Ba4Mg(Fe2O5)2 crystallizes in the triclinic P1 space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 7-coordinate geometry to one O(1), one O(2), one O(3), one O(4), one O(5), one O(7), and one O(9) atom. In the second Ba site, Ba(2) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(2), one O(3), one O(4), one O(8), and two equivalent O(6) atoms. In the third Ba site, Ba(3) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(2), one O(3), one O(4), one O(5), and two equivalent O(7) atoms. In the fourth Ba site, Ba(4) is bonded in a 7-coordinate geometry to one O(1), one O(2), one O(3), one O(4), one O(6), one O(8), and one O(9) atom. Mg(1) is bonded to one O(5), one O(6), one O(7), one O(8), and one O(9) atom to form distorted MgO5 trigonal bipyramids that share  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra,  an edgeedge with one Fe(3)O4 tetrahedra, and  an edgeedge with one Fe(4)O4 tetrahedra. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded in a square co-planar geometry to one O(1), one O(2), one O(3), and one O(4) atom. In the second Fe site, Fe(2) is bonded in a square co-planar geometry to one O(1), one O(2), one O(3), and one O(4) atom. In the third Fe site, Fe(3) is bonded to one O(10), one O(5), one O(8), and one O(9) atom to form FeO4 tetrahedra that share corners with two equivalent Fe(4)O4 tetrahedra,  a cornercorner with one Mg(1)O5 trigonal bipyramid, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. In the fourth Fe site, Fe(4) is bonded to one O(10), one O(6), one O(7), and one O(9) atom to form distorted FeO4 tetrahedra that share corners with two equivalent Fe(3)O4 tetrahedra,  a cornercorner with one Mg(1)O5 trigonal bipyramid, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. There are ten inequivalent O sites. In the first O site, O(1) is bonded to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Fe(1), and one Fe(2) atom to form distorted OBa4Fe2 octahedra that share corners with two equivalent O(4)Ba4Fe2 octahedra, corners with two equivalent O(10)Ba2Fe2 tetrahedra, corners with two equivalent O(8)Ba2MgFe trigonal pyramids, edges with two equivalent O(4)Ba4Fe2 octahedra,  an edgeedge with one O(5)Ba2MgFe trigonal pyramid, faces with two equivalent O(2)Ba4Fe2 octahedra, and faces with two equivalent O(3)Ba4Fe2 octahedra. The corner-sharing octahedral tilt angles are 1°. In the second O site, O(2) is bonded to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Fe(1), and one Fe(2) atom to form distorted OBa4Fe2 octahedra that share corners with two equivalent O(3)Ba4Fe2 octahedra, corners with two equivalent O(10)Ba2Fe2 tetrahedra, corners with two equivalent O(5)Ba2MgFe trigonal pyramids, corners with two equivalent O(8)Ba2MgFe trigonal pyramids, edges with two equivalent O(3)Ba4Fe2 octahedra, faces with two equivalent O(1)Ba4Fe2 octahedra, and faces with two equivalent O(4)Ba4Fe2 octahedra. The corner-sharing octahedral tilt angles are 1°. In the third O site, O(3) is bonded to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Fe(1), and one Fe(2) atom to form distorted OBa4Fe2 octahedra that share corners with two equivalent O(2)Ba4Fe2 octahedra, corners with two equivalent O(10)Ba2Fe2 tetrahedra, corners with two equivalent O(5)Ba2MgFe trigonal pyramids, corners with two equivalent O(8)Ba2MgFe trigonal pyramids, edges with two equivalent O(2)Ba4Fe2 octahedra, faces with two equivalent O(1)Ba4Fe2 octahedra, and faces with two equivalent O(4)Ba4Fe2 octahedra. The corner-sharing