The effect of cascade induced gas resolution on bubble formation in metals

Transmission electron microscopy observations of bubble structures formed during He ion implantation by accelerators indicate that bubbles nucleate at very low He concentrations (<10 appm) and displacement doses (<10−3 dpa), depending on temperature, and grow with increasing He concentration and dose at almost constant density after the nucleation peak. At intermediate temperatures, experimental data for higher doses indicate that bubble densities start (already at doses well below 1 dpa) to increase almost linearly with He concentration and dose, now at essentially constant bubble size. In the present contribution it is shown that this high dose feature of bubble formation may be attributed to the nucleation of bubbles under the internal He generation resulting from the resolution of He atoms from existing bubbles by displacement cascades. A simple analytical model, assuming that a certain fraction of He atoms in a bubble is resolved per dpa and that di-He clusters form a stable bubble nucleus, is presented, yielding for high doses a linear increase of the bubble density with dose at constant bubble size. This model is used to discuss the contribution of He bubbles to the hardening of metals under irradiation associated with He production, particularly its dependence on He concentration, displacement dose, and He-to-dpa ratio.