An analytical model has been developed for the size-induced strain and stiffness of a nanocrystal from the perspective of thermodynamics and continuum medium mechanics. A core-shell structure with surface skin shell of an atomic diameter has been considered for the nanocrystal structure. Contribution from chemical and structural effects to the surface energy has also been considered. It has been found that the elastic modulus increases with the inverse of crystal size and the vibration frequency is higher than that of the bulk. The theoretical predictions are consistent with experimental observations.
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Ouyang et al. (2006) studied this question.
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