Patterns of chaos: fractal statistics and the oscillatory chemistry of zircon

Abstract

The distribution of trace elements in zircon is typically heterogeneous, a result of processes operating during crystal growth. The spatial distribution and abundances of minor and trace elements in zircon from a compositionally zoned pluton have been quantifed by fractal statistics and microprobe analysis. The crystals exhibit oscillatory zonation distribution patterns (OZPs). Trace element abundances indicate that the “xenotime” coupled substitution mechanism dominates the incorporation of trace elements into the zircon lattice. There is no general trend of trace element enrichment in zircon from mafic to felsic whole-rock samples, despite some differences, including the restriction of Th in zircon from felsic rocks by the co-crystallisation of accessory allanite. Zircon OZPs have been quantifed by image analysis and self-affine fractal statistics. A pluton-wide zircon Hurst exponent ( H) value of 0.44 reveals that as a function of time, trace elements are not randomly incorporated into growing crystals, but experience external forcing, evidenced by the decrease of the mean Lyapounov exponent (λ m) with increasing magmatic differentiation. This correlation represents a progressive, quantifiable decrease of the degree of chaos of zircon OZPs from mafic to felsic whole-rock samples. This relationship is related to ordering in the melt by polymerisation, as expressed by the strong correlation (R 2 = 0.96) with NBO/T. A model is presented here, where the oscillatory distribution of trace elements in zircon is controlled by dynamics at the zircon/melt interface involving cation substitution, diffusion, and melt polymerisation and structure generation. The combined affect of these processes on the character of zircon OZPs is to decrease the degree of chaos preserved in the crystals trace element pattern with progressive magmatic differentiation.