Crystal growth interface-reaction controlled

Because interface reaction and mass/heat transfer are sequential steps, crystal growth rate is controlled hy the slowest step of interface reactions and mass/heat transfer. For a crystal growing from its own melt, the growth rate may be controlled either by interface reaction or heat transfer because mass transfer is not necessary. For a crystal growing from a melt or an aqueous solution of different composition, the growth rate may be controlled either by interface reaction or mass transfer because heat transfer is much more rapid than mass transfer. Different controls lead to different consequences, including the following cases ... 

The concentration profiles for crystal growth under different controls and their evolution with time are shown in Figure 1-11. Whether crystal growth (or dissolution) is controlled by interface reaction or mass transfer can be determined experimentally using these criteria. Theoretically, when departure from equilibrium (i.e., degree of oversaturation or undercooling) is small (e.g., undercooling... 

Microemulsions [191, 192] are transparent, optically isotropic and thermodynamically stable liquids. They contain dispersion of polar and nonpolar solvent, usually water or aqueous solutions and oils. Adding surfactants stabilizes droplets of 1-100 nm in size. Due to amphiphilic properties of the surface active substances containing lipophilic groups and one or two lyophobic C-H chains mainly collected at the interface of two liquid phases, they cannot be mixed under normal conditions. Unlike traditional macroemulsion, which is kinetically stabilized only by the external mechanical energy supply, nano-domains in the microemulsions are formed spontaneously. Their size depends on the microemulsion composition, temperature and elastic properties of the separating film of surfactant. In particular, in the case of water-oil microemulsions with spherical nanosized micelles of water dispersed in oil, water droplets can be used as nanoreactors and templates for the solid nanoparticles fabrication. Since the reaction is initiated by the spatially restricted water and micelle, heterogeneous nucleation and crystal growth can be controlled. 

Dehydration reactions are typically both endothermic and reversible. Reported kinetic characteristics for water release show various a—time relationships and rate control has been ascribed to either interface reactions or to diffusion processes. Where water elimination occurs at an interface, this may be characterized by (i) rapid, and perhaps complete, initial nucleation on some or all surfaces [212,213], followed by advance of the coherent interface thus generated, (ii) nucleation at specific surface sites [208], perhaps maintained during reaction [426], followed by growth or (iii) (exceptionally) water elimination at existing crystal surfaces without growth [62]. 

Figure 1-11 Concentration profile for (a) crystal growth controlled by interface reaction (the concentration profile is flat and does not change with time), (b) diffusive crystal growth with t2 = 4fi and = 4t2 (the profile is an error function and propagates according to (c) convective crystal growth (the profile is an exponential function and does not change with time), and (d) crystal growth controlled by both interface reaction and diffusion (both the interface concentration and the length of the profile vary).

The above is for isothermal crystal growth. In nature, crystallization occurs in a continuously cooled magma. The cooling rate plays a main role in controlling crystallization, and the nucleation and interface-reaction rates shown in Figure 1-14 are instructive in understanding crystallization under various cooling rates. 

Nucleation is necessary for the new phase to form, and is often the most difficult step. Because the new phase and old phase have the same composition, mass transport is not necessary. However, for very rapid interface reaction rate, heat transport may play a role. The growth rate may be controlled either by interface reaction or heat transport. Because diffusivity of heat is much greater than chemical diffusivity, crystal growth controlled by heat transport is expected to be much more rapid than crystal growth controlled by mass transport. For vaporization of liquid (e.g., water vapor) in air, because the gas phase is already present (air), nucleation is not necessary except for vaporization (bubbling) beginning in the interior. Similarly, for ice melting (ice water) in nature, nucleation does not seem to be difficult. 

Crystal dissolution/melting/growth may be controlled by interface reaction rate (Figure 1-lla), meaning that mass/heat transfer rate is very high and interface reaction rate is low. Examples include dissolution of minerals with low... 

Crystal dissolution and growth may also be controlled by both mass or heat transport and interface reaction (Figure 1-1 Id). In this case, the interface reaction... 

When an ionic single crystal is immersed in solution, the surrounding solution becomes saturated with respect to the substrate ions, so, initially the system is at equilibrium and there is no net dissolution or growth. With the UME positioned close to the substrate, the tip potential is stepped from a value where no electrochemical reactions occur to one where the electrolysis of one type of the lattice ion occurs at a diffusion controlled rate. This process creates a local undersaturation at the crystal-solution interface, perturbs the interfacial equilibrium, and provides the driving force for the dissolution reaction. The perturbation mode can be employed to initiate, and quantitatively monitor, dissolution reactions, providing unequivocal information on the kinetics and mechanism of the process. 

Mam heterogeneous processes such as dissolution of minerals, formation of he solid phase (precipitation, nucleation, crystal growth, and biomineraliza-r.on. redox processes at the solid-water interface (including light-induced reactions), and reductive and oxidative dissolutions are rate-controlled at the surface (and not by transport) (10). Because surfaces can adsorb oxidants and reductants and modify redox intensity, the solid-solution interface can catalyze rumv redox reactions. Surfaces can accelerate many organic reactions such as ester hvdrolysis (11). 

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