Ba3MgMn3O9 is Orthorhombic Perovskite-derived structured and crystallizes in the monoclinic Cm space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 8-coordinate geometry to one O(1), one O(5), two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms. In the second Ba site, Ba(2) is bonded in a 8-coordinate geometry to one O(1), one O(4), two equivalent O(2), two equivalent O(5), and two equivalent O(6) atoms. In the third Ba site, Ba(3) is bonded in a distorted q6 geometry to two equivalent O(1), two equivalent O(3), two equivalent O(6), and four equivalent O(2) atoms. Mg(1) is bonded in a square co-planar geometry to two equivalent O(3) and two equivalent O(6) atoms. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(1), one O(5), two equivalent O(2), and two equivalent O(6) atoms to form a mixture of corner and face-sharing MnO6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the second Mn site, Mn(2) is bonded to one O(1), one O(4), two equivalent O(2), and two equivalent O(3) atoms to form a mixture of corner and face-sharing MnO6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the third Mn site, Mn(3) is bonded to one O(4), one O(5), two equivalent O(3), and two equivalent O(6) atoms to form face-sharing MnO6 octahedra. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Ba(1), one Ba(2), two equivalent Ba(3), one Mn(1), and one Mn(2) atom to form distorted OBa4Mn2 octahedra that share corners with two equivalent O(1)Ba4Mn2 octahedra, corners with four equivalent O(4)Ba3Mn2 trigonal bipyramids, and corners with four equivalent O(5)Ba3Mn2 trigonal bipyramids. The corner-sharing octahedral tilt angles are 3°. In the second O site, O(2) is bonded in a distorted linear geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Mn(1), and one Mn(2) atom. In the third O site, O(3) is bonded in a 5-coordinate geometry to one Ba(1), one Ba(3), one Mg(1), one Mn(2), and one Mn(3) atom. In the fourth O site, O(4) is bonded to one Ba(2), two equivalent Ba(1), one Mn(2), and one Mn(3) atom to form distorted OBa3Mn2 trigonal bipyramids that share corners with four equivalent O(1)Ba4Mn2 octahedra,  a cornercorner with one O(5)Ba3Mn2 trigonal bipyramid, corners with two equivalent O(4)Ba3Mn2 trigonal bipyramids, and edges with two equivalent O(5)Ba3Mn2 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 27-69°. In the fifth O site, O(5) is bonded to one Ba(1), two equivalent Ba(2), one Mn(1), and one Mn(3) atom to form distorted OBa3Mn2 trigonal bipyramids that share corners with four equivalent O(1)Ba4Mn2 octahedra,  a cornercorner with one O(4)Ba3Mn2 trigonal bipyramid, corners with two equivalent O(5)Ba3Mn2 trigonal bipyramids, and edges with two equivalent O(4)Ba3Mn2 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 21-70°. In the sixth O site, O(6) is bonded in a 5-coordinate geometry to one Ba(2), one Ba(3), one Mg(1), one Mn(1), and one Mn(3) atom.
