Ba7Ti2Nb4O21 crystallizes in the trigonal R-3m space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) 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(4)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra,  a faceface with one Nb(2)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with three equivalent Nb(1)O6 octahedra. In the second Ba site, Ba(2) is bonded in a 12-coordinate geometry to three equivalent O(1) and nine equivalent O(3) atoms. In the third Ba site, Ba(3) is bonded to three equivalent O(1), three equivalent O(4), and six equivalent O(2) atoms to form BaO12 cuboctahedra that share corners with nine equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(4)O12 cuboctahedra,  a faceface with one Nb(1)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with four equivalent Nb(2)O6 octahedra. In the fourth Ba site, Ba(4) is bonded to six equivalent O(2) and six equivalent O(4) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(4)O12 cuboctahedra, faces with six equivalent Ba(3)O12 cuboctahedra, faces with two equivalent Ti(1)O6 octahedra, and faces with six equivalent Nb(2)O6 octahedra. Ti(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form TiO6 octahedra that share corners with three equivalent Nb(1)O6 octahedra, corners with three equivalent Nb(2)O6 octahedra,  a faceface with one Ba(4)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 8-12°. There are two inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form distorted NbO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra,  a faceface with one Ba(3)O12 cuboctahedra, and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 12°. In the second Nb site, Nb(2) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form NbO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Nb(2)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(4)O12 cuboctahedra, and faces with four equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-8°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 1-coordinate geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Ti(1), and one Nb(1) atom. In the second O site, O(2) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(4), two equivalent Ba(3), one Ti(1), and one Nb(2) atom. In the third O site, O(3) is bonded in a distorted single-bond geometry to one Ba(1), three equivalent Ba(2), and one Nb(1) atom. In the fourth O site, O(4) is bonded to two equivalent Ba(3), two equivalent Ba(4), and two equivalent Nb(2) atoms to form a mixture of distorted face and corner-sharing OBa4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 0-60°.
Ba7Ti2Nb4O21 crystallizes in the trigonal R-3m space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) 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(4)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra,  a faceface with one Nb(2)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with three equivalent Nb(1)O6 octahedra. All Ba(1)-O(2) bond lengths are 3.06 Å. All Ba(1)-O(3) bond lengths are 2.73 Å. All Ba(1)-O(1) bond lengths are 2.94 Å. In the second Ba site, Ba(2) is bonded in a 12-coordinate geometry to three equivalent O(1) and nine equivalent O(3) atoms. All Ba(2)-O(1) bond lengths are 3.23 Å. There are three shorter (2.81 Å) and six longer (2.96 Å) Ba(2)-O(3) bond lengths. In the third Ba site, Ba(3) is bonded to three equivalent O(1), three equivalent O(4), and six equivalent O(2) atoms to form BaO12 cuboctahedra that share corners with nine equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(4)O12 cuboctahedra,  a faceface with one Nb(1)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with four equivalent Nb(2)O6 octahedra. All Ba(3)-O(1) bond lengths are 2.83 Å. All Ba(3)-O(4) bond lengths are 2.98 Å. All Ba(3)-O(2) bond lengths are 2.93 Å. In the fourth Ba site, Ba(4) is bonded to six equivalent O(2) and six equivalent O(4) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(4)O12 cuboctahedra, faces with six equivalent Ba(3)O12 cuboctahedra, faces with two equivalent Ti(1)O6 octahedra, and faces with six equivalent Nb(2)O6 octahedra. All Ba(4)-O(2) bond lengths are 2.91 Å. All Ba(4)-O(4) bond lengths are 2.93 Å. Ti(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form TiO6 octahedra that share corners with three equivalent Nb(1)O6 octahedra, corners with three equivalent Nb(2)O6 octahedra,  a faceface with one Ba(4)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 8-12°. All Ti(1)-O(1) bond lengths are 1.87 Å. All Ti(1)-O(2) bond lengths are 2.24 Å. There are two inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form distorted NbO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra,  a faceface with one Ba(3)O12 cuboctahedra, and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 12°. All Nb(1)-O(1) bond lengths are 2.30 Å. All Nb(1)-O(3) bond lengths are 1.87 Å. In the second Nb site, Nb(2) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form NbO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Nb(2)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(4)O12 cuboctahedra, and faces with four equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-8°. All Nb(2)-O(2) bond lengths are 1.97 Å. All Nb(2)-O(4) bond lengths are 2.13 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 1-coordinate geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Ti(1), and one Nb(1) atom. In the second O site, O(2) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(4), two equivalent Ba(3), one Ti(1), and one Nb(2) atom. In the third O site, O(3) is bonded in a distorted single-bond geometry to one Ba(1), three equivalent Ba(2), and one Nb(1) atom. In the fourth O site, O(4) is bonded to two equivalent Ba(3), two equivalent Ba(4), and two equivalent Nb(2) atoms to form a mixture of distorted face and corner-sharing OBa4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 0-60°.