Oscillatory zoning in a (Ba,Sr)SO4 solid solution: Macroscopic and cellular automata models

Many minerals exhibit oscillatory zoning (OZ), whereby their chemical composition varies more or less regularly along a crystal core-to-rim profile. A well-known example of oscillatory zoning was previously obtained in the (Ba,Sr)SO4 solid solution system under controlled laboratory conditions. The OZ crystals were precipitated at room temperature from counter-diffusing aqueous solutions. In this contribution, we review a macroscopic model for the self-organized formation of oscillatory zoning in such binary solid solution. The model combines diffusive solute transport and an autocatalytic continuous crystal growth with a rate dependent on the mineral surface composition. Oscillatory solutions are obtained. It is also shown that fluctuations in the aqueous solution concentrations may contribute to the OZ formation by causing noise-induced transitions in the crystal growth regimes. We also present, for the first time, a cellular automata-based microscopic model, which considers diffusive motion and autocatalytic attachment kinetics of individual molecular units. OZ is obtained when the probability of attachment of a unit onto the crystal surface is calculated from the crystal composition averaged over the crystal surface (mean-field approach). However, OZ fails to develop when this probability is calculated from the local crystal composition at the attachment site in the absence of a lateral synchronization mechanism.