# Nucleation

Nucleation is the first step in the formation of either a new thermodynamic phase or a new structure via self-assembly or self-organization. Nucleation is typically defined to be the process that determines how long an observer has to wait before the new phase or self-organized structure appears. Nucleation is often found to be very sensitive to impurities in the system. Because of this, it is often important to distinguish between heterogeneous nucleation and homogeneous nucleation. Heterogeneous nucleation occurs at nucleation sites on surfaces in the system. Homogeneous nucleation occurs away from a surface.

Nucleation is usually a process, so even in two identical systems nucleation will occur at different times. This behaviour is similar to radioactive decay. A common mechanism is illustrated in the animation to the right. This shows nucleation of a new phase (shown in red) in an existing phase (white). In the existing phase microscopic fluctuations of the red phase appear and decay continuously, until an unusually large fluctuation of the new red phase is so large it is more favourable for it to grow than to shrink back to nothing. This nucleus of the red phase then grows and converts the system to this phase. The standard theory that describes this behaviour for the nucleation of a new thermodynamic phase is called classical nucleation theory.

For nucleation of a new thermodynamic phase, such as the formation of ice in water below 0 °C, if the system is not evolving with time and nucleation occurs in one step, then the probability that nucleation has not occurred should undergo exponential decay as seen in radioactive decay. This is seen for example in the nucleation of ice in supercooled small water droplets. The decay rate of the exponential gives the nucleation rate. Classical nucleation theory is a widely used approximate theory for estimating these rates, and how they vary with variables such as temperature. It correctly predicts that the time you have to wait for nucleation decreases extremely rapidly when supersaturated.

It is not just new phases such as liquids and crystals that form via nucleation followed by growth. The self-assembly process that forms objects like the amyloid aggregates associated with Alzheimer's disease also starts with nucleation. Energy consuming self-organising systems such as the microtubules in cells also show nucleation and growth.

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