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 8-coordinate geometry to one O(1), one O(10), one O(2), one O(4), one O(7), one O(9), and two equivalent O(5) atoms. In the second Ba site, Ba(2) is bonded in a 7-coordinate geometry to one O(1), one O(10), one O(3), one O(4), one O(6), one O(8), and one O(9) atom. In the third Ba site, Ba(3) is bonded in a 4-coordinate geometry to one O(2), one O(3), one O(5), one O(7), and one O(9) atom. In the fourth Ba site, Ba(4) is bonded in a 8-coordinate geometry to one Fe(2), one O(1), one O(10), one O(2), one O(3), one O(6), one O(8), and one O(9) atom. Mg(1) is bonded to one O(1), one O(2), one O(3), and one O(7) atom to form MgO4 tetrahedra that share  a cornercorner with one Fe(4)O4 tetrahedra and corners with two equivalent Fe(1)O5 trigonal bipyramids. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(2), one O(4), one O(5), and one O(6) atom to form distorted FeO5 trigonal bipyramids that share  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, and corners with two equivalent Mg(1)O4 tetrahedra. In the second Fe site, Fe(2) is bonded in a trigonal planar geometry to one Ba(4), one O(3), one O(4), and one O(8) 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 and  a cornercorner with one Fe(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 FeO4 tetrahedra that share  a cornercorner with one Mg(1)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, and  a cornercorner with one Fe(1)O5 trigonal bipyramid. There are ten inequivalent O sites. In the first O site, O(1) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), one Mg(1), and one Fe(1) atom. In the second O site, O(2) is bonded to one Ba(1), one Ba(3), one Ba(4), one Mg(1), and one Fe(1) atom to form distorted OBa3MgFe trigonal bipyramids that share corners with three equivalent O(9)Ba4Fe2 octahedra and corners with two equivalent O(4)Ba2Fe2 trigonal pyramids. The corner-sharing octahedral tilt angles range from 41-72°. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Ba(2), one Ba(3), one Ba(4), one Mg(1), and one Fe(2) atom. In the fourth O site, O(4) is bonded to one Ba(1), one Ba(2), one Fe(1), and one Fe(2) atom to form distorted OBa2Fe2 trigonal pyramids that share corners with two equivalent O(9)Ba4Fe2 octahedra and corners with two equivalent O(2)Ba3MgFe trigonal bipyramids. The corner-sharing octahedral tilt angles range from 5-84°. In the fifth O site, O(5) is bonded in a 5-coordinate geometry to one Ba(3), two equivalent Ba(1), one Fe(1), and one Fe(3) atom. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Ba(2), one Ba(4), one Fe(1), and one Fe(4) atom. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to one Ba(1), one Ba(3), one Mg(1), and one Fe(4) atom. In the eighth O site, O(8) is bonded in a 4-coordinate geometry to one Ba(2), one Ba(4), one Fe(2), and one Fe(3) atom. In the ninth O site, O(9) is bonded to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Fe(3), and one Fe(4) atom to form distorted OBa4Fe2 octahedra that share corners with three equivalent O(2)Ba3MgFe trigonal bipyramids and corners with two equivalent O(4)Ba2Fe2 trigonal pyramids. In the tenth O site, O(10) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), one Fe(3), and one Fe(4) atom.
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 8-coordinate geometry to one O(1), one O(10), one O(2), one O(4), one O(7), one O(9), and two equivalent O(5) atoms. The Ba(1)-O(1) bond length is 2.90 Å. The Ba(1)-O(10) bond length is 3.08 Å. The Ba(1)-O(2) bond length is 2.76 Å. The Ba(1)-O(4) bond length is 2.64 Å. The Ba(1)-O(7) bond length is 2.80 Å. The Ba(1)-O(9) bond length is 3.02 Å. There is one shorter (2.98 Å) and one longer (3.32 Å) Ba(1)-O(5) bond length. In the second Ba site, Ba(2) is bonded in a 7-coordinate geometry to one O(1), one O(10), one O(3), one O(4), one O(6), one O(8), and one O(9) atom. The Ba(2)-O(1) bond length is 2.70 Å. The Ba(2)-O(10) bond length is 2.94 Å. The Ba(2)-O(3) bond length is 2.74 Å. The Ba(2)-O(4) bond length is 2.66 Å. The Ba(2)-O(6) bond length is 2.99 Å. The Ba(2)-O(8) bond length is 2.89 Å. The Ba(2)-O(9) bond length is 2.93 Å. In the third Ba site, Ba(3) is bonded