HfZrO4 crystallizes in the monoclinic Cm space group. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a distorted body-centered cubic geometry to one O(12), one O(5), one O(6), one O(8), two equivalent O(3), and two equivalent O(9) atoms. In the second Hf site, Hf(2) is bonded in a body-centered cubic geometry to one O(1), one O(11), one O(12), one O(2), one O(3), one O(5), one O(7), and one O(9) atom. In the third Hf site, Hf(3) is bonded in a body-centered cubic geometry to one O(12), one O(5), one O(6), one O(8), two equivalent O(1), and two equivalent O(7) atoms. There are three inequivalent Zr sites. In the first Zr site, Zr(1) is bonded in a body-centered cubic geometry to one O(1), one O(10), one O(3), one O(4), one O(6), one O(7), one O(8), and one O(9) atom. In the second Zr site, Zr(2) is bonded in a distorted body-centered cubic geometry to one O(10), one O(11), one O(2), one O(4), two equivalent O(1), and two equivalent O(7) atoms. In the third Zr site, Zr(3) is bonded in a body-centered cubic geometry to one O(10), one O(11), one O(2), one O(4), two equivalent O(3), and two equivalent O(9) atoms. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Hf(2), one Hf(3), one Zr(1), and one Zr(2) atom to form distorted OHf2Zr2 tetrahedra that share corners with two equivalent O(1)Hf2Zr2 tetrahedra, corners with two equivalent O(11)Hf2Zr2 tetrahedra, corners with two equivalent O(8)Hf2Zr2 tetrahedra, corners with two equivalent O(9)Hf2Zr2 tetrahedra, corners with two equivalent O(5)Hf4 tetrahedra, corners with two equivalent O(4)Zr4 tetrahedra, corners with four equivalent O(7)Hf2Zr2 tetrahedra,  an edgeedge with one O(2)Hf2Zr2 tetrahedra,  an edgeedge with one O(3)Hf2Zr2 tetrahedra,  an edgeedge with one O(6)Hf2Zr2 tetrahedra,  an edgeedge with one O(7)Hf2Zr2 tetrahedra,  an edgeedge with one O(12)Hf4 tetrahedra, and  an edgeedge with one O(10)Zr4 tetrahedra. In the second O site, O(2) is bonded to two equivalent Hf(2), one Zr(2), and one Zr(3) atom to form OHf2Zr2 tetrahedra that share corners with two equivalent O(12)Hf4 tetrahedra, corners with two equivalent O(10)Zr4 tetrahedra, corners with four equivalent O(11)Hf2Zr2 tetrahedra, corners with four equivalent O(3)Hf2Zr2 tetrahedra, corners with four equivalent O(7)Hf2Zr2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra,  an edgeedge with one O(4)Zr4 tetrahedra, edges with two equivalent O(1)Hf2Zr2 tetrahedra, and edges with two equivalent O(9)Hf2Zr2 tetrahedra. In the third O site, O(3) is bonded to one Hf(1), one Hf(2), one Zr(1), and one Zr(3) 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(6)Hf2Zr2 tetrahedra, corners with two equivalent O(7)Hf2Zr2 tetrahedra, corners with two equivalent O(12)Hf4 tetrahedra, corners with two equivalent O(10)Zr4 tetrahedra, corners with four equivalent O(9)Hf2Zr2 tetrahedra,  an edgeedge with one O(1)Hf2Zr2 tetrahedra,  an edgeedge with one O(11)Hf2Zr2 tetrahedra,  an edgeedge with one O(8)Hf2Zr2 tetrahedra,  an edgeedge with one