Mg6YTi crystallizes in the orthorhombic Amm2 space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Ti(1) atoms to form MgY2Mg8Ti2 cuboctahedra that share corners with four equivalent Y(1)Mg10Ti2 cuboctahedra; corners with four equivalent Ti(1)Y2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Y(1)Mg10Ti2 cuboctahedra; edges with two equivalent Ti(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Y2Mg10 cuboctahedra; edges with four equivalent Mg(2)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Mg8Ti2 cuboctahedra; and faces with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra. In the second Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Ti(1) atoms to form MgY2Mg8Ti2 cuboctahedra that share corners with four equivalent Y(1)Mg10Ti2 cuboctahedra; corners with four equivalent Ti(1)Y2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Y(1)Mg10Ti2 cuboctahedra; edges with two equivalent Ti(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Y2Mg10 cuboctahedra; edges with four equivalent Mg(2)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Mg8Ti2 cuboctahedra; and faces with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Ti(1) atoms to form distorted MgY2Mg8Ti2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ti2 cuboctahedra; corners with four equivalent Mg(3)Y2Mg10 cuboctahedra; corners with ten Mg(2,2)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with two equivalent Mg(3)Y2Mg10 cuboctahedra; edges with two equivalent Mg(2)Y2Mg8Ti2 cuboctahedra; edges with four equivalent Mg(1)Y2Mg8Ti2 cuboctahedra; edges with four equivalent Y(1)Mg10Ti2 cuboctahedra; edges with four equivalent Ti(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; and faces with eight Mg(1,1,1)Y2Mg8Ti2 cuboctahedra. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Ti(1) atoms to form distorted MgY2Mg8Ti2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ti2 cuboctahedra; corners with four equivalent Mg(3)Y2Mg10 cuboctahedra; corners with ten Mg(2,2)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with two equivalent Mg(3)Y2Mg10 cuboctahedra; edges with two equivalent Mg(2)Y2Mg8Ti2 cuboctahedra; edges with four equivalent Mg(1)Y2Mg8Ti2 cuboctahedra; edges with four equivalent Y(1)Mg10Ti2 cuboctahedra; edges with four equivalent Ti(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; and faces with eight Mg(1,1,1)Y2Mg8Ti2 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(2,2); and two equivalent Y(1) atoms to form MgY2Mg10 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ti2 cuboctahedra; corners with six equivalent Mg(3)Y2Mg10 cuboctahedra; corners with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; edges with four equivalent Y(1)Mg10Ti2 cuboctahedra; edges with eight Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with four Mg(1,1)Y2Mg8Ti2 cuboctahedra; faces with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; and faces with six equivalent Ti(1)Y2Mg10 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(3); four Mg(1,1); four Mg(2,2); and two equivalent Ti(1) atoms to form distorted MgMg10Ti2 cuboctahedra that share corners with four equivalent Mg(3)Y2Mg10 cuboctahedra; corners with six equivalent Mg(4)Mg10Ti2 cuboctahedra; corners with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(3)Y2Mg10 cuboctahedra; edges with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; edges with four equivalent Ti(1)Y2Mg10 cuboctahedra; edges with eight Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Mg8Ti2 cuboctahedra; faces with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; and faces with six equivalent Y(1)Mg10Ti2 cuboctahedra. In the seventh Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Ti(1) atoms to form MgY2Mg8Ti2 cuboctahedra that share corners with four equivalent Y(1)Mg10Ti2 cuboctahedra; corners with four equivalent Ti(1)Y2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Y(1)Mg10Ti2 cuboctahedra; edges with two equivalent Ti(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Y2Mg10 cuboctahedra; edges with four equivalent Mg(2)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Mg8Ti2 cuboctahedra; and faces with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra. In the eighth Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Ti(1) atoms to form MgY2Mg8Ti2 cuboctahedra that share corners with four equivalent Y(1)Mg10Ti2 cuboctahedra; corners with four equivalent Ti(1)Y2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Y(1)Mg10Ti2 cuboctahedra; edges with two equivalent Ti(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Y2Mg10 cuboctahedra; edges with four equivalent Mg(2)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Mg8Ti2 cuboctahedra; and faces with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra. Y(1) is