in a 4-coordinate geometry to one O(2), one O(3), one O(5), one O(7), and one O(9) atom. The Ba(3)-O(2) bond length is 2.80 Å. The Ba(3)-O(3) bond length is 2.64 Å. The Ba(3)-O(5) bond length is 2.62 Å. The Ba(3)-O(7) bond length is 2.89 Å. The Ba(3)-O(9) bond length is 3.15 Å. In the fourth Ba site, Ba(4) is bonded in a 8-coordinate geometry to one Fe(2), one O(1), one O(10), one O(2), one O(3), one O(6), one O(8), and one O(9) atom. The Ba(4)-Fe(2) bond length is 3.07 Å. The Ba(4)-O(1) bond length is 3.09 Å. The Ba(4)-O(10) bond length is 3.23 Å. The Ba(4)-O(2) bond length is 2.68 Å. The Ba(4)-O(3) bond length is 3.39 Å. The Ba(4)-O(6) bond length is 2.62 Å. The Ba(4)-O(8) bond length is 2.73 Å. The Ba(4)-O(9) bond length is 2.89 Å. Mg(1) is bonded to one O(1), one O(2), one O(3), and one O(7) atom to form MgO4 tetrahedra that share  a cornercorner with one Fe(4)O4 tetrahedra and corners with two equivalent Fe(1)O5 trigonal bipyramids. The Mg(1)-O(1) bond length is 1.94 Å. The Mg(1)-O(2) bond length is 1.99 Å. The Mg(1)-O(3) bond length is 2.02 Å. The Mg(1)-O(7) bond length is 1.96 Å. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(2), one O(4), one O(5), and one O(6) atom to form distorted FeO5 trigonal bipyramids that share  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, and corners with two equivalent Mg(1)O4 tetrahedra. The Fe(1)-O(1) bond length is 1.98 Å. The Fe(1)-O(2) bond length is 2.23 Å. The Fe(1)-O(4) bond length is 2.00 Å. The Fe(1)-O(5) bond length is 2.30 Å. The Fe(1)-O(6) bond length is 2.48 Å. In the second Fe site, Fe(2) is bonded in a trigonal planar geometry to one Ba(4), one O(3), one O(4), and one O(8) atom. The Fe(2)-O(3) bond length is 1.87 Å. The Fe(2)-O(4) bond length is 1.88 Å. The Fe(2)-O(8) bond length is 1.92 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 and  a cornercorner with one Fe(1)O5 trigonal bipyramid. The Fe(3)-O(10) bond length is 1.94 Å. The Fe(3)-O(5) bond length is 1.83 Å. The Fe(3)-O(8) bond length is 1.92 Å. The Fe(3)-O(9) bond length is 1.96 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 FeO4 tetrahedra that share  a cornercorner with one Mg(1)O4 tetrahedra, corners with two equivalent Fe(3)O4 tetrahedra, and  a cornercorner with one Fe(1)O5 trigonal bipyramid. The Fe(4)-O(10) bond length is 1.97 Å. The Fe(4)-O(6) bond length is 1.85 Å. The Fe(4)-O(7) bond length is 1.89 Å. The Fe(4)-O(9) bond length is 2.00 Å. There are ten inequivalent O sites. In the first O site, O(1) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), one Mg(1), and one Fe(1) atom. In the second O site, O(2) is bonded to one Ba(1), one Ba(3), one Ba(4), one Mg(1), and one Fe(1) atom to form distorted OBa3MgFe trigonal bipyramids that share corners with three equivalent O(9)Ba4Fe2 octahedra and corners with two equivalent O(4)Ba2Fe2 trigonal pyramids. The corner-sharing octahedral tilt angles range from 41-72°. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Ba(2), one Ba(3), one Ba(4), one Mg(1), and one Fe(2) atom. In the fourth O site, O(4) is bonded to one Ba(1), one Ba(2), one Fe(1), and one Fe(2) atom to form distorted OBa2Fe2 trigonal pyramids that share corners with two equivalent O(9)Ba4Fe2 octahedra and corners with two equivalent O(2)Ba3MgFe trigonal bipyramids. The corner-sharing octahedral tilt angles range from 5-84°. In the fifth O site, O(5) is bonded in a 5-coordinate geometry to one Ba(3), two equivalent Ba(1), one Fe(1), and one Fe(3) atom. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Ba(2), one Ba(4), one Fe(1), and one Fe(4) atom. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to one Ba(1), one Ba(3), one Mg(1), and one Fe(4) atom. In the eighth O site, O(8) is bonded in a 4-coordinate geometry to one Ba(2), one Ba(4), one Fe(2), and one Fe(3) atom. In the ninth O site, O(9) is bonded to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Fe(3), and one Fe(4) atom to form distorted OBa4Fe2 octahedra that share corners with three equivalent O(2)Ba3MgFe trigonal bipyramids and corners with two equivalent O(4)Ba2Fe2 trigonal pyramids. In the tenth O site, O(10) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), one Fe(3), and one Fe(4) atom.