<P> where R (\ displaystyle R) is radius of the sphere . This driving pressure is very similar in nature to the Laplace pressure that occurs in foams . </P> <P> In comparison to phase transformations the energy available to drive grain growth is very low and so it tends to occur at much slower rates and is easily slowed by the presence of second phase particles or solute atoms in the structure . </P> <P> 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 </P> <P> d 2 − d 0 2 = k t (\ displaystyle d ^ (2) - (d_ (0)) ^ (2) = kt \, \!) </P>

How can grain growth in a weld be controlled