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Morphological instabilities in pattern formation by precipitation and crystallization processes

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Abstract

Morphological instabilities in periodic patterns occurring both in precipitation and crystallization processes (Liesegang rings and crystal zoning) are investigated and compared with similar patterns in geological samples (zebra rocks and mud bands in snow sediments). In classical Liesegang systems, undisturbed parallel or concentric precipitation bands are emanated from even or concentric diffusion sources in homogeneous diffusion matrices of gelatine or other gels. In the case of superposing diffusion sources, sources with undulatory curvatures or local diffusion barriers there may occur several types of instabilities within the sequence of regular patterns: (a) gaps within the bands forming radial alleys free of precipitate, (b) transition from broken bands to speckled patterns and (c) apparent branching of bands linked together by so-called anastomoses. Calculations with a competitive particle growth (CPG) model show that lateral instabilities in Liesegang bands (gaps and radial alleys of gaps) are the result of Ostwald ripening effects taking place after precipitation. Apparent branching of bands or formation of anastomoses can be simulated with a prenucleation model according to Ostwald's supersaturation theory. Similar irregularities can be observed in zebra rocks (e.g. banded siderite) whose bandings are commonly explained by sequential sedimentation processes. A very different mechanism is assumed to be responsible for the origin of mud bands in snow sediments. An initially homogeneous distribution of intrinsic mud in snow sediments can be arranged into parallel bands according to a crystal zoning mechanism which is based on repeated thawing and freezing of the snow sediment due to the daily alternation of sun and darkness.

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References

  • Amstutz GD, Park WC (1967) Stylolytes of diagenetic age and their role in the interpretation of the southern Illinois fluorspar deposits. Min Dep 2:44–53

    Article  Google Scholar 

  • Bhatnagar Sh S, Mathur K (1922) Studien über Bandstrukturen. Die Synthese gebänderter Steine. (Vorbericht). Koll-Z 30:368–371

    Article  Google Scholar 

  • Breitner HJ (1948) Rhythmische Kristallisation beim Gefrieren von Wasser. Koll-Z 111:80–82

    Article  Google Scholar 

  • Dee GT (1986) Patterns produced by precipitation at a moving reaction front. Phys Rev Lett 57:275–278

    Article  Google Scholar 

  • Feeney R, Schmidt SL, Strickholm P, Chadam J, Ortoleva P (1983) Periodic precipitation and coarsening waves: applications of the competitive particle growth model. J Chem Phys 78:1293–1311

    Article  Google Scholar 

  • Fisher GW, Lasaga AC (1993) Irreversible thermodynamics in petrology. In: Lasaga AC, Kirkpatrick RJ (eds) Kinetics of geochemical processes. Reviews in mineralogy, vol. 8. Washington DC, pp 171–209

  • Fontboté L (1993) Self-organization fabrics in carbonate-hosted ore deposits: the example of diagenetic crystallization rhythmites (DCRs). In: Hach-Ali, Torres-Ruiz, Gervilla (eds) Current research in geology applied to ore deposits, pp 11–14

  • Fontboté L, Amstutz GC (1983) Facies and sequence analysis of diagenetic crystallization rhythmites in strata-bound Pb-Zn-(Ba-F) deposits in the Triassic of Central and Southern Europe. In: Schneider HG (ed) Mineral deposits of the Alps and of the alpine epoch in Europe, Springer, Berlin Heidelberg New York, pp 347–358

    Chapter  Google Scholar 

  • Hedges ES (1932) Liesegang rings and other periodic structures. Chapman and Hall, London, 122 pp

    Google Scholar 

  • Jacob KH (1974) Deutung der Genese von Fluoritlagerstätten anhand ihrer Spurenelemente — insbesondere an fraktionierten seltenen Erden. PhD thesis, Technische Universität Berlin, 155 pp

  • Jacob KH, Krug HJ, Dietrich S (1992) Lagerstättenbildung durch Energiepotentiale in der Lithosphäre. Erzmetall 45:505–513

    Google Scholar 

  • Hatschek E (1920) Eine Reihe von abnormen Liesegang'schen Schichtungen. Koll-Z 27:225–229

    Article  Google Scholar 

  • Hatschek E (1920) A Series of Abnormal Liesegang Stratifications. Biochemical J 14:418–421

    Article  Google Scholar 

  • Hatschek E (1921) Anomalous Liesegang Stratifications Produced by the Action of Light. Proc Roy Soc Lond Ser A 99:496–503

    Article  Google Scholar 

  • Henisch HK (1988) Crystals in Gels and Liesegang Rings. Cambridge University Press, Cambridge, 196 pp

    Book  Google Scholar 

  • Henisch HK (1991) Periodic Precipitation. Pergamon Press, Oxford, 117 pp

    Google Scholar 

  • Kai S (1993) Pattern Formation in Precipitation. In: Formation, Dynamics & Statistics of Patterns II. Kawasaki, K. & Suzuki, M. (Eds.), World Scientific Publishers, Singapore, pp 206–265

    Chapter  Google Scholar 

  • Klever N (1984) Stationäre Konvektion in porösen Medien — numerische Untersuchungen an unterschiedlichen Fragestellungen aus der Hydrothermik und der Schneemetamorphose. Berliner Geowiss Abh, Reihe B, Heft 11, 114 pp

  • Knöll (1942) Zur Anwendung der Liesegangschen Achattheorien. Koll-Z 101:296–300

    Article  Google Scholar 

  • Krug HJ, Jacob KH (1993) Genese und Fragmentierung rhythmischer Bänderungen durch Selbstorganisation. Z dt geol Ges 144:451–460

