Fe13O19 crystallizes in the monoclinic C2/m space group. There are seven inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O7 pentagonal bipyramids, and edges with three equivalent Fe(1)O6 octahedra. The corner-sharing octahedra are not tilted. In the second Fe site, Fe(2) is bonded to one O(4), one O(6), two equivalent O(8), and three equivalent O(3) atoms to form distorted FeO7 pentagonal bipyramids that share corners with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(5)O7 pentagonal bipyramids, and edges with four equivalent Fe(2)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 49°. In the third Fe site, Fe(3) is bonded in a 7-coordinate geometry to one O(10), two equivalent O(2), two equivalent O(5), and two equivalent O(9) atoms. In the fourth Fe site, Fe(4) is bonded in a 8-coordinate geometry to one O(10), one O(6), two equivalent O(3), two equivalent O(4), and two equivalent O(5) atoms. In the fifth Fe site, Fe(5) is bonded to one O(8), two equivalent O(4), two equivalent O(7), and two equivalent O(9) atoms to form distorted FeO7 pentagonal bipyramids that share corners with two equivalent Fe(6)O6 octahedra, edges with two equivalent Fe(2)O7 pentagonal bipyramids, and faces with two equivalent Fe(5)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 69°. In the sixth Fe site, Fe(6) is bonded to two equivalent O(9) and four equivalent O(10) atoms to form FeO6 octahedra that share corners with four equivalent Fe(5)O7 pentagonal bipyramids and edges with two equivalent Fe(6)O6 octahedra. In the seventh Fe site, Fe(7) is bonded in a 8-coordinate geometry to one O(6), two equivalent O(2), two equivalent O(8), and three equivalent O(7) atoms. There are ten inequivalent O sites. In the first O site, O(5) is bonded to one Fe(1), two equivalent Fe(3), and two equivalent Fe(4) atoms to form distorted OFe5 trigonal bipyramids that share corners with two equivalent O(4)Fe5 square pyramids, corners with two equivalent O(3)Fe5 trigonal bipyramids, corners with two equivalent O(9)Fe5 trigonal bipyramids,  an edgeedge with one O(4)Fe5 square pyramid,  an edgeedge with one O(3)Fe5 trigonal bipyramid,  an edgeedge with one O(9)Fe5 trigonal bipyramid, edges with two equivalent O(5)Fe5 trigonal bipyramids, and edges with two equivalent O(10)Fe4 trigonal pyramids. In the second O site, O(6) is bonded in a 3-coordinate geometry to one Fe(2), one Fe(4), one Fe(7), and two equivalent Fe(1) atoms. In the third O site, O(7) is bonded to two equivalent Fe(5) and three equivalent Fe(7) atoms to form a mixture of distorted edge and corner-sharing OFe5 square pyramids. In the fourth O site, O(8) is bonded to one Fe(5), two equivalent Fe(2), and two equivalent Fe(7) atoms to form a mixture of edge and corner-sharing OFe5 square pyramids. In the fifth O site, O(9) is bonded to one Fe(6), two equivalent Fe(3), and two equivalent Fe(5) atoms to form distorted OFe5 trigonal bipyramids that share corners with two equivalent O(4)Fe5 square pyramids, corners with two equivalent O(7)Fe5 square pyramids, corners with two equivalent O(8)Fe5 square pyramids,  a cornercorner with one O(9)Fe5 trigonal bipyramid, corners with two equivalent O(5)Fe5 trigonal bipyramids, corners with two equivalent O(10)Fe4 trigonal pyramids,  an edgeedge with one O(4)Fe5 square pyramid,  an edgeedge with one O(7)Fe5 square pyramid,  an edgeedge with one O(5)Fe5 trigonal bipyramid, edges with two equivalent O(9)Fe5 trigonal bipyramids, and edges with two equivalent O(10)Fe4 trigonal pyramids. In the sixth O site, O(10) is bonded to one Fe(3), one Fe(4), and two equivalent Fe(6) atoms to form OFe4 trigonal pyramids that share corners with two equivalent O(4)Fe5 square pyramids, corners with two equivalent O(3)Fe5 trigonal bipyramids, corners with two equivalent O(9)Fe5 trigonal bipyramids, corners with four equivalent O(10)Fe4 trigonal pyramids, edges with two equivalent O(5)Fe5 trigonal bipyramids, edges with two equivalent O(9)Fe5 trigonal bipyramids, and  an edgeedge with one O(10)Fe4 trigonal pyramid. In the seventh O site, O(1) is bonded in a square co-planar