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# Crystal Growth Inhibition by Mobile Randomly Distributed Stoppers

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posted on 2020-02-03, 12:48 authored by James P. Lee-Thorp, Alexander G. Shtukenberg, Robert V. KohnCrystal growth is inhibited by the
presence of impurities. Cabrera
and Vermilyea introduced a model in 1958, in which the impurities
are modeled as immobile stoppers. The quantitative consequences of
this model have mainly been explored for the special case where the
stoppers are immobile and arranged in a periodic array. Here we use
numerical simulation to explore what happens when the stopper locations
are randomly distributed and the stoppers have finite lifetimes. As
this problem has just two nondimensional parameters, namely, nondimensionalized
versions of the mean stopper distance and the mean stopper lifetime,
we are able to explore a large region of the parameter space using
simulation. The stopper density is measured by the percolation parameter,
a nondimensionalized inverse distance between stoppers, ζ. Our
results show that when the stopper density is relatively small (ζ
below about 0.8), the macroscopic velocity of the step is roughly
the same for randomly located stoppers as for a periodic array of
stoppers. Moreover, in this regime the average velocity is almost
independent of the stopper lifetime. For large stopper densities (more
precisely, when the percolation parameter ζ is above about 0.8),
the situation is entirely different. For periodically placed immobile
stoppers, the average velocity drops sharply to 0 at ζ = 1.
For randomly located immobile stoppers, by contrast, the average velocity
remains positive for ζ well above 1, and it approaches 0 gradually
rather than abruptly. For randomly located stoppers with finite lifetimes,
the average velocity has a nonzero asymptote for large ζ; thus,
for large stopper densities, the average velocity depends mainly on
the mean stopper lifetime. In this regime, the inhibition kinetics
predicted by our model resemble those of the Bliznakov kink blocking
mechanism.