Abstract
Based on a continuum model of nucleation and growth in two and three dimensions we present results for grain size and cluster size distributions for different nucleation and growth mechanisms. The percolative properties of these systems are determined with respect to percolation threshold and appropriate exponents for volume, surface, and hull of the clusters. The universal behaviour of these systems is confirmed. The present results are applicable for the description of crystallization processes in igneous rocks as well as for understanding the structure of pore spaces in sedimentary rocks.
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References
Adler J, Meir Y, Aharony A, Harris AB (1990) Series study of percolation moments in general dimension. Phys Rev B 41: 9183–9206.
Axe JD, Yamada Y (1986) Scaling relations for grain autocorrelation functions during nucleation and growth. Phys Rev B 34: 1599–1606.
Balberg I, Binenbaum N (1985) Cluster structure and conductivity of three-dimensional continuum systems. Phys Rev A 31: 1222–1225.
Bradley RM, Strenski PN, Debierre J-M (1991) Surfaces of percolation clusters in three dimensions. Phys Rev B 44: 76–84.
Christian JW (1965) The Theory of Transformations in Metals and Alloys. Pergamon Press, Oxford.
Gawlinski ET, Stanley HE (1981) Continuum percolation in two dimensions: Monte Carlo tests of scaling and universality for non-interacting discs. J Phys A: Math Gen 14: L291–299.
Harris AB (1974) Effect of random defects on the critical behaviour of Ising models. J Phys C: Solid State Phys 7: 1671–1692.
Hoshen J, Kopelman R (1976) Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm. Phys Rev B 14: 3438–3445.
Kertész J, Vicsek T (1982) Monte Carlo renormalization group study of the percolation problem of discs with a distribution of radii. Z Phys B: Condensed Matter 45: 345–350.
Lee SB (1990) Universality of continuum percolation. Phys Rev B 42: 4877–4880.
Lorenz B (1987) Grain size distribution in the Kolmogorov model for nucleation and growth: heterogeneous versus homogeneous nucleation. Cryst Res Tech 22: 869–875.
Lorenz B (1989a) Simulation of grain-size distributions in nucleation and growth processes. Acta metall 37: 2689–2692.
Lorenz B (1989b) On the scaling behaviour of correlation functions for nucleation and growth reactions. J Crystal Growth 94: 569–571.
Lorenz B (1990) Influence of nucleation mechanism on the evolution of microstructures during nucleation and growth. Mat Sci Forum 62–64: 737–738.
Lorenz B, Orgzall I (1991) Kinetics of high pressure phase transitions in the diamond anvil cell. In: Hochheimer HD, Etters RD (eds) Frontiers of High Pressure Research. Plenum Press, New York, pp 243–251.
Lorenz B, Orgzall I, Däßler R (1991) Theoretical and experimental investigation of the precipitation kinetics of B2-phase KCl from the solution under high pressure. High Press Res 6: 309–324.
Lorenz B, Orgzall I, Heuer H-O (1993) Universality and cluster structures in continuum models of percolation with two different radius distributions. J Phys A: Math Gen 26: 4711–4722.
Margolina A, Rosso M (1992) Illumination: a new method for studying 3D percolation fronts in a concentration gradient. J Phys A: Math Gen 25 3901–3912.
Orgzall I, Lorenz B (1988) Computer simulation of cluster-size distributions in nucleation and growth processes. Acta metall 36: 627–631.
Orgzall I, Lorenz B (1992) The clustersize distribution in nucleation and growth processes: Diffusion controlled vs. interface limited growth. Scripta Metall et Mater 26: 889–894.
Phani MK, Dhar D (1984) Continuum percolation with discs having a distribution of radii. J Phys A: Math Gen 17: L645–649.
Rosso M (1989) Concentration gradient approach to continuum percolation in two dimensions. J Phys A: Math Gen 22: L131–136.
Sapoval B, Rosso M, Gouyet JF (1985) The fractal nature of a diffusion front and the relation to percolation. J Physique Lett 46: L149–156.
Spohn T, Hort M, Fischer H (1988) Numerical simulation of the crystallization of multicomponent melts in thin dikes or sills. 1. The liquidus phase. J Geophys Res B 93: 4880–4894.
Stauffer D (1985) Introduction to Percolation Theory. Taylor and Francis, London.
Thompson AH, Katz AJ, Krohn CE (1987) The microgeometry and transport properties of sedimentary rock. Adv Phys 36: 625–694.
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© 1994 Springer-Verlag Berlin Heidelberg
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Orgzall, I., Lorenz, B. (1994). Structure and Fractal Properties in Geological Crystallization Processes Due to Nucleation and Growth. In: Kruhl, J.H. (eds) Fractals and Dynamic Systems in Geoscience. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07304-9_24
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DOI: https://doi.org/10.1007/978-3-662-07304-9_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-07306-3
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