Chapter 5 Phason modes in aperiodic crystals

Abstract

This chapter focuses on the dynamical aspects of the phason modes in aperiodic crystals. The hyperspace description of quasiperiodic structures together with the hydrodynamic mode analysis provides a useful approach to understanding the common aspects of phason dynamics in different structural classes of aperiodic crystals. A phason mode is, in this approach, characterized by its wavevector and a polarization vector that lie in the perpendicular space. Phason dynamics has been observed in all the different classes of aperiodic crystal, and has been shown to be in agreement with the hydrodynamic theory. The chapter reviews the case of binary composites where one expects some degree of mixing between phason and acoustic degrees of freedom. It also reviews a few experimental results on the A1PdMn icosahedral phase to illustrate the concepts of quenched and thermal phasons, of phason strains, spatially homogeneous or not, of phason elasticity, and of phason-driven structural phase transitions. The chapter also highlights the future developments and remaining challenges in this exciting field.