Oscillatory Zoning in Minerals

In most petrographic studies zoning is invariably described qualitatively in terms of its optical character, this often reflects the distribution of some property or feature of interest such as refractive index or cathodoluminescence; such optical characteristics are determined by the mineral chemistry and or structure.  In order to understand the significance of oscillatory zoning patterns (OZP) it is important that we develop a quantitative means of describing the patterns as well as a means of linking the chemical and structural information to the optical features.  In this way we will be able to (1) compare zoning patterns in natural minerals and (2) compare natural patterns with the products of numerical models.  This work is needed to set out the framework for considering minerals as dynamical systems.  I have shown, using image and numerical analysis, that it is possible to determine Lyapounov exponents and fractal dimensions for trace‑element oscillatory zoning in minerals.  In cases where the exponents are negative this shows that the patterns are chaotic which is a strong indication that the chemical variation is the product of local self-organized processes and chemical feedback operating at the growth interface of the mineral with its environment.   This is distinct from larger-scale changes in the bulk composition of the system.

 

This initial work was done on accessory minerals from igneous rocks.  Auto correlation and fractal analysis has also been applied to trace element zoning and optical zoning in agate and calcite from surficial environments. Here the objective was to assess the distribution of Fe, Zn and Sr in two different minerals from different environments.  Using spectral analysis, Sr and Zn in agate showed the same periodicity whereas Fe had a much larger periodic component possibly indicating that Sr and Zn substituted in the 2+ oxidation state and Fe oscillated between the Fe2+ and Fe 3+ states.  The measured Hurst exponents for the zoning patterns are in the range 0.14 to 0.28 indicating fractal scaling and anti-persistent behavior of the system or a tendency to oscillate, which again argues for some self-organization at the growth interface. One possible explanation of the chemical variation is that the Sr and Zn distributions were primarily influenced by local self-organization at the mineral surface whereas the Fe distribution was primarily controlled by changes in oxidation state influenced by larger-scale environmental conditions.

A chaotic system is very sensitive to initial conditions. One set of initial conditions may give rise to a pattern very different from a set of initial conditions that is only slightly different. (Rather than interpreting radically different geological histories and therefore different equations there may be one system and set of governing equations and only slightly different starting conditions). The rate at which two trajectories diverge from only slightly different initial conditions is described by the Lyapounov exponent. This is a measure of chaos.

linescan zircon



Zircon

These images shows oscillatory zoning in a zircon from Thailand and grey level variation across such a pattern; the aperiodic greylevel variation has a positive Lyapounov exponent.

 

Calcite                                                                                                         Modeled Pattern

calcitemodel

Bryksina, N.A., Halden N.M. & Mejia, S. (2006) Qualitative and Quantitative Characteristics of Modeled and Natural Oscillatory Zoning Patterns in Calcite.  Mathematical Geology 38, 635 -655.

Bryksina, N.A. and Halden N.M. (2005) Oscillatory Zoning in Calcite from the Rossland Area, British Columbia, Canada: Statistical and Fractal Characteristics of Trace Element Distributions. Cheng, Q. & Bonham Carter G. (eds) Proceedings of the IAMG’05 GIS and Spatial Analysis 1: 323-328

Bryxina, N.A., Halden, N.M. & Ripinen O.I. (2002) Oscillatory zoning in an agate from Kazakhstan: autocorrelation functions and fractal statistics of trace element distributions. Mathematical Geology 34, 8, 915-927.

Bryxina, N.A., Sheplev V.S., Ripinen, O.I., Halden, N.M., Campbell J.L., and Teesdale W.J. (2000) Qualitative analyses of dynamic model of Wang-Merino and quantitative estimates of trace elements distributions in sample from Arc-Bogdo (Mongolia). Geology and Geophysics, N 9, p. 1287-1297  (in Russian)

Bryxina, N. A., Dublyansky, Yu. V., Halden, N.M., Campbell, J.L. Teesdale W.J. (1999) Statistical characteristics of oscillatory zoning in cave calcite - popcorn from Hungary. Dokl. Akad. Nauk., vol. 372, N 4,  514-517 (in Russian)

Bryxina, N.A., Ripinen, O. I., Halden, N.M.,Campbell J.L., Teesdale, W.J., Reverdatto V.V. (1999) Statistical characteristics of oscillatory zoning in agate from Arc-Bogdo, Mongolia. Dokl. Akad. Nauk., vol. 368, ¹ 3, .360-363 (in Russian)

Halden, N.M. (1996) Determination of Lyapounov exponents for trace-element oscillatory zoning patterns in minerals. Canadian Mineralogist. 34, 1127-1135.

Halden, .N.M., Hawthorne, F.C. Campbell, J.L., Teesdale, W.J. and Maxwell, J.A. (1993) Chemical characterization of oscillatory zoning in zircon using 2 - 3 MeV µ-PIXE. Canadian Mineralogist 31, 637 - 648.

Halden, N.M. and Hawthorne, F.C. (1993) Quantitative description of oscillatory zoning in zircon. American Mineralogist. 78, 1113 - 1116.

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