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Properties of steel can be influenced by several factors:

Composition

Increasing the amount of carbon in steel increases its strength and hardness. Carbon in the form of carbides (like Fe-Fe3C), which are hard themselves and act as strengthening agents in steel alloys through dispersion strengthening. Increasing carbon content also has the general affect of lowering the temperature. Looking at the phase diagram is helpful in understanding this effect: iron (Fe) has a higher temperature than iron-carbide (Fe3C).

Heat Treatments

Heat treating affects strength, ductility, hardness, or impact resistance. Annealing, normalizing, etc. affect the microstructure of steel. Steel can be made into various microstructures - martensite, bainite, pearlite, cementite, ferrite (in no particular order) - each of which has different properties. Martensite is the strongest microstructure, with increased ductility through tempering to tempered martensite. Tempering encourages carbon diffusion, resulting in improved strength and ductility as the trapped carbon from the rapid quench to martensite is allowed to diffuse.

Surface Treatments

If you're talking about a part, then surface treatments will affect the surface hardness. For example, adding Zinc will increase the strength and corrosion resistance of the part. Case hardening is another way to strengthen the exterior of the specimen.

Note: Strength and ductility for steels are usually inversely related, so improving one typically means sacrificing the other (i.e. increasing the strength usually makes steel more brittle, therefore less ductile). The deciding factor then typically is application.

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