Nucleation frequency

Using the fluxing technique, Lau and Kui [33] determined that the critical cooling rate for forming a 7-mm diameter bulk amorphous Pd4QNi4()P2o cylinder was 0.75 K/sec. From this value, they estimated that the steady-state nucleation frequency was on the order of lO" m s. On the other hand, Drehman and Greer [34] estimated that the steady state nucleation frequency at 590 K is 10 m" s, which is also the maximum... 

The regime governed by coalescence was examined in more detail. The process of film rupture is initiated by the spontaneous formation of a small hole. The nucleation frequency. A, of a hole that reaches a critical size, above which it becomes unstable and grows, determines the lifetime of the films with respect to coalescence. A mean field description [19] predicts that A varies with temperature T according to an Arrhenius law ... 

Assuming that the pre-exponential factor in eq. (IV. 18) is determined by the ratio of the number of molecules per unit volume of metastable phase, n0, to the life time of critical nuclei, ta, let us examine how the nature of the phase transition influences the nucleation frequency. 

Figure 1. Spectrum of ice nucleation frequency displayed by a genetically homogeneous population of bacteria coli strain...

Macroscopic effects at boiling are associated with changes in the intrinsic characteristics of the process (e.g., bubble shape and sizes, nucleation frequency, etc.). Let s discuss the existing experimental data in more detail. 

The crystallization of an amorphous material proceeds by the processes of nucleation and growth, and the crystallization rate is suppressed by reducing either (or both) of these processes. We discuss first the kinetics of nucleation. Turnbull and Cohen, using nucleation theory and a number of assumptions, arrive at Eq. (1.1) (see Turnbull (1969)) as a reasonable upper limit to the nucleation frequency as a function of undercooling. 

Fig. 1.3 Dependence of the homogeneous nucleation frequency (I) on undercooling for various values of (after Turnbull (1969)).

For monatomic systems, the steady state nucleation frequency per unit volume in a clean system (homogeneous nucleation), neglecting strain energy (valid for the crystallization of a fluid), is given by the equation (Turnbull and Fisher (1949)),... 

We consider now heterogeneous nucleation, which is a nucleation catalyzed by the presence of foreign material. Important examples of such catalyzing materials are impurity particles (motes) and container walls. Theoretical analysis (see Turnbull (1956) for review) results in the equation (analogous to Eq. 1.15) for the heterogeneous nucleation frequency. 

The less energy that has to be expended for the recirculation process, the fewer crystal nuclei will be produced. The nucleation frequency is therefore the key to producing different crystal sizes (compare Figure 11.1). The designs of crystallizers also differ from one another mainly with respect to the specific amount of energy e, which has to be expended for the recirculation process. For the different types of crystallizers, these specific energy inputs vary from around 10 W/kg for the FC types down to 0.1-1 W/kg for the DTB types and to below 0.1 W/kg for the fluidized bed crystallizers. 

From this it can be deduced that when the rotating speed is reduced, that is, the tip speed is lowered, and there is a simultaneous increase in the size of the pump impeller, the energy of the collisions with the crystals also decreases. Consequently, the secondary nucleation frequency is lower and the mean crystal size increases. 

The nucleation rate or nucleation frequency, J, is the number of crystals that form in a supersaturated solution per unit of time and unit of volume. Here, we only need to recall that ... 

Figure 9.7 presents the time variations of the supersaturation profiles relatively for the CBZ and CBZ/NCT solid phases. The primary nucleation of CBZ/NCT first occurred at a supersaturation ratio 15% lower than the CBZ supersaturation ratio. A possible explanation lies in the fact that there may be a better affinity with the solvent of the CBZ/NCT nuclei than with that of the CBZ nuclei leading to a higher nucleation frequency of CBZ/NCT than CBZ. Ten minutes later, CBZ primary nucleation occurred. One could assume that the presence of the co-crystal form in suspension may favour a nucleation of CBZ crystals on the surface of CBZ/NCT solid form. 

---