Self-Consistent Einstein Model and Surface Debye Temperature

On the basis of a self-consistent Einstein model, which has been applied to a theory of melting of metallic fine particles in a previous publication, we discuss the problem of the surface Debye temperature. A semi-infinite metal crystal with a plane surface is considered and the vibrational frequency of each atom is self-consistly determined as function of atomic position. By making use of a simplified interatomic potential, an expression for the difference between square of the bulk and surface Debye temperatures is derived.