Phase Equilibria and Metastability

I come now to the second leg of our notional tripod - phase equilibria. 

In the penultimate sentence, I have used the word phase . This concept was unknown to von Widmanstiitten, and neither was it familiar to Henry Sorby (1826 1908), an English amateur scientist who was the prime pioneer in the microscopic 

There are those who say nowadays that Gibbs s papers, including his immortal paper on heterogeneous equilibria, present no particular difficulties to the reader. 

The prehistory of the phase rule, the steps taken by Gibbs and the crucial importance of the rule in understanding phase equilibria, are outlined in an article published in a German journal to mark its centenary (Pelzow and Henig 1977). 

after the War, Tammann moved further towards physics by becoming interested in the mechanism of plastic deformation and the repair of deformed metals by the process of recrystallisation (following in the footsteps of Ewing and Rosenhain in Cambridge at the turn of the century), paving the way for the very extensive studies of these topics that followed soon after. Tammann thus followed 

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

Numerous investigations have been done regarding the liquidus surface, die isothermal sections and the vertical sections in the stable and metastable systems. The other investigations on die ternary system concern the solubility measurements of carbon in the "y and liquid phases which go always widi activity measme-ments, the determination of the phase diagram under high pressures and die kinetics studies of die austenite transformation in martensite or bainite because these phases are important in die forecast of mechanical properties of steel. The main experimental investigations on crystal structure, phase equilibria and thermodynamics are gathered in Table 1. 

The hydration equilibria and phase transformations associated with a cytotoxic drug, BBR3576, have been studied [72]. The initially hydrated form could be made to undergo a phase transition where it lost approximately half of its water content, but the hemidesolvated product could be easily rehydrated to regenerate the starting material. If however, the original sample was completely dehydrated, the substance first formed a metastable anhydrate phase that underwent an irreversible exothermic transition to a new anhydrate crystal form. The hydration of this latter anhydrate form yielded a new hydrate phase whose structure was different from that of the initial material. 

Thermo-Calc (Sundman et al. 1985, Andersson et al. 2002). ft features a wide spectrum of thermodynamic models, databases and modules making it possible to perform calculations on most problems involving phase equilibria (phase transformation, stable and metastable equilibria, etc.). The calculations are performed using databases produced by an expert evaluation of experimental data. There are thermodynamic databases available for many different systems and applications. 

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. 

AI is stable at lower temperature while A2 at higher temperature and the transition from A j to A 2 is accompanied by increase in molar volume. Both A j andA2 are denser than the liquid phase. If no metastable equilibria are observed, a P-T phase diagram for the system drawn. Each area of the P-T diagram labelled ... 

Compared with the solid and gaseous phases, the aqueous solution has numerous complications. Therefore, we will first mention methods by which one can predict the composition of the solution in the presence of a given solid and gaseous phase. Later we shall remember that the formulae already attributed to the solid phases are inadequate. There is sometimes a multiplicity of solids, each having the same formula but differing from each other in chemical behavior. Within this multiplicity of solid phases, all are metastable but one. Some kinds of metastable solids and metastable equilibria will be discussed later. 

Thermodynamic data form the basis for future theoretical developments, because the data represent the physical reality and they have been painstakingly obtained. Usually a period of several months (or even years) is required to construct an experimental apparatus and, due to long metastable periods, it is not uncommon to obtain only one pressure-temperature data point per 1 or 2 days of experimental effort. Phase equilibria data are presented in Section 6.3.1 for simple hydrates (Section 6.3.1.1), binary (Section 6.3.1.2), ternary (Section 6.3.1.3),... 

Metastable Equilibria The change of SR to SM occurs very slowly. If enough time for the change is not allowed and SR is heated rapidly, it is possible to pass well above the transition point (B) without obtaining SM. In that case, the curve AB extends to O. The curve AO is known as metastable vaporisation curve of SR. The phases SR and Sv will be in metastable equilibrium along this curve. It is a univariant system. 

It should be noted that both stable and metastable compounds may occur in reaction couples. Analysis of the available experimental data shows that the growth of metastable compound layers is observed relatively rarely. The possibility of formation of metastable compounds is usually mentioned in the explanatory text accompanying the equilibrium phase diagram of any binary system. For certain systems, diagrams of both stable and metastable equilibria have been proposed.142145193 215-225... 

It is instructive to consider the free-energy hierarchy and the metastable phase equilibria when crystallization of an amorphous material is discussed. Koster and Herold [56] discussed these aspects of crystallization and showed that crystallization reactions of amorphous alloys can be classified into the following three types polymorphic, primary and eutectic crystallization reactions. Among these three types, the slowest crystal growth process is expected for primary crystallization and thus, primary crystallization is ideal for tailoring fine microstructures upon decomposition of amorphous alloys. 

Similarly, the phase equilibria are known with certainty, and free energy measurements are available (although not as closely spaced as one might wish) to define the ferrous oxide phase as having continuity over a wide stoichiometric range at 1000° K. The evidence is incompatible with the idea that these and other compounds owe their existence to ordering processes or are metastable with respect to discrete intermediate phases. 

Fig. A.2. Sulfuric acid freezing point temperature versus mass % H2S04 in acid. The dashed lines show metastable phases. Source Gable, C.M., Betz, H.F. and Maron, S.H. (1950) Phase equilibria of the system sulfur trioxide-water, Journal of the American Chemical Society, Vol. 72, 1445 1448. www.chemistry.org...

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