Egg shells are my exclusive source of calcium besides that already in tap water and minor traces in other compost, and of course what was already in the soil itself. I mix it into the soil at time of transplant after stomping on a bin full with the end of a piece of wood 2x4.
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They do not need to be completely turned to powder, nor ashed or baked if you use enough and they are in the soil instead of on top. Acid in (typical) rain and/or woody material in your soil like mulch or peat moss will acidify and break them down. Obviously this means they work best with slightly acidic soil which peppers like anyway.
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In my growing conditions the small particles, averaging a little smaller than the diameter of a BB, almost fully disintegrate by the end of a growing season when I turn more compost into the soil (and more egg shells) to age over the rest of fall and winter for next spring. That's the key to using egg shells, that it's a long term solution rather than a fix for an immediate calcium deficiency (with an exception mentioned below).
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If you did not amend your soil with them ahead of time then powdering them will help get them down into the soil, and ashing then powdering them even more so. If you have a calcium emergency you can also dissolve them in vinegar for immediate availability to the plant but be careful! Don't add too much vinegar, agitate the mixture so it fully reacts leaving some pieces of shell behind as evidence it isn't too acidic still (or test the pH yourself), and leave it sitting to react for a few hours before watering the plant with it.
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Do not use a lot of egg shell vinegar solution at once as you can kill a plant with too great a quantity while it is very hard to use too much crushed egg shell alone.