Calculated Size Distributions for Gas Bubble Migration and Coalescence in Solids

Abstract

Bubble coalescence in solids is assumed to result when collisions occur between bubbles as they migrate by surface diffusion through the solid. The migration of an isolated pore is examined in detail and the results are applied in a finite-difference approach, programmed for a digital computer, to predict the variation of the number of bubbles per unit volume as a function both of bubble size and of post-irradiation annealing time. Two idealized models of bubble coalescence have been treated. The first model considers coalescence resulting from random migration of the bubbles, and the second considers coalescence resulting from llnidirectional, biased migration, such as would result in the presence of a thermal gradient. Both models are based on surface diffusion migration of randomly distributed bubbles in a perfect, infinite solid. The results give the predicted variation with time of the entire distribution of bubble sizes, so that various parameters, including the mean bubble radius and volume change, can be predicted. Comparison of the predicted values to parameters measured in appropriate experiments could provide a means of measuring fundamental properties of materials. The results can also be applied to the problem of swelling of reactor fuel materials because of trapped fission gases. Although the present analysis is limited by a number of simplifying assumptions, it is clear that the presence of a thermal gradient can greatly enhance the swelling rate.

Sintering of nickel steam-reforming catalysts: effects of temperature and steam and hydrogen pressures

“…Gruber [28] derived an expression for the diffusion of gas bubbles in metals, which also describes the diffusion of spherical metallic particles on a planar noninteracting ceramic carrier [29]. The obtained expression links the diffusion constant for metal atoms, D atom , at a metal particle to the diffusion of the metal particle, D particle ,…”

“…To derive this expression Gruber [28] used that a flux of metal atoms across a unit length, J s , is given by…”

Void nucleation, growth, and coalescence in irradiated metals

“…This gives both the correct monomer value and size-dependence for large cluster diffusion [11,12], although the activation energy for void migration should more properly be that for surface diffusion. This diffusivity takes no account of the effect of reversible pinning [43], or internal gas pressure on the migration [44], or radiationenhanced diffusion [45], or, e.g., that vacancy dimer diffusion may be D v 2 D v .…”

“…For example, the generation and aggregation of helium impurities is not explicitly modeled. Size-dependent void diffusion [11,12] is neglected, and thus direct void-void coalescence is not included. Dislocation loop formation, migration, and coalescence is not explicitly simulated, either.…”

Helium gas bubble migration in uranium mononitride in a temperature gradient

“…We assumed 10,000 calories per mole to obtain order of magnitude calculations of the surface diffusion coefficient. This is the value assumed by Gruber (27) in his calculations for the migration of helium bubbles in copper. Shewrnon (20) energy.…”