Qualitative and Quantitative Characteristics of Modeled and Natural Oscillatory Zoning Patterns in Calcite

Four types of oscillatory zoning patterns (OZP) produced by a dynamic model are described qualitatively and quantitatively and displayed as simulated cathodoluminescence images. The behavior of the dynamic model was investigated in terms of the parameter θ, which is the ratio of diffusivities of Ca²⁺ and H₂CO₃, and in terms of the parameter γ, which is the product of θ and the ratio of concentrations of Ca²⁺ and H₂CO₃ far away from the crystal surface. Qualitatively, the dynamics of the model has been characterized by a stable focus, an unstable focus changing to a stable node or to a stable limit cycle, and by periodical behavior with constant amplitude. Quantitative characteristics, including amplitude of oscillations and duration of oscillations, change between the patterns. It is shown that the process of forming oscillatory zoning in calcite with conditions corresponding to periodical behavior with constant amplitude is very slow in comparison to other OZPs. The oscillatory zoning pattern in a natural calcite crystal is described qualitatively in terms of four general OZPs produced by the dynamic model.