Ba3MgTiWO9 is (Cubic) Perovskite-derived structured and crystallizes in the hexagonal P6_3mc space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(1), three equivalent O(3), and six equivalent O(2) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Ti(1)O6 octahedra, faces with three equivalent Ba(3)O12 cuboctahedra, faces with four equivalent Ba(2)O12 cuboctahedra,  a faceface with one Ti(1)O6 octahedra, faces with three equivalent Mg(1)O6 octahedra, and faces with three equivalent W(1)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. In the second Ba site, Ba(2) is bonded to three equivalent O(1), three equivalent O(2), and six equivalent O(3) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra, corners with three equivalent W(1)O6 octahedra, faces with three equivalent Ba(3)O12 cuboctahedra, faces with four equivalent Ba(1)O12 cuboctahedra,  a faceface with one W(1)O6 octahedra, faces with three equivalent Mg(1)O6 octahedra, and faces with three equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles are 10°. In the third Ba site, Ba(3) is bonded to three equivalent O(2), three equivalent O(3), and six equivalent O(1) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Ba(2)O12 cuboctahedra, corners with six equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, faces with two equivalent Mg(1)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with three equivalent W(1)O6 octahedra. Mg(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form MgO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent W(1)O6 octahedra, faces with two equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 4-8°. Ti(1) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form distorted TiO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Mg(1)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one W(1)O6 octahedra. The corner-sharing octahedral tilt angles are 8°. W(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form WO6 octahedra that share corners with three equivalent Ba(2)O12 cuboctahedra, corners with three equivalent Mg(1)O6 octahedra,  a faceface with one Ba(2)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles are 4°. There are three inequivalent O sites. In the first O site, O(1) is bonded to one Ba(1), one Ba(2), two equivalent Ba(3), one Ti(1), and one W(1) atom to form a mixture of distorted face and corner-sharing OBa4TiW octahedra. The corner-sharing octahedral tilt angles range from 8-60°. In the second O site, O(2) is bonded in a distorted linear geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Mg(1), and one W(1) atom. In the third O site, O(3) is bonded in a distorted linear geometry to one Ba(1), one Ba(3), two equivalent Ba(2), one Mg(1), and one Ti(1) atom.
Ba3MgTiWO9 is (Cubic) Perovskite-derived structured and crystallizes in the hexagonal P6_3mc space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(1), three equivalent O(3), and six equivalent O(2) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Ti(1)O6 octahedra, faces with three equivalent Ba(3)O12 cuboctahedra, faces with four equivalent Ba(2)O12 cuboctahedra,  a faceface with one Ti(1)O6 octahedra, faces with three equivalent Mg(1)O6 octahedra, and faces with three equivalent W(1)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. All Ba(1)-O(1) bond lengths are 2.88 Å. All Ba(1)-O(3) bond lengths are 3.05 Å. All Ba(1)-O(2) bond lengths are 2.94 Å. In the second Ba site, Ba(2) is bonded to three equivalent O(1), three equivalent O(2), and six equivalent O(3) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra, corners with three equivalent W(1)O6 octahedra, faces with three equivalent Ba(3)O12 cuboctahedra, faces with four equivalent Ba(1)O12 cuboctahedra,  a faceface with one W(1)O6 octahedra, faces with three equivalent Mg(1)O6 octahedra, and faces with three equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles are 10°. All Ba(2)-O(1) bond lengths are 2.93 Å. All Ba(2)-O(2) bond lengths are 3.10 Å. All Ba(2)-O(3) bond lengths are 2.94 Å. In the third Ba site, Ba(3) is bonded to three equivalent O(2), three equivalent O(3), and six equivalent O(1) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Ba(2)O12 cuboctahedra, corners with six equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, faces with two equivalent Mg(1)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with three equivalent W(1)O6 octahedra. All Ba(3)-O(2) bond lengths are 3.00 Å. All Ba(3)-O(3) bond lengths are 2.90 Å. All Ba(3)-O(1) bond lengths are 2.94 Å. Mg(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form MgO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent W(1)O6 octahedra, faces with two equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 4-8°. All Mg(1)-O(2) bond lengths are 2.17 Å. All Mg(1)-O(3) bond lengths are 2.11 Å. Ti(1) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form distorted TiO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Mg(1)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one W(1)O6 octahedra. The corner-sharing octahedral tilt angles are 8°. All Ti(1)-O(1) bond lengths are 2.22 Å. All Ti(1)-O(3) bond lengths are 1.84 Å. W(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form WO6 octahedra that share corners with three equivalent Ba(2)O12 cuboctahedra, corners with three equivalent Mg(1)O6 octahedra,  a faceface with one Ba(2)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles are 4°. All W(1)-O(1) bond lengths are 1.99 Å. All W(1)-O(2) bond lengths are 1.93 Å. There are three inequivalent O sites. In the first O site, O(1) is bonded to one Ba(1), one Ba(2), two equivalent Ba(3), one Ti(1), and one W(1) atom to form a mixture of distorted face and corner-sharing OBa4TiW octahedra. The corner-sharing octahedral tilt angles range from 8-60°. In the second O site, O(2) is bonded in a distorted linear geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Mg(1), and one W(1) atom. In the third O site, O(3) is bonded in a distorted linear geometry to one Ba(1), one Ba(3), two equivalent Ba(2), one Mg(1), and one Ti(1) atom.