Ba4Mg(RhO3)4 is Orthorhombic Perovskite-derived structured and crystallizes in the triclinic P1 space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 12-coordinate geometry to one O(10), one O(11), one O(12), one O(7), one O(8), one O(9), two equivalent O(1), two equivalent O(4), and two equivalent O(5) atoms. In the second Ba site, Ba(2) is bonded in a 12-coordinate geometry to one Mg(1), one O(10), one O(11), one O(12), one O(7), one O(9), two equivalent O(2), two equivalent O(3), and two equivalent O(6) atoms. In the third Ba site, Ba(3) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), one O(6), two equivalent O(10), two equivalent O(11), and two equivalent O(7) atoms to form distorted BaO12 cuboctahedra that share corners with six equivalent Ba(3)O12 cuboctahedra, corners with three equivalent Rh(1)O6 octahedra, faces with three equivalent Rh(2)O6 octahedra, and faces with three equivalent Rh(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-12°. In the fourth Ba site, Ba(4) is bonded in a 8-coordinate geometry to one Rh(3), one O(1), one O(12), one O(4), one O(5), one O(9), and two equivalent O(8) atoms. Mg(1) is bonded in a 3-coordinate geometry to one Ba(2), one O(3), one O(6), and one O(8) atom. There are four inequivalent Rh sites. In the first Rh site, Rh(1) is bonded to one O(1), one O(12), one O(4), one O(5), one O(8), and one O(9) atom to form RhO6 octahedra that share corners with three equivalent Ba(3)O12 cuboctahedra and  a faceface with one Rh(4)O6 octahedra. In the second Rh site, Rh(2) is bonded to one O(10), one O(11), one O(2), one O(3), one O(6), and one O(7) atom to form RhO6 octahedra that share corners with three equivalent Rh(4)O6 octahedra and faces with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 9-15°. In the third Rh site, Rh(3) is bonded in a distorted trigonal planar geometry to one Ba(4), one O(12), one O(2), and one O(9) atom. In the fourth Rh site, Rh(4) is bonded to one O(1), one O(10), one O(11), one O(4), one O(5), and one O(7) atom to form RhO6 octahedra that share corners with three equivalent Rh(2)O6 octahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one Rh(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-15°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one Ba(3), one Ba(4), two equivalent Ba(1), one Rh(1), and one Rh(4) atom. In the second O site, O(2) is bonded in a 5-coordinate geometry to one Ba(3), two equivalent Ba(2), one Rh(2), and one Rh(3) atom. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Ba(3), two equivalent Ba(2), one Mg(1), and one Rh(2) atom. In the fourth O site, O(4) is bonded in a 6-coordinate geometry to one Ba(3), one Ba(4), two equivalent Ba(1), one Rh(1), and one Rh(4) atom. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one Ba(3), one Ba(4), two equivalent Ba(1), one Rh(1), and one Rh(4) atom. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Ba(3), two equivalent Ba(2), one Mg(1), and one Rh(2) atom. In the seventh O site, O(7) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Rh(2), and one Rh(4) atom. In the eighth O site, O(8) is bonded in a 2-coordinate geometry to one Ba(1), two equivalent Ba(4), one Mg(1), and one Rh(1) atom. In the ninth O site, O(9) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), one Rh(1), and one Rh(3) atom. In the tenth O site, O(10) is bonded in a 5-coordinate geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Rh(2), and one Rh(4) atom. In the eleventh O site, O(11) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Rh(2), and one Rh(4) atom. In the twelfth O site, O(12) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), one Rh(1), and one Rh(3) atom.
Ba4Mg(RhO3)4 is Orthorhombic Perovskite-derived structured and crystallizes in the triclinic P1 space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 12-coordinate geometry to one O(10), one O(11), one O(12), one O(7), one O(8), one O(9), two equivalent O(1), two equivalent O(4), and two equivalent O(5) atoms. The Ba(1)-O(10) bond length is 2.67 Å. The Ba(1)-O(11) bond length is 2.92 Å. The Ba(1)-O(12) bond length is 3.27 Å. The Ba(1)-O(7) bond length is 2.92 Å. The Ba(1)-O(8) bond length is 3.06 Å. The Ba(1)-O(9) bond length is 3.28 Å. There is one shorter (2.93 Å) and one longer (3.16 Å) Ba(1)-O(1) bond length. There is one shorter (2.94 Å) and one longer (3.16 Å) Ba(1)-O(4) bond length. Both Ba(1)-O(5) bond lengths are 2.93 Å. In the second Ba site, Ba(2) is bonded in a 12-coordinate geometry to one Mg(1), one O(10), one O(11), one O(12), one O(7), one O(9), two equivalent O(2), two equivalent O(3), and two equivalent O(6) atoms. The Ba(2)-Mg(1) bond length is 3.36 Å. The Ba(2)-O(10) bond length is 3.43 Å. The Ba(2)-O(11) bond length is 2.67 Å. The Ba(2)-O(12) bond length is 3.27 Å. The Ba(2)-O(7) bond length is 2.67 Å. The Ba(2)-O(9) bond length is 3.27 Å. Both Ba(2)-O(2) bond lengths are 2.94 Å. There is one shorter (2.76 