Significance of the green stone?

[Lostgaeriel]

Finwe suggested:

By the time that the War of the Ring was underway, it was revealed that Aragorn was the Heir of Isildur. His spies would have brought him the news that the people of Gondor were calling him Elessar.

But Aragorn revealed himself to Sauron using the Palantir of Orthanc, remember? That was on March 6 at Dunharrow, well before he arrived in Minas Tirith to do the "hands of the healer" thing. And I believe he was wearing the Elessar - Galadriel game him "a great stone of a clear green, set in a silver brooch that was wrought in the likeness of an eagle with outspread wings". Sauron didn't have to wait to get the news from his spies.

But regarding Tolkien's choice of a green stone to be the identitifier of the King, I would still like to know if anyone has found any other examples in Medieval literature of green stones with healing powers. As per my post in the "Aragorn's Elfstone" thread.

I've recently read Chrétien de Troyes Perceval and Wolfram Von Eschenbach's Parzival (translations, of course) and was amazed to find that in Wolfram's version, the Grail (graal - a serving platter) was made of a single green stone or gem - presumably emerald. Not only that, but it has healing powers.

Is this a recurring motif in literature or just a coincidence?