CALCULATIONS OF POINT-DEFECT PROPERTIES IN COPPER, SILVER, AND GOLD BASED ON THREE-BODY INTEhWTIONS

The last twenty years have seen many attempts to calculate formation energies and formation volumes of vacancies and interstitials in facecentred cubic metals. (Johnson [l] has given an authoritative review; for recent developments see refs. [2,3] .) Judged by the effort spent, however, the progress achieved must be considered small. The majority of the model calculations on point-defects in Cu carried out during the above-mentioned period suffer from the following principal deficiencies: (i) The model potential is fitted either to the cohesive energy and then yields unrealistic values for the defect formation energies (see, e.g. ref. [4]), or to the vacancy formation energy, a quantity which one would wish to calculate [2-41. (ii) Only two-body potentials have been used. This implies the validity of Cauchy’s relation cl2 = c+, between the elastic moduli unless the pair potential is noncentral (i.e., angle-dependent) or an external pressure p = (cl2 c&/2, called the Cauchy pressure, is applied. In Cu and even more so in Ag and Au Cauchy’s relation is violated; hence an exact matching of the elastic moduli by the usual two-body potentials is impossible. Both ways of accounting for the deviations from Cauchy’s relation in Cu, Ag, and Au with pair potentials have been tried [S-7] but did not prove successful. (iii) The experimental value of the vacancy relaxation volume in CSr [-(0.20 f O.O5)s2 [8], SZ = atomic volume] could not be reproduced *r . The situation can be drastically improved with the aid of model potentials developed recently [lo]. The basic idea is to expand the cohesive energy per atom EC in m-body contributions E,(@ (cf. ref. [ 11 J) according to