Void nucleation as a diffusive instability

Abstract

The dynamics of vacancies in a system with both production and annihilation mechanisms have been analyzed as to their coalescence to form voids. The modeling 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 among vacancies, (iii) their loss due to mechanisms like recombination with interstitials and absorption at dislocations, grain boundaries, etc., and (iv) their production by incoming radiation. The recombination with interstitials is treated in two schemes. The resulting equations are analyzed for a domain, under the boundary condition that the domain boundaries are perfect sinks. Such a domain should mimic grains in materials. The equations exhibit two kinds of behaviors depending upon the magnitude of the production rate P. If P is below a certain value Pth, the equations have steady-state solutions which are approached from the initial thermal state. When P≥Pth, a coalescence instability occurs in time, which can be thought of as resulting from a negative diffusion coefficient. We have made theoretical estimates of Pth in both the schemes which are in very good agreement with numerical calculations.