geometry to four equivalent Fe(1) atoms. In the eighth O site, O(2) is bonded in a 5-coordinate geometry to one Fe(1), two equivalent Fe(3), and two equivalent Fe(7) atoms. In the ninth O site, O(3) is bonded to two equivalent Fe(4) and three equivalent Fe(2) atoms to form distorted OFe5 trigonal bipyramids that share corners with four equivalent O(4)Fe5 square pyramids, corners with four equivalent O(8)Fe5 square pyramids, corners with two equivalent O(5)Fe5 trigonal bipyramids, corners with two equivalent O(10)Fe4 trigonal pyramids,  an edgeedge with one O(8)Fe5 square pyramid,  an edgeedge with one O(5)Fe5 trigonal bipyramid, edges with four equivalent O(3)Fe5 trigonal bipyramids, and  a faceface with one O(4)Fe5 square pyramid. In the tenth O site, O(4) is bonded to one Fe(2), two equivalent Fe(4), and two equivalent Fe(5) atoms to form distorted OFe5 square pyramids that share corners with two equivalent O(7)Fe5 square pyramids, corners with two equivalent O(5)Fe5 trigonal bipyramids, corners with two equivalent O(9)Fe5 trigonal bipyramids, corners with four equivalent O(3)Fe5 trigonal bipyramids, corners with two equivalent O(10)Fe4 trigonal pyramids,  an edgeedge with one O(7)Fe5 square pyramid, edges with two equivalent O(4)Fe5 square pyramids, edges with two equivalent O(8)Fe5 square pyramids,  an edgeedge with one O(5)Fe5 trigonal bipyramid,  an edgeedge with one O(9)Fe5 trigonal bipyramid, and  a faceface with one O(3)Fe5 trigonal bipyramid.
Fe13O19 crystallizes in the monoclinic C2/m space group. There are seven inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O7 pentagonal bipyramids, and edges with three equivalent Fe(1)O6 octahedra. The corner-sharing octahedra are not tilted. The Fe(1)-O(2) bond length is 2.00 Å. The Fe(1)-O(5) bond length is 2.07 Å. Both Fe(1)-O(1) bond lengths are 2.06 Å. Both Fe(1)-O(6) bond lengths are 1.94 Å. In the second Fe site, Fe(2) is bonded to one O(4), one O(6), two equivalent O(8), and three equivalent O(3) atoms to form distorted FeO7 pentagonal bipyramids that share corners with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(5)O7 pentagonal bipyramids, and edges with four equivalent Fe(2)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 49°. The Fe(2)-O(4) bond length is 2.10 Å. The Fe(2)-O(6) bond length is 2.00 Å. Both Fe(2)-O(8) bond lengths are 2.14 Å. There are two shorter (2.14 Å) and one longer (2.15 Å) Fe(2)-O(3) bond length. In the third Fe site, Fe(3) is bonded in a 7-coordinate geometry to one O(10), two equivalent O(2), two equivalent O(5), and two equivalent O(9) atoms. The Fe(3)-O(10) bond length is 2.15 Å. Both Fe(3)-O(2) bond lengths are 2.09 Å. Both Fe(3)-O(5) bond lengths are 2.25 Å. Both Fe(3)-O(9) bond lengths are 2.21 Å. In the fourth Fe site, Fe(4) is bonded in a 8-coordinate geometry to one O(10), one O(6), two equivalent O(3), two equivalent O(4), and two equivalent O(5) atoms. The Fe(4)-O(10) bond length is 2.00 Å. The Fe(4)-O(6) bond length is 2.55 Å. Both Fe(4)-O(3) bond lengths are 2.19 Å. Both Fe(4)-O(4) bond lengths are 2.36 Å. Both Fe(4)-O(5) bond lengths are 2.13 Å. In the fifth Fe site, Fe(5) is bonded to one O(8), two equivalent O(4), two equivalent O(7), and two equivalent O(9) atoms to form distorted FeO7 pentagonal bipyramids that share corners with two equivalent Fe(6)O6 octahedra, edges with two equivalent Fe(2)O7 pentagonal bipyramids, and faces with two equivalent Fe(5)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 69°. The Fe(5)-O(8) bond length is 2.12 Å. Both Fe(5)-O(4) bond lengths are 2.09 Å. Both Fe(5)-O(7) bond lengths are 2.16 Å. Both Fe(5)-O(9) bond lengths are 2.20 Å. In the sixth Fe site, Fe(6) is bonded to two equivalent O(9) and four equivalent O(10) atoms to form FeO6 octahedra that share corners with four equivalent Fe(5)O7 pentagonal bipyramids and edges with two equivalent Fe(6)O6 octahedra. Both Fe(6)-O(9) bond lengths are 2.00 Å. All Fe(6)-O(10) bond lengths are 2.00 Å. In the seventh Fe site, Fe(7) is bonded in a 8-coordinate geometry to one O(6), two equivalent O(2), two equivalent O(8), and three