I would like to know how to create a rough looking green emerald in Cycles.
It should look like that, but can be even rougher and doesn't have to be that translucent.
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Maybe this will help get you started. You will still have a lot of work to do in order to refine the materials and lighting to get this to work.
Here's a link to the Fracture Modifier branch which was used to break up a model. https://www.dropbox.com/sh/xiuirkoo0rac5tw/AAB2XQbs9K5uTIYcbDPUDW1Ca