O(9)Hf2Zr2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra, and  an edgeedge with one O(4)Zr4 tetrahedra. In the fourth O site, O(4) is bonded to one Zr(2), one Zr(3), and two equivalent Zr(1) atoms to form distorted OZr4 tetrahedra that share corners with two equivalent O(11)Hf2Zr2 tetrahedra, corners with two equivalent O(8)Hf2Zr2 tetrahedra, corners with four equivalent O(1)Hf2Zr2 tetrahedra, corners with four equivalent O(9)Hf2Zr2 tetrahedra, corners with four equivalent O(10)Zr4 tetrahedra,  an edgeedge with one O(2)Hf2Zr2 tetrahedra,  an edgeedge with one O(6)Hf2Zr2 tetrahedra, edges with two equivalent O(3)Hf2Zr2 tetrahedra, and edges with two equivalent O(7)Hf2Zr2 tetrahedra. In the fifth O site, O(5) is bonded to one Hf(1), one Hf(3), and two equivalent Hf(2) atoms to form distorted OHf4 tetrahedra that share corners with two equivalent O(11)Hf2Zr2 tetrahedra, corners with two equivalent O(8)Hf2Zr2 tetrahedra, corners with four equivalent O(1)Hf2Zr2 tetrahedra, corners with four equivalent O(9)Hf2Zr2 tetrahedra, corners with four equivalent O(12)Hf4 tetrahedra,  an edgeedge with one O(2)Hf2Zr2 tetrahedra,  an edgeedge with one O(6)Hf2Zr2 tetrahedra, edges with two equivalent O(3)Hf2Zr2 tetrahedra, and edges with two equivalent O(7)Hf2Zr2 tetrahedra. In the sixth O site, O(6) is bonded to one Hf(1), one Hf(3), and two equivalent Zr(1) atoms to form OHf2Zr2 tetrahedra that share corners with two equivalent O(12)Hf4 tetrahedra, corners with two equivalent O(10)Zr4 tetrahedra, corners with four equivalent O(3)Hf2Zr2 tetrahedra, corners with four equivalent O(7)Hf2Zr2 tetrahedra, corners with four equivalent O(8)Hf2Zr2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra,  an edgeedge with one O(4)Zr4 tetrahedra, edges with two equivalent O(1)Hf2Zr2 tetrahedra, and edges with two equivalent O(9)Hf2Zr2 tetrahedra. In the seventh O site, O(7) is bonded to one Hf(2), one Hf(3), 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(6)Hf2Zr2 tetrahedra, corners with two equivalent O(7)Hf2Zr2 tetrahedra, corners with two equivalent O(12)Hf4 tetrahedra, corners with two equivalent O(10)Zr4 tetrahedra, corners with four equivalent O(1)Hf2Zr2 tetrahedra,  an edgeedge with one O(1)Hf2Zr2 tetrahedra,  an edgeedge with one O(11)Hf2Zr2 tetrahedra,  an edgeedge with one O(8)Hf2Zr2 tetrahedra,  an edgeedge with one O(9)Hf2Zr2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra, and  an edgeedge with one O(4)Zr4 tetrahedra. In the eighth O site, O(8) is bonded to one Hf(1), one Hf(3), and two equivalent Zr(1) atoms to form distorted OHf2Zr2 tetrahedra that share 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, corners with four equivalent O(9)Hf2Zr2 tetrahedra,  an edgeedge with one O(12)Hf4 tetrahedra,  an edgeedge with one O(10)Zr4 tetrahedra, edges with two equivalent O(3)Hf2Zr2 tetrahedra, and edges with two equivalent O(7)Hf2Zr2 tetrahedra. In the ninth O site, O(9) is bonded to one Hf(1), one Hf(2), one Zr(1), and one Zr(3) atom to form distorted OHf2Zr2 tetrahedra that