Pattern Formation Far from Equilibrium in the Electrochemical Deposition of Metals.

The patterns which evolve in growing systems such as snowflakes shed light on the more general problem of self-organization in nonequilibrium phenomena. In particular, how microscopic processes such as the attachment of an atom to a growing surface can influence the shape of a structure many orders of magnitude larger has been an open question until quite recently. The two-dimensionaI electrochemical deposition of metals provides an opportunity to watch these processes in action and from these observations to deduce principles which may pertain to a wide class of nonequilibrium systems. Direct observation of growing electrodeposits allows classification of patterns as a function of growth conditions, including electrolyte concentration, applied voltage, and cell geometry. By collecting the metal aggregates and submitting them to electron diffraction, x-ray diffraction, and chemical analyses, we can track the interrelationship between microstructure and morphology. The combination of these results points toward the putative self-organization principle which governs pattern formation in this model system. Electrodeposition results in a surprisingly wide range of patterns. Near equilibrium, ragged branched structures evolve displaying the scale-invariance of fractals. At the fastest growth rates, stable dendrites, resembling the branches of a snowflake, form. Between the fractal and dendritic regimes, branched aggregates grow, but without fractal scaling properties. These radially symmetric electrodeposits are termed dense radial aggregates. This thesis provides a possible explanation for the stability of the dense radial pattern and predicts its appearance in other pattern-forming systems. As electrodeposits change from disordered fractals to orderly dendrites, we observe a simultaneous and unexpected microscopic reordering. The crystals which form, moreover, display a novel superlattice structure. This thesis suggests a mechanism for rapid ordering in electrodeposition which would account for the microstructural trends and may shed light on the origin of dendrites in electrodeposition. This work was supported by the National Science Foundation under Grants No. DMR 84-04975, DMR 85-05474, DMR 88-05156, and DMR 88-15908 and by U. S. Army Research Office Grant No. DAAG-29-83-K-0131. The author also acknowledges receipt of a Rackham Predoctoral Fellowship.