page_title: Crystal growth
section_title: Diffusion-control
hierarchical_section_title: Crystal growth / Morphology / Diffusion-control
caption_attribution_description: English: Manganese oxide dendrites on a limestone bedding plane from Solnhofen, Germany. Scale in mm.
context_page_description: A crystal is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. Crystal growth is a major stage of a crystallization process, and consists in the addition of new atoms, ions, or polymer strings into the characteristic arrangement of the crystalline lattice. The growth typically follows an initial stage of either homogeneous or heterogeneous nucleation, unless a "seed" crystal, purposely added to start the growth, was already present.
  The action of crystal growth yields a crystalline solid whose atoms or molecules are close packed, with fixed positions in space relative to each other.
  The crystalline state of matter is characterized by a distinct structural rigidity and very high resistance to deformation. Most crystalline solids have high values both of Young's modulus and of the shear modulus of elasticity. This contrasts with most liquids or fluids, which have a low shear modulus, and typically exhibit the capacity for macroscopic viscous flow.
context_section_description: Very commonly when the supersaturation (or degree of supercooling) is high, and sometimes even when it is not high, growth kinetics may be diffusion-controlled. Under such conditions, the polyhedral crystal form will be unstable, it will sprout protrusions at its corners and edges where the degree of supersaturation is at its highest level. The tips of these protrusions will clearly be the points of highest supersaturation. It is generally believed that the protrusion will become longer (and thinner at the tip) until the effect of interfacial free energy in raising the chemical potential slows the tip growth and maintains a constant value for the tip thickness.
  In the subsequent tip-thickening process, there should be a corresponding instability of shape. Minor bumps or "bulges" should be exaggerated — and develop into rapidly growing side branches. In such an unstable (or metastable) situation, minor degrees of anisotropy should be sufficient to determine directions of significant branching and growth. The most appealing aspect of this argument, of course, is that it yields the primary morphological features of dendritic growth.
caption: Manganese dendrites on a limestone bedding plane from Solnhofen, Germany. Scale in mm.
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