ABSTRACT
Grain boundaries have more than five degrees of freedom if the material has been treated by heat, deformation, irradiation, etc. The five degrees of freedom are from the relative orientation of the two grains on the two sides of the grain-boundary as well as the orientation of the grain-boundary. These five degrees of freedom are statistically averaged over many grains in the material and hence are not really free to be adjusted unless the material has a texture. Two more freedoms are introduced here, namely, the impurity content and the porosity content. These two degrees of freedom can be adjusted externally. It is shown how these two extra parameters may influence the Hall-Petch relationship between strength and grain size.