    Google Scholar 

  • Krug HJ, Jacob KH, Dietrich S (1994) The formation and fragmentation of periodic bands through precipitation and Ostwald ripening. In: Kruhl JH (ed) Fractals and dynamic systems in geoscience. Springer-Verlag, Heidelberg, pp 269–282

    Chapter  Google Scholar 

  • Küster E (1916) Über die morphologischen Charaktere der Liesegang'schen Ringe. = Beiträge zur Kenntnis der Liesegang'schen Ringe und verwandter Phänomene IV. Koll-Z 18:107–116

    Article  Google Scholar 

  • Küster E (1931) Über Zonenbildung in kolloidalen Medien. Gustav Fischer Verlag, Jena, 124 pp

    Google Scholar 

  • Kuhnert L, Niedersen U (1987) Selbstorganisation chemischer Strukturen. Ostwalds Klassiker der exakten Wissenschaften, Bd. 272, Geest und Portig, Leipzig, 112 pp

    Google Scholar 

  • Landmesser M (1988) Structural characteristics of agates and their genetic significance. Neues Jahrbuch Min Abh 159:223–235

    Google Scholar 

  • Liesegang RE (1896) A-Linien. Lieseg photogr Arch 21:321–326; reprinted in: Kuhnert and Niedersen (1987)

    Google Scholar 

  • Liesegang RE (1913) Geologische Diffusionen. Verlag Th. Steinkopf, Dresden und Leipzig, 180 pp

    Google Scholar 

  • Liesegang RE (1914) Pseudoklase. Neues Jahrb für Min Geol Pal., 39. Beil.-Bd. (Festschrift für Max Bauer), 268–276

  • Liesegang RE (1915) Die Achate. Verlag Th. Steinkopf, Dresden und Leipzig, 122 pp

    Google Scholar 

  • Liesegang RE (1939) Spiralenbildung bei Niederschlägen in Gallerten. Koll-Z 87:57–58

    Article  Google Scholar 

  • Merino E (1984) Survey of geochemical self-patterning phenomena. In: Nicolis G, Baras F (eds) Chemical instabilities, D. Reidel, Dordrecht, pp 305–328

    Chapter  Google Scholar 

  • Müller SC, Kai S, Ross J (1982) Curiosities in Periodic Precipitation Patterns. Science 216:635–637

    Article  Google Scholar 

  • Nicolis G, Prigogine I (1987) Die Erforschung des Komplexen. Piper, München, 384 pp (Amer. ed. entitled: Exploring complexity, New York 1989)

    Google Scholar 

  • Nitzan A, Ortoleva P, Ross J (1974) Nucleation in systems with multiple stationary states. Farad Symp Chem Soc, No. 9, 241–253

    Article  Google Scholar 

  • Ortoleva P (1994) Geochemical self-organization. (Oxford Monographs on Geology and Geophysics, No. 23), Oxford Univ. Press, Oxford, New York, 244 pp

    Google Scholar 

  • Ortoleva PJ, Merino E, Moore C, Chadam J (1987) Geochemical self-organization 1: Reaction-transport feedbacks and modeling approach. Amer J Sci 287:979–1007

    Article  Google Scholar 

  • Ostwald W (1897) A-Linien von R. E. Liesegang (paper review). Z phys Chem 23:365

    Google Scholar 

  • Ostwald W (1899) Lehrbuch der allgemeinen Chemie, 2. umgearb. Aufl., II, 2.: Verwandtschaftslehre. Engelmann, Leipzig, 1190 pp

    Google Scholar 

  • Ostwald Wo (1925) Zur Theorie der Liesegang'schen Ringe. Koll-Z Erg.-Bd. (Festband für R. Zsigmondy) 36:380–390

    Google Scholar 

  • Rothmund V (1907) Löslichkeit und Loslichkeitsbeeinflussung. Leipzig 1907, 196 pp

  • Schildknecht H (1964) Zonenschmelzen. Verlag Chemie, Weinheim

    Google Scholar 

  • Schutz GG (1971) Die schichtgebundene Zinkblendelagerstätte San Vicente in Ostperu und ihr geologischer Rahmen. PhD Thesis, RWTH Aachen, 165 pp

  • Stern KH (1954) The Liesegang phenomenon. Chem Revs 54:79–99

    Article  Google Scholar 

  • Tillmans J, Heublein O (1915) Neues von den Liesegangschen Ringen. Umschau 19:930–933

    Google Scholar 

  • Trainer DW (1931) “Zebra” Rock. Amer Mineral 16:221–225

    Google Scholar 

  • Watanabe M (1924) Zonal Precipitation of Ores from a Mixed Solution. Econ Geol 19:497–503

    Article  Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik, AG Dissipative Strukturen, Technische Universität Berlin, Geb. 2.14, Rudower Chaussee 5, D-12489, Berlin, Germany

    H. -J. Krug & H. Brandstädter

  2. Institut für Angewandte Geophysik, Petrologie und Lagerstättenforschung, Technische Universität Berlin, Ernst-Reuter-Platz 1, Sekr. BH 4, D-10587, Berlin, Germany

    K. H. Jacob

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  1. H. -J. Krug
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  2. H. Brandstädter
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  3. K. H. Jacob
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Krug, H.J., Brandstädter, H. & Jacob, K.H. Morphological instabilities in pattern formation by precipitation and crystallization processes. Geol Rundsch 85, 19–28 (1996). https://doi.org/10.1007/BF00192056

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