Mg6ZrBi crystallizes in the orthorhombic Amm2 space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 12-coordinate geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Zr(1)Mg10Bi2 cuboctahedra; corners with six equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with two equivalent Zr(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Bi(1)Mg10Zr2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3,3,3); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with six equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; faces with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Zr(1)Mg10Bi2 cuboctahedra. In the sixth Mg site, Mg(1) is bonded in a 12-coordinate geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms. In the seventh Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. In the eighth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. Zr(1) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3); and two equivalent Bi(1) atoms to form distorted ZrMg10Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zr2 cuboctahedra; corners with six equivalent Zr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Bi2 cuboctahedra. Bi(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3,3,3); and two equivalent Zr(1) atoms to form BiMg10Zr2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with six equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; faces with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Mg(2)Mg10Zr2 cuboctahedra.
Mg6ZrBi crystallizes in the orthorhombic Amm2 space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 12-coordinate geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms. There is one shorter (3.16 Å) and one longer (3.43 Å) Mg(1)-Mg(1) bond length. There is one shorter (3.19 Å) and one longer (3.25 Å) Mg(1)-Mg(2) bond length. Both Mg(1)-Mg(3) bond lengths are 3.14 Å. Both Mg(1)-Mg(4) bond lengths are 3.16 Å. There is one shorter (3.13 Å) and one longer (3.31 Å) Mg(1)-Zr(1) bond length. Both Mg(1)-Bi(1) bond lengths are 3.24 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Zr(1)Mg10Bi2 cuboctahedra; corners with six equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with two equivalent Zr(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Bi(1)Mg10Zr2 cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.18 Å. The Mg(2)-Mg(1) bond length is 3.25 Å. All Mg(2)-Mg(3,3) bond lengths are 3.17 Å. Both Mg(2)-Zr(1) bond lengths are 3.29 Å. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. There is one shorter (3.27 Å) and one longer (3.32 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(4) bond lengths are 3.22 Å. Both Mg(3)-Zr(1) bond lengths are 3.18 Å. There is one shorter (3.21 Å) and one longer (3.22 Å) Mg(3)-Bi(1) bond length. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.14 Å. Both Mg(3)-Mg(4) bond lengths are 3.22 Å. Both Mg(3)-Zr(1) bond lengths are 3.18 Å. There is one shorter (3.21 Å) and one longer (3.22 Å) Mg(3)-Bi(1) bond length. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3,3,3); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with six equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; faces with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Zr(1)Mg10Bi2 cuboctahedra. Both Mg(4)-Mg(1) bond lengths are 3.16 Å. Both Mg(4)-Mg(3,3) bond lengths are 3.22 Å. Both Mg(4)-Bi(1) bond lengths are 3.29 Å. In the sixth Mg site, Mg(1) is bonded in a 12-coordinate geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms. There is one shorter (3.16 Å) and one longer (3.43 Å) Mg(1)-Mg(1) bond length. Both Mg(1)-Mg(3) bond lengths are 3.14 Å. There is one shorter (3.13 Å) and one longer (3.31 Å) Mg(1)-Zr(1) bond length. Both Mg(1)-Bi(1) bond lengths are 3.24 Å. In the seventh Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.14 Å. Both Mg(3)-Mg(2) bond lengths are 3.17 Å. There is one shorter (3.27 Å) and one longer (3.32 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Zr(1) bond lengths are 3.18 Å. There is one shorter (3.21 Å) and one longer (3.22 Å) Mg(3)-Bi(1) bond length. In the eighth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Zr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Zr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; and faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra. Both Mg(3)-Mg(2) bond lengths are 3.17 Å. Both Mg(3)-Zr(1) bond lengths are 3.18 Å. There is one shorter (3.21 Å) and one longer (3.22 Å) Mg(3)-Bi(1) bond length. Zr(1) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3); and two equivalent Bi(1) atoms to form distorted ZrMg10Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zr2 cuboctahedra; corners with six equivalent Zr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Bi(1)Mg10Zr2 cuboctahedra; edges with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; faces with four Mg(3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Bi2 cuboctahedra. Both Zr(1)-Bi(1) bond lengths are 3.17 Å. Bi(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3,3,3); and two equivalent Zr(1) atoms to form BiMg10Zr2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with six equivalent Bi(1)Mg10Zr2 cuboctahedra; corners with eight Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; edges with four equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Zr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Zr2 cuboctahedra; faces with four Mg(3,3,3,3)Mg8Zr2Bi2 cuboctahedra; and faces with six equivalent Mg(2)Mg10Zr2 cuboctahedra.