bonded to two equivalent Mg(3); four Mg(1,1,1,1); four Mg(2,2); and two equivalent Ti(1) atoms to form YMg10Ti2 cuboctahedra that share corners with four equivalent Ti(1)Y2Mg10 cuboctahedra; corners with six equivalent Y(1)Mg10Ti2 cuboctahedra; corners with eight Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Ti(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(3)Y2Mg10 cuboctahedra; edges with four Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; edges with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; faces with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Ti2 cuboctahedra. Ti(1) is bonded to two equivalent Mg(4); four Mg(1,1,1,1); four Mg(2,2); and two equivalent Y(1) atoms to form TiY2Mg10 cuboctahedra that share corners with four equivalent Y(1)Mg10Ti2 cuboctahedra; corners with six equivalent Ti(1)Y2Mg10 cuboctahedra; corners with eight Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Y(1)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with four Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; edges with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; faces with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; and faces with six equivalent Mg(3)Y2Mg10 cuboctahedra.
Mg6YTi crystallizes in the orthorhombic Amm2 space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Ti(1) atoms to form MgY2Mg8Ti2 cuboctahedra that share corners with four equivalent Y(1)Mg10Ti2 cuboctahedra; corners with four equivalent Ti(1)Y2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Y(1)Mg10Ti2 cuboctahedra; edges with two equivalent Ti(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Y2Mg10 cuboctahedra; edges with four equivalent Mg(2)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Mg8Ti2 cuboctahedra; and faces with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra. There is one shorter (3.23 Å) and one longer (3.28 Å) Mg(1)-Mg(1) bond length. Both Mg(1)-Mg(2) bond lengths are 3.21 Å. Both Mg(1)-Mg(3) bond lengths are 3.17 Å. Both Mg(1)-Mg(4) bond lengths are 3.22 Å. There is one shorter (3.24 Å) and one longer (3.26 Å) Mg(1)-Y(1) bond length. There is one shorter (3.18 Å) and one longer (3.32 Å) Mg(1)-Ti(1) bond length. In the second Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Ti(1) atoms to form MgY2Mg8Ti2 cuboctahedra that share corners with four equivalent Y(1)Mg10Ti2 cuboctahedra; corners with four equivalent Ti(1)Y2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Y(1)Mg10Ti2 cuboctahedra; edges with two equivalent Ti(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Y2Mg10 cuboctahedra; edges with four equivalent Mg(2)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Mg8Ti2 cuboctahedra; and faces with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.21 Å. Both Mg(1)-Mg(3) bond lengths are 3.17 Å. Both Mg(1)-Mg(4) bond lengths are 3.22 Å. There is one shorter (3.24 Å) and one longer (3.26 Å) Mg(1)-Y(1) bond length. There is one shorter (3.18 Å) and one longer (3.32 Å) Mg(1)-Ti(1) bond length. In the third Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Ti(1) atoms to form distorted MgY2Mg8Ti2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ti2 cuboctahedra; corners with four equivalent Mg(3)Y2Mg10 cuboctahedra; corners with ten Mg(2,2)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with two equivalent Mg(3)Y2Mg10 cuboctahedra; edges with two equivalent Mg(2)Y2Mg8Ti2 cuboctahedra; edges with four equivalent Mg(1)Y2Mg8Ti2 cuboctahedra; edges with four equivalent Y(1)Mg10Ti2 cuboctahedra; edges with four equivalent Ti(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; and faces with eight Mg(1,1,1)Y2Mg8Ti2 cuboctahedra. There is one shorter (3.08 Å) and one longer (3.43 Å) Mg(2)-Mg(2) bond length. There is one shorter (3.21 Å) and one longer (3.30 Å) Mg(2)-Mg(3) bond length. There is one shorter (3.10 Å) and one longer (3.40 Å) Mg(2)-Mg(4) bond length. Both Mg(2)-Y(1) bond lengths are 3.22 Å. Both Mg(2)-Ti(1) bond lengths are 3.11 Å. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Ti(1) atoms to form distorted MgY2Mg8Ti2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ti2 cuboctahedra; corners with four equivalent Mg(3)Y2Mg10 cuboctahedra; corners with ten Mg(2,2)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with two equivalent Mg(3)Y2Mg10 cuboctahedra; edges with two equivalent Mg(2)Y2Mg8Ti2 cuboctahedra; edges with four equivalent Mg(1)Y2Mg8Ti2 cuboctahedra; edges with four equivalent Y(1)Mg10Ti2 cuboctahedra; edges with four equivalent Ti(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; and faces with eight Mg(1,1,1)Y2Mg8Ti2 cuboctahedra. There is one shorter (3.21 Å) and one longer (3.30 Å) Mg(2)-Mg(3) bond length. There is one shorter (3.10 Å) and one longer (3.40 