Structural relationships between single atom type crystal structures and intermetallic compound structures, as illustrated by Laves‐ and Hume‐Rothery phases

In comparison to the single atom type crystal structures, which are relatively simple and are concentrated in four types of structure (Cu, W, Mg, diamond), the crystal structures of intermetallic phases are manifold and often very complicated. At first sight there is no obvious connection between these types of crystal structures, however, a transition mechanism must exist for the solid-state transition from the simple single atom type crystal structures to the intermetallic phase structures. Such a mechanism would show the inner connection between the structures. In this work the topic is dealt with from a crystallographic point of view. The transition between the structures can be described by the three steps (1) substitution of atoms, (2) systematically ejection of particular atoms from the emerging intermediate structure and (3) spatial relaxation especially of the atoms around the newly formed interstices. This general structural phase transition path will be discussed for two of the intermetallic classes, the Laves phases and the Hume-Rothery phases. A suitable way of showing this is by making a comparison between the coordination polyhedra (atomic environments) of the single atom type crystal structures and those of the derived intermetallic crystal structures.