Frequency Spectra of Free Lattices and Particle Size Effects on the Heat Capacity of Solids

The effect of particle size on the heat capacity of solids has been investigated using lattices with free boundaries as models. A monatomic lattice shows a low temperature effect associated with the acoustic modes. This can be compared with results obtained from a continuum model. With a diatomic lattice, however, an effect is also associated with the optical modes and is apparent at higher temperatures. The possibility that this latter effect can explain some recent experimental results is examined.