Ba3MgTi2O7 crystallizes in the triclinic P1 space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 9-coordinate geometry to one O(7), two equivalent O(2), two equivalent O(5), and four equivalent O(1) atoms. In the second Ba site, Ba(2) is bonded in a 8-coordinate geometry to two equivalent O(2), two equivalent O(5), and four equivalent O(6) atoms. In the third Ba site, Ba(3) is bonded in a 9-coordinate geometry to one O(1), two equivalent O(3), two equivalent O(4), and four equivalent O(7) atoms. Mg(1) is bonded in a 3-coordinate geometry to one O(3), one O(4), and one O(6) atom. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(6), two equivalent O(2), and two equivalent O(5) atoms to form corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles are 2°. In the second Ti site, Ti(2) is bonded to one O(7), two equivalent O(3), and two equivalent O(4) atoms to form distorted corner-sharing TiO5 square pyramids. There are seven inequivalent O sites. In the first O site, O(1) is bonded to one Ba(3), four equivalent Ba(1), and one Ti(1) atom to form distorted OBa5Ti octahedra that share corners with four equivalent O(2)Ba4Ti2 octahedra, corners with four equivalent O(5)Ba4Ti2 octahedra, corners with four equivalent O(1)Ba5Ti octahedra, edges with four equivalent O(1)Ba5Ti octahedra, faces with two equivalent O(2)Ba4Ti2 octahedra, and faces with two equivalent O(5)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 3-59°. In the second O site, O(2) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Ti(1) atoms to form distorted OBa4Ti2 octahedra that share corners with two equivalent O(2)Ba4Ti2 octahedra, corners with four equivalent O(1)Ba5Ti octahedra, edges with two equivalent O(2)Ba4Ti2 octahedra, faces with two equivalent O(1)Ba5Ti octahedra, and faces with four equivalent O(5)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 2-59°. In the third O site, O(3) is bonded in a 5-coordinate geometry to two equivalent Ba(3), one Mg(1), and two equivalent Ti(2) atoms. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to two equivalent Ba(3), one Mg(1), and two equivalent Ti(2) atoms. In the fifth O site, O(5) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Ti(1) atoms to form distorted OBa4Ti2 octahedra that share corners with two equivalent O(5)Ba4Ti2 octahedra, corners with four equivalent O(1)Ba5Ti octahedra, edges with two equivalent O(5)Ba4Ti2 octahedra, faces with two equivalent O(1)Ba5Ti octahedra, and faces with four equivalent O(2)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 2-59°. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to four equivalent Ba(2), one Mg(1), and one Ti(1) atom. In the seventh O site, O(7) is bonded in a 6-coordinate geometry to one Ba(1), four equivalent Ba(3), and one Ti(2) atom.
Ba3MgTi2O7 crystallizes in the triclinic P1 space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 9-coordinate geometry to one O(7), two equivalent O(2), two equivalent O(5), and four equivalent O(1) atoms. The Ba(1)-O(7) bond length is 2.78 Å. Both Ba(1)-O(2) bond lengths are 2.79 Å. There is one shorter (2.79 Å) and one longer (2.80 Å) Ba(1)-O(5) bond length. There are a spread of Ba(1)-O(1) bond distances ranging from 2.86-2.99 Å. In the second Ba site, Ba(2) is bonded in a 8-coordinate geometry to two equivalent O(2), two equivalent O(5), and four equivalent O(6) atoms. There is one shorter (2.75 Å) and one longer (2.77 Å) Ba(2)-O(2) bond length. There is one shorter (2.76 Å) and one longer (2.77 Å) Ba(2)-O(5) bond length. There are a spread of Ba(2)-O(6) bond distances ranging from 2.81-3.05 Å. In the third Ba site, Ba(3) is bonded in a 9-coordinate geometry to one O(1), two equivalent O(3), two equivalent O(4), and four equivalent O(7) atoms. The Ba(3)-O(1) bond length is 2.78 Å. There is one shorter (2.81 Å) and one longer (3.01 Å) Ba(3)-O(3) bond length. There is one shorter (2.80 Å) and one longer (3.00 Å) Ba(3)-O(4) bond length. There are a spread of Ba(3)-O(7) bond distances ranging from 2.73-3.12 Å. Mg(1) is bonded in a 3-coordinate geometry to one O(3), one O(4), and one O(6) atom. The Mg(1)-O(3) bond length is 2.11 Å. The Mg(1)-O(4) bond length is 2.11 Å. The Mg(1)-O(6) bond length is 2.01 Å. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(6), two equivalent O(2), and two equivalent O(5) atoms to form corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles are 2°. The Ti(1)-O(1) bond length is 1.95 Å. The Ti(1)-O(6) bond length is 2.13 Å. There is one shorter (1.99 Å) and one longer (2.11 Å) Ti(1)-O(2) bond length. There is one shorter (1.98 Å) and one longer (2.11 Å) Ti(1)-O(5) bond length. In the second Ti site, Ti(2) is bonded to one O(7), two equivalent O(3), and two equivalent O(4) atoms to form distorted corner-sharing TiO5 square pyramids. The Ti(2)-O(7) bond length is 1.99 Å. There is one shorter (1.85 Å) and one longer (2.29 Å) Ti(2)-O(3) bond length. There is one shorter (1.85 Å) and one longer (2.29 Å) Ti(2)-O(4) bond length. There are seven inequivalent O sites. In the first O site, O(1) is bonded to one Ba(3), four equivalent Ba(1), and one Ti(1) atom to form distorted OBa5Ti octahedra that share corners with four equivalent O(2)Ba4Ti2 octahedra, corners with four equivalent O(5)Ba4Ti2 octahedra, corners with four equivalent O(1)Ba5Ti octahedra, edges with four equivalent O(1)Ba5Ti octahedra, faces with two equivalent O(2)Ba4Ti2 octahedra, and faces with two equivalent O(5)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 3-59°. In the second O site, O(2) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Ti(1) atoms to form distorted OBa4Ti2 octahedra that share corners with two equivalent O(2)Ba4Ti2 octahedra, corners with four equivalent O(1)Ba5Ti octahedra, edges with two equivalent O(2)Ba4Ti2 octahedra, faces with two equivalent O(1)Ba5Ti octahedra, and faces with four equivalent O(5)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 2-59°. In the third O site, O(3) is bonded in a 5-coordinate geometry to two equivalent Ba(3), one Mg(1), and two equivalent Ti(2) atoms. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to two equivalent Ba(3), one Mg(1), and two equivalent Ti(2) atoms. In the fifth O site, O(5) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Ti(1) atoms to form distorted OBa4Ti2 octahedra that share corners with two equivalent O(5)Ba4Ti2 octahedra, corners with four equivalent O(1)Ba5Ti octahedra, edges with two equivalent O(5)Ba4Ti2 octahedra, faces with two equivalent O(1)Ba5Ti octahedra, and faces with four equivalent O(2)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 2-59°. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to four equivalent Ba(2), one Mg(1), and one Ti(1) atom. In the seventh O site, O(7) is bonded in a 6-coordinate geometry to one Ba(1), four equivalent Ba(3), and one Ti(2) atom.