The Iron-carbon diagram and the Time-Temperature-Transformation (TTT) curves are both important tools used in the study of phase transformations in iron-carbon alloys. However, they are determined under different conditions.

- Equilibrium and Non-equilibrium Conditions:
The concept of equilibrium refers to a state where all the thermodynamic properties of a system remain constant over time. In the context of phase transformations, it means that the phases present in a material are in their most stable form and there is no further transformation occurring.

On the other hand, non-equilibrium conditions refer to situations where the system is not at equilibrium. This can occur when the material is rapidly cooled or heated, preventing the phases from reaching their stable forms.

- Iron-Carbon Diagram:
The iron-carbon diagram, also known as the phase diagram or the Fe-C diagram, is a graphical representation of the phases that can exist in iron-carbon alloys as a function of temperature and carbon content. It shows the different regions of stability for the phases, such as ferrite, austenite, cementite, and graphite.

The iron-carbon diagram is determined under equilibrium conditions. It is constructed by conducting controlled heating and cooling experiments on iron-carbon alloys and analyzing the resulting microstructures using techniques like optical microscopy. The diagram provides valuable information about the phase transformations that occur during the cooling and heating of iron-carbon alloys.

- TTT Curves:
The TTT curves, or Time-Temperature-Transformation curves, provide information about the kinetics of phase transformations in iron-carbon alloys. They show the time required for a phase transformation to occur at a given temperature.

The TTT curves are determined under non-equilibrium conditions. They are obtained by rapidly quenching the alloy from a high temperature to a specific temperature and holding it at that temperature for a defined period of time. After the holding time, the alloy is cooled or heated further, and the resulting microstructure is analyzed.

- Conclusion:
In summary, the Iron-carbon diagram is determined under equilibrium conditions, while the TTT curves are determined under non-equilibrium conditions. The diagram provides information about the stable phases at different temperatures and carbon contents, while the TTT curves provide information about the kinetics of phase transformations at specific temperatures and holding times.