LaBa4Nb3TiO15 crystallizes in the trigonal P3m1 space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(1), three equivalent O(5), and six equivalent O(4) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(2)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra,  a faceface with one Ba(3)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 three equivalent Nb(3)O6 octahedra. In the second Ba site, Ba(2) is bonded to three equivalent O(2), three equivalent O(5), and six equivalent O(3) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(4)O12 cuboctahedra,  a faceface with one Ti(1)O6 octahedra, faces with three equivalent Nb(1)O6 octahedra, and faces with three equivalent Nb(2)O6 octahedra. In the third Ba site, Ba(3) 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(4)O12 cuboctahedra, corners with six equivalent Ba(3)O12 cuboctahedra, corners with three equivalent Nb(3)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra,  a faceface with one Nb(1)O6 octahedra, and faces with three equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles are 25°. In the fourth Ba site, Ba(4) is bonded to three equivalent O(3), three equivalent O(4), and six equivalent O(5) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with six equivalent Ba(4)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra,  a faceface with one Nb(2)O6 octahedra,  a faceface with one Nb(3)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with three equivalent Nb(1)O6 octahedra. La(1) is bonded in a 3-coordinate geometry to three equivalent O(2) atoms. Ti(1) is bonded to three equivalent O(4) and three equivalent O(5) atoms to form TiO6 octahedra that share corners with three equivalent Nb(1)O6 octahedra, corners with three equivalent Nb(3)O6 octahedra,  a faceface with one Ba(2)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(4)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 6-10°. There are three inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to three equivalent O(3) and three equivalent O(5) 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,  a faceface with one Ba(3)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, and faces with three equivalent Ba(4)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 2-6°. In the second Nb site, Nb(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form NbO6 octahedra that share corners with three equivalent Nb(1)O6 octahedra,  a faceface with one Ba(4)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, and faces with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 2°. In the third Nb site, Nb(3) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form NbO6 octahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with three equivalent Ti(1)O6 octahedra,  a faceface with one Ba(4)O12 cuboctahedra, and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 10°. There are five inequivalent O sites. In the first O site, O(1) is bonded in a distorted single-bond geometry to one Ba(1), one Ba(3), and one Nb(3) atom. In the second O site, O(2) is bonded in a 5-coordinate geometry to one Ba(2), two equivalent Ba(3), one La(1), and one Nb(2) atom. In the third O site, O(3) is bonded in a distorted linear geometry to one Ba(3), one Ba(4), two equivalent Ba(2), one Nb(1), and one Nb(2) atom. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to one Ba(4), two equivalent Ba(1), one Ti(1), and one Nb(3) atom. In the fifth O site, O(5) is bonded to one Ba(1), one Ba(2), two equivalent Ba(4), one Ti(1), and one Nb(1) atom to form a mixture of distorted face and corner-sharing OBa4TiNb octahedra. The corner-sharing octahedral tilt angles range from 2-60°.
LaBa4Nb3TiO15 crystallizes in the trigonal P3m1 space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(1), three equivalent O(5), and six equivalent O(4) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(2)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra,  a faceface with one Ba(3)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 three equivalent Nb(3)O6 octahedra. All Ba(1)-O(1) bond lengths are 2.74 Å. All Ba(1)-O(5) bond lengths are 2.99 Å. All Ba(1)-O(4) bond lengths are 2.91 Å. In the second Ba site, Ba(2) is bonded to three equivalent O(2), three equivalent O(5), and six equivalent O(3) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(4)O12 cuboctahedra,  a faceface with one Ti(1)O6 octahedra, faces with three equivalent Nb(1)O6 octahedra, and faces with three equivalent Nb(2)O6 octahedra. All Ba(2)-O(2) bond lengths are 2.85 Å. All Ba(2)-O(5) bond lengths are 2.89 Å. All Ba(2)-O(3) bond lengths are 2.91 Å. In the third Ba site, Ba(3) 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(4)O12 cuboctahedra, corners with six equivalent Ba(3)O12 cuboctahedra, corners with three equivalent Nb(3)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra,  a faceface with one Nb(1)O6 octahedra, and faces with three equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles are 25°. All Ba(3)-O(1) bond lengths are 2.80 Å. All Ba(3)-O(3) bond lengths are 3.00 Å. All Ba(3)-O(2) bond lengths are 2.91 Å. In the fourth Ba site, Ba(4) is bonded to three equivalent O(3), three equivalent O(4), and six equivalent O(5) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with six equivalent Ba(4)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra,  a faceface with one Nb(2)O6 octahedra,  a faceface with one Nb(3)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with three equivalent Nb(1)O6 octahedra. All Ba(4)-O(3) bond lengths are 2.92 Å. All Ba(4)-O(4) bond lengths are 2.85 Å. All Ba(4)-O(5) bond lengths are 2.91 Å. La(1) is bonded in a 3-coordinate geometry to three equivalent O(2) atoms. All La(1)-O(2) bond lengths are 2.43 Å. Ti(1) is bonded to three equivalent O(4) and three equivalent O(5) atoms to form TiO6 octahedra that share corners with three equivalent Nb(1)O6 octahedra, corners with three equivalent Nb(3)O6 octahedra,  a faceface with one Ba(2)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(4)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 6-10°. All Ti(1)-O(4) bond lengths are 1.88 Å. All Ti(1)-O(5) bond lengths are 2.20 Å. There are three inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to three equivalent O(3) and three equivalent O(5) 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,  a faceface with one Ba(3)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, and faces with three equivalent Ba(4)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 2-6°. All Nb(1)-O(3) bond lengths are 2.09 Å. All Nb(1)-O(5) bond lengths are 1.99 Å. In the second Nb site, Nb(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form NbO6 octahedra that share corners with three equivalent Nb(1)O6 octahedra,  a faceface with one Ba(4)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, and faces with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 2°. All Nb(2)-O(2) bond lengths are 1.94 Å. All Nb(2)-O(3) bond lengths are 2.16 Å. In the third Nb site, Nb(3) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form NbO6 octahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with three equivalent Ti(1)O6 octahedra,  a faceface with one Ba(4)O12 cuboctahedra, and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 10°. All Nb(3)-O(1) bond lengths are 1.88 Å. All Nb(3)-O(4) bond lengths are 2.25 Å. There are five inequivalent O sites. In the first O site, O(1) is bonded in a distorted single-bond geometry to one Ba(1), one Ba(3), and one Nb(3) atom. In the second O site, O(2) is bonded in a 5-coordinate geometry to one Ba(2), two equivalent Ba(3), one La(1), and one Nb(2) atom. In the third O site, O(3) is bonded in a distorted linear geometry to one Ba(3), one Ba(4), two equivalent Ba(2), one Nb(1), and one Nb(2) atom. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to one Ba(4), two equivalent Ba(1), one Ti(1), and one Nb(3) atom. In the fifth O site, O(5) is bonded to one Ba(1), one Ba(2), two equivalent Ba(4), one Ti(1), and one Nb(1) atom to form a mixture of distorted face and corner-sharing OBa4TiNb octahedra. The corner-sharing octahedral tilt angles range from 2-60°.