K3Yb(SO4)3 crystallizes in the monoclinic Cc space group. There are three inequivalent K sites. In the first K site, K(1) is bonded in a 6-coordinate geometry to one O(10), one O(2), one O(3), one O(4), one O(6), and one O(8) atom. In the second K site, K(2) is bonded in a 6-coordinate geometry to one O(10), one O(5), one O(6), one O(9), and two equivalent O(1) atoms. In the third K site, K(3) is bonded to one O(5), one O(7), one O(8), one O(9), and two equivalent O(11) atoms to form distorted KO6 octahedra that share corners with two equivalent K(3)O6 octahedra,  a cornercorner with one S(1)O4 tetrahedra, corners with two equivalent S(3)O4 tetrahedra,  an edgeedge with one Yb(1)O6 octahedra, and  an edgeedge with one S(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 54°. Yb(1) is bonded to one O(1), one O(12), one O(2), one O(4), one O(5), and one O(7) atom to form YbO6 octahedra that share  a cornercorner with one S(1)O4 tetrahedra, corners with two equivalent S(3)O4 tetrahedra, and  an edgeedge with one K(3)O6 octahedra. There are three inequivalent S sites. In the first S site, S(1) is bonded to one O(11), one O(3), one O(6), and one O(7) atom to form SO4 tetrahedra that share  a cornercorner with one K(3)O6 octahedra,  a cornercorner with one Yb(1)O6 octahedra, and  an edgeedge with one K(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 44-69°. In the second S site, S(2) is bonded in a trigonal non-coplanar geometry to one O(12), one O(4), and one O(9) atom. In the third S site, S(3) is bonded to one O(1), one O(10), one O(5), and one O(8) atom to form SO4 tetrahedra that share corners with two equivalent K(3)O6 octahedra and corners with two equivalent Yb(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 30-68°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 2-coordinate geometry to two equivalent K(2), one Yb(1), and one S(3) atom. In the second O site, O(2) is bonded in a distorted bent 150 degrees geometry to one K(1) and one Yb(1) atom. In the third O site, O(3) is bonded in a distorted single-bond geometry to one K(1) and one S(1) atom. In the fourth O site, O(4) is bonded in a distorted bent 120 degrees geometry to one K(1), one Yb(1), and one S(2) atom. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one K(2), one K(3), one Yb(1), and one S(3) atom. In the sixth O site, O(6) is bonded in a distorted single-bond geometry to one K(1), one K(2), and one S(1) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one K(3), one Yb(1), and one S(1) atom. In the eighth O site, O(8) is bonded in a distorted single-bond geometry to one K(1), one K(3), and one S(3) atom. In the ninth O site, O(9) is bonded in a distorted single-bond geometry to one K(2), one K(3), and one S(2) atom. In the tenth O site, O(10) is bonded in a distorted single-bond geometry to one K(1), one K(2), and one S(3) atom. In the eleventh O site, O(11) is bonded in a 3-coordinate geometry to two equivalent K(3) and one S(1) atom. In the twelfth O site, O(12) is bonded in a bent 120 degrees geometry to one Yb(1) and one S(2) atom.
K3Yb(SO4)3 crystallizes in the monoclinic Cc space group. There are three inequivalent K sites. In the first K site, K(1) is bonded in a 6-coordinate geometry to one O(10), one O(2), one O(3), one O(4), one O(6), and one O(8) atom. The K(1)-O(10) bond length is 2.77 Å. The K(1)-O(2) bond length is 2.79 Å. The K(1)-O(3) bond length is 2.72 Å. The K(1)-O(4) bond length is 3.30 Å. The K(1)-O(6) bond length is 2.86 Å. The K(1)-O(8) bond length is 2.74 Å. In the second K site, K(2) is bonded in a 6-coordinate geometry to one O(10), one O(5), one O(6), one O(9), and two equivalent O(1) atoms. The K(2)-O(10) bond length is 2.68 Å. The K(2)-O(5) bond length is 3.00 Å. The K(2)-O(6) bond length is 3.00 Å. The K(2)-O(9) bond length is 3.04 Å. There is one shorter (2.94 Å) and one longer (3.15 Å) K(2)-O(1) bond length. In the third K site, K(3) is bonded to one O(5), one O(7), one O(8), one O(9), and two equivalent O(11) atoms to form distorted KO6 octahedra that share corners with two equivalent K(3)O6 octahedra,  a cornercorner with one S(1)O4 tetrahedra, corners with two equivalent S(3)O4 tetrahedra,  an edgeedge with one Yb(1)O6 octahedra, and  an edgeedge with one S(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 54°. The K(3)-O(5) bond length is 2.90 Å. The K(3)-O(7) bond length is 2.82 Å. The K(3)-O(8) bond length is 2.76 Å. The K(3)-O(9) bond length is 2.91 Å. There is one shorter (2.53 Å) and one longer (2.82 Å) K(3)-O(11) bond length. Yb(1) is bonded to one O(1), one O(12), one O(2), one O(4), one O(5), and one O(7) atom to form YbO6 octahedra that share  a cornercorner with one S(1)O4 tetrahedra, corners with two equivalent S(3)O4 tetrahedra, and  an edgeedge with one K(3)O6 octahedra. The Yb(1)-O(1) bond length is 2.31 Å. The Yb(1)-O(12) bond length is 2.40 Å. The Yb(1)-O(2) bond length is 2.40 Å. The Yb(1)-O(4) bond length is 2.38 Å. The Yb(1)-O(5) bond length is 2.27 Å. The Yb(1)-O(7) bond length is 2.35 Å. There are three inequivalent S sites. In the first S site, S(1) is bonded to one O(11), one O(3), one O(6), and one O(7) atom to form SO4 tetrahedra that share  a cornercorner with one K(3)O6 octahedra,  a cornercorner with one Yb(1)O6 octahedra, and  an edgeedge with one K(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 44-69°. The S(1)-O(11) bond length is 1.48 Å. The S(1)-O(3) bond length is 1.49 Å. The S(1)-O(6) bond length is 1.50 Å. The S(1)-O(7) bond length is 1.50 Å. In the second S site, S(2) is bonded in a trigonal non-coplanar geometry to one O(12), one O(4), and one O(9) atom. The S(2)-O(12) bond length is 1.49 Å. The S(2)-O(4) bond length is 1.50 Å. The S(2)-O(9) bond length is 1.49 Å. In the third S site, S(3) is bonded to one O(1), one O(10), one O(5), and one O(8) atom to form SO4 tetrahedra that share corners with two equivalent K(3)O6 octahedra and corners with two equivalent Yb(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 30-68°. The S(3)-O(1) bond length is 1.51 Å. The S(3)-O(10) bond length is 1.49 Å. The S(3)-O(5) bond length is 1.50 Å. The S(3)-O(8) bond length is 1.48 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 2-coordinate geometry to two equivalent K(2), one Yb(1), and one S(3) atom. In the second O site, O(2) is bonded in a distorted bent 150 degrees geometry to one K(1) and one Yb(1) atom. In the third O site, O(3) is bonded in a distorted single-bond geometry to one K(1) and one S(1) atom. In the fourth O site, O(4) is bonded in a distorted bent 120 degrees geometry to one K(1), one Yb(1), and one S(2) atom. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one K(2), one K(3), one Yb(1), and one S(3) atom. In the sixth O site, O(6) is bonded in a distorted single-bond geometry to one K(1), one K(2), and one S(1) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one K(3), one Yb(1), and one S(1) atom. In the eighth O site, O(8) is bonded in a distorted single-bond geometry to one K(1), one K(3), and one S(3) atom. In the ninth O site, O(9) is bonded in a distorted single-bond geometry to one K(2), one K(3), and one S(2) atom. In the tenth O site, O(10) is bonded in a distorted single-bond geometry to one K(1), one K(2), and one S(3) atom. In the eleventh O site, O(11) is bonded in a 3-coordinate geometry to two equivalent K(3) and one S(1) atom. In the twelfth O site, O(12) is bonded in a bent 120 degrees geometry to one Yb(1) and one S(2) atom.