A model of oscillatory zoning in solid solutions grown from aqueous solutions: Applications to the (Ba,Sr)SO4 system

Abstract

Barite-celestite crystals can be synthesized from aqueous solutions during counter-diffusion in a gel column connecting two reservoirs. It is known that such crystals may exhibit oscillatory zoning, whereby the barium composition in the crystal fluctuates more or less regularly from the core of the crystal to its rim. We present here a simple model of oscillatory zoning in such binary solid solutions A1A2 grown from aqueous solutions. The model combines diffusive transport of the relevant ions with an autocatalytic growth process. The latter is formulated as a continuous growth in which the probability of finding a kink site on the growing surface depends on the chemical composition of that surface. Thus, an A1-rich surface favors the growth of A1 over A2, as long as A1 is present in the vicinity of the surface. Precipitation results in a local depletion of A1 in the aqueous solution, and the system may switch to a A2 growth mode, until diffusion replenishes the amount of A1, and so on. We use a dynamical equation for the molar fraction of component A1 in the crystal, which results from mass conservation across the rough crystal-solution interface. Linear stability analysis and direct numerical solutions show that the system exhibits oscillatory behavior. Using the barite-celestite system as a framework, the scaling is consistent with the experimental observations. We discuss the variety of zoning patterns and textures numerically obtained as the concentrations of reactants in the reservoirs vary. This model might help in understanding the formation of oscillatory zoning in hydrothermal environments.