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.
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. The Pr(1)-O(1) bond length is 2.61 Å. The Pr(1)-O(2) bond length is 2.52 Å. The Pr(1)-O(4) bond length is 2.33 Å. The Pr(1)-O(8) bond length is 2.37 Å. There is one shorter (2.45 Å) and one longer (2.49 Å) Pr(1)-O(3) bond length. There is one shorter (2.61 Å) and one longer (2.64 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(4), one O(8), three equivalent O(1), and three equivalent O(2) atoms. The Pr(2)-O(4) bond length is 2.29 Å. The Pr(2)-O(8) bond length is 2.37 Å. All Pr(2)-O(1) bond lengths are 2.56 Å. All Pr(2)-O(2) bond lengths are 2.58 Å. 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. The Hf(1)-O(1) bond length is 2.19 Å. The Hf(1)-O(2) bond length is 2.16 Å. The Hf(1)-O(5) bond length is 2.16 Å. The Hf(1)-O(7) bond length is 2.52 Å. There is one shorter (2.16 Å) and one longer (2.18 Å) Hf(1)-O(3) bond length. There is one shorter (2.17 Å) and one longer (2.18 Å) Hf(1)-O(6) bond length. 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. The Hf(2)-O(5) bond length is 2.50 Å. The Hf(2)-O(7) bond length is 2.26 Å. All Hf(2)-O(1) bond lengths are 2.21 Å. All Hf(2)-O(2) bond lengths are 2.11 Å. 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.