Transition Zone Theory of Crystal Growth and Viscosity

Crystal growth and viscous relaxation are known to be activated processes, albeit inadequately described by transition state theories. By considering a transition zone and accounting for the Kauzmann-type temperature dependence of configurational entropy we here develop transition zone theory (TZT). Entropic and enthalpic activation probabilities scale with the cooperativity of the reactant, and the attempt frequency prefactor (kBT/h) is scaled by a characteristic phonon wavelength equal to twice the lattice constant for crystal growth, and the speed of sound squared for viscous relaxation. TZT accurately describes the temperature-dependent crystal growth rates and viscosity of diverse materials over the entire temperature ranges Tg to Tm and Tg to Tc, respectively, and affords a detailed mechanistic understanding of condensed matter reactions similar to that afforded to molecular chemistry by the Eyring equation.