BaMg14Sn crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(7); four Mg(3,3); four Mg(5,5); and two equivalent Sn(1) atoms to form BaMg10Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Ba(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Ba2Mg10 cuboctahedra; and faces with four Mg(5,5)BaMg10Sn cuboctahedra. There are nine inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four equivalent Mg(4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg10Sn2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Ba2Mg10 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)BaMg11 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four equivalent Mg(4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Sn(1)Ba2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Sn(1) atoms. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Ba2Mg10 cuboctahedra; corners with six equivalent Mg(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)BaMg10Sn cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(7)BaMg11 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)BaMg10Sn cuboctahedra. In the fifth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Ba(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Sn(1) atoms. In the sixth Mg site, Mg(5) is bonded to one Ba(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 Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra; corners with ten equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Mg(7)BaMg11 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 Sn(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Mg10Sn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Sn(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the seventh Mg site, Mg(5) is bonded to one Ba(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 Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra; corners with ten Mg(5,5)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Mg(7)BaMg11 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 Sn(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Mg10Sn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Sn(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with four equivalent Mg(5)BaMg10Sn cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the eighth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(7); four Mg(5,5); and one Sn(1) atom. In the ninth Mg site, Mg(7) is bonded to one Ba(1); one Mg(2); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(6); and four Mg(5,5) atoms to form distorted MgBaMg11 cuboctahedra that share corners with six equivalent Mg(7)BaMg11 cuboctahedra; corners with eight equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four Mg(5,5)BaMg10Sn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra;  a faceface with one Ba(1)Mg10Sn2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Sn(1)Ba2Mg10 cuboctahedra; and faces with four Mg(5,5)BaMg10Sn cuboctahedra. Sn(1) is bonded to two equivalent Ba(1); two equivalent Mg(6); four Mg(3,3); and four Mg(5,5) atoms to form SnBa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Sn(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; and faces with six equivalent Mg(7)BaMg11 cuboctahedra.
BaMg14Sn crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(7); four Mg(3,3); four Mg(5,5); and two equivalent Sn(1) atoms to form BaMg10Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Ba(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Ba2Mg10 cuboctahedra; and faces with four Mg(5,5)BaMg10Sn cuboctahedra. Both Ba(1)-Mg(7) bond lengths are 3.41 Å. There are two shorter (3.32 Å) and two longer (3.33 Å) Ba(1)-Mg(3,3) bond lengths. All Ba(1)-Mg(5,5) bond lengths are 3.40 Å. Both Ba(1)-Sn(1) bond lengths are 3.32 Å. There are nine inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four equivalent Mg(4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg10Sn2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Ba2Mg10 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)BaMg11 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.32 Å. Both Mg(1)-Mg(6) bond lengths are 3.28 Å. There are two shorter (3.29 Å) and two longer (3.35 Å) Mg(1)-Mg(4) bond lengths. All Mg(1)-Mg(5,5) bond lengths are 3.13 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four equivalent Mg(4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Sn(1)Ba2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.18 Å. There are two shorter (3.31 Å) and two longer (3.33 Å) Mg(2)-Mg(4) bond lengths. All Mg(2)-Mg(5,5) bond lengths are 3.19 Å. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Sn(1) atoms. There is one shorter (3.23 Å) and one longer (3.40 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5) bond lengths are 3.34 Å. Both Mg(3)-Mg(6) bond lengths are 3.25 Å. Both Mg(3)-Mg(7) bond lengths are 3.34 Å. There is one shorter (3.19 Å) and one longer (3.45 Å) Mg(3)-Sn(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 equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Ba2Mg10 cuboctahedra; corners with six equivalent Mg(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)BaMg10Sn cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(7)BaMg11 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)BaMg10Sn cuboctahedra. There is one shorter (3.29 Å) and one longer (3.34 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5) bond lengths are 3.14 Å. Both Mg(4)-Mg(6) bond lengths are 3.29 Å. Both Mg(4)-Mg(7) bond lengths are 3.12 Å. In the fifth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Ba(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Sn(1) atoms. Both Mg(3)-Mg(5,5) bond lengths are 3.34 Å. Both Mg(3)-Mg(6) bond lengths are 3.25 Å. Both Mg(3)-Mg(7) bond lengths are 3.34 Å. There is one shorter (3.19 Å) and one longer (3.45 Å) Mg(3)-Sn(1) bond length. In the sixth Mg site, Mg(5) is bonded to one Ba(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 Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra; corners with ten equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Mg(7)BaMg11 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 Sn(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Mg10Sn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Sn(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. There is one shorter (3.20 Å) and one longer (3.43 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.32 Å) and one longer (3.33 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.22 Å) and one longer (3.43 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Sn(1) bond length is 3.32 Å. In the seventh Mg site, Mg(5) is bonded to one Ba(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 Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra; corners with ten Mg(5,5)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Mg(7)BaMg11 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 Sn(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Mg10Sn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Sn(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with four equivalent Mg(5)BaMg10Sn cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. The Mg(5)-Mg(4) bond length is 3.14 Å. There is one shorter (3.32 Å) and one longer (3.33 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.22 Å) and one longer (3.43 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Sn(1) bond length is 3.32 Å. In the eighth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(7); four Mg(5,5); and one Sn(1) atom. Both Mg(6)-Mg(7) bond lengths are 3.32 Å. The Mg(6)-Sn(1) bond length is 3.28 Å. In the ninth Mg site, Mg(7) is bonded to one Ba(1); one Mg(2); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(6); and four Mg(5,5) atoms to form distorted MgBaMg11 cuboctahedra that share corners with six equivalent Mg(7)BaMg11 cuboctahedra; corners with eight equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four Mg(5,5)BaMg10Sn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra;  a faceface with one Ba(1)Mg10Sn2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Sn(1)Ba2Mg10 cuboctahedra; and faces with four Mg(5,5)BaMg10Sn cuboctahedra. Sn(1) is bonded to two equivalent Ba(1); two equivalent Mg(6); four Mg(3,3); and four Mg(5,5) atoms to form SnBa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Sn(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; and faces with six equivalent Mg(7)BaMg11 cuboctahedra.