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.
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. The Hf(1)-O(1) bond length is 2.20 Å. The Hf(1)-O(2) bond length is 2.18 Å. The Hf(1)-O(5) bond length is 2.23 Å. The Hf(1)-O(8) bond length is 2.20 Å. Both Hf(1)-O(3) bond lengths are 2.19 Å. There is one shorter (2.21 Å) and one longer (2.22 Å) Hf(1)-O(6) bond length. 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. The Hf(2)-O(5) bond length is 2.17 Å. The Hf(2)-O(8) bond length is 2.25 Å. All Hf(2)-O(1) bond lengths are 2.17 Å. All Hf(2)-O(2) bond lengths are 2.24 Å. 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. The Zr(1)-O(1) bond length is 2.22 Å. The Zr(1)-O(2) bond length is 2.26 Å. The Zr(1)-O(4) bond length is 2.20 Å. The Zr(1)-O(7) bond length is 2.22 Å. Both Zr(1)-O(3) bond lengths are 2.24 Å. There is one shorter (2.21 Å) and one longer (2.22 Å) Zr(1)-O(6) bond length. 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. The Zr(2)-O(4) bond length is 2.26 Å. The Zr(2)-O(7) bond length is 2.19 Å. All Zr(2)-O(1) bond lengths are 2.27 Å. All Zr(2)-O(2) bond lengths are 2.19 Å. 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.