On the extrinsic Hall-Petch to inverse Hall-Petch transition in nanocrystalline Ni-Co electrodeposits

Dislocation phenomena described with free volume concept and Eyring's rate process theory

“…The same prediction is obtained with the molecular simulation method for methane hydrates, 53 which shows the Hall–Petch equation breakdowns and a dome-shaped correlation instead. Similar examples can be found in many articles, 34,37–39 indicating that the empirical Hall–Petch equation doesn't truly reflect what happens when solid materials are under shear.…”

“…Clearly, eqn (28) and ( 29) deviate from the Hall-Petch equation, t ¼ t 0 þ kd À 1 2 while t 0 and k are constants. A generic form of the Hall-Petch equation, t = t 0 + kd Àn with n a constant is frequently used in the literature, but there are many pieces of evidence indicating that the Hall-Petch equation only tells a partial story [34][35][36][37][38] and there is an inverse Hall-Petch or a dome shape relationship between the stress and the grain size. [34][35][36][37][38][39] This topic will be discussed again after all relevant equations are derived.…”