Diffusion-reaction model for positron trapping and annihilation at spherical extended defects and in precipitate-matrix composites

Abstract

The exact solution of a diffusion−reaction model for the trapping and annihilation of positrons in small extended spherical defects (clusters, voids, small precipitates) with competitive rate-limited trapping in vacancy-type point defects is presented. Closed-form expressions are obtained for the mean positron lifetime and for the intensities of the two positron lifetime components associated with trapping at defects. The exact solutions can be conveniently applied for the analysis of experimental data and allow an assessment in how far the usual approach, which takes diffusion limitation into account by means of effective diffusion-trapping rates, is appropriate. The model is further extended for application to larger precipitates where diffusion-and reaction limited trapping is not only considered for the trapping from the matrix into the precipitate−matrix interface but also for the trapping from inside the precipitates into the interfaces. This makes the model applicable to all type of composite structures where spherical objects are embedded in a matrix irrespective of their size and their number density.

Influence of high-pressure torsion deformation on the corrosion behaviour of a bioresorbable Mg-based alloy studied by positron annihilation

“…The assignment of τ 2 to GBs is further supported by quantitatively considering the intensity of the e + annihilation component which is expected for trapping at grain boundaries (GBs) and matrix-precipitate interfaces based on the microstructural parameters quoted in section III A. For this purpose, our models of diffusion-and reaction-limited e + trapping at the aforementioned defect types [42][43][44][45] were applied by making use of the solutions which are summarized in the appendix.…”

“…Solutions for diffusion-and reaction limited e + trapping at precipitate-matrix interfaces of spherical-shaped precipitates were presented by Würschum et al 44 The mean e + lifetime reads (ref. 44…”

Microscopic Aspects of Artificial Ageing in Al-Mg-Si Alloys

“…The reason for this lies in the extended nature of the precipitates and the large value for the specific trapping rate of their interfaces [51] as can be calculated using the formalism given in Ref. [52].…”

“…We are grateful to Roland Würschum for pointing out that the formalism given Ref. [52] can be used to show that saturated positron trapping can take place even in overaged alloys.…”

Positron trapping and annihilation at interfaces between matrix and cylindrical or spherical precipitates modeled by diffusion-reaction theory

“…It is, however, well known that e + trapping at such extended defects like precipitates cannot be correctly described by standard rate theory but demands for analysis in the framework of diffusion-reaction theory. Whereas diffusionlimited e + trapping at grain boundaries of crystallites (or equivalently at surfaces of particles) has been quantatively modeled by several groups [1,2,3,4,5], diffusion-limited e + trapping at interfaces of precipitate−matrix composites is more complex and has not been treated until recently [6]. In addition to diffusion-limited interface trapping from the interior of the precipitate, in particular the interfacial trapping from the surrounding matrix has to be treated taking into account diffusion limitation.…”