Å) Mg(2)-Mg(4) bond length. Both Mg(2)-Y(1) bond lengths are 3.22 Å. Both Mg(2)-Ti(1) bond lengths are 3.11 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(2,2); and two equivalent Y(1) atoms to form MgY2Mg10 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ti2 cuboctahedra; corners with six equivalent Mg(3)Y2Mg10 cuboctahedra; corners with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; edges with four equivalent Y(1)Mg10Ti2 cuboctahedra; edges with eight Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with four Mg(1,1)Y2Mg8Ti2 cuboctahedra; faces with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; and faces with six equivalent Ti(1)Y2Mg10 cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.26 Å. Both Mg(3)-Y(1) bond lengths are 3.23 Å. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(3); four Mg(1,1); four Mg(2,2); and two equivalent Ti(1) atoms to form distorted MgMg10Ti2 cuboctahedra that share corners with four equivalent Mg(3)Y2Mg10 cuboctahedra; corners with six equivalent Mg(4)Mg10Ti2 cuboctahedra; corners with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(3)Y2Mg10 cuboctahedra; edges with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; edges with four equivalent Ti(1)Y2Mg10 cuboctahedra; edges with eight Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Mg8Ti2 cuboctahedra; faces with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; and faces with six equivalent Y(1)Mg10Ti2 cuboctahedra. All Mg(4)-Mg(1,1) bond lengths are 3.22 Å. Both Mg(4)-Ti(1) bond lengths are 3.18 Å. In the seventh Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Ti(1) atoms to form MgY2Mg8Ti2 cuboctahedra that share corners with four equivalent Y(1)Mg10Ti2 cuboctahedra; corners with four equivalent Ti(1)Y2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Y(1)Mg10Ti2 cuboctahedra; edges with two equivalent Ti(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Y2Mg10 cuboctahedra; edges with four equivalent Mg(2)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Mg8Ti2 cuboctahedra; and faces with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra. There is one shorter (3.23 Å) and one longer (3.28 Å) Mg(1)-Mg(1) bond length. Both Mg(1)-Mg(2) bond lengths are 3.21 Å. Both Mg(1)-Mg(3) bond lengths are 3.17 Å. There is one shorter (3.24 Å) and one longer (3.26 Å) Mg(1)-Y(1) bond length. There is one shorter (3.18 Å) and one longer (3.32 Å) Mg(1)-Ti(1) bond length. In the eighth Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Ti(1) atoms to form MgY2Mg8Ti2 cuboctahedra that share corners with four equivalent Y(1)Mg10Ti2 cuboctahedra; corners with four equivalent Ti(1)Y2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Y(1)Mg10Ti2 cuboctahedra; edges with two equivalent Ti(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Y2Mg10 cuboctahedra; edges with four equivalent Mg(2)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Mg8Ti2 cuboctahedra; and faces with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.21 Å. Both Mg(1)-Mg(3) bond lengths are 3.17 Å. There is one shorter (3.24 Å) and one longer (3.26 Å) Mg(1)-Y(1) bond length. There is one shorter (3.18 Å) and one longer (3.32 Å) Mg(1)-Ti(1) bond length. Y(1) is bonded to two equivalent Mg(3); four Mg(1,1,1,1); four Mg(2,2); and two equivalent Ti(1) atoms to form YMg10Ti2 cuboctahedra that share corners with four equivalent Ti(1)Y2Mg10 cuboctahedra; corners with six equivalent Y(1)Mg10Ti2 cuboctahedra; corners with eight Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Ti(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(3)Y2Mg10 cuboctahedra; edges with four Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; edges with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(3)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; faces with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Ti2 cuboctahedra. Both Y(1)-Ti(1) bond lengths are 3.26 Å. Ti(1) is bonded to two equivalent Mg(4); four Mg(1,1,1,1); four Mg(2,2); and two equivalent Y(1) atoms to form TiY2Mg10 cuboctahedra that share corners with four equivalent Y(1)Mg10Ti2 cuboctahedra; corners with six equivalent Ti(1)Y2Mg10 cuboctahedra; corners with eight Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; edges with two equivalent Y(1)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ti2 cuboctahedra; edges with four Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; edges with eight Mg(2,2)Y2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ti2 cuboctahedra; faces with two equivalent Y(1)Mg10Ti2 cuboctahedra; faces with two equivalent Ti(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1,1,1)Y2Mg8Ti2 cuboctahedra; faces with four Mg(2,2)Y2Mg8Ti2 cuboctahedra; and faces with six equivalent Mg(3)Y2Mg10 cuboctahedra.