A thorough answer might require several books. The method of production & all thermal & mechanical processing play a role in a material's properties. Often alloying elements in combinations play a role -- for steels, there are asustenite formers, ferrite formers & of course carbon affects microstructure in combination with all of these & thermal processing.
You mentioned alloying elements, but S & P, often considered impurities rather than alloying elements, often have a negative effect. However, Mn at the correct level can largely negate small amounts (0.05 wt%) of S.
Some good introductory reading on steel -- alloying, embrittlement, fracture, heat treatment, mechanical testing, microstructure, etc., here:
Of course, you could simply use wrought aluminum or austenitic stainlesses for low temperatures. Their crystal structures have more slip systems available for plastic deformation than the usual steels.