Theory for the anomalous light scattering in growing ice crystals

A theory is presented for the anomalous light scattering which has been observed at the surface of a growing ice crystal. The theory is based on a model for the production and distribution of defects at and near the growing interface. Analysis of this model shows under appropriate conditions that the surface distribution exhibits multiple uniform or nonuniform stationary states. Connected with the occurrence of the multiple stationary states is a critical growth velocity at which the surface undergoes a transition from a state of low average defect density to a state of high average defect density. Using hydrodynamic fluctuation theory, we calculate the structure factor for quasielastic light scattering from defects in the surface layer. The model accounts for the following qualitative observations: a threshold for anomalous scattering, the change in spectrum of scattered light, hysteresis, and spreading in time of the scattering region. Using the measured spectral linewidth, the measured critical velocity, and the experimental estimate of the scattering layer, we deduce from the model that the scattering region will spread with a constant velocity of 5 μm ${\sec }^{\mathrm{-}1}$. This number falls within a factor of 2 of the experimental value. On the basis of the model suggestions are made for further experiments.