Elimination of irradiation point defects in crystalline solids: Sink strengths

Abstract

The rate theory of irradiation effects in crystalline solids rests on a set of two ordinary differential equations which, for each type of point defect (vacancy and self-interstitial), describe the balance between the production of defects on the one hand and their annihilation on the other. The latter process occurs either by mutual recombination, a bimolecular reaction, or by elimination on point defect sinks, a first-order reaction. The elimination rate is proportional to the defect concentration times the defect diffusion coefficient times a geometrical factor, the ``sink strength.'' The classical expression of sink strengths is obtained by solving the diffusion equation of point defects in a cell, which contains the sink, and ensuring that the mean value of the defect concentration in the cell equals the concentration in the rate theory. We propose an alternative criterion. Since the amplitude of the irradiation effects of practical relevance is dictated by the partitioning of the defect annihilation between mutual recombination and elimination on sinks, we propose that the value of the sink strength should give the correct value for the latter partitioning. The sink strengths so defined, scaled to their classical value, are evaluated for sink geometries of practical interest and expressed as a function of one dimensionless parameter, which is a function of the irradiation flux and temperature. Depending on the irradiation conditions, the correcting factors for individual sink strengths may be large (several orders of magnitude). When several types of sinks compete, we further impose that the partitioning of the elimination among the various types of sinks has the correct value. The sink strengths, as defined in this work, are additive, at variance with the classical ones. According to our definition, the dislocation bias, which measures the relative difference between the sink strengths of dislocations respectively for interstitials and vacancies, is shown to increase with the strength of neutral sinks around the dislocation. It ranges from zero when the dislocations are the only sinks to several ${10}^{\ensuremath{-}1}$ when the neutral sinks have a strength much larger than that of dislocations. The computation of the correcting factor is presented in such a way that it can be easily incorporated into the rate theory of irradiation effects.