Li5Cr3(PO4)4 crystallizes in the triclinic P1 space group. There are five inequivalent Li sites. In the first Li site, Li(1) is bonded in a rectangular see-saw-like geometry to one O(13), one O(14), one O(15), and one O(9) atom. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(10), one O(13), one O(14), and one O(16) atom. In the third Li site, Li(3) is bonded in a 4-coordinate geometry to one O(14), one O(16), one O(3), and one O(6) atom. In the fourth Li site, Li(4) is bonded to one O(13), one O(15), one O(4), and one O(5) atom to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(4)O4 tetrahedra,  a cornercorner with one Li(5)O5 trigonal bipyramid, corners with two equivalent Cr(3)O5 trigonal bipyramids, and  an edgeedge with one P(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 68°. In the fifth Li site, Li(5) is bonded to one O(1), one O(12), one O(16), one O(3), and one O(5) atom to form LiO5 trigonal bipyramids that share  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(2)O4 tetrahedra,  a cornercorner with one P(4)O4 tetrahedra, corners with two equivalent P(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 trigonal pyramid, and  an edgeedge with one Cr(2)O6 octahedra. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded in a rectangular see-saw-like geometry to one O(1), one O(10), one O(2), and one O(9) atom. In the second Cr site, Cr(2) is bonded to one O(11), one O(12), one O(5), one O(6), one O(7), and one O(8) atom to form CrO6 octahedra that share  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(2)O4 tetrahedra, corners with two equivalent P(3)O4 tetrahedra, corners with two equivalent P(4)O4 tetrahedra,  a cornercorner with one Li(4)O4 trigonal pyramid,  an edgeedge with one Li(5)O5 trigonal bipyramid, and  an edgeedge with one Cr(3)O5 trigonal bipyramid. In the third Cr site, Cr(3) is bonded to one O(11), one O(15), one O(2), one O(4), and one O(6) atom to form CrO5 trigonal bipyramids that share  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(2)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra, corners with two equivalent P(4)O4 tetrahedra, corners with two equivalent Li(4)O4 trigonal pyramids, and  an edgeedge with one Cr(2)O6 octahedra. There are four inequivalent P sites. In the first P site, P(1) is bonded to one O(1), one O(11), one O(13), and one O(9) atom to form PO4 tetrahedra that share  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Li(5)O5 trigonal bipyramid,  a cornercorner with one Cr(3)O5 trigonal bipyramid, and  a cornercorner with one Li(4)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 52°. In the second P site, P(2) is bonded to one O(10), one O(12), one O(14), and one O(2) atom to form PO4 tetrahedra that share  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Li(5)O5 trigonal bipyramid, and  a cornercorner with one Cr(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 51°. In the third P site, P(3) is bonded to one O(15), one O(3), one O(5), and one O(7) atom to form PO4 tetrahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Cr(3)O5 trigonal bipyramid, corners with two equivalent Li(5)O5 trigonal bipyramids, and  an edgeedge with one Li(4)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 42-46°. In the fourth P site, P(4) is bonded to one O(16), one O(4), one O(6), and one O(8) atom to form PO4 tetrahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(5)O5 trigonal bipyramid, corners with two equivalent Cr(3)O5 trigonal bipyramids, and  a cornercorner with one Li(4)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 37-46°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a trigonal planar geometry to one Li(5), one Cr(1), and one P(1) atom. In the second O site, O(2) is bonded in a trigonal planar geometry to one Cr(1), one Cr(3), and one P(2) atom. In the third O site, O(3) is bonded in a trigonal planar geometry to one Li(3), one Li(5), and one P(3) atom. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to one Li(4), one Cr(3), and one P(4) atom. In the fifth O site, O(5) is bonded to one Li(4), one Li(5), one Cr(2), and one P(3) atom to form distorted OLi2CrP tetrahedra that share  a cornercorner with one O(16)Li3P trigonal pyramid and  an edgeedge with one O(15)Li2CrP trigonal pyramid. