Case studies in phase transformations

Studying such phase transformations by conventional techniques (e.g., X-ray powder diffraction) may not be feasible for potent dmgs that are present in the formulation at low levels. Other methods may be more appropriate for such cases, like solid-state NMR techniques.57 The different analytical techniques used to study potential phase transformations will not be discussed here, because this is the focus of another chapter in this book. 

Currently, techniques for analyzing powder diffraction that involve the analytical dissection of measured Bragg reflection shapes " " can be used to derive a data set similar to that for a single crystal. As a result, crystal structures may be determined, and in some cases, refined anisotropically using powder diffraction data for X rays or neutrons. Powder diffraction methods can be used at a wide variety of temperatures and pressures and are well suited for studies of phase transformations. 

In the previous sections we have discussed two different applications of gas-phase catalysis. Although different in nature, both case studies had the common feature that (1) all employed educts and the obtained products were gaseous and (2) the change in volume of the gas phase resulting from the educt conversion is negligible. For a number of reactions, especially for reactions in the petrochemical industry both of the above-mentioned features cannot be neglected, we will discuss classic examples and present technical approaches to overcome the obstacles related to the chemical transformations. 

In the remainder of this article, discussion of surfactant dissolution mechanisms and rates proceeds from the simplest case of pure nonionic surfactants to nonionic surfactant mixtures, mixtures of nonionics with anionics, and finally to development of myehnic figures during dissolution, with emphasis on studies in one anionic surfactant/water system. Not considered here are studies of rates of transformation between individual phases or aggregate structures in surfactant systems, e.g., between micelles and vesicles. Reviews of these phenomena, which include some of the information summarized below, have been given elsewhere [7,15,29]. 

They usually suppose that the mobility of atoms at leaching temperature is too low to rearrange for the phase transformation. However, transformation has clearly occurred except in a few cases. One of the motivations for our research studies on Raney catalysts is to clarify what happens during the leaching process. 

Regardless of whether the non-imaging of a species is due to preferential field evaporation or to preferential field ionization, the distinguisha-bility of alloy components in ordered alloys makes much easier the identification of lattice defects and of all types of domains, such as orientational and translational domains, and the discernment of order-disorder phase boundaries in ordered alloys, as well as facilitating the study of clustering and order-disorder phase transformation, etc.88 In most cases, image interpretations become self-obvious. For example in PtCo, which has the LI 0 structure, a Co layer can be distinguished from a... 

An interesting class of exact self-similar solutions (H2) can be deduced for the case where the newly formed phase density is a function of temperature only. The method involves a transformation to Lagrangian coordinates, based upon the principle of conservation of mass within the new phase. A similarity variable akin to that employed by Zener (Z2) is then introduced which immobilizes the moving boundary in the transformed space. A particular case which has been studied in detail is that of a column of liquid, initially at the saturation temperature T , in contact with a flat, horizontal plate whose temperature is suddenly increased to a large value, Tw T . Suppose that the density of nucleation sites is so great that individual bubbles coalesce immediately upon formation into a continuous vapor film of uniform thickness, which increases with time. Eventually the liquid-vapor interface becomes severely distorted, in part due to Taylor instability but the vapor film growth, before such effects become important, can be treated as a one-dimensional problem. This problem is closely related to reactor safety problems associated with fast power transients. The assumptions made are ... 

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