New phase formation

ZeTdovich YaB (1943) On the theory of new phase formation cavitation. Acta Physicochim URSS 18 1-7... 

The above rate equations confirm the suggested explanation of dynamics of silver particles on the surface of zinc oxide. They account for their relatively fast migration and recombination, as well as formation of larger particles (clusters) not interacting with electronic subsystem of the semiconductor. Note, however, that at longer time intervals, the appearance of a new phase (formation of silver crystals on the surface) results in phase interactions, which are accompanied by the appearance of potential jumps influencing the electronic subsystem of a zinc oxide film. Such an interaction also modifies the adsorption capability of the areas of zinc oxide surface in the vicinity of electrodes [43]. 

These processes either lead to the formation of a new solid phase or the original solid phase grows or disappears. In addition to the electrochemical laws discussed earlier, this group of phenomena must be explained on the basis of the theory of new phase formation (crystallization, condensation, etc.). 

By way of illustration, we note that in the recombination problem mentioned above the energies of the electrons are the variables in the diffusion equation, the bottleneck is the region of energies near the boundary of the continuous spectrum, and the slowness of the process is related to the small amount of energy transfer from an electron to a heavy particle in one collision. In the problem of escaping electrons in a plasma, slowness is ensured by the weakness of the electric field, the independent variable in the diffusion equation is the momentum component along the field, and the bottleneck is determined, as in the kinetics of new phase formation, by the saddle point of the integral. 

Items a and c are pure hydrodynamic problems d is much closer to a physical chemist. However, in the present article, we shall consider only problem b, treating it as a particular case of the general theory of new phase formation. 

Volmer [3] was the first to pose the question of the consequences of Gibbs ideas for the kinetics of new phase formation. The most important conclusion is that the probability of formation of a nucleus depends on the supersaturation as exp(—A/kT). For condensation of a vapor, Volmer chose as a factor the number of collisions of vapor molecules (per unit time in a unit volume). In more recent papers by Farkas [4], Becker and Doring... 

Recently, Kramers [7] has generalized the theory of the intermediate state (activated complex) by considering systems which over the entire course of the transition are subjected to random exterior forces, so that the motion acquires the character of Brownian motion of a particle in a field of forces. In view of the high generality of Kramers derivations and their complexity, and for the sake of completeness of the present article, we shall give a simplified derivation of the equations,2 bearing in mind the processes of new phase formation in which we are interested. 

A new phase formation inside solid connects with a creation of solid-solid interfaces. A total process is controlled by a diffusion transport of the absorbed species to these interfaces. At these interfaces similar Eq. (66) should be used... 

Now possibilities of the MC simulation allow to consider complex surface processes that include various stages with adsorption and desorption, surface reaction and diffusion, surface reconstruction, and new phase formation, etc. Such investigations become today as natural analysis of the experimental studying. The following papers [282-285] can be referred to as corresponding examples. Authors consider the application of the lattice models to the analysis of oscillatory and autowave processes in the reaction of carbon monoxide oxidation over platinum and palladium surfaces, the turbulent and stripes wave patterns caused by limited COads diffusion during CO oxidation over Pd(110) surface, catalytic processes over supported nanoparticles as well as crystallization during catalytic processes. 

The new phases are characterized by considerable volume changes in relation to the basic material. The stresses occur on the interphase boundaries, and microcracks are formed. The example of such damage is metal embrittlement when forming hydride phases. The internal stresses also have an effect on kinetics of a new phase growth. Let us consider the residual stresses in a hollow cylinder. Maximal concentration of the impurity atoms occurs on the area boundary, where the new phase formation takes place. Its further growth is realized at the expense of impurity atoms diffusion. The task of defining kinetics of the new phase growth in the hollow cylinder is mathematically formulated as follows... 

Sha ML, Wu GZ, Liu YS et al (2009) Drastic phase transition in ionic liquid [Dmim][Cl] confined between graphite walls new phase formation. J Phys Chem C 113 4618 622... 

In agreement with eq. (IV. 15) the work of critical nucleus formation is inversely proportional to the second power of the supersaturation, and thus a noticeable supersaturation is required for a new phase to spontaneously form in homogeneous system. The frequently observed new phase formation that occurs at low supersaturation (and even in the absence of the latter) is caused by the presence of foreign inclusions, that cause the process to follow the heterogeneous path. 

Zeldovich, Y. B. (1942) Theory of new-phase formation Cavitation, J. Exp. Theor. Phys. (USSR) 12, 525-538. 

S, A, Kukushkin and A, V. Osipov. New phase formation on sohd surfaces and thin film condensation. Prog. Surf. Set, 5 1-107, 1996... 

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