The surfaces o
f and boundaries between crystals are singular with atomically flat structures a
t low temperatures and undergo roughening transitions at high temperatures to di
sordered states. The coarsening of grain s in polycrystalline systems criticall
y depends on these structural transitions of the interfaces. If the grains in li
quid matrix are polyhedral with atomically flat surfaces and free of surface def
ects, they coarsen by two dimensional nucleation of surface steps. Because the
step nucleation rate abruptly increases at a critical supersaturation, only larg
e grains can grow rapidly and abnormal gra in growth (AGG) occurs. The nucleatio
n theory predicts that there will be minimum driving force and temperature and maximum step free energy for AGG, and the observations in WC-Co, alumina with anorthite and MgO, and TaC-Ni are qualitatively consistent with these predictions.If the grains are nearly spherical with atomically rough surface, the grains undergo normal diffusion controlled growth in agreement with the theories of Ostwald ripening.
  In the single phase polycrystals without any liquid phase, the grain boundaries of any general misorientation angles can be faceted with macroscopic hill-and-valley structures at low temperatures, particularly in the presence of certain impurities. Some of the facet planes are expected to be singular corresponding to the cusps in the radial plot of the grain boundary energy against the grain boundary normal. Some facet planes have indeed been observed to have ordered structures. In Ni, Cu, Ag, a stainless steel, a Ni-base superalloy, alumina (with and without MgO), and BaTiO3, the abnormal grain growth is observed when all or some of the grain boundaries are faceted. When all of the grain boundaries become defaceted (rough) at high temperatures or with additives, normal grain growth is observed. The faceted grain boundaries thus appear to move by a step mechanism similarly to the polyhedral grains in liquid. The AGG rate is observed to increase with increasing density of dislocations produced by slight deformation. The double twins also induce AGG in BaTiO3 only when the grain boundaries become faceted by heat-treating in air. When the grain boundaries become rough by heat-treating in H2 atomosphere, the double twins do not affect the grain boundary movement. These observations provide an additional evidence for the step growth of the faceted grain boundaries. Although these results indicate that the grain coarsening is critically dependent on the structural change of the grain surfaces and grain boundaries, more quantitative analysis and observations are needed.