Surface Thermodynamics and Vibrational Entropy

Abstract

As with bulk material, a few thermodynamic variables determine the stability and equilibrium properties of solid surfaces. Since the environment at the surface is typically very different from that in the bulk, as a result of the lack of symmetry created by the presence of the surface, thermodynamics plays an important role in determining surface structure and dynamics. The quantity of interest here is the surface free energy, which inherently includes the contribution of vibrational (and configurational) entropy. Given the existence of surfaces vibrational modes whose features are distinct from those in the bulk, and dependent on local surface geometry and electronic structure, the emphasis in this chapter is on the characteristics of vibrational entropy, which, in turn, affect surface thermodynamical quantities that are in excess of values in the bulk. Special attention is paid to characteristics of vibrational density of states of low and high Miller index surfaces and their contribution to vibrational entropy, and, hence, to thermodynamical functions. In fact, it is argued that the distinguishing features in the vibrational density of states, namely enhancement of the number of modes at low frequencies and appearance of modes above the bulk band, highlight the impact of the undercoordinated atoms at surfaces, steps, and kink sites and lead to variations in the local surface electronic structure. The characteristics found on high Miller index surfaces in particular pave the way for understanding vibrational dynamics of nanoparticles. Contact is made with experimental data where available.