The Study Of Quantum Size Effects And Calorifics Properties In A Nanosphere

When the size of matter is reduced to the nanometer scale, the number of atoms and electrons inside become countable and there appear quantum effects such as the size effect , the phase coherence effect and nonlinear optical effect. The renowned physicist Richard Feynman foresaw the way to the science of nanotechnology. He suggested the possibility of controlling individual atoms and molecules. Now this fiction become realization in nanotechnology. It is certain that quantum device and quantum information technology's invention and development from the development of informational society. There appears some new quantum devices such as resonant tunneling devices, signal electron devices and quantum computer devices, and their prospect are spectacular.In recent years, nanometer-scale mechanical systems have attracted a great deal of attention due to their unique physical properties and their potential use in nanotechnology. It is well known that the vibrational spectrum of an isolated nanocrystal is discrete with an energy gap in the low-energy in contrast with that of the same bulk which has a continuous spectrum down to zero. At low frequency, an excess of vibrational modes is found as compared to the bulk, and the vibrational DOS reveal a tendency of approaching the bulk relation with the increase in nanocrystal size. Any property of a nanoparticle that depend on the low-frequency vibrational spectrum, such as its low-temperature thermodynamic properties or low-energy electronic relaxation rate, will be different in bulk crystal. Because of the extremely small size and volume-to-surface ratio of these systems, interactions with their surroundings can dramatically alter their properties.In this thesis, continuum medium theory and many body theory are applied to study the thermodynamic properties in a nanoparticle, which is weakly coupled to a substrate. The research benefits ours understanding the experimental results observed and provides theoretical guidance on producing nanoscale devices. An isolated elastic spherical represents nanoparticle, the phonon of the bulk substrate act as a bath of harmonic oscillators which has a continuous vibrational DOS at low energy. Continuous media theory used to study eigenvectors and eigenmodes in the nanoparticle under the stress free boundary conditions. The local acoustic phonon DOS of nanoparticle is calculated by solving the Dyson equation of phonon propagator, we show that environmental interaction is especially important at low frequencies. we study an hollow spherical nanoparticle weak coupled to an semi-infinite substrate. We found the vibrational spectrum of an hollow nanoparticle is broaden, and there is an obvious differenc as compared to an isolated nanoparticle, We studied the thermodynamical properties by low frequency vibrational spectrum of an hollow nanoparticle.