In pure Ni 3 Al phase atoms of aluminium are placed at the vertices of the cubic cell and form the sublattice A . Atoms of nickel are located at centers of the faces and form the sublattice B . The phase is not strictly stoichiometric.
32.
In the non-simply laced cases B, C, G and F, the root lattice is spanned by the short roots and the long roots span a sublattice, invariant under the Weyl group, equal to " r " 2 / 2 times the coroot lattice, where " r " is the length of a long root.
33.
In the adjacent table, | ? < | denotes the number of short roots, " I " denotes the index in the root lattice of the sublattice generated by long roots, " D " denotes the determinant of the Cartan matrix, and | " W " | denotes the order of the Weyl group.
34.
For each element a in a normal skew lattice S, the set a \ wedge S \ wedge a de�ned by { a \ wedge x \ wedge a | x \ in S } or equivalently { x \ in S | x \ leq a } is a sublattice of S, and conversely . ( Thus normal skew lattices have also been called local lattices . ) When both \ wedge and \ vee are normal, S splits isomorphically into a product T \ times D of a lattice T and a rectangular skew lattice D, and conversely.
