The fractal geometry of oscillatory zoning in crystals: Application to zircon
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ABSTRACT: Finite difference numerical simulations were used to characterise the rates of diffusion-controlled dissolution and growth of zircon in melts of granitic composition under geologically realistic conditions. The simulations incorporated known solubility and Zr diffusivity relationships for melts containing 3 wt% dissolved H 2 O and were carried out in both one and thre dimensions under conditions of constant temperature, linearly time-dependent temperature and for a variety of host system thermal histories. The rate of zircon dissolution at constant temperature depends systematically on time (t½−12;), temperature (exp T −1 ) and degree of undersaturation of the melt with respect to zircon (in ppm Zr). Linear dissolution and growth rates fall in the range 10 −19 10 −15 cm s −1 at temperatures of 650-850°C. Radial rates are strongly dependent on crystal size (varying in inverse proportion to the radius, r ): for r>30 μm, dissolution and growth rates fall between 10 −17 and 10 −13 cm s −1 . During crustal magmatism, the chances of survival for relict cores of protolith zircons depend on several factors, the most important of which are: the initial radius of the zircon; the intensity and duration of the magmatic event; and the volume of the local melt reservoir with which the zircon interacts. In general, only the largest protolith zircons (>120 μm radius) are likely to survive magmatic events exceeding 850°C. Conversely, only the smallest zircons (<50 μm radius) are likely to be completely consumed during low-temperature anatexis (i.e. not exceeding ≍700°C). The effects of stirring the zircon-melt system are unimportant to dissolution and growth behaviour; except under circumstances of extreme shearing (e.g. filter pressing?), zircon dissolution is controlled by diffusion of Zr in the melt.
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Other| June 01, 1997 Statistical characteristics and origin of oscillatory zoning in crystals Terje Holten; Terje Holten University of Oslo, Department of Geology, Oslo, Norway Search for other works by this author on: GSW Google Scholar Bjorn Jamtveit; Bjorn Jamtveit Search for other works by this author on: GSW Google Scholar Paul Meakin; Paul Meakin Search for other works by this author on: GSW Google Scholar Massimo Cortini; Massimo Cortini Search for other works by this author on: GSW Google Scholar Jon Blundy; Jon Blundy Search for other works by this author on: GSW Google Scholar Hakon Austrheim Hakon Austrheim Search for other works by this author on: GSW Google Scholar American Mineralogist (1997) 82 (5-6): 596–606. https://doi.org/10.2138/am-1997-5-619 Article history first online: 02 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Tools Icon Tools Get Permissions Search Site Citation Terje Holten, Bjorn Jamtveit, Paul Meakin, Massimo Cortini, Jon Blundy, Hakon Austrheim; Statistical characteristics and origin of oscillatory zoning in crystals. American Mineralogist 1997;; 82 (5-6): 596–606. doi: https://doi.org/10.2138/am-1997-5-619 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu nav search search input Search input auto suggest search filter All ContentBy SocietyAmerican Mineralogist Search Advanced Search Abstract Complex intracrystalline zoning patterns in hydrothermal garnet and vesuvianite and magmatic plagioclase were analyzed by statistical methods to test for fractal behavior. The zoning data were collected by electron and proton microprobe, and backscattered electron images and polarized micrographs were digitized. The analysis shows that self-affine fractal geometry can be used to characterize the zoning patterns of vesuvianite and some garnet patterns. The range of power-law scaling extended up to two decades. The results from the plagioclase samples were not sufficient to determine whether or not the zoning patterns were self-affine. The measured Hurst exponents are mostly in the range 0.25–0.45, indicating fractal scaling and anti-persistent behavior. This means that an increasing compositional trend in the past favors a decreasing trend in the future and vice versa. No distinct periodic components of the zoning patterns were found.The influence of environmental changes (external fluctuations) on a simple crystal growth model was investigated by numerical simulations. The concentration at the boundary of a diffusion layer was allowed to vary as a Brownian-motion curve, and the effect of the external fluctuation on diffusion and local growth kinetics was investigated. We conclude that factors operating on scales much larger than the local interface processes are most important in controlling the zonation. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.
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Crystals characterized by oscillatory zoning show evidence for a quasi-cyclic alternation in the chemical composition of discrete growth-shells from tens of nanometers to tens of micrometers in thickness. Oscillatory zoning is most commonly observed and studied in crystals of magmatic plagioclase, but sensitive imaging techniques (e.g., Nomarski interference contrast microscopy, cathodoluminescence, back-scattered electron imaging, X-ray topographs) reveal its presence in many other minerals. Through the application of these techniques and an exhaustive review of the literature, oscillatory zoning is shown to occur in at least 75 rock-forming and accessory minerals comprising most major mineral classes: silicates (hydrous and anhydrous), sulfides, oxides, halides, carbonates, phosphates, and sulfates. Such mineral zoning is a common but often well-concealed phenomenon in magmatic rocks (particularly alkaline ones), hydrothermally altered rocks, mineralized rocks, and carbonate sequences. Mechanisms of oscillatory zoning are discussed, including the less-studied effects of adsorption and elastic stress in near-surface growth-layers. Its non-equilibrium chemistry makes oscillatory zoning a rich subject for further research.
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