Crystals can create resources on Private Islands. Only crops or blocks that haven't been placed by a player count towards a collection and give skill experience. For example the Nether Wart Crystal can be used to farm Nether Warts if traveling to the Blazing Fortress is too tedious or deadly.
Only one Crystal of each type can be placed at once. If multiple crystals are acquired by placing an island, taking the crystal and placing another island, still only one of each type can be placed. If an Island is placed while the island's corresponding crystal is already on the Private Island, no Crystal will be spawned.
Nether Wart Crystal
Dark Oak Crystal
The Dark Oak Crystal can be spawned by placing a Roofed Forest Island. This crystal can not be picked up as opposed to the other Crystals. It can only be removed from the island but is not obtainable as a placeable item.