Ideal grain growth is a special case of normal grain growth where boundary motion is driven only by local curvature of the grain boundary. It results in the reduction of the total amount of grain boundary surface area i.e. total energy of the system. Additional contributions to the driving force by e.g. elastic strains or temperature gradients are neglected. If it holds that the rate 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 d is the initial grain size, d is the final grain size and k is a temperature dependent constant given by an exponential law:
where k 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.