A procedure for measuring the helium density and pressure in nanometre-sized bubbles in irradiated materials using electron-energy-loss spectroscopy

Abstract

A procedure for measuring the density of He in nanometre-sized bubbles in materials using electron-energy-loss spectroscopy is given. It involves measuring the scattering probability of an electron as a result of exciting a ls electron in He to the 2p state. An expression for the cross-section of this interaction is obtained, taking into account some relativistic effects, the q dependence of the matrix element and the effect of a non-zero convergence angle of the incident electron beam. An accuracy of about 10% in the calculation of the He density can be achieved using this technique. The procedure is demonstrated using spectra obtained from He bubbles in irradiated PE16 alloy specimens and used to make preliminary investigations into the relationship between the blue shift of the ls ← 2p transition in He with atomic density and the relationship between the pressure in the bubbles and the bubble radius. The best estimate of the pressure in the He bubbles shows it to be less than half that required to achieve equilibrium with the surface tension of the metal, if the usually accepted value of the surface tension is used. The blue shifts observed for bubbles of diameter 50 and 250 Å can be extrapolated, within experimental error, to those obtained by Jäger et al. for much higher helium densities.