Phase transformations, homogeneous

VACANCY-MEDIATED PHASE TRANSFORMATIONS HOMOGENEOUS OR HETEROGENEOUS ... 

Homogeneous LaMn03 nanopowder with the size of 19-55 nm and with the specific surface area of 17-22 m2/g has been synthesized using a surfactant, sodium dodecyl sulphate (SDS) to prevent agglomeration [47], The sonochemically prepared LaMn03 showed a lower phase transformation temperature of 700°C, as compared to the LaMn03 prepared by other conventional methods which has been attributed to the homogenization caused by sonication. Also, a sintered density of 97% of the powders was achieved for the sonochemically prepared powders at low temperature than that of conventionally prepared powders. 

Using this thermodynamic picture, classic nucleation and growth theory was used to describe the phase transformation that occurs in these materials, despite the relatively unique synthesis method that is employed. The governing equation for homogeneous nucleation that describes the change in free energy associated with the formation of a spherical crystalline nucleus in an amorphous host is as follows ... 

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). 

Name some kinetic problems that you have already encountered or you may encounter in the future in your research. Then decide whether they belong to (i) kinetics of homogeneous reactions (ii) mass transfer, or (iii) kinetics of heterogeneous reactions (including phase transformation). 

Conventional routes to ceramics involve precipitation from solution, drying, size reduction by milling, and fusion. The availability of well-defined mono-dispersed particles in desired sizes is an essential requirement for the formation of advanced ceramics. The relationship between the density of ceramic materials and the sizes and packing of their parent particles has been examined theoretically and modeled experimentally [810]. Colloid and surface chemical methodologies have been developed for the reproducible formation of ceramic particles [809-812]. These methodologies have included (i) controlled precipitation from homogeneous solutions (ii) phase transformation (iii) evaporative deposition and decomposition and (iv) plasma- and laser-induced reactions. 

By a change of temperature or pressure, it is often possible to cross the phase limits of a homogeneous crystal. It supersaturates with respect to one or several of its components, and the supersaturated components eventually precipitate. This is an additive reaction. It occurs either externally at the surfaces, or in the crystal bulk by nucleation and growth. Reactions of this kind from initially homogeneous and supersaturated solid solutions will be discussed in Chapter 12 on phase transformations. Internal reactions in the sense of the present chapter occur after crystal A has been brought into contact with reactant B, and the product AB forms isothermally in the interior of A or B. Point defect fluxes are responsible for the matter transport during internal reactions, and local equilibrium is often established throughout. 

The conditions for continuous phase transformations (described in Chapter 17) derive from considerations of the molar free energy of a homogeneous, spatially uniform system with no interfaces. For phase transformations involving nonconserved... 

F.K. LeGoues, H.I. Aaronson, Y.W. Lee, and G.J. Fix. Influence of crystallography upon critical nucleus shapes and kinetics of homogeneous f.c.c.-f.c.c. nucleation. I. The classical theory regime. In International Conference on Solid—>Solid Phase Transformations, pages 427-431, Warrendale, PA, 1982. The Minerals, Metals and Materials Society. 

The ring-opening of oxiranes, leading to the formation of isomeric carbonyl compounds by the action of acid catalysts as a result of rearrangement, is of continuing interest (refs. 1-4). However, most of these studies focus mainly on the transformations of terpene oxides or oxiranes with other functional groups in the liquid phase, under homogeneous reaction conditions. 

This chapter deals with the thermodynamics of one-phase systems, and it is understood that the phase is homogeneous and at uniform temperature. The basic structure of thermodynamics provides the tools for the treatment of more complicated systems in later chapters. This book starts with the fundamentals of thermodynamics, but the reader really needs some prior experience with thermodynamics at the level of undergraduate thermodynamics (Silbey and Alberty, 2001). Legendre transforms play an important role in this chapter, and the best single reference on Legendre transforms is Callen (1960, 1985). Other useful references for basic thermodynamics are Tisza (1966), Beattie and Oppenheim (1979), Bailyn (1994), and Greiner, Neise, and Stocker (1995). 

The phase transformations observed at very low sodium concentrations behave in the familiar fashion of numerous alloy systems. These all show lowering of the transition temperature with increasing solute concentration, the appearance of two phases at temperatures intermediate between the regions of homogeneity, and an orderly progression from lower to higher crystal symmetry as the temperature increases. 

Note that the residual stress aM — 0 on the elastic properties becomes homogeneous (Ef = Em = EL). While connections between the residual stresses and constituent properties are rigorous, experimental determination is still necessary, because ft is not readily predictable. In general, ft includes terms associated with the thermal expansion difference, ay— am, as well as volume changes that occur either upon crystallization or during phase transformations. For CVI systems, intrinsic stresses may also be present. 

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