BaMg6Hf crystallizes in the tetragonal P4/mmm space group. Ba(1) is bonded to four equivalent Mg(1) and eight equivalent Mg(2) atoms to form BaMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra, corners with eight equivalent Hf(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, and faces with four equivalent Hf(1)Mg12 cuboctahedra. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Ba(1), eight equivalent Mg(2), and two equivalent Hf(1) atoms to form distorted MgBa2Hf2Mg8 cuboctahedra that share corners with twelve equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, edges with four equivalent Ba(1)Mg12 cuboctahedra, edges with four equivalent Hf(1)Mg12 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, and faces with six equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra. In the second Mg site, Mg(2) is bonded in a 10-coordinate geometry to two equivalent Ba(1), two equivalent Mg(2), four equivalent Mg(1), and two equivalent Hf(1) atoms. Hf(1) is bonded to four equivalent Mg(1) and eight equivalent Mg(2) atoms to form HfMg12 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra, corners with eight equivalent Ba(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Ba(1)Mg12 cuboctahedra, and faces with four equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra.
BaMg6Hf crystallizes in the tetragonal P4/mmm space group. Ba(1) is bonded to four equivalent Mg(1) and eight equivalent Mg(2) atoms to form BaMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra, corners with eight equivalent Hf(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, and faces with four equivalent Hf(1)Mg12 cuboctahedra. All Ba(1)-Mg(1) bond lengths are 3.35 Å. All Ba(1)-Mg(2) bond lengths are 3.56 Å. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Ba(1), eight equivalent Mg(2), and two equivalent Hf(1) atoms to form distorted MgBa2Hf2Mg8 cuboctahedra that share corners with twelve equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, edges with four equivalent Ba(1)Mg12 cuboctahedra, edges with four equivalent Hf(1)Mg12 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, and faces with six equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra. All Mg(1)-Mg(2) bond lengths are 3.37 Å. Both Mg(1)-Hf(1) bond lengths are 3.35 Å. In the second Mg site, Mg(2) is bonded in a 10-coordinate geometry to two equivalent Ba(1), two equivalent Mg(2), four equivalent Mg(1), and two equivalent Hf(1) atoms. Both Mg(2)-Mg(2) bond lengths are 2.96 Å. Both Mg(2)-Hf(1) bond lengths are 3.17 Å. Hf(1) is bonded to four equivalent Mg(1) and eight equivalent Mg(2) atoms to form HfMg12 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra, corners with eight equivalent Ba(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Ba(1)Mg12 cuboctahedra, and faces with four equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra.