Crystal growth nuclei

An intrinsic surface is built up between both phases in coexistence at a first-order phase transition. For the hard sphere crystal-melt interface [51] density, pressure and stress profiles were calculated, showing that the transition from crystal to fluid occurs over a narrow range of only two to three crystal layers. Crystal growth rate constants of a Lennard-Jones (100) surface [52] were calculated from the fluctuations of interfaces. There is evidence for bcc ordering at the surface of a critical fee nucleus [53]. 

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. 

Primary crystallization occurs when chain segments from a molten polymer that is below its equilibrium melting temperature deposit themselves on the growing face of a crystallite or a nucleus. Primary crystal growth takes place in the "a and b directions, relative to the unit cell, as shown schematically in Fig. 7.8. Inevitably, either the a or b direction of growth is thermodynamically favored and lamellae tend to grow faster in one direction than the other. The crystallite thickness, i.e., the c dimension of the crystallite, remains constant for a given crystallization temperature. Crystallite thickness is proportional to the crystallization temperature. 

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. 

The particle size of the resulting pigment can only be influenced to a limited extent by adjusting the reaction parameters, because the decisive factor is the ratio of the rate of formation of the crystal nucleus to the rate of crystal growth. 

When the attachment of the substrate to the precipitate to be formed is strong, the clusters tend to spread themselves out on the substrate and form thin surface islands. A special limiting case is the formation of a surface nucleus on a seed crystal of the same mineral (as in surface nucleation crystal growth). As the cohesive bonding within the cluster becomes stronger relative to the bonding between the cluster and the substrate, the cluster will tend to grow three-dimensionally (Steefel and Van Cappellen, 1990). 

Another mechanism for crystal growth is known as Ostwald ripening. If a small nucleus or embryo is close to a larger crystal, the ions formed by (partial) dissolution of the smaller, less stable crystal can be incorporated into the larger crystal. As the smaller crystal becomes even smaller, its dissolution will become ever more favorable and eventually it will disappear. The result is that the larger crystals grow at the expense of the smaller ones. 

At a temperature below Tm the free enthalpy of the crystal is lower than that of the liquid hence the polymer will tend to crystallize. A crystal can, however, only be formed from a nucleus. The process of crystallization can thus be split-up into two different processes nucleus formation and crystal growth. 

From the rate of nucleus formation and the rate of crystal growth the rate of crystallization results, which can be schematically represented as the product of both, as shown in Figure 4.7. The rate of crystallization is zero at Tg and at Tm, and shows a maximum somewhere in between, a maximum which is lower when the chains are longer. 

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