Li3CrFe3O8 crystallizes in the hexagonal P6_3mc space group. Li(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form distorted LiO6 octahedra that share corners with seven equivalent Fe(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Li(1)O6 octahedra, and  a faceface with one Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-47°. Cr(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form CrO6 octahedra that share corners with six equivalent Fe(1)O6 octahedra, edges with three equivalent Fe(1)O6 octahedra, and edges with six equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles are 50°. Fe(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form FeO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with seven equivalent Li(1)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  a faceface with one Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-50°. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Li(1), one Cr(1), and two equivalent Fe(1) atoms to form distorted OLi2CrFe2 square pyramids that share corners with two equivalent O(1)Li2CrFe2 square pyramids, corners with seven equivalent O(2)Li2CrFe2 square pyramids, edges with two equivalent O(4)Li3Fe3 octahedra, edges with two equivalent O(3)Li3Fe3 pentagonal pyramids, edges with two equivalent O(1)Li2CrFe2 square pyramids, and edges with two equivalent O(2)Li2CrFe2 square pyramids. In the second O site, O(2) is bonded to two equivalent Li(1), one Cr(1), and two equivalent Fe(1) atoms to form OLi2CrFe2 square pyramids that share corners with two equivalent O(2)Li2CrFe2 square pyramids, corners with seven equivalent O(1)Li2CrFe2 square pyramids, edges with two equivalent O(4)Li3Fe3 octahedra, edges with two equivalent O(3)Li3Fe3 pentagonal pyramids, edges with two equivalent O(1)Li2CrFe2 square pyramids, and edges with two equivalent O(2)Li2CrFe2 square pyramids. In the third O site, O(3) is bonded to three equivalent Li(1) and three equivalent Fe(1) atoms to form distorted OLi3Fe3 pentagonal pyramids that share corners with six equivalent O(4)Li3Fe3 octahedra, edges with six equivalent O(1)Li2CrFe2 square pyramids, and edges with six equivalent O(2)Li2CrFe2 square pyramids. The corner-sharing octahedral tilt angles range from 2-8°. In the fourth O site, O(4) is bonded to three equivalent Li(1) and three equivalent Fe(1) atoms to form OLi3Fe3 octahedra that share corners with six equivalent O(3)Li3Fe3 pentagonal pyramids, edges with six equivalent O(1)Li2CrFe2 square pyramids, and edges with six equivalent O(2)Li2CrFe2 square pyramids.
Li3CrFe3O8 crystallizes in the hexagonal P6_3mc space group. Li(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form distorted LiO6 octahedra that share corners with seven equivalent Fe(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Li(1)O6 octahedra, and  a faceface with one Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-47°. The Li(1)-O(3) bond length is 2.21 Å. The Li(1)-O(4) bond length is 2.10 Å. Both Li(1)-O(1) bond lengths are 2.24 Å. Both Li(1)-O(2) bond lengths are 2.01 Å. Cr(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form CrO6 octahedra that share corners with six equivalent Fe(1)O6 octahedra, edges with three equivalent Fe(1)O6 octahedra, and edges with six equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles are 50°. All Cr(1)-O(1) bond lengths are 1.96 Å. All Cr(1)-O(2) bond lengths are 2.01 Å. Fe(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form FeO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with seven equivalent Li(1)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  a faceface with one Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-50°. The Fe(1)-O(3) bond length is 2.02 Å. The Fe(1)-O(4) bond length is 2.02 Å. Both Fe(1)-O(1) bond lengths are 2.07 Å. Both Fe(1)-O(2) bond lengths are 2.06 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Li(1), one Cr(1), and two equivalent Fe(1) atoms to form distorted OLi2CrFe2 square pyramids that share corners with two equivalent O(1)Li2CrFe2 square pyramids, corners with seven equivalent O(2)Li2CrFe2 square pyramids, edges with two equivalent O(4)Li3Fe3 octahedra, edges with two equivalent O(3)Li3Fe3 pentagonal pyramids, edges with two equivalent O(1)Li2CrFe2 square pyramids, and edges with two equivalent O(2)Li2CrFe2 square pyramids. In the second O site, O(2) is bonded to two equivalent Li(1), one Cr(1), and two equivalent Fe(1) atoms to form OLi2CrFe2 square pyramids that share corners with two equivalent O(2)Li2CrFe2 square pyramids, corners with seven equivalent O(1)Li2CrFe2 square pyramids, edges with two equivalent O(4)Li3Fe3 octahedra, edges with two equivalent O(3)Li3Fe3 pentagonal pyramids, edges with two equivalent O(1)Li2CrFe2 square pyramids, and edges with two equivalent O(2)Li2CrFe2 square pyramids. In the third O site, O(3) is bonded to three equivalent Li(1) and three equivalent Fe(1) atoms to form distorted OLi3Fe3 pentagonal pyramids that share corners with six equivalent O(4)Li3Fe3 octahedra, edges with six equivalent O(1)Li2CrFe2 square pyramids, and edges with six equivalent O(2)Li2CrFe2 square pyramids. The corner-sharing octahedral tilt angles range from 2-8°. In the fourth O site, O(4) is bonded to three equivalent Li(1) and three equivalent Fe(1) atoms to form OLi3Fe3 octahedra that share corners with six equivalent O(3)Li3Fe3 pentagonal pyramids, edges with six equivalent O(1)Li2CrFe2 square pyramids, and edges with six equivalent O(2)Li2CrFe2 square pyramids.