Critical radius

Critical radius is the minimum size that must be formed by atoms clustering together in the liquid before the solid particle is stable and begins to grow.

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The atoms would then form a dendrite. The crystal growth continues in three dimensions, the atoms attaching themselves in certain preferred directions, usually along the axes of a crystal, forming a characteristic tree-like structure of a dendrite.

example: the critical radius for spheric-like dendride in an ideal system is

,

where γ is the surface energy, and δG_v is Gibbs energy per volume.

See also

• Nucleation
• Ostwald ripening

References

• N.H.Fletcher, Size Effect in Heterogeneous Nucleation, J.Chem.Phys.29, 1958, 572.