Displacement of the Fermi Level Due to Impurities in a Random Distribution

The displacement of the Fermi level, ΔEF, on alloying, when impurity atoms are in a random distribution, is investigated in terms of a cellular structure where spherical cells, each containing an impurity atom at its center, have various sizes. This model is a simple extension of Friedel's model in which all the cells have an equal size. An appropriate distribution function of cell sizes is estimated by the aid of a computer simulation. For a random distribution of impurity atoms, ΔEFp is found to depend more linearly on the impurity concentration than expected from Friedel's model. A comparison is made with experimental data reported in literature for copper alloys.