Thermodynamics of Metastability

The singularity of the single entropy function OH H D is absent from either of the two branches or in Sne( , V). 

At this moment, this is merely an assumption, which needs to be tested. We will show later by exact calculations that it is vaUd in these calculations. This is also the case in other exact calculations that have been carried out in our group [36,37,44, 46-48]. 

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The transformation of the crystalline into the glassy state by solid-state reactions is extensively reviewed in its theoretical and experimental aspects. First, we give some historical background and describe the thermodynamics of metastable phase formations, adding as well the kinetic requirements for the amorphization process. Then we discuss the different experimental routes into the amorphous state hydriding, thin diffusion couples, and other driven systems. In the discussion and the summary, we close the gap between the melting phenomena and the amorphization and provide a tentative outlook. 

Thermodynamics of Metastable Phase Equilibria and Metastable Phase Diagrams... 

Many classic explanations for the behavior of liquid bulk water have been developed [16-18]. A truly coherent picture of the thermodynamics of metastable water should make clear (a) the anomalous behavior of the thermodynamic parameters in the supercooled region, (b) the properties and nature of the transition between the two glassy phases LDA and HDA, and (c) the relationship between supercooled and glassy water. 

The interpretation of metastable phases in terms of Gibbsian thermodynamics is set out simply in a paper by van den Broek and Dirks (1987). 

Traditional solid-state synthesis involves the direct reaction of stoichiometric quantities of pure elements and precursors in the solid state, at relatively high temperatures (ca. 1,000 °C). Briefly, reactants are measured out in a specific ratio, ground together, pressed into a pellet, and heated in order to facilitate interdiffusion and compound formation. The products are often in powdery and multiphase form, and prolonged annealing is necessary in order to manufacture larger crystals and pure end-products. In this manner, thermodynamically stable products under the reaction conditions are obtained, while rational design of desired products is limited, as little, if any, control is possible over the formation of metastable intermediates. ... 

The temperature dependences of the isothermal elastic moduli of aluminium are given in Figure 5.2 [10]. Here the dashed lines represent extrapolations for T> 7fus. Tallon and Wolfenden found that the shear modulus of A1 would vanish at T = 1.677fus and interpreted this as the upper limit for the onset of instability of metastable superheated aluminium [10]. Experimental observations of the extent of superheating typically give 1.1 Tfus as the maximum temperature where a crystalline metallic element can be retained as a metastable state [11], This is considerably lower than the instability limits predicted from the thermodynamic arguments above. 

Although the formation of a large number of metastable materials that are far from equilibrium cannot be explained thermodynamically, thermodynamics predicts that they will with time transform to the stable phase or phase mixture, often via intermediate phases. More than one hundred years ago, Ostwald pointed out that... 

Vacuum Distillation.—The organic chemist must continually bear in mind that almost all substances with which he has to deal are, from the thermodynamical standpoint, metastable. In all cases, however, increased temperature favours the setting up of the true equilibrium—here decomposition—and hence it is appropriate to adopt the rule Never endanger substances unnecessarily. 

The isolation and/or NMR spectroscopic characterization of cr-complexes, as that shown by 1, have received considerable attention over the past two decades, because of the relationship between the formation of such adducts and that of the metastable cyclohexadienyl intermediates postulated in the S Ar mechanism. The detailed structures of these adducts are now well known, and their reactions, the kinetics and thermodynamics of their formation and decomposition, as well as their spectral properties have been investigated in detail5,11,12. Although these studies constitute an important contribution to the understanding of the intermediates involved in Ar, they will not be discussed in this chapter since they have been recently reviewed furthermore, most of the cr-adducts were formed by the addition of anionic nucleophiles13,5,11. 

The discussion above points out the importance of characterizing the degree of metastability of a monolayer before attempting to draw thermodynamic inferences from ir-A curves. Unfortunately, this precaution is mentioned only rarely in the monolayer literature. Undoubtedly, kinetic factors in molecular orientation are of great inherent interest, but first they should be clearly identified. 

Pritzker, M. D. and Yoon, R. H., 1984a. Thermodynamic calculations on sulphide flotation systems I. galena-ethyl xanthate system in the absence of metastable species. Inter. J. Miner. Process, 12 95 - 125... 

Fig. 8.6 Formation of metastable phases of higher Gibbs energy of formation during the discharge of Li FeSj. Upon recharging the electrode returns to the thermodynamically more favourable phases.

Kristiakova, K., Svec, P. Deanko, M. (2004) Cluster structure and thermodynamics of formation of (nano)crystalline phases in disordered metastable metallic systems. Mat. Sci. Eng. A 375-377,136. 

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. 

The aim of this chapter is to introduce the reader to some of the ways in which the CALPHAD approach has been combined with kinetics to predict the formation of phases and/or microstructures under conditions which are not considered to be in equilibrium. Broadly speaking, the combination of thermodynamics and kinetics can be broken down into at least two separate approaches (1) the calculation of metastable equilibria and (2) the direct coupling of thermodynamic and kinetic modelling. 

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