Chapter 76 Elasticity, Dislocations and their Motion in Quasicrystals

Abstract

Publisher Summary Quasi-crystals have a special type of elastic degrees of freedom, termed “phason degrees of freedom.” Quasi-crystals are accompanied by the phason elastic field in addition to the phonon (conventional) elastic field. The generalized elasticity of quasi-crystals is described in terms of the two types of elastic fields. Within linear elasticity, the elastic free energy of quasi-crystals consists of three types of quadratic terms: phonon–phonon, phason–phason, and phonon–phason coupling terms. Correspondingly, elasticity of quasi-crystals comprises the three parts: pure phonon elasticity, pure phason elasticity, and phonon–phason coupling. The chapter reviews the characteristic features of elasticity, dislocations, and their motion in quasi-crystals. It also reviews elastic properties of quasi-crystals. Quasi-crystals have the phason elastic degrees of freedom in addition to the phonon (conventional) elastic degrees of freedom. The chapter discusses the generalized elastic theory constructed by incorporating the two types of elastic degrees of freedom. The explicit formulae are presented for the two most important classes of quasi-crystals—that is, icosahedral and decagonal quasi-crystals. The chapter also discusses the detailed mechanisms of dislocation glide and dislocation climb.