Crystal growth pathway

B. Gilbert, H. Z. Zhang, F, Huang, M, R Finnegan, G, A, Waychunas, and J. F. Banfleld. Special phase transformation and crystal growth pathways observed in nanoparticles. Geochem. Trans., 4 20-27, 2003... 

Martin, this volume Waychunas, this volume) lead to the speculation that nanoparticle aggregation is a pathway for crystal growth from molecules to microcrystals in many systems under some conditions. However, processes involving particles with sizes between those of molecules and 2 nm are very difficult to study with the level of detail needed to clearly resolve reaction mechanisms (though, of course, the existence of particle aggregates can be documented fairly easily). 

Size-dependent structure and properties of Earth materials impact the geological processes they participate in. This topic has not been fully explored to date. Chapters in this volume contain descriptions of the inorganic and biological processes by which nanoparticles form, information about the distribution of nanoparticles in the atmosphere, aqueous environments, and soils, discussion of the impact of size on nanoparticle structure, thermodynamics, and reaction kinetics, consideration of the nature of the smallest nanoparticles and molecular clusters, pathways for crystal growth and colloid formation, analysis of the size-dependence of phase stability and magnetic properties, and descriptions of methods for the study of nanoparticles. These questions are explored through both theoretical and experimental approaches. 

Zeolite formation in nature follows pathways which are familiar in laboratory synthesis. Zeolite nucleation, crystallisation and crystal growth lake place as a result of slow... 

Microporous framework solids are synthesised via solvent-mediated crystallisations from mixtures of reactive precursors. The reaction pathway is controlled by kinetic as well as thermodynamic considerations so that equilibrium phase diagrams, so relevant in the high-temperature preparation of ceramics, are not useful here. Rather, synthetic routes have been developed empirically via a major synthetic effort that continues today. The continuing industrial and academic interest in these materials provides a powerful incentive to understand the principles underlying their formation through the processes of gel formation and evolution, nucleation and crystal growth. 

Dissolution, precipitation, and crystallization that can occur during dissolution of an amorphous system are summarized in Fig. 15.4 (Alonzo et al. 2010). Modified Noyes and Whitney equation is used to describe the dissolution pathway, where dc/dl represents the dissolution rate which is directly proportional to the surface area (A) and the difference between the solution concentration (C) and the equilibrium concentration (Cgq Alonzo et al. 2010). In the nucleation path, J represents the nucleation rate, which is proportional to the degree of supersaturation (S). For the growth path, the rate of crystal growth is also proportional to the difference between the actual solution concentration and the equilibrium concentration (Alonzo et al. 2010). 

After a few minutes, co-crystal growth began. A constant cooling rate of 12 °C was then applied down to 10 °C. Figure 9.8(b) presents the kinetic pathways of two runs performed at two different initial compositions. The crystallization starting points were both in domain 4d at the starting temperature of 35 °C. 

Experiments were performed with the CBZ/NCT/ethanol system in domains of the phase diagram that were always undersaturated with respect to NCT (see Figure 9.9). Crystallizations were started in domains 2a or 3. Once the equilibrium was reached at 25 °C, a known amount of NCT in dry form was added in order to shift the overall composition of the slurry in domain 4a in the phase diagram. The previously stable CBZ solid phase became metastable. Henceforth the stable phase was the CBZ/NCT co-crystal. A SMPT started with the primary nucleation of the co-crystals if they were absent in the slurry and continued with the dissolution of the CBZ crystals and with co-crystal growth, until the new equilibrium was reached. Three kinetic pathways are displayed in Figure 9.9. 

Compared with run 52, the passage from domain 2 to domain 4 in run 54 was much slower. This slowness was due to the induction time of the co-crystal primary nucleation and to the great quantity of co-crystals produced. Run 61 differed from run 54 by the amount of CBZ crystals in the initial slurry (0.63 wt% for run 61) and also by the amount of NCT used to trigger the SMPT from domains 2 to 4. The differences in the pathways could be translated in terms of kinetics. First, the induction time of co-crystal primary nucleation at point G was reduced to 15 minutes due to a higher CBZ/NCT supersaturation ratio. Second, no plateau of CBZ dissolution o-crystal growth was detected and the pathway was parallel to the bisecting line up until the final equilibrium (point H ). An important desupersaturation rate was also observed. 

Compatibilization. The pathway to cure the shortcomings of a blend is compat-ibilization. The result is a nanocomposite. In our experiments the compatibilizer itself appears to inhibit crystal growth additionally (Fig. 5.10 at = 0). On the other hand, addition of more compatibilizer makes the nanostructure more stable when subjected to mechanical loading (Figs.5.3, 5.4, 5.8). Admittedly, this stability is the stability of an already degraded stmcmre. As shown by the necking-induced local strain-relaxation (Fig. 5.2), the compatibilizer increases the elasticity of the material. 

Figure B3.3.10. Contour plots of the free energy landscape associated with crystal niicleation for spherical particles with short-range attractions. The axes represent the number of atoms identifiable as belonging to a high-density cluster, and as being in a crystalline environment, respectively, (a) State point significantly below the metastable critical temperature. The niicleation pathway involves simple growth of a crystalline nucleus, (b) State point at the metastable critical temperature. The niicleation pathway is significantly curved, and the initial nucleus is liqiiidlike rather than crystalline. Thanks are due to D Frenkel and P R ten Wolde for this figure. For fiirther details see [189].

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