An iso-activity 'line' (or surface in a quaternary system) of C in a certain solution can be seen as the collection of compositions where C has the same tendency to undergo a reaction.

The easiest example of this is the line for an activity equal to 1. On this line, the solution would be in equilibrium with pure graphite. Any activity higher than 1 would mean the solution is unstable, as at equilibrium graphite would precipitate out of the system.

Activities lower than 1 might also result in the precipitation of other compounds, for example Fe3C, although the point at which these compounds precipitate would depend both on the activity of C and the activity of (in this example) Fe. (This isn't a perfect example as Fe3C is actually a metastable compound)

I am not myself familiar with ThermoCalc. I know that FactSage has the option to calculate iso-activity lines on ternary diagrams.

Thank you Tijl for answering. It is helpful.

Hello,

In Thermocalc, an iso-activity line can be calculated by setting a condition in the calculation : 

1/ the value of the activity of a species in a phase acr(specie,phase)

For example, for C in BCC_A2 with an activity of 0.2 add : acr(C,BCC_A2)=0.2

2/ the value of the activity of a component in the system

For example, for C with an activity of 0.2 in the system add : acr(C)=0.2

Do not forget to add a reference state for C (generally Graphite) : set-ref C graphite * *

where the to stars represents the temperature and pressure of the calculation.

Regards 

Thank you Gossé Stéphane for your answer. It is really helpful.