I once read a science fiction story -- in Asimov's magazine -- about terrorists attempting to make a dirty bomb. There are many problems. If you just use big chunks, you get big chunks that are east to find and dispose of. To get an effective weapon you have to grind it into powder, an activity not endorsed by OSHA. It is more hazardous to the terrorists than to their intended victims.
And that is why any attempt to manufacture an effective dirty bomb can be traced. The equipment needed is not available at your neighborhood machine shop.
Plutonium burns. Mix chunks with a high-temperature combustant like thermite and you might get plutonium-oxide soot wafting into the atmosphere