*2.2. Construction of the Ideal TTT Diagram from the Constant Cooling Rate CCT Diagram*

The ideal isothermal transformation time, *τ*, can be calculated using Equation (5) [19,29]

$$\frac{1}{\pi(\Delta T\_{\text{CCT}})} = \frac{d\theta\_{\text{c}}(\Delta T\_{\text{CCT}})}{d\Delta T\_{\text{CCT}}} \tag{5}$$

where the function ˙ *θ*c(Δ*T*) is the constant cooling rate required to produce a transformation start exactly at the point of undercooling, Δ*T*CCT (or, equivalently, Δ*T*CCT is the amount of undercooling at which the transformation starts for constant cooling rate ˙ *θ*c). Applying the chain rule of differentiation we obtain

$$\frac{1}{\tau(T\_{\rm s,cct})} = -\frac{d\dot{\theta}\_{\rm c}(T\_{\rm s,cct})}{dT\_{\rm s,cct}}\tag{6}$$

where *T*s,cct is the transformation start temperature in the CCT diagram.

2.2.1. Construction of the Ideal TTT Diagram from (*t*85(*T*s,cct), *T*s,cct) CCT Diagram

The numerical value of the ideal isothermal start time can be obtained by taking the difference approximation of Equation (6) and solving for *<sup>τ</sup>*(*T*s,cct) ≈ −Δ*T*s,cct/<sup>Δ</sup> ˙ *θ*c(*T*s,cct), where Δ*T*s,cct = (*T*s,cct + *<sup>h</sup>*/2) <sup>−</sup> (*T*s,cct <sup>−</sup> *<sup>h</sup>*/2) = *<sup>h</sup>* and <sup>Δ</sup> ˙ *θ*c(*T*s,cct) = ˙ *<sup>θ</sup>*c(*T*s,cct <sup>+</sup> *<sup>h</sup>*/2) <sup>−</sup> ˙ *θ*c(*T*s,cct − *h*/2) for a sufficiently small *h* value. The numerical value for the isothermal start time can be calculated using Equations (1), (2) and (7).

$$\begin{split} \tau \left( T\_{\rm s,cct} \right) &\approx -\frac{\Delta T\_{\rm s,cct}}{\Delta \theta\_{\rm c} \left( T\_{\rm s,cct} \right)} \\ &= \frac{h}{300 \left[ \frac{1}{t\_{\rm 85} \left( T\_{\rm s,cct} - h/2 \right)} - \frac{1}{t\_{\rm 85} \left( T\_{\rm s,cct} + h/2 \right)} \right]} \end{split} \tag{7}$$

where *t*85(*T*s,cct ± *h*/2) represent the function values of *t*85(*T*) at *T* = *T*s,cct ± *h*/2. When the value *h* = 0.1 K was used, the recalculation of the CCT diagram from the TTT diagram using Equation (12) successfully replicated the original CCT diagram (as shown in Figures 3 and 4).
