Pattern Formation during Crystal Growth: Theory

  • J. S. Langer
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 77)


These lectures will focus on two different versions of the problem of pattern formation during crystal growth. We shall look first at the free growth of dendrites and, next, at directional solidification of cellular structures and eutectics. In the first case, a study of the stability of the dendrite tip and related sidebranching deformations leads naturally to an hypothesis that the dendrite operates at or near a point of marginal instability. This hypothesis seems to be in agreement with experimental observations. The second case is a direct analog of the Bénard problem in hydrodynamics. Again, a marginal instability seems to play some role in pattern selection; but the situation is unclear at the moment. We shall see that there are possibilities for a variety of kinds of interesting behavior in these systems.


Pattern Formation Marginal Stability Solidification Front Lamellar Spacing Eutectic Growth 
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Copyright information

© Plenum Press, New York 1982

Authors and Affiliations

  • J. S. Langer
    • 1
  1. 1.Physics Department and Center for the Joining of MaterialsCarnegie-Mellon UniversityPittsburghUSA

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