Annealing is usually done on a solid, so I assume you will be operating below the melting point of magnesium, or

Emanuel Cooper Can I use standard porcelain (with glaze) or ceramic crucibles?

Nikolay Orlov

You can try (how many repeats can you afford and how will you analyze the purity of your annealed Mg?). But standard porcelain is much more likely to react than quartz, or than one of the ceramic options I recommended above.

Emanuel Cooper Yes, I found periclase crucibles! And another question: is it possible to anneal galvanized samples in such crucibles without negative consequences?

I would really appreciate your response!

The relevant point would be which side of the galvanized samples is in direct contact with the crucible. If it's a less reactive material, that makes it easier because then you wouldn't have the possibly crucial Mg-crucible contact.

A detailed explanation and importance of materials to be used for annealing/sintering Mg is already provided by Prof. Emanuel Cooper

I am adding one more possible solution, i.e. use of graphite tube. You can insert the graphite tube with small hole on lid inside a suitable diameter of quartz tube (i mean two concentric tube where diameter if quartz tube > graphite tube). Keep materials in quartz tube with closed lid on top of it, insert it in quartz tube, seal the quartz tube under vacuum. In case if annealing or sintering is done under inert atmosphere then you may not require the quartz tube and sealing of it. Hope this will be helpful.