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14 SMT Magazine • November 2015 Together, the three stages of the process de- scribe the formation of a new microstructure of lower free energy in the solid state. Recovery stage, sensitive to point defects, reduces lattice strain but does not involve any microstructural change. In contrast to recovery, the ability to make structural changes that occur in recrys- tallization by decreasing dislocation density generates a new set of fine strain-free grains. Recrystallized grains are often the result of pre- existing regions that are highly misoriented in relation to the material surrounding them. This high degree of misorientation offers the needed growth mobility for the region from which the new grains originate. If the temperature is high- er than that required for recrystallization, grain growth continues. Fundamentals of physical metallurgy indicates that, as discussed in Part 2, the nucleation and growth of stress-free grains comprises four steps: •Nucleation: incubation time •Growth of nuclei: high rate growth of new grains •Impingement of grains: with limited space, some nuclei at some point get to touch each other, which prevents subsequent growth •Conventional growth: when new grains fill all the volume, the process of classical growth starts, and the remainder follows the conventional growth rate (the rate is proportional to the square root of time). Its driving force is to decrease interfacial energy The second step of grain growth—the growth of nuclei—proceeds until the driving force for this process diminishes and at that point the recrystallization is complete. The main variables that affect recrystalliza- tion are 1) the composition; 2) time; 3) tem- perature; 4) the amount of prior deformation (strain); 5) the initial grain size; and 6) the amount of recovery prior to recrystallization. A higher level of strain increases the nucleation rate and lowers the threshold temperature that is required for structural rearrangement. Both compressive and tensile stresses can participate in the initiation of the process. Recrystallization requires a threshold strain level and a threshold temperature. The temperature at which recrystallization occurs is usually at a fraction of the melting temperature of an alloy, and the rate of recrys- tallization follows an Arrhenius-type equation. The required recrystallization temperature, varying with the initial grain size, increases with the increasing grain size. With all other conditions being equal, lower initial strain also increases the recrystallization temperature. Additionally, impurities in tin can increase its recrystallization temperature. If the test tem- perature is elevated (in relative terms), this el- evated temperature may activate or accelerate the first two stages of recrystallization by over- riding the nominal recrystallization tempera- ture. As the recrystallization temperature can change with the impurity inclusions (e.g., rare earth elements, other doping elements, etc.), a different testing temperature that is selected to use, in relation to the actual recrystallization temperature, may render a different outcome in test results. At a given composition, the initial grain size, strain level and recrystallization tempera- ture are interrelated, working hand-in-hand. Grain Growth vs. Solubility vs. external Temperature The external temperature in relation to the solubility of the secondary element(s) in tin primary matrix can affect the paths of grain growth. Since the grain boundary is the region of high energy, it makes attractive sites for the nucleation of precipitates and other second- phases. sMT prospecTs & perspecTIves A LooK AT THe THeory beHIND TIN WHISKer PHeNomeNA, PArT 3 " recrystallization requires a threshold strain level and a threshold temperature. "

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