Kinetics of coarsening of helium bubbles during implantation and post-implantation annealing

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.

[1]  B. N. Singh,et al.  An analysis of the bubble formation behaviour under different experimental conditions , 1992 .

[2]  J. Katz,et al.  Effect of insoluble gas molecules on nucleation of voids in materials supersaturated with both vacancies and interstitials , 1973 .

[3]  Jung,et al.  Helium desorption from Fe and V by atomic diffusion and bubble migration. , 1991, Physical review. B, Condensed matter.

[4]  The effect of the immobilization of helium bubbles generated during irradiation on their growth by coalescence , 1984 .

[5]  J. Evans,et al.  Breakaway bubble growth during the annealing of helium bubbles in metals , 2004 .

[6]  E. E. Gruber.  Calculated Size Distributions for Gas Bubble Migration and Coalescence in Solids , 1967 .

[7]  Donald R. Olander,et al.  Fundamental Aspects of Nuclear Reactor Fuel Elements , 1976 .

[8]  Kinetics of the early‐stage gas porosity development caused by bubble coalescence , 1975 .

[9]  S. Chandrasekhar.  Stochastic problems in Physics and Astronomy , 1943 .

[10]  A. Foreman,et al.  Gas diffusion and temperature dependence of bubble nucleation during irradiation , 1986 .

[11]  F. A. Nichols,et al.  Kinetics of diffusional motion of pores in solids: A review , 1969 .

[12]  M. Speight.  Bubble diffusion and coalescence during the heat treatment of materials containing irradiation-induced gases , 1964 .

[13]  R. Stoller,et al.  The effects of helium implantation on microstructural evolution in an austenitic alloy , 1988 .

[14]  N. Ghoniem,et al.  Stablility of helium-vacancy clusters during irradiation , 1984 .

[15]  N. Ghoniem,et al.  An analytical approach to void growth in metals under intense radiation pulsing , 1981 .

[16]  P. Goodhew,et al.  Helium bubble behaviour in b. c. c. metals below 0.65Tm , 1981, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[17]  J. Katz,et al.  Effect of mobile helium on void nucleation in materials during irradiation , 1974 .

[18]  V. F. Chkuaseli.  Modelling of inert gas bubble behaviour during annealing of irradiated molybdenum , 1992 .

[19]  Daniel D. McCracken,et al.  Numerical methods and FORTRAN programming , 1964 .

[20]  R. Zeller,et al.  Quantitative determination of the pressure of He in bubbles in Al and Ni , 1982 .

[21]  H. Trinkaus.  Energetics and formation kinetics of helium bubbles in metals , 1983 .

[22]  A. Foreman,et al.  Relative role of gas generation and displacement rates in cavity nucleation and growth , 1984 .

[23]  S. M. Murphy,et al.  The nucleation and growth of gas bubbles in irradiated metals , 1990 .

[24]  J. Evans.  Mechanisms of void coarsening in helium implanted silicon , 2002 .

[25]  N. Ghoniem.  Nucleation and growth theory of cavity evolution under conditions of cascade damage and high helium generation , 1990 .

[26]  H. Trinkaus,et al.  Influence of cascade damage on helium diffusion and bubble nucleation , 1990 .

[27]  G. W. Greenwood,et al.  An analysis of the diffusion of fission gas bubbles and its effect on the behaviour of reactor fuels , 1963 .

[28]  The growth of gas-bubbles by coalescence in solids during continuous gas generation , 1983 .

[29]  H. Schroeder,et al.  A simulation study of the migration and coalescence of gas bubbles in metals , 1994 .

[30]  K. C. Russell.  Nucleation of voids in irradiated metals , 1971 .

[31]  H. Trinkaus.  On the modeling of the high-temperature embrittlement of metals containing helium , 1983 .

[32]  M. Kiritani,et al.  Analysis of the Clustering Process of Supersaturated Lattice Vacancies , 1973 .