Oscillatory zoning in crystal growth: A constitutional undercooling mechanism

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Abstract
A simple isothermal constitutional mechanism is proposed to explain the oscillatory compositional zoning observed in many natural crystals. The model is based on the diffusion equation in an open system and realistic crystal-growth kinetics. A phenomenological partitioning coefficient K is introduced to relate the composition in the melt to the composition in the growing front. For concreteness, the model is applied to the plagioclase feldspar system, a geologically important solid-solution series. Growth rates are obtained from experimental growth data. A linear stability analysis of the model is presented. It is seen that for K>1 the steady state is stable. It is possible, however, to define an effective partitioning coefficient which may be smaller than unity. In this case, the system may undergo a Hopf bifurcation and develop an oscillatory behavior. Direct numerical solutions indicate that oscillatory and chaotic zonings can indeed be obtained.