The lever rule (e.g. for a two-phase microstructure) actually applies at the temperature, where equilibrium is being established. In many cases, however, once an equilibrium has been established after annealing some time at elevated temperature, the microstructure can be successfully retained by quenching to room temperature. This is possible in many alloy systems. Occasionally, you get changes upon cooling (e.g. by martensitic phase transformation). Nevertheless it may still be possible to estimate how the microstructure may have looked like at the annelealing temperature. But then the results pertain still to the high annealing temperature.

Low temperature equilibria is an issue, of course. Of course, there are a lot of works which INADEQUATELY extrapolate high temperature equilibria to low temperatures. To some extent thermodynamic models can be used to estimate, how equilibria should look like at low T which are difficult to establish experimentally.

How do I predict the microstructure then if it is water quenched?I will not be able to use the Fe-C phase diagram.What is the alternative.If someone asks me how to calculate the weight fraction of martensite then how do I calculate that?

In a large majority of materials you will simply retain the microstructure. Austenite in Fe-C, on the other hand, it is an exception, which untergoes a not quenchable martensitic tranformation. So if you do efficient quenching (small specimen) all austenite will get martensite and retained austenite. Hence, as common practice, retained austenite + martensite are interpreted to be the prior austenite.

If you water-quench, you deviate from equilibrium conditions. Once you do that, you can no longer use a phase diagram. In some cases, as suggested by Andreas, there is no further phase transformation or appreciable diffusion, so the lever rule happens to still give the right answer.

If you want to calculate/estimate martensite weight fraction, you need to take into account the quenching rate and the hardenability of the steel. Some empirical relations exist for specific systems, but usually this is determined experimentally using tests like the Jominy end quench test.

Aashranth B. Andreas Leineweber Lets say I have a steel sample(now whether that is hypoeutectoid or hypereutectoid that is a separate question).And I wish to find the microstructure o the steel sample at 950 degree Celsius. Now if I furnace cool that to a room temperature then I will be losing the microstructure that I am supposed to get at 950 degree centrigade.Again if I quench it formation of martensite etc will take place which will kill the purpose.How do I retain the microstructure in such ferrous and in particular steel samples?If my explanation /understanding about the topic is incorrect please correct me then and there.

If you want to find out the microstructure present at 950°C you must not furnace cool, you must quench, simple as that. If you furnace cool, the microstructure will (almost sure) change (info typically contained in CCT diagrams).

Transforming into martensite does NOT kill the purpose, because you can be almost sure that what is martensite after quenching had been austenite at the annelealing (equilibration temperature).

Andreas Leineweber Yes but tell me something. I might want to find the weight percentage/fraction of proeutectoid ferrite. Will that be possible if I form martensite?

At furnace temp., say 950°C, you will have ferrite + austenite structure. The proportion between the two depends on C content and temperature. If you quench the sample, ferrite will NOT undergo phase changes, and austenite will transform into martensite. This way, at room temperature, you will see ferrite where ferrite was at 950°C, and martensite (+ little remaining austenite) where austenite was at high temp. Pls, bear in mind that this will work only if you use quenching. If slow cooling is applied, your piece of steel will behave according to Fe-Fe3C phase diagram.

If you know the chemical composition of your steel, do not turn the furnace on. Just look at the Fe-Fe3C phase diagram and apply the lever rule. Remember that the lever rule works at any temperature, provided your sample is at equilibrium state (and, of course, the alloy is in two phase region).

Depending on the alloying elements the Fe-Fe3C system may not be sufficient. But it may be first estimate. But with respect to proeutectoid ferrite I agree with the statement of Jaroslaw Ferenc.

In non-equilibrium condition you have to get access to non-equilibrium phase diagram of your alloying system matching your condition. It is also important to notice that alloying elements will change Fe-C phase diagram. These make your prediction not precise enough. Then, you may choose to calculate percentage of different phases using image analysis applicatoins, or XRD. You can also use TTT diagrams for your alloying system.Thermal Analysis could also be used.

About your last question, here the same, It is hard to calculate concise percentages using phase diagrams.

By the way, having a high enough cooling rate, your alloy may contain retained A, F and M.

First, phase diagrams are generally based on a cooling rate of 1 degree C per second. This is the average cooling as the rate changes during solidification and phase changes. But even that is a simplification. Nucleation plays a significant role, and nucleants are often extremely fine particles. We produce an instrument that measures phases produced during solidification by the energy they release. The units are the percentage of the total Heat of Fusion. Phase formation is also driven by negative pressure inside the casting. The partial vacuum caused by the shrinkage of solidification reduces the energy necessary to start the nucleation of certain structures. As I said, it is complex.

We have found three predictors of hardness in the micro-energy analysis of white iron - all which tie back into the physics of carbide energy. The die-off of energy production (2nd derivative peak) is quicker with less carbide, the temperature at which the carbide phase begins, and finally the percent of the carbide energy vs. the total heat of fusion of the sample. One exceeds 90% correlation and two approach 98% correlation with hardness.