PrHfO4 crystallizes in the tetragonal P4_3 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(3), one O(7), one O(8), two equivalent O(4), and two equivalent O(6) atoms. In the second Pr site, Pr(2) is bonded in a body-centered cubic geometry to one O(1), one O(3), one O(7), one O(8), two equivalent O(2), and two equivalent O(4) 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(3), one O(7), one O(8), two equivalent O(5), and two equivalent O(6) atoms. In the second Hf site, Hf(2) is bonded in a 8-coordinate geometry to one O(1), one O(3), one O(7), one O(8), two equivalent O(2), and two equivalent O(5) 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(2)Pr2Hf2 tetrahedra, corners with two equivalent O(3)Pr2Hf2 tetrahedra, corners with two equivalent O(6)Pr2Hf2 tetrahedra, corners with two equivalent O(4)Pr4 tetrahedra, corners with four equivalent O(8)Pr2Hf2 tetrahedra,  an edgeedge with one O(2)Pr2Hf2 tetrahedra,  an edgeedge with one O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(6)Pr2Hf2 tetrahedra, and  an edgeedge with one O(4)Pr4 tetrahedra. In the second O site, O(2) is bonded to two equivalent Pr(2) and two equivalent Hf(2) atoms to form OPr2Hf2 tetrahedra that share corners with two equivalent O(1)Pr2Hf2 tetrahedra, corners with two equivalent O(8)Pr2Hf2 tetrahedra, corners with two equivalent O(4)Pr4 tetrahedra, corners with four equivalent O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(1)Pr2Hf2 tetrahedra,  an edgeedge with one O(8)Pr2Hf2 tetrahedra,  an edgeedge with one O(4)Pr4 tetrahedra, and edges with two equivalent O(2)Pr2Hf2 tetrahedra. In the third O site, O(3) 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(1)Pr2Hf2 tetrahedra, corners with two equivalent O(8)Pr2Hf2 tetrahedra, corners with two equivalent O(4)Pr4 tetrahedra, corners with four equivalent O(2)Pr2Hf2 tetrahedra, corners with four equivalent O(6)Pr2Hf2 tetrahedra,  an edgeedge with one O(1)Pr2Hf2 tetrahedra,  an edgeedge with one O(8)Pr2Hf2 tetrahedra, and  an edgeedge with one O(4)Pr4 tetrahedra. In the fourth O site, O(4) is bonded to two equivalent Pr(1) and two equivalent Pr(2) atoms to form OPr4 tetrahedra that share corners with two equivalent O(1)Pr2Hf2 tetrahedra, corners with two equivalent O(2)Pr2Hf2 tetrahedra, corners with two equivalent O(3)Pr2Hf2 tetrahedra, corners with two equivalent O(6)Pr2Hf2 tetrahedra, corners with two equivalent O(8)Pr2Hf2 tetrahedra, corners with four equivalent O(4)Pr4 tetrahedra,  an edgeedge with one O(1)Pr2Hf2 tetrahedra,  an edgeedge with one O(2)Pr2Hf2 tetrahedra,  an edgeedge with one O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(6)Pr2Hf2 tetrahedra, and  an edgeedge with one O(8)Pr2Hf2 tetrahedra. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to two equivalent Hf(1) and two equivalent Hf(2) atoms. In the sixth O site, O(6) is bonded to two equivalent Pr(1) and two equivalent Hf(1) atoms to form OPr2Hf2 tetrahedra that share corners with two equivalent O(1)Pr2Hf2 tetrahedra, corners with two equivalent O(8)Pr2Hf2 tetrahedra, corners with two equivalent O(4)Pr4 tetrahedra, corners with four equivalent O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(1)Pr2Hf2 tetrahedra,  an edgeedge with one O(8)Pr2Hf2 tetrahedra,  an edgeedge with one O(4)Pr4 tetrahedra, and edges with two equivalent O(6)Pr2Hf2 tetrahedra. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to one Pr(1), one Pr(2), one Hf(1), and one Hf(2) atom. In the eighth O site, O(8) 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(2)Pr2Hf2 tetrahedra, corners with two equivalent O(3)Pr2Hf2 tetrahedra, corners with two equivalent O(6)Pr2Hf2 tetrahedra, corners with two equivalent O(4)Pr4 tetrahedra, corners with four equivalent O(1)Pr2Hf2 tetrahedra,  an edgeedge with one O(2)Pr2Hf2 tetrahedra,  an edgeedge with one O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(6)Pr2Hf2 tetrahedra, and  an edgeedge with one O(4)Pr4 tetrahedra.
