Abstract
It has been observed for a long time that not all individual minerals have a uniform chemical composition. Many of them exhibit complex growth patterns, such as oscillatory zoning (in which the chemical composition fluctuates along a traverse within the crystal) or branching patterns (characterized by a tree-like crystal form) that arise spontaneously as a result of growth kinetics. Liesegang was among the first to investigate the kinetics of a class of growth patterns: periodic precipitation. Until fairly recently (Lasaga and Kirkpatrick, 1981), the importance of kinetics in geochemistry was largely overlooked.
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References
Allègre, C.J., Provost, A. and Jaupart, C., 1981, Oscillatory zoning: A pathological case of crystal growth, Nature 294, 223–228.
Anderson, G.M., 1975, Precipitation of Mississippi Valley-type ores, Economic Geology 70, 937–942.
Anderson, G.M., 1991, Organic maturation and ore precipitation in southeast Missouri, Economic Geology 86, 909–926.
Arndt, N.T., Naldrett, A.J. and Pyke, D.R., 1977, Komatiitic and iron-rich tholeiitic lavas of Munro Township, northeastern Ontario, Journal ofPetrology 18, 319–369.
Barnes, H.L., 1979, Solubilities of ore minerals, in H.L. Barnes (ed.), Geochemistry of Hydrothermal Ore Deposits, 2nd ed., John Wiley & Sons, New York, pp. 404–460.
Barnola, J.M., Raynaud, D., Korotkevich, Y.S. and Lorius, C., 1987, Vostok ice core provides 160, 000 year record of atmospheric CO2, Nature 329, 408–414.
Boudreau, A.E., 1995, Crystal aging and the formation of fine-scale igneous layering, Mineralogy and Petrology 54, 55–69.
Brady, R.M. and Ball, R.C., 1984, Fractal growth of copper electrodeposits, Nature 309, 523–530.
Brandeis, G., Jaupart, C. and Allègre, C.J., 1984, Nucleation, crystal growth and the thermal regime of cooling magmas, Journal of Geophysical Research 89, 10161–10177.
Büki, A., Kárpáti-Smidróczki, E. and Zrinyi, M., 1995, Computer simulation of regular Liesegang structures, Journal of Chemical Physics 103, 10387–10392.
Carlsaw, H.S. and Jaeger, J.C., 1959, Conduction of Heat in Solids, 2nd ed., Oxford University Press, New York, 510 pp.
Cathles, L.M. and Smith, A.T., 1983, Thermal constraints on the formation of Mississippi Valley-type leadzinc deposits and their implications for basin dewatering and deposit genesis, Economic Geology 78, 983–1002.
Chernavskii, D.S., Polezhaev, A.A. and Müller, S.C., 1991, A model of pattern formation by precipitation, Physica D 54, 160–170.
Daccord, G. and Lenormand, R., 1987, Fractal patterns from chemical dissolution, Nature 325, 41–43.
Dee, G.T., 1986, Patterns produced by precipitation at a moving reaction front, Physical Review Letters 57, 275–278.
Farmer, J.D. and Sidorowich, J.J., 1987, Predicting chaotic time series, Physical Review Letters 59, 845–848.
Feeney, R., Schmidt, S.L., Strickholm, P., Chadam, J. and Ortoleva, P., 1983, Periodic precipitation and coarsening waves: Applications of the competitive particle growth model, Journal of Chemical Physics 78, 1293–1311.
Fowler, A.D. and Anderson, M.T., 1991, Geopressure zones as proximal sources of hydrothermal fluids in sedimentary basins and the origin of Mississippi Valley-type deposits in shale-rich sequences, Transactions of the Institution ofMining and Metallurgy 100, B 14–B 17.
Fowler, A.D. and L’Heureux, I., 1996, Self-organized banded sphalerite and branching galena in the Pine Point ore deposit, Northwest Territories, The Canadian Mineralogist 34, 1211–1222.
Fowler, A.D. and Roach, D.E., 1993, Dimensionality analysis of time series data: Nonlinear methods, Computers and Geosciences 19, 41–52.
Fowler, A.D. and Roach, D.E., 1996, A model and simulation of branching mineral growth from cooling contacts and glasses, Mineralogical Magazine 60, 595–601.
Fowler, A.D., Stanley, H.E. and Daccord, G., 1989, Disequilibrium silicate mineral textures: Fractal and non-fractal features, Nature 341, 134–138.
Garven, G., 1985, The role of regional fluid flow in the genesis of the Pine Point deposit, Western Canada Sedimentary Basin, Economic Geology 80, 307–324.
Haase, C.S., Chadam, J., Feinn, D. and Ortoleva, P., 1980, Oscillatory zoning in plagioclase feldspar, Science 209, 272–274.
Halden, N.M. and Hawthorne, F.C., 1993, The fractal geometry of oscillatory zoning in crystals: Application to zircon, American Mineralogist 78, 1113–1116.
