Induction and latent periods

A period of time usually elapses between the achievement of supersaturation and the appearance of crystals. This time lag, generally referred to as an induction period , is considerably influenced by the level of supersaturation, state of agitation, presence of impurities, viscosity, etc. 

The existence of an induction period in a supersaturated system is contrary to expectations from the classical theory of homogeneous nucleation (section 5.1.1), which assumes ideal steady-state conditions and predicts immediate nucleation once supersaturation is achieved. The induction period may therefore be considered as being made up of several parts. For example, a certain relaxation time , c, is required for this system to achieve a quasi-steady-state distribution of molecular clusters. Time is also required for the formation of a stable nucleus, and then for the nucleus to grow to a detectable size, tg. So the induction period, tmd, may be written. 

It is difficult, if not impossible, to isolate these separate quantities. The relaxation time depends to a great extent on the system viscosity and, hence, diffusivity. Nielsen (1964) has suggested that tr where 

In some systems, particularly at low supersaturation, another time lag may be observed. To distinguish it from the induction period, defined above as the point at which crystals are first detected in the system, the term latent period will be used, and is defined here as the onset of a significant change in the system, e.g. the occurrence of massive nucleation or some clear evidence of substantial solution desupersaturation. 

The presence of seed crystals generally reduces the induction period, but does not necessarily eliminate it. Even if the system is seeded at time t = 0, a measurable induction period tmd may elapse before new crystals are detected. By definition, these are secondary nuclei and they may appear in several bursts throughout the latent period, making it difficult to attach any real significance to the induction time itself For these reasons it may be preferable to record the latent period as the more practical characteristic of the system. Factors that can influence the induction and latent periods and the rate of desupersaturation are temperature, agitation, heat effects during crystallization, seed size, seed surface area and the presence of impurities. 

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