Kinetics of first Other Phase Transitions Bu Vitaly V Slezov
Phase transitions of first-order are phenomena, widely occurring in nature. Among them are: evaporation and condensation, melting and solidification, sublimation and condensation into a solid phase, some structural transitions in the solid state, transitions connected with the decomposition into different phases in multicomponent liquid and solid systems, etc.
The classical explanation of the questions why and when phase transitions of first-order take place was based on thermodynamic concepts, which has been developed already more than hundred years ago. In the first half of the 20th century, huge efforts have been undertaken to determine not only why and when the phase transition takes place, but how it proceeds. To answer this question not only thermodynamics but also kinetic theories had to be developed and applied. An example was the classical theory of nucleation of the evolving phase which goes back to the 30th of the last century and is due to Becker and Döring, Kaischew and Stranski, Frenkel and Zeldovich and others.
First-order phase transformations in a system starting from a metastable initial state proceed via the new-phase nucleation mechanism. The kinetics of such phase transformation can be usually divided into three stages. Let us consider a system supersaturated with certain species inducing a diffusive mass transfer (e.g. by the atoms of a dissolved material in the process of precipitation of other phases from a supersaturated solid or liquid solution; or by vacancies and interstitial atoms in the growth of pores and dislocation loops, or by the atoms of a gas in the growth of gas-filled bubbles etc.). The first stages of decomposition, when the supersaturation, for example, with point defects is large enough, is characterized by intensive generation of viable nucleation centers larger than some critical size. At this stage, the amount of material in the nucleation centers is small, compared with that in the solution, and the supersaturation is essentially constant.
The second transient, or intermediate, stage of the decomposition process begins when the amount of material in the new phase becomes comparable with the initial quantity thus resulting in a decrease of the supersaturation. At this stage, the number of precipitates is practically constant and the volume of the new phase increases mainly through the independent growth of the precipitates.
Finally at the third, late stage of the phase transition, when the already formed aggregates of the newly evolving phase become large enough to allow to essentially decrease the supersaturation, surface tension and the conservation laws for atom species or point defects begin to play a crucial role in the phase transformation, thus resulting in a specific mechanism of the kinetics of new phase growth. This stage of the phase transformation was originally discovered in the analysis of decomposition of metastable solutions by Ostwald in 1900. This late stage of diffusive decomposition of dispersed systems is characterized by an increase in the mean size of new phase macroscopic centers, as a result of diffusive mass transfer from the smaller- to the larger-sized centers, the larger-sized centers “devouring” the smaller ones. From a thermodynamic point of view, this behavior is due to a decrease of the free energy of the system as a consequence of a reduction of the interfacial area and the surface energy contributions to the thermodynamic functions. Stochastic generation of new stable nucleation centers at this stage is highly improbable since they must be macroscopic in size. A considerable “diffusive” interaction between grown-up centers of the new phase appears, since each particular center “feels” the self-consistent diffusion field of the entire ensemble of point- and macrospecies of the new phase.
This phenomenon is commonly denoted as “Ostwald ripening” or, more frequently, as “coarsening”, or sometimes as “coalescence”, though the latter term is, in fact, inadequate. Although the late stage of the phase transition (or decomposition of the originally existing phase), determined by the diffusive interaction between new phase centers, has been analyzed by many authors, an incomplete set of equations has usually been solved, giving size distribution functions which did not obey the law of conservation of point defects. The detailed kinetics of a dispersed system cannot be revealed within such a reduced theoretical framework. The author, together with I.M. Lifshitz, had the opportunity to work out the theory of this late stage in the 50th of the last century giving a first correct solution of these highly non-linear problems.
The book presents the complete description of all three stages of first-order phase transitions, thus allowing one to model the whole course of the first-order phase transition kinetics. Special attention is given to transient stages in nucleation characterized by the establishment of steady-state conditions of nucleation and the determination of the time required for its approach and period of existence of the different stages of the nucleation-growth process.
Phase transformation processes may also proceed through the process of spinodal decomposition of an initially unstable phase. To this end the system should be quickly driven into the totally unstable state. The last chapter of the book deals with the kinetics of the spinodal decomposition. It is interesting that also in this case the whole process can be subdivided into three stages, in some way analogous to the transition in metastable system. Moreover, it is shown that both nucleation-growth and spinodal decomposition processes can be described in a unique way in terms of a generalized cluster model accounting appropriately for both size and composition (or density) changes of the clusters of the newly evolving phase in the course of their evolution to the respective macrophases.
The theoretical results obtained are illustrated in the book by experimental evidences. First of all it concerns the processes of phase decomposition in multicomponent systems, including isotope mixtures of solid helium.
In the course of the work on different aspects of the kinetics of phase formation, I had the pleasure to work together with a number of colleagues. To all of them I would like to express here my sincere thanks. In particular, it is a pleasure to thank the Scientific Editor of this book, Dr. Jürn W. P. Schmelzer, for his advices and gracious assistance in so many ways in the preparation of the present book for publication.
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