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Li(3), one Cr(2), one Cr(3), and one P(4) atom. In the seventh O site, O(7) is bonded in a bent 150 degrees geometry to one Cr(2) and one P(3) atom. In the eighth O site, O(8) is bonded in a bent 150 degrees geometry to one Cr(2) and one P(4) atom. In the ninth O site, O(9) is bonded in a trigonal planar geometry to one Li(1), one Cr(1), and one P(1) atom. In the tenth O site, O(10) is bonded in a trigonal planar geometry to one Li(2), one Cr(1), and one P(2) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal planar geometry to one Cr(2), one Cr(3), and one P(1) atom. In the twelfth O site, O(12) is bonded in a distorted trigonal planar geometry to one Li(5), one Cr(2), and one P(2) atom. In the thirteenth O site, O(13) is bonded in a rectangular see-saw-like geometry to one Li(1), one Li(2), one Li(4), and one P(1) atom. In the fourteenth O site, O(14) is bonded in a rectangular see-saw-like geometry to one Li(1), one Li(2), one Li(3), and one P(2) atom. In the fifteenth O site, O(15) is bonded to one Li(1), one Li(4), one Cr(3), and one P(3) atom to form distorted edge-sharing OLi2CrP trigonal pyramids. In the sixteenth O site, O(16) is bonded to one Li(2), one Li(3), one Li(5), and one P(4) atom to form distorted corner-sharing OLi3P trigonal pyramids.
Li5Cr3(PO4)4 crystallizes in the triclinic P1 space group. There are five inequivalent Li sites. In the first Li site, Li(1) is bonded in a rectangular see-saw-like geometry to one O(13), one O(14), one O(15), and one O(9) atom. The Li(1)-O(13) bond length is 2.09 Å. The Li(1)-O(14) bond length is 2.00 Å. The Li(1)-O(15) bond length is 2.08 Å. The Li(1)-O(9) bond length is 2.00 Å. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(10), one O(13), one O(14), and one O(16) atom. The Li(2)-O(10) bond length is 2.04 Å. The Li(2)-O(13) bond length is 2.02 Å. The Li(2)-O(14) bond length is 2.10 Å. The Li(2)-O(16) bond length is 2.03 Å. In the third Li site, Li(3) is bonded in a 4-coordinate geometry to one O(14), one O(16), one O(3), and one O(6) atom. The Li(3)-O(14) bond length is 1.96 Å. The Li(3)-O(16) bond length is 2.22 Å. The Li(3)-O(3) bond length is 1.93 Å. The Li(3)-O(6) bond length is 2.17 Å. In the fourth Li site, Li(4) is bonded to one O(13), one O(15), one O(4), and one O(5) atom to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(4)O4 tetrahedra,  a cornercorner with one Li(5)O5 trigonal bipyramid, corners with two equivalent Cr(3)O5 trigonal bipyramids, and  an edgeedge with one P(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 68°. The Li(4)-O(13) bond length is 1.96 Å. The Li(4)-O(15) bond length is 2.23 Å. The Li(4)-O(4) bond length is 1.98 Å. The Li(4)-O(5) bond length is 2.08 Å. In the fifth Li site, Li(5) is bonded to one O(1), one O(12), one O(16), one O(3), and one O(5) atom to form LiO5 trigonal bipyramids that share  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(2)O4 tetrahedra,  a cornercorner with one P(4)O4 tetrahedra, corners with two equivalent P(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 trigonal pyramid, and  an edgeedge with one Cr(2)O6 octahedra. The Li(5)-O(1) bond length is 2.10 Å. The Li(5)-O(12) bond length is 2.19 Å. The Li(5)-O(16) bond length is 2.04 Å. The Li(5)-O(3) bond length is 2.08 Å. The Li(5)-O(5) bond length is 2.22 Å. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded in a rectangular see-saw-like geometry to one O(1), one O(10), one O(2), and one O(9) atom. The Cr(1)-O(1) bond length is 2.03 Å. The Cr(1)-O(10) bond length is 2.06 Å. The Cr(1)-O(2) bond length is 2.06 Å. The Cr(1)-O(9) bond length is 2.05 Å. In the second Cr site, Cr(2) is bonded to one O(11), one O(12), one O(5), one O(6), one O(7), and one O(8) atom to form CrO6 octahedra that share  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(2)O4 tetrahedra, corners with two equivalent P(3)O4 tetrahedra, corners with two equivalent P(4)O4 tetrahedra,  a cornercorner with one Li(4)O4 trigonal pyramid,  an edgeedge with one Li(5)O5 trigonal bipyramid, and  an edgeedge with one Cr(3)O5 trigonal bipyramid. The Cr(2)-O(11) bond length is 2.09 Å. The Cr(2)-O(12) bond length is 2.02 Å. The Cr(2)-O(5) bond length is 2.05 Å. The Cr(2)-O(6) bond length is 2.07 Å. The Cr(2)-O(7) bond length is 1.97 Å. The Cr(2)-O(8) bond length is 1.97 Å. In the third Cr site, Cr(3) is bonded to one O(11), one O(15), one O(2), one O(4), and one O(6) atom to form CrO5 trigonal bipyramids that share  