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Working on nanocrystal materials, I was curious to calculate the ratio of surface atoms to bulk atoms. However, when I provided this ratio to a professor, he said it's common to assume a surface to be 5-10 lattice constants thick. It was a passing comment, but I'm curious if anyone has any insights on what delineates the bulk of a crystal from the surface of a crystal?

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5-10 lattice constants is just a rule-of-thumb. Surface effects decay into the material - i.e., surface states have finite extension, surface charge is being screened, etc. Most of these are associated with some exponential scale of decay, $\sim e^{-x/l}$, where $l$ can be taken as the surface thickness.

As a simple example, one could mention skin effect in metals - the electric field within the bulk of the metal is screened, whereas the surface effects are limited to the skin depth.

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