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10 SMT Magazine • July 2015 tem enables the analyses of atomic layers in na- noscale. Complementarily, these analyses pave the groundwork for the engineering of grain and interphase boundaries. In the context of an ideal crystal structure, the boundary between one grain and its neigh- bours (i.e., g.b.) is treated as a planar defect, which associated with a certain amount of energy. As a result, there is a thermody- namic driving force for the total area of boundary to be reduced. Grain boundaries limit the lengths and mo- tions of dislocations and can also serve as attractive sites for nucleation of pre- cipitates and second-phases. When the stress reaches a certain level, it drives the formation of a new struc- ture in order to achieve low- er energy or stress-free state. Driving to the stress-free state involves several stages: • seeding of nuclei (nucleation spots) • nucleation • grain and sub-grain growth • impingement of grains • classical grain growth Through the reduction in the dislocation density and the movement of dislocation to lower-energy positions, internal residual stress- es are lowered. At a temperature when disloca- tions are more mobile, they tend to pile up to lower the strain energy of the system by rear- ranging the excess dislocations into low angle tilt boundaries by a few degree misorientation (polygonization). The tangles of dislocations lead to sharp two-dimensional boundaries and the dislocation density within these areas de- crease. These areas are sub-grains. Coarsening occurs after polygonization, where low angle boundaries recruit more dislocations while growing. Some sub-grains will have more dislo- cations around them than others, which builds high mobility. In turn, the sub-grains garner more dislocations while growing so there are more dislocations around them until the dislo- cations are dissipated in this cyclic process. This creates a cycle of growth. Classical grain growth is driven only by local curvature of the grain boundary, which results in the reduction of the total amount of grain boundary surface area. The driving force for this growth is es - sentially the surface energy of the grain boundaries. Af- ter recrystallization, if the temperature is maintained high enough, the grain size will grow, which is moti- vated by a reduction in the actual number of grains per volume resulting in the re- duced total area of grain boundary. The energy avail- able to drive grain growth is usually very low and the growth tends to occur at a slow rate and is easily slowed by the presence of second phase particles or solute at- oms in the structure. This grain growth is the third identifiable stage of energy release during shelf life un- der elevated (high enough) temperature. The process will measurably decrease the yield strength of the material as the yield stress is in- versely proportional to the mean grain diameter. Ductility, on the other hand, increases. Grain boundaries' high interfacial energy and relatively weak bonding often makes them preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. The properties of the second phase af- fect the g.b. A drastic example is that when the second phase, having a low melting point and zero contact angle, is being heated above the melting point of the second phase, it will cause the material to fall apart along its grain Classical grain growth is driven only by local curvature of the grain boundary, which results in the reduction of the total amount of grain boundary surface area. the driving force for this growth is essentially the surface energy of the grain boundaries. After recrystal- lization, if the temperature is maintained high enough, the grain size will grow, which is motivated by a reduction in the actual number of grains per volume resulting in the reduced total area of grain boundary. " " smt ProsPeCts & PersPeCtives THE THEORy BEHIND TIN WHISKER PHENOMENA, PART 2 continues