Overall Rate of Transformation Johnson-Mehl and Avrami Equations

2 Overall Rate of Transformation Johnson-Mehl and Avrami Equations 

The overall fraction of material transformed as a function of time [F(t)] can be derived assuming nucleation and growth of spherical particles where both the nucleation rate (IV) and the growth rate (G) are constant as a function of time. The derivation is beyond the scope of the present text but results in a formula for F(t) with the following form  

This equation, which relates the fraction transformed to the nucleation rate, the growth rate, and the time elapsed since the start of the transformation (at constant temperature), is known as the Johnson-Mehl equation. The fact that the exponential term depends on can be understood on the basis that growth is assumed to proceed spherically, and thus the volume transformed increases with the cube power of the linear growth rate. 

LIQUID-SOLID AND SOLID-SOLID PHASE TRANSFORMATIONS 

In this example, the overall transformation process is fastest for T=T2, corresponding to the temperature where the growth rate is maximized. At both T = Ti and T = T, the transformation rate is slow, although for different reasons in each case. At r = Tj transformation is slow because the driving force for transformation is small, while at T = transformation is slow because atomic mobility (i.e., diffusion) is slow. 

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