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Unformatted text preview: Lecture 5 Kinetics: Effects of Small Systems Size effects are important when systems are small (nano). Small systems would have a large surface to volume ratio ( 2 3 4 3 4 3 r r r π π = ), and a large # of broken bonds (or dangling bonds if not metallic) per unit volume. The unstable small structures have large reactivity. You probably have heard of using nano systems and their large surface areas for catalytic and sensing applications. In the following, we will use “surface smoothing”, i.e., the decay of surface features, as an example to illustrate the fast evolution of micro/nano structure, due to enhanced kinetics. Surface smoothing via surface diffusion We already discussed the large driving force for change, in small systems, such as for melting, coarsening, dissolution, etc. We now address the question “how fast?”. Due to the large surface to volume ratio, one would expect tremendous amounts of surface diffusion, a short-circuit path for mass transport. 1 Let us analyze the decay of surface nanoscale undulation shown in class. The flux of atomic transport is, according to Fick’s first law, driven by chemical potential gradient (often perceived as composition gradient), the driving force we already discussed in the last lecture. J D C M μ = - ∇ = - ∇ where D is diffusivity and M is mobility (will be explained later). We will express the M and chemical potential gradient in terms of parameters we can measure in experiments. a) How is M related to D ? Let’s link chemical potential and composition first. Let us look at the chemical potential gradient for a dilute solution, where activity a scales with composition C (for ideal solution, a = C )....
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This note was uploaded on 03/30/2010 for the course EN 510.422 taught by Professor Dr.evanma during the Spring '10 term at Johns Hopkins.
- Spring '10