Reaction of positronium with doped ions in silica-based glasses in the size determination of subnanometer structural open spaces

Positron annihilation spectroscopy is employed to estimate the size of subnanometer-scale open spaces in insulating materials. In most cases, the size is estimated from the lifetime of long-lived ortho-positronium (o-Ps) by pickoff annihilation using a simplified model. However, reactions of Ps with surrounding electrons other than the pickoff reaction, such as spin conversion or chemical reaction, could give a substantially underestimated size using the simplified model. In the present paper, we report that the size of the open spaces can be evaluated correctly by the angular correlation of positron annihilation radiation (ACAR) with a magnetic field using the spin-polarization effect on Ps formation, even if such reactions of Ps occur in the material. This method is applied to the subnanometer-scale structural open spaces of silica-based glass doped with Fe. We demonstrate the influence of the Ps reaction on size-estimation of the open spaces from the o-Ps lifetime. Furthermore, the type of reaction, whether spin conversion or chemical, is distinguished from the magnetic field dependence of the Ps self-annihilation component intensity in the ACAR spectra. The Ps reaction in silica-based glass doped with Fe is a chemical reaction (most likely oxidation) rather than spin conversion, with Fe ions. The chemical quenching rate with Fe ions is determined from the dependence of the o-Ps lifetime on the Fe content.