eli5: where does the tension in ceramics come from?

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Recently, I got to go on an unofficial friend tour of an art conservation lab in a museum. We met one of the conservationists who was repairing a shattered ancient Greek pottery vase. She pointed out an imperfection in the restoration work and said that it could never be like it was again because pottery is under tension, which is lost when it breaks, and that’s why broken pieces will never fit back together exactly.

My question is: why is this? Where does that tension come from? I assume it comes from the firing process, but I’d like to know how. And why does glass not do this? Or does it?

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