FWIW I do have a degree in metallurgy, as well as experience in firearms manufacture. You might have to bear with me a bit here, but here's my view:
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<br>Quenching and tempering of Steels
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<br>By way of background, in the typical medium-carbon steel after annealing the structure is made up of ferrite (essentially pure iron) and cementite (iron carbide). If you heat that structure enough, the structure transforms to austenite. Now, if you cool very slowly you're back where you started as the austenite transforms back again to ferrite and cementite (though you may have relieved any internal stresses - this is annealing).
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<br>If, however, you cool very quickly (quench), the ferrite and cementite don't have time to form, so what you get is a structure called martensite, in which very fine needles of carbide are finely dispersed through a ferritic matrix.
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<br>This structure is glass-hard and very brittle, and not much use unless you carry out controlled heating to a temperature below the austenite transformation to temper the structure.
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<br>The role of cryogenic quenching
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<br>In some alloy steels the transformation from austenite to martensite is not complete at room temperature. The result is that grains of austenite are retained in the martensite. This can be a problem in that grains of austenite are softer than the martensite around them, leading to "soft spots" and difficulties with machining, as well as the fact that austenite has a different volume leading to distortion and retained stresses. It is a particular problem with certain die steels, and that is where cryogenic quenching was developed: to ensure that the transformation is complete. Note however that this is the mode of operation of cryo quenching: to solve problems with retained austenite in quenched and tempered steels.
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<br>Cryo and rifle barrels
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<br>It is unlikely that cryogenic quenching has any real effect on rifle barrels. Generally speaking these are not used in the quenched and tempered condition, but instead are typically subject to varying degrees of cold forming (hammer forging, and to a lesser extent button rifling) or else drilled and broached from bar stock, and then normalised.
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<br>Ironically, if cryogenic quenching did have an effect on a finished barrel, it would probaly show up as distortion, due to the volume change as any retained austenite transformed to martensite.
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