Hall-Petch Type Behavior of Milled Nano-Powders

A simple theoretical model was developed to explain the experimental Hall-Petch relationship obtained in the case of milled nano-powders. The decrease of the mean crystallite size and the increase of the relative lattice micro-strain r as function of the milling tune are well known experimental facts. The relative micro-strain versus reciprocal grain size epsiv=f(1/D) presents at the beginning a rapid increase and for large milling time tends to a constant value. The dependence epsiv=f(1/D^frac12) is linear and in a good agreement with the experimental Hall-Petch relationship. This behavior is explained in the frame of the plastic deformation of a polycrystalline material due to the pile-up and movement of dislocations. The mechanism of grain size reduction is discussed in terms of the mechanical energy converted into heat and to the stored internal energy related to the melting point of the material