Crystallization is a process in which a
material changes from an unordered,
amorphous state into an ordered,
crystalline state. The unordered state is often a
liquid, as crystallization usually takes place during the
solidification of
crystalline materials, but crystallization can also occur within a
solid material.
The process of crystallization involves two important steps: nucleation and crystal growth.
When a liquid is cooled to a temperature below its melting point, the difference in the Gibbs free energy between the liquid state and the solid state results in a driving force for solidification. However, the spontaneous solidification that you might expect does not always occur. Under specific circumstances it is possible to supercool a liquid considerably. The reason for this is that the liquid-to-solid phase transition starts with the formation of very small solid particles called nuclei (single nucleus).
The random movement of the particles atoms or molecules forms nuclei in the liquid. In any moment, this random movement brings particles together in a way that closely resembles the crystalline structure. However, at temperatures above the melting point the presence of a solid particle in the liquid means an increase in free energy and is therefore energetically unfavourable. At these temperatures the clusters of particles are unstable and will fall apart again. When the temperature drops below the melting point however, the increase in free energy caused by the formation of a (small) liquid-solid interface is compensated by the decrease in free energy caused by the presence of a small amount of solid. That means that from that point on the nuclei are stable and can grow further. The process above is called homogeneous nucleation, where nuclei have the same composition as the final solid. There is also a process called heterogeneous nucleation, where the nuclei form in contact with the wall of the mould the liquid is in, for example. Heterogeneous nucleation can also involve small solid particles (with a different composition than the melt) in the liquid where crystal growth can start. In industrial processes foreign particles are sometimes introduced with the express intention to start solidification. This is done to influence the final microstructure of the material. When no nucleation occurs, which is theoretically possible, crystallization does not take place. However, the more undercooling you get, the bigger the driving force towards crystallization gets, and the smaller the nuclei can be and still be stable. So under extreme undercooling, a jolt to the container in which the liquid finds itself can be sufficient to throw a small group of atoms together close enough to form a nucleus.
When stable nuclei have formed they can grow further when new particles migrate to the surface of the nucleus by diffusion and stick there.
Basically there are two kinds of solid-liquid interface: an atomically rough or diffuse interface (generally associated with metallic systems), and an atomically flat and smooth interface that is sharply defined (associated with non-metals). The mechanism of crystal growth depends on the type of interface that is present.
Each particle in a solid 'prefers' to be surrounded by the maximum amount of neighbour particles, as this situation is the most favourable, energetically speaking. You can understand this by imagining a material like diamond, which consists of C-atoms, arranged in tetrahedrons. Each C-atom has four electrons it wishes to share with a neighbouring atom in a bond. A C-atom on the surface will not be surrounded by enough neighbours and will have one or more bonding electrons floating around feeling miserable.
The same goes for any particle arriving at the surface of the forming solid. Imagine the particle as a small cube.When the particle arrives at a flat surface and sticks there, the number of 'broken bonds' increases by four (one for every side of the cube. At the bottom side a bond has formed, the topside doesn't count because it replaces the broken bond that was already there at the surface). This is not a favourable situation and therefore there is little probability of the atom remaining attached to the surface, and not jumping back into the liquid. When however a sufficiently large number of atoms join on the surface in the shape of a small disc (much in the same way as the formation of a homogeneous nucleus), the disc on the surface forms an 'anchor point' for other atoms to attach to where the increase in broken bonds is less ,and the surface fills up rather quickly. This mechanism leads to lateraland discontinuous growth . Another possibility is the presence of ledges on the surface that can act as sources for growth.
When the surface of the solid is atomically rough, there are always positions present where atoms from the liquid can latch on and growth will be continuous and diffusion controlled.
Source: D.A. Porter and K.E. Easterling, Phase Transformations in Metals and Alloys, Chapman & Hall, 1992