K4Hf5O12 crystallizes in the trigonal P-3m1 space group. There are two inequivalent K sites. In the first K site, K(1) is bonded in a 9-coordinate geometry to three equivalent O(1) and six equivalent O(2) atoms. In the second K site, K(2) is bonded to three equivalent O(2) and nine equivalent O(1) atoms to form KO12 cuboctahedra that share corners with six equivalent K(2)O12 cuboctahedra, faces with three equivalent K(2)O12 cuboctahedra, faces with three equivalent Hf(2)O6 octahedra, and faces with four equivalent Hf(3)O6 octahedra. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 6-coordinate geometry to six equivalent O(2) atoms. In the second Hf site, Hf(2) is bonded to six equivalent O(1) atoms to form HfO6 octahedra that share corners with six equivalent Hf(3)O6 octahedra and faces with six equivalent K(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 7°. In the third Hf site, Hf(3) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form distorted HfO6 octahedra that share corners with three equivalent Hf(2)O6 octahedra and faces with four equivalent K(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 7°. There are two inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one K(1), three equivalent K(2), one Hf(2), and one Hf(3) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one K(2), two equivalent K(1), one Hf(3), and two equivalent Hf(1) atoms.
K4Hf5O12 crystallizes in the trigonal P-3m1 space group. There are two inequivalent K sites. In the first K site, K(1) is bonded in a 9-coordinate geometry to three equivalent O(1) and six equivalent O(2) atoms. All K(1)-O(1) bond lengths are 2.66 Å. All K(1)-O(2) bond lengths are 2.94 Å. In the second K site, K(2) is bonded to three equivalent O(2) and nine equivalent O(1) atoms to form KO12 cuboctahedra that share corners with six equivalent K(2)O12 cuboctahedra, faces with three equivalent K(2)O12 cuboctahedra, faces with three equivalent Hf(2)O6 octahedra, and faces with four equivalent Hf(3)O6 octahedra. All K(2)-O(2) bond lengths are 3.25 Å. There are six shorter (2.88 Å) and three longer (2.95 Å) K(2)-O(1) bond lengths. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 6-coordinate geometry to six equivalent O(2) atoms. There are three shorter (2.04 Å) and three longer (2.18 Å) Hf(1)-O(2) bond lengths. In the second Hf site, Hf(2) is bonded to six equivalent O(1) atoms to form HfO6 octahedra that share corners with six equivalent Hf(3)O6 octahedra and faces with six equivalent K(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 7°. All Hf(2)-O(1) bond lengths are 2.07 Å. In the third Hf site, Hf(3) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form distorted HfO6 octahedra that share corners with three equivalent Hf(2)O6 octahedra and faces with four equivalent K(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 7°. All Hf(3)-O(1) bond lengths are 1.95 Å. All Hf(3)-O(2) bond lengths are 2.28 Å. There are two inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one K(1), three equivalent K(2), one Hf(2), and one Hf(3) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one K(2), two equivalent K(1), one Hf(3), and two equivalent Hf(1) atoms.