Ba4MgTi3O10 crystallizes in the triclinic P1 space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 11-coordinate geometry to one Mg(1), one O(3), one O(4), two equivalent O(7), two equivalent O(8), and four equivalent O(10) atoms. In the second Ba site, Ba(2) is bonded in a 9-coordinate geometry to one O(9), two equivalent O(7), two equivalent O(8), and four equivalent O(1) atoms. In the third Ba site, Ba(3) is bonded in a 11-coordinate geometry to one Mg(1), one O(3), one O(4), two equivalent O(5), two equivalent O(6), and four equivalent O(2) atoms. In the fourth Ba site, Ba(4) is bonded in a 9-coordinate geometry to one O(1), two equivalent O(5), two equivalent O(6), and four equivalent O(9) atoms. Mg(1) is bonded in a rectangular see-saw-like geometry to one Ba(1), one Ba(3), two equivalent O(3), and two equivalent O(4) atoms. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(10), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles are 6°. In the second Ti site, Ti(2) is bonded to one O(9), two equivalent O(5), and two equivalent O(6) atoms to form corner-sharing TiO5 square pyramids. In the third Ti site, Ti(3) is bonded to one O(1), two equivalent O(7), and two equivalent O(8) atoms to form corner-sharing TiO5 square pyramids. There are ten inequivalent O sites. In the first O site, O(1) is bonded to one Ba(4), four equivalent Ba(2), and one Ti(3) atom to form distorted OBa5Ti octahedra that share corners with two equivalent O(5)Ba4Ti2 octahedra, corners with two equivalent O(6)Ba4Ti2 octahedra, corners with four equivalent O(7)Ba4Ti2 octahedra, corners with four equivalent O(8)Ba4Ti2 octahedra, corners with four equivalent O(1)Ba5Ti octahedra, edges with four equivalent O(1)Ba5Ti octahedra, edges with four equivalent O(9)Ba5Ti octahedra, faces with two equivalent O(7)Ba4Ti2 octahedra, and faces with two equivalent O(8)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 5-58°. In the second O site, O(2) is bonded in a 1-coordinate geometry to four equivalent Ba(3) and one Ti(1) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Ba(1), one Ba(3), two equivalent Mg(1), and two equivalent Ti(1) atoms. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Ba(1), one Ba(3), two equivalent Mg(1), and two equivalent Ti(1) atoms. In the fifth O site, O(5) is bonded to two equivalent Ba(3), two equivalent Ba(4), and two equivalent Ti(2) atoms to form distorted OBa4Ti2 octahedra that share corners with two equivalent O(5)Ba4Ti2 octahedra, corners with two equivalent O(1)Ba5Ti octahedra, corners with four equivalent O(9)Ba5Ti octahedra, edges with two equivalent O(5)Ba4Ti2 octahedra, faces with two equivalent O(9)Ba5Ti octahedra, and faces with four equivalent O(6)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 10-58°. In the sixth O site, O(6) is bonded to two equivalent Ba(3), two equivalent Ba(4), and two equivalent Ti(2) atoms to form distorted OBa4Ti2 octahedra that share corners with two equivalent O(6)Ba4Ti2 octahedra, corners with two equivalent O(1)Ba5Ti octahedra, corners with four equivalent O(9)Ba5Ti octahedra, edges with two equivalent O(6)Ba4Ti2 octahedra, faces with two equivalent O(9)Ba5Ti octahedra, and faces with four equivalent O(5)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 11-58°. In the seventh O site, O(7) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Ti(3) atoms to form distorted OBa4Ti2 octahedra that share corners with two equivalent O(7)Ba4Ti2 octahedra, corners with two equivalent O(9)Ba5Ti octahedra, corners with four equivalent O(1)Ba5Ti octahedra, edges with two equivalent O(7)Ba4Ti2 octahedra, faces with two equivalent O(1)Ba5Ti octahedra, and faces with four equivalent O(8)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 11-58°. In the eighth O site, O(8) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Ti(3) atoms to form distorted OBa4Ti2 octahedra that share corners with two equivalent O(8)Ba4Ti2 octahedra, corners with two equivalent