When the clay is well cracked and dried, rinse with a garden hose. Let dry a couple of days and repeat the cycle. Then you are ready for the next step. If the crystal only has a very light iron staining, then a few days soaking in a weak oxalic acid solution in a covered plastic bucket will remove it. If the iron staining is heavy, then we must cook the quartz in an acid solution.
People have many ways to clean quartz, all involving basically the same scenario.
Your specimens may be coated by iron or manganese oxides, with or without clay and you wish to remove the staining so the specimens are as clean as possible. The most commonly used, readily accessible chemical for cleaning quartz is oxalic acid, which may be bought as a white crystalline powder. It may be purchased from many mineral dealers in Arkansas, especially those who specialize in quartz. When mixed with water at a measure of a few ounces per gallon and then heated to just below a boil, oxalic acid is capable of removing all but the most stubborn iron staining. It is a weak organic acid, but don't kid yourself, it will hurt you especially if you breath the fumes.