Supplementary information

The JMAK kinetics is derived in [#!RaghavanPhaseTrans!#]; we outline the mathematical steps here and refer the interested reader to [#!RaghavanPhaseTrans!#].

Assuming spherical particles, a nucleation rate of $N$, and a growth rate of $V$, the volume fraction of transformed phase ($X$) at time $t=\tau$ can be shown to obey the differential equation

$$\frac{dX}{1-X} = \frac{4}{3} \pi V^3 (t-\tau) N d \tau$$ (24)

Integrating this equation, one obtains the JMAK kinetics, namely,

$$X = 1 - \exp {\left(- \frac{\pi}{3} N V^3 t^4 \right)}$$ (25)

There are cases wherein JMAK kinetics might fail; one such case is the crystallization kinetics in certain polymers. The modification to JMAK in such cases is discussed in greater detail in [#!ModellingBook!#].