An Application of the Cellular Method to a Vacancy in Metal

Abstract

The distribution of electrons around a vacancy in metal is studied using a model which was introduced in our previous paper in order to treat the impurity atom.
The arrangement of nuclei of matrix metal at each lattice point, except one where the nucleus is missing, i.e., vacancy, is treated by the cellular method. The deviation of the potential in the cells neighboring to the vacancy, from the periodic one for the pure metal is taken into account. In the first approximation, the lattice distortion due to the vacancy is neglected.
The Thomas-Fermi equation, in which all the electrons, i.e., valence electrons as well as core ones, are taken into account, is solved numerically in each cell and connected smoothly by a suitable set of boundary conditions.
As a result of our calculations for the case of a vacancy in copper, we find that there is the charge of −1.7e inside the atomic sphere for the vacancy.