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

The distribution of trace elements in zircon is typically heterogeneous, a result of processes operating during crystal growth. The spatial distributi on and abundances of minor and trace elements in zircon from a compositiona lly zoned pluton have been quantifed by fractal statistics and microprobe a nalysis. The crystals exhibit oscillatory zonation distribution patterns (O ZPs). Trace element abundances indicate that the "xenotime" coupled substit ution mechanism dominates the incorporation of trace elements into the zirc on lattice. There is no general trend of trace element enrichment in zircon from mafic to felsic whole-rock samples, despite some differences, includi ng the restriction of Th in zircon from felsic rocks by the co-crystallisat ion of accessory allanite. Zircon OZPs have been quantifed by image analysis and self-affine fractal s tatistics. A pluton-wide zircon Hurst exponent (H) value of 0.44 reveals th at as a function of time, trace elements are not randomly incorporated into growing crystals, but experience external forcing, evidenced by the decrea se of the mean Lyapounov exponent (lambda(m)) with increasing magmatic diff erentiation. This correlation represents a progressive, quantifiable decrea se of the degree of chaos of zircon OZPs from mafic to felsic whole-rock sa mples. This relationship is related to ordering in the melt by polymerisati on, 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 ca tion substitution, diffusion, and melt polymerisation and structure generat ion. 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. Copyright (C) 2000 Else vier Science Ltd.