O(9)Ba5Ti octahedra, corners with four equivalent O(1)Ba5Ti octahedra, edges with two equivalent O(8)Ba4Ti2 octahedra, faces with two equivalent O(1)Ba5Ti octahedra, and faces with four equivalent O(7)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 12-58°. In the ninth O site, O(9) is bonded to one Ba(2), four equivalent Ba(4), and one Ti(2) atom to form distorted OBa5Ti octahedra that share corners with two equivalent O(7)Ba4Ti2 octahedra, corners with two equivalent O(8)Ba4Ti2 octahedra, corners with four equivalent O(5)Ba4Ti2 octahedra, corners with four equivalent O(6)Ba4Ti2 octahedra, corners with four equivalent O(9)Ba5Ti octahedra, edges with four equivalent O(1)Ba5Ti octahedra, edges with four equivalent O(9)Ba5Ti octahedra, faces with two equivalent O(5)Ba4Ti2 octahedra, and faces with two equivalent O(6)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 5-58°. In the tenth O site, O(10) is bonded in a 1-coordinate geometry to four equivalent Ba(1) and one Ti(1) atom.
Ba4MgTi3O10 crystallizes in the triclinic P1 space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 11-coordinate geometry to one Mg(1), one O(3), one O(4), two equivalent O(7), two equivalent O(8), and four equivalent O(10) atoms. The Ba(1)-Mg(1) bond length is 3.03 Å. The Ba(1)-O(3) bond length is 3.31 Å. The Ba(1)-O(4) bond length is 3.26 Å. There is one shorter (2.74 Å) and one longer (2.82 Å) Ba(1)-O(7) bond length. There is one shorter (2.71 Å) and one longer (2.83 Å) Ba(1)-O(8) bond length. There are a spread of Ba(1)-O(10) bond distances ranging from 2.65-3.39 Å. In the second Ba site, Ba(2) is bonded in a 9-coordinate geometry to one O(9), two equivalent O(7), two equivalent O(8), and four equivalent O(1) atoms. The Ba(2)-O(9) bond length is 2.79 Å. Both Ba(2)-O(7) bond lengths are 2.84 Å. There is one shorter (2.85 Å) and one longer (2.87 Å) Ba(2)-O(8) bond length. There are two shorter (2.86 Å) and two longer (2.87 Å) Ba(2)-O(1) bond lengths. In the third Ba site, Ba(3) is bonded in a 11-coordinate geometry to one Mg(1), one O(3), one O(4), two equivalent O(5), two equivalent O(6), and four equivalent O(2) atoms. The Ba(3)-Mg(1) bond length is 3.03 Å. The Ba(3)-O(3) bond length is 3.29 Å. The Ba(3)-O(4) bond length is 3.22 Å. There is one shorter (2.74 Å) and one longer (2.82 Å) Ba(3)-O(5) bond length. There is one shorter (2.72 Å) and one longer (2.83 Å) Ba(3)-O(6) bond length. There are a spread of Ba(3)-O(2) bond distances ranging from 2.67-3.34 Å. In the fourth Ba site, Ba(4) is bonded in a 9-coordinate geometry to one O(1), two equivalent O(5), two equivalent O(6), and four equivalent O(9) atoms. The Ba(4)-O(1) bond length is 2.80 Å. There is one shorter (2.83 Å) and one longer (2.84 Å) Ba(4)-O(5) bond length. There is one shorter (2.83 Å) and one longer (2.86 Å) Ba(4)-O(6) bond length. There are two shorter (2.86 Å) and two longer (2.87 Å) Ba(4)-O(9) bond lengths. Mg(1) is bonded in a rectangular see-saw-like geometry to one Ba(1), one Ba(3), two equivalent O(3), and two equivalent O(4) atoms. There is one shorter (2.02 Å) and one longer (2.04 Å) Mg(1)-O(3) bond length. There is one shorter (2.01 Å) and one longer (2.05 Å) Mg(1)-O(4) bond length. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(10), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles are 6°. The Ti(1)-O(10) bond length is 2.02 Å. The Ti(1)-O(2) bond length is 2.01 Å. There is one shorter (1.98 Å) and one longer (2.08 Å) Ti(1)-O(3) bond length. There is one shorter (1.98 Å) and one longer (2.07 Å) Ti(1)-O(4) bond length. In the second Ti site, Ti(2) is bonded to one O(9), two equivalent O(5), and two equivalent O(6) atoms to form corner-sharing TiO5 square pyramids. The Ti(2)-O(9) bond length is 1.94 Å. There is one shorter (2.03 Å) and one longer (2.04 Å) Ti(2)-O(5) bond length. There is one shorter (2.02 Å) and one longer (2.03 Å) Ti(2)-O(6) bond length. In the third Ti site, Ti(3) is bonded to one O(1), two equivalent O(7), and two