Lattice Dynamics of Microcrystallites

Abstract

We have calculated the allowed frequency modes for simple cubic microcrystallites with free boundaries, taking the nearest-neighbor interaction. The mean-square displacement (m.s.d.) and the mean-square velocities (m.s.v.) in different directions, for atoms in different positions on the lattice, have been evaluated. Two different sets of force constants have been used. We find that for surface atoms, m.s.d. for motion along the surface is nearly the same as for motion perpendicular to the surface. m.s.d. is maximum for corner atoms and minimum for atoms in bulk. On the other hand, m.s.v. is maximum for atoms in bulk and minimum for corner atoms. At any fixed site, we find that both m.s.d. and m.s.v. increase with increasing crystal size, and tend to an asymptotic value. For one set of force constants we have also calculated the specific heat of microcrystallites at various temperatures, as a function of crystallite size. The effective Debye temperature is estimated, and its variation, both with crystallite size and sample temperature, is discussed.