Crystallization from solutions is a complex process completed in several stages. The first stage is the formation of supersaturated solution because the spontaneous appearance of a new phase can occur only when a system is in a nonequilibrium condition. In the next stage, molecules dissolved in solution begin to aggregate to relieve the supersaturation and move the system toward equilibrium. The molecular aggregation process eventually leads to the formation of nuclei that can act as centers of crystallization. A nucleus can be defined as the minimum amount of a new phase capable of independent existence (Khamskii 1969). The nature of nuclei (i.e., whether they are amorphous particles or tiny crystals) is still unknown. The birth of these small nuclei in an initially metastable phase is called nucleation, which is a major mechanism of first-order phase transition. Kashchiev and van Rosmalen (2003) describe nucleation as the process of fluctuational appearance of nanoscopically small clusters of the new crystalline phase, which can grow spontaneously to macroscopic sizes. The growth stage, which immediately follows nucleation, is governed by the diffusion of particles, called growth units, to the surface of the existing nuclei and their incorporation into the structure of the crystal lattice (Khamskii 1969). This stage continues until all the solute in excess of saturation is consumed for the development of mature crystals. The initial stages of crystallization, which can be defined as the period between the achievement of supersaturation and the formation of nuclei, plays a decisive role in determining properties of the resulting solid phase, such as purity, crystal structure, and particle size. Thus higher levels of control over crystallization cannot be achieved without understanding the fundamentals of nucleation.

Crystallization can be regarded as a self-assembly process in which randomly organized molecules in a fluid come together to form an ordered three-dimensional molecular array with a periodic repeating pattern. It is vital to many processes occurring in nature and manufacturing. Geologic crystallization is responsible from huge deposits of carbonates, sulfates, and phosphates that often grow in mountains and quarries. This process occurs over long periods of time, often at high temperatures and pressures, and results in large and usually highly ordered crystals such as diamond.