Crystal Nucleation and Growth

The growth of thin films on solid surfaces is important in technology, and nucleation is one of the keys for understanding the growth mechanism. The ability of STM to image local structures down to atomic detail makes it ideal for the study of nucleation, thin film growth, and crystal growth. 

By taking STM images of a smaller area, it was found that the spontaneous formation of ordered arrays of Ni islands is determined by the herringbone reconstruction of the Au(lll) surface. It is clear that the Ni islands locate at the elbows of the herringbone structure. A detailed study of the atomic-resolution STM image and the local atomic structure near the elbows indicates that at each vertex of the elbow, there is a dislocation. Energetically, the dislocation site is the most probable location for the nickel deposition to nucleate. 

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Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

Over 50 acidic, basic, and neutral aluminum sulfate hydrates have been reported. Only a few of these are well characterized because the exact compositions depend on conditions of precipitation from solution. Variables such as supersaturation, nucleation and crystal growth rates, occlusion, nonequilihrium conditions, and hydrolysis can each play a role ia the final composition. Commercial dry alum is likely not a single crystalline hydrate, but rather it contains significant amounts of amorphous material. 

Physical properties of the acid and its anhydride are summarized in Table 1. Other references for more data on specific physical properties of succinic acid are as follows solubiUty in water at 278.15—338.15 K (12) water-enhanced solubiUty in organic solvents (13) dissociation constants in water—acetone (10 vol %) at 30—60°C (14), water—methanol mixtures (10—50 vol %) at 25°C (15,16), water—dioxane mixtures (10—50 vol %) at 25°C (15), and water—dioxane—methanol mixtures at 25°C (17) nucleation and crystal growth (18—20) calculation of the enthalpy of formation using semiempitical methods (21) enthalpy of solution (22,23) and enthalpy of dilution (23). For succinic anhydride, the enthalpies of combustion and sublimation have been reported (24). 

Scaling is not always related to temperature. Calcium carbonate and calcium sulfate scaling occur on unheated surfaces when their solubiUties are exceeded in the bulk water. Metallic surfaces are ideal sites for crystal nucleation because of their rough surfaces and the low velocities adjacent to the surface. Corrosion cells on the metal surface produce areas of high pH, which promote the precipitation of many cooling water salts. Once formed, scale deposits initiate additional nucleation, and crystal growth proceeds at an accelerated rate. 

Supersaturation has been observed to affect contact nucleation, but the mechanism by which this occurs is not clear. There are data (19) that infer a direct relationship between contact nucleation and crystal growth. This relationship has been explained by showing that the effect of supersaturation on contact nucleation must consider the reduction in interfacial supersaturation due to the resistance to diffusion or convective mass transfer (20). 

Initially, crystallization is a two-step process viz. nucleation and crystal growth requiring a change of free energy (Gibbs, 1928), as shown schematically in Figure 5.1. 

Several authors have presented methods for the simultaneous estimation of crystal growth and nucleation kinetics from batch crystallizations. In an early study, Bransom and Dunning (1949) derived a crystal population balance to analyse batch CSD for growth and nucleation kinetics. Misra and White (1971), Ness and White (1976) and McNeil etal. (1978) applied the population balance to obtain both nucleation and crystal growth rates from the measurement of crystal size distributions during a batch experiment. In a refinement, Tavare and... 

It has been shown that an increase in crystallizer residence time, or decrease in feed concentration, reduces the working level of supersaturation. This decrease in supersaturation results in a decrease in both nucleation and crystal growth. This in turn leads to a decrease in crystal surface area. By mass balance, this then causes an increase in the working solute concentration and hence an increase in the working level of supersaturation and so on. There is thus a complex feedback loop within a continuous crystallizer, illustrated in Figure 7.11. 

Rates of nucleation and crystal growth may be given, respectively, as... 

Polymers crystallize from the molten state by the two-step process of nucleation and crystal growth. Nucleation initiates crystallization, followed by the addition of linear chain segments to the crystal nucleus. 

There are obviously two steps involved in the preparation of crystal matter from a solution, the crystals must first form and then grow. The formation of a new solid phase either on an inert particle in the solution or in the solution itself is called nucleation. The increase in size of this nucleus with a layer-by-layer addition of solute is called crystal growth. Both nucleation and crystal growth have supersaturation as a common driving force. Unless a solution is supersaturated, crystals can neither form nor grow. The particle-size distribution of this weight, however, will depend on the relationship between the two processes of nucleation and growth. 

Polymer crystallization is usually divided into two separate processes primary nucleation and crystal growth [1]. The primary nucleation typically occurs in three-dimensional (3D) homogeneous disordered phases such as the melt or solution. The elementary process involved is a molecular transformation from a random-coil to a compact chain-folded crystallite induced by the changes in ambient temperature, pH, etc. Many uncertainties (the presence of various contaminations) and experimental difficulties have long hindered quantitative investigation of the primary nucleation. However, there are many works in the literature on the early events of crystallization by var-... 

According to Hoffman s crystallization theory, a drop in the heat of fusion corresponds to an exponential decrease in nucleation and crystal growth rates [63]. Implicitly, the rate of crystallization is severely retarded by the presence of 3HV comonomer [64, 69, 72]. These low crystallization rates can hamper the melt processing of these copolymers since they necessitate longer processing cycle times. 

As discussed in section 2.4.4 the coordinating ability of a solvent will often affect the rate of nucleation and crystal growth differently between two polymorphs. This can be used as an effective means of process control and information on solvent effects can often be obtained from polymorph screening experiments. There are no theoretical methods available at the present time which accurately predict the effect of solvents on nucleation rates in the industrial environment. 

RELATIVE SUPERSATURATION. The free energy that drives nucleation and crystal growth is directly related to a substance s relative supersaturation (RS), and the latter is a unitless parameter equal to [X]instantaneous/... 

Haas, C. Drent, J. The Interface between a Protein Crystal and an Aqueous Solution and Its Effects on Nucleation and Crystal Growth. J. Phys. Chem. B 2000, 104, 368-377. 

In some test runs that the melt mixtxire in the optical cell was compressed to a desired pressxore and kept under the same pressu e for fifteen minutes, no crystal appeared. As shown in Figure 3, these test results were often obtained for the system with 80.0 mole percent benzene at 283 K, under the supersaturation of 20 megapascales. But in some other tests using different melt compositions, some nucleation and crystal growth were observed under almost same operational conditions. 

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