Fast domain growth through density-dependent diffusion in a driven lattice gas.

Abstract

We study electromigration in a driven diffusive lattice gas (DDLG) whose continuous Monte Carlo dynamics generate higher particle mobility in areas with lower particle density. At low vacancy concentrations and low temperatures, vacancy domains tend to be faceted: the external driving force causes large domains to move much more quickly than small ones, producing exponential domain growth. At higher vacancy concentrations and temperatures, even small domains have rough boundaries: velocity differences between domains are smaller, and modest simulation times produce an average domain length scale which roughly follows L\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{\zeta}}}$, where \ensuremath{\zeta} varies from roughly 0.55 at 50% filling to roughly 0.75 at 70% filling. This growth is faster than the ${\mathit{t}}^{1/3}$ behavior of a standard conserved-order-parameter Ising model. Some runs may be approaching a scaling regime. A simple scaling picture which neglects velocity fluctuations, but includes the cluster-size dependence of the velocity, predicts growth with L\ensuremath{\sim}${\mathit{t}}^{1/2}$. At low fields and early times, fast growth is delayed until the characteristic domain size reaches a crossover length which follows ${\mathit{L}}_{\mathrm{cross}}$\ensuremath{\propto}${\mathit{E}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}}$. Rough numerical estimates give \ensuremath{\beta}=0.37 and simple theoretical arguments give \ensuremath{\beta}=1/3. Our conclusion that small driving forces can significantly enhance coarsening may be relevant to the ${\mathrm{YB}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ electromigration experiments of Moeckly et al.