Nucleation sequential process

Doubts about the impact on crystallization of such processes have already been raised by the present author in a paper that, very gracefully, Gert Strobl allowed to be published in parallel with his own contribution that presented a different viewpoint [8]. In that paper, the preeminence of a more classical nucleation and growth scheme (Fig. 1) was advocated crystallization is viewed as a more sequential process in which incoming stems probe the crystal growth face and are accepted if they fulfill the correct criteria. If not, the incoming stems are rejected or must undertake conformational adjustments. In other words, the classical nucleation and growth process can be seen as dominated or controlled by the crystal (substrate structure, or... 

Thin-film formation is described as a sequential process which includes nucleation, coalescence and subsequent thickness growth, whereby all states can be influenced by deposition parameters, such as temperature, pressure, gas flow rate, etc. [3,4], For physical vapour deposition (PVD) processes, significant works have been published and progess made in understanding the microstructure evolution of the films. In the atomistics of growth processes, there exists much in common bewteen CVD and PVD. Theories from PVD processes can thus be used to analyse the microstructure evolution of CVD processes [5, 6],... 

If this phase transformation is a sequential process where even crystalline phases are transformed to other crystalline phases, characteristic changes observable in the stability range (D) of phase I must correspond to the incubation period (BO for the second crystalline phase (II), where the nucleation of the subsequent product takes place. As a consequence, the recrystallization process (period E) of phase I and the growing period (CO of phase II are of the same time scale. This sequential recrystallization process finally leads to thermodynamically more stable products such as cristobalite and quartz. 

Polymer crystallization can be roughly divided into two sequential processes crystal nucleation and crystal growth. When the sizes of ordered domains generated by thermal fluctuations become so large that the trend to increase the surface free... 

Figure 4.9 illustrates the sequential process of nucle-ation, which shows AG(N) against N. AG (A ) corresponds to critical nano-nucleation. In the nucleation theory, the so-called net flow of nucleation (j) plays an important role in the nucleation process as illustrated in Figure 4.9 (also see Section 4.4). As the zero-th approximation, critical nano-nucleation should become the main controlling process with an activation barrier in nucleation following Eyring s kinetic theory of absolute reaction rate (theory of absolute reaction rate) [30]. Hence,y can be given by... 

The nucleation rate is calculated following the method of Frank and Tosi (39) by incorporating the assumptions outlined above. In this method a set of sequential processes, with forward and backward rates, is calculated, in this case starting at the critical size nucleus. The nucleation rate can then be written as (34)... 

A pre-factor 1/r contains a time scale r or a frequency which for instance corresponds to the hard phonon or to an atomic frequency. The growth rate of the crystal is proportional to this rate (23). As will be shown later, the nucleus once formed expands in a time scale shorter than the one necessary for nucleation. If the process consists of a series of sequential subprocesses, the global velocity is governed by the slowest one. Therefore, this nucleation process determines the growth rate of a faceted surface. 

Conceptually similar to those of Lahav are the experiments performed by Kon-depudi as well as by other groups working with saturated solutions of compounds, which exist in the crystal state in two enantiomorphous forms. In particular, the primary homogeneous nucleation process of the chiral crystals of sodium chlorate and sodium bromate is very slow compared to the sequential step of crystal growth. Kondepudi et al. (1990) and McBride et al. (1991) have demonstrated that when... 

Crystallization and reactivity in two-dimensional (2D) and 3D crystals provide a simple route for mirror-symmetry breaking. Of particular importance are the processes of the self assembly of non-chiral molecules or a racemate that undergo fast racemization prior to crystallization, into a single crystal or small number of enantiomorphous crystals of the same handedness. Such spontaneous asymmetric transformation processes are particularly efficient in systems where the nucleation of the crystals is a slow event in comparison to the sequential step of crystal growth (Havinga, 1954 Penzien and Schmidt, 1969 Kirstein et al, 2000 Ribo et al 2001 Lauceri et al, 2002 De Feyter et al, 2001). The chiral crystals of quartz, which are composed from non-chiral Si02 molecules is an exemplary system that displays such phenomenon. 

Kroto McKay 1988) (figure 8), which are transients and, by a process of further nucleation, yield fullerenes. Indeed, C60 could in theory be built up entirely from C4 (diyne) units by sequential cycloadditions (Kroto Walton 1992) (figure 9). 

Crystallization processes comprise two sequential steps crystal nucleation followed by crystal growth. Kondepudi et al. demonstrated in a series of experiments that spontaneous symmetry breaking may be induced by growing crystals of non-chiral molecules such as sodium chlorate, binaphthyl, and p, p -dimethyl-chalcone, which crystallize as enantiomorphous crystals of... 

A clear distinction between crystallisation and precipitation is not always possible from a practical point of view [57] hence, it is more convenient to consider precipitation as a very fast crystallisation process. Crystallisation is a result of the combined effects of nucleation, nucleus growth and secondary processes inside the suspension such as agglomeration, ageing and recrystallisation. Depending on the reaction conditions, the above processes can occur together or sequentially during the crystallisation period. 

Recall that, in nucleation theory [125-134], the size at which for the first time an island becomes more stable with the addition of just one more atom is defined as the critical island size i. In describing the statistical consequences of continuing this process of sequential trapping, in effect i = 1 in this calculation. 

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