Constant rate crystallization

It will be shown in a later section that the solution of a differential population balance requires a knowledge of tbe relationship between growth rate and size of the growing ciystals Moreover, this relationship can often be deduced from the form of population density deta. A special condition, which simplifies such belances, results when all crystals in the magma grow at (he sama constant rate. Crystal-solvent systems that show this behavior ate said to follow tha AL Law proposed by McCabe.1 while systetes that do not are said to exhibit anomalous growth. 

Here we have two opposing processes. At a given temperature, molecules leave the surface of the crystal at a constant rate, tending to increase the concentration in solution. On the other hand, dissolved molecules are continually striking the surface and precipitating, tending to... 

Kinetics over the Mo(lOO) Crystal Surface. We have studied the hydrodesulfurization of thiophene over the initially clean Mo(lOO) single crystal surface in the temperature range 520K - 690K and at reactant pressures of 100 Torr < P(H ) 800 Torr and 0.1 Torr P(Th) < 10 Torr. Under these conditions the reaction is catalyzed at a constant rate for a period of approximately one hour after which the rate begins to decrease with time. The rates reported here are all initial rates of reaction calculated from data collected in the period over which they remain constant. 

The polymer crystallization depends sensitively on the temperature Tc at which it occurs, more precisely on the degree of undercooling A T=Tm-Tc below the melting temperature Tm. Since we have to estimate Tm, at least roughly, of our lamellar crystal model, we first study the melting process of a lamella during the temperature increase at a constant rate. 

The primary nucleation process is divided into two periods in CNT one is the so called induction period and the other is the steady (or stationary) nucleation period (Fig. 2) [16,17]. It has been proposed by CNT that small (nanometer scale) nuclei will be formed spontaneously by thermal fluctuation after quenching into the supercooled melt, some of the nuclei could grow into a critical nucleus , and some of the critical nuclei will finally survive into macroscopic crystals. The induction period is defined as the period where the nucleation rate (I) increases with time f, whereas the steady period is that where I nearly saturates to a constant rate (fst). It should be noted that I is a function of N and t,I = I(N, t). In Fig. 2, N and N mean the size of a nucleus and that of the critical nucleus, respectively. The size N is defined... 

For crystal growth at constant rate, if the crystal composition can respond to interface melt composition through surface equilibrium, steady state may be reached (Smith et ah, 1956). At steady state, (dCldt) = 0 by definition. Hence,... 

During crystal dissolution at constant rate, some authors used an equation similar to Equation 4-43b to extract D values. However, because of the opposite sign for crystal dissolution versus growth, the concentration profile would be... 

Because is a function of t, the crystal grown from melt at constant rate will... 

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