Correlations between the minimum grain size produced by milling and material parameters

In this paper, data reported for the minimum average grain size that was obtained by ball milling are analyzed. It is shown that when the normalized minimum average grain size, dmin/b (where dmin is the minimum average grain size and b is the Burger vector) is plotted as a function of melting temperature, Tm, the activation energy for diffusion, Q, or the normalized hardness, H/G (where H is the hardness and G is the shear modulus), the resultant curves are similar in trend. The curves exhibit two regions: region I and region II. In region I, dmin/b decreases rapidly with increasing Tm, Q, or H/G, while in region II, dmin/b decreases very slowly with each of these three parameters. The relationship between the normalized minimum average grain size and the normalized hardness is explained in terms of the limit of a dislocation pile-up in nanocrystalline materials.