To be quite honest, I’m in a bit of a pickle myself.

I’d like to help you, but these materials have been needed everywhere recently. I already resupplied the Quartermasters near the Elysian garrisons before you asked me for them.
According to my ledger... let’s see... Tozel at the Temple of Scales has a blue fragment, and Turen at the Altar of Avarice has a green one.

I’d like to help you, but these materials have been needed everywhere recently. I already resupplied the Quartermasters in the Elyos fortresses before you asked me for them.

I think you should probably go and convince Tozel in the Temple of Scales first, before you go and see Turen. Turen is always extremely thorough, you see.
I’ll give you the red fragment first.

Go speak to Sarakiel, and take care of yourself out there.
Hello there. We sell items that you won’t find in many other places.

Take a little look around.
Ah, so you’re looking for fragments as well. I do have some blue fragments.