Point defects and their interaction with impurities in metals

Abstract

A statistical thermodynamical theory based on a density-independent pair potential is first used in the hot crystal to relate the monovacancy formation energy E_v to properties of the liquid at the melting temperature T_m. Whereas the theory works quantitatively for the close-packed crystals Ar and Kr, there are larger deviations between theory and experiment for close-packed metals, and the reasons for this are discussed. For other solids, open structures stand out; b.c.c. metals, such as Na and K, require careful treatment of (a) ionic relaxation and (b) sp hybridization, and the theory is not appropriate for Ge and Si because of the change in the nature of the bonding through T_m. Two other correlations that are discussed are between (i)E_v and rigidity, G, and (ii)E_v and surface energy. Some brief comments are added on the energy of formation of self-interstitials.

The second part of the paper is concerned with the consequences of the generalization of the density-independent pair potential theory to binary alloys. The new feature stressed is the size-difference, δ, between the components. A prediction concerning the effect of δ on the vacancy formation energy in a dilute mixture is shown to be borne out in a suitably chosen metallic binary alloy. The paper concludes with some comments on the relation of the present treatment to the embedded atom model predictions for vacancies in cold crystals, which complements the present work.