Let's start with clarifying the terms 'Crystal" and "Growth". The word "crystal" originates from the Greek κριος (coldness) or κριµος (ice). The father of crystal fabrication technology is A. Verneuil with his flame-fusion growth method he described in 1902.
What are crystals? Crystals are ordered arrangements of atoms (or molecules). Materials in crystalline form has special optical and electrical properties, in many cases improved properties over randomly arranged materials(also said to be amorphous or glassy)
What causes crystals to "grow"? The driving force for crystallization comes from the lowering of the potential energy of the atoms or molecules when they form bonds to each other.
The crystal growth process starts with the nucleation stage. Several atoms or molecules in a supersaturated vapor or liquid start forming clusters; the bulk free energy of the cluster is less than that of the vapor or liquid. The total free energy of the cluster is increased by the surface energy (surface tension), however, this is significant only when the cluster is small. A cluster of radius smaller than a critical radius, r*will evaporate (or dissolve in the solution) a cluster of radius greater than r* will become stable, will increase its size by the addition of other atoms and is thus "growing"! The critical radius r* also defines a critical energy barrier, DG, that we need to overcome in order to obtain a stable nucleus that will keep growing, eventually become a large single crystal!
Thermodynamics can help us describe the process. Assuming a spherical shape for the nucleus the free energy of its formation is:
DG = 4P r2 s + (4/3)P r3 )Gv
where DG is the total free energy; r is the radius of cluster; s is the surface tension; DGvis the free energy change per unit volume forming the stable solidification from vapor or liquid. The total free energy DG goes through a maximum DG*at a critical radius r* which can be obtained by derivation of total free energy as given above with respect to radius and solving:
(dDGo/dr) = 0