equivalent O(8) atoms to form corner-sharing TiO5 square pyramids. The Ti(3)-O(1) bond length is 1.93 Å. There is one shorter (2.03 Å) and one longer (2.04 Å) Ti(3)-O(7) bond length. There is one shorter (2.02 Å) and one longer (2.04 Å) Ti(3)-O(8) bond length. There are ten inequivalent O sites. In the first O site, O(1) is bonded to one Ba(4), four equivalent Ba(2), and one Ti(3) atom to form distorted OBa5Ti octahedra that share corners with two equivalent O(5)Ba4Ti2 octahedra, corners with two equivalent O(6)Ba4Ti2 octahedra, corners with four equivalent O(7)Ba4Ti2 octahedra, corners with four equivalent O(8)Ba4Ti2 octahedra, corners with four equivalent O(1)Ba5Ti octahedra, edges with four equivalent O(1)Ba5Ti octahedra, edges with four equivalent O(9)Ba5Ti octahedra, faces with two equivalent O(7)Ba4Ti2 octahedra, and faces with two equivalent O(8)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 5-58°. In the second O site, O(2) is bonded in a 1-coordinate geometry to four equivalent Ba(3) and one Ti(1) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Ba(1), one Ba(3), two equivalent Mg(1), and two equivalent Ti(1) atoms. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Ba(1), one Ba(3), two equivalent Mg(1), and two equivalent Ti(1) atoms. In the fifth O site, O(5) is bonded to two equivalent Ba(3), two equivalent Ba(4), and two equivalent Ti(2) atoms to form distorted OBa4Ti2 octahedra that share corners with two equivalent O(5)Ba4Ti2 octahedra, corners with two equivalent O(1)Ba5Ti octahedra, corners with four equivalent O(9)Ba5Ti octahedra, edges with two equivalent O(5)Ba4Ti2 octahedra, faces with two equivalent O(9)Ba5Ti octahedra, and faces with four equivalent O(6)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 10-58°. In the sixth O site, O(6) is bonded to two equivalent Ba(3), two equivalent Ba(4), and two equivalent Ti(2) atoms to form distorted OBa4Ti2 octahedra that share corners with two equivalent O(6)Ba4Ti2 octahedra, corners with two equivalent O(1)Ba5Ti octahedra, corners with four equivalent O(9)Ba5Ti octahedra, edges with two equivalent O(6)Ba4Ti2 octahedra, faces with two equivalent O(9)Ba5Ti octahedra, and faces with four equivalent O(5)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 11-58°. In the seventh O site, O(7) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Ti(3) atoms to form distorted OBa4Ti2 octahedra that share corners with two equivalent O(7)Ba4Ti2 octahedra, corners with two equivalent O(9)Ba5Ti octahedra, corners with four equivalent O(1)Ba5Ti octahedra, edges with two equivalent O(7)Ba4Ti2 octahedra, faces with two equivalent O(1)Ba5Ti octahedra, and faces with four equivalent O(8)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 11-58°. In the eighth O site, O(8) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Ti(3) atoms to form distorted OBa4Ti2 octahedra that share corners with two equivalent O(8)Ba4Ti2 octahedra, corners with two equivalent O(9)Ba5Ti octahedra, corners with four equivalent O(1)Ba5Ti octahedra, edges with two equivalent O(8)Ba4Ti2 octahedra, faces with two equivalent O(1)Ba5Ti octahedra, and faces with four equivalent O(7)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 12-58°. In the ninth O site, O(9) is bonded to one Ba(2), four equivalent Ba(4), and one Ti(2) atom to form distorted OBa5Ti octahedra that share corners with two equivalent O(7)Ba4Ti2 octahedra, corners with two equivalent O(8)Ba4Ti2 octahedra, corners with four equivalent O(5)Ba4Ti2 octahedra, corners with four equivalent O(6)Ba4Ti2 octahedra, corners with four equivalent O(9)Ba5Ti octahedra, edges with four equivalent O(1)Ba5Ti octahedra, edges with four equivalent O(9)Ba5Ti octahedra, faces with two equivalent O(5)Ba4Ti2 octahedra, and faces with two equivalent O(6)Ba4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 5-58°. In the tenth O site, O(10) is bonded in a 1-coordinate geometry to four equivalent Ba(1) and one Ti(1) atom.