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Take-home lessons from the conference on Thin Film and Crystal Growth Mechanisms
The conference at Mount Holyoke introduced me to an amazingly diverse group of scientists working with ordered structures. Their investigations take place under several distinct contexts and with a variety of applications motivating their work. Despite the discrepancies among their methods, the multiple communities represented at the conference managed to share their ongoing research so that even non-specialists could benefit from the majority of the talks and posters.
One of the major divisions among the conference participants is reflected in the conference name itself (which came up for review during Thursday's business meeting, but survived the popular vote when competing with two other suggested names). This conference attracts people from two broad research areas: the thin film community, for whom the interesting crystals have a layered structure; and the crystal growth community, which focuses on the formation of fully three-dimensional crystals in solution. This year's conference chair, Peter Vekilov, arranged for the first session of talks to reach out to both communities, with a broad overview of nanotechnology presented by Ellen Williams, and a discussion of current debates among crystal growth researchers presented by Alexander Chernov. Subsequent sessions focused more narrowly on either thin films or formation of three-dimensional crystals.
Within the community of crystal growth researchers, the focus of investigation is further narrowed according to the motivating application area, or the preferred analytical techniques. My first acquaintance at the conference, Dragan Nikic, works with solutions of protein crystals and therefore had to wait several days before the session topics aligned more closely with his background. I did not have to wait nearly as long to attend talks very closely related to my work on evolution of crystal surfaces. The session on Monday morning ended with two excellent talks on that topic, with rigorous results and concise explanations of the relevant mathematical techniques.
As an example of this rigorous approach to crystal surface evolution, Vesselin Tonchev described an innovative method for determining the approximate behavior of step-step interaction equations, using experimentally observable quantities and scaling laws. I found this discussion interesting, especially since the step-step interaction equation used in recent work has not yet been given adequate justification. Tonchev's method, however, does not seem to provide more than the leading-order term in the expression for forces between steps, so it can confirm our currently postulated relation but cannot offer improvements to include weaker physical interactions. I would be interested in seeing if similar scaling law arguments could shed light on the nature of long-range interactions among steps, or whether the dominance of nearest-neighbor interactions prohibits any such conclusions from experimentally observable quantities.
Some crystal growth researchers did not appreciate the usefulness of continuum methods, especially when their computing capabilities enable them to simulate surface evolution by keeping track of every molecule. Kristin Fichthorn and her group, for example, routinely employ molecular dynamics simulations to supplement their experimental work, and they shy away from taking continuum limits out of concern that interactions at the atomic level might be lost in the process. Biased as I already am in favor of continuum methods and the qualitative predictions they facilitate, I would like to understand more fully the objections of the molecular dynamics people and see whether their doubts are justified.
Subsequent sessions began to feature fewer theorists and greater emphasis on experimental work, and the thin film community finally saw more of their research discussed in the talks. Giovanni Constantini of the Max Planck Institut (Stuttgart) explained lucidly the appearance of quantum dots during strained epitaxial growth, in which a substrate and a deposition material with different lattice parameters are grown in layers, transitioning between several regular patterns throughout the deposition process. John Venables continued this theme with his talk on visualization of deposition and annealing processes, and from the subsequent discussion I learned to distinguish between the elastic strain of heteroepitaxy and the strain induced by surface defects (which includes the step system in my current project).
The deceptive similarity between terrace diffusion and the island deposition described by Venables kept me busy in the days after his talk, trying to fit an incompatible theory of elastic strain into the system of step-flow equations. In an attempt to salvage this effort, I suggested that we apply shell theory as a model of the steps that would permit easier calculation of the elastic strain, but it turns out that shells would behave quite differently from steps, and only the latter system has been verified against experimental results. Because the underlying physics is completely different in a stacked-disk model, shell theory would fail to reveal any useful information about the evolution of crystal surfaces. Nevertheless, there might be an interesting experimental system that does correspond to a stack of disks with time-dependent radii, and I would like to pursue the analogy further before dismissing it entirely. Illustrating the danger of dismissing a model because of non-physical assumptions, the zero-range processes that were mentioned during lunch have been found to capture the behavior of certain step systems, even though their starting assumptions make no mention of step-step interactions or even the geometry of the crystal surface. I would therefore like to study zero-range processes and understand under which experimental regimes they provide useful predictions.