Calculation of the radial distribution function of bubbles in the aluminum hydrogen system

Aluminum foils of 99.99% purity were charged with hydrogen using a gas plasma method with a voltage in the range of 1.0-1.2 keV and current densities ranging from 0.66 to 0.81 mA cm(-2), resulting in the introduction of a large amount of hydrogen. X-ray diffraction measurements indicated that within experimental error there was a zero change in lattice parameter after plasma charging. This result is contradictory to almost all other FCC materials, which exhibit a lattice expansion when the hydrogen enters the lattice interstitially. It is hypothesised that the hydrogen does not enter the lattice interstitially, but instead forms a II-vacancy complex at the surface which diffuses into the volume and then clusters to form H-2 bubbles. The nature and agglomeration of the bubbles were studied with a variety of techniques, such as small angle, ultra small angle and inelastic neutron scattering (SANS, USANS and INS), transmission and scanning electron microscopy (TEM and SEM), precision density measurements (PDM) and X-ray diffraction. The USANS and SANS results indicated scattering from a wide range of bubble sizes from <10 Angstrom up to micron size bubbles. Subsequent SEM and TEM measurements revealed the existence of bubbles on the surface, as well as in the bulk and INS experiments show that hydrogen is in the bulk in the form of H-2 molecules. In this paper we calculate the radial distribution function of the bubbles from the SANS and USANS results using methods based on the models derived by Brill et al., Fedorova et al. and Mulato et al. The scattering is assumed to be from independent spherical bubbles. Mulato et al. model is modified by incorporating smearing effects, which consider the instrumental resolution of the 30 m SANS spectrometer at NIST. The distribution functions calculated from the two methods are compared, and these distributions are then compared with the range of particle sizes found from TEM and SEM techniques. (C) 1999 Elsevier Science S.A. All rights reserved.