Metastable phase equilibria and kinetics

Obviously the sea is an open, dynamic system with variable inputs and outputs of mass and energy for which the state of equilibrium is a construct. As we have seen, the concept of free energy, however, is no less important in dynamic systems. In considering equilibria and kinetics in ocean systems, it is useful to recall that different time scales need to be identified for the various processes. When a particular reaction of a phase or species has—within the time scale of consideration—a negligible rate, it is permissive to define a metastable equilibrium state. Similarly, in a flow system the time-invariant condition of a well-mixed volume approaches chemical equilibrium when the residence time is sufficiently large relative to the appropriate time scale of the reaction. 

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. 

For a system that cannot follow the experimentally enforced (usually strong) changes, even by establishing the previously discussed metastable phase equilibria due to backward nucleation, the boundary lines shift almost freely along both the concentration and temperature axes. Thereby the regions of unstable phases are formed to be described in terms of the kinetics of the physical-chemical processes (especially fluxes of mass and heat). 

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. 

The approaches described previously assume that reactions will be suppressed, without giving any specific mechanism, and then rationalise the behaviour of the process using calculated metastable equilibria. A more innovative approach was taken by Saunders (1984) and Saunders and Miodownik (1985, 1987) for the prediction of phases formed by vapour co-deposition of alloys. It was postulated that the formation of phases on the substrate is controlled by the diffiisional breakdown of iiiUy intermixed depositing atoms so that three kinetic regimes are observed ... 

In analyzing the physicochemical conditions of metamorphism of complex heterogeneous stratified sequences it is necessary to take into account the possible existence of metastable but kinetically stable mineral associations, wide variations in the composition of the fluids in individual parts of the pile being metamorphosed, equilibria of mosaic character, and the presence of systems closed to water or with an insufficiency of it. These particulars require preliminary consideration of several controversial problems of the theory of metamorphism, especially reactions in the case of complex fluids and in the case of different pressures on the solid phases and fluid analysis of the processes in which H2O and COj take part at high pressures, when the properties of these very important volatile components become different, also seems to be very important. 

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