Kinetics of coarsening of helium bubbles during implantation and post-implantation annealing S.I. Golubov a,b , R.E. Stoller a, * , S.J. Zinkle a , A.M. Ovcharenko c a Materials Science and Technology Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831-6138, USA b Center for Materials Processing, The University of Tennessee, East Stadium Hall, Knoxville, TN 37996-0750, USA c ARIAM, 82 Lenin Av., Obninsk, Kaluga Region 249038, Russian Federation Abstract To understand the effects of He on irradiated metals requires modeling of helium-vacancy cluster evolution. A new method of solving the two-dimensional master equation (ME) describing He-vacancy cluster evolution has been applied to calculate helium bubble evolution in a stainless steel irradiated with alpha particles near room temperature and annealed in the temperature range of 600–900 °C. For the first time, the evolution of the helium bubble size distribution function was precisely calculated in 2-D phase space and good agreement with experimental results was obtained. The results indicate that Brownian motion of bubbles via surface vacancy diffusion provides a reasonable explanation for bubble evolution during annealing, most bubbles are found to be near the equilibrium state during the evolution at temperatures of 700 °C and higher, lack of vacancies at temperatures lower than 700 °C prevents bubble growth, and use of a non-ideal He equation of state (EOS) increases the bubble density and size relative to the case when the ideal EOS is used. Ó 2006 Elsevier B.V. All rights reserved. PACS: 61.80.Az; 61.72.Cc; 61.72.Ji; 61.72.Qq 1. Introduction Precipitation of helium introduced into metals by (n, a) reactions that occur in fission and fusion reac- tors influences microstructure evolution of materi- als. It has been established that helium atoms assist the nucleation and growth of cavities in irradiated materials leading to swelling and mechanical prop- erty changes. Modeling of helium-vacancy cluster evolution is required to develop an understanding of the role of He. The literature contains several par- tial treatments of the problem where two coarsening mechanisms, namely Ostwald ripening (OR) [1–13] and bubble migration and coalescence (BMC) [14–20,7,21–25] have been considered. However an accurate treatment of the second mechanism is com- plicated and the previous work has been done in a semi-quantitative way. For example, when, calculat- ing bubble coalescence driven by BMC, it has com- monly been assumed that bubbles maintain mechanical equilibrium during their evolution. Such an approach simplifies the calculations by permitting the transformation of a 2-D kinetic equation describing the evolution two independent variables 0022-3115/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jnucmat.2006.12.032 * Corresponding author. E-mail address: rkn@ornl.gov (R.E. Stoller). Journal of Nuclear Materials 361 (2007) 149–159 www.elsevier.com/locate/jnucmat