More on the effect of vacancies on metal characteristics. Work function and surface energy

Within the density functional method, a simple method for determining the dependence of the work function of electrons and specific surface energy of the metal on the relative density of internal vacancies $c_v$ is proposed. Preserving the style of the stabilized jellium model, the preliminarily calculated volume shift of the conductivity zone bottom $\varepsilon^{(0)}\propto c_{v}$ in a specific homogeneous metal is introduced into a one-dimensional functional as the zero-point energy. Using the quantity $c_v$ as a small parameter, linear corrections to the abovementioned quantities are found. The expansion coefficients are expressed in terms of characteristics of a defectless metal. Calculations for Na and Al are carried out by the Kohn–Sham method. Temperature dependences of Al characteristics have been constructed in the thermodynamic limit.