KMg14Zr crystallizes in the hexagonal P-6m2 space group. K(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form KMg12 cuboctahedra that share corners with six equivalent K(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with six Mg(2,2)K2Mg10 cuboctahedra; edges with twelve Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six Mg(2,2)K2Mg10 cuboctahedra; faces with six Mg(3,3)KMg10Zr cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent K(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; corners with eight Mg(2,2)K2Mg10 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent Mg(2)K2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with ten Mg(3,3)KMg10Zr cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent K(1); two equivalent Mg(4); four Mg(2,2); and four Mg(3,3) atoms to form distorted MgK2Mg10 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)K2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with four Mg(2,2)K2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent K(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(2,2)K2Mg10 cuboctahedra; and faces with ten Mg(3,3)KMg10Zr cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent K(1); two equivalent Mg(4); four equivalent Mg(2); and four Mg(3,3) atoms to form distorted MgK2Mg10 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)K2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)K2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent K(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(2)K2Mg10 cuboctahedra; and faces with ten Mg(3,3)KMg10Zr cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one K(1); two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Zr(1) atom to form distorted MgKMg10Zr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)KMg10Zr cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)K2Mg10 cuboctahedra; edges with four Mg(3,3)KMg10Zr cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra;  a faceface with one K(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)K2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)KMg10Zr cuboctahedra. In the fifth Mg site, Mg(3) is bonded to one K(1); two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); and one Zr(1) atom to form distorted MgKMg10Zr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)KMg10Zr cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(2,2)K2Mg10 cuboctahedra; edges with four equivalent Mg(3)KMg10Zr cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra;  a faceface with one K(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)K2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)KMg10Zr cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); 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)KMg10Zr cuboctahedra; edges with six Mg(2,2)K2Mg10 cuboctahedra; edges with six Mg(3,3)KMg10Zr cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent K(1)Mg12 cuboctahedra; faces with three Mg(2,2)K2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; and faces with six Mg(3,3)KMg10Zr cuboctahedra. Zr(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)K2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with twelve Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent K(1)Mg12 cuboctahedra; faces with six Mg(3,3)KMg10Zr cuboctahedra; faces with six equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
KMg14Zr crystallizes in the hexagonal P-6m2 space group. K(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form KMg12 cuboctahedra that share corners with six equivalent K(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with six Mg(2,2)K2Mg10 cuboctahedra; edges with twelve Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six Mg(2,2)K2Mg10 cuboctahedra; faces with six Mg(3,3)KMg10Zr cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. All K(1)-Mg(2,2) bond lengths are 3.31 Å. All K(1)-Mg(3,3) bond lengths are 3.31 Å. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent K(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; corners with eight Mg(2,2)K2Mg10 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent Mg(2)K2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with ten Mg(3,3)KMg10Zr cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.21 Å. There are two shorter (3.29 Å) and two longer (3.33 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3,3) bond lengths are 3.10 Å. Both Mg(1)-Zr(1) bond lengths are 3.31 Å. In the second Mg site, Mg(2) is bonded to two equivalent K(1); two equivalent Mg(4); four Mg(2,2); and four Mg(3,3) atoms to form distorted MgK2Mg10 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)K2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with four Mg(2,2)K2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent K(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(2,2)K2Mg10 cuboctahedra; and faces with ten Mg(3,3)KMg10Zr cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.22 Å. There are two shorter (3.24 Å) and two longer (3.38 Å) Mg(2)-Mg(2,2) bond lengths. All Mg(2)-Mg(3,3) bond lengths are 3.27 Å. In the third Mg site, Mg(2) is bonded to two equivalent K(1); two equivalent Mg(4); four equivalent Mg(2); and four Mg(3,3) atoms to form distorted MgK2Mg10 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)K2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)K2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent K(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(2)K2Mg10 cuboctahedra; and faces with ten Mg(3,3)KMg10Zr cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.22 Å. All Mg(2)-Mg(3,3) bond lengths are 3.27 Å. In the fourth Mg site, Mg(3) is bonded to one K(1); two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Zr(1) atom to form distorted MgKMg10Zr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)KMg10Zr cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)K2Mg10 cuboctahedra; edges with four Mg(3,3)KMg10Zr cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra;  a faceface with one K(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)K2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)KMg10Zr cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.31 Å. There are two shorter (3.26 Å) and two longer (3.36 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Zr(1) bond length is 3.13 Å. In the fifth Mg site, Mg(3) is bonded to one K(1); two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); and one Zr(1) atom to form distorted MgKMg10Zr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)KMg10Zr cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(2,2)K2Mg10 cuboctahedra; edges with four equivalent Mg(3)KMg10Zr cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra;  a faceface with one K(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)K2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)KMg10Zr cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.31 Å. The Mg(3)-Zr(1) bond length is 3.13 Å. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); 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)KMg10Zr cuboctahedra; edges with six Mg(2,2)K2Mg10 cuboctahedra; edges with six Mg(3,3)KMg10Zr cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent K(1)Mg12 cuboctahedra; faces with three Mg(2,2)K2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; and faces with six Mg(3,3)KMg10Zr cuboctahedra. Zr(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)K2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with twelve Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent K(1)Mg12 cuboctahedra; faces with six Mg(3,3)KMg10Zr cuboctahedra; faces with six equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.