Growth kinetics of precipitates: misfitting and non-misfitting

Quantitative studies on diffusional growth of an isolated
precipitate in a supersaturated matrix date back to the classic work of
C Zener (1949) and F C Frank
(1950); while Zener-Frank (ZF) theory is for precipitates that are
non-misfitting, misfitting precipitates have been studied by Laraia,
Johnson and Voorhees (1988) (hereafter, LJV). Both ZF and LJV are sharp
interface models (and are mostly analytical); further, the assumptions
made in these theories make it difficult to verify their results by
experiments. However, simulations based on computational models offer an attractive alternative: "numerical experiments."

We
have used a phase field model whose parameters make it resemble closely
the ZF and LJV systems: isotropic interfacial energy, isotropic
diffusivity, constant diffusivity in the matrix (and precipitate, too),
isotropic elastic moduli, dilatational misfit. However, interface
curvature is always present in our 2D simulations, while ZF and LJV
theories neglect its influence on growth.

I'm enclosing below the abstract and the preprint of the paper by
R. Mukherjee et al. This work is from a part of the masters thesis of
the lead author, Rajdip Mukherjee, who's pursuing a PhD in materials engineering at IISc, Bangalore.

Phase field study of precipitate growth: Effect of misfit strain and interface curvature

R. Mukherjee(1), T A Abinandanan(1), and M P Gururajan(2)

(1) Department of Materials Engineering, Indian Institute of Science, Bangalore - 560 012. India.

(2) Department of Applied Mechanics, Indian Institute of Technology - Delhi, Hauz Khas New Delhi 110016. India.

We have used phase field simulations to study the effect of misfit and interfacial

curvature on diffusion-controlled growth of an isolated, precipitate in
a supersaturated matrix. Treating our simulations as computer
experiments, we compare our simulation results with those from
Zener-Frank and Laraia-Johnson-Voorhees theories for the growth of
non-misfitting and misfitting precipitates, respectively. The agreement
between simulations and ZF theory is very good in 1D systems. In 2D
systems with interfacial curvature (with and without misfit), we find
good agreement between theory and simulations, but only at large
supersaturations, where we find Gibbs-Thomson effect is less completely
realized. At small supersaturations, the convergence of instantaneous
growth coefficient in simulations towards its theoretical value could
not be tracked to completion, because the diffusional field reached the
system boundary. Also at small supersaturations, the elevation in
precipitate composition matches well with the theoretically predicted
Gibbs-Thomson effect in both misfitting and non-misfitting systems,