BaMg14Si crystallizes in the hexagonal P-6m2 space group. Ba(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form BaMg12 cuboctahedra that share corners with six equivalent Ba(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(1)Mg10Si2 cuboctahedra, edges with six equivalent Mg(2)Ba2Mg10 cuboctahedra, faces with two equivalent Si(1)Mg12 cuboctahedra, faces with six equivalent Mg(2)Ba2Mg10 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Si(1) atoms to form distorted MgMg10Si2 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Si2 cuboctahedra, corners with eight equivalent Mg(2)Ba2Mg10 cuboctahedra, edges with two equivalent Si(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Si2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Si(1)Mg12 cuboctahedra, and faces with four equivalent Mg(1)Mg10Si2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(2), and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Si(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Ba2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Mg10Si2 cuboctahedra, edges with two equivalent Ba(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with two equivalent Mg(1)Mg10Si2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with four equivalent Mg(2)Ba2Mg10 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to one Ba(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one Si(1) atom. In the fourth Mg site, Mg(4) is bonded to three equivalent Mg(1), three equivalent Mg(2), and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with six equivalent Mg(2)Ba2Mg10 cuboctahedra, edges with six equivalent Mg(1)Mg10Si2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Ba(1)Mg12 cuboctahedra, faces with three equivalent Mg(2)Ba2Mg10 cuboctahedra, faces with three equivalent Mg(1)Mg10Si2 cuboctahedra, and faces with three equivalent Si(1)Mg12 cuboctahedra. Si(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form distorted SiMg12 cuboctahedra that share corners with six equivalent Si(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(2)Ba2Mg10 cuboctahedra, edges with six equivalent Mg(1)Mg10Si2 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with six equivalent Mg(1)Mg10Si2 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra.
BaMg14Si crystallizes in the hexagonal P-6m2 space group. Ba(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form BaMg12 cuboctahedra that share corners with six equivalent Ba(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(1)Mg10Si2 cuboctahedra, edges with six equivalent Mg(2)Ba2Mg10 cuboctahedra, faces with two equivalent Si(1)Mg12 cuboctahedra, faces with six equivalent Mg(2)Ba2Mg10 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. All Ba(1)-Mg(2) bond lengths are 3.25 Å. All Ba(1)-Mg(3) bond lengths are 3.44 Å. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Si(1) atoms to form distorted MgMg10Si2 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Si2 cuboctahedra, corners with eight equivalent Mg(2)Ba2Mg10 cuboctahedra, edges with two equivalent Si(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Si2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Si(1)Mg12 cuboctahedra, and faces with four equivalent Mg(1)Mg10Si2 cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.31 Å. There are two shorter (3.17 Å) and two longer (3.33 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3) bond lengths are 3.10 Å. Both Mg(1)-Si(1) bond lengths are 3.25 Å. In the second Mg site, Mg(2) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(2), and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Si(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Ba2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Mg10Si2 cuboctahedra, edges with two equivalent Ba(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with two equivalent Mg(1)Mg10Si2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with four equivalent Mg(2)Ba2Mg10 cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.22 Å. There are two shorter (3.13 Å) and two longer (3.37 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(3) bond lengths are 3.42 Å. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to one Ba(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one Si(1) atom. Both Mg(3)-Mg(4) bond lengths are 3.26 Å. There are two shorter (3.24 Å) and two longer (3.26 Å) Mg(3)-Mg(3) bond lengths. The Mg(3)-Si(1) bond length is 3.09 Å. In the fourth Mg site, Mg(4) is bonded to three equivalent Mg(1), three equivalent Mg(2), and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with six equivalent Mg(2)Ba2Mg10 cuboctahedra, edges with six equivalent Mg(1)Mg10Si2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Ba(1)Mg12 cuboctahedra, faces with three equivalent Mg(2)Ba2Mg10 cuboctahedra, faces with three equivalent Mg(1)Mg10Si2 cuboctahedra, and faces with three equivalent Si(1)Mg12 cuboctahedra. Si(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form distorted SiMg12 cuboctahedra that share corners with six equivalent Si(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(2)Ba2Mg10 cuboctahedra, edges with six equivalent Mg(1)Mg10Si2 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with six equivalent Mg(1)Mg10Si2 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra.