Void Nucleation as a Diffusive Instability

摘要

The dynamics of vacancies in a system with mechanisms of production and annihilation of vacancies have been analyzed in reference to their coalescence to form voids. The modelling of the phenomena is done by introducing a vacancy concentration field. An equation for this field is formulated which incorporates in a simplified way (i) vacancy diffusion, (ii) mutual pairwise interaction amongst vacancies, (iii) their loss due to mechanisms like recombination with interstitials and absorption at dislocations, grain boundaries, etc. and (iv) their production by agencies like incoming radiation. The resulting equation is analyzed for a domain, under the boundary condition that the domain boundaries are perfect sinks. Such a domain should mimic grains in materials. The equation exhibits two kinds of behaviours depending upon the magnitude of the production rate P. If P is below a certain value Psub(th), the equation has steady state solutions which are approached from the initial thermal state. When P >= Psub(th), a coalescence instability occurs in time, which can be thought of as resulting from a negative diffusion coefficient. We have made theoretical estimates of Psub(th) for two simple domain geometries. 14 refs, 3 figs. (Atomindex citation 17:029477)