Isothermal transformation characteristics

In the description of the principle of this method in Chapter 2 it was explained that a knowledge of the transformation behaviour of a steel made it possible to control the cooling of the weld HAZ and so to produce certain preferred, i.e. less crack sensitive, microstructures. To use this technique it is necessary to know the isothermal transformation characteristics of the steel. These may be obtained from the steel-makers data sheets or from one of the collections of such data. As explained in Chapter 2, a temperature is selected... 

Phil] Philips, C.W., Frey, D.N., Isothermal Transformation Characteristics of an Iron-Chromium Alloys of Titanium , J. Metals, 4(4), 381-385 (1952) (Crys. Structure, Experimental, Morphology, Phase Relations, 6)... 

The combination of low-aluminum, medium-zirconium, and high-tin strengthens and stabilizes the alpha phase. Considerable strengthening at all temperatures is derived from the active eutectoid compound TixSiy. The alloy may be classified as both a weakly stabiHzed, martensitic alloy and an active eutectoid. It displays the isothermal transformation characteristics of two-phase titanixim alloys. 

Finally, at even lower transformation temperatures, a completely new reaction occurs. Austenite transforms to a new metastable phase called martensite, which is a supersaturated solid solution of carbon in iron and which has a body-centred tetragonal crystal structure. Furthermore, the mechanism of the transformation of austenite to martensite is fundamentally different from that of the formation of pearlite or bainite in particular martensitic transformations do not involve diffusion and are accordingly said to be diffusionless. Martensite is formed from austenite by the slight rearrangement of iron atoms required to transform the f.c.c. crystal structure into the body-centred tetragonal structure the distances involved are considerably less than the interatomic distances. A further characteristic of the martensitic transformation is that it is predominantly athermal, as opposed to the isothermal transformation of austenite to pearlite or bainite. In other words, at a temperature midway between (the temperature at which martensite starts to form) and m, (the temperature at which martensite... 

In an amorphous material, the aUoy, when heated to a constant isothermal temperature and maintained there, shows a dsc trace as in Figure 10 (74). This trace is not a characteristic of microcrystalline growth, but rather can be well described by an isothermal nucleation and growth process based on the Johnson-Mehl-Avrami (JMA) transformation theory (75). The transformed volume fraction at time /can be written as... 

Stoeckli (1981), McEnaney and Mays (1991), Hutson and Yang (1997) and others (see Rudzinski and Everett, 1992) have attempted to provide a theoretical basis for the DR and DA equations in terms of an integral transform or a generalized adsorption isotherm, which may be expressed in the form of Equation (4.52). However, in practice the DR and DA equations are usually applied empirically and consequently the derived quantities (micropore volume, characteristic energy and structural constant) are not always easy to interpret. 

Simulations—isoergic and isothermal, by molecular dynamics and Monte Carlo—as well as analytic theory have been used to study this process. The diagnostics that have been used include study of mean nearest interparticle distances, kinetic energy distributions, pair distribution functions, angular distribution functions, mean square displacements and diffusion coefficients, velocity autocorrelation functions and their Fourier transforms, caloric curves, and snapshots. From the simulations it seems that some clusters, such as Ar, 3 and Ar, 9, exhibit the double-valued equation of state and bimodal kinetic energy distributions characteristic of the phase change just described, but others do not. Another kind of behavior seems to occur with Arss, which exhibits a heterogeneous equilibrium, with part of the cluster liquid and part solid. 

The in situ Raman spectroscopy method has also been used to study the particle size-dependent molecular rearrangements that take place during the dehydration of trehalose dihydrate.73 Different phases were sieved into fractions <45-pm and >425-pm particle size, and the Raman spectra obtained at various times during an isothermal heating at 80°C. After being heated for 210 minutes, the <45-pm dihydrate material appeared to become amorphous while the >425-pm dihydrate material transformed into the crystalline anhydrate phase. Ratios of various characteristic scattering peaks were used to follow the kinetics of the phase transformations. 

Rhee et al. developed a theory of displacement chromatography based on the mathematical theory of systems of quasi-linear partial differential equations and on the use of the characteristic method to solve these equations [10]. The h- transform is basically an eqmvalent theory, developed from a different point of view and more by definitions [9]. It is derived for the stoichiometric exchemge of ad-sorbