Molten tin solidifies with a constant nucleation rate and grains growing at a…

PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Non-equilibrium statistical mechanics and stochastic thermodynamics

Soft Matter at the Thermal Scale, Ch Nucleation and the lifetime of a metastable phase

Problem

Molten tin solidifies with a constant nucleation rate I=1.0×1015 m−3 s−1I=1.0\times10^{15}\,\mathrm{m^{-3}\,s^{-1}} and grains growing at a constant radial rate G=1.0×10−6 m s−1G=1.0\times10^{-6}\,\mathrm{m\,s^{-1}}. Using the Avrami equation for constant nucleation and growth rates, X=1−exp⁡ ⁣(−π3IG3t4)X = 1-\exp\!\left(-\tfrac{\pi}{3}IG^3t^4\right), calculate the transformed fraction XX after t=3.0 st=3.0\,\mathrm{s}.

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