The Hall-Petch relationship can fail when the grain size is below a critical value of tens of nanometres. This occurs particularly for coatings having porous surfaces. In this study, electrodeposited nanostructured Co-Ni coatings from four different nickel electroplating baths having grain sizes in the range of 11–23 nm have been investigated. The finest grain size, approximately 11 nm, was obtained from a coating developed from the nickel sulphate bath. The Co-Ni coatings have a mixed face centred cubic and hexagonal close-packed structures with varying surface morphologies and different porosities. A cluster-pore mixture model has been proposed by considering no contribution from pores to the hardness. As the porosity effect was taken into consideration, the calculated pore-free hardness is in agreement with the ordinary Hall-Petch relationship even when the grain size is reduced to 11 nm for the Co-Ni coatings with 77±2 at% cobalt. The present model was applied to other porous nanocrystalline coatings, and the Hall-Petch relationship was maintained.
- hall-petch relationship