TABLE OF CONTENTS The main reason for the variation of the thermodynamic characteristics of nanocrystals in comparison with bulk materials is the variation of the phonon spectrum, i.e. the variation of the distribution function of frequencies of atomic vibrations (the term 'frequency distribution function' will be used). This is confirmed by the results of investigation [94] of single crystal Si and silicon powder by the inelastic scattering of slow thermal neutrons. The frequency distribution function, g( ?), for a fine powder and bulk silicon greatly differ. Neutron scattering was also used for obtaining phonon spectra of MgO particles ( D ~ 11, 16 and 23 nm), TiN particles ( D ~ 30 nm) and bulk specimens of MgO and TiN [95 97]. According to [19], the phonon spectrum of small particles does not contain low frequency modes which are present in the spectra of bulk crystals. The waves whose half-length exceeds the longest size D of the particle may form in the nanoparticles. Therefore, the phonon spectrum is restricted by some minimum frequency ? min ~ c/2 D (where c is the velocity of sound) on the lower limit of vibration frequency. There is no such restriction in bulk solids. The numerical value of ? min depends on the properties of the substance and the shape and size of the particles. It may be expected that a decrease of the particle size should displace the phonon spectrum...
