Immense heat, like Orodruin
This is briefly discussed in Unfinished Tales; much like the One Ring, there was no power known to man that could physically harm the palantíri; it was believed that only heat (on the order of Mount Doom) was capable of destroying them:
They were very heavy but perfectly smooth, and would suffer no damage if by accident or malice they were unseated and rolled off their tables. They were indeed unbreakable by any violence then controlled by men though some believed that great heat, such as that of Orodruin, might shatter them, and surmised that this had been the fate of the Ithil-stone in the fall of Barad-dûr.
Unfinished Tales Part IV Chapter III: "The Palantíri"
Dragon-fire, or at least fire from a particularly old dragon (of which none exist in Middle-earth by the Third Age) could accomplish the same.
That said, I do find it worthy of note that Tolkien uses the phrase "some believed", indicating that this was in-universe speculation rather than the narrator stating a fact. But it's all we have to go on, so there you go.
Could it be rendered unusable without violence?
This is actually substantially easier; in fact there are three known ways you could accomplish this:
- Take it over the Sea (or generally beyond the reach of Men), which is what happens towhat happens to the Stone of Elostirion; other stones (specifically, the stones of Amon Sûl, Annúminas, and Osgiliath) were put beyond the reach of Men by being buried at sea; you could add the Ithil-stone to this list as well, if the lore of men is wrong and Mount Doom actually couldn't destroy it.
You could presumably still communicate with these stones by use of another stone, but you probably wouldn't get anything interesting out of them and you certainly couldn't actually look through them yourself 2. You could render two stones unusable by using them to communicate, and simply keeping the connection open; it's said that only the Osgiliath stone (which was lost at sea) had the power to spy on two Stones communicating:
Sauron could not break in on these conferences: only the surveyor using the Master Stone of Osgiliath could "eavesdrop." While two of the other Stones were in response, the third would find them both blank.
Unfinished Tales Part IV Chapter III: "The Palantíri"
- Do...whatever it is Denethor did. I've discussed previously that the Stone of Minas Tirith was rendered unusablerendered unusable (except by a person of great strength of will, like Aragorn) following Denethor's suicide. It's never made entirely clear what actually caused this effect, but it's the only indication given of a Stone being "broken" in this way
