Materials in Dark Alliance are used to craft better gear or upgrade the existing one. In Dark Alliance, you have five different Crystals, that correspond to one of the five different rarity levels.
You can also upgrade any Crystals to the next level, the requirements vary depending on the tier you are trying to level. The only crystal that can't be upgraded is the Legendary Crystals.
Common Crystals: 10 to 1. Costs 50.
Uncommon Crystals: 8 to 1. Costs 150.
Rare Crystals: 6 to 1. Costs 500.
Epic Crystals: 3 to 1. Costs 1,250.
Legendary Crystals: N/A
On the other hand, all crystals, except for the Common Crystals, can be downgraded to the tier below the one you have selected.
Common Crystals: N/A
Uncommon Crystals: 1 to 10. Costs 25.
Rare Crystals: 1 to 8. Costs 75.
Epic Crystals: 1 to 6. Costs 250.
Legendary Crystals: 1 to 3: Costs 625.