RbMg14Hf crystallizes in the hexagonal P-6m2 space group. Rb(1) is bonded to six Mg(1,1) and six Mg(3,3) atoms to form RbMg12 cuboctahedra that share corners with six equivalent Rb(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six Mg(1,1)Rb2Mg10 cuboctahedra; edges with twelve Mg(3,3)RbHfMg10 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; faces with six Mg(1,1)Rb2Mg10 cuboctahedra; and faces with six Mg(3,3)RbHfMg10 cuboctahedra. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Rb(1); two equivalent Mg(4); four Mg(1,1); and four Mg(3,3) atoms to form distorted MgRb2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Rb2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with two equivalent Rb(1)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four Mg(1,1)Rb2Mg10 cuboctahedra; edges with eight Mg(3,3)RbHfMg10 cuboctahedra; faces with two equivalent Rb(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(1,1)Rb2Mg10 cuboctahedra; and faces with ten Mg(3,3)RbHfMg10 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Rb(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight Mg(1,1)Rb2Mg10 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)RbHfMg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(1)Rb2Mg10 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Hf2Mg10 cuboctahedra; and faces with ten Mg(3,3)RbHfMg10 cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Rb(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form distorted MgRb2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Rb2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with two equivalent Rb(1)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(1)Rb2Mg10 cuboctahedra; edges with eight equivalent Mg(3)RbHfMg10 cuboctahedra; faces with two equivalent Rb(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(1)Rb2Mg10 cuboctahedra; and faces with ten Mg(3,3)RbHfMg10 cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one Rb(1); two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Hf(1) atom to form distorted MgRbHfMg10 cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)RbHfMg10 cuboctahedra; edges with two equivalent Rb(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four Mg(1,1)Rb2Mg10 cuboctahedra; edges with four Mg(3,3)RbHfMg10 cuboctahedra;  a faceface with one Rb(1)Mg12 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with five Mg(1,1)Rb2Mg10 cuboctahedra; and faces with six Mg(3,3)RbHfMg10 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to one Rb(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one Hf(1) atom to form distorted MgRbHfMg10 cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)RbHfMg10 cuboctahedra; edges with two equivalent Rb(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(1)Rb2Mg10 cuboctahedra; edges with four equivalent Mg(3)RbHfMg10 cuboctahedra;  a faceface with one Rb(1)Mg12 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with five Mg(1,1)Rb2Mg10 cuboctahedra; and faces with six Mg(3,3)RbHfMg10 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three Mg(1,1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)RbHfMg10 cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six Mg(1,1)Rb2Mg10 cuboctahedra; edges with six Mg(3,3)RbHfMg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Rb(1)Mg12 cuboctahedra; faces with three equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with three Mg(1,1)Rb2Mg10 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; and faces with six Mg(3,3)RbHfMg10 cuboctahedra. Hf(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form HfMg12 cuboctahedra that share corners with six equivalent Hf(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Rb2Mg10 cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with twelve Mg(3,3)RbHfMg10 cuboctahedra; faces with two equivalent Rb(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; and faces with six Mg(3,3)RbHfMg10 cuboctahedra.
RbMg14Hf crystallizes in the hexagonal P-6m2 space group. Rb(1) is bonded to six Mg(1,1) and six Mg(3,3) atoms to form RbMg12 cuboctahedra that share corners with six equivalent Rb(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six Mg(1,1)Rb2Mg10 cuboctahedra; edges with twelve Mg(3,3)RbHfMg10 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; faces with six Mg(1,1)Rb2Mg10 cuboctahedra; and faces with six Mg(3,3)RbHfMg10 cuboctahedra. All Rb(1)-Mg(1,1) bond lengths are 3.32 Å. All Rb(1)-Mg(3,3) bond lengths are 3.36 Å. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Rb(1); two equivalent Mg(4); four Mg(1,1); and four Mg(3,3) atoms to form distorted MgRb2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Rb2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with two equivalent Rb(1)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four Mg(1,1)Rb2Mg10 cuboctahedra; edges with eight Mg(3,3)RbHfMg10 cuboctahedra; faces with two equivalent Rb(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(1,1)Rb2Mg10 cuboctahedra; and faces with ten Mg(3,3)RbHfMg10 cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.22 Å. There are two shorter (3.25 Å) and two longer (3.38 Å) Mg(1)-Mg(1,1) bond lengths. All Mg(1)-Mg(3,3) bond lengths are 3.32 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Rb(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight Mg(1,1)Rb2Mg10 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)RbHfMg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(1)Rb2Mg10 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Hf2Mg10 cuboctahedra; and faces with ten Mg(3,3)RbHfMg10 cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.24 Å. There are two shorter (3.30 Å) and two longer (3.33 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(3,3) bond lengths are 3.09 Å. Both Mg(2)-Hf(1) bond lengths are 3.32 Å. In the third Mg site, Mg(1) is bonded to two equivalent Rb(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form distorted MgRb2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Rb2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with two equivalent Rb(1)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(1)Rb2Mg10 cuboctahedra; edges with eight equivalent Mg(3)RbHfMg10 cuboctahedra; faces with two equivalent Rb(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(1)Rb2Mg10 cuboctahedra; and faces with ten Mg(3,3)RbHfMg10 cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.22 Å. All Mg(1)-Mg(3) bond lengths are 3.32 Å. In the fourth Mg site, Mg(3) is bonded to one Rb(1); two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Hf(1) atom to form distorted MgRbHfMg10 cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)RbHfMg10 cuboctahedra; edges with two equivalent Rb(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four Mg(1,1)Rb2Mg10 cuboctahedra; edges with four Mg(3,3)RbHfMg10 cuboctahedra;  a faceface with one Rb(1)Mg12 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with five Mg(1,1)Rb2Mg10 cuboctahedra; and faces with six Mg(3,3)RbHfMg10 cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.32 Å. There are two shorter (3.25 Å) and two longer (3.39 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Hf(1) bond length is 3.13 Å. In the fifth Mg site, Mg(3) is bonded to one Rb(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one Hf(1) atom to form distorted MgRbHfMg10 cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)RbHfMg10 cuboctahedra; edges with two equivalent Rb(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(1)Rb2Mg10 cuboctahedra; edges with four equivalent Mg(3)RbHfMg10 cuboctahedra;  a faceface with one Rb(1)Mg12 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with five Mg(1,1)Rb2Mg10 cuboctahedra; and faces with six Mg(3,3)RbHfMg10 cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.32 Å. The Mg(3)-Hf(1) bond length is 3.13 Å. In the sixth Mg site, Mg(4) is bonded to three Mg(1,1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)RbHfMg10 cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six Mg(1,1)Rb2Mg10 cuboctahedra; edges with six Mg(3,3)RbHfMg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Rb(1)Mg12 cuboctahedra; faces with three equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with three Mg(1,1)Rb2Mg10 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; and faces with six Mg(3,3)RbHfMg10 cuboctahedra. Hf(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form HfMg12 cuboctahedra that share corners with six equivalent Hf(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Rb2Mg10 cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with twelve Mg(3,3)RbHfMg10 cuboctahedra; faces with two equivalent Rb(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; and faces with six Mg(3,3)RbHfMg10 cuboctahedra.