Ba3MgMn3O9 is Orthorhombic Perovskite-derived structured and crystallizes in the monoclinic Cm space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 8-coordinate geometry to one O(1), one O(5), two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms. The Ba(1)-O(1) bond length is 2.69 Å. The Ba(1)-O(5) bond length is 2.79 Å. Both Ba(1)-O(2) bond lengths are 2.78 Å. Both Ba(1)-O(3) bond lengths are 2.75 Å. Both Ba(1)-O(4) bond lengths are 3.03 Å. In the second Ba site, Ba(2) is bonded in a 8-coordinate geometry to one O(1), one O(4), two equivalent O(2), two equivalent O(5), and two equivalent O(6) atoms. The Ba(2)-O(1) bond length is 2.76 Å. The Ba(2)-O(4) bond length is 2.69 Å. Both Ba(2)-O(2) bond lengths are 2.77 Å. Both Ba(2)-O(5) bond lengths are 3.01 Å. Both Ba(2)-O(6) bond lengths are 2.76 Å. In the third Ba site, Ba(3) is bonded in a distorted q6 geometry to two equivalent O(1), two equivalent O(3), two equivalent O(6), and four equivalent O(2) atoms. Both Ba(3)-O(1) bond lengths are 2.82 Å. Both Ba(3)-O(3) bond lengths are 2.94 Å. Both Ba(3)-O(6) bond lengths are 2.92 Å. There are two shorter (3.04 Å) and two longer (3.07 Å) Ba(3)-O(2) bond lengths. Mg(1) is bonded in a square co-planar geometry to two equivalent O(3) and two equivalent O(6) atoms. Both Mg(1)-O(3) bond lengths are 1.99 Å. Both Mg(1)-O(6) bond lengths are 2.00 Å. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(1), one O(5), two equivalent O(2), and two equivalent O(6) atoms to form a mixture of corner and face-sharing MnO6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. The Mn(1)-O(1) bond length is 2.01 Å. The Mn(1)-O(5) bond length is 2.00 Å. Both Mn(1)-O(2) bond lengths are 2.00 Å. Both Mn(1)-O(6) bond lengths are 2.15 Å. In the second Mn site, Mn(2) is bonded to one O(1), one O(4), two equivalent O(2), and two equivalent O(3) atoms to form a mixture of corner and face-sharing MnO6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. The Mn(2)-O(1) bond length is 2.15 Å. The Mn(2)-O(4) bond length is 2.11 Å. Both Mn(2)-O(2) bond lengths are 2.06 Å. Both Mn(2)-O(3) bond lengths are 2.23 Å. In the third Mn site, Mn(3) is bonded to one O(4), one O(5), two equivalent O(3), and two equivalent O(6) atoms to form face-sharing MnO6 octahedra. The Mn(3)-O(4) bond length is 1.96 Å. The Mn(3)-O(5) bond length is 2.03 Å. Both Mn(3)-O(3) bond lengths are 1.93 Å. Both Mn(3)-O(6) bond lengths are 1.95 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Ba(1), one Ba(2), two equivalent Ba(3), one Mn(1), and one Mn(2) atom to form distorted OBa4Mn2 octahedra that share corners with two equivalent O(1)Ba4Mn2 octahedra, corners with four equivalent O(4)Ba3Mn2 trigonal bipyramids, and corners with four equivalent O(5)Ba3Mn2 trigonal bipyramids. The corner-sharing octahedral tilt angles are 3°. In the second O site, O(2) is bonded in a distorted linear geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Mn(1), and one Mn(2) atom. In the third O site, O(3) is bonded in a 5-coordinate geometry to one Ba(1), one Ba(3), one Mg(1), one Mn(2), and one Mn(3) atom. In the fourth O site, O(4) is bonded to one Ba(2), two equivalent Ba(1), one Mn(2), and one Mn(3) atom to form distorted OBa3Mn2 trigonal bipyramids that share corners with four equivalent O(1)Ba4Mn2 octahedra,  a cornercorner with one O(5)Ba3Mn2 trigonal bipyramid, corners with two equivalent O(4)Ba3Mn2 trigonal bipyramids, and edges with two equivalent O(5)Ba3Mn2 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 27-69°. In the fifth O site, O(5) is bonded to one Ba(1), two equivalent Ba(2), one Mn(1), and one Mn(3) atom to form distorted OBa3Mn2 trigonal bipyramids that share corners with four equivalent O(1)Ba4Mn2 octahedra,  a cornercorner with one O(4)Ba3Mn2 trigonal bipyramid, corners with two equivalent O(5)Ba3Mn2 trigonal bipyramids, and edges with two equivalent O(4)Ba3Mn2 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 21-70°. In the sixth O site, O(6) is bonded in a 5-coordinate geometry to one Ba(2), one Ba(3), one Mg(1), one Mn(1), and one Mn(3) atom.