Henisch, H.K., 1991, Periodic Precipitation, Pergamon Press, New York, 122 pp.
Higman, S.L. and Pearce, T.H., 1993, Spatiotemporal dynamics in oscillatory zoned magmatic plagioclase, Geophysical Research Letters 29, 1935–1938.
Hilborn, R.C., 1994, Chaos and Nonlinear Dynamics, Oxford University Press, New York, 654 pp.
Hinzer, K., 1996, Characterization of oscillatory zoning in sphalerite, B.Sc. Thesis, University of Ottawa, Ottawa.
Holten, T., Jamtveit, B., Meakin, P., Cortini, M., Blundy, J. and Austrheim, H., 1997a, Statistical characteristics and origin of oscillatory zoning in crystals, American Mineralogist 82, 596–606.
Holten, T., Jamtveit, B. and Meakin, P., 1997b, Self-affine geometry of agate, European.Journal ofMineralogy, to be published.
Horsthemke, W. and Lefever, R., 1984, Noise-Induced Transitions, Springer-Verlag, Berlin, 318 pp.
Jackson, S.A. and Beales, F.W., 1967, An aspect of sedimentary basin evolution: The concentration of Mississippi Valley-type ores during the late stages of diagenesis, Bulletins of Canadian Petrology and Geology 15, 393–433.
Jamtveit, B., 1991, Oscillatory zonation patterns in hydrothermal grossular-andradite garnet: Nonlinear dynamics in regions of immiscibility, American Mineralogist 76, 1319–1327.
Jones, B. and Renaut, W.R., 1995, Noncrystallographic calcite dendrites from hot-spring deposits at lake Bogoria, Kenya, Journal of Sedimentary Research A65, 154–169.
Keith, H.D. and Padden, F.J., Jr., 1963, A phenomenological theory of spherulitic crystallization, Journal of Applied Physics 34, 2409–2421.
Kirkpatrick, R.J., Klein, L., Uhlmann, D.R. and Hays, J.F.G., 1979, Rates and processes of crystal growth in the system anorthite-albite, Journal of Geophysical Research 84, 3671–3676.
Koenig, F.O., 1950, On the thermodynamic relation between surface tension and curvature, Journal ofChemical Physics 18, 449–459.
Lasaga, A.C., 1982, Toward a master equation in crystal growth, American Journal ofScience 282, 1264–1288.
Lasaga, A.C. and Kirkpatrick, R.J. (eds.), 1981, Kinetics of Geochemical Processes, Mineralogical Society of America, Washington, DC, 398 pp.
L’Heureux, I., 1993, Oscillatory zoning in crystal growth: A constitutional undercooling mechanism, Physical Review E 48, 4460–4469.
L’Heureux, I., 1997, Oscillatory zoning in plagioclase: Thermal effects, Physica A 239, 137–146.
L’Heureux, I. and Fowler, A.D., 1996a, Dynamical model of oscillatory zoning in plagioclase with nonlinear partition relation, Geophysical Research Letters 23, 17–20.
L’Heureux, I. and Fowler, A.D., 1996b, Isothermal constitutive undercooling as a model for oscillatory zoning in plagioclase, The Canadian Mineralogist 34, 1137–1147.
Lofgren, G.E. and Russell, W.J., 1986, Dynamic crystallization of chondrules melts of porphyritic and radial • pyroxene, Geochimica et Cosmochimica Acta 50, 1715–1726.
Lofgren, G.E., 1974, An experimental study of plagioclase crystal morphology: Isothermal crystallization, American Journal of Science 274, 243–273.
Lovett, R., Ortoleva, P. and Ross, J., 1978, Kinetic instabilities in first order phase transitions, Journal of Chemical Physics 69, 947–955.
Markov, I.V., 1996, Crystal Growth for Beginners, World Scientific Publishers, Singapore, 422 pp.
McLimans, R.K., Barnes, H.L. and Ohmoto, H., 1980, Sphalerite stratigraphy of the upper Mississippi Valley lead-zinc district, southeast Wisconsin, Economic Geology 75, 351–361.
Merino, E., Wang, Y. and Deloule, E., 1995, Genesis of agates in flood basalts: Twisting of chalcedony fibers and trace-element geochemistry, American Journal of Science 295, 1156–1176.
Nakai, S., Halliday, A.N., Kesler, S.E., Jones, H.D., Kyle, R.J. and Lane, T.S., 1993, Rb-Sr dating of sphalerites from Mississippi Valley-type (MVT) ore deposits, Geochimica et Cosmochimica Acta 57, 417–427.
Niemeyer, L., Pietronero, L. and Wiesmann, H.J., 1984, Fractal dimension of dielectric breakdown, Physical Review Letters 52, 103 3–103 6.
Nittmann, J. and Stanley, H.E., 1986, Tip splitting without interfacial tension and dendritic growth patterns arising from molecular anisotropy, Nature 321, 663–668.
