Hf3Sc4O12 crystallizes in the triclinic P-1 space group. There are four inequivalent Sc sites. In the first Sc site, Sc(1) is bonded in a 7-coordinate geometry to one O(12), one O(2), one O(3), one O(4), one O(6), and two equivalent O(7) atoms. In the second Sc site, Sc(2) is bonded in a 7-coordinate geometry to one O(10), one O(11), one O(12), one O(3), one O(5), one O(8), and one O(9) atom. In the third Sc site, Sc(3) is bonded in a 7-coordinate geometry to one O(10), one O(11), one O(12), one O(4), one O(6), one O(7), and one O(9) atom. In the fourth Sc site, Sc(4) is bonded in a 7-coordinate geometry to one O(11), one O(8), one O(9), two equivalent O(1), and two equivalent O(5) atoms. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 7-coordinate geometry to one O(1), one O(11), one O(3), one O(4), one O(5), and two equivalent O(8) atoms. In the second Hf site, Hf(2) is bonded in a 7-coordinate geometry to one O(10), one O(12), one O(7), two equivalent O(2), and two equivalent O(6) atoms. In the third Hf site, Hf(3) is bonded in an octahedral geometry to one O(1), one O(10), one O(2), one O(3), one O(4), and one O(9) atom. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to two equivalent Sc(4), one Hf(1), and one Hf(3) atom. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Sc(1), one Hf(3), and two equivalent Hf(2) atoms. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Sc(1), one Sc(2), one Hf(1), and one Hf(3) atom. In the fourth O site, O(4) is bonded to one Sc(1), one Sc(3), one Hf(1), and one Hf(3) atom to form distorted OHf2Sc2 tetrahedra that share  a cornercorner with one O(5)HfSc3 tetrahedra,  a cornercorner with one O(7)HfSc3 tetrahedra, corners with two equivalent O(6)Hf2Sc2 tetrahedra, corners with two equivalent O(8)Hf2Sc2 tetrahedra, corners with two equivalent O(12)HfSc3 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra. In the fifth O site, O(5) is bonded to one Sc(2), two equivalent Sc(4), and one Hf(1) atom to form OHfSc3 tetrahedra that share  a cornercorner with one O(4)Hf2Sc2 tetrahedra,  a cornercorner with one O(12)HfSc3 tetrahedra, corners with two equivalent O(11)HfSc3 tetrahedra, corners with three equivalent O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(5)HfSc3 tetrahedra. In the sixth O site, O(6) is bonded to one Sc(1), one Sc(3), and two equivalent Hf(2) atoms to form OHf2Sc2 tetrahedra that share  a cornercorner with one O(11)HfSc3 tetrahedra, corners with two equivalent O(4)Hf2Sc2 tetrahedra, corners with two equivalent O(12)HfSc3 tetrahedra, corners with three equivalent O(7)HfSc3 tetrahedra,  an edgeedge with one O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(12)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra. In the seventh O site, O(7) is bonded to one Sc(3), two equivalent Sc(1), and one Hf(2) atom to form distorted OHfSc3 tetrahedra that share  a cornercorner with one O(4)Hf2Sc2 tetrahedra,  a cornercorner with one O(11)HfSc3 tetrahedra, corners with two equivalent O(12)HfSc3 tetrahedra, corners with three equivalent O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(4)Hf2Sc2 tetrahedra,  an edgeedge with one O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(12)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra. In the eighth O site, O(8) is bonded to one Sc(2), one Sc(4), and two equivalent Hf(1) atoms to form OHf2Sc2 tetrahedra that share  a cornercorner with one O(12)HfSc3 tetrahedra, corners with two equivalent O(4)Hf2Sc2 tetrahedra, corners with two equivalent O(11)HfSc3 tetrahedra, corners with three equivalent O(5)HfSc3 tetrahedra,  an edgeedge with one O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(5)HfSc3 tetrahedra. