PATTERN FORMATION IN FIRST-ORDER PHASE TRANSITIONS

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Abstract
Recent developments in the theory of pattern formation in diffusional growth are reviewed. Asymptotic analysis and scaling arguments are used to construct a morphology diagram in parameter space. The relevant variables spanning this space are the anisotropy ∈ of the capillary length and the dimensionless undercooling Δ. Structures are classified according to whether they are compact or fractal and whether they possess orientational order or not. Explicit expressions for selected velocities and typical length scales are given in the scaling regime. For compact structures the theory provides a prescription how to go beyond scaling results.

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