Kinetics phase transformations

H. Qu, M. Louhi-Kultanen, J. Rantanen and J. Kallas, Solvent-mediated phase transformation kinetics of an anhy-drate/hydrate system, Cryst. Growth Des., 6, 2053-2060 (2006). 

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. 

CHEMICAL REACTION AND PHASE TRANSFORMATION KINETICS IN SOLIDS... 

Avrami Analysis The Avrami equation, a general approach for description of isothermal phase transformation kinetics originally developed for polymers (46), is often used for describing nucleation and crystal growth in fats. The Avrami equation is given as... 

Much of the work to date on particle size effects on phase transformation kinetics has involved materials of technological interest (e.g., CdS and related materials, see Jacobs and Alivisatos, this volume) or other model compounds with characteristics that make them amenable to experimental studies. Jacobs and Alivisatos (this volume) tackle the question of pressure driven phase transformations where crystal size is largely invariant. In some ways, analysis of the kinetics of temperature-motivated phase transformations in nanoscale materials is more complex because crystal growth occurs simultaneously with polymorphic reactions. However, temperature is an important geological reality and is also a relevant parameter in design of materials for higher temperature applications. Thus, we consider the complicated problem of temperature-driven reaction kinetics in nanomaterials. 

When a surfactant-water or surfactant-brine mixture is carefully contacted with oil in the absence of flow, bulk diffusion and, in some cases, adsorption-desorption or phase transformation kinetics dictate the way in which the equilibrium state is approached and the time required to reach it. Nonequilibrium behavior in such systems is of interest in connection with certain enhanced oil recovery processes where surfactant-brine mixtures are injected into underground formations to diplace globules of oil trapped in the porous rock structure. Indications exist that recovery efficiency can be affected by the extent of equilibration between phases and by the type of nonequilibrium phenomena which occur (J ). In detergency also, the rate and manner of oily soil removal by solubilization and "complexing" or "emulsification" mechanisms are controlled by diffusion and phase transformation kinetics (2-2). 

The duration of t depends, in particular, on how distant from Tn the configurative point is, i.e. on the degree of overheating (T — Tn) or overcooling (Tn —T). Problems associated with the induction period are discussed in the literature on phase transformation kinetics. 

With respect to the dynamics, both solid-state NMR and DS revealed a relatively immobile core within the crystalline phase. Perylene derivatives that do not crystallize undergo an isotropic liquid-to-glass transformation at a temperature that was found to depend on the number of methylene units in the alkyl chains. The phase transformation kinetics from the high temperature isotropic phase to the crystalline phase at lower temperatures revealed a long-lived metastable state as a result of the soft potential. The crystalline phase is formed via nucleation and growth. The transformation kinetics is controlled by the nucleation barriers. The existence of slow molecular dynamics and of very slow phase transformation suggests that care should be taken in establishing the equilibrium phases of discotic liquid crystals. 

T. Feldmann and G.P. Demopoulos, Phase Transformation Kinetics of Calcium Sulfate Phases in Strong CaC -HCl solutions, Hydrometallurgy, 2012 (Article In Press), DOT 10.1016/j.hydromet.2012.08.015... 

Weinberg (1992a), Weinberg et al. (1997), and Zanotto (1997), reported in detail on transformation kinetics via nucleation and crystal growth. The standard theory of this type of phase transformation kinetics was developed by Johnson and Mehl and Avrami and Kolmogorov (see Weinberg et al., 1997). Therefore, this theory is called the JMAK theory. The JMAK equation (Eq. 1-6) is universal and applicable to glass-ceramics. 

The macroscopic development of crystallinity in polymers, is generally described by the following equation obtained from the classical theory of Avarmi for phase-transformation kinetics [1] ... 

Source W.W. Cias, Phase Transformation Kinetics, Microstructures, and Hardenability of the T]-6Ai-2Sn-4Zr-6Mo Titanium Ailoy," Rp-27-71 -02, Climax Molytxlenum, 2 March 1972... 

---