Grain growth in metals

Abstract The sizes and shapes of grains in annealed metals, characterised respectively by the grain diameters and the interfacial angles, are shown to be lognormally distributed in planar sections as well as in space. The similarity of the size and shape distributions facilitates the treatment of grain growth as a univariant statistical problem in which the mean rate of growth of the grains is obtained as the resultant of the surface tension-controlled rate of growth of the individual grains in the distribution. The most probable initial and instantaneous grain diameters D 0 ∗ and D ∗ , which have approximately the same respective values whether referred to planar or spatial distributions, are then found to be related to the time of isothermal growth t by the equation (D ∗ ) 2 − (D 0 ∗ 2 = ( λVaσ h )t exp ( −H kT ), where λ is a numerical constant of order unity, V the volume per atom, a the lattice spacing, σ the specific grain-boundary energy, h Plank's constant, and H the activation energy for grain-boundary self-diffusion. Agreement with experimental results is good.