Å) and one longer (3.34 Å) Ba(2)-O(3) bond length. There is one shorter (2.76 Å) and one longer (3.33 Å) Ba(2)-O(6) bond length. In the third Ba site, Ba(3) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), one O(6), two equivalent O(10), two equivalent O(11), and two equivalent O(7) atoms to form distorted BaO12 cuboctahedra that share corners with six equivalent Ba(3)O12 cuboctahedra, corners with three equivalent Rh(1)O6 octahedra, faces with three equivalent Rh(2)O6 octahedra, and faces with three equivalent Rh(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-12°. The Ba(3)-O(1) bond length is 3.21 Å. The Ba(3)-O(2) bond length is 2.87 Å. The Ba(3)-O(3) bond length is 2.78 Å. The Ba(3)-O(4) bond length is 3.21 Å. The Ba(3)-O(5) bond length is 3.33 Å. The Ba(3)-O(6) bond length is 2.78 Å. There is one shorter (2.95 Å) and one longer (2.96 Å) Ba(3)-O(10) bond length. There is one shorter (2.83 Å) and one longer (3.25 Å) Ba(3)-O(11) bond length. There is one shorter (2.82 Å) and one longer (3.26 Å) Ba(3)-O(7) bond length. In the fourth Ba site, Ba(4) is bonded in a 8-coordinate geometry to one Rh(3), one O(1), one O(12), one O(4), one O(5), one O(9), and two equivalent O(8) atoms. The Ba(4)-Rh(3) bond length is 3.16 Å. The Ba(4)-O(1) bond length is 2.73 Å. The Ba(4)-O(12) bond length is 2.84 Å. The Ba(4)-O(4) bond length is 2.73 Å. The Ba(4)-O(5) bond length is 2.58 Å. The Ba(4)-O(9) bond length is 2.84 Å. Both Ba(4)-O(8) bond lengths are 2.97 Å. Mg(1) is bonded in a 3-coordinate geometry to one Ba(2), one O(3), one O(6), and one O(8) atom. The Mg(1)-O(3) bond length is 1.96 Å. The Mg(1)-O(6) bond length is 1.96 Å. The Mg(1)-O(8) bond length is 1.89 Å. There are four inequivalent Rh sites. In the first Rh site, Rh(1) is bonded to one O(1), one O(12), one O(4), one O(5), one O(8), and one O(9) atom to form RhO6 octahedra that share corners with three equivalent Ba(3)O12 cuboctahedra and  a faceface with one Rh(4)O6 octahedra. The Rh(1)-O(1) bond length is 2.04 Å. The Rh(1)-O(12) bond length is 2.03 Å. The Rh(1)-O(4) bond length is 2.04 Å. The Rh(1)-O(5) bond length is 2.16 Å. The Rh(1)-O(8) bond length is 1.97 Å. The Rh(1)-O(9) bond length is 2.03 Å. In the second Rh site, Rh(2) is bonded to one O(10), one O(11), one O(2), one O(3), one O(6), and one O(7) atom to form RhO6 octahedra that share corners with three equivalent Rh(4)O6 octahedra and faces with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 9-15°. The Rh(2)-O(10) bond length is 2.05 Å. The Rh(2)-O(11) bond length is 2.10 Å. The Rh(2)-O(2) bond length is 2.09 Å. The Rh(2)-O(3) bond length is 2.01 Å. The Rh(2)-O(6) bond length is 2.01 Å. The Rh(2)-O(7) bond length is 2.10 Å. In the third Rh site, Rh(3) is bonded in a distorted trigonal planar geometry to one Ba(4), one O(12), one O(2), and one O(9) atom. The Rh(3)-O(12) bond length is 1.89 Å. The Rh(3)-O(2) bond length is 1.90 Å. The Rh(3)-O(9) bond length is 1.89 Å. In the fourth Rh site, Rh(4) is bonded to one O(1), one O(10), one O(11), one O(4), one O(5), and one O(7) atom to form RhO6 octahedra that share corners with three equivalent Rh(2)O6 octahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one Rh(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-15°. The Rh(4)-O(1) bond length is 2.04 Å. The Rh(4)-O(10) bond length is 2.09 Å. The Rh(4)-O(11) bond length is 2.02 Å. The Rh(4)-O(4) bond length is 2.04 Å. The Rh(4)-O(5) bond length is 2.03 Å. The Rh(4)-O(7) bond length is 2.03 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one Ba(3), one Ba(4), two equivalent Ba(1), one Rh(1), and one Rh(4) atom. In the second O site, O(2) is bonded in a 5-coordinate geometry to one Ba(3), two equivalent Ba(2), one Rh(2), and one Rh(3) atom. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Ba(3), two equivalent Ba(2), one Mg(1), and one Rh(2) atom. In the fourth O site, O(4) is bonded in a 6-coordinate geometry to one Ba(3), one Ba(4), two equivalent Ba(1), one Rh(1), and one Rh(4) atom. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one Ba(3), one Ba(4), two equivalent Ba(1), one Rh(1), and one Rh(4) atom. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Ba(3), two equivalent Ba(2), one Mg(1), and one Rh(2) atom. In the seventh O site, O(7) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Rh(2), and one Rh(4) atom. In the eighth O site, O(8) is bonded in a 2-coordinate geometry to one Ba(1), two equivalent Ba(4), one Mg(1), and one Rh(1) atom. In the ninth O site, O(9) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), one Rh(1), and one Rh(3) atom. In the tenth O site, O(10) is bonded in a 5-coordinate geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Rh(2), and one Rh(4) atom. In the eleventh O site, O(11) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Rh(2), and one Rh(4) atom. In the twelfth O site, O(12) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), one Rh(1), and one Rh(3) atom.