Phase transformations, nucleation rate

Fig. 1.10. Nucleation rate J (nuclei/volume time) as a function of the temperature of the phase transformation water ice (Fig. 4 from [ 1.6]).

Addition of Nb into the Fe-Co-Si-B system from the previous case leads to transformation of 40 vol.% into grains of bcc-Fe(Co) with dimensions 30nm (Fig. 2). Even smaller nanograins of bcc-Fe(Mo), not exceeding 8nm are obtained by crystallization of Fe-Mo-Cu-B (Fig. 3), where the stability of the clustered amorphous remains keeps the content of nanocrystalline phase lower than 25 vol.% till almost lOOOK. The reasons for this behavior can be traced to drastically enhanced nucleation rate via heterogeneous or instantaneous nucleation, which can decrease the amount of nanocrystallized volume in the first transformation stage even below 20 vol.% [5]. 

The scope of kinetics includes (i) the rates and mechanisms of homogeneous chemical reactions (reactions that occur in one single phase, such as ionic and molecular reactions in aqueous solutions, radioactive decay, many reactions in silicate melts, and cation distribution reactions in minerals), (ii) diffusion (owing to random motion of particles) and convection (both are parts of mass transport diffusion is often referred to as kinetics and convection and other motions are often referred to as dynamics), and (iii) the kinetics of phase transformations and heterogeneous reactions (including nucleation, crystal growth, crystal dissolution, and bubble growth). 

Complex phase transformation requires nucleation, interface reaction, and mass transport the interplay of these factors controls the rate of complex phase transformations. Because nucleation, interface reaction, and mass transport are sequential steps for the formation and growth of new phases, the slowest step controls the reaction rate. Table 4-1 shows some examples of phase transformations and the sequential steps. 

Nucleation and Growth (Round 1). Phase transformations, such as the solidification of a solid from a liquid phase, or the transformation of one solid crystal form to another (remember allotropy ), are important for many industrial processes. We have investigated the thermodynamics that lead to phase stability and the establishment of equilibrium between phases in Chapter 2, but we now turn our attention toward determining what factors influence the rate at which transformations occur. In this section, we will simply look at the phase transformation kinetics from an overall rate standpoint. In Section 3.2.1, we will look at the fundamental principles involved in creating ordered, solid particles from a disordered, solid phase, termed crystallization or devitrification. 

In view of the importance of macroscopic structure, further studies of liquid crystal formation seem desirable. Certainly, the rates of liquid crystal nucleation and growth are of interest in some applications—in emulsions and foams, for example, where formation of liquid crystal by nonequilibrium processes is an important stabilizing factor—and in detergency, where liquid crystal formation is one means of dirt removal. As noted previously and as indicated by the work of Tiddy and Wheeler (45), for example, rates of formation and dissolution of liquid crystals can be very slow, with weeks or months required to achieve equilibrium. Work which would clarify when and why phase transformation is fast or slow would be of value. Another topic of possible interest is whether the presence of an interface which orients amphiphilic molecules can affect the rate of liquid crystal formation at, for example, the surfaces of drops in an emulsion. 

Temperature dependence of pearlite nucleation and growth rates in a 0.78% C, 0.63% Mn steel of ASTM grain size 5.25. Data from R. F. Mehl and A. Dube, Phase Transformations in Solids (New York Wiley, 1951), 545. Reprinted with permission of John Wiley Sons, Inc. 

Phase transformations in heterogeneous catalysis have been described recently by topochemical kinetic models [111-115]. These models were taken from solid chemistry, where they had been developed for "gas-solid reactions. The products of such reactions are solids. When gas is in contact with the initial solid, the reaction rate is negligible. But as nucleates of the phase... 

Nucleation and growth kinetics — Nucleation-and-growth is the principal mechanism of phase transformation in electrochemical systems, widely seen in gas evolution, metal deposition, anodic film formation reactions, and polymer film deposition, etc. It is also seen in solid-state phase transformations (e.g., battery materials). It is characterized by the complex coupling of two processes (nucleation and phase growth of the new phase, typically a crystal), and may also involve a third process (diffusion) at high rates of reaction. In the absence of diffusion, the observed electric current due to the nucleation and growth of a large number of independent crystals is [i]... 

The majority of polymorphic transformations can be described in terras of nucleation and growth [17]. The nuclei of a new phase are formed at one rate, and then grow at a second rate. Phase transformation is observed when these rates become significant, a process usually controlled by tenperature. 

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