BaMg14Y is beta-derived structured and crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(7); four Mg(3,3,3); four Mg(5,5); and two equivalent Y(1) atoms to form BaY2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Ba(1)Y2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Y(1)Ba2Mg10 cuboctahedra; edges with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with eight Mg(5,5)BaYMg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Y(1)Ba2Mg10 cuboctahedra; faces with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; faces with four Mg(5,5)BaYMg10 cuboctahedra; and faces with six equivalent Mg(6)YMg11 cuboctahedra. There are ten 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)Y2Mg10 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(6)YMg11 cuboctahedra; edges with eight Mg(5,5)BaYMg10 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Y(1)Ba2Mg10 cuboctahedra; faces with four Mg(5,5)BaYMg10 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 Y(1)Ba2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3,3)Ba2Y2Mg8 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)BaYMg10 cuboctahedra; faces with two equivalent Ba(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(5,5)BaYMg10 cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)YMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Ba(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Y(1) atoms to form distorted MgBa2Y2Mg8 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)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Ba(1)Y2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Y(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with four Mg(5,5)BaYMg10 cuboctahedra; edges with four equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Ba(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Y(1)Ba2Mg10 cuboctahedra; and faces with eight Mg(5,5)BaYMg10 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 Ba(1)Y2Mg10 cuboctahedra; corners with four equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; corners with four equivalent Y(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(7)BaMg11 cuboctahedra; edges with four Mg(5,5)BaYMg10 cuboctahedra; edges with four equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Mg(3)Ba2Y2Mg8 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; faces with two equivalent Mg(6)YMg11 cuboctahedra; and faces with eight Mg(5,5)BaYMg10 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Ba(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Y(1) atoms to form distorted MgBa2Y2Mg8 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)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Ba(1)Y2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Y(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with four Mg(5,5)BaYMg10 cuboctahedra; edges with four equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Ba(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Y(1)Ba2Mg10 cuboctahedra; and faces with eight Mg(5,5)BaYMg10 cuboctahedra. 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 Y(1) atom to form distorted MgBaYMg10 cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra; corners with four equivalent Mg(6)YMg11 cuboctahedra; corners with ten equivalent Mg(5)BaYMg10 cuboctahedra; edges with two equivalent Ba(1)Y2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Mg(7)BaMg11 cuboctahedra; edges with two equivalent Mg(5)BaYMg10 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 Mg(6)YMg11 cuboctahedra; edges with two equivalent Y(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Y2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Y(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; faces with four equivalent Mg(5)BaYMg10 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 Y(1) atom to form distorted MgBaYMg10 cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra; corners with four equivalent Mg(6)YMg11 cuboctahedra; corners with ten equivalent Mg(5)BaYMg10 cuboctahedra; edges with two equivalent Ba(1)Y2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Mg(7)BaMg11 cuboctahedra; edges with two equivalent Mg(5)BaYMg10 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 Mg(6)YMg11 cuboctahedra; edges with two equivalent Y(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Y2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Y(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; faces with four equivalent Mg(5)BaYMg10 cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the eighth Mg site, Mg(6) is bonded to one Mg(1); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(7); four Mg(5,5); and one Y(1) atom to form MgYMg11 cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra; corners with six equivalent Mg(6)YMg11 cuboctahedra; corners with eight Mg(5,5)BaYMg10 cuboctahedra; edges with two equivalent Mg(7)BaMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Y(1)Ba2Mg10 cuboctahedra; edges with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; edges with four Mg(5,5)BaYMg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Y(1)Ba2Mg10 cuboctahedra; faces with two Mg(3,3)Ba2Y2Mg8 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with three equivalent Ba(1)Y2Mg10 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; and faces with four Mg(5,5)BaYMg10 cuboctahedra. 