The Kinetics of Phase Transformations

For the sake of simplicity, let us first eonsider the soUdifieation of a pure material, assuming that nuclei of the solid phase form in the interior of the liquid as atoms cluster together so as to form a packing arrangement similar to that foimd in the solid phase. 

Figpre 10.1 Schematic diagram showing the nucleation of a spherical solid particle in a Uquid. 

Total free energy change for a solidification transformation 

For homogeneous nucleation, critical radius of a stable solid particle nucleus 

substitution of this expression for r into Equation 10.1 yields the following expression for AG  

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Measured surface areas (11-point BET analyses) for pure phases such as ferrihydrite, goethite and hematite are in the range as proposed by Cornell Schwertmann (2003) (Table 1). Preliminary XRD analyses showed that temperature impacts the kinetics of phase transformation of ferrihydrite. Data indicated that after seven days, the rate of transformation from ferrihydrite to more crystalline forms, if it was occurring, was too slow to be measured at 25°C (Fig. 1). In contrast to the 25°C experiment, significant, transformations were observed at 50 (Fig. 2) and 75°C (Fig. 3) after 24... 

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). 

In the processing of nanoparticles, coarsening is common, and may be accompanied by phase transformation to the macroscopic stable structure. Here we will focus on the kinetics of phase transformations and crystal growth in nanocrystalline particles. We will show later that conventional kinetic models that are widely employed for analysis of macroscopic materials behavior may have to be modified prior to their application to nanomaterials. 

J. Burke, The Kinetics of Phase Transformations in Metals, Pergamon, Oxford, 1965. 

The activation energy of the phase transformations of silica was estimated on the basis of the equations describing the kinetics of phase transformations (Emanuel and Knorre 1984). Similar results were obtained in the laboratory under hydrothermal conditions (Mizutani 1966). 

Only a few generalities can be advanced regarding the kinetics of phase transformation. Constant temperature solution mediated transformations typically proceed much faster than do those in the solid state. The rate of a solution mediated transformation is proportional to the solubility of the species involved, and this is particularly true of the relaxation transformations previously mentioned. Some transformations that proceed rapidly and are apparently occurring in the solid state may be taking place in the absorbed water layer or in the amorphous fractions. Hydrate transformations can be thought of as reactions that are not necessarily occurring in the solid state, since the water may be in the vapor phase. These may even be considered as solution mediated, which would explain the relative rapidity with which many hydration/ dehydration reactions occur. 

Many phenomena have inherently long time scales. Examples include the kinetics of phase transformations, and the deformation of high viscosity materials including many... 

Differential Scanning Calorimetry (DSC) has become a convenient and widely used tool for studying the kinetics of phase transformations. The volume fraction (x) of the sample transformed in crystalline phase during the crystallization event has been obtained from the DSC curve as a function of temperature (T). The volume fraction of precipitated crystal can be obtained from the DSC curve by using... 

At low and medium supersaturations, hydrophilic cations form different crystal hydrates by heterogeneous nucleation and subsequent crystal growth and phase transformation. Dehydration curves give information on the modes of water incorporation resulting from different modes of crystallization. A useful application of thermal analysis is the analytical approach by determining the mass loss due to dehydration, it was possible to quantitatively determine the proportion of different calcium oxalate hydrates in mixtures, which have been qualitatively analyzed by other techniques (X-ray powder diffraction, IR spectroscopy, etc.). The method yielded excellent results in studies of the kinetics of phase transformation and has been successfully used to demonstrate the potential of surfactant micelles to control the nature of the crystallizing phase. 

It is important to note that the treatments relating to the kinetics of phase transformations in Section 10.3 are constrained to the condition of constant temperature. By way of contrast, the discussion of this section pertains to phase transformations that occm with changing temperatirre.This same distinction exists between Sections 10.5 (Isothermal Transformatiorr Diagrams) and 10.6 (Continuous-Cooling Transformation Diagrams). 

Crystallization of Blends The first polymer blend was made from two polymeric mbbers in 1846, but polymer blend technology and a scientific understanding of the underlying principles controlling the compatibility (or lack of) in polymer mixtures (alloys as they have been named recently) has taken place only in the latter part of the current century. Many blends are non-crystalline but our interest in this document is focused on the kinetics of phase transformations of binary and ternary systems that receives more attention annually. Some of these systems can be very complicated, often comprised of multiple phases that m involve homopolymers, copolymers, mesophases and the like. Polymorphism and even isomorphism may occur... 

The kinetics of phase transformation and wear resistance of in-situ processed titanium matrix composites based on B-Fe-Ti has been studied by [1999Bra]. The sintering parameters employed when using the powder metallurgical route were improved with the aim of increasing wear resistance. 

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