Density Of Helium In Bubbles Research Articles

A variable-gap model for calculating free energies of helium bubbles in metals

We propose a variable-gap energy model for helium bubbles in metals, based on molecular dynamics (MD) calculations. The emphasis is put on the appropriate description of the helium-metal repulsion, which can be modelled as a variable-size gap between regions occupied by helium and metal atoms. Each contribution to the bubble energy is parametrized on MD calculations performed in iron. The model is shown to reproduce accurately the dissociation energies obtained by MD over a large range of helium-to-vacancy ratios. Improvements over previous models are shown on a few equilibrium properties: binding energies, solid to fluid transition, helium density in bubbles and validity of Laplace law. Beyond the iron case, such a model should be valid in other metals where helium behavior is similar.

Gas densities in he bubbles and their size distribution in nickel measured by neutron scattering

The density of helium in bubbles produced in two Ni isotopes by α-implantation and isochronal annealing has been measured by the contrast variation method of SANS. A further evaluation of the SANS data after the last annealing step at 1123 K yielded a bimodal size distribution. Assuming equilibrium bubbles a consistent set of parameters characterizing the bubble populations could be extracted from the scattering data. Those parameters for the “small” and “large” bubbles are: The atomic He densities are 0.7 and 0.17 of the atomic Ni density, the mean radii are 1.2 and 13 nm, the volume fractions are 0.011 and 0.0074 and the He contents are 790 appm and 120 appm, respectively. The values for the “small” bubbles are in good agreement with the TEM results. However, the existence of “large” bubbles could not be confirmed by TEM, probably because of a spatially inhomogeneous distribution.

The density of helium in bubbles in implanted materials: Results from VUV absorption and eel spectroscopy

The novel application of vacuum ultra-violet absorption spectroscopy and electron energy loss spectroscopy to helium bubbles in metals is presented. These measurements, carried out on thin aluminium films containing different concentrations of helium and various bubble size distributions, were aimed at determining the density (and thus pressure) of helium in bubbles by observing the shift and broadening of the IS-2P transition in the helium. The data coupled with a theoretical model developed by the authors (see following paper) indicate densities as high as 1023 He cm−3 for specimens containing small bubbles. Data are also presented on the effect that annealing and cooling have on these spectra. The annealing experiments give rise to fairly complex changes in absorption peak structure but with a general shift towards the unperturbed resonance line. The cooling experiment gives rise to a further shift and a narrowing of the absorption spectrum on cooling to 77 K which is tentatively identified as the liquid/solid transition in the helium. Finally, fluorescence spectrum of an Al/He specimen excited with low energy electrons is presented.

The density of helium in bubbles in implanted materials: Theoretical interpretation of VUV absorption and EELS spectroscopy

The shape of the He resonance absorption line of He bubbles in metals is discussed in terms of He-metal and He-He interactions. For bubble radii larger than 10 A the metal matrix effects are found to be negligible. For small vacancy clusters there is as yet no quantitative calculation of the role of the metal conduction electrons in determining the position and width of the He resonance excitation. The He-He interactions are treated within static line broadening theory which assumes pairwise additivity of the interactions. These are taken from ab initio quantum mechanical calculations of 2p excimer potential energy curves due to Guberman and Goddard and to Gupta and Matsen. The radial pair distribution function required by our statistical line shape calculation is computed from two theoretical models of the dense fluid: either the exact solution of Percus-Yevick's equation for hard spheres or a Molecular Dynamics computer simulation based on an accurate pair potential. The two approaches give very similar results. The blue shift of the resonance line is found to depend nearly linearly on density but our value for the slope differs substantially from the prediction of a model band structure calculation performed by the Julich group in the framework of density functional theory.

The bubble coalescence model of radiation blistering

The existence of overpressurized gas bubbles, and a suitable mechanism for bubble growth during low temperature ion implantations, are the essential ingredients for the validity of a gas-driven blister formation mechanism. In this paper, taking into account the difference between the formation energy of helium interstitials and the free energy change of a bubble per helium atom added, we have theoretically shown that such bubbles indeed exist, and their growth is driven by their bias for vacancies and anti-bias for interstitials which arise because of the overpressure-induced compressive stress field around them. The relations for helium density in bubbles and the bubble overpressure are derived. The role of interbubble interaction and the effect of bubbles on the elastic properties of the material have been taken into account to determine the dose dependence of the integrated lateral stress and the critical conditions for interbubble coalescence/fracture. It is shown that the observed sublinearity and the relief of integrated lateral stress are a natural consequence of the attractive interbubble interaction and do not uniquely relate to the blister formation as considered in the stress model. The derived conditions for coalescence agree well with the available data. It is argued that the present treatment provides a sound theoretical basis for the gas pressure model of radiation blistering.

Optical measurements of the density of helium in small bubbles in aluminium films

Some preliminary measurements are reported on the density of helium in bubbles in metal films using optical spectroscopy in the far vacuum ultra-violet. The technique consists of measuring (by transmission through the films) the optical absorption resulting from the transition 1 1 S 0 → 2 1 P 1 due to the helium in the bubbles. This transition, in a rarefied gas, occurs at 584 Å (21.2eV) but because of the gas density in the bubbles is observed to be broadened and shifted to higher energy (blue shifted). The measurements imply, for specimens with high gas concentrations (0.5–3 at% He), a gas density in the bubbles greater than 10 23 atoms cm −3.