equivalent O(7) atoms. The Fe(7)-O(6) bond length is 2.64 Å. Both Fe(7)-O(2) bond lengths are 2.56 Å. Both Fe(7)-O(8) bond lengths are 2.14 Å. There is one shorter (2.10 Å) and two longer (2.16 Å) Fe(7)-O(7) bond lengths. There are ten inequivalent O sites. In the first O site, O(5) is bonded to one Fe(1), two equivalent Fe(3), and two equivalent Fe(4) atoms to form distorted OFe5 trigonal bipyramids that share corners with two equivalent O(4)Fe5 square pyramids, corners with two equivalent O(3)Fe5 trigonal bipyramids, corners with two equivalent O(9)Fe5 trigonal bipyramids,  an edgeedge with one O(4)Fe5 square pyramid,  an edgeedge with one O(3)Fe5 trigonal bipyramid,  an edgeedge with one O(9)Fe5 trigonal bipyramid, edges with two equivalent O(5)Fe5 trigonal bipyramids, and edges with two equivalent O(10)Fe4 trigonal pyramids. In the second O site, O(6) is bonded in a 3-coordinate geometry to one Fe(2), one Fe(4), one Fe(7), and two equivalent Fe(1) atoms. In the third O site, O(7) is bonded to two equivalent Fe(5) and three equivalent Fe(7) atoms to form a mixture of distorted edge and corner-sharing OFe5 square pyramids. In the fourth O site, O(8) is bonded to one Fe(5), two equivalent Fe(2), and two equivalent Fe(7) atoms to form a mixture of edge and corner-sharing OFe5 square pyramids. In the fifth O site, O(9) is bonded to one Fe(6), two equivalent Fe(3), and two equivalent Fe(5) atoms to form distorted OFe5 trigonal bipyramids that share corners with two equivalent O(4)Fe5 square pyramids, corners with two equivalent O(7)Fe5 square pyramids, corners with two equivalent O(8)Fe5 square pyramids,  a cornercorner with one O(9)Fe5 trigonal bipyramid, corners with two equivalent O(5)Fe5 trigonal bipyramids, corners with two equivalent O(10)Fe4 trigonal pyramids,  an edgeedge with one O(4)Fe5 square pyramid,  an edgeedge with one O(7)Fe5 square pyramid,  an edgeedge with one O(5)Fe5 trigonal bipyramid, edges with two equivalent O(9)Fe5 trigonal bipyramids, and edges with two equivalent O(10)Fe4 trigonal pyramids. In the sixth O site, O(10) is bonded to one Fe(3), one Fe(4), and two equivalent Fe(6) atoms to form OFe4 trigonal pyramids that share corners with two equivalent O(4)Fe5 square pyramids, corners with two equivalent O(3)Fe5 trigonal bipyramids, corners with two equivalent O(9)Fe5 trigonal bipyramids, corners with four equivalent O(10)Fe4 trigonal pyramids, edges with two equivalent O(5)Fe5 trigonal bipyramids, edges with two equivalent O(9)Fe5 trigonal bipyramids, and  an edgeedge with one O(10)Fe4 trigonal pyramid. In the seventh O site, O(1) is bonded in a square co-planar geometry to four equivalent Fe(1) atoms. In the eighth O site, O(2) is bonded in a 5-coordinate geometry to one Fe(1), two equivalent Fe(3), and two equivalent Fe(7) atoms. In the ninth O site, O(3) is bonded to two equivalent Fe(4) and three equivalent Fe(2) atoms to form distorted OFe5 trigonal bipyramids that share corners with four equivalent O(4)Fe5 square pyramids, corners with four equivalent O(8)Fe5 square pyramids, corners with two equivalent O(5)Fe5 trigonal bipyramids, corners with two equivalent O(10)Fe4 trigonal pyramids,  an edgeedge with one O(8)Fe5 square pyramid,  an edgeedge with one O(5)Fe5 trigonal bipyramid, edges with four equivalent O(3)Fe5 trigonal bipyramids, and  a faceface with one O(4)Fe5 square pyramid. In the tenth O site, O(4) is bonded to one Fe(2), two equivalent Fe(4), and two equivalent Fe(5) atoms to form distorted OFe5 square pyramids that share corners with two equivalent O(7)Fe5 square pyramids, corners with two equivalent O(5)Fe5 trigonal bipyramids, corners with two equivalent O(9)Fe5 trigonal bipyramids, corners with four equivalent O(3)Fe5 trigonal bipyramids, corners with two equivalent O(10)Fe4 trigonal pyramids,  an edgeedge with one O(7)Fe5 square pyramid, edges with two equivalent O(4)Fe5 square pyramids, edges with two equivalent O(8)Fe5 square pyramids,  an edgeedge with one O(5)Fe5 trigonal bipyramid,  an edgeedge with one O(9)Fe5 trigonal bipyramid, and  a faceface with one O(3)Fe5 trigonal bipyramid.