Dependence of thermal expansion coefficient on size and shape of a silicon nanocrystal at various temperatures

Abstract

Dependence of the thermal expansion coefficient (αp) on the size (number N of atoms) and shape of the nanocrystal surface of an elementary monatomic substance is studied using the model of a nanocrystal in the form of a rectangular parallelepiped with a variable shape of the surface (RP model). Calculations for a silicon nanocrystal have shown that αp(N) increases with a decrease in the nanocrystal size more noticeably the lower the temperature. The larger the deviation of the nanocrystal shape from the most energetically stable shape (cube for the RP model), the more noticeable is the increase in function αp(N) upon an isothermal decrease in N. With an isomorphic decrease in N along the isotherm at 100 K, function αp(N) increases and it is transformed into a positive region for a certain size.