LiMg6Hf crystallizes in the orthorhombic Amm2 space group. Li(1) is bonded to two equivalent Mg(2); four Mg(1,1); four equivalent Mg(3); and two equivalent Hf(1) atoms to form LiHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Li2Mg10 cuboctahedra; corners with six equivalent Li(1)Hf2Mg10 cuboctahedra; corners with eight Mg(1,1)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Li2Mg10 cuboctahedra; edges with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Li2Mg10 cuboctahedra; edges with eight equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; faces with two equivalent Li(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Hf(1)Li2Mg10 cuboctahedra; faces with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Li(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Hf(1) atoms to form distorted MgLi2Hf2Mg8 cuboctahedra that share corners with four equivalent Li(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(2)Li2Mg10 cuboctahedra; corners with ten Mg(1,1)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Li(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(1)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Li2Mg10 cuboctahedra; faces with two equivalent Li(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Hf(1)Li2Mg10 cuboctahedra; faces with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; and faces with eight equivalent Mg(3)Li2Hf2Mg8 cuboctahedra. In the second Mg site, Mg(1) is bonded to two equivalent Li(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Hf(1) atoms to form distorted MgLi2Hf2Mg8 cuboctahedra that share corners with four equivalent Li(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(2)Li2Mg10 cuboctahedra; corners with ten Mg(1,1)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Li(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(1)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Li2Mg10 cuboctahedra; faces with two equivalent Li(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Hf(1)Li2Mg10 cuboctahedra; faces with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; and faces with eight equivalent Mg(3)Li2Hf2Mg8 cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Li(1); two equivalent Mg(4); four Mg(1,1); and four equivalent Mg(3) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Li(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Li2Mg10 cuboctahedra; corners with eight Mg(1,1)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Li(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; edges with eight equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; faces with two equivalent Li(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; and faces with six equivalent Hf(1)Li2Mg10 cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Li(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Hf(1) atoms to form distorted MgLi2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Li2Mg10 cuboctahedra; corners with ten equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Li2Mg10 cuboctahedra; edges with four equivalent Li(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(1)Li2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Li(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Hf(1)Li2Mg10 cuboctahedra; faces with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; and faces with eight Mg(1,1)Li2Hf2Mg8 cuboctahedra. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four equivalent Mg(3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Li2Mg10 cuboctahedra; corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Li2Mg10 cuboctahedra; edges with eight Mg(1,1)Li2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Hf(1)Li2Mg10 cuboctahedra; faces with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; and faces with six equivalent Li(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Li(1); two equivalent Mg(4); four Mg(1,1); and four equivalent Mg(3) atoms to form HfLi2Mg10 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with six equivalent Hf(1)Li2Mg10 cuboctahedra; corners with eight equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Li(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with eight Mg(1,1)Li2Hf2Mg8 cuboctahedra; faces with two equivalent Li(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Li2Mg10 cuboctahedra; faces with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(2)Li2Mg10 cuboctahedra.
LiMg6Hf crystallizes in the orthorhombic Amm2 space group. Li(1) is bonded to two equivalent Mg(2); four Mg(1,1); four equivalent Mg(3); and two equivalent Hf(1) atoms to form LiHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Li2Mg10 cuboctahedra; corners with six equivalent Li(1)Hf2Mg10 cuboctahedra; corners with eight Mg(1,1)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Li2Mg10 cuboctahedra; edges with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Li2Mg10 cuboctahedra; edges with eight equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; faces with two equivalent Li(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Hf(1)Li2Mg10 cuboctahedra; faces with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. Both Li(1)-Mg(2) bond lengths are 3.17 Å. There are two shorter (3.14 Å) and two longer (3.22 Å) Li(1)-Mg(1,1) bond lengths. All Li(1)-Mg(3) bond lengths are 3.12 Å. Both Li(1)-Hf(1) bond lengths are 3.13 Å. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Li(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Hf(1) atoms to form distorted MgLi2Hf2Mg8 cuboctahedra that share corners with four equivalent Li(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(2)Li2Mg10 cuboctahedra; corners with ten Mg(1,1)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Li(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(1)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Li2Mg10 cuboctahedra; faces with two equivalent Li(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Hf(1)Li2Mg10 cuboctahedra; faces with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; and faces with eight equivalent Mg(3)Li2Hf2Mg8 cuboctahedra. There is one shorter (3.11 Å) and one longer (3.22 Å) Mg(1)-Mg(1) bond length. Both Mg(1)-Mg(2) bond lengths are 3.18 Å. Both Mg(1)-Mg(3) bond lengths are 3.14 Å. Both Mg(1)-Mg(4) bond lengths are 3.13 Å. Both Mg(1)-Hf(1) bond lengths are 3.10 Å. In the second Mg site, Mg(1) is bonded to two equivalent Li(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Hf(1) atoms to form distorted MgLi2Hf2Mg8 cuboctahedra that share corners with four equivalent Li(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(2)Li2Mg10 cuboctahedra; corners with ten Mg(1,1)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Li(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(1)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Li2Mg10 cuboctahedra; faces with two equivalent Li(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Hf(1)Li2Mg10 cuboctahedra; faces with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; and faces with eight equivalent Mg(3)Li2Hf2Mg8 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.18 Å. Both Mg(1)-Mg(3) bond lengths are 3.14 Å. Both Mg(1)-Mg(4) bond lengths are 3.13 Å. Both Mg(1)-Hf(1) bond lengths are 3.10 Å. In the third Mg site, Mg(2) is bonded to two equivalent Li(1); two equivalent Mg(4); four Mg(1,1); and four equivalent Mg(3) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Li(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Li2Mg10 cuboctahedra; corners with eight Mg(1,1)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Li(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; edges with eight equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; faces with two equivalent Li(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; and faces with six equivalent Hf(1)Li2Mg10 cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.14 Å. All Mg(2)-Mg(3) bond lengths are 3.14 Å. In the fourth Mg site, Mg(3) is bonded to two equivalent Li(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Hf(1) atoms to form distorted MgLi2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Li2Mg10 cuboctahedra; corners with ten equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Li2Mg10 cuboctahedra; edges with four equivalent Li(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(1)Li2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Li(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Hf(1)Li2Mg10 cuboctahedra; faces with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; and faces with eight Mg(1,1)Li2Hf2Mg8 cuboctahedra. There is one shorter (3.11 Å) and one longer (3.22 Å) Mg(3)-Mg(3) bond length. There is one shorter (3.14 Å) and one longer (3.22 Å) Mg(3)-Mg(4) bond length. Both Mg(3)-Hf(1) bond lengths are 3.18 Å. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four equivalent Mg(3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Li2Mg10 cuboctahedra; corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Li2Mg10 cuboctahedra; edges with eight Mg(1,1)Li2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Li2Mg10 cuboctahedra; faces with two equivalent Hf(1)Li2Mg10 cuboctahedra; faces with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; and faces with six equivalent Li(1)Hf2Mg10 cuboctahedra. Both Mg(4)-Hf(1) bond lengths are 3.17 Å. Hf(1) is bonded to two equivalent Li(1); two equivalent Mg(4); four Mg(1,1); and four equivalent Mg(3) atoms to form HfLi2Mg10 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with six equivalent Hf(1)Li2Mg10 cuboctahedra; corners with eight equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Li(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; edges with eight Mg(1,1)Li2Hf2Mg8 cuboctahedra; faces with two equivalent Li(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Li2Mg10 cuboctahedra; faces with four Mg(1,1)Li2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(3)Li2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(2)Li2Mg10 cuboctahedra.