That soldering is a miracle there is no doubt. Just coincidentally, copper, the best practical conductor of electricity, can be bonded electrically and mechanically with solder at temperatures below 250C. This coincidence of nature enables electronics, the largest industry in the world, to thrive and prosper. If copper did not exist, some would argue that aluminum could be used as it is a good conductor if electricity. But alas, aluminum cannot be soldered, so it is not easy to bond aluminum to aluminum at low temperatures. Silver, the best conductor of electricity is 1000 times more scarce than copper, hence is impractical due to cost. So copper's abundance and equally its ability to be soldered is a blessing to humankind.
The essence of solder is tin. Tin forms the intermetallics with copper that makes the bond. Lead in tin-lead solder and silver and copper in lead-free solder only "go along for the ride" as they do not form the intermetallic bond with copper. However, the metals in the solder do dramatically affect the ability of the solder to wet and the mechanical properties of the final joint.
My sense is that there is not much theoretical understanding of why alloying elements in the tin based solder affects its wetting so profoundly. As an example tin-lead solder wets copper very well, whereas lead-free solder typically does not. So some of my goals this year are:
1. More fundamentally how alloying elements affect tin's ability to wet copper.
2. How # 1 relates to surface tension.
3. Why small amounts of some elements (e.g. < 0.1% nickel, < 0.05 cerium) affect lead-free solder's properties so greatly.
4. Why lead-free solder attacks stainless steel so much more aggressively than leaded solder.
If anyone has answers to these questions, please share them with us.