share corners with two equivalent O(1)Hf2Zr2 tetrahedra, corners with two equivalent O(11)Hf2Zr2 tetrahedra, corners with two equivalent O(8)Hf2Zr2 tetrahedra, corners with two equivalent O(9)Hf2Zr2 tetrahedra, corners with two equivalent O(5)Hf4 tetrahedra, corners with two equivalent O(4)Zr4 tetrahedra, corners with four equivalent O(3)Hf2Zr2 tetrahedra,  an edgeedge with one O(2)Hf2Zr2 tetrahedra,  an edgeedge with one O(3)Hf2Zr2 tetrahedra,  an edgeedge with one O(6)Hf2Zr2 tetrahedra,  an edgeedge with one O(7)Hf2Zr2 tetrahedra,  an edgeedge with one O(12)Hf4 tetrahedra, and  an edgeedge with one O(10)Zr4 tetrahedra. In the tenth O site, O(10) is bonded to one Zr(2), one Zr(3), and two equivalent Zr(1) atoms to form OZr4 tetrahedra that share corners with two equivalent O(2)Hf2Zr2 tetrahedra, corners with two equivalent O(6)Hf2Zr2 tetrahedra, corners with four equivalent O(3)Hf2Zr2 tetrahedra, corners with four equivalent O(7)Hf2Zr2 tetrahedra, corners with four equivalent O(4)Zr4 tetrahedra,  an edgeedge with one O(11)Hf2Zr2 tetrahedra,  an edgeedge with one O(8)Hf2Zr2 tetrahedra, edges with two equivalent O(1)Hf2Zr2 tetrahedra, and edges with two equivalent O(9)Hf2Zr2 tetrahedra. In the eleventh O site, O(11) is bonded to two equivalent Hf(2), one Zr(2), and one Zr(3) atom to form distorted OHf2Zr2 tetrahedra that share 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(2)Hf2Zr2 tetrahedra, corners with four equivalent O(9)Hf2Zr2 tetrahedra,  an edgeedge with one O(12)Hf4 tetrahedra,  an edgeedge with one O(10)Zr4 tetrahedra, edges with two equivalent O(3)Hf2Zr2 tetrahedra, and edges with two equivalent O(7)Hf2Zr2 tetrahedra. In the twelfth O site, O(12) is bonded to one Hf(1), one Hf(3), and two equivalent Hf(2) atoms to form OHf4 tetrahedra that share corners with two equivalent O(2)Hf2Zr2 tetrahedra, corners with two equivalent O(6)Hf2Zr2 tetrahedra, corners with four equivalent O(3)Hf2Zr2 tetrahedra, corners with four equivalent O(7)Hf2Zr2 tetrahedra, corners with four equivalent O(5)Hf4 tetrahedra,  an edgeedge with one O(11)Hf2Zr2 tetrahedra,  an edgeedge with one O(8)Hf2Zr2 tetrahedra, edges with two equivalent O(1)Hf2Zr2 tetrahedra, and edges with two equivalent O(9)Hf2Zr2 tetrahedra.
HfZrO4 crystallizes in the monoclinic Cm space group. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a distorted body-centered cubic geometry to one O(12), one O(5), one O(6), one O(8), two equivalent O(3), and two equivalent O(9) atoms. The Hf(1)-O(12) bond length is 2.02 Å. The Hf(1)-O(5) bond length is 2.51 Å. The Hf(1)-O(6) bond length is 2.03 Å. The Hf(1)-O(8) bond length is 2.45 Å. Both Hf(1)-O(3) bond lengths are 2.03 Å. Both Hf(1)-O(9) bond lengths are 2.44 Å. In the second Hf site, Hf(2) is bonded in a body-centered cubic geometry to one O(1), one O(11), one O(12), one O(2), one O(3), one O(5), one O(7), and one O(9) atom. The Hf(2)-O(1) bond length is 2.10 Å. The Hf(2)-O(11) bond length is 2.11 Å. The Hf(2)-O(12) bond length is 2.35 Å. The Hf(2)-O(2) bond