Finite-amplitude instability in growth step trains with overlapping step supply fields

We have expanded our numerical model of coupled bulk transport in solution and interfacial kinetics in crystal growth [Vekilov, Lin, and Rosenberger, Phys. Rev. E 55, 3202 (1997)] by explicitly including adsorption on and des orption from terraces between growth steps, surface diffusion, and incorpor ation into steps. At the steps, the surface (adsorption layer) concentratio n C-s is assumed to be either continuous, i.e., have the same values at the top and bottom of a step, or to be discontinuous, i.e., to take on differe nt, respective terrace-width-dependent values. In order to maximize spatial resolution about individual steps, we use a mesoscale grid at the solution -crystal interface, which moves with the step positions and adjusts to the changing terrace widths during the simulation. This model was evaluated wit h transport and kinetics parameters characteristic for the growth of lysozy me crystals from aqueous solutions. With continuous C-s at steps, the simul ations reproduced the results of our previous model in which the step suppl y field overlap was only indirectly accounted for by a step-density-depende nt deceleration parameter in the step velocity. When discontinuities in C-s were allowed, significantly higher bunching instability resulted. More imp ortantly, we found that step bunching may or may not occur, depending on th e specific step-density perturbation (magnitude, sign and rate of step-dens ity change). This is why linear stability analyses do not predict the unste ady growth behavior observed in our experiments and obtained in our simulat ions. [S1063-651X(99)03203-1].