Steel is a mixture of iron and carbon atoms. At working temperatures, the iron can “dissolve” more carbon than it can at lower temperatures. When you heat-treat steel, typically by quenching in water or oil, you are very rapidly cooling the steel. This prevents the “dissolved” carbon from exiting the structure of the iron atoms; they get trapped in there. This forms a different crystal structure in the steel than untreated steel. This alternative structure, because there is additional carbon stuck in it, is harder than untreated steel.
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