TTT diagrams and JMAK kinetics

The overall nucleation and growth kinetics are generally represented, for isothermal transformations, using the TTT (Time-Temperature-Transformation) diagrams. In Fig. 28 we show a schemamtic TTT diagram; the time and temperature are plotted in the $x$ and $y$-axes respectively; the beginning and ending of transformations are drawn (by arbitrarily taking 1 and 99% transformation as the beginning and ending of the transformation respectively). As shown, the typical TTT diagrams are C curves; in terms of time versus fraction transformed, these are the so called S curves as shown in Fig. 28. The C-curve indicates that the incubation time, that is the time taken for the transformation to start at every temperature is the lowest at intermediate temperatures; this is because, as we discussed in this module and the previous one, both the nucleation and growth kinetics are faster at the intermediate temperatures; at low undercoolings (high temperatures), the driving forces for the transformation are very low making the kinetics to be slower; at high undercoolings (low temperatures), on the other hand, the diffusional kinetics is very slow making the overall transformation kinetics to be very slow. Finally, the S curves of the type shown in Fig. 28 can be understood in terms of what is known as the Johnson-Mehl-Avrami-Kolmogorov (JMAK) kinetics; see the supplementary information at the end of this module for a derivation of the JMAK kinetics.

Figure 28: The TTT diagram (C curves) and the fraction transformed as a function of time at different temperatures (S curves).

[scale=0.6,angle=0]Figures/TTTSandC.pdf