Figure 1:
This is a phase diagram of an iron-carbon compound (steel at low wt% C). It is only true for equilibrium cooling/heating (slowly). More on Phase Diagrams here!
This is because in non equilibrium cooling, when the steel is undercooled (below the eutectoid temp), there is a rate of transformation of austenite. This is determined by the rate of diffusion (high temp = high diffusion = fast transformation) and rate of nucleation (low temp = high nucleation = fast transformation).
This means that the time your steel is left at a certain temp determines how much, if any, of your austenite has transformed into pearlite (or bainite & martensite).
In equilibrium cooling, the temperature decreases very slowly. This means that during cooling and phase changes, the metal remains homogeneous throughout its microstructure. For example, when passing through the eutectoid, the whole microstructure will simultaneously transform from austenite to pearlite (alternating layers of ferrite and cementite). Rather than the outside of the metal changing before the core.
Equilibrium type of cooling is easier to understand, but in reality, it isn't practical. Firstly, it takes too long, slowing production. Secondly, it may not give an ideal micro-structure (neither does non-equilibrium), meaning heat treatments will probably need to be done anyway, so there's no reason to waste the time. With non-equilibrium cooling, there are some tricks you can use to get the best properties out of your metal.
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The main type of non-equilibrium cooling is quenching (basically dunking your metal in a bucket of water). This rapidly reduces the temperature so that there is no time for carbon to diffuse out of austenites FCC structure (to form cementite) meaning that there's not enough room for ferrites BCC to form. Instead, martensite will begin to form, a structure not present on the phase diagram.
Martensitic Transformation: Very Cool!
It has a BCT unit cell (a taller BCC cell with an interstitial carbon in it). When heat treated, carbon can diffuse, so martensite will form pearlite. However, it will have a quite different micro-structure that has more favorable properties than the pearlite formed in equilibrium. More Applications Here!
Figure 2:
This figure shows different possible micro-structures being formed from non-equilibrium cooling of steel.
In slow cooling, carbon has sufficient time to diffuse, and so pearlite is formed.
In moderate cooling, bainite (long and thin strips of cementite in ferrite matrix) will be formed (if time left is sufficient). This is because the temp isn't too low that carbon can't diffuse out of austenite (so it can form long thin strips of cementite), while the temp isn't high enough that there is high nucleation of ferrite, so there are many grains, forming a matrix.
In fast cooling (quenching), part of the austinite will form martensite, (depending of amount of under-cooling). It is important that it is fast enough to avoid the 'nose' on the TTT diagram otherwise some pearlite will form.