octahedral tilt angles are 1°. In the fourth O site, O(4) is bonded to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Fe(1), and one Fe(2) atom to form distorted OBa4Fe2 octahedra that share corners with two equivalent O(1)Ba4Fe2 octahedra, corners with two equivalent O(10)Ba2Fe2 tetrahedra, corners with two equivalent O(5)Ba2MgFe trigonal pyramids, edges with two equivalent O(1)Ba4Fe2 octahedra,  an edgeedge with one O(8)Ba2MgFe trigonal pyramid, faces with two equivalent O(2)Ba4Fe2 octahedra, and faces with two equivalent O(3)Ba4Fe2 octahedra. The corner-sharing octahedral tilt angles are 1°. In the fifth O site, O(5) is bonded to one Ba(1), one Ba(3), one Mg(1), and one Fe(3) atom to form distorted OBa2MgFe trigonal pyramids that share corners with two equivalent O(2)Ba4Fe2 octahedra, corners with two equivalent O(3)Ba4Fe2 octahedra, corners with two equivalent O(4)Ba4Fe2 octahedra, corners with two equivalent O(10)Ba2Fe2 tetrahedra,  an edgeedge with one O(1)Ba4Fe2 octahedra, and  an edgeedge with one O(8)Ba2MgFe trigonal pyramid. The corner-sharing octahedral tilt angles range from 30-91°. In the sixth O site, O(6) is bonded in a 2-coordinate geometry to one Ba(4), two equivalent Ba(2), one Mg(1), and one Fe(4) atom. In the seventh O site, O(7) is bonded in a 2-coordinate geometry to one Ba(1), two equivalent Ba(3), one Mg(1), and one Fe(4) atom. In the eighth O site, O(8) is bonded to one Ba(2), one Ba(4), one Mg(1), and one Fe(3) atom to form distorted OBa2MgFe trigonal pyramids that share corners with two equivalent O(1)Ba4Fe2 octahedra, corners with two equivalent O(2)Ba4Fe2 octahedra, corners with two equivalent O(3)Ba4Fe2 octahedra, corners with two equivalent O(10)Ba2Fe2 tetrahedra,  an edgeedge with one O(4)Ba4Fe2 octahedra, and  an edgeedge with one O(5)Ba2MgFe trigonal pyramid. The corner-sharing octahedral tilt angles range from 30-91°. In the ninth O site, O(9) is bonded in a 5-coordinate geometry to one Ba(1), one Ba(4), one Mg(1), one Fe(3), and one Fe(4) atom. In the tenth O site, O(10) is bonded to one Ba(2), one Ba(3), one Fe(3), and one Fe(4) atom to form distorted OBa2Fe2 tetrahedra that share corners with two equivalent O(1)Ba4Fe2 octahedra, corners with two equivalent O(2)Ba4Fe2 octahedra, corners with two equivalent O(3)Ba4Fe2 octahedra, corners with two equivalent O(4)Ba4Fe2 octahedra, corners with two equivalent O(5)Ba2MgFe trigonal pyramids, and corners with two equivalent O(8)Ba2MgFe trigonal pyramids. The corner-sharing octahedral tilt angles range from 23-68°.
Ba4Mg(Fe2O5)2 crystallizes in the triclinic P1 space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 7-coordinate geometry to one O(1), one O(2), one O(3), one O(4), one O(5), one O(7), and one O(9) atom. The Ba(1)-O(1) bond length is 2.69 Å. The Ba(1)-O(2) bond length is 2.69 Å. The Ba(1)-O(3) bond length is 2.70 Å. The Ba(1)-O(4) bond length is 2.70 Å. The Ba(1)-O(5) bond length is 2.80 Å. The Ba(1)-O(7) bond length is 2.96 Å. The Ba(1)-O(9) bond length is 2.97 Å. In the second Ba site, Ba(2) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(2), one O(3), one O(4), one O(8), and two equivalent O(6) atoms. The Ba(2)-O(1) bond length is 2.92 Å. The Ba(2)-O(10) bond length is 2.78 Å. The Ba(2)-O(2) bond length is 2.92 Å. The Ba(2)-O(3) bond length is 2.92 Å. The Ba(2)-O(4) bond length is 2.90 Å. The Ba(2)-O(8) bond length is 2.68 Å. There is one shorter (2.94 Å) and one longer (3.19 Å) Ba(2)-O(6) bond length. In the third Ba