the subgrain size and boundary energy (Doherty, 2005): where ρ is the dislocation density, G is the shear modulus, b is the Burgers vector of the dislocations, γs is the subgrain boundary energy and ds is the subgrain size. Nucleation Historically it was assumed that the nucleation rate of new recrystallized grains would be determined by the thermal fluctuation model successfully used for solidification and precipitation phenomena. In this theory it is assumed that as a result of the natural movement of atoms (which increases with temperature) small nuclei would spontaneously arise in the matrix. The formation of these nuclei would be associated with an energy requirement due to the formation of a new interface and an energy liberation due to the formation of a new volume of lower energy material. If the nuclei were larger than some critical radius then it would be thermodynamically stable and could start to grow. The main problem with this theory is that the stored energy due to dislocations is very low (0.1–1 J m-3) while the energy of a grain boundary is quite high (~0.5 J m-3). Calculations based on these values found that the observed nucleation rate was greater than the calculated one by some impossibly large factor (~1050). As a result, the alternate theory proposed by Cahn in 1949 is now universally accepted. The recrystallized grains do not nucleate in the classical fashion but rather grow from pre-existing sub-grains and cells. The 'incubation time' is then a period of recovery where sub-grains with low-angle boundaries (<1–2°) begin to accumulate dislocations and become increasingly misoriented with respect to their neighbors. The increase in misorientation increases the mobility of the boundary and so the rate of growth of the sub-grain increases. If one sub-grain in a local area happens to have an advantage over its neighbors (such as locally high dislocation densities, a greater size or favorable orientation) then this sub-grain will be able to grow more rapidly than its competitors. As it grows its boundary becomes increasingly misoriented with respect to the surrounding material until it can be recognized as an entirely new strain-free grain. Kinetics Recrystallization kinetics are commonly observed to follow the profile shown. There is an initial 'nucleation period' t0 where the nuclei form, and then begin to grow at a constant rate consuming the deformed matrix. Although the process does not strictly follow classical nucleation theory it is