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Kinetics and Microstructural Control
· The energy required to overcome the activation barrier for nucleus formation comes from lattice thermal fluctuations and is governed by the Boltzmann relationship 
for the Probability of ΔGhet*
            P
Het= exp {- ΔGhet*(T)/ kT}
· The lower value of ΔG* for heterogeneous nucleation, exponentially favors this nucleation process over homogeneous nucleation.