Method for determining the electron and positron work function from a metal containing vacancies

A method is proposed that combines self-consistent solutions for a monovacancy in metal without regard to the outer surface and the solution in the stable jelly model for metal with homogeneous volume and flat surface, but a lowered vacancy density due to the presence of a superlattice of vacancy voids with relative concentration $c_{v}$. When using $c_{v}$ as a small parameter, all energy characteristics are expanded in a functional series. Zero expansion terms relate to defect-free metal, and linear in $c_{v}$ corrections are expressed in terms of its characteristics. Exact formulas allowing the consideration of the effect of vacancies on the electron and positron work function are derived. Characteristics are calculated at various temperatures for Al and Na by the Kohn–Sham method. The method application to spherical clusters is briefly discussed.