Hostname: page-component-848d4c4894-89wxm Total loading time: 0 Render date: 2024-07-08T04:51:32.806Z Has data issue: false hasContentIssue false
  • English
  • Français

A Model and Simulation of Branching Mineral Growth from Cooling Contacts and Glasses

Published online by Cambridge University Press:  05 July 2018

Anthony D. Fowler  and
Daniel E. Roach
Anthony D. Fowler
Affiliation:
Ottawa Carleton Geoscience Centre, and Department of Geology, University of Ottawa, 770 King Edward Ave. Ottawa, ON, K1N 6N5, Canada
Daniel E. Roach
Affiliation:
Ottawa Carleton Geoscience Centre, and Department of Geology, University of Ottawa, 770 King Edward Ave. Ottawa, ON, K1N 6N5, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

Silicate minerals grown from glasses, and rapidly cooled melts, often have non-compact branching or ‘spherulitic’ morphology. The branching patterns are observed in volcanic rocks, glasses, meteorites, slags and sometimes in shallow level intrusive rocks. Experiments, observations, theory and simulations all support the concept that the crystal morphology is the result of growth under diffusion limited conditions. We show that in a silicate melt under appropriate conditions the equations for heat transfer and chemical-diffusion reduce to the Laplace equation. This means that the temperature or chemical gradient is a steady state field. Interaction between this field and a random variable (Brownian motion of growth species) is modelled and yields complex branching objects. The growing cluster affects the field such that an in-filled structure cannot be formed. The branching structures of the model crystal are remarkably similar to those formed in nature, and to those produced in laboratory experiments, implying that the model captures the essence of the branching-growth process.

Keywords

branching mineral growthglasscoolingdiffusion-limited aggregation
Type
Experimental Mineralogy
Information
Mineralogical Magazine , Volume 60 , Issue 401 , August 1996 , pp. 595 - 601
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ben-Jacob, E. and Garik, P. (1990) The formation of patterns in non-equilibrium growth. Mzmre, 343, 523-30.Google Scholar
Brady, R.M. and Ball, R.C. (1984) Fractal growth of copper electrodeposits. Nature., 309, 225 —9.CrossRefGoogle Scholar
Bryan, W.B. (1972) Morphology of quench crystals in submarine basalts. J. Geophys. Res., 77, 5812–9.CrossRefGoogle Scholar
Carlsaw, H.S. and Jaeger, J.C. (1959) Conduction of Heat in Solids. second edition. Oxford University Press, New York. 510 pp.Google Scholar
Daccord, G. and Lenormand, R. (1987) Fractal patterns from chemical dissolution. Nature, 325, 41–43.CrossRefGoogle Scholar
Donaldson, C.H. (1974) Olivine crystal types in Harrisitic Rocks of the Rhum Pluton and in Archean Spinifex Rocks. Geol. Soc. Amer. Bull., 85, 1721–6.2.0.CO;2>CrossRefGoogle Scholar
Fowler, A.D., Jensen, L.S. and Péloquin, A.S. (1987) Varioles in Archean basalts: Products of spherulitic crystallization. Can. Mineral., 25, 275–89.Google Scholar
Fowler, A.D., Stanley, H.E. and Daccord, G. (1989): Disequilibrium silicate mineral textures: fractal and non-fractal features. Nature, 341, 134–8.CrossRefGoogle Scholar
Gould, H. and Tobochnik, J. (1987) An Introduction to Computer Simulation Methods, Applications to Physical Systems Part 2. Addison-Wesley, New York, 695 pp.Google Scholar
Jackson, K.A. (1958) Mechanisms of Growth, in Liquids, Metals and Solidification. American Society of Metals, Cleveland, Ohio. 180 pp.Google Scholar
Keith, H.D. and Padden, F.J. Jr. (1963) A phenomenological theory of spherulite crystallization. J. Appl. Phys., 34, 2409–21.CrossRefGoogle Scholar
Kirkpatrick, R.J., Klein, L., Uhlmann, D.R. and Hays, J.F. (1979) Rates and processes of crystal growth in the system anorthite-albite. J. Geophys. Res., 84, 3671–6.CrossRefGoogle Scholar
Kouchi, A., Tsuchiyama, A. and Sunagawa, I. (1986) Effect of stirring on crystallization kinetics of basalt: texture and element partitioning. Contrib. Mineral Petrol,, 93, 429–38.CrossRefGoogle Scholar
Lofgren, G. (1974) An experimental study of plagioclase morphology: isothermal crystallization. Amer. J. 274, 243—73.Google Scholar
Niemeyer, L., Pietronero, L. and Wiesmann, H.J. (1984) Fractal dimension of dielectric breakdown. Phys. Rev. Lett., 52, 1033–6.CrossRefGoogle Scholar
Nittmann, J. and Stanley, H.E. (1986) Tip splitting without interfacial tension and dendritic growth patterns arising from molecular anisotropy. Nature, 321, 663–8.CrossRefGoogle Scholar
Shore, M. (1996) Cooling and Crystallization of Komatiites. Unpublished Ph.D. thesis, University of Ottawa.Google Scholar
Tiller, W.A. (1991) The Science of Crystallization: Macroscopic Phenomena and Defect Generation. Cambridge University Press.CrossRefGoogle Scholar
Tsonis, A.A. (1991) A fractal study of dielectric breakdown in the atmosphere. In Non-linear Variability in Geophysics Scaling and Fractals(Schertzer, D. and Lovejoy, S., eds.) Kluwer Academic Publishers, Dordrecht. 318 pp.Google Scholar