The effective sink strength of a random array of voids in irradiated material

Abstract

The mean sink strength of a distribution of voids in a solid containing a diffusing population of defects is defined unambiguously in terms of the spatial average of the solution of a particular steady-state diffusion problem. A variational characterization of this problem then leads to lower bounds for the sink strength. The voids are supposed to be distributed according to some stochastic process; this feature is incorporated by extremizing the expectation value of the variational functional with respect to simple configuration-dependent trial fields. This results in bounds for the sink strength which involve correlations between small numbers of voids. The bounds are highly sensitive to the statistics of the void distribution and in fact, may in some cases demonstrate that a postulated correlation function is inconceivable as a result of any stochastic mixing process. This occurs for the ‘well-stirred’ approximation, at a volume concentration around 0.2, at which the strict lower bound becomes infinite, corresponding to the expectation of a quadratic functional known to be definite becoming indefinite. Results are compared with those obtained from a self-consistent calculation and from small-concentration perturbation theory. It is demonstrated that a suitably constructed version of the latter yields a strict lower bound which can actually exceed the self-consistent estimate at high concentrations. In such cases, therefore, it is the more reliable.