Modelling of kink nucleation and propagation along steps of finite length

A discrete model for kink nucleation and propagation along steps of finite length is developed. The step velocities were calculated as a function of the step length, the first order rate constants, k_s and k_K, for kink nucleation and propagation respectively, and a kink interaction parameter. The two limiting kinetic regimes of short and long steps as well as the intermediate transitional regime were considered. For very short steps, S² ? $\text{k}{}_{\mathrm{<mtext>K</mtext>}}\text{k}{}_{\mathrm{<mtext>s</mtext>}}$, the velocity varied directly with the number of sites S. Steps which met the criterion S² ? $\text{k}{}_{\mathrm{<mtext>K</mtext>}}\text{k}{}_{\mathrm{<mtext>s</mtext>}}$, were shown to have velocities on the order (2k_Kk_s)^{$\text{1}\text{2}$}, independent of step length. Step velocities were constant over large ranges of the kink interaction parameter. The steps were shown to be “sharp” for zero or attractive kink interaction, but with sufficiently large kink repulsion very diffuse steps could be formed. The density of kinks and numbers of kinks nucleated along an atom row were also calculated.