Lattice vibrations and specific heat of a small particle

By using an elastic body approximation, lattice vibrations of a small particle are discussed. Consideration of both vector fields and a scalar field yields the proper vibrational modes. Eigenfrequencies of the elastic vibrations are derived by considering circumstances surrounding a small particle: matrix effect, surface relaxation effect, local clamping effect and shape effect. Among these, the surface relaxation effect and the local clamping effect are shown to be responsible for the specific heat of a small particle observed by Novotony and Meincke (1973).

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