Abstract
Along grain boundaries of quartz from metamorphic and igneous rocks complex interfingering (sutures) may occur. Under the light microscope the lengths of the sutures range from approximately 10–1000 μm. The sutured grain boundaries are statistically self-similar over one to two orders of magnitude. They represent fractals. Their mathematical counterpart are Koch curves which are developed after two to four iterations. The fractal (Hausdorff-Besicovitch) dimensions D of sutured quartz grain boundaries from different grades of metamorphism are between ca. 1.05 and 1.30. The D-value decreases with increasing temperature during formation of the sutures. On a statistical basis, D can be used as a measure of this temperature and, therefore, as a deformation-related thermometer.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Altenberger U, Hamm N, Kruhl JH (1987) Movements and metamorphism north of the Insubric Line between Val Loana and Val d'Ossola, N. Italy. Jahrb Geol B.-A. Wien 130:365–374
Blumör T, Dollinger J, Knobel M, Mutter A, Zarda S, Kowalczyk G (1995) Plattenkalk series and Kastania phyllites of the Taygetos Mt.: new results on structure and succession. Bull Geol Soc Greece (in press)
Büttner S, Kruhl JH (1996) The evolution of a late-Variscan high-T-low-P region: the southeastern margin of the Bohemian Massif. Geol Rundsch (submitted)
Daccord G, Nittman J, Stanley HE (1986) Fractal viscous fingers — experimental results. In: Stanley HE, Ostrowsky N (eds) On growth and form. Martinus Nijhoff, Boston
Gillespie PA, Howard CB, Walsh JJ, Watterson J (1993) Measurement and characterisation of spatial distributions of fractures. Tectonophysics 226:113–141
Kaye BH (1989) A random walk through fractal dimensions. VCH, Weinheim
Kruhl JH, Huntemann T (1991) The structural state of the former lower continental crust in Calabria (S. Italy). Geol Rundsch 80:289–302
Kruhl JH, Nega M, Milla HE (1995) The fractal shape of grain boundary sutures: reality, model and application as a geothermometer. 2nd Int Conf on Fractals and Dynamic Systems in Geoscience, Frankfurt, Book of Abstracts: 31–32
Mandelbrot BB (1967) How long is the coast of Britain? Statistical self-similarity and fractal dimension. Science 155:636–638
Mandelbrot BB (1983) The fractal geometry of nature, 2nd edn. Freeman, New York
Poirier JP (1985) Creep of crystals. Cambridge University Press, London
Stanley HE, Ostrowsky N (eds) (1988) Random fluctuations and pattern growth: experiments and models. NATO ASI Series E, 157, Kluwer, London
Voll G (1969) Klastische Mineralien aus den Sedimentserien der Schottischen Highlands und ihr Schicksal bei aufsteigender Regional- und Kontaktmetamorphose. Habilitationsschrift, Fak. f.Bergb.u.Hüttenw., TU Berlin, D83:360 pp
Voss RF (1988) Fractals in nature: from characterization to simulation. In: Peitgen H-O, Saupe E (eds) The science of fractal images. Springer, Berlin Heidelberg New York, pp 21–70
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kruhl, J.H., Nega, M. The fractal shape of sutured quartz grain boundaries: application as a geothermometer. Geol Rundsch 85, 38–43 (1996). https://doi.org/10.1007/BF00192058
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00192058