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(2)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra, corners with two equivalent P(4)O4 tetrahedra, corners with two equivalent Li(4)O4 trigonal pyramids, and  an edgeedge with one Cr(2)O6 octahedra. The Cr(3)-O(11) bond length is 2.12 Å. The Cr(3)-O(15) bond length is 2.06 Å. The Cr(3)-O(2) bond length is 2.11 Å. The Cr(3)-O(4) bond length is 2.11 Å. The Cr(3)-O(6) bond length is 2.30 Å. There are four inequivalent P sites. In the first P site, P(1) is bonded to one O(1), one O(11), one O(13), and one O(9) atom to form PO4 tetrahedra that share  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Li(5)O5 trigonal bipyramid,  a cornercorner with one Cr(3)O5 trigonal bipyramid, and  a cornercorner with one Li(4)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 52°. The P(1)-O(1) bond length is 1.55 Å. The P(1)-O(11) bond length is 1.59 Å. The P(1)-O(13) bond length is 1.54 Å. The P(1)-O(9) bond length is 1.55 Å. In the second P site, P(2) is bonded to one O(10), one O(12), one O(14), and one O(2) atom to form PO4 tetrahedra that share  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Li(5)O5 trigonal bipyramid, and  a cornercorner with one Cr(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 51°. The P(2)-O(10) bond length is 1.55 Å. The P(2)-O(12) bond length is 1.55 Å. The P(2)-O(14) bond length is 1.54 Å. The P(2)-O(2) bond length is 1.58 Å. In the third P site, P(3) is bonded to one O(15), one O(3), one O(5), and one O(7) atom to form PO4 tetrahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Cr(3)O5 trigonal bipyramid, corners with two equivalent Li(5)O5 trigonal bipyramids, and  an edgeedge with one Li(4)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 42-46°. The P(3)-O(15) bond length is 1.59 Å. The P(3)-O(3) bond length is 1.53 Å. The P(3)-O(5) bond length is 1.58 Å. The P(3)-O(7) bond length is 1.54 Å. In the fourth P site, P(4) is bonded to one O(16), one O(4), one O(6), and one O(8) atom to form PO4 tetrahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(5)O5 trigonal bipyramid, corners with two equivalent Cr(3)O5 trigonal bipyramids, and  a cornercorner with one Li(4)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 37-46°. The P(4)-O(16) bond length is 1.54 Å. The P(4)-O(4) bond length is 1.56 Å. The P(4)-O(6) bond length is 1.59 Å. The P(4)-O(8) bond length is 1.53 Å. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a trigonal planar geometry to one Li(5), one Cr(1), and one P(1) atom. In the second O site, O(2) is bonded in a trigonal planar geometry to one Cr(1), one Cr(3), and one P(2) atom. In the third O site, O(3) is bonded in a trigonal planar geometry to one Li(3), one Li(5), and one P(3) atom. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to one Li(4), one Cr(3), and one P(4) atom. In the fifth O site, O(5) is bonded to one Li(4), one Li(5), one Cr(2), and one P(3) atom to form distorted OLi2CrP tetrahedra that share  a cornercorner with one O(16)Li3P trigonal pyramid and  an edgeedge with one O(15)Li2CrP trigonal pyramid. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Li(3), one Cr(2), one Cr(3), and one P(4) atom. In the seventh O site, O(7) is bonded in a bent 150 degrees geometry to one Cr(2) and one P(3) atom. In the eighth O site, O(8) is bonded in a bent 150 degrees geometry to one Cr(2) and one P(4) atom. In the ninth O site, O(9) is bonded in a trigonal planar geometry to one Li(1), one Cr(1), and one P(1) atom. In the tenth O site, O(10) is bonded in a trigonal planar geometry to one Li(2), one Cr(1), and one P(2) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal planar geometry to one Cr(2), one Cr(3), and one P(1) atom. In the twelfth O site, O(12) is bonded in a distorted trigonal planar geometry to one Li(5), one Cr(2), and one P(2) atom. In the thirteenth O site, O(13) is bonded in a rectangular see-saw-like geometry to one Li(1), one Li(2), one Li(4), and one P(1) atom. In the fourteenth O site, O(14) is bonded in a rectangular see-saw-like geometry to one Li(1), one Li(2), one Li(3), and one P(2) atom. In the fifteenth O site, O(15) is bonded to one Li(1), one Li(4), one Cr(3), and one P(3) atom to form distorted edge-sharing OLi2CrP trigonal pyramids. In the sixteenth O site, O(16) is bonded to one Li(2), one Li(3), one Li(5), and one P(4) atom to form distorted corner-sharing OLi3P trigonal pyramids.