Crystalline nuclei

Figure B3.3.10. Contour plots of the free energy landscape associated with crystal niicleation for spherical particles with short-range attractions. The axes represent the number of atoms identifiable as belonging to a high-density cluster, and as being in a crystalline environment, respectively, (a) State point significantly below the metastable critical temperature. The niicleation pathway involves simple growth of a crystalline nucleus, (b) State point at the metastable critical temperature. The niicleation pathway is significantly curved, and the initial nucleus is liqiiidlike rather than crystalline. Thanks are due to D Frenkel and P R ten Wolde for this figure. For fiirther details see [189].

Using this thermodynamic picture, classic nucleation and growth theory was used to describe the phase transformation that occurs in these materials, despite the relatively unique synthesis method that is employed. The governing equation for homogeneous nucleation that describes the change in free energy associated with the formation of a spherical crystalline nucleus in an amorphous host is as follows ... 

In this section we give a brief summary of the classical Becker-Doring theory of nucleation [39] and then implement the results for the polymer crystallization. Let a crystalline nucleus of radius r contain A repeat units such that... 

Finally the oligomers form a crystalline nucleus and the reaction becomes now exothermic due to the added heat of crystallization during simultaneous or successive polymerization and crystallization. The crystals of polyoxymethylene observed are hexagonal with the polymer chain peuallel to the c-axis (2,82). They increase with time in lateral dimensions as well as in thickness, taking a p5mmidal shape 82). The addition of new oligomers on the lateral surface would explain an autocatalytic acceleration of the reaction with time as well as the pyramidal shape 82). 

The rate of crystallite nucleation /(/ ) is described by a (6.54)-type expression, where N and AG ff are replaced by the critical crystalline nucleus size, N, and the free energy of nucleation, AG. ... 

The factor ip is determined by the so-called Volmer equation (24) (XIV), which involves the contact angle, between the crystalline nucleus (c) and the impurity (s). The latter is controlled by the interfacial energy, o , of the different phases (HQuid, I, crystalline nucleus, c, and solid impurity, s) (XV) and corresponds to the angle of wetting in solid-liquid systems. 

Fig. 3.11 Generation of a single crystalline nucleus by using a local variable...

The key property that makes phase change materials attractive for applications in nonvolatile memories is the fast crystallization which allows for a full crystallization in PCM devices on the time scale of 10-100 ns. The fact that both nucleation rate and crystal growth velocity are very large has stimulated direct simulations of the crystallization process by DFT-MD [13-16]. Simulations with up to 180-atom cell and periodic boundary conditions shed light on the atomistic mechanism of formation of the crystalline nucleus and on the role of four-membered rings as seeding structures for nucleation [13-16]. 

Primary nucleation is the process by which a crystalline nucleus is formed in the melt state. After the nucleus is formed, a new layer grows on the face of the existing one with a secondary nucleation, a process similar to primary nucleation. The crystallization does not stop with the growth of the crystals, but a process... 

Figure 8.9 (a) The difference between the probability of a crystalline nucleus to grow and... 

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