The dependence of normal and abnormal grain growth in silver on annealing temperature and atmosphere
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temperatures, all crystals in equilibrium with a surrounding fluid are predicted[1,2,3] and have been observed[4–7] to have atomically flat (or smooth or singular) surfaces of low index planes and hence polyhedral shapes. Following the proposal of Burton et al.[8] the roughening transition of the crystal surface has been extensively studied both theoretically[9] and experimentally using the diffraction techniques[10] and indirectly by observing the macroscopic shape changes.[11] The growth of crystals with either smooth or rough surface has also been studied extensively, and it has now been fairly well established that the smooth surfaces grow by two-dimensional nucleation of steps if they do not have defects. The growth of the rough surfaces is controlled by diffusion in the surrounding fluid and often becomes dendritic. For systems of grains dispersed in multicomponent liquid matrix, abnormal grain coarsening occurs only if the grains have polyhedral shapes and normal coarsening if they are spherical. In certain materials such as NbC-Co,[12,13] the surface roughening transition occurs at high temperatures with concurrent changes of the grain shape and the growth behavior. Park et al.[14] proposed that the abnormal coarsening of the polyhedral grains occurred by two-dimensional nucleation of surface steps or by spiral growth on surface defects. The spherical grains with a rough surface grow normally with the rate determined by diffusion in the liquid matrix. Recently, it has been proposed that the same correlation JAE BON KOO, formerly Graduate Student, Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, is Associate Researcher, Samsung SDI Co., Ltd., Suwon 442-731, Korea. DUK YONG YOON, Professor, is with the Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea. Manuscript submitted November 15, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A
exists in single-phase polycrystals between the grain boundary structure and the grain coarsening behavior, as indicated by the observations in pure Ni.[15,16] Rottman[17] showed the possibility of the roughening transition of low-angle grain boundaries, and Shvindlerman and Straumal[18] collected various indirect experimental evidence for the roughening transitions of grain boundaries in pure metals, which were observed to occur in the temperature ranges between about 0.3 and 0.9 Tm , where Tm is the melting point. The coincidence site lattice (CSL) type boundaries in Al and Au[19] and even the general boundaries in Ni[15] were observed to be faceted at low temperatures and undergo defaceting transitions at temperatures above 0.5 Tm. Oxygen in Ni,[20] Bi in Cu,[21] and Te in Fe[22] were found to induce faceting of grain boundaries. If grain boundaries are faceted, it is likely that at least some of the facet planes have singular structures corresponding to the cusps in the plot of the grain boundary energy ␥ against the inclination angle or the normal direc
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