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 four equivalent Mg(6)YMg11 cuboctahedra; corners with six equivalent Mg(7)BaMg11 cuboctahedra; corners with eight Mg(5,5)BaYMg10 cuboctahedra; edges with two equivalent Ba(1)Y2Mg10 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(6)YMg11 cuboctahedra; edges with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; edges with four Mg(5,5)BaYMg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra;  a faceface with one Ba(1)Y2Mg10 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra; faces with two Mg(3,3)Ba2Y2Mg8 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Y(1)Ba2Mg10 cuboctahedra; and faces with four Mg(5,5)BaYMg10 cuboctahedra. In the tenth Mg site, Mg(3) is bonded to two equivalent Ba(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Y(1) atoms to form distorted MgBa2Y2Mg8 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)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Ba(1)Y2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Y(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with four Mg(5,5)BaYMg10 cuboctahedra; edges with four equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Ba(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Y(1)Ba2Mg10 cuboctahedra; and faces with eight Mg(5,5)BaYMg10 cuboctahedra. Y(1) is bonded to two equivalent Ba(1); two equivalent Mg(6); four Mg(3,3,3); and four Mg(5,5) atoms to form YBa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Y(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ba(1)Y2Mg10 cuboctahedra; edges with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; edges with four equivalent Mg(6)YMg11 cuboctahedra; edges with eight Mg(5,5)BaYMg10 cuboctahedra; faces with two equivalent Ba(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; faces with four Mg(5,5)BaYMg10 cuboctahedra; and faces with six equivalent Mg(7)BaMg11 cuboctahedra.
BaMg14Y is beta-derived structured and crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(7); four Mg(3,3,3); four Mg(5,5); and two equivalent Y(1) atoms to form BaY2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Ba(1)Y2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Y(1)Ba2Mg10 cuboctahedra; edges with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with eight Mg(5,5)BaYMg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Y(1)Ba2Mg10 cuboctahedra; faces with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; faces with four Mg(5,5)BaYMg10 cuboctahedra; and faces with six equivalent Mg(6)YMg11 cuboctahedra. Both Ba(1)-Mg(7) bond lengths are 3.44 Å. There are two shorter (3.33 Å) and two longer (3.35 Å) Ba(1)-Mg(3,3,3) bond lengths. All Ba(1)-Mg(5,5) bond lengths are 3.46 Å. Both Ba(1)-Y(1) bond lengths are 3.34 Å. There are ten 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)Y2Mg10 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(6)YMg11 cuboctahedra; edges with eight Mg(5,5)BaYMg10 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Y(1)Ba2Mg10 cuboctahedra; faces with four Mg(5,5)BaYMg10 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 3.34 Å. Both Mg(1)-Mg(6) bond lengths are 3.28 Å. There are two shorter (3.31 Å) and two longer (3.37 Å) Mg(1)-Mg(4) bond lengths. All Mg(1)-Mg(5,5) bond lengths are 3.14 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 Y(1)Ba2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3,3)Ba2Y2Mg8 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)BaYMg10 cuboctahedra; faces with two equivalent Ba(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(5,5)BaYMg10 cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)YMg11 cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.24 Å. All Mg(2)-Mg(4) bond lengths are 3.34 Å. All Mg(2)-Mg(5,5) bond lengths are 3.19 Å. In the third Mg site, Mg(3) is bonded to two equivalent Ba(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Y(1) atoms to form distorted MgBa2Y2Mg8 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)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Ba(1)Y2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Y(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with four Mg(5,5)BaYMg10 cuboctahedra; edges with four equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Ba(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Y(1)Ba2Mg10 cuboctahedra; and faces with eight Mg(5,5)BaYMg10 cuboctahedra. Both Mg(3)-Mg(3) bond lengths are 3.34 Å. Both Mg(3)-Mg(5,5) bond lengths are 3.40 Å. Both Mg(3)-Mg(6) bond lengths are 3.30 Å. Both Mg(3)-Mg(7) bond lengths are 3.37 Å. There is one shorter (3.27 Å) and one longer (3.41 Å) Mg(3)-Y(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 Ba(1)Y2Mg10 cuboctahedra; corners with four equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; corners with four equivalent Y(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(7)BaMg11 cuboctahedra; edges with four Mg(5,5)BaYMg10 cuboctahedra; edges with four equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Mg(3)Ba2Y2Mg8 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; faces with two equivalent Mg(6)YMg11 cuboctahedra; and faces with eight Mg(5,5)BaYMg10 cuboctahedra. There is one shorter (3.32 Å) and one longer (3.36 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5,5) bond lengths are 3.14 Å. Both Mg(4)-Mg(6) bond lengths are 3.27 Å. Both Mg(4)-Mg(7) bond lengths are 3.16 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent Ba(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Y(1) atoms to form distorted MgBa2Y2Mg8 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)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Ba(1)Y2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Y(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with four Mg(5,5)BaYMg10 cuboctahedra; edges with four equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Ba(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Y(1)Ba2Mg10 cuboctahedra; and faces with eight Mg(5,5)BaYMg10 cuboctahedra. Both Mg(3)-Mg(5,5) bond lengths are 3.40 Å. Both Mg(3)-Mg(6) bond lengths are 3.30 Å. Both Mg(3)-Mg(7) bond lengths are 3.37 Å. There is one shorter (3.27 Å) and one longer (3.41 Å) Mg(3)-Y(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 Y(1) atom to form distorted MgBaYMg10 cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra; corners with four equivalent Mg(6)YMg11 cuboctahedra; corners with ten equivalent Mg(5)BaYMg10 cuboctahedra; edges with two equivalent Ba(1)Y2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Mg(7)BaMg11 cuboctahedra; edges with two equivalent Mg(5)BaYMg10 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 Mg(6)YMg11 cuboctahedra; edges with two equivalent Y(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Y2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Y(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; faces with four equivalent Mg(5)BaYMg10 cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. There is one shorter (3.23 Å) and one longer (3.45 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.33 Å) and one longer (3.36 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.21 Å) and one longer (3.47 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Y(1) bond length is 3.39 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 Y(1) atom to form distorted MgBaYMg10 cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra; corners with four equivalent Mg(6)YMg11 cuboctahedra; corners with ten equivalent Mg(5)BaYMg10 cuboctahedra; edges with two equivalent Ba(1)Y2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Mg(7)BaMg11 cuboctahedra; edges with two equivalent Mg(5)BaYMg10 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 Mg(6)YMg11 cuboctahedra; edges with two equivalent Y(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Y2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Y(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; faces with four equivalent Mg(5)BaYMg10 cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. There is one shorter (3.33 Å) and one longer (3.36 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.21 Å) and one longer (3.47 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Y(1) bond length is 3.39 Å. In the eighth Mg site, Mg(6) is bonded to one Mg(1); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(7); four Mg(5,5); and one Y(1) atom to form MgYMg11 cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra; corners with six equivalent Mg(6)YMg11 cuboctahedra; corners with eight Mg(5,5)BaYMg10 cuboctahedra; edges with two equivalent Mg(7)BaMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Y(1)Ba2Mg10 cuboctahedra; edges with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; edges with four Mg(5,5)BaYMg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Y(1)Ba2Mg10 cuboctahedra; faces with two Mg(3,3)Ba2Y2Mg8 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with three equivalent Ba(1)Y2Mg10 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; and faces with four Mg(5,5)BaYMg10 cuboctahedra. Both Mg(6)-Mg(7) bond lengths are 3.34 Å. The Mg(6)-Y(1) bond length is 3.35 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 four equivalent Mg(6)YMg11 cuboctahedra; corners with six equivalent Mg(7)BaMg11 cuboctahedra; corners with eight Mg(5,5)BaYMg10 cuboctahedra; edges with two equivalent Ba(1)Y2Mg10 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(6)YMg11 cuboctahedra; edges with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; edges with four Mg(5,5)BaYMg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra;  a faceface with one Ba(1)Y2Mg10 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra; faces with two Mg(3,3)Ba2Y2Mg8 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Y(1)Ba2Mg10 cuboctahedra; and faces with four Mg(5,5)BaYMg10 cuboctahedra. In the tenth Mg site, Mg(3) is bonded to two equivalent Ba(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Y(1) atoms to form distorted MgBa2Y2Mg8 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)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Ba(1)Y2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; edges with two equivalent Y(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with four Mg(5,5)BaYMg10 cuboctahedra; edges with four equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Ba(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ba2Y2Mg8 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with two equivalent Y(1)Ba2Mg10 cuboctahedra; and faces with eight Mg(5,5)BaYMg10 cuboctahedra. Both Mg(3)-Mg(3) bond lengths are 3.34 Å. Both Mg(3)-Mg(5,5) bond lengths are 3.40 Å. Both Mg(3)-Mg(6) bond lengths are 3.30 Å. Both Mg(3)-Mg(7) bond lengths are 3.37 Å. There is one shorter (3.27 Å) and one longer (3.41 Å) Mg(3)-Y(1) bond length. Y(1) is bonded to two equivalent Ba(1); two equivalent Mg(6); four Mg(3,3,3); and four Mg(5,5) atoms to form YBa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Y(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ba(1)Y2Mg10 cuboctahedra; edges with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; edges with four equivalent Mg(6)YMg11 cuboctahedra; edges with eight Mg(5,5)BaYMg10 cuboctahedra; faces with two equivalent Ba(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(6)YMg11 cuboctahedra; faces with four Mg(3,3,3)Ba2Y2Mg8 cuboctahedra; faces with four Mg(5,5)BaYMg10 cuboctahedra; and faces with six equivalent Mg(7)BaMg11 cuboctahedra.