Morphology transitions during non-equilibrium growth: II. Morphology diagram and characterization of the transition

https://doi.org/10.1016/0378-4371(92)90411-IGet rights and content

Abstract

In a preceding paper we have presented a new diffusion-transition approach to study pattern formation in systems described by a conserved order parameter on a square lattice. Here we describe and analyze two of the different morphologies observed during growth far from equilibrium: the dense branching morphology (DBM) and the dendritic morphology. Both have been found to represent clearly distinct morphological “phases”. They can be characterized by their envelope: convex for DBM and concave for dendritic morphology. They both propagate at constant velocity. The velocity scales with different powers of the chemical potential for the two different morphologies. For the DBM, the branch width is proportional to the diffusion length. The transitions between the morphologies and their growth behavior are studied as a function of the chemical potential and the macroscopic driving force (supersaturation).

References (45)

  • M. Ben-Amar et al.

    Physica D

    (1987)
  • E. Ben-Jacob et al.

    Phys. Rev. A

    (1988)
  • T. Vicsek

    Phys. Rev. A

    (1985)
  • S.K. Chan et al.

    J. Cryst. Growth

    (1976)
  • O. Shochet et al.

    Physica A

    (1992)
  • O. Shochet, R. Kupferman and E. Ben-Jacob, in: Pattern Formation in Physical Systems and in Biology, P. Meakin, L....
  • A. Classen et al.

    Phys. Rev. A

    (1991)
  • D.A. Kessler et al.

    Adv. Phys.

    (1988)
  • E. Ben-Jacob et al.

    Phys. Rev. Lett.

    (1984)
  • D.A. Kessler et al.

    Phys. Rev. A

    (1986)
  • R. Combescot et al.

    Phys. Rev. Lett.

    (1986)

    Phys. Rev. A

    (1984)
  • M. Kruskal et al.

    Aeronautical Research Associated of Princeton

    Technical Memo, 85-25

    (1985)
  • J.S. Langer

    Science

    (1989)
  • J.S. Langer
  • E. Ben-Jacob et al.

    Nature

    (1990)
  • E. Brener et al.

    Adv. Phys.

    (1991)
  • E. Ben-Jacob et al.

    Superlatt. Microstruct.

    (1987)
  • E. Ben-Jacob et al.

    Physica D

    (1989)
  • J. Nittmann et al.

    Nature

    (1986)
  • D.G. Grier et al.

    Phys. Rev. Lett.

    (1986)
  • E. Ben-Jacob et al.

    Phys. Rev. Lett.

    (1985)
  • P. Oswald et al.

    MRS Bul.

    (Jan. 1991)
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