A colloidal suspension contains a fixed number density of pre-existing crystal nuclei…

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

A colloidal suspension contains a fixed number density n0=1.0×1014 m−3n_0 = 1.0\times10^{14}\,\mathrm{m^{-3}} of pre-existing crystal nuclei (no further nucleation occurs) that grow as spheres at a constant radial rate G=5.0×10−8 m s−1G=5.0\times10^{-8}\,\mathrm{m\,s^{-1}}. Using the Avrami equation for pre-existing sites, X=1−exp⁡ ⁣(−43πn0G3t3)X = 1-\exp\!\left(-\tfrac{4}{3}\pi n_0G^3t^3\right), calculate the transformed fraction XX after t=300 st=300\,\mathrm{s}.

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