A combined experimental and theoretical study of small and large vacancy clusters in tungsten

Tungsten is considered to be used in the future fusion reactors as plasma-facing material. In such extreme environments, defects are induced in materials that modify their macroscopic properties such as the mechanical ones. It is of paramount importance to be able to determine concentration and size of the vacancy defects, from the mono vacancy to the large cavities, to validate the models developed to predict the evolution of the microstructure of irradiated materials. Positrons are very useful non-destructive probes that can characterize vacancy-type defects in materials. We present a combined experimental and theoretical study on detecting and estimating the sizes of vacancy clusters that are invisible with electron microscopy in tungsten, using positron annihilation spectroscopy. We here model the positron annihilation in the tungsten lattice and in vacancy-type defects using state-of-the-art first principles methodology. The Doppler broadening spectra and positron lifetimes in tungsten are calculated with two-component density functional theory with local density approximation and weighted density approximation. Our calculations are in excellent agreement with our experimental results. We show that the sizes of vacancy clusters in tungsten can be well estimated by combining both positron lifetimes and Doppler broadening spectra. We also determine the limit of validity of the canonical calculation method, which here is shown to fail when the vacancy clusters grow beyond their nucleation stage. This work is a first step needed to better interpret the measured positron annihilation characteristics (Doppler and lifetime) in tungsten and then extract quantitative data on small vacancy defects required to improve the understanding of early-stage vacancy defect evolution in tungsten. The method used in this paper could be used to study other metallic materials.