Crystalline Growth Rate

AG is the free energy difference between the solid and melt flo is an atomic dimension 

---

Table 1.3 Maximum Crystalline Growth Rate and Maximum Degree of Crystallinity for Various Thermoplastics...

Figure 14 Crystalline growth rate per nuclear energy deposition density at 350°C for BP preamorphized by 100-keV As implantation as a function of ion current density of 400-keV Ar and 400-keV Kr and corresponding nuclear energy deposition density rate.

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. 

Another matrix diffusional implant consists of an outer layer of micronized, crystalline 17P-estradiol dispersed in siUcone mbber over a nonmedicated, cylindrical siUcone mbber core. The system, implanted subcutaneously in the ears of cattie, releases estradiol for up to 400 days with kinetics to improve growth rate and feed efficiency (83). 

Effects of Impurities nd Solvent. The presence of impurities usually decreases the growth rates of crystalline materials, and problems associated with the production of crystals smaller than desired are commonly attributed to contamination of feed solutions. Strict protocols should be followed in operating units upstream from a crystallizer to minimize the possibiUty of such occurrences. Equally important is monitoring the composition of recycle streams so as to detect possible accumulation of impurities. Furthermore, crystalliza tion kinetics used in scaleup should be obtained from experiments on solutions as similar as possible to those expected in the full-scale process. 

Over 565,000 t/yr of nonftber crystalline nylons is sold worldwide (63). Since markets are controUed by the economy, a modest growth of 5—8%/yr is expected. Although currently only ca 900 t/yr of amorphous nylons is sold worldwide (64), a growth rate of 10% is expected because of increased research activity. Currently, the amorphous nylon resins compete with PEI and polyesters in many appHcations. 

In the analysis of crystal growth, one is mainly interested in macroscopic features like crystal morphology and growth rate. Therefore, the time scale in question is rather slower than the time scale of phonon frequencies, and the deviation of atomic positions from the average crystalline lattice position can be neglected. A lattice model gives a sufiicient description for the crystal shapes and growth [3,34,35]. 

The measured growth rates are illustrated by the circles in Fig. 7. The interface velocity is plotted versus the interface temperature T. The value of T is always greater than Tq because of the release of the latent heat at the interface. Dimensionless units for T and the velocity are used here. The maximum velocity corresponds to 80m /s for argon. The most surprising aspect is the rapid crystallization at low temperatures. Most materials exhibit sharply reduced rates at low temperatures, as expected for an activated growth process. That is, the kinetics can be represented as the product of an Arrhenius factor F(T) and a term that accounts for the net production of crystalline material as a result of the atoms ordering and disordering at the interface,... 

We have discussed simulations that were intended to elucidate aspects of crystal growth under diverse conditions. In most cases a direct simulation of growth using realistic conditions is impractical. The growth rate may be many orders of magnitude slower than that required to produce observable crystalline material in the available computer time. We have described several methods to obtain information about the crystallization process in this situation. 

Though the overall crystallinity showed a monotonic increase until around 330 K with lowering temperature, the detailed growth rate of each lamella... 

---