site, Ba(3) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(2), one O(3), one O(4), one O(5), and two equivalent O(7) atoms. The Ba(3)-O(1) bond length is 2.90 Å. The Ba(3)-O(10) bond length is 2.78 Å. The Ba(3)-O(2) bond length is 2.91 Å. The Ba(3)-O(3) bond length is 2.91 Å. The Ba(3)-O(4) bond length is 2.92 Å. The Ba(3)-O(5) bond length is 2.69 Å. There is one shorter (2.92 Å) and one longer (3.22 Å) Ba(3)-O(7) bond length. In the fourth Ba site, Ba(4) is bonded in a 7-coordinate geometry to one O(1), one O(2), one O(3), one O(4), one O(6), one O(8), and one O(9) atom. The Ba(4)-O(1) bond length is 2.70 Å. The Ba(4)-O(2) bond length is 2.70 Å. The Ba(4)-O(3) bond length is 2.69 Å. The Ba(4)-O(4) bond length is 2.69 Å. The Ba(4)-O(6) bond length is 2.96 Å. The Ba(4)-O(8) bond length is 2.80 Å. The Ba(4)-O(9) bond length is 2.97 Å. Mg(1) is bonded to one O(5), one O(6), one O(7), one O(8), and one O(9) atom to form distorted MgO5 trigonal bipyramids that share  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra,  an edgeedge with one Fe(3)O4 tetrahedra, and  an edgeedge with one Fe(4)O4 tetrahedra. The Mg(1)-O(5) bond length is 2.14 Å. The Mg(1)-O(6) bond length is 2.16 Å. The Mg(1)-O(7) bond length is 2.15 Å. The Mg(1)-O(8) bond length is 2.14 Å. The Mg(1)-O(9) bond length is 2.10 Å. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded in a square co-planar geometry to one O(1), one O(2), one O(3), and one O(4) atom. The Fe(1)-O(1) bond length is 2.05 Å. The Fe(1)-O(2) bond length is 2.05 Å. The Fe(1)-O(3) bond length is 2.05 Å. The Fe(1)-O(4) bond length is 2.05 Å. In the second Fe site, Fe(2) is bonded in a square co-planar geometry to one O(1), one O(2), one O(3), and one O(4) atom. The Fe(2)-O(1) bond length is 2.05 Å. The Fe(2)-O(2) bond length is 2.05 Å. The Fe(2)-O(3) bond length is 2.05 Å. The Fe(2)-O(4) bond length is 2.05 Å. In the third Fe site, Fe(3) is bonded to one O(10), one O(5), one O(8), and one O(9) atom to form FeO4 tetrahedra that share corners with two equivalent Fe(4)O4 tetrahedra,  a cornercorner with one Mg(1)O5 trigonal bipyramid, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The Fe(3)-O(10) bond length is 1.92 Å. The Fe(3)-O(5) bond length is 1.88 Å. The Fe(3)-O(8) bond length is 1.88 Å. The Fe(3)-O(9) bond length is 2.00 Å. In the fourth Fe site, Fe(4) is bonded to one O(10), one O(6), one O(7), and one O(9) atom to form distorted FeO4 tetrahedra that share corners with two equivalent Fe(3)O4 tetrahedra,  a cornercorner with one Mg(1)O5 trigonal bipyramid, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The Fe(4)-O(10) bond length is 1.98 Å. The Fe(4)-O(6) bond length is 1.88 Å. The Fe(4)-O(7) bond length is 1.88 Å. The Fe(4)-O(9) bond length is 1.97 Å. There are ten inequivalent O sites. In the first O site, O(1) is bonded to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Fe(1), and one Fe(2) atom to form distorted OBa4Fe2 octahedra that share corners with two equivalent O(4)Ba4Fe2 octahedra, corners with two equivalent O(10)Ba2Fe2 tetrahedra, corners with two equivalent O(8)Ba2MgFe trigonal pyramids, edges with two equivalent O(4)Ba4Fe2 octahedra,  an edgeedge with one O(5)Ba2MgFe trigonal pyramid, faces with two equivalent O(2)Ba4Fe2 octahedra, and faces with two equivalent O(3)Ba4Fe2 octahedra. The corner-sharing octahedral tilt angles are 1°. In the second O site, O(2) is bonded to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Fe(1), and one Fe(2) atom to form distorted OBa4Fe2 octahedra that share