On the statistical thermodynamics of a free-standing nanocrystal: Silicon

Abstract

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 Θ, Gruneisen parameter γ, melting temperature T_m, surface energy σ, surface pressure P_sf, elastic modulus B_T, Poisson ratio μ, thermal expansion coefficient α_p, and specific heats c_v and c_p. Calculations performed for silicon have shown that the functions Θ, T_m, σ, and B_T decrease, whereas the functions γ, |P_sf|, μ, α_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.