length is 2.32 Å. The Hf(2)-O(3) bond length is 2.32 Å. The Hf(2)-O(5) bond length is 2.11 Å. The Hf(2)-O(7) bond length is 2.30 Å. The Hf(2)-O(9) bond length is 2.10 Å. In the third Hf site, Hf(3) is bonded in a body-centered cubic geometry to one O(12), one O(5), one O(6), one O(8), two equivalent O(1), and two equivalent O(7) atoms. The Hf(3)-O(12) bond length is 2.21 Å. The Hf(3)-O(5) bond length is 2.22 Å. The Hf(3)-O(6) bond length is 2.19 Å. The Hf(3)-O(8) bond length is 2.22 Å. Both Hf(3)-O(1) bond lengths are 2.21 Å. Both Hf(3)-O(7) bond lengths are 2.20 Å. There are three inequivalent Zr sites. In the first Zr site, Zr(1) is bonded in a body-centered cubic geometry to one O(1), one O(10), one O(3), one O(4), one O(6), one O(7), one O(8), and one O(9) atom. The Zr(1)-O(1) bond length is 2.14 Å. The Zr(1)-O(10) bond length is 2.32 Å. The Zr(1)-O(3) bond length is 2.34 Å. The Zr(1)-O(4) bond length is 2.13 Å. The Zr(1)-O(6) bond length is 2.35 Å. The Zr(1)-O(7) bond length is 2.38 Å. The Zr(1)-O(8) bond length is 2.13 Å. The Zr(1)-O(9) bond length is 2.14 Å. In the second Zr site, Zr(2) is bonded in a distorted body-centered cubic geometry to one O(10), one O(11), one O(2), one O(4), two equivalent O(1), and two equivalent O(7) atoms. The Zr(2)-O(10) bond length is 2.06 Å. The Zr(2)-O(11) bond length is 2.48 Å. The Zr(2)-O(2) bond length is 2.05 Å. The Zr(2)-O(4) bond length is 2.44 Å. Both Zr(2)-O(1) bond lengths are 2.49 Å. Both Zr(2)-O(7) bond lengths are 2.05 Å. In the third Zr site, Zr(3) is bonded in a body-centered cubic geometry to one O(10), one O(11), one O(2), one O(4), two equivalent O(3), and two equivalent O(9) atoms. The Zr(3)-O(10) bond length is 2.21 Å. The Zr(3)-O(11) bond length is 2.24 Å. The Zr(3)-O(2) bond length is 2.23 Å. The Zr(3)-O(4) bond length is 2.23 Å. Both Zr(3)-O(3) bond lengths are 2.23 Å. Both Zr(3)-O(9) bond lengths are 2.25 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Hf(2), one Hf(3), one Zr(1), and one Zr(2) atom to form distorted OHf2Zr2 tetrahedra that share corners with two equivalent O(1)Hf2Zr2 tetrahedra, corners with two equivalent O(11)Hf2Zr2 tetrahedra, corners with two equivalent O(8)Hf2Zr2 tetrahedra, corners with two equivalent O(9)Hf2Zr2 tetrahedra, corners with two equivalent O(5)Hf4 tetrahedra, corners with two equivalent O(4)Zr4 tetrahedra, corners with four equivalent O(7)Hf2Zr2 tetrahedra,  an edgeedge with one O(2)Hf2Zr2 tetrahedra,  an edgeedge with one O(3)Hf2Zr2 tetrahedra,  an edgeedge with one O(6)Hf2Zr2 tetrahedra,  an edgeedge with one O(7)Hf2Zr2 tetrahedra,  an edgeedge with one O(12)Hf4 tetrahedra, and  an edgeedge with one O(10)Zr4 tetrahedra. In the second O site, O(2) is bonded to two equivalent Hf(2), one Zr(2), and one Zr(3) atom to form OHf2Zr2 tetrahedra that share corners with two equivalent O(12)Hf4 tetrahedra, corners with two equivalent O(10)Zr4 tetrahedra, corners with four equivalent O(11)Hf2Zr2 tetrahedra, corners with four equivalent O(3)Hf2Zr2 tetrahedra, corners