9 - Crystal lattice dynamics, structure, and thermodynamics

Summary

This chapter mostly explains the role of graphene as a prototype crystalline membrane. We discuss peculiarities of phonon spectra of two-dimensional crystals, such as existence of soft flexural modes and unavoidably decisive role of anharmonic effects, the physical origin of negative thermal expansion of graphene and Mermin–Wagner theorem forbidding long-range crystalline order for two-dimensional materials. We consider mechanics and statistical mechanics of crystalline membranes and especially the role of thermal fluctuations resulting in intrinsic ripples. At the end of this chapter, we give a basic introduction to Raman spectroscopy which is one of the most important experimental tools to probe the properties of graphene.