Mg5Bi crystallizes in the trigonal R32 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to four Mg(2,2,2,2); six equivalent Mg(1); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with eighteen Mg(1,1)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Bi2 cuboctahedra; edges with eight Mg(2,2,2,2)Mg9Bi3 cuboctahedra; faces with four equivalent Bi(1)Mg12 cuboctahedra; faces with eight Mg(1,1)Mg10Bi2 cuboctahedra; and faces with eight Mg(2,2,2,2)Mg9Bi3 cuboctahedra. In the second Mg site, Mg(2) is bonded to three equivalent Mg(2); six Mg(1,1); and three equivalent Bi(1) atoms to form distorted MgMg9Bi3 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve Mg(2,2,2)Mg9Bi3 cuboctahedra; edges with six equivalent Mg(2)Mg9Bi3 cuboctahedra; edges with twelve Mg(1,1)Mg10Bi2 cuboctahedra; faces with four Mg(2,2)Mg9Bi3 cuboctahedra; faces with four equivalent Bi(1)Mg12 cuboctahedra; and faces with twelve Mg(1,1)Mg10Bi2 cuboctahedra. In the third Mg site, Mg(2) is bonded to three equivalent Mg(2); six Mg(1,1); and three equivalent Bi(1) atoms to form distorted MgMg9Bi3 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve Mg(2,2,2)Mg9Bi3 cuboctahedra; edges with six equivalent Mg(2)Mg9Bi3 cuboctahedra; edges with twelve Mg(1,1)Mg10Bi2 cuboctahedra; faces with four Mg(2,2)Mg9Bi3 cuboctahedra; faces with four equivalent Bi(1)Mg12 cuboctahedra; and faces with twelve Mg(1,1)Mg10Bi2 cuboctahedra. In the fourth Mg site, Mg(1) is bonded to four Mg(2,2,2); six equivalent Mg(1); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with eighteen Mg(1,1,1)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Bi2 cuboctahedra; edges with eight Mg(2,2,2)Mg9Bi3 cuboctahedra; faces with four equivalent Bi(1)Mg12 cuboctahedra; faces with eight Mg(1,1)Mg10Bi2 cuboctahedra; and faces with eight Mg(2,2,2)Mg9Bi3 cuboctahedra. In the fifth Mg site, Mg(2) is bonded to three equivalent Mg(2); six Mg(1,1,1); and three equivalent Bi(1) atoms to form distorted MgMg9Bi3 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve Mg(2,2,2)Mg9Bi3 cuboctahedra; edges with six equivalent Mg(2)Mg9Bi3 cuboctahedra; edges with twelve Mg(1,1,1)Mg10Bi2 cuboctahedra; faces with four Mg(2,2)Mg9Bi3 cuboctahedra; faces with four equivalent Bi(1)Mg12 cuboctahedra; and faces with twelve Mg(1,1,1)Mg10Bi2 cuboctahedra. In the sixth Mg site, Mg(2) is bonded to three equivalent Mg(2); six Mg(1,1,1); and three equivalent Bi(1) atoms to form distorted MgMg9Bi3 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve Mg(2,2,2)Mg9Bi3 cuboctahedra; edges with six equivalent Mg(2)Mg9Bi3 cuboctahedra; edges with twelve Mg(1,1,1)Mg10Bi2 cuboctahedra; faces with four equivalent Mg(2)Mg9Bi3 cuboctahedra; faces with four equivalent Bi(1)Mg12 cuboctahedra; and faces with twelve Mg(1,1,1)Mg10Bi2 cuboctahedra. In the seventh Mg site, Mg(1) is bonded to four Mg(2,2); six equivalent Mg(1); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with eighteen Mg(1,1)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Bi2 cuboctahedra; edges with eight Mg(2,2)Mg9Bi3 cuboctahedra; faces with four equivalent Bi(1)Mg12 cuboctahedra; faces with eight Mg(1,1)Mg10Bi2 cuboctahedra; and faces with eight Mg(2,2)Mg9Bi3 cuboctahedra. Bi(1) is bonded to six Mg(1,1) and six Mg(2,2) atoms to form BiMg12 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve Mg(2,2,2)Mg9Bi3 cuboctahedra; edges with six equivalent Bi(1)Mg12 cuboctahedra; edges with twelve Mg(1,1)Mg10Bi2 cuboctahedra; faces with eight Mg(2,2,2,2)Mg9Bi3 cuboctahedra; and faces with twelve Mg(1,1)Mg10Bi2 cuboctahedra.
Mg5Bi crystallizes in the trigonal R32 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to four Mg(2,2,2,2); six equivalent Mg(1); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with eighteen Mg(1,1)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Bi2 cuboctahedra; edges with eight Mg(2,2,2,2)Mg9Bi3 cuboctahedra; faces with four equivalent Bi(1)Mg12 cuboctahedra; faces with eight Mg(1,1)Mg10Bi2 cuboctahedra; and faces with eight Mg(2,2,2,2)Mg9Bi3 cuboctahedra. All Mg(1)-Mg(2,2,2,2) bond lengths are 3.27 Å. There are two shorter (3.23 Å) and four longer (3.25 Å) Mg(1)-Mg(1) bond lengths. Both Mg(1)-Bi(1) bond lengths are 3.27 Å. In the second Mg site, Mg(2) is bonded to three equivalent Mg(2); six Mg(1,1); and three equivalent Bi(1) atoms to form distorted MgMg9Bi3 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve Mg(2,2,2)Mg9Bi3 cuboctahedra; edges with six equivalent Mg(2)Mg9Bi3 cuboctahedra; edges with twelve Mg(1,1)Mg10Bi2 cuboctahedra; faces with four Mg(2,2)Mg9Bi3 cuboctahedra; faces with four equivalent Bi(1)Mg12 cuboctahedra; and faces with twelve Mg(1,1)Mg10Bi2 cuboctahedra. All Mg(2)-Mg(2) bond lengths are 3.25 Å. The Mg(2)-Mg(1) bond length is 3.27 Å. All Mg(2)-Bi(1) bond lengths are 3.25 Å. In the third Mg site, Mg(2) is bonded to three equivalent Mg(2); six Mg(1,1); and three equivalent Bi(1) atoms to form distorted MgMg9Bi3 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve Mg(2,2,2)Mg9Bi3 cuboctahedra; edges with six equivalent Mg(2)Mg9Bi3 cuboctahedra; edges with twelve Mg(1,1)Mg10Bi2 cuboctahedra; faces with four Mg(2,2)Mg9Bi3 cuboctahedra; faces with four equivalent Bi(1)Mg12 cuboctahedra; and faces with twelve Mg(1,1)Mg10Bi2 cuboctahedra. The Mg(2)-Mg(1) bond length is 3.27 Å. All Mg(2)-Bi(1) bond lengths are 3.25 Å. In the fourth Mg site, Mg(1) is bonded to four Mg(2,2,2); six equivalent Mg(1); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with eighteen Mg(1,1,1)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Bi2 cuboctahedra; edges with eight Mg(2,2,2)Mg9Bi3 cuboctahedra; faces with four equivalent Bi(1)Mg12 cuboctahedra; faces with eight Mg(1,1)Mg10Bi2 cuboctahedra; and faces with eight Mg(2,2,2)Mg9Bi3 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.27 Å. There are two shorter (3.23 Å) and four longer (3.25 Å) Mg(1)-Mg(1) bond lengths. Both Mg(1)-Bi(1) bond lengths are 3.27 Å. In the fifth Mg site, Mg(2) is bonded to three equivalent Mg(2); six Mg(1,1,1); and three equivalent Bi(1) atoms to form distorted MgMg9Bi3 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve Mg(2,2,2)Mg9Bi3 cuboctahedra; edges with six equivalent Mg(2)Mg9Bi3 cuboctahedra; edges with twelve Mg(1,1,1)Mg10Bi2 cuboctahedra; faces with four Mg(2,2)Mg9Bi3 cuboctahedra; faces with four equivalent Bi(1)Mg12 cuboctahedra; and faces with twelve Mg(1,1,1)Mg10Bi2 cuboctahedra. All Mg(2)-Mg(2) bond lengths are 3.25 Å. The Mg(2)-Mg(1) bond length is 3.27 Å. All Mg(2)-Bi(1) bond lengths are 3.25 Å. In the sixth Mg site, Mg(2) is bonded to three equivalent Mg(2); six Mg(1,1,1); and three equivalent Bi(1) atoms to form distorted MgMg9Bi3 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve Mg(2,2,2)Mg9Bi3 cuboctahedra; edges with six equivalent Mg(2)Mg9Bi3 cuboctahedra; edges with twelve Mg(1,1,1)Mg10Bi2 cuboctahedra; faces with four equivalent Mg(2)Mg9Bi3 cuboctahedra; faces with four equivalent Bi(1)Mg12 cuboctahedra; and faces with twelve Mg(1,1,1)Mg10Bi2 cuboctahedra. All Mg(2)-Mg(2) bond lengths are 3.25 Å. All Mg(2)-Mg(1,1) bond lengths are 3.27 Å. All Mg(2)-Bi(1) bond lengths are 3.25 Å. In the seventh Mg site, Mg(1) is bonded to four Mg(2,2); six equivalent Mg(1); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with eighteen Mg(1,1)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Bi2 cuboctahedra; edges with eight Mg(2,2)Mg9Bi3 cuboctahedra; faces with four equivalent Bi(1)Mg12 cuboctahedra; faces with eight Mg(1,1)Mg10Bi2 cuboctahedra; and faces with eight Mg(2,2)Mg9Bi3 cuboctahedra. There are two shorter (3.23 Å) and four longer (3.25 Å) Mg(1)-Mg(1) bond lengths. Both Mg(1)-Bi(1) bond lengths are 3.27 Å. Bi(1) is bonded to six Mg(1,1) and six Mg(2,2) atoms to form BiMg12 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve Mg(2,2,2)Mg9Bi3 cuboctahedra; edges with six equivalent Bi(1)Mg12 cuboctahedra; edges with twelve Mg(1,1)Mg10Bi2 cuboctahedra; faces with eight Mg(2,2,2,2)Mg9Bi3 cuboctahedra; and faces with twelve Mg(1,1)Mg10Bi2 cuboctahedra.