Ortoleva, P., 1990, Role of attachment kinetic feedback in the oscillatory zoning of crystals grown from melts, Earth Sciences Review 29, 3–8.
Ortoleva, P., 1994, Geochemical Self-Organization, Oxford University Press, New York, 411 pp.
Ortoleva, P., Chen, Y. and Chen, W., 1994, Agates, geodes, concretions and orbicules: Self-organized zoning and morphology, in J.H. Kruhl (ed.), Fractals and Dynamic Systems in Geoscience, Springer-Verlag, Berlin, pp. 283–305.
Ostwald, W., 1897, Lehrbuch der allgemeine Chemie, Engelman, Leipzig, 778 pp.
Pearce, T.H., 1994, Recent work on oscillatory zoning in plagioclase, in I. Parsons (ed.), Feldpars and Their Reactions, NATO ASI Series, Kluwer Academic Publishers, Dordrecht, pp. 313–346.
Pearce, T.H. and Kolisnik, A.M., 1990, Observations of plagioclase zoning using interference imaging, Earth Sciences Review 29, 9–26.
Peitgen, H.O., Jürgens, H. and Saupe, D., 1992, Chaos and Fractals: New Frontiers of Science, Springer-Verlag, New York, 984 pp.
Plumlee, G.S., Leach, D.L., Hofstra, A.H., Landis, G.P., Rowan, E.L. and Viets, J.G., 1994, Chemical reaction path modeling of ore deposition in Mississippi Valley-type Pb-Zn deposits of the Ozark region, U.S. mid-continent, Economic Geology 63, 451–471.
Prager, S., 1956, Periodic precipitation, Journal of Chemical Physics 25, 279–283.
Rasband, S.N., 1990, Chaotic Dynamics of Nonlinear Systems, John Wiley & Sons, New York, 230 pp.
Roedder, E., 1968, The noncolloidal origin of “colloform” textures in sphalerite ore, Economic Geology 63, 451–471.
Rutley, F., 1985, Notes on some peculiarities in the microscopic structure of feldspars, Quarterly Journal of the Geological Society ofLondon 31, 479–488.
Saunders, J.A. and Schoenly, P.A., 1995, Fractal structure of electrum dendrites in bonanza epithermal Au-Ag deposits, in C.C. Barton and P.R. La Pointe (eds.), Fractals in the Earth Sciences, Plenum Press, New York, pp. 251–261.
Shinohara, S., 1970, A theory of one-dimensional Liesegang phenomena, Journal of the Physical Society of Japan 29, 1073–1087.
Shore, M. and Fowler, A.D., 1996, Oscillatory zoning in minerals: A common phenomenon, The Canadian Mineralogist 34, 1111–1126.
Smith, D.A., 1984, On Ostwald’s supersaturation theory of rhythmic precipitation (Liesegang’s rings), Journal of Chemical Physics 81, 3102–3115.
Stauffer, D., 1976, Kinetic theory of two-component (“heteromolecular”) nucleation and condensation, Journal ofAerosol Sciences 7, 319–333.
Stern, K.H., 1954, The Liesegang phenomenon, Chemical Review 54, 79–99.
Sugihara, G. and May, R.M., 1990, Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series, Nature 344, 734–741.
Sverjensky, D.A., 1981, The origin of Mississippi Valley-type in the Viburnum trend, southeast Missouri, Economic Geology 76, 1848–1872.
Wang, J.-H. and Wu, J.-P., 1995, Oscillatory zonation of minerals and self-organization in silicate solid-solution systems: A new nonlinear dynamic model, European Journal ofMineralogy 7, 1089–1100.
Wang, Y. and Merino, E., 1990, Self-organizational origin of agates: Banding, fiber twisting, composition, and dynamic crystallization model, Geochimica et Cosmochimica Acta 54, 1627–1638.
Wang, Y. and Merino, E., 1992, Dynamic model of oscillatory zoning of trace elements in calcite: Double layer, inhibition, and self-organization, Geochimica et Cosmochimica Acta 56, 587–596.
Wang, Y. and Merino, E., 1993, Oscillatory magma crystallization by feedback between the concentrations of the reactant species and mineral growth rates, Journal ofPetrology 34, 369–382.
Wang, Y. and Merino, E., 1995, Origin of fibrosity and banding in agates from flood basalts, American Journal of Science 295, 49–77.
Witten, T.A. and Sander, L.M., 1983, Diffusion-limited aggregation, Physical Review B 27, 5686–5697.
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L’heureux, I., Fowler, A.D. (1999). Branching and Oscillatory Patterns in Plagioclase and Mississippi-Valley Type Sphalerite Deposits. In: Jamtveit, B., Meakin, P. (eds) Growth, Dissolution and Pattern Formation in Geosystems. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9179-9_4
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DOI: https://doi.org/10.1007/978-94-015-9179-9_4
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