ABSTRACT
This chapter examines the magnitude of the thermal fluctuations and discusses the roughening transition of solids. In thermal equilibrium, the surfaces of fluids and even solids are not perfectly flat; neither are the interfaces between two different phases. Thermal fluctuations roughen the regions between two materials; how strong these effects are depends on dimensionality and on temperature. For fluid interfaces, two-dimensional systems with one-dimensional interfaces have a mean-square roughness of the interface that varies linearly with the system size; the corresponding quantity in three-dimensional systems is logarithmic with the system size. In order to study the fluctuations of interfaces and surfaces, one first needs an expression for the free energy of an interface with a shape that is not necessarily flat. While the Rayleigh instability of a cylindrical surface is driven by the surface energy, the flat surface of a thin film can become unstable under the influence of van der Waals forces.
