Ba3MgNb2O9 is (Cubic) Perovskite-derived structured and crystallizes in the trigonal P-3m1 space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to six equivalent O(1) and six equivalent O(2) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra, faces with six equivalent Ba(2)O12 cuboctahedra, faces with two equivalent Mg(1)O6 octahedra, and faces with six equivalent Nb(1)O6 octahedra. In the second Ba site, Ba(2) is bonded to three equivalent O(2) and nine equivalent O(1) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with nine equivalent Ba(2)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, faces with three equivalent Mg(1)O6 octahedra, and faces with five equivalent Nb(1)O6 octahedra. Mg(1) is bonded to six equivalent O(1) atoms to form MgO6 octahedra that share corners with six equivalent Nb(1)O6 octahedra, faces with two equivalent Ba(1)O12 cuboctahedra, and faces with six equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 3°. Nb(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form NbO6 octahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Nb(1)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and faces with five equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-3°. There are two inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to one Ba(1), three equivalent Ba(2), one Mg(1), and one Nb(1) atom. In the second O site, O(2) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Nb(1) atoms to form a mixture of distorted corner and face-sharing OBa4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 0-60°.
Ba3MgNb2O9 is (Cubic) Perovskite-derived structured and crystallizes in the trigonal P-3m1 space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to six equivalent O(1) and six equivalent O(2) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra, faces with six equivalent Ba(2)O12 cuboctahedra, faces with two equivalent Mg(1)O6 octahedra, and faces with six equivalent Nb(1)O6 octahedra. All Ba(1)-O(1) bond lengths are 2.92 Å. All Ba(1)-O(2) bond lengths are 2.93 Å. In the second Ba site, Ba(2) is bonded to three equivalent O(2) and nine equivalent O(1) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with nine equivalent Ba(2)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, faces with three equivalent Mg(1)O6 octahedra, and faces with five equivalent Nb(1)O6 octahedra. All Ba(2)-O(2) bond lengths are 2.93 Å. There are six shorter (2.93 Å) and three longer (2.96 Å) Ba(2)-O(1) bond lengths. Mg(1) is bonded to six equivalent O(1) atoms to form MgO6 octahedra that share corners with six equivalent Nb(1)O6 octahedra, faces with two equivalent Ba(1)O12 cuboctahedra, and faces with six equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 3°. All Mg(1)-O(1) bond lengths are 2.14 Å. Nb(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form NbO6 octahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Nb(1)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and faces with five equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-3°. All Nb(1)-O(1) bond lengths are 1.96 Å. All Nb(1)-O(2) bond lengths are 2.13 Å. There are two inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to one Ba(1), three equivalent Ba(2), one Mg(1), and one Nb(1) atom. In the second O site, O(2) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Nb(1) atoms to form a mixture of distorted corner and face-sharing OBa4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 0-60°.