Advertisement

Characteristic Dimensions and Times for Dynamic Crystallization

  • Geneviève Brandeis
  • Claude Jaupart
Part of the NATO ASI Series book series (ASIC, volume 196)

Abstract

This study focusses on the role of the crystallization kinetics. We describe the evolution of crystallization in natural conditions and make a dimensional analysis of the problem. Given characteristic values for the rates of nucleation and crystal growth, I and Y, the crystallization time-scale τ is (I.Y3)−1/4. The thickness of the crystallization interval, i.e. the moving region where magma is partially crystallized, is equal to {κ.τ} 1/2. This gives the thickness of the crystal mush which lies at the chamber bottom. The crystal size is equal to {Y/I} 1/4 and is sensitive to the temperature regime. These scaling laws show that the crystallization parameters are weakly sensitive to the values of the kinetic rates. Disturbing the normal crystallization regime acts to perturb the crystal size over a distance equal to a few times the thickness of the crystallization interval. These theoretical predictions can be checked against petrological observations. Crystal size data from dike margins are used to constrain the peak rates of nucleation and growth to be about 1 cm−3 .sec−1 and 10−7 cm.sec−1 respectively. For conditions prevailing in the deep interior of magma chambers, the rates of nucleation and growth are much smaller than these values. A constraint is provided by the mean crystal size which is always close to 1 mm. We suggest values of 10−5 cm−3 .sec−1 and 10−9 cm.sec−1 for the rates of nucleation and growth respectively. For these, the crystal mush has a thickness of a few metres. Also, the crystallization time-scale is about 108s. This is similar to values for the cooling time of a kilometre-sized chamber, which shows that crystallizing magma has time to record the effects of convective processes which operate in the chamber interior. This explains why the igneous structures of large intrusions are more complex than those of sills and dikes.

Keywords

Crystal Size Magma Chamber Country Rock Crystallization Kinetic Contrib Mineral Petrol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Avrami M (1939) Kinetics of phase change. I. General theory. J Chem Phys 7: 1103–1112.CrossRefGoogle Scholar
  2. Avrami M (1940) Kinetics of phase change. II. Transformation-Time relation for random distribution of nuclei. J Chem Phys 8: 212–224.CrossRefGoogle Scholar
  3. Avrami M (1941) Kinetics of phase change. III. Granulation, phase change and microstructure. J Chem Phys 9: 177–184.CrossRefGoogle Scholar
  4. Baker MB and Grove TL (1985) Kinetic controls on pyroxene nucleation and metastable liquid lines of descent in basaltic andesite. Am Mineral 70: 279–287Google Scholar
  5. Baronnet A (1984) Growth kinetics of the silicates. A review of basic concepts. Fortschr Mineral 62: 187–232Google Scholar
  6. Brandeis G, Jaupart C, Allegre CJ (1984) Nucleation, Crystal growth and the thermal regime of cooling magmas. J Geophys Res 89: 10161–10177CrossRefGoogle Scholar
  7. Brandeis G, Jaupart C (1986a) The kinetics of nucleation and crystal growth and scaling laws for magmatic crystallization. Contrib Mineral Petrol, sub.Google Scholar
  8. Brandeis G, Jaupart C (1986b) Crystal sizes in intrusions of different dimensions: constraints on the cooling regime and the crystallization kinetics. Geochim Cosmochim Acta: in pressGoogle Scholar
  9. Bryan WB (1972) Morphology of quench crystals in submarine basalts. J Geophys Res 77: 5812–5819.CrossRefGoogle Scholar
  10. Cahn JW (1967) On the morphological stability of growing crystals. In Preiser HS (ed) Crystal Growth. Pergamon Press.Google Scholar
  11. Campbell IH (1978) Some problems with the cumulus theory. Lithos 11: 311–323CrossRefGoogle Scholar
  12. Chen CF, Turner JS (1980) Crystallization in a double-diffusive system. J Geophys Res 85: 2573–2593.CrossRefGoogle Scholar
  13. Donaldson CH (1976) An experimental investigation of olivine morphology. Contrib Mineral Petrol 57: 187–213CrossRefGoogle Scholar
  14. Donaldson CH (1979) An experimental investigation of the delay in nucleation of olivine in mafic magmas. Contrib Mineral Petrol 69: 21–32CrossRefGoogle Scholar
  15. Dowty E (1980) Crystal growth and nucleation theory and the numerical simulation of igneous crystallization. In: Hargraves RB (ed) Physics of Magmatic Processes. Princeton University Press: 419–485.Google Scholar
  16. Fenn PM (1977) The nucleation and growth of alkali feldspars from hydrous melts. Can Mineral 15: 135–161Google Scholar
  17. Gibb FGF (1974) Supercooling and crystallization of plagioclase from a basaltic magma. Mineral Mag 39: 641–653CrossRefGoogle Scholar
  18. Gray NH (1970) Crystal growth and nucleation in two large diabase dikes. Can J Earth Sci 7: 366–375CrossRefGoogle Scholar
  19. Hess HH (1960) Stillwater igenous complex, Montana: A quantitative mineralogical study. Geol Soc Am Mem 80Google Scholar
  20. Huppert HE, Sparks RSJ (1980) The fluid dynamics of a basaltic magmaGoogle Scholar
  21. chamber replenished by influx of hot, dense ultrabasic magma. Contrib Mineral Petrol 75: 279–289.Google Scholar
  22. Huppert HE, Worster MG (1985) Dynamic solidification of a binary alloy. Nature 314: 703–707.CrossRefGoogle Scholar
  23. Irvine TN (1974) Petrology of the Duke Island ultramafic complex, Southeastern Alaska. Geol Soc Am Mem 138.Google Scholar
  24. Jaeger JC (1968) Cooling and solidification of igneous rocks. In: Hess HH,Poldervaart A (eds) Basalts: The Poldervaart Treatise on Rocks of Basaltic Composition, vol.2. New York, John Wiley & Sons:503–536Google Scholar
  25. Jackson ED (1961) Primary textures and mineral associations in the ultramafic zone of the Stillwater complex, Montana. U S Geol Sury Prof Pap 358Google Scholar
  26. Jaupart C, Brandeis G, Allegre CJ (1984) Stagnant layers at the bottom of convecting magma chambers. Nature 308: 535–538CrossRefGoogle Scholar
  27. Jaupart C, Brandeis G (1986) The stagnant bottom layer of convecting magma chambers. Earth Planet Sci Lett: in pressGoogle Scholar
  28. Johnson WA, Mehl RF (1939) Reaction kinetics in processes of nucleation and growth. Trans Am Inst Min Metall Pet Eng 135: 416–442.Google Scholar
  29. Kerr RC, Tait SR (1986) Crystallization and compositional convection in a porous medium with application to layered intrusions. J Geophys Res 91: 3591–3608.CrossRefGoogle Scholar
  30. Kirkpatrick RJ (1975) Crystal growth from the melt: a review. Am Mineral 60: 798–814Google Scholar
  31. Kirkpatrick RJ (1976) Towards a kinetic model for the crystallization of magma bodies. J Geophys Res 81: 2565–2571CrossRefGoogle Scholar
  32. Kirkpatrick RJ (1977) Nucleation and growth of plagioclase, Makaopuhi and Alae lava lakes, Kilauea volcano, Hawaii. Geol Soc Am Bull 88: 78–84CrossRefGoogle Scholar
  33. Kirkpatrick RJ (1983) Theory of nucleation in silicate melts. Am Mineral 68: 66–77.Google Scholar
  34. Kirkpatrick RJ, Kuo LC, Melchior J (1981) Crystal growth in incongruently melting compositions: programmed cooling experiments with diopside. Am Mineral 66: 223–241.Google Scholar
  35. Lasaga AC (1982) Towards a master equation in crystal growth. Amer J Sci 282: 1264–1320CrossRefGoogle Scholar
  36. Lofgren GE (1980) Experimental studies on the dynamic crystallization of silicate melts. In: Hargraves RB (ed) Physics of Magmatic Processes. Princeton Univ Press: 487–551.Google Scholar
  37. Loomis TP (1982) Numerical simulations of crystallization processes of plagioclase in complex melts: the origin of major and oscillatory zoning in plagioclase. Contrib Mineral Petrol 81: 219–229CrossRefGoogle Scholar
  38. McBirney AR, Noyes RM (1979) Crystallization and layering of the Skaergaard intrusion. J Petrol 20: 487–554CrossRefGoogle Scholar
  39. Morse SA (1969) The Kiglapait layered intrusion, Labrador. Geol Soc Am Mem 112Google Scholar
  40. Morse SA (1980) Basalts and Phase Diagrams. Springer Verlag, 493 pp. Parsons I (1979) The Klokken gabbro-syenite complex, south Greenland:cryptic variation and origin of inversely graded layering. J Petrol 20: 653–694Google Scholar
  41. Parsons I, Butterfield WA (1981) Sedimentary features of the Nunarssuit and Klokken syenites. J Geol Soc Lond 138: 289–306.CrossRefGoogle Scholar
  42. Randolph AD, Larson MA (1971) Theory of Particulate Processes. Academic Press, 251 pp.Google Scholar
  43. Shaw HR (1965) Comments on viscosity, crystal settling and convection in granitic magmas. Amer J Sci 263: 120–153CrossRefGoogle Scholar
  44. Swanson SE (1977) Relation of nucleation and crystal-growth rate to the development of granitic textures. Am Mineral 62: 966–978Google Scholar
  45. Tait SR, Ruppert HE, Sparks RSJ (1984) The role of compositional convection in the formation of adcumulate rocks. Lithos 17: 139–146CrossRefGoogle Scholar
  46. Tsuchiyama A (1983) Crystallization kinetics in the system CaMgSi2 Oo -CaAl2 Sit Od: the delay in nucleation of diopside and anorthite. Am Mineral 68: 687–698.Google Scholar
  47. Turnbull D, Fischer JC (1949) Rate of nucleation in condensed systems, J Chem Phys 17: 71–73.CrossRefGoogle Scholar
  48. Wager LR (1959) Differing powers of crystal nucleation as a factor producing diversity in layered igneous intrusions. Geol Mag 96: 75–80.CrossRefGoogle Scholar
  49. Wager LR, Brown GM (1968) Layered Igneous Rocks. Oliver and Boyd, Edinburgh.Google Scholar
  50. Walker F (1940) Differentiation of the Palisade diabase, New Jersey. Geol Soc Amer Bull 51: 1059–1106Google Scholar
  51. Walker D, Kirkpatrick RJ, Longhi J, Hays JF (1976) Crystallization history of lunar picritic basalt 12002: phase equilibria and cooling-rate studies. Geol Soc Am Bull 87: 646–656.CrossRefGoogle Scholar
  52. Winkler HGF (1949) Crystallization of basaltic magma as recorded by variation of crystal size in dikes. Mineral Mag 28: 557–574CrossRefGoogle Scholar
  53. Worster MG (1986) Solidification of an alloy from a cooled boundary. J Fluid Mech 167: 481–501.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1987

Authors and Affiliations

  • Geneviève Brandeis
    • 1
  • Claude Jaupart
    • 1
  1. 1.Institut de Physique du GlobeUniversité Paris 6 et 7Paris Cedex 05France

Personalised recommendations