the iron-iron carbide (Fe-Fe3C) phase diagram

This is the single most important map in all of metallurgy, the backbone of steel and cast iron. It plots temperature against carbon content, from pure iron up to 6.7 wt% carbon where cementite sits, and tells you which iron phases exist at each point. Read it and you understand why a red-hot steel is soft and non-magnetic, while the same steel cooled is hard and magnetic.

More precisely, the axes are temperature versus weight percent carbon, running from pure iron to Fe3C at 6.7% C. The key phases are ferrite (alpha, BCC, dissolving up to only 0.022% C), austenite (gamma, FCC, dissolving up to 2.14% C), and cementite (Fe3C, a hard carbide). Two key features anchor it: a eutectic at 4.30% C and 1147 degrees C (Liquid to austenite plus cementite, the cast-iron range) and a eutectoid at 0.76% C and 727 degrees C (austenite to ferrite plus cementite, meaning pearlite, the steel range). Alloys below 2.14% C are steels, above are cast irons.

Almost all steel heat treatment is navigation on this diagram: heat up into the austenite field to dissolve carbon uniformly, then control how you cool. But it is an equilibrium diagram, so it shows ferrite, pearlite, and cementite, not the fast-cooled martensite that actually hardens quenched steel. It is also really the metastable Fe-Fe3C line; given enough time and some silicon, graphite (the true equilibrium) forms instead, as in gray cast iron.