If I could chime in on soldering piezo elements.
1) Use plenty of flux.
2) Use leaded solder.
3) Use plenty of flux
I have also used solder paste in the past, which has flux built in, but this is not necessary. Search ebay for "mechanic solder paste".
The trick is to prepare everything in advance, work fast, since the element is heat sensitive, and apply some good quality flux (you can never have too much flux). Pick up one of the cheap flux pens (also from ebay) and use that if you don't already have some suitable flux.
Place the piezo element on some bluetac or rodico.
Tin the end of the wires you are using, and cut the tinned end to about 1 to 1.5mm in length, not any longer.
Hold the wire in place with another bit of bluetac (not attached to the disk though), and move it till it sits exactly where you want it.
Hold the soldering iron on the wire, just long enough to transfer in enough heat to melt the pre-tinned wire, the pre-applied flux and the solder paste, or solder to get them to melt.
Remove the iron, and let the solder re-solidify. The whole operation should take perhaps a couple of seconds.
Clean any flux residue off with isopropanol or surgical spirit and an old toothbrush.
Job done.
As you might have gathered I've played this game a few times before.
https://stm32duino.com/viewtopic.php?f=3&t=1329&p=17153&hilit=piezo+elements#p17153
BTW the piezo elements also are available pre-wired, so you can save yourself the challenge, by spending a few cents more. Finally, don't pay more than a few cents for the elements. They are cheap as chips on ebay if you search carefully, as are electret, ceramic and magnetic microphone elements.