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Sc(2), one Sc(3), one Sc(4), and one Hf(3) atom. In the tenth O site, O(10) is bonded in a 3-coordinate geometry to one Sc(2), one Sc(3), one Hf(2), and one Hf(3) atom. In the eleventh O site, O(11) is bonded to one Sc(2), one Sc(3), one Sc(4), and one Hf(1) atom to form distorted OHfSc3 tetrahedra that share  a cornercorner with one O(6)Hf2Sc2 tetrahedra,  a cornercorner with one O(7)HfSc3 tetrahedra, corners with two equivalent O(8)Hf2Sc2 tetrahedra, corners with two equivalent O(5)HfSc3 tetrahedra,  an edgeedge with one O(4)Hf2Sc2 tetrahedra,  an edgeedge with one O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(12)HfSc3 tetrahedra, and  an edgeedge with one O(5)HfSc3 tetrahedra. In the twelfth O site, O(12) is bonded to one Sc(1), one Sc(2), one Sc(3), and one Hf(2) atom to form OHfSc3 tetrahedra that share  a cornercorner with one O(8)Hf2Sc2 tetrahedra,  a cornercorner with one O(5)HfSc3 tetrahedra, corners with two equivalent O(4)Hf2Sc2 tetrahedra, corners with two equivalent O(6)Hf2Sc2 tetrahedra, corners with two equivalent O(7)HfSc3 tetrahedra,  an edgeedge with one O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra.
Hf3Sc4O12 crystallizes in the triclinic P-1 space group. There are four inequivalent Sc sites. In the first Sc site, Sc(1) is bonded in a 7-coordinate geometry to one O(12), one O(2), one O(3), one O(4), one O(6), and two equivalent O(7) atoms. The Sc(1)-O(12) bond length is 2.06 Å. The Sc(1)-O(2) bond length is 2.15 Å. The Sc(1)-O(3) bond length is 2.60 Å. The Sc(1)-O(4) bond length is 2.10 Å. The Sc(1)-O(6) bond length is 2.29 Å. There is one shorter (2.14 Å) and one longer (2.16 Å) Sc(1)-O(7) bond length. In the second Sc site, Sc(2) is bonded in a 7-coordinate geometry to one O(10), one O(11), one O(12), one O(3), one O(5), one O(8), and one O(9) atom. The Sc(2)-O(10) bond length is 2.13 Å. The Sc(2)-O(11) bond length is 2.14 Å. The Sc(2)-O(12) bond length is 2.16 Å. The Sc(2)-O(3) bond length is 2.14 Å. The Sc(2)-O(5) bond length is 2.05 Å. The Sc(2)-O(8) bond length is 2.28 Å. The Sc(2)-O(9) bond length is 2.57 Å. In the third Sc site, Sc(3) is bonded in a 7-coordinate geometry to one O(10), one O(11), one O(12), one O(4), one O(6), one O(7), and one O(9) atom. The Sc(3)-O(10) bond length is 2.63 Å. The Sc(3)-O(11) bond length is 2.15 Å. The Sc(3)-O(12) bond length is 2.14 Å. The Sc(3)-O(4) bond length is 2.13 Å. The Sc(3)-O(6) bond length is 2.09 Å. The Sc(3)-O(7) bond length is 2.26 Å. The Sc(3)-O(9) bond length is 2.08 Å. In the fourth Sc site, Sc(4) is bonded in a 7-coordinate geometry to one O(11), one O(8), one O(9), two equivalent O(1), and two equivalent O(5) atoms. The Sc(4)-O(11) bond length is 2.24 Å. The Sc(4)-O(8) bond length is 2.09 Å. The Sc(4)-O(9) bond length is 2.11 Å. There is one shorter (2.12 Å) and one longer (2.62 Å) Sc(4)-O(1) bond length. There is one shorter (2.13 Å) and one longer (2.15 Å) Sc(4)-O(5) bond length. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 7-coordinate geometry to one O(1), one O(11), one O(3), one O(4), one O(5), and two equivalent O(8) atoms. The Hf(1)-O(1) bond length is 2.07 Å. The Hf(1)-O(11) bond length is 2.03 Å. The Hf(1)-O(3) bond length is 2.09 Å. The Hf(1)-O(4) bond length is 2.46 Å. The Hf(1)-O(5) bond length is 2.18 Å. There is one shorter (2.13 Å) and one longer (2.15 Å) Hf(1)-O(8) bond length. In the second Hf site, Hf(2) is bonded in a 7-coordinate geometry to one O(10), one O(12), one O(7), two equivalent O(2), and two equivalent O(6) atoms. The Hf(2)-O(10) bond length is 2.05 Å. The Hf(2)-O(12) bond length is 2.16 Å. The Hf(2)-O(7) bond length is 2.03 Å. There is one shorter (2.10 Å) and one longer (2.60 Å) Hf(2)-O(2) bond length. There is one shorter (2.10 Å) and one longer (2.15 Å) Hf(2)-O(6) bond length. In the third Hf site, Hf(3) is bonded in an octahedral geometry to one O(1), one O(10), one O(2), one O(3), one O(4), and one O(9) atom. The Hf(3)-O(1) bond length is 2.05 Å. The Hf(3)-O(10) bond length is 2.08 Å. The Hf(3)-O(2) bond length is 2.07 Å. The Hf(3)-O(3) bond length is 2.05 Å. The Hf(3)-O(4) bond length is 2.07 Å. The Hf(3)-O(9) bond length is 2.04 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to two equivalent Sc(4), one Hf(1), and one Hf(3) atom. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Sc(1), one Hf(3), and two equivalent Hf(2) atoms. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Sc(1), one Sc(2), one Hf(1), and one Hf(3) atom. In the fourth O site, O(4) is bonded to one Sc(1), one Sc(3), one Hf(1), and one Hf(3) atom to form distorted OHf2Sc2 tetrahedra that share  a cornercorner with one O(5)HfSc3 tetrahedra,  a cornercorner with one O(7)HfSc3 tetrahedra, corners with two equivalent O(6)Hf2Sc2 tetrahedra, corners with two equivalent O(8)Hf2Sc2 tetrahedra, corners with two equivalent O(12)HfSc3 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra. In the fifth O site, O(5) is bonded to one Sc(2), two equivalent Sc(4), and one Hf(1) atom to form OHfSc3 tetrahedra that share  a cornercorner with one O(4)Hf2Sc2 tetrahedra,  a cornercorner with one O(12)HfSc3 tetrahedra, corners with two equivalent O(11)HfSc3 tetrahedra, corners with three equivalent O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(5)HfSc3 tetrahedra. In the sixth O site, O(6) is bonded to one Sc(1), one Sc(3), and two equivalent Hf(2) atoms to form OHf2Sc2 tetrahedra that share  a cornercorner with one O(11)HfSc3 tetrahedra, corners with two equivalent O(4)Hf2Sc2 tetrahedra, corners with two equivalent O(12)HfSc3 tetrahedra, corners with three equivalent O(7)HfSc3 tetrahedra,  an edgeedge with one O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(12)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra. In the seventh O site, O(7) is bonded to one Sc(3), two equivalent Sc(1), and one Hf(2) atom to form distorted OHfSc3 tetrahedra that share  a cornercorner with one O(4)Hf2Sc2 tetrahedra,  a cornercorner with one O(11)HfSc3 tetrahedra, corners with two equivalent O(12)HfSc3 tetrahedra, corners with three equivalent O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(4)Hf2Sc2 tetrahedra,  an edgeedge with one O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(12)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra. In the eighth O site, O(8) is bonded to one Sc(2), one Sc(4), and two equivalent Hf(1) atoms to form OHf2Sc2 tetrahedra that share  a cornercorner with one O(12)HfSc3 tetrahedra, corners with two equivalent O(4)Hf2Sc2 tetrahedra, corners with two equivalent O(11)HfSc3 tetrahedra, corners with three equivalent O(5)HfSc3 tetrahedra,  an edgeedge with one O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(5)HfSc3 tetrahedra. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Sc(2), one Sc(3), one Sc(4), and one Hf(3) atom. In the tenth O site, O(10) is bonded in a 3-coordinate geometry to one Sc(2), one Sc(3), one Hf(2), and one Hf(3) atom. In the eleventh O site, O(11) is bonded to one Sc(2), one Sc(3), one Sc(4), and one Hf(1) atom to form distorted OHfSc3 tetrahedra that share  a cornercorner with one O(6)Hf2Sc2 tetrahedra,  a cornercorner with one O(7)HfSc3 tetrahedra, corners with two equivalent O(8)Hf2Sc2 tetrahedra, corners with two equivalent O(5)HfSc3 tetrahedra,  an edgeedge with one O(4)Hf2Sc2 tetrahedra,  an edgeedge with one O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(12)HfSc3 tetrahedra, and  an edgeedge with one O(5)HfSc3 tetrahedra. In the twelfth O site, O(12) is bonded to one Sc(1), one Sc(2), one Sc(3), and one Hf(2) atom to form OHfSc3 tetrahedra that share  a cornercorner with one O(8)Hf2Sc2 tetrahedra,  a cornercorner with one O(5)HfSc3 tetrahedra, corners with two equivalent O(4)Hf2Sc2 tetrahedra, corners with two equivalent O(6)Hf2Sc2 tetrahedra, corners with two equivalent O(7)HfSc3 tetrahedra,  an edgeedge with one O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra.