K3Lu(PO4)2 crystallizes in the monoclinic P2_1/m space group. There are three inequivalent K sites. In the first K site, K(1) is bonded in a 7-coordinate geometry to one O(6), two equivalent O(3), two equivalent O(4), and two equivalent O(5) atoms. In the second K site, K(2) is bonded in a 9-coordinate geometry to one O(1), one O(6), two equivalent O(3), two equivalent O(4), and three equivalent O(2) atoms. In the third K site, K(3) is bonded in a 9-coordinate geometry to one O(2), one O(5), two equivalent O(3), two equivalent O(4), and three equivalent O(6) atoms. Lu(1) is bonded to one O(1), one O(5), two equivalent O(3), and two equivalent O(4) atoms to form LuO6 octahedra that share corners with three equivalent P(1)O4 tetrahedra and corners with three equivalent P(2)O4 tetrahedra. There are two inequivalent P sites. In the first P site, P(1) is bonded to one O(1), one O(2), and two equivalent O(3) atoms to form PO4 tetrahedra that share corners with three equivalent Lu(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 39-44°. In the second P site, P(2) is bonded to one O(5), one O(6), and two equivalent O(4) atoms to form PO4 tetrahedra that share corners with three equivalent Lu(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-18°. There are six inequivalent O sites. In the first O site, O(1) is bonded in a 2-coordinate geometry to one K(2), one Lu(1), and one P(1) atom. In the second O site, O(2) is bonded in a distorted single-bond geometry to one K(3), three equivalent K(2), and one P(1) atom. In the third O site, O(3) is bonded in a 5-coordinate geometry to one K(1), one K(2), one K(3), one Lu(1), and one P(1) atom. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to one K(1), one K(2), one K(3), one Lu(1), and one P(2) atom. In the fifth O site, O(5) is bonded in a 2-coordinate geometry to one K(3), two equivalent K(1), one Lu(1), and one P(2) atom. In the sixth O site, O(6) is bonded in a distorted single-bond geometry to one K(1), one K(2), three equivalent K(3), and one P(2) atom.
K3Lu(PO4)2 crystallizes in the monoclinic P2_1/m space group. There are three inequivalent K sites. In the first K site, K(1) is bonded in a 7-coordinate geometry to one O(6), two equivalent O(3), two equivalent O(4), and two equivalent O(5) atoms. The K(1)-O(6) bond length is 2.76 Å. Both K(1)-O(3) bond lengths are 2.71 Å. Both K(1)-O(4) bond lengths are 2.88 Å. Both K(1)-O(5) bond lengths are 2.87 Å. In the second K site, K(2) is bonded in a 9-coordinate geometry to one O(1), one O(6), two equivalent O(3), two equivalent O(4), and three equivalent O(2) atoms. The K(2)-O(1) bond length is 2.95 Å. The K(2)-O(6) bond length is 3.14 Å. Both K(2)-O(3) bond lengths are 2.89 Å. Both K(2)-O(4) bond lengths are 2.98 Å. There is one shorter (2.65 Å) and two longer (2.90 Å) K(2)-O(2) bond lengths. In the third K site, K(3) is bonded in a 9-coordinate geometry to one O(2), one O(5), two equivalent O(3), two equivalent O(4), and three equivalent O(6) atoms. The K(3)-O(2) bond length is 2.66 Å. The K(3)-O(5) bond length is 2.95 Å. Both K(3)-O(3) bond lengths are 2.98 Å. Both K(3)-O(4) bond lengths are 3.13 Å. There is one shorter (2.95 Å) and two longer (3.07 Å) K(3)-O(6) bond lengths. Lu(1) is bonded to one O(1), one O(5), two equivalent O(3), and two equivalent O(4) atoms to form LuO6 octahedra that share corners with three equivalent P(1)O4 tetrahedra and corners with three equivalent P(2)O4 tetrahedra. The Lu(1)-O(1) bond length is 2.16 Å. The Lu(1)-O(5) bond length is 2.27 Å. Both Lu(1)-O(3) bond lengths are 2.22 Å. Both Lu(1)-O(4) bond lengths are 2.22 Å. There are two inequivalent P sites. In the first P site, P(1) is bonded to one O(1), one O(2), and two equivalent O(3) atoms to form PO4 tetrahedra that share corners with three equivalent Lu(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 39-44°. The P(1)-O(1) bond length is 1.55 Å. The P(1)-O(2) bond length is 1.53 Å. Both P(1)-O(3) bond lengths are 1.57 Å. In the second P site, P(2) is bonded to one O(5), one O(6), and two equivalent O(4) atoms to form PO4 tetrahedra that share corners with three equivalent Lu(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-18°. The P(2)-O(5) bond length is 1.57 Å. The P(2)-O(6) bond length is 1.54 Å. Both P(2)-O(4) bond lengths are 1.57 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded in a 2-coordinate geometry to one K(2), one Lu(1), and one P(1) atom. In the second O site, O(2) is bonded in a distorted single-bond geometry to one K(3), three equivalent K(2), and one P(1) atom. In the third O site, O(3) is bonded in a 5-coordinate geometry to one K(1), one K(2), one K(3), one Lu(1), and one P(1) atom. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to one K(1), one K(2), one K(3), one Lu(1), and one P(2) atom. In the fifth O site, O(5) is bonded in a 2-coordinate geometry to one K(3), two equivalent K(1), one Lu(1), and one P(2) atom. In the sixth O site, O(6) is bonded in a distorted single-bond geometry to one K(1), one K(2), three equivalent K(3), and one P(2) atom.