Solid phase thermodynamic aspects

The thermodynamic aspects of hydride formation from gaseous hydrogen are described by means of pressure-composition isotherms in equilibrium (AG = 0). While the solid solution and hydride phase coexist, the isotherms show a flat plateau, the length of which determines the amount of H2 stored. In the pure P-phase, the H2 pressure rises steeply vfith increase in concentration. The two-phase region ends in a critical point T, above which the transition from the a- to the P-phase is continuous. The equilibrium pressure peq as a function of temperature is related to the changes AH° and AS° of enthalpy and entropy ... 

The thermodynamics of formation and transformation of a solid phase into another are characterized by two aspects, both of them explaining the difficulty to produce solids of homogeneous composition. The more important of these is nucleation The other is the tendency of certain components of the solid to diffuse to, or away from, surfaces. These aspects, however, cannot be considered in isolation. Chemical reactions involve the breaking of bonds and formation of new ones. This involves kinetically limited processes. In many cases, diffusion brings about additional kinetic limitations. The final result is the combination of the effects of all these processes. 

Solid-state electrochemistry is an important and rapidly developing scientific field that integrates many aspects of classical electrochemical science and engineering, materials science, solid-state chemistry and physics, heterogeneous catalysis, and other areas of physical chemistry. This field comprises - but is not limited to - the electrochemistry of solid materials, the thermodynamics and kinetics of electrochemical reactions involving at least one solid phase, and also the transport of ions and electrons in solids and interactions between solid, liquid and/or gaseous phases, whenever these processes are essentially determined by the properties of solids and are relevant to the electrochemical reactions. The range of applications includes many types of batteries and fuel cells, a variety of sensors and analytical appliances, electrochemical pumps and compressors, ceramic membranes with ionic or mixed ionic-electronic conductivity, solid-state electrolyzers and electrocatalytic reactors, the synthesis of new materials with improved properties and corrosion protection, supercapacitors, and electrochromic and memory devices. 

This seetion will deseribe the eurrent status of research in two different aspects of nanocrystal phase behaviom melting and solid-solid phase transitions. In the case of melting, thermodynamic considerations of smface energies can explain the redueed melting point observed in many nanoerystals. Strictly thermodynamic models, however, are not adequate to deseribe solid-solid phase transitions in these materials. 

The quality of thermodynamic models carmot be better than the quality of the data on which they are based. The quality aspect includes both the numerical values of the thermodynamic data used in the model and the completeness of the chemical model used, e.g., the inclusion of all the relevant dissolved chemical species and solid phases. For the user it is important to consider that the selected data set presented in this review (Chapters III and IV) is certainly not complete with respect to all the conceivable systems and conditions there are gaps in the information. The gaps are pointed out in the various sections of Part III, and this information may be used as a basis for the... 

The structure and arrangement of cellulosic chains play an important role in the formation of liquid crystals. At present, neither the conformation of cellulosics nor the solvent bound to the chain in the case of a lyotropic mesophase are known for these liquid-crystalline systems. Nevertheless, these structural features form the basis for a discussion of structural and thermodynamic aspects. Information on cellulosics is available for the two borderline cases next to the LC state, i.e., for the solvent built-in solid state as well as for the pure solid state, obtained by X-ray, NMR, and potential energy analysis on one side, and for the semi-dilute state from light-scattering experiments on the other side. These data have to be evaluated for a discussion of possible structures and models in liquid-crystalline phases. 

Liquid-solid and solid-solid phase transformations are also known as condensed-matter phase transformations. Condensed-matter phase transformations, like other kinetic processes, are driven by thermodynamics. When a region of matter can lower its total free energy by changing its composition, structure, symmetry, density, or any other phase-defining aspect, a phase transformation can occur. 

