Growth rate temperature dependence

Batch crystallization studies of D-fructose from aqueous ethanolic solutions demonstrate that crystal growth rate is dependent on supersaturation (possibly to the 1.25 power), ethanol content and temperature. It appears that solution viscosity also has an effect. Growth rates of up to 1 pm/mln were measured. 

Fig. 6.26. Growth rate in dependence of metal-organic precursor flow (DMZ) for AP-CVD ZnO F films deposited at a substrate temperature of 300°C. These films are deposited from DMZ, oxygen, and fluorocarbon doping gas. Reprinted with permission from [24]...

The carbon atoms arriving at the substrate surface must exceed a certain concentration at the solid-gas interface to reach and exceed the critical nucleus size. Therefore the diamond nucleation density as well as the growth rate are dependent on the relative rates of bulk and surface diffusion of carbon atoms. ° These are different for different substrates. Thus, the nucleation process needs a temperature dependent incubation time which is related to the time required to form critical size diamond clusters on the substrate surface. The nucleation rate, which is initially negligible, reaches a maximum after a certain time period and tends to zero for longer deposition times. ... 

There are some further aspects to the craze growth behavior at stationary crack tips in PMMA There is a temperature dependence, the rate of craze growth increasing as the temperature is raised. The growth rate also depends on Kj when... 

Subcritical crack growth is determined by the temperature, the material, and, for the low-temperature processes, the environment. In a given system, the crack-growth rate frequently depends on the stress intensity factor K only. Below a certain, temperature-dependent limiting value Ajo, crack growth... 

It should be noted here that Equation (7.19a) and Equation (7.19b) are readily obtained from the Avrami equation (Eq. 7.6b) by simple integration by parts. Denoting the growth rate and nucleation rate temperature dependencies as g(T) and /(T), respectively, and assuming that the temperature T is a linear function of time t, one obtains the following expressions for expectancy E T), for the temperature-dependent nucleation rate and for the instantaneous nucleation, respectively ... 

The applications of this simple measure of surface adsorbate coverage have been quite widespread and diverse. It has been possible, for example, to measure adsorption isothemis in many systems. From these measurements, one may obtain important infomiation such as the adsorption free energy, A G° = -RTln(K ) [21]. One can also monitor tire kinetics of adsorption and desorption to obtain rates. In conjunction with temperature-dependent data, one may frirther infer activation energies and pre-exponential factors [73, 74]. Knowledge of such kinetic parameters is useful for teclmological applications, such as semiconductor growth and synthesis of chemical compounds [75]. Second-order nonlinear optics may also play a role in the investigation of physical kinetics, such as the rates and mechanisms of transport processes across interfaces [76]. 

Effects of Rate Conditions. It is essential for commercial a-quartz crystals to have usable perfection growth at a high rate and at pressure and temperature conditions that allow economical equipment design. The dependence of rate on the process parameters has been studied (8,14) and may be summarized as follows. Growth rate depends on crystallographic direction the (0001) is one of the fastest directions. Because AS is approximately linear with AT, the growth rate is linear with AT. Growth rate has an Arrhenius equation dependence on the temperature in the crystallization zone ... 

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