O30  1  0.498  0.997  0.463  1.0
  O  O31  1  0.290  0.210  0.250  1.0
  O  O32  1  0.284  0.791  0.251  1.0
  O  O33  1  0.507  0.993  0.250  1.0
  O  O34  1  0.997  0.003  0.276  1.0
  O  O35  1  0.715  0.785  0.250  1.0
  O  O36  1  0.001  0.499  0.250  1.0
  O  O37  1  0.497  0.503  0.224  1.0
  O  O38  1  0.709  0.216  0.249  1.0
  O  O39  1  0.503  0.002  0.037  1.0
  Pr  Pr40  1  0.246  0.999  0.876  1.0
  Pr  Pr41  1  0.751  0.999  0.876  1.0
  Pr  Pr42  1  0.501  0.749  0.624  1.0
  Pr  Pr43  1  0.501  0.254  0.624  1.0
  Pr  Pr44  1  0.254  0.501  0.376  1.0
  Pr  Pr45  1  0.749  0.501  0.376  1.0
  Pr  Pr46  1  0.999  0.751  0.124  1.0
  Pr  Pr47  1  0.999  0.246  0.124  1.0
[/CIF]
.