with four equivalent O(7)Hf2Zr2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra,  an edgeedge with one O(4)Zr4 tetrahedra, edges with two equivalent O(1)Hf2Zr2 tetrahedra, and edges with two equivalent O(9)Hf2Zr2 tetrahedra. In the third O site, O(3) is bonded to one Hf(1), one Hf(2), one Zr(1), and one Zr(3) 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(6)Hf2Zr2 tetrahedra, corners with two equivalent O(7)Hf2Zr2 tetrahedra, corners with two equivalent O(12)Hf4 tetrahedra, corners with two equivalent O(10)Zr4 tetrahedra, corners with four equivalent O(9)Hf2Zr2 tetrahedra,  an edgeedge with one O(1)Hf2Zr2 tetrahedra,  an edgeedge with one O(11)Hf2Zr2 tetrahedra,  an edgeedge with one O(8)Hf2Zr2 tetrahedra,  an edgeedge with one O(9)Hf2Zr2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra, and  an edgeedge with one O(4)Zr4 tetrahedra. In the fourth O site, O(4) is bonded to one Zr(2), one Zr(3), and two equivalent Zr(1) atoms to form distorted OZr4 tetrahedra that share corners with two equivalent O(11)Hf2Zr2 tetrahedra, corners with two equivalent O(8)Hf2Zr2 tetrahedra, corners with four equivalent O(1)Hf2Zr2 tetrahedra, corners with four equivalent O(9)Hf2Zr2 tetrahedra, corners with four equivalent O(10)Zr4 tetrahedra,  an edgeedge with one O(2)Hf2Zr2 tetrahedra,  an edgeedge with one O(6)Hf2Zr2 tetrahedra, edges with two equivalent O(3)Hf2Zr2 tetrahedra, and edges with two equivalent O(7)Hf2Zr2 tetrahedra. In the fifth O site, O(5) is bonded to one Hf(1), one Hf(3), and two equivalent Hf(2) atoms to form distorted OHf4 tetrahedra that share corners with two equivalent O(11)Hf2Zr2 tetrahedra, corners with two equivalent O(8)Hf2Zr2 tetrahedra, corners with four equivalent O(1)Hf2Zr2 tetrahedra, corners with four equivalent O(9)Hf2Zr2 tetrahedra, corners with four equivalent O(12)Hf4 tetrahedra,  an edgeedge with one O(2)Hf2Zr2 tetrahedra,  an edgeedge with one O(6)Hf2Zr2 tetrahedra, edges with two equivalent O(3)Hf2Zr2 tetrahedra, and edges with two equivalent O(7)Hf2Zr2 tetrahedra. In the sixth O site, O(6) is bonded to one Hf(1), one Hf(3), and two equivalent Zr(1) atoms to form OHf2Zr2 tetrahedra that share corners with two equivalent O(12)Hf4 tetrahedra, corners with two equivalent O(10)Zr4 tetrahedra, corners with four equivalent O(3)Hf2Zr2 tetrahedra, corners with four equivalent O(7)Hf2Zr2 tetrahedra, corners with four equivalent O(8)Hf2Zr2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra,  an edgeedge with one O(4)Zr4 tetrahedra, edges with two equivalent O(1)Hf2Zr2 tetrahedra, and edges with two equivalent O(9)Hf2Zr2 tetrahedra. In the seventh O site, O(7) is bonded to one Hf(2), one Hf(3), 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(6)Hf2Zr2 tetrahedra, corners with two equivalent O(7)Hf2Zr2 tetrahedra, corners with two equivalent O(12)Hf4 tetrahedra, corners with two equivalent O(10)Zr4 tetrahedra, corners with four equivalent O(1)Hf2Zr2 tetrahedra,  an edgeedge with one O(1)Hf2Zr2 tetrahedra,  an edgeedge with