**3. Monte Carlo simulations**

form locally into a more or less equiaxed grain structure by recrystallization. An example is presented in Fig. 3 where the cross-section images of a solder interconnection after 6000 thermal cycles are shown. Part of the solder interconnection was recrystallized near the component side after 6000 thermal cycles (see Fig. 3b). It is noteworthy that optical micro‐ scopy with polarized light shows the areas of different orientations with different colors and it is an excellent tool for observing the recrystallized region. In the recrystallized region a continuous network of high angle grain boundaries provides favorable sites for cracks to nucleate and to propagate intergranularly, which can lead to an early failure of the compo‐ nent. This kind of failure mode is regarded as the recrystallization-assisted cracking. More

**Figure 3.** Micrographs of the solder interconnection after 6000 thermal cycles; (a) optical bright field image, (b) cross-

In the near-eutectic SnAgCu alloys, mainly two kinds of IMC precipitates, Cu6Sn5 and Ag3Sn, can form upon solidification. The size of intermetallic particles (IMPs) varies a lot: the small and finely distributed IMPs are located at the boundaries of tin cells (eutectic structure) while the relatively large IMPs are randomly distributed in the bulk solder. Fine particles usually prevent the motion of grain boundaries by exerting a pinning force, and therefore, suppress the progress of recrystallization. The influence of fine particles on recrys‐ tallization has been studied in earlier work, e.g. [40]. It is believed that fine particles do not remarkably affect the distribution of stored energy within the grains. However, coarse parti‐ cles exert localized stress and strain concentrations due to the mismatch of mechanical prop‐ erties and thermal expansion coefficients during thermal cycling. Dislocation density is increased in the particle-affected deformation regions, which provide favorable sites for nu‐

details can be found in the references [14, 26, 28].

94 Recent Developments in the Study of Recrystallization

**2.3. Effect of intermetallic compound precipitates**

polarized light image.

cleation of recrystallization.

Many models have been developed to simulate microstructural evolution, such as vertex model, Monte Carlo (MC) Potts model, phase field model, and cellular automata (CA) mod‐ el [22, 23, 41, 42]. For modeling recrystallization, the MC Potts model and CA model are per‐ haps the two most popular candidates. In general, the MC Potts model and CA model are similar to each other since both models include a lattice, use discrete orientations and de‐ scribe stored energy in terms of a scalar stored energy term. The MC Potts model provides a convenient way to simulate the changes in microstructures and it has been successfully ap‐ plied to simulate the recrystallization process in solder interconnections as well as in many other applications, e.g. [38, 39, 43-45].
