On a synthesis of crystal population dynamics and trace element partitioning models: A mechanism for zoning in minerals

Abstract

Crystal zoning is considered in the context of the evolution of a population of crystals. Crystal size distribution (CSD) theory provides an important framework and constraints that are applied in a numerical model of crystal nucleation and growth in an infinite half-sheet which proxies for a sill. The CSD/crystal population approach is combined with a relatively simple principle of trace element (TE) partitioning for batch crystallization. A model of crystal nucleation and growth that is applied to a constrained volume of magma is modified by the addition of a co-precipitating phase and TE modeling. The coprecipitating phase does not consume the TE and so the TE's concentration in the residual liquid increases. Thus the primary phase for which the TE is compatible incorporates more as it grows. A single partition coefficient value is used and is held constant. One crystal in the much larger, evolving population of crystals is tracked and TE concentration in the crystal vs. time is recorded as the crystal grows. In general, TE concentration within the crystal initially decreases while only the primary phase is present and then begins to increase in that crystal when the second/coprecipitating phase appears. For the relatively short solidification interval utilized in the modeling, one half-cycle of oscillation: high concentration to low to high, or normal to reverse zoning, is demonstrated. Beyond the TE's partition coefficient, the presence and magnitude of zoning is dependent upon the time the second phase begins within the solidification interval and the mass proportion of crystallization of primary phase to second phase—which is held constant throughout the remainder of solidification once the second phase appears. The model, as currently implemented, is based solely on thermal and mass balances. A multi-faceted crystallization history, one involving, e.g., more complicated phase equilibria, crystal fractionation, convection, and magma mixing would expose the tracked crystal to changing surroundings such that the mass balance mechanism that yielded the half-cycle of zoning obtained here would perhaps continue to yield oscillatory zoning.