From the classical theory of Eqs. (2), (3), (4) and (5), it can be deduced that smaller particles were more effective in refining the microstructure, enhancing the hardness, suppressing the IMC growth and enhancing the shear strength. However, the experimental results showed that the addition of 76 nm Ag nanoparticles generated the best improvement, not the smaller Ag particles of 31 nm indicated by the theoretical analysis. The finding that appropriately sized Ag nanoparticles (76 nm) generated the best improvement may be attributable to nanoparticle agglomeration behavior. It is well known that the surface H 89 of nanoparticles is relatively high due to their high specific surface area, which makes nanoparticles unstable as surface-active materials . To achieve a stable state, it is natural for the nanoparticles to minimize their surface energy by agglomerating into larger particles . In this study, the doped Ag nanoparticles were mixed into the Sn58Bi solder paste and then reflowed to prepare the composite solders. During the reflow process, Ag nanoparticles reacted with Sn in the solder alloy and formed numerous Ag3Sn nanoparticles dispersed in the solder matrix. Meanwhile, the small sized Ag and Ag3Sn nanoparticles in some local regions of the molten solder were possible to agglomerate into large particles, in order to reduce the surface energy and achieve a stable state. The reaction and agglomeration might simultaneously occur during reflow and finally result in the formation of some agglomerated Ag3Sn particles in large size. In addition, the agglomeration of Ag3Sn nanoparticles may also occur during the following liquid reaction test. It is noted that the average size of the spotted Ag3Sn IMC particles in Fig. 4a is about 380 nm, which is much larger than the doped 31 ± 5 nm of the Ag nanoparticles. The formation of Ag3Sn can be expressed as:equation(6)3Ag+Sn→Ag3Sn.3Ag+Sn→Ag3Sn.During the reaction, 3 mol Ag reacted with 1 mol Sn and formed 1 mol Ag3Sn. The molar volumes of Ag, Sn and Ag3Sn are 11.2 × 10−6, 16.6 × 10−6 and 45.3 × 10−6 m3/mol, respectively . Assuming that the Ag and Ag3Sn particles are spherical, a 31 nm sized Ag nanoparticle could form an Ag3Sn particle with size of 31×45.3/(11.2×3)3=34nm after reacting with Sn. Hence, the 380 nm sized Ag3Sn particles shown in Fig. 4a were formed by the reaction between Sn and a few Ag nanoparticles, which proved that the agglomeration behavior occurred.