Ba3MgTi2O7 crystallizes in the monoclinic Cm space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to one O(3), two equivalent O(2), and three equivalent O(1) atoms to form a mixture of distorted corner and edge-sharing BaO6 octahedra. The corner-sharing octahedral tilt angles range from 69-70°. In the second Ba site, Ba(2) is bonded in a 4-coordinate geometry to two equivalent O(2) and two equivalent O(4) atoms. Mg(1) is bonded in a rectangular see-saw-like geometry to two equivalent O(3) and two equivalent O(4) atoms. Ti(1) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(4), and two equivalent O(3) atoms. There are four inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Ba(1) and one Ti(1) atom to form distorted OBa3Ti tetrahedra that share  a cornercorner with one O(4)Ba2Mg2Ti2 octahedra, corners with five equivalent O(2)Ba3Ti tetrahedra, corners with six equivalent O(1)Ba3Ti tetrahedra, and  an edgeedge with one O(2)Ba3Ti tetrahedra. The corner-sharing octahedral tilt angles are 27°. In the second O site, O(2) is bonded to one Ba(2), two equivalent Ba(1), and one Ti(1) atom to form distorted OBa3Ti tetrahedra that share  a cornercorner with one O(4)Ba2Mg2Ti2 octahedra, corners with three equivalent O(2)Ba3Ti tetrahedra, corners with five equivalent O(1)Ba3Ti tetrahedra,  an edgeedge with one O(4)Ba2Mg2Ti2 octahedra, and  an edgeedge with one O(1)Ba3Ti tetrahedra. The corner-sharing octahedral tilt angles are 69°. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Ba(1), one Mg(1), and two equivalent Ti(1) atoms. In the fourth O site, O(4) is bonded to two equivalent Ba(2), two equivalent Mg(1), and two equivalent Ti(1) atoms to form distorted OBa2Mg2Ti2 octahedra that share corners with four equivalent O(4)Ba2Mg2Ti2 octahedra, corners with two equivalent O(1)Ba3Ti tetrahedra, corners with two equivalent O(2)Ba3Ti tetrahedra, and edges with two equivalent O(2)Ba3Ti tetrahedra. The corner-sharing octahedral tilt angles range from 2-9°.
Ba3MgTi2O7 crystallizes in the monoclinic Cm space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to one O(3), two equivalent O(2), and three equivalent O(1) atoms to form a mixture of distorted corner and edge-sharing BaO6 octahedra. The corner-sharing octahedral tilt angles range from 69-70°. The Ba(1)-O(3) bond length is 2.81 Å. There is one shorter (2.70 Å) and one longer (2.73 Å) Ba(1)-O(2) bond length. There are a spread of Ba(1)-O(1) bond distances ranging from 2.66-2.72 Å. In the second Ba site, Ba(2) is bonded in a 4-coordinate geometry to two equivalent O(2) and two equivalent O(4) atoms. Both Ba(2)-O(2) bond lengths are 2.68 Å. There is one shorter (2.74 Å) and one longer (3.12 Å) Ba(2)-O(4) bond length. Mg(1) is bonded in a rectangular see-saw-like geometry to two equivalent O(3) and two equivalent O(4) atoms. Both Mg(1)-O(3) bond lengths are 1.98 Å. There is one shorter (2.00 Å) and one longer (2.02 Å) Mg(1)-O(4) bond length. Ti(1) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(4), and two equivalent O(3) atoms. The Ti(1)-O(1) bond length is 1.83 Å. The Ti(1)-O(2) bond length is 1.84 Å. The Ti(1)-O(4) bond length is 2.31 Å. There is one shorter (2.00 Å) and one longer (2.19 Å) Ti(1)-O(3) bond length. There are four inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Ba(1) and one Ti(1) atom to form distorted OBa3Ti tetrahedra that share  a cornercorner with one O(4)Ba2Mg2Ti2 octahedra, corners with five equivalent O(2)Ba3Ti tetrahedra, corners with six equivalent O(1)Ba3Ti tetrahedra, and  an edgeedge with one O(2)Ba3Ti tetrahedra. The corner-sharing octahedral tilt angles are 27°. In the second O site, O(2) is bonded to one Ba(2), two equivalent Ba(1), and one Ti(1) atom to form distorted OBa3Ti tetrahedra that share  a cornercorner with one O(4)Ba2Mg2Ti2 octahedra, corners with three equivalent O(2)Ba3Ti tetrahedra, corners with five equivalent O(1)Ba3Ti tetrahedra,  an edgeedge with one O(4)Ba2Mg2Ti2 octahedra, and  an edgeedge with one O(1)Ba3Ti tetrahedra. The corner-sharing octahedral tilt angles are 69°. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Ba(1), one Mg(1), and two equivalent Ti(1) atoms. In the fourth O site, O(4) is bonded to two equivalent Ba(2), two equivalent Mg(1), and two equivalent Ti(1) atoms to form distorted OBa2Mg2Ti2 octahedra that share corners with four equivalent O(4)Ba2Mg2Ti2 octahedra, corners with two equivalent O(1)Ba3Ti tetrahedra, corners with two equivalent O(2)Ba3Ti tetrahedra, and edges with two equivalent O(2)Ba3Ti tetrahedra. The corner-sharing octahedral tilt angles range from 2-9°.