one O(11)Hf2Zr2 tetrahedra,  an edgeedge with one O(8)Hf2Zr2 tetrahedra,  an edgeedge with one O(9)Hf2Zr2 tetrahedra,  an edgeedge with one O(5)Hf4 tetrahedra, and  an edgeedge with one O(4)Zr4 tetrahedra. In the eighth O site, O(8) is bonded to one Hf(1), one Hf(3), and two equivalent Zr(1) atoms to form distorted OHf2Zr2 tetrahedra that share 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, corners with four equivalent O(9)Hf2Zr2 tetrahedra,  an edgeedge with one O(12)Hf4 tetrahedra,  an edgeedge with one O(10)Zr4 tetrahedra, edges with two equivalent O(3)Hf2Zr2 tetrahedra, and edges with two equivalent O(7)Hf2Zr2 tetrahedra. In the ninth O site, O(9) is bonded to one Hf(1), one Hf(2), one Zr(1), and one Zr(3) atom to form distorted OHf2Zr2 tetrahedra that share corners with two equivalent O(1)Hf2Zr2 tetrahedra, corners with two equivalent O(11)Hf2Zr2 tetrahedra, corners with two equivalent O(8)Hf2Zr2 tetrahedra, corners with two equivalent O(9)Hf2Zr2 tetrahedra, corners with two equivalent O(5)Hf4 tetrahedra, corners with two equivalent O(4)Zr4 tetrahedra, corners with four equivalent O(3)Hf2Zr2 tetrahedra,  an edgeedge with one O(2)Hf2Zr2 tetrahedra,  an edgeedge with one O(3)Hf2Zr2 tetrahedra,  an edgeedge with one O(6)Hf2Zr2 tetrahedra,  an edgeedge with one O(7)Hf2Zr2 tetrahedra,  an edgeedge with one O(12)Hf4 tetrahedra, and  an edgeedge with one O(10)Zr4 tetrahedra. In the tenth O site, O(10) is bonded to one Zr(2), one Zr(3), and two equivalent Zr(1) atoms to form OZr4 tetrahedra that share corners with two equivalent O(2)Hf2Zr2 tetrahedra, corners with two equivalent O(6)Hf2Zr2 tetrahedra, corners with four equivalent O(3)Hf2Zr2 tetrahedra, corners with four equivalent O(7)Hf2Zr2 tetrahedra, corners with four equivalent O(4)Zr4 tetrahedra,  an edgeedge with one O(11)Hf2Zr2 tetrahedra,  an edgeedge with one O(8)Hf2Zr2 tetrahedra, edges with two equivalent O(1)Hf2Zr2 tetrahedra, and edges with two equivalent O(9)Hf2Zr2 tetrahedra. In the eleventh O site, O(11) is bonded to two equivalent Hf(2), one Zr(2), and one Zr(3) atom to form distorted OHf2Zr2 tetrahedra that share 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(2)Hf2Zr2 tetrahedra, corners with four equivalent O(9)Hf2Zr2 tetrahedra,  an edgeedge with one O(12)Hf4 tetrahedra,  an edgeedge with one O(10)Zr4 tetrahedra, edges with two equivalent O(3)Hf2Zr2 tetrahedra, and edges with two equivalent O(7)Hf2Zr2 tetrahedra. In the twelfth O site, O(12) is bonded to one Hf(1), one Hf(3), and two equivalent Hf(2) atoms to form OHf4 tetrahedra that share corners with two equivalent O(2)Hf2Zr2 tetrahedra, corners with two equivalent O(6)Hf2Zr2 tetrahedra, corners with four equivalent O(3)Hf2Zr2 tetrahedra, corners with four equivalent O(7)Hf2Zr2 tetrahedra, corners with four equivalent O(5)Hf4 tetrahedra,  an edgeedge with one O(11)Hf2Zr2 tetrahedra,  an edgeedge with one O(8)Hf2Zr2 tetrahedra, edges with two equivalent O(1)Hf2Zr2 tetrahedra, and edges with two equivalent O(9)Hf2Zr2 tetrahedra.