NaMg6Hf crystallizes in the orthorhombic Amm2 space group. Na(1) is bonded to two equivalent Mg(3), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(2) atoms to form NaMg12 cuboctahedra that share corners with four equivalent Na(1)Mg12 cuboctahedra, corners with eight equivalent Hf(1)Mg12 cuboctahedra, edges with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Na(1)Mg12 cuboctahedra, faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, and faces with four equivalent Hf(1)Mg12 cuboctahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Na(1), two equivalent Mg(3), two equivalent Mg(4), four equivalent Mg(2), and two equivalent Hf(1) atoms to form distorted MgNa2Hf2Mg8 cuboctahedra that share corners with twelve equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Na(1)Mg12 cuboctahedra, edges with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Hf(1)Mg12 cuboctahedra, edges with eight equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Na(1)Mg12 cuboctahedra, faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(1)Na2Hf2Mg8 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Na(1), two equivalent Mg(3), two equivalent Mg(4), four equivalent Mg(1), and two equivalent Hf(1) atoms to form distorted MgNa2Hf2Mg8 cuboctahedra that share corners with twelve equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Na(1)Mg12 cuboctahedra, edges with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Hf(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Na(1)Mg12 cuboctahedra, faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(2)Na2Hf2Mg8 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Na(1), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form distorted MgNa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, corners with eight equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Na(1)Mg12 cuboctahedra, edges with four equivalent Hf(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Na(1)Mg12 cuboctahedra, faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, and faces with four equivalent Mg(4)Na2Hf2Mg8 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Na(1), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form MgNa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, corners with eight equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Na(1)Mg12 cuboctahedra, edges with four equivalent Hf(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Na(1)Mg12 cuboctahedra, faces with two equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, and faces with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra. Hf(1) is bonded to two equivalent Mg(3), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(2) atoms to form HfMg12 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra, corners with eight equivalent Na(1)Mg12 cuboctahedra, edges with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Na(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, and faces with four equivalent Mg(2)Na2Hf2Mg8 cuboctahedra.
NaMg6Hf crystallizes in the orthorhombic Amm2 space group. Na(1) is bonded to two equivalent Mg(3), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(2) atoms to form NaMg12 cuboctahedra that share corners with four equivalent Na(1)Mg12 cuboctahedra, corners with eight equivalent Hf(1)Mg12 cuboctahedra, edges with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Na(1)Mg12 cuboctahedra, faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, and faces with four equivalent Hf(1)Mg12 cuboctahedra. Both Na(1)-Mg(3) bond lengths are 3.31 Å. Both Na(1)-Mg(4) bond lengths are 3.50 Å. There are two shorter (3.19 Å) and two longer (3.25 Å) Na(1)-Mg(1) bond lengths. All Na(1)-Mg(2) bond lengths are 3.21 Å. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Na(1), two equivalent Mg(3), two equivalent Mg(4), four equivalent Mg(2), and two equivalent Hf(1) atoms to form distorted MgNa2Hf2Mg8 cuboctahedra that share corners with twelve equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Na(1)Mg12 cuboctahedra, edges with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Hf(1)Mg12 cuboctahedra, edges with eight equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Na(1)Mg12 cuboctahedra, faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(1)Na2Hf2Mg8 cuboctahedra. Both Mg(1)-Mg(3) bond lengths are 3.22 Å. Both Mg(1)-Mg(4) bond lengths are 3.14 Å. There are two shorter (3.25 Å) and two longer (3.27 Å) Mg(1)-Mg(2) bond lengths. There is one shorter (3.21 Å) and one longer (3.23 Å) Mg(1)-Hf(1) bond length. In the second Mg site, Mg(2) is bonded to two equivalent Na(1), two equivalent Mg(3), two equivalent Mg(4), four equivalent Mg(1), and two equivalent Hf(1) atoms to form distorted MgNa2Hf2Mg8 cuboctahedra that share corners with twelve equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Na(1)Mg12 cuboctahedra, edges with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Hf(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Na(1)Mg12 cuboctahedra, faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(2)Na2Hf2Mg8 cuboctahedra. There is one shorter (3.06 Å) and one longer (3.38 Å) Mg(2)-Mg(3) bond length. There is one shorter (3.04 Å) and one longer (3.40 Å) Mg(2)-Mg(4) bond length. Both Mg(2)-Hf(1) bond lengths are 3.15 Å. In the third Mg site, Mg(3) is bonded to two equivalent Na(1), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form distorted MgNa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, corners with eight equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Na(1)Mg12 cuboctahedra, edges with four equivalent Hf(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Na(1)Mg12 cuboctahedra, faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, and faces with four equivalent Mg(4)Na2Hf2Mg8 cuboctahedra. Both Mg(3)-Hf(1) bond lengths are 3.11 Å. In the fourth Mg site, Mg(4) is bonded to two equivalent Na(1), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form MgNa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, corners with eight equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Na(1)Mg12 cuboctahedra, edges with four equivalent Hf(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Na(1)Mg12 cuboctahedra, faces with two equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, and faces with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra. Both Mg(4)-Hf(1) bond lengths are 3.13 Å. Hf(1) is bonded to two equivalent Mg(3), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(2) atoms to form HfMg12 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra, corners with eight equivalent Na(1)Mg12 cuboctahedra, edges with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(2)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Na2Hf2Mg8 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Na(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Na2Hf2Mg8 cuboctahedra, and faces with four equivalent Mg(2)Na2Hf2Mg8 cuboctahedra.