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From both practical and fundamental standpoints, the mechanical behavior of ultrathin epitaxial films (1-20 monolayers) is an area of expanding interest. An important aspect of this is strain relaxation by interfacial misfit dislocation. If the lattice mismatch between the film and substrate is sufficiently large, strain relaxation will occur at thicknesses less than a typical dislocation core radius. Conventional strain-relaxation theory is developed under the assumption that the film thickness is much larger than the core radius and consequently fails to describe behavior in the ultrathin-film limit. In this work, we develop an alternative model of strain relaxation tailored for this regime. This is accomplished by replacing the conventional (discrete) dislocation with a Peierls-Nabarro (distributed) dislocation, which explicitly describes core deformation. The energetics calculation is carried out using the same assumptions and simplifications employed in conventional theory, but now applied to the alternative dislocation paradigm. The behavior of the standard and modified theories is contrasted by application to experimental strain-relaxation data.
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