Question

4)

Describe the relationship between the hardness and grain size of the nanocrystalline grain material and plot it with a schematic diagram along with the critical grain size

In short sentence

Answer 1

The hardness and strength of the nano composites increases along with the grain size up to dc ( critical grain size). But usually toughness goes down if the grain size decreases.at critical grain size hardeness will be maximam. There are two critical grain sizes that corresponds to the changes in strengthening mechanism. The equation includes Hall - Petch relation in the range of d>dcr1. For dcr1>d>dcr2, the power in the Hall - Petch relation varies from -1/2 to -1. In a nanometer (nm) range (d<dcr2) there are posibileties of softerning (in case of "weak" boundaries) as well as significant strengthening .

Copper films were electrodeposited under various conditions and the relationship between the hardness and grain size of the films was investigated. The Vickers hardness depended on the processing conditions. This is because the processing conditions affected the grain size. In particular, nanocrystalline Cu film with a grain size of 31nm was obtained by optimizing the electrodeposition conditions. The hardness of the nanocrystalline film deviated from the Hall–Petch relationship because the grain size dependence of hardness is smaller for the grain sizes of 100nm. Also, the constants Hv0 and kHv in the Hall–Petch relationship for films processed with thiourea were different from those for films processed with gelatin. The differences may not be related to texture but to superabundant vacancies generated in the process of electrodeposition.