The unusual size effect of eutectic Sn/Pb alloys in the micro regime: Experiments and modeling

Abstract

Eutectic alloys are widely used as solder-joint materials due to their suppressed melting points, but when used in micro-devices with small dimensions, their characteristic lamellar microstructure may lead to an internal length scale that affects strength. Here, we report an unusual ‘smaller-being-weaker’ phenomenon in eutectic Sn/Pb alloys with fine lamellar microstructure, namely, in the specimen-size regime close to and slightly larger than the interphase lamellar spacing, the strength decreases with decreasing size, while above this regime the strength tends towards the bulk value. Theoretical modeling indicates that in a fine lamellar microstructure, high contents of dislocations are retained, so that strength is governed by mutual dislocation interactions, rather than by dislocation starvation. Therefore, in smaller samples, fewer interphase lamellar boundaries are present to block dislocations, thus resulting in a ‘smaller-being-weaker’ behavior. In samples a lot larger than the lamellar spacing, significant strengthening arises from Taylor hardening and mutual dislocation interactions as a result of significant dislocation retention by the interphase boundaries, so that strength does not depend on specimen size anymore. In a course lamellar microstructure, however, even a larger micro-specimen may contain insufficient interphase boundaries to significantly retain dislocations, and strength may be governed by the starvation effect due to significant loss of dislocations at free surfaces. In this case, the size effect of strength may become a lot milder, or even exhibit the conventional “smaller-being-stronger” behavior. The results here supplement conventional knowledge on size effects in micro-scaled crystalline materials, and provide important implications on solder-joint design in micro-devices.