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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.

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

$r_c = \frac{-2\gamma}{\delta G_v}$,

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