With regard to purity, the relevant aspect in the present context concerns the uniformity of the solid phase, that is, the absence of any excess of A or B. This is best ensured when the co-crystal is the only and thermodynamically most stable solid state form over the whole crystallization process. Therefore, in the case of cooling crystallization, the location of the co-crystal domain as a function of temperature becomes relevant for a systematic optimization of the crystallization process. Ideally the complete phase diagram of the system should be known with some accuracy. 

Thermodynamic Aspects of Solubility At equilibrium in a saturated solution, the chemical potential, or partial molal free energy, of the solute must be the same in the solution as in the solid phase. If we consider two different saturated solutions, there-fore, both in equilibrium with the same solid phase, the chemical potential of the solute must be the same in both. The chemical potential ( ) and activity (c) are related by the equation p — po — RT In o, where Po is the chemical potential of the substance in the standard state. Hence, if the same standard state is chosen for all the solutions considered, the activity of the solute must be the same in all. 

All of the theoretical considerations outlined above have been established assuming an ideal system without any boundary conditions. It should be pointed out, however, that in practice, all the studied systems, especially in SHE chemistry, have finite dimensions (time and volume). As only ideal system were considered, edge effects, pseudo-coUoid formation, sorption phenomena, redox processes with impurities or surfaces, medimn effects, etc., have not been taken into account. AU these effects, representing the most important part from the deviation from ideahty, cannot be predicted with formal thermodynamics and/or kinetics. Thus, radiochemists who intend to perform experiments at the scale of one atom must be aware that the presence of any solid phase (walls of capUlary tubes, vessels, etc.) can perturb the experimental system. It is important to check that these edge effects are negligible at tracer levels before performing experiments on the scale of an atom [4, 5]. The foUowing section describes experimental techniques used in SHE chemistry see Liquid-Phase Chemistry of Superheavy Elements and Gas-Phase Chemistry of Superheavy Elements for a detailed discussion of SHE chemistry experiments and Experimental Techniques for more technical aspects. 

Abstract The contact between a solid and a liquid involves the phenomenon of wetting. This is the intuitive, intimate contact between the two phases. We consider here thermodynamic aspects of wetting, which involves three phases in fact, since the environment must be taken into account. Methods for determining wetting characteristics are discussed. 

Chemical vapor deposition is a synthesis process in which the chemical constituents react in the vapor phase near or on a heated substrate to form a solid deposit. The CVD technology combines several scientific and engineering disciplines including thermodynamics, plasma physics, kinetics, fluid dynamics, and of course chemistry. In this chapter, the fundamental aspects of these disciplines and their relationship will be examined as they relate to CVD. 

The availability of thermodynamically reliable quantities at liquid interfaces is advantageous as a reference in examining data obtained by other surface specific techniques. The model-independent solid information about thermodynamics of adsorption can be used as a norm in microscopic interpretation and understanding of currently available surface specific experimental techniques and theoretical approaches such as molecular dynamics simulations. This chapter will focus on the adsorption at the polarized liquid-liquid interfaces, which enable us to externally control the phase-boundary potential, providing an additional degree of freedom in studying the adsorption of electrified interfaces. A main emphasis will be on some aspects that have not been fully dealt with in previous reviews and monographs [8-21]. 

The basic question is how to perform extrapolations so as to obtain a consistent set of values, taking into account various complications such as the potential presence of mechanical instability. Additional complications arise for elements which have a magnetic component in their Gibbs energy, as this gives rise to a markedly non-linear contribution with temperature. This chapter will concern itself with various aspects of these problems and also how to estimate the thermodynamic properties of metastable solid solutions and compound phases, where similar problems arise when it is impossible to obtain data by experimental methods. 

At particular critical points (Tq, Pc) on the phase diagram of a substance, two phases can be found in thermodynamic equilibrium. Therefore, upon application of a pressure or a temperature gradient, a transformation occurs from one phase into the other. This is a phase transition, in many aspects similar to a transformation implying the change of aggregation state. However, the extent of the changes in a solid to solid transformation is much smaller. For example, latent heat or latent volumes associated with the transformations are quite small, sometimes even difficult to detect. 

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