PrHfO4 crystallizes in the tetragonal P4_3 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(3), one O(7), one O(8), two equivalent O(4), and two equivalent O(6) atoms. The Pr(1)-O(1) bond length is 2.51 Å. The Pr(1)-O(3) bond length is 2.55 Å. The Pr(1)-O(7) bond length is 2.69 Å. The Pr(1)-O(8) bond length is 2.63 Å. There is one shorter (2.34 Å) and one longer (2.35 Å) Pr(1)-O(4) bond length. There is one shorter (2.45 Å) and one longer (2.50 Å) Pr(1)-O(6) bond length. In the second Pr site, Pr(2) is bonded in a body-centered cubic geometry to one O(1), one O(3), one O(7), one O(8), two equivalent O(2), and two equivalent O(4) atoms. The Pr(2)-O(1) bond length is 2.60 Å. The Pr(2)-O(3) bond length is 2.58 Å. The Pr(2)-O(7) bond length is 2.68 Å. The Pr(2)-O(8) bond length is 2.53 Å. There is one shorter (2.48 Å) and one longer (2.50 Å) Pr(2)-O(2) bond length. There is one shorter (2.33 Å) and one longer (2.34 Å) Pr(2)-O(4) bond length. 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(3), one O(7), one O(8), two equivalent O(5), and two equivalent O(6) atoms. The Hf(1)-O(1) bond length is 2.16 Å. The Hf(1)-O(3) bond length is 2.23 Å. The Hf(1)-O(7) bond length is 2.16 Å. The Hf(1)-O(8) bond length is 2.15 Å. There is one shorter (2.21 Å) and one longer (2.49 Å) Hf(1)-O(5) bond length. There is one shorter (2.12 Å) and one longer (2.17 Å) Hf(1)-O(6) bond length. In the second Hf site, Hf(2) is bonded in a 8-coordinate geometry to one O(1), one O(3), one O(7), one O(8), two equivalent O(2), and two equivalent O(5) atoms. The Hf(2)-O(1) bond length is 2.18 Å. The Hf(2)-O(3) bond length is 2.24 Å. The Hf(2)-O(7) bond length is 2.14 Å. The Hf(2)-O(8) bond length is 2.13 Å. There is one shorter (2.10 Å) and one longer (2.18 Å) Hf(2)-O(2) bond length. There is one shorter (2.16 Å) and one longer (2.57 Å) Hf(2)-O(5) bond length. 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(2)Pr2Hf2 tetrahedra, corners with two equivalent O(3)Pr2Hf2 tetrahedra, corners with two equivalent O(6)Pr2Hf2 tetrahedra, corners with two equivalent O(4)Pr4 tetrahedra, corners with four equivalent O(8)Pr2Hf2 tetrahedra,  an edgeedge with one O(2)Pr2Hf2 tetrahedra,  an edgeedge with one O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(6)Pr2Hf2 tetrahedra, and  an edgeedge with one O(4)Pr4 tetrahedra. In the second O site, O(2) is bonded to two equivalent Pr(2) and two equivalent Hf(2) atoms to form OPr2Hf2 tetrahedra that share corners with two equivalent O(1)Pr2Hf2 tetrahedra, corners with two equivalent O(8)Pr2Hf2 tetrahedra, corners with two equivalent O(4)Pr4 tetrahedra, corners with four equivalent O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(1)Pr2Hf2 tetrahedra,  an edgeedge with one O(8)Pr2Hf2 tetrahedra,  an edgeedge with one O(4)Pr4 tetrahedra, and edges with two equivalent O(2)Pr2Hf2 tetrahedra. In the third O site, O(3) 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(1)Pr2Hf2 tetrahedra, corners with two equivalent O(8)Pr2Hf2 tetrahedra, corners with two equivalent O(4)Pr4 tetrahedra, corners with four equivalent O(2)Pr2Hf2 tetrahedra, corners with four equivalent O(6)Pr2Hf2 tetrahedra,  an edgeedge with one O(1)Pr2Hf2 tetrahedra,  an edgeedge with one O(8)Pr2Hf2 tetrahedra, and  an edgeedge with one O(4)Pr4 tetrahedra. In the fourth O site, O(4) is bonded to two equivalent Pr(1) and two equivalent Pr(2) atoms to form OPr4 tetrahedra that share corners with two equivalent O(1)Pr2Hf2 tetrahedra, corners with two equivalent O(2)Pr2Hf2 tetrahedra, corners with two equivalent O(3)Pr2Hf2 tetrahedra, corners with two equivalent O(6)Pr2Hf2 tetrahedra, corners with two equivalent O(8)Pr2Hf2 tetrahedra, corners with four equivalent O(4)Pr4 tetrahedra,  an edgeedge with one O(1)Pr2Hf2 tetrahedra,  an edgeedge with one O(2)Pr2Hf2 tetrahedra,  an edgeedge with one O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(6)Pr2Hf2 tetrahedra, and  an edgeedge with one O(8)Pr2Hf2 tetrahedra. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to two equivalent Hf(1) and two equivalent Hf(2) atoms. In the sixth O site, O(6) is bonded to two equivalent Pr(1) and two equivalent Hf(1) atoms to form OPr2Hf2 tetrahedra that share corners with two equivalent O(1)Pr2Hf2 tetrahedra, corners with two equivalent O(8)Pr2Hf2 tetrahedra, corners with two equivalent O(4)Pr4 tetrahedra, corners with four equivalent O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(1)Pr2Hf2 tetrahedra,  an edgeedge with one O(8)Pr2Hf2 tetrahedra,  an edgeedge with one O(4)Pr4 tetrahedra, and edges with two equivalent O(6)Pr2Hf2 tetrahedra. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to one Pr(1), one Pr(2), one Hf(1), and one Hf(2) atom. In the eighth O site, O(8) 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(2)Pr2Hf2 tetrahedra, corners with two equivalent O(3)Pr2Hf2 tetrahedra, corners with two equivalent O(6)Pr2Hf2 tetrahedra, corners with two equivalent O(4)Pr4 tetrahedra, corners with four equivalent O(1)Pr2Hf2 tetrahedra,  an edgeedge with one O(2)Pr2Hf2 tetrahedra,  an edgeedge with one O(3)Pr2Hf2 tetrahedra,  an edgeedge with one O(6)Pr2Hf2 tetrahedra, and  an edgeedge with one O(4)Pr4 tetrahedra.