#volatilization

The “white sun” is a synonym for the white stone.

You can see the material being heated in the flask, with the peacock’s tail appearing.  Here’s the description, from Adam McLean’s alchemy website:

Volatilisation through liquid.

Here our white sun, without any imposition of a hand, nor opening of the flask a second time, is melted, the heat having been continued, with many coloured vapours resembling the tail of a peacock, then our white sun  is being volatilised through a liquid.

Seems like Jaime and Brienne both achieved the White Stone--but got stuck there.