Theory of bubble growth in crystals and implications concerning nuclear fuel

Abstract

The displacement of material necessary to accommodate the growth of bubbles in crystals can occur by matrix atom diffusion or by plastic flow. For a fixed amount of internal gas, growth continues until an equilibrium is achieved between the pressure and surface tension. For further growth, more gas must be supplied to the bubble, and this can occur if dissolved gas is present or if gas atoms are being created by nuclear fission. The growth rate may then be controlled by the accommodation process or by the diffusive supply of gas. Current theories consider these processes to be independent, with one or the other being rate controlling. In the present paper, the interaction between them is investigated theoretically. This interaction is shown to modify the gas atom concentration profile near the bubble, leading to significant changes in the gas supply rate to the bubble. A novel mechanism of gas supply to the bubble is also identified, which results from the accommodation process itself. As the material nearest to the bubble is diffusively consumed, the gas within this material must be deposited into the bubble. A critical concentration of gas is predicted, at which the gas supplied by this mechanism can lead to spontaneous growth without the need for any diffusive supply through the crystal lattice. Oxide nuclear fuels are used increasingly to improve fractional ‘burnups’ of fissionable atoms, and it is shown that these materials are used in operating regimes where the above mechanisms are predicted to dominate.