The evolution of the nanoscale dissipative structures in a distribution of defects within the isothermally irradiated f.c.c. crystal

Abstract

A kinetic model for the influence of external noises such as fluctuations of the vacancies’ generation rate and inhomogeneity of irradiated f.c.c. crystal on the formation of nanoscale modulated dissipative structure in a spatial distribution of vacancies is considered. The generation rate of vacancies all over the sites and a density of their dislocation-type sinks are modelled as independent random uniform stationary fields and with certain defined parameters of fluctuation correlations – spatial and temporal ones. Such stochastic fields can induce a spatial redistribution of vacancies that can lead to their density stationary uniform field or stochastic one. By the average value and correlation functions of these fluctuations, the conditions are determined for interacting fluctuations of the vacancies’ density, under which this homogeneous random field becomes unstable in relation to the stochastic field with a spatially periodic mean distribution of vacancies’ density. For instance, with f.c.c. nickel as a model of the irradiated functional material, the temperature dependence of spatial period d(T) of the modulated dissipative structure of vacancies’ subsystem in f.c.c. crystal is numerically forecasted and analysed, taking into account the total (‘electrochemical’ + ‘strain-induced’) interaction between vacancies. Such d(T)-dependence is also determined by the kinetic characteristics of vacancies’ redistribution.

Keywords:

• irradiated functional materials
• vacancies
• nanoscale dissipative structure
• ‘electrochemical’ interaction
• ‘strain-induced’ interaction

Acknowledgements

One of the authors (Y.B.P.) acknowledges the assistance he has received from the Centre for Advanced Materials Processing (CAMP) of the twenty-first century Frontier R&D Program funded by the Ministry of Science and Technology, Korea.

Notes

1. By definition, migration activation energy of vacancies is a height of the potential barrier separating the initial and final positions of the atom near vacancy, which is jumping into this vacant site [12–14]. As assumed within the model taking into account the effects of dilation in the vicinity of vacancy, for transition of the oscillating atom into the neighbouring vacancy, it is not required to impart additional energy to ‘ascend’ an intermediate neighbouring saddle of an intracrystalline potential relief, but it is sufficiently wait for such fluctuation, at which neighbouring atoms forming this saddle by their fields will part so that the saddle will ‘sag’, its height will go to zero, and the atom will pass into the neighbouring vacant site without obstruction. Energy of formation of such fluctuation, at which width of formed interstitial clearance is equal to diameter of the atom passing through it, can be estimated within the scope of the linear theory of elasticity taking into account the anisotropy of a crystal, without adjustable parameters [12–14].