Critical growth rates

Although the balance equations are linear, in the absence of bulk convection, the unknown shape of the melt-crystal interface and the dependence of the melting temperature on the energy and curvature of the surface make the model for microscopic interface shape rich in nonlinear structure. For a particular value of the spatial wavelength, a family of cellular interfaces evolves from the critical growth rate VC(X) when the velocity is increased. 

The validity of this model was tested by the critical growth rate method on the AgBr system (Figure 10). 6 was... 

Most precipitation systems exhibit a metastable supersaturation zone where supersaturation is too low for nucleation to take place. As the supersaturation is increased, the point at which nucleation just begins to occur corresponds to the maximum metastable (critical) supersaturation allowable without nucleation. If crystals are present at this moment in the precipitation vessel, they grow at a maximum (critical) growth rate. 

Figure 6.5 Dependence of critical growth rates on crystal size for AgBr octahedra. (Wey and Strong 1977a.)...

The critical growth rate method enables one to delineate the region of allowable growth rates for a given precipitating closed... 

Also discussed are precipitation specific experimental techniques, such as supersaturation measurements, constant composition (CC) method, instantaneous mixing devices, maximum (critical) growth rate experiments, and sizing. Due to the intrinsic difficulties with the direct supersaturation measurements and the microsecond characteristic time scale of precipitation reaction and nucleation, the CC method is used to study the precipitation kinetics. For the same reasons, the critical growth experiments are used to delineate the domain of the reactant feed rate that assures a renucleation-free process and a unimodal CSD. 

In order to calculate the above cooling profiles, one needs to know the values of the growth rate G, the nuclei size Lj,/, and the nucleation rate Bo - For the seeded run, the value of the growth rate G must be lower than the critical growth rate, which can be determined experimentally in growth kinetics experiments (Karpinski 1981)... 

Figure 16. Dependence of critical growth rate of diamond crystals on 100 faces of seed crystals, on...

The power spectrum of the light, scattered from the ice-water interface at conditions close to equilibrium, contains only Raman and Brillouin contributions. There is no Rayleigh scattering. At a critical growth rate an onset of quasi elastic light scat-... 

---