On the Statistical Thermodynamics of a Free-Standing Nanocrystal: Silicon

The dependence of the thermodynamic parameters of a free-standing nanocrystal of simple matter on its size, density, temperature, and surface shape has been studied. The following parameters have been analyzed: Debye temperature Theta, Gruneisen parameter gamma, melting temperature T-m, surface energy sigma, surface pressure P-sf, elastic modulus B-T, Poisson ratio mu, thermal expansion coefficient alpha(p), and specific heats c(v) and c(p). Calculations performed for silicon have shown that the functions Theta, T-m, sigma, and B-T decrease, whereas the functions gamma, vertical bar P-sf vertical bar, mu, alpha(p), c(v), and c(p) increase with an isomorphic decrease in the number of atoms N. The stronger the nanocrystal shape deviates from the most energetically stable shape, the more pronounced the change in the aforementioned functions with an isothermal decrease in N is.