corners with two equivalent O(3)Ba4Fe2 octahedra, corners with two equivalent O(10)Ba2Fe2 tetrahedra, corners with two equivalent O(5)Ba2MgFe trigonal pyramids, corners with two equivalent O(8)Ba2MgFe trigonal pyramids, edges with two equivalent O(3)Ba4Fe2 octahedra, faces with two equivalent O(1)Ba4Fe2 octahedra, and faces with two equivalent O(4)Ba4Fe2 octahedra. The corner-sharing octahedral tilt angles are 1°. In the third O site, O(3) is bonded to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Fe(1), and one Fe(2) atom to form distorted OBa4Fe2 octahedra that share corners with two equivalent O(2)Ba4Fe2 octahedra, corners with two equivalent O(10)Ba2Fe2 tetrahedra, corners with two equivalent O(5)Ba2MgFe trigonal pyramids, corners with two equivalent O(8)Ba2MgFe trigonal pyramids, edges with two equivalent O(2)Ba4Fe2 octahedra, faces with two equivalent O(1)Ba4Fe2 octahedra, and faces with two equivalent O(4)Ba4Fe2 octahedra. The corner-sharing octahedral tilt angles are 1°. In the fourth O site, O(4) is bonded to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Fe(1), and one Fe(2) atom to form distorted OBa4Fe2 octahedra that share corners with two equivalent O(1)Ba4Fe2 octahedra, corners with two equivalent O(10)Ba2Fe2 tetrahedra, corners with two equivalent O(5)Ba2MgFe trigonal pyramids, edges with two equivalent O(1)Ba4Fe2 octahedra,  an edgeedge with one O(8)Ba2MgFe trigonal pyramid, faces with two equivalent O(2)Ba4Fe2 octahedra, and faces with two equivalent O(3)Ba4Fe2 octahedra. The corner-sharing octahedral tilt angles are 1°. In the fifth O site, O(5) is bonded to one Ba(1), one Ba(3), one Mg(1), and one Fe(3) atom to form distorted OBa2MgFe trigonal pyramids that share corners with two equivalent O(2)Ba4Fe2 octahedra, corners with two equivalent O(3)Ba4Fe2 octahedra, corners with two equivalent O(4)Ba4Fe2 octahedra, corners with two equivalent O(10)Ba2Fe2 tetrahedra,  an edgeedge with one O(1)Ba4Fe2 octahedra, and  an edgeedge with one O(8)Ba2MgFe trigonal pyramid. The corner-sharing octahedral tilt angles range from 30-91°. In the sixth O site, O(6) is bonded in a 2-coordinate geometry to one Ba(4), two equivalent Ba(2), one Mg(1), and one Fe(4) atom. In the seventh O site, O(7) is bonded in a 2-coordinate geometry to one Ba(1), two equivalent Ba(3), one Mg(1), and one Fe(4) atom. In the eighth O site, O(8) is bonded to one Ba(2), one Ba(4), one Mg(1), and one Fe(3) atom to form distorted OBa2MgFe trigonal pyramids that share corners with two equivalent O(1)Ba4Fe2 octahedra, corners with two equivalent O(2)Ba4Fe2 octahedra, corners with two equivalent O(3)Ba4Fe2 octahedra, corners with two equivalent O(10)Ba2Fe2 tetrahedra,  an edgeedge with one O(4)Ba4Fe2 octahedra, and  an edgeedge with one O(5)Ba2MgFe trigonal pyramid. The corner-sharing octahedral tilt angles range from 30-91°. In the ninth O site, O(9) is bonded in a 5-coordinate geometry to one Ba(1), one Ba(4), one Mg(1), one Fe(3), and one Fe(4) atom. In the tenth O site, O(10) is bonded to one Ba(2), one Ba(3), one Fe(3), and one Fe(4) atom to form distorted OBa2Fe2 tetrahedra that share corners with two equivalent O(1)Ba4Fe2 octahedra, corners with two equivalent O(2)Ba4Fe2 octahedra, corners with two equivalent O(3)Ba4Fe2 octahedra, corners with two equivalent O(4)Ba4Fe2 octahedra, corners with two equivalent O(5)Ba2MgFe trigonal pyramids, and corners with two equivalent O(8)Ba2MgFe trigonal pyramids. The corner-sharing octahedral tilt angles range from 23-68°.