Li4Mg crystallizes in the trigonal R-3m space group. There are six inequivalent Li sites. In the first Li site, Li(1) is bonded to three equivalent Li(2), six equivalent Li(1), and three equivalent Mg(1) atoms to form LiLi9Mg3 cuboctahedra that share corners with three equivalent Li(2)Li12 cuboctahedra; corners with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with six equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine Li(2,2)Li12 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; faces with six equivalent Li(2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with six equivalent Mg(1)Li6Mg6 cuboctahedra. In the second Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. In the third Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. In the fourth Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. In the fifth Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. In the sixth Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. Mg(1) is bonded to six equivalent Li(1) and six equivalent Mg(1) atoms to form MgLi6Mg6 cuboctahedra that share corners with six Li(2,2)Li12 cuboctahedra; corners with six equivalent Mg(1)Li6Mg6 cuboctahedra; edges with six Li(2,2)Li12 cuboctahedra; edges with six equivalent Mg(1)Li6Mg6 cuboctahedra; edges with twelve equivalent Li(1)Li9Mg3 cuboctahedra; faces with six equivalent Mg(1)Li6Mg6 cuboctahedra; and faces with twelve equivalent Li(1)Li9Mg3 cuboctahedra.
Li4Mg crystallizes in the trigonal R-3m space group. There are six inequivalent Li sites. In the first Li site, Li(1) is bonded to three equivalent Li(2), six equivalent Li(1), and three equivalent Mg(1) atoms to form LiLi9Mg3 cuboctahedra that share corners with three equivalent Li(2)Li12 cuboctahedra; corners with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with six equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine Li(2,2)Li12 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; faces with six equivalent Li(2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with six equivalent Mg(1)Li6Mg6 cuboctahedra. All Li(1)-Li(2) bond lengths are 3.11 Å. All Li(1)-Li(1) bond lengths are 3.07 Å. All Li(1)-Mg(1) bond lengths are 3.11 Å. In the second Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. There are six shorter (3.07 Å) and three longer (3.11 Å) Li(2)-Li(2,2) bond lengths. In the third Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. All Li(2)-Li(1) bond lengths are 3.11 Å. All Li(2)-Li(2) bond lengths are 3.07 Å. In the fourth Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. All Li(2)-Li(1) bond lengths are 3.11 Å. There are six shorter (3.07 Å) and three longer (3.11 Å) Li(2)-Li(2,2) bond lengths. In the fifth Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. All Li(2)-Li(1) bond lengths are 3.11 Å. There are six shorter (3.07 Å) and three longer (3.11 Å) Li(2)-Li(2,2) bond lengths. In the sixth Li site, Li(2) is bonded to three equivalent Li(1) and nine Li(2,2) atoms to form LiLi12 cuboctahedra that share corners with three equivalent Li(1)Li9Mg3 cuboctahedra; corners with three equivalent Mg(1)Li6Mg6 cuboctahedra; corners with six equivalent Li(2)Li12 cuboctahedra; edges with three equivalent Mg(1)Li6Mg6 cuboctahedra; edges with nine equivalent Li(1)Li9Mg3 cuboctahedra; edges with twelve Li(2,2)Li12 cuboctahedra; faces with six equivalent Li(1)Li9Mg3 cuboctahedra; and faces with twelve Li(2,2)Li12 cuboctahedra. All Li(2)-Li(1) bond lengths are 3.11 Å. All Li(2)-Li(2) bond lengths are 3.07 Å. Mg(1) is bonded to six equivalent Li(1) and six equivalent Mg(1) atoms to form MgLi6Mg6 cuboctahedra that share corners with six Li(2,2)Li12 cuboctahedra; corners with six equivalent Mg(1)Li6Mg6 cuboctahedra; edges with six Li(2,2)Li12 cuboctahedra; edges with six equivalent Mg(1)Li6Mg6 cuboctahedra; edges with twelve equivalent Li(1)Li9Mg3 cuboctahedra; faces with six equivalent Mg(1)Li6Mg6 cuboctahedra; and faces with twelve equivalent Li(1)Li9Mg3 cuboctahedra. All Mg(1)-Mg(1) bond lengths are 3.07 Å.