Well, I hope I'm not polluting the RF side of the forum with too much non-RF stuff, but since it seems that some very nice comments are coming out of this thread, please allow me to share some info I've come across.
Looks like Amptek have a solid state X-ray generator based on the pyroelectric effect:
http://amptek.com/products/cool-x-pyroelectric-x-ray-generator/#4Small size, low power. Also, it looks like the base is a Peltier module, so the heating can't be something like several hundred degrees C
Whe I first saw this, I thought it was ... not dooable. But the I started reading some scientific papers about these kinds of crystals and the pyroelectric effect, and it realy seems that it is possible.
A similar DIY version to what I want to do, can be found here:
http://www.intechopen.com/books/scanning-electron-microscopy/palmtop-epmaYou can have a look on the site, or just download the PDF attached
This is also another very nice article on how to do things DIY:
http://www.rapp-instruments.de/index8.htm Click on the "Pyroelektrische Röntgenquelle" and Voila!
What got me going on the SAW filters as a source for the crystals was this:
http://www.edn.com/design/wireless-networking/4413442/SAW--BAW-and-the-future-of-wireless together with a german site that unfortunately can not find right now that mentions the same source for getting LiNnO3.
Indeed, there is a certain geometry required, for maximum efficiency of generated X-rays, but as far as I understood it, any shape should allow me to generate some (small-er) amount of X-rays.
So , basically, right now I'm shooting for a proof-of-concept type of deal, that's why I was scavenging on the net for some cheap sources for the crystals.
Curious thing is, that like it was mentioned on this thread, a crystal from an ordinary lighter might also work, with much less efficiency, however. So I think I'm going to try this, as a backup solution.
Also, I have to mention that I didn't make much sense in my las post, so let's put things in order. The crystal itself isn't responsible for generating the X-rays. The crystal is put in a small vacuum chamber, together with a metal "target". When heated, the crystal will give off electrons, which will strike the taget, which in turn generates the actual X-rays.