Learn German: Ich suche ein Kilo Kristall für mein Projekt. - I am looking for one kilo of crystal for my project.

When talking about a specific quantity of a material or substance, German normally places the material right after the quantity without any linking word. This is called a partitive apposition. You do not need a partitive genitive (like Kristalls) or the preposition von, especially when the material is a bare noun without an adjective.

What case is Kristall in here?

It is in the accusative case, just like ein Kilo. In a partitive apposition, the measured material usually matches the case of the measurement word. Since the verb suchen takes a direct object in the accusative, both ein Kilo and Kristall are accusative here.

If I wanted to say 'a kilo of pure crystal', would I finally use the genitive?

You can, but you do not have to! When an adjective is added to the material, you can either keep them in the same case (ein Kilo reinen Kristall) or use the partitive genitive (ein Kilo reinen Kristalls). The apposition remains more common in everyday speech.

Can I use suchen nach instead of just suchen here?

Yes, both work. You can use suchen with a direct accusative object (Ich suche ein Kilo) or with nach plus the dative case (Ich suche nach einem Kilo). Using the direct accusative is very natural when looking for a specific item to fulfill a need, like in a project.