K4ZrO4 crystallizes in the triclinic P-1 space group. There are four inequivalent K sites. In the first K site, K(1) is bonded to one O(3), two equivalent O(1), and two equivalent O(2) atoms to form distorted KO5 square pyramids that share  a cornercorner with one Zr(1)O4 tetrahedra, corners with three equivalent K(4)O5 trigonal bipyramids, corners with two equivalent K(3)O4 trigonal pyramids, edges with two equivalent K(1)O5 square pyramids, edges with two equivalent Zr(1)O4 tetrahedra, and edges with three equivalent K(4)O5 trigonal bipyramids. In the second K site, K(2) is bonded in a 4-coordinate geometry to one O(1), one O(2), one O(3), and one O(4) atom. In the third K site, K(3) is bonded to two equivalent O(3) and two equivalent O(4) atoms to form distorted KO4 trigonal pyramids that share corners with two equivalent K(1)O5 square pyramids, corners with four equivalent Zr(1)O4 tetrahedra, corners with two equivalent K(4)O5 trigonal bipyramids, and edges with two equivalent K(3)O4 trigonal pyramids. In the fourth K site, K(4) is bonded to one O(3), two equivalent O(1), and two equivalent O(2) atoms to form distorted KO5 trigonal bipyramids that share corners with three equivalent K(1)O5 square pyramids, corners with three equivalent Zr(1)O4 tetrahedra, corners with two equivalent K(3)O4 trigonal pyramids, edges with three equivalent K(1)O5 square pyramids,  an edgeedge with one Zr(1)O4 tetrahedra, and edges with two equivalent K(4)O5 trigonal bipyramids. Zr(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form ZrO4 tetrahedra that share  a cornercorner with one K(1)O5 square pyramid, corners with three equivalent K(4)O5 trigonal bipyramids, corners with four equivalent K(3)O4 trigonal pyramids, edges with two equivalent K(1)O5 square pyramids, and  an edgeedge with one K(4)O5 trigonal bipyramid. There are four inequivalent O sites. In the first O site, O(1) is bonded to one K(2), two equivalent K(1), two equivalent K(4), and one Zr(1) atom to form distorted edge-sharing OK5Zr octahedra. In the second O site, O(2) is bonded in a 6-coordinate geometry to one K(2), two equivalent K(1), two equivalent K(4), and one Zr(1) atom. In the third O site, O(3) is bonded in a 6-coordinate geometry to one K(1), one K(2), one K(4), two equivalent K(3), and one Zr(1) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one K(2), two equivalent K(3), and one Zr(1) atom.
K4ZrO4 crystallizes in the triclinic P-1 space group. There are four inequivalent K sites. In the first K site, K(1) is bonded to one O(3), two equivalent O(1), and two equivalent O(2) atoms to form distorted KO5 square pyramids that share  a cornercorner with one Zr(1)O4 tetrahedra, corners with three equivalent K(4)O5 trigonal bipyramids, corners with two equivalent K(3)O4 trigonal pyramids, edges with two equivalent K(1)O5 square pyramids, edges with two equivalent Zr(1)O4 tetrahedra, and edges with three equivalent K(4)O5 trigonal bipyramids. The K(1)-O(3) bond length is 2.73 Å. There is one shorter (2.72 Å) and one longer (2.77 Å) K(1)-O(1) bond length. There is one shorter (2.90 Å) and one longer (2.94 Å) K(1)-O(2) bond length. In the second K site, K(2) is bonded in a 4-coordinate geometry to one O(1), one O(2), one O(3), and one O(4) atom. The K(2)-O(1) bond length is 2.76 Å. The K(2)-O(2) bond length is 2.76 Å. The K(2)-O(3) bond length is 2.77 Å. The K(2)-O(4) bond length is 2.68 Å. In the third K site, K(3) is bonded to two equivalent O(3) and two equivalent O(4) atoms to form distorted KO4 trigonal pyramids that share corners with two equivalent K(1)O5 square pyramids, corners with four equivalent Zr(1)O4 tetrahedra, corners with two equivalent K(4)O5 trigonal bipyramids, and edges with two equivalent K(3)O4 trigonal pyramids. There is one shorter (2.67 Å) and one longer (2.70 Å) K(3)-O(3) bond length. There is one shorter (2.64 Å) and one longer (2.66 Å) K(3)-O(4) bond length. In the fourth K site, K(4) is bonded to one O(3), two equivalent O(1), and two equivalent O(2) atoms to form distorted KO5 trigonal bipyramids that share corners with three equivalent K(1)O5 square pyramids, corners with three equivalent Zr(1)O4 tetrahedra, corners with two equivalent K(3)O4 trigonal pyramids, edges with three equivalent K(1)O5 square pyramids,  an edgeedge with one Zr(1)O4 tetrahedra, and edges with two equivalent K(4)O5 trigonal bipyramids. The K(4)-O(3) bond length is 2.86 Å. There is one shorter (2.67 Å) and one longer (2.75 Å) K(4)-O(1) bond length. There is one shorter (2.73 Å) and one longer (2.76 Å) K(4)-O(2) bond length. Zr(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form ZrO4 tetrahedra that share  a cornercorner with one K(1)O5 square pyramid, corners with three equivalent K(4)O5 trigonal bipyramids, corners with four equivalent K(3)O4 trigonal pyramids, edges with two equivalent K(1)O5 square pyramids, and  an edgeedge with one K(4)O5 trigonal bipyramid. The Zr(1)-O(1) bond length is 1.98 Å. The Zr(1)-O(2) bond length is 1.99 Å. The Zr(1)-O(3) bond length is 1.98 Å. The Zr(1)-O(4) bond length is 1.98 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded to one K(2), two equivalent K(1), two equivalent K(4), and one Zr(1) atom to form distorted edge-sharing OK5Zr octahedra. In the second O site, O(2) is bonded in a 6-coordinate geometry to one K(2), two equivalent K(1), two equivalent K(4), and one Zr(1) atom. In the third O site, O(3) is bonded in a 6-coordinate geometry to one K(1), one K(2), one K(4), two equivalent K(3), and one Zr(1) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one K(2), two equivalent K(3), and one Zr(1) atom.