of growth is proportional to the driving force and that the driving force is proportional to the total amount of grain boundary energy, then it can be shown that the time t required to reach a given grain size is approximated by the equation where d0 is the initial grain size, d is the final grain size and k is a temperature dependent constant given by an exponential law: where k0 is a constant, T is the absolute temperature and Q is the activation energy for boundary mobility. Theoretically, the activation energy for boundary mobility should equal that for self-diffusion but this is often found not to be the case. In general these equations are found to hold for ultra-high purity materials but rapidly fail when even tiny concentrations of solute are introduced. Self-similarity An old-standing topic in grain growth is the evolution of the grains size distribution. Inspired by the work of Lifshitz and Slyozov on Ostwald ripening, Hillert has suggested that in a normal grain growth process the size distribution function must converge to a self-similar solution, i.e. it becomes invariant when the grain size is scaled with a characteristic length of the system that is proportional to the average grain size . Several simulation studies, however, have shown that the size distribution deviates from the Hillert's self-similar solution. Hence a search for a new possible self-similar solution was initiated that indeed led to a new class of self-similar distribution functions. Large-scale phase field simulations have shown that there is indeed a self-similar behavior possible within the new distribution functions. It was shown that the origin of the deviation from Hillert's distribution is indeed the geometry of grains specially when they are shrinking. Normal vs abnormal In common with recovery and recrystallisation, growth phenomena can be separated into continuous and discontinuous mechanisms. In the former the microstructure evolves from state A to B (in this case the grains get larger) in a uniform manner. In the latter, the changes occur heterogeneously and specific transformed and untransformed regions may be identified. Abnormal or discontinuous grain growth is characterised by a subset of grains growing at a high rate and at the expense of their neighbours and tends to result in a microstructure dominated by a few very large grains. In order for this to occur the subset of grains must possess some advantage over their competitors such as a