Helium bubble behaviour in b. c. c. metals below 0.65Tm

Abstract
We have considered the methods available for distinguishing between the rate-controlling mechanisms for gas bubble migration in metals at temperatures below 0.6$T_m$. We show that several combinations of mechanism, gas behaviour and rate-controlling process give rise to similar power laws describing the rate of growth of populations of bubbles by migration and coalescence. We have therefore extended the model developed by Gruber (1967) to take account of the condition of constant gas pressure in the bubbles, which is likely to obtain at low temperatures in the absence of continuous irradiation damage, and the additional possibility that the nucleation of a surface ledge can control the migration rate of faceted bubbles. The experimental growth rates of helium bubbles, which we have measured in niobium, niobium-zirconium alloys and vanadium, are shown to be consistent with bubble migration by a surface diffusion mechanism controlled by the surface diffusion coefficient for small bubbles but by ledge nucleation for larger bubbles. The bubble size above which the (slow) ledge nucleation process controls growth is sensitively affected by the ledge energy. We show that the addition of zirconium to niobium can alter the ledge energy by an order of magnitude by cleansing the bubble faces of oxygen. Subsequent segregation of Zr-O complexes to the bubbles further alters the ledge energy. The bubble growth rate, and hence the swelling and embrittlement behaviour of the material under these conditions, is therefore very sensitive to the material purity and to segregation effects either induced thermally or accelerated by transmutation and irradiation damage. We find that the ledge energy on the (100) face of pure niobium is ca. 11 x 10$^{-11}$ J/m, which is decreased to ca. 4 x 10$^{-11}$ J/m by the segregation of Zr-O to the surfaces. The ledge energy at a similar surface in niobium containing 400/10$^6$ oxygen is as low as 1.2 x 10$^{-11}$ J/m. In vanadium we find a ledge energy of 3.4 x 10$^{-11}$ J/m. These ledge energies result in the effective cessation of bubble growth at bubble sizes in the range 2-20 nm.