Mg6AlSn crystallizes in the orthorhombic Amm2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Al(1), and two equivalent Sn(1) atoms to form distorted MgMg8Al2Sn2 cuboctahedra that share corners with four equivalent Al(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Mg10Al2 cuboctahedra; corners with ten equivalent Mg(1)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Mg(1)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Al(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(2)Mg8Al2Sn2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Sn2 cuboctahedra; faces with two equivalent Al(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Al2 cuboctahedra; faces with four equivalent Mg(1)Mg8Al2Sn2 cuboctahedra; and faces with eight Mg(2,2)Mg8Al2Sn2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Al(1), and two equivalent Sn(1) atoms to form distorted MgMg8Al2Sn2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Al2 cuboctahedra; corners with four equivalent Mg(4)Mg10Sn2 cuboctahedra; corners with ten Mg(2,2)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg10Al2 cuboctahedra; edges with two equivalent Mg(4)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg8Al2Sn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Al2Sn2 cuboctahedra; edges with four equivalent Al(1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Sn2 cuboctahedra; faces with two equivalent Al(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Al2 cuboctahedra; faces with four Mg(2,2)Mg8Al2Sn2 cuboctahedra; and faces with eight Mg(1,1)Mg8Al2Sn2 cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Al(1), and two equivalent Sn(1) atoms to form distorted MgMg8Al2Sn2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Al2 cuboctahedra; corners with four equivalent Mg(4)Mg10Sn2 cuboctahedra; corners with ten Mg(2,2)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg10Al2 cuboctahedra; edges with two equivalent Mg(4)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg8Al2Sn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Al2Sn2 cuboctahedra; edges with four equivalent Al(1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Sn2 cuboctahedra; faces with two equivalent Al(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Al2 cuboctahedra; faces with four Mg(2,2)Mg8Al2Sn2 cuboctahedra; and faces with eight equivalent Mg(1)Mg8Al2Sn2 cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(2,2); and two equivalent Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Sn2 cuboctahedra; corners with six equivalent Mg(3)Mg10Al2 cuboctahedra; corners with eight Mg(2,2)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Mg(4)Mg10Sn2 cuboctahedra; edges with four Mg(2,2)Mg8Al2Sn2 cuboctahedra; edges with four equivalent Al(1)Mg10Sn2 cuboctahedra; edges with eight Mg(1,1)Mg8Al2Sn2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Sn2 cuboctahedra; faces with two equivalent Al(1)Mg10Sn2 cuboctahedra; faces with four equivalent Mg(1)Mg8Al2Sn2 cuboctahedra; faces with four Mg(2,2)Mg8Al2Sn2 cuboctahedra; and faces with six equivalent Sn(1)Mg10Al2 cuboctahedra. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(3); four Mg(1,1); four Mg(2,2); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Al2 cuboctahedra; corners with six equivalent Mg(4)Mg10Sn2 cuboctahedra; corners with eight Mg(2,2)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four Mg(2,2)Mg8Al2Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg10Al2 cuboctahedra; edges with eight Mg(1,1)Mg8Al2Sn2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Al2 cuboctahedra; faces with four Mg(1,1)Mg8Al2Sn2 cuboctahedra; faces with four Mg(2,2)Mg8Al2Sn2 cuboctahedra; and faces with six equivalent Al(1)Mg10Sn2 cuboctahedra. In the sixth Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Al(1), and two equivalent Sn(1) atoms to form distorted MgMg8Al2Sn2 cuboctahedra that share corners with four equivalent Al(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Mg10Al2 cuboctahedra; corners with ten Mg(1,1)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Mg(1)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Al(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(2)Mg8Al2Sn2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Sn2 cuboctahedra; faces with two equivalent Al(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Al2 cuboctahedra; faces with four Mg(1,1)Mg8Al2Sn2 cuboctahedra; and faces with eight equivalent