Ba3MgCr2O8 crystallizes in the triclinic P1 space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 10-coordinate geometry to one O(1), one O(6), one O(7), one O(8), two equivalent O(3), two equivalent O(4), and two equivalent O(5) atoms. In the second Ba site, Ba(2) is bonded in a 10-coordinate geometry to one O(2), one O(3), one O(4), one O(5), two equivalent O(6), two equivalent O(7), and two equivalent O(8) atoms. In the third Ba site, Ba(3) is bonded in a 12-coordinate geometry to one O(3), one O(4), one O(5), one O(6), one O(7), one O(8), three equivalent O(1), and three equivalent O(2) atoms. Mg(1) is bonded to one O(3), one O(4), one O(5), one O(6), one O(7), and one O(8) atom to form distorted MgO6 octahedra that share  a faceface with one Cr(1)O4 trigonal pyramid and  a faceface with one Cr(2)O4 trigonal pyramid. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(1), one O(6), one O(7), and one O(8) atom to form distorted CrO4 trigonal pyramids that share  a faceface with one Mg(1)O6 octahedra. In the second Cr site, Cr(2) is bonded to one O(2), one O(3), one O(4), and one O(5) atom to form distorted CrO4 trigonal pyramids that share  a faceface with one Mg(1)O6 octahedra. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to one Ba(1), three equivalent Ba(3), and one Cr(1) atom. In the second O site, O(2) is bonded in a distorted linear geometry to one Ba(2), three equivalent Ba(3), and one Cr(2) atom. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Mg(1), and one Cr(2) atom. In the fourth O site, O(4) is bonded in a 6-coordinate geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Mg(1), and one Cr(2) atom. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Mg(1), and one Cr(2) atom. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(3), two equivalent Ba(2), one Mg(1), and one Cr(1) atom. In the seventh O site, O(7) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(3), two equivalent Ba(2), one Mg(1), and one Cr(1) atom. In the eighth O site, O(8) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(3), two equivalent Ba(2), one Mg(1), and one Cr(1) atom.
Ba3MgCr2O8 crystallizes in the triclinic P1 space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 10-coordinate geometry to one O(1), one O(6), one O(7), one O(8), two equivalent O(3), two equivalent O(4), and two equivalent O(5) atoms. The Ba(1)-O(1) bond length is 2.55 Å. The Ba(1)-O(6) bond length is 2.94 Å. The Ba(1)-O(7) bond length is 2.95 Å. The Ba(1)-O(8) bond length is 2.95 Å. There is one shorter (3.00 Å) and one longer (3.01 Å) Ba(1)-O(3) bond length. There is one shorter (3.00 Å) and one longer (3.01 Å) Ba(1)-O(4) bond length. Both Ba(1)-O(5) bond lengths are 3.00 Å. In the second Ba site, Ba(2) is bonded in a 10-coordinate geometry to one O(2), one O(3), one O(4), one O(5), two equivalent O(6), two equivalent O(7), and two equivalent O(8) atoms. The Ba(2)-O(2) bond length is 2.55 Å. The Ba(2)-O(3) bond length is 2.94 Å. The Ba(2)-O(4) bond length is 2.95 Å. The Ba(2)-O(5) bond length is 2.94 Å. Both Ba(2)-O(6) bond lengths are 3.00 Å. There is one shorter (3.00 Å) and one longer (3.01 Å) Ba(2)-O(7) bond length. There is one shorter (3.00 Å) and one longer (3.01 Å) Ba(2)-O(8) bond length. In the third Ba site, Ba(3) is bonded in a 12-coordinate geometry to one O(3), one O(4), one O(5), one O(6), one O(7), one O(8), three equivalent O(1), and three equivalent O(2) atoms. The Ba(3)-O(3) bond length is 2.95 Å. The Ba(3)-O(4) bond length is 2.99 Å. The Ba(3)-O(5) bond length is 2.96 Å. The Ba(3)-O(6) bond length is 2.94 Å. The Ba(3)-O(7) bond length is 2.98 Å. The Ba(3)-O(8) bond length is 2.98 Å. There are a spread of Ba(3)-O(1) bond distances ranging from 3.31-3.49 Å. There are a spread of Ba(3)-O(2) bond distances ranging from 3.35-3.53 Å. Mg(1) is bonded to one O(3), one O(4), one O(5), one O(6), one O(7), and one O(8) atom to form distorted MgO6 octahedra that share  a faceface with one Cr(1)O4 trigonal pyramid and  a faceface with one Cr(2)O4 trigonal pyramid. The Mg(1)-O(3) bond length is 2.13 Å. The Mg(1)-O(4) bond length is 2.13 Å. The Mg(1)-O(5) bond length is 2.13 Å. The Mg(1)-O(6) bond length is 2.13 Å. The Mg(1)-O(7) bond length is 2.13 Å. The Mg(1)-O(8) bond length is 2.13 Å. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(1), one O(6), one O(7), and one O(8) atom to form distorted CrO4 trigonal pyramids that share  a faceface with one Mg(1)O6 octahedra. The Cr(1)-O(1) bond length is 1.72 Å. The Cr(1)-O(6) bond length is 1.84 Å. The Cr(1)-O(7) bond length is 1.84 Å. The Cr(1)-O(8) bond length is 1.84 Å. In the second Cr site, Cr(2) is bonded to one O(2), one O(3), one O(4), and one O(5) atom to form distorted CrO4 trigonal pyramids that share  a faceface with one Mg(1)O6 octahedra. The Cr(2)-O(2) bond length is 1.72 Å. The Cr(2)-O(3) bond length is 1.84 Å. The Cr(2)-O(4) bond length is 1.84 Å. The Cr(2)-O(5) bond length is 1.84 Å. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to one Ba(1), three equivalent Ba(3), and one Cr(1) atom. In the second O site, O(2) is bonded in a distorted linear geometry to one Ba(2), three equivalent Ba(3), and one Cr(2) atom. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Mg(1), and one Cr(2) atom. In the fourth O site, O(4) is bonded in a 6-coordinate geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Mg(1), and one Cr(2) atom. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Mg(1), and one Cr(2) atom. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(3), two equivalent Ba(2), one Mg(1), and one Cr(1) atom. In the seventh O site, O(7) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(3), two equivalent Ba(2), one Mg(1), and one Cr(1) atom. In the eighth O site, O(8) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(3), two equivalent Ba(2), one Mg(1), and one Cr(1) atom.