CaMg14Hf crystallizes in the orthorhombic Amm2 space group. Ca(1) is bonded to two equivalent Mg(6); four Mg(3,3); four Mg(5,5,5); and two equivalent Hf(1) atoms to form CaHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. There are eleven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four Mg(4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)CaMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Ca(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Hf(1) atoms to form distorted MgCa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; corners with four equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Ca(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Hf(1) atoms to form distorted MgCa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; corners with four equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. In the seventh Mg site, Mg(5) is bonded to one Ca(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgCaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)CaHfMg10 cuboctahedra; and faces with four Mg(4,4)Mg12 cuboctahedra. In the eighth Mg site, Mg(5) is bonded to one Ca(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgCaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)CaHfMg10 cuboctahedra; and faces with four Mg(4,4)Mg12 cuboctahedra. In the ninth Mg site, Mg(5) is bonded to one Ca(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgCaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)CaHfMg10 cuboctahedra; and faces with four Mg(4,4)Mg12 cuboctahedra. In the tenth Mg site, Mg(6) is bonded to one Ca(1); one Mg(1); two equivalent Mg(3); two equivalent Mg(4); two equivalent Mg(7); and four Mg(5,5,5) atoms to form distorted MgCaMg11 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with six equivalent Mg(6)CaMg11 cuboctahedra; corners with eight Mg(5,5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four Mg(5,5,5)CaHfMg10 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Hf(1)Ca2Mg10 cuboctahedra; and faces with four Mg(5,5,5)CaHfMg10 cuboctahedra. In the eleventh Mg site, Mg(7) is bonded to one Mg(2); two equivalent Mg(3); two equivalent Mg(4); two equivalent Mg(6); four Mg(5,5,5); and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with six equivalent Mg(7)HfMg11 cuboctahedra; corners with eight Mg(5,5,5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four Mg(5,5,5)CaHfMg10 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; and faces with four Mg(5,5,5)CaHfMg10 cuboctahedra. Hf(1) is bonded to two equivalent Ca(1); two equivalent Mg(7); four Mg(3,3); and four Mg(5,5,5) atoms to form HfCa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; and faces with six equivalent Mg(6)CaMg11 cuboctahedra.
CaMg14Hf crystallizes in the orthorhombic Amm2 space group. Ca(1) is bonded to two equivalent Mg(6); four Mg(3,3); four Mg(5,5,5); and two equivalent Hf(1) atoms to form CaHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. Both Ca(1)-Mg(6) bond lengths are 3.26 Å. There are two shorter (3.22 Å) and two longer (3.27 Å) Ca(1)-Mg(3,3) bond lengths. All Ca(1)-Mg(5,5,5) bond lengths are 3.25 Å. Both Ca(1)-Hf(1) bond lengths are 3.28 Å. There are eleven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.28 Å. Both Mg(1)-Mg(6) bond lengths are 3.17 Å. There are two shorter (3.24 Å) and two longer (3.25 Å) Mg(1)-Mg(4,4) bond lengths. All Mg(1)-Mg(5,5,5) bond lengths are 3.19 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four Mg(4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)CaMg11 cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.21 Å. There are two shorter (3.24 Å) and two longer (3.25 Å) Mg(2)-Mg(4,4) bond lengths. All Mg(2)-Mg(5,5,5) bond lengths are 3.14 Å. In the third Mg site, Mg(3) is bonded to two equivalent Ca(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Hf(1) atoms to form distorted MgCa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. There is one shorter (3.25 Å) and one longer (3.30 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5,5) bond lengths are 3.21 Å. Both Mg(3)-Mg(6) bond lengths are 3.24 Å. Both Mg(3)-Mg(7) bond lengths are 3.17 Å. There is one shorter (3.16 Å) and one longer (3.33 Å) Mg(3)-Hf(1) bond length. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; corners with four equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. There is one shorter (3.27 Å) and one longer (3.28 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5,5) bond lengths are 3.16 Å. Both Mg(4)-Mg(6) bond lengths are 3.14 Å. Both Mg(4)-Mg(7) bond lengths are 3.24 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent Ca(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Hf(1) atoms to form distorted MgCa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. There is one shorter (3.25 Å) and one longer (3.30 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5,5) bond lengths are 3.21 Å. Both Mg(3)-Mg(6) bond lengths are 3.24 Å. Both Mg(3)-Mg(7) bond lengths are 3.17 Å. There is one shorter (3.16 Å) and one longer (3.33 Å) Mg(3)-Hf(1) bond length. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; corners with four equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. There is one shorter (3.27 Å) and one longer (3.28 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5,5) bond lengths are 3.16 Å. Both Mg(4)-Mg(6) bond lengths are 3.14 Å. Both Mg(4)-Mg(7) bond lengths are 3.24 Å. In the seventh Mg site, Mg(5) is bonded to one Ca(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgCaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)CaHfMg10 cuboctahedra; and faces with four Mg(4,4)Mg12 cuboctahedra. There is one shorter (3.18 Å) and one longer (3.37 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.19 Å) and one longer (3.30 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.20 Å) and one longer (3.29 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Hf(1) bond length is 3.18 Å. In the eighth Mg site, Mg(5) is bonded to one Ca(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgCaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)CaHfMg10 cuboctahedra; and faces with four Mg(4,4)Mg12 cuboctahedra. There is one shorter (3.18 Å) and one longer (3.37 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.19 Å) and one longer (3.30 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.20 Å) and one longer (3.29 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Hf(1) bond length is 3.18 Å. In the ninth Mg site, Mg(5) is bonded to one Ca(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgCaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)CaHfMg10 cuboctahedra; and faces with four Mg(4,4)Mg12 cuboctahedra. There is one shorter (3.19 Å) and one longer (3.30 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.20 Å) and one longer (3.29 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Hf(1) bond length is 3.18 Å. In the tenth Mg site, Mg(6) is bonded to one Ca(1); one Mg(1); two equivalent Mg(3); two equivalent Mg(4); two equivalent Mg(7); and four Mg(5,5,5) atoms to form distorted MgCaMg11 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with six equivalent Mg(6)CaMg11 cuboctahedra; corners with eight Mg(5,5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four Mg(5,5,5)CaHfMg10 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Hf(1)Ca2Mg10 cuboctahedra; and faces with four Mg(5,5,5)CaHfMg10 cuboctahedra. Both Mg(6)-Mg(7) bond lengths are 3.28 Å. In the eleventh Mg site, Mg(7) is bonded to one Mg(2); two equivalent Mg(3); two equivalent Mg(4); two equivalent Mg(6); four Mg(5,5,5); and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with six equivalent Mg(7)HfMg11 cuboctahedra; corners with eight Mg(5,5,5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four Mg(5,5,5)CaHfMg10 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; and faces with four Mg(5,5,5)CaHfMg10 cuboctahedra. The Mg(7)-Hf(1) bond length is 3.19 Å. Hf(1) is bonded to two equivalent Ca(1); two equivalent Mg(7); four Mg(3,3); and four Mg(5,5,5) atoms to form HfCa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; and faces with six equivalent Mg(6)CaMg11 cuboctahedra.