The shapes and structures of grain boundaries formed beto its step free energy, 5 ' 6 it becomes 0 when the roughening tween the basal (0001) surface of large alumina grains and transition occurs. The roughening transition is thus characterized randomly oriented small alumina grains are shown to depend by the shape change from flat to curved. A crystal surface with an on the additions of SiO 2 , CaO, and MgO. If a sapphire crystal orientation which does not appear in the equilibrium shape can is sintered at 1620'C in contact with high-purity alumina develop a hill-and-valley (h&v) shape 3 ' 5 and undergo defaceting powder, the grain boundaries formed between the (0001) transition with temperature increase or composition change. For sapphire surface and the small alumina grains are curved and example, the exposure of alumina surfaces with h&v shapes to do not show any hill-and-valley structure when observed MgO atmosphere was observed to induce the defaceting transiunder transmission electron microscopy (TEM). These obsertion.' Because the defaceting transition is usually equivalent to the vations indicate that the grain boundaries are atomically rounding of the edges and corners of the equilibrium crystal shape, rough. When 100 ppm (by mole) of SiO 2 and 50 ppm of CaO it implies an eventual roughening transition of the singular surface are added, the (0001) surfaces of the single crystal and the if the temperature or composition change proceeds further. elongated abnormal grains form flat grain boundaries with Following the initial proposal of Hart,' the possibility of grain most of the fine matrix grains as observed at all scales boundary transition has also been studied. Several molecular including high-resolution TEM. These grain boundaries, dynamics simulations ' 1 2 showed gradual grain boundary disorwhich maintain their flat shape even at the triple junctions, are dering with temperature increase above about 0.5T., where Tm is possible if and only if they are singular corresponding to cusps the melting point. By making an analogy to the surface roughenin the polar plots of the grain boundary energy as a function of ing, Rottman" 3 showed that low-angle grain boundaries in Cu the grain boundary normal. When MgO is added to the could undergo roughening transitions. Defaceting transitions with specimen containing SiO, and CaO, the flat (0001) grain temperature increase'14-7 and composition change's"9 have been boundaries become curved at all scales of observation, indicatobserved in metals. Dahmen and Westmacott2° observed a nearly ing that they are atomically rough. The grain boundaries obsred als. Dahn and anotoer aine between small matrix grains also become defaceted and hence polyhedral aluminum grain (embedded in another aluminum grain) atomically rough.developing rounded edges on heating to a high temperature and changing reversibly on cooling. There has also been indirect experimental evidence for grain boundary transitions from the