Crystal size critical

The resistance to nucleation is associated with the surface energy of forming small clusters. Once beyond a critical size, the growth proceeds with the considerable driving force due to the supersaturation or subcooling. It is the definition of this critical nucleus size that has consumed much theoretical and experimental research. We present a brief description of the classic nucleation theory along with some examples of crystal nucleation and growth studies. 

Initiation of growth may also proceed by formation of metastable structures when nucleation is inhibited. Multiply twinned structures have been observed for a number of metals. Their presence indicates an icosohedral or decahedral precursor cluster which has decomposed to a multiply twinned crystal at a critical size [117, 118], Another example of metastable intermediate structures was reported by Dietterle et al. 

As before, the saturation ratio S can also be expressed as a/ao, where a and a0 are the actual and equilibrium activities, respectively, of the solutes that characterize the solubility. Once nuclei of critical size Xj+1 (in Eq. 6.1) have been formed, crystallization is spontaneous. 

If a heap of crysts of uniform size is used, the impact sensitivity is independent of the size of the individual crysts in the heap and remains approx of the same sensitivity. It seems that there may be two factors involved in detonation of crystals. First, the probability of explosion is determined by the number of potential initiation centers or hot spots and this is naturally greater for large individual crysts than for smaller ones. The second is the fact that the reaction cannot grow to an expln unless the crystal exceeds a critical size. 

After clusters attain a critical size in the system and the nucleation stage is complete, the growth stage commences in a narrower sense. Since the structure is already formed, the solute component will be incorporated into the crystal at the expense of a much smaller energy than that necessary for nucleation. Here, the interface structure between the solid and liquid phases that appeared as a result of... 

A certain minimum-sized fragment is required to induce crystallization. The size of such a critical nucleus is on the order of 100 molecules (a diameter of 100 A) (Van Hook 1961). 

The critical unit operations that should be monitored and/or optimized are the reaction and fermentation steps for the purpose of increasing API yield and reducing the residual impurity profile. Other critical unit operations that are especially important to the end user (pharmaceutical dosage form operations) include precipitation or crystallization, milling, sizing, and purification operations, which may affect the physical properties (particle size and shape, bulk powder flow, blend uniformity, and compressibility) of the API. 

Classically, the process by which crystals are deposited involves the initial clustering of solutes in supersaturated solution into stable or transient assemblies (nucleation) followed by growth once the assembly has reached a critical size. The process is shown below ... 

D nucleus, building blocks just adsorb on the faces and then diffuse together and cluster. Once the nucleus has reached critical size, it becomes stable and exhibits some class K faces, where growth units can be incorporated that convert the class K face to class S. The process continues until all the K faces are filled the S sites then begin to fill, resulting in a perfect crystal that has all F faces. The kinetics of the growth is typically diffusion-controlled at the rate R ... 

A physico-chemical basis for the critical size requirement has been described. There is evidence that chemical events rather than diffusion can govern subsequent linear growth of zeolite crystals. 

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