LuFe2O4 is Aluminum carbonitride-like structured and crystallizes in the trigonal R-3m space group. Lu(1) is bonded to six equivalent O(1) atoms to form distorted LuO6 octahedra that share corners with six equivalent Fe(1)O5 trigonal bipyramids and edges with six equivalent Lu(1)O6 octahedra. Fe(1) is bonded to one O(1) and four equivalent O(2) atoms to form FeO5 trigonal bipyramids that share corners with three equivalent Lu(1)O6 octahedra, corners with six equivalent Fe(1)O5 trigonal bipyramids, and edges with three equivalent Fe(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 63°. There are two inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Lu(1) and one Fe(1) atom to form OLu3Fe tetrahedra that share corners with nine equivalent O(1)Lu3Fe tetrahedra, corners with four equivalent O(2)Fe4 trigonal pyramids, and edges with three equivalent O(1)Lu3Fe tetrahedra. In the second O site, O(2) is bonded to four equivalent Fe(1) atoms to form OFe4 trigonal pyramids that share corners with four equivalent O(1)Lu3Fe tetrahedra, corners with six equivalent O(2)Fe4 trigonal pyramids, and edges with three equivalent O(2)Fe4 trigonal pyramids.
LuFe2O4 is Aluminum carbonitride-like structured and crystallizes in the trigonal R-3m space group. Lu(1) is bonded to six equivalent O(1) atoms to form distorted LuO6 octahedra that share corners with six equivalent Fe(1)O5 trigonal bipyramids and edges with six equivalent Lu(1)O6 octahedra. All Lu(1)-O(1) bond lengths are 2.25 Å. Fe(1) is bonded to one O(1) and four equivalent O(2) atoms to form FeO5 trigonal bipyramids that share corners with three equivalent Lu(1)O6 octahedra, corners with six equivalent Fe(1)O5 trigonal bipyramids, and edges with three equivalent Fe(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 63°. The Fe(1)-O(1) bond length is 2.00 Å. There are three shorter (2.02 Å) and one longer (2.18 Å) Fe(1)-O(2) bond length. There are two inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Lu(1) and one Fe(1) atom to form OLu3Fe tetrahedra that share corners with nine equivalent O(1)Lu3Fe tetrahedra, corners with four equivalent O(2)Fe4 trigonal pyramids, and edges with three equivalent O(1)Lu3Fe tetrahedra. In the second O site, O(2) is bonded to four equivalent Fe(1) atoms to form OFe4 trigonal pyramids that share corners with four equivalent O(1)Lu3Fe tetrahedra, corners with six equivalent O(2)Fe4 trigonal pyramids, and edges with three equivalent O(2)Fe4 trigonal pyramids.