Crystal growth relative rates

Models used to describe the growth of crystals by layers call for a two-step process (/) formation of a two-dimensional nucleus on the surface and (2) spreading of the solute from the two-dimensional nucleus across the surface. The relative rates at which these two steps occur give rise to the mononuclear two-dimensional nucleation theory and the polynuclear two-dimensional nucleation theory. In the mononuclear two-dimensional nucleation theory, the surface nucleation step occurs at a finite rate, whereas the spreading across the surface is assumed to occur at an infinite rate. The reverse is tme for the polynuclear two-dimensional nucleation theory. Erom the mononuclear two-dimensional nucleation theory, growth is related to supersaturation by the equation. 

Flow of mother Hquor through the cooled tubes is initiated, and crystals are grown on the tube surfaces. The heat transfer rate should be controUed so as to moderate crystal growth, thereby producing a relatively uniform layer of high purity soHds. 

Therefore we have two extremes in crystal habit in sodium chloride, the octahedron and the skeleton, the prevailing shape depending upon the relative rates of growth in different directions in the crystal lattice. The common cube shape is formed when a balance in the two rates of growth prevails. 

It has been reported that the overall rate of crystallization of pure PHB is relatively low compared to that of common synthetic polymers, showing a maximum in the temperature range of 55-60°C [23]. The spherulite growth rate kinetics have been evaluated [59] in terms of the theory by Hoffmann et al. [63], At about 90 °C, the spherulite growth rate displayed a maximum, which is not excessively low compared to that of common synthetic polymers. Therefore it was stated that the low overall crystallization rate of PHB centers on the nuclea-tion process rather than the subsequent crystal growth. Indeed, it has been shown that PHB has an exceptionally low level of heterogeneous nuclei [18]. 

We define the linear growth rate Vg as the linear velocity of displacement of a crystal face relative to some fixed point in the crystal. vg may be known as a function of c and c , derived from the theory of transport control, and as a function of c and cs as well, derived from the theory of surface control. Then c may be eliminated by equating the two mathematical expressions... 

Reaction Time. The rate of formation of to at reflux temperature is illustrated in Figure 2. The rate was estimated by taking samples from the reaction mixture at various times and examining them by x-ray diffraction. The crystallization is characterized by an unusually long induction period of about 13 hr, which is followed by a relatively slow crystal growth. No alteration of the zeolite was observed during an extra 50 hr reaction time after crystallization had been completed. 

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