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Devil's staircase in kinetically limited growth.

G J Ackland1

  • 1Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08855-0849, USA. gjackland@ed.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 22, 2002
PubMed
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The devil's staircase describes complex surface phase diagrams where crystal growth, driven by kinetics, can lead to an infinite series of intermediate phases. These structures may not represent the true equilibrium state, complicating growth law determination.

Area of Science:

  • Surface science
  • Statistical mechanics
  • Materials science

Background:

  • The devil's staircase describes equilibrium phase diagrams with densely packed ordered phases.
  • A key example is the one-dimensional Ising model, where competing forces lead to rational periodicity.
  • Crystal growth often involves kinetic processes, freezing surface layers that may not be the thermodynamic ground state.

Purpose of the Study:

  • To investigate the relationship between kinetic growth processes and equilibrium ground states in systems exhibiting devil's staircase behavior.
  • To analyze how crystal growth, influenced by kinetics, approaches the equilibrium ground state.

Main Methods:

  • Analysis of surface or equilibrium phase diagrams.
  • Modeling of crystal growth kinetics.

Related Experiment Videos

  • Examination of the one-dimensional Ising model as a classic example.

    • Main Results:

    • Kinetically controlled crystal growth can lead to structures that approach the equilibrium ground state via a devil's staircase.
    • This process involves traversing an infinite number of intermediate phases.
    • The resulting grown structure is uniquely defined by growth kinetics, not necessarily the thermodynamic ground state.

    Conclusions:

    • Kinetically driven crystal growth can result in complex, non-equilibrium structures resembling a devil's staircase.
    • Determining simple growth laws from such structures is challenging due to the infinity of intermediate phases.
    • Understanding kinetic effects is crucial for interpreting complex surface structures.