The Al$_{3}$Ni$_{2}$ Structure as Approximant of Quasicrystals

The present paper discusses the approximant nature of the Al$_{3}$Ni$_{2}$ structure from the viewpoint of valence electron concentration (VEC) correspondence as well as from atomic structure correlation. Its VEC is close to that of corresponding quasicrystals and its atomic structure can be described by layers stacked along the direction corresponding to the 10-fold axis of the decagonal phase. A large orthorhombic pseudocell is proposed whose edges are integer multiplication of those of a basic CsCl unit along directions corresponding to the orthogonal 10-fold and two 2-fold axes of the decagonal phase. Thus its structure can be expressed in the form of Al$_{3}$Ni$_{2}$-(1,3,3) or Al$_{3}$Ni$_{2}$-(3,1,3), the integers being the multiplicity of the CsCl unit along the three directions. The generalization of this expression to several other approximants indicates that approximants can be related to each other by packing the basic CsCl pseudocells in different ways