Mg(2)Mg8Al2Sn2 cuboctahedra. Al(1) is bonded to two equivalent Mg(3); four Mg(1,1); four equivalent Mg(2); and two equivalent Sn(1) atoms to form AlMg10Sn2 cuboctahedra that share corners with four equivalent Sn(1)Mg10Al2 cuboctahedra; corners with six equivalent Al(1)Mg10Sn2 cuboctahedra; corners with eight Mg(1,1)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four Mg(1,1)Mg8Al2Sn2 cuboctahedra; edges with eight Mg(2,2)Mg8Al2Sn2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Al(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Al2 cuboctahedra; faces with four Mg(1,1)Mg8Al2Sn2 cuboctahedra; faces with four equivalent Mg(2)Mg8Al2Sn2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Sn2 cuboctahedra. Sn(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(2,2); and two equivalent Al(1) atoms to form SnMg10Al2 cuboctahedra that share corners with four equivalent Al(1)Mg10Sn2 cuboctahedra; corners with six equivalent Sn(1)Mg10Al2 cuboctahedra; corners with eight Mg(1,1)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Al(1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(4)Mg10Sn2 cuboctahedra; edges with four Mg(1,1)Mg8Al2Sn2 cuboctahedra; edges with eight Mg(2,2)Mg8Al2Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Sn2 cuboctahedra; faces with two equivalent Al(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Al2 cuboctahedra; faces with four Mg(1,1)Mg8Al2Sn2 cuboctahedra; faces with four Mg(2,2)Mg8Al2Sn2 cuboctahedra; and faces with six equivalent Mg(3)Mg10Al2 cuboctahedra.
Mg6AlSn crystallizes in the orthorhombic Amm2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Al(1), and two equivalent Sn(1) atoms to form distorted MgMg8Al2Sn2 cuboctahedra that share corners with four equivalent Al(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Mg10Al2 cuboctahedra; corners with ten equivalent Mg(1)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Mg(1)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Al(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(2)Mg8Al2Sn2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Sn2 cuboctahedra; faces with two equivalent Al(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Al2 cuboctahedra; faces with four equivalent Mg(1)Mg8Al2Sn2 cuboctahedra; and faces with eight Mg(2,2)Mg8Al2Sn2 cuboctahedra. Both Mg(1)-Mg(1) bond lengths are 3.18 Å. Both Mg(1)-Mg(2) bond lengths are 3.16 Å. Both Mg(1)-Mg(3) bond lengths are 3.18 Å. Both Mg(1)-Mg(4) bond lengths are 3.18 Å. There is one shorter (3.12 Å) and one longer (3.13 Å) Mg(1)-Al(1) bond length. Both Mg(1)-Sn(1) bond lengths are 3.12 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Al(1), and two equivalent Sn(1) atoms to form distorted MgMg8Al2Sn2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Al2 cuboctahedra; corners with four equivalent Mg(4)Mg10Sn2 cuboctahedra; corners with ten Mg(2,2)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg10Al2 cuboctahedra; edges with two equivalent Mg(4)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg8Al2Sn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Al2Sn2 cuboctahedra; edges with four equivalent Al(1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Sn2 cuboctahedra; faces with two equivalent Al(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Al2 cuboctahedra; faces with four Mg(2,2)Mg8Al2Sn2 cuboctahedra; and faces with eight Mg(1,1)Mg8Al2Sn2 cuboctahedra. There is one shorter (3.11 Å) and one longer (3.25 Å) Mg(2)-Mg(2) bond length. There is one shorter (3.08 Å) and one longer (3.17 Å) Mg(2)-Mg(3) bond length. There is one shorter (3.10 Å) and one longer (3.15 Å) Mg(2)-Mg(4) bond length. Both Mg(2)-Al(1) bond lengths are 3.16 Å. Both Mg(2)-Sn(1) bond lengths are 3.19 Å. In the third Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Al(1), and two equivalent Sn(1) atoms to form distorted MgMg8Al2Sn2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Al2 cuboctahedra; corners with four equivalent Mg(4)Mg10Sn2 cuboctahedra; corners with ten Mg(2,2)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg10Al2 cuboctahedra; edges with two equivalent Mg(4)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg8Al2Sn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Al2Sn2 cuboctahedra; edges with four equivalent Al(1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Sn2 cuboctahedra; faces with two equivalent Al(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Al2 cuboctahedra; faces with four Mg(2,2)Mg8Al2Sn2 cuboctahedra; and faces with eight equivalent Mg(1)Mg8Al2Sn2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.16 Å. There is one shorter (3.08 Å) and one longer (3.17 Å) Mg(2)-Mg(3) bond length. There is one shorter (3.10 Å) and one longer (3.15 Å) Mg(2)-Mg(4) bond length. Both Mg(2)-Al(1) bond lengths are 3.16 Å. Both Mg(2)-Sn(1) bond lengths are 3.19 Å. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(2,2); and two equivalent Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Sn2 cuboctahedra; corners with six equivalent Mg(3)Mg10Al2 cuboctahedra; corners with eight Mg(2,2)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Mg(4)Mg10Sn2 cuboctahedra; edges with four Mg(2,2)Mg8Al2Sn2 cuboctahedra; edges with four equivalent Al(1)Mg10Sn2 cuboctahedra; edges with eight Mg(1,1)Mg8Al2Sn2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Sn2 cuboctahedra; faces with two equivalent Al(1)Mg10Sn2 cuboctahedra; faces with four equivalent Mg(1)Mg8Al2Sn2 cuboctahedra; faces with four Mg(2,2)Mg8Al2Sn2 cuboctahedra; and faces with six equivalent Sn(1)Mg10Al2 cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.18 Å. Both Mg(3)-Al(1) bond lengths are 3.14 Å. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(3); four Mg(1,1); four Mg(2,2); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Al2 cuboctahedra; corners with six equivalent Mg(4)Mg10Sn2 cuboctahedra; corners with eight Mg(2,2)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four Mg(2,2)Mg8Al2Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg10Al2 cuboctahedra; edges with eight Mg(1,1)Mg8Al2Sn2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Al2 cuboctahedra; faces with four Mg(1,1)Mg8Al2Sn2 cuboctahedra; faces with four Mg(2,2)Mg8Al2Sn2 cuboctahedra; and faces with six equivalent Al(1)Mg10Sn2 cuboctahedra. Both Mg(4)-Mg(1) bond lengths are 3.18 Å. Both Mg(4)-Sn(1) bond lengths are 3.17 Å. In the sixth Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Al(1), and two equivalent Sn(1) atoms to form distorted MgMg8Al2Sn2 cuboctahedra that share corners with four equivalent Al(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Mg10Al2 cuboctahedra; corners with ten Mg(1,1)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Mg(1)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Al(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(2)Mg8Al2Sn2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Sn2 cuboctahedra; faces with two equivalent Al(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Al2 cuboctahedra; faces with four Mg(1,1)Mg8Al2Sn2 cuboctahedra; and faces with eight equivalent Mg(2)Mg8Al2Sn2 cuboctahedra. Both Mg(1)-Mg(1) bond lengths are 3.18 Å. Both Mg(1)-Mg(2) bond lengths are 3.16 Å. Both Mg(1)-Mg(3) bond lengths are 3.18 Å. There is one shorter (3.12 Å) and one longer (3.13 Å) Mg(1)-Al(1) bond length. Both Mg(1)-Sn(1) bond lengths are 3.12 Å. Al(1) is bonded to two equivalent Mg(3); four Mg(1,1); four equivalent Mg(2); and two equivalent Sn(1) atoms to form AlMg10Sn2 cuboctahedra that share corners with four equivalent Sn(1)Mg10Al2 cuboctahedra; corners with six equivalent Al(1)Mg10Sn2 cuboctahedra; corners with eight Mg(1,1)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four Mg(1,1)Mg8Al2Sn2 cuboctahedra; edges with eight Mg(2,2)Mg8Al2Sn2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Al(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Al2 cuboctahedra; faces with four Mg(1,1)Mg8Al2Sn2 cuboctahedra; faces with four equivalent Mg(2)Mg8Al2Sn2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Sn2 cuboctahedra. Both Al(1)-Sn(1) bond lengths are 3.18 Å. Sn(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(2,2); and two equivalent Al(1) atoms to form SnMg10Al2 cuboctahedra that share corners with four equivalent Al(1)Mg10Sn2 cuboctahedra; corners with six equivalent Sn(1)Mg10Al2 cuboctahedra; corners with eight Mg(1,1)Mg8Al2Sn2 cuboctahedra; edges with two equivalent Al(1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(4)Mg10Sn2 cuboctahedra; edges with four Mg(1,1)Mg8Al2Sn2 cuboctahedra; edges with eight Mg(2,2)Mg8Al2Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Sn2 cuboctahedra; faces with two equivalent Al(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Al2 cuboctahedra; faces with four Mg(1,1)Mg8Al2Sn2 cuboctahedra; faces with four Mg(2,2)Mg8Al2Sn2 cuboctahedra; and faces with six equivalent Mg(3)Mg10Al2 cuboctahedra.