Size dependent hardness of silver single crystals

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Abstract
The hardness of thick, high-purity, epitaxially grown silver on sodium chloride is found to be dependent on the size of the indentation for sizes below ≃10 μm. The measurement of the size effect has been made in two ways. In one, the hardness has been calculated from the load-displacement curve obtained from an instrumented microhardness testing machine and assuming a geometric self-similarity in the indenter shape. In the other measurement, the hardness was obtained from the load exerted by the microhardness tester divided by the indentation impression area as measured by atomic force microscopy. The observed variation in microhardness with indentation size is consistent with a simplified strain gradient plasticity model in which the densities of the geometrically necessary and statistically stored dislocations are fitting parameters. An equally good fit can also be made with a simple geometric scaling relationship. Transmission electron microscopy observations of a thin (≃50 nm) epitaxial gold film embedded in the silver layers revealed that the deformation was primarily restricted to the sharp edges of the indentation. In addition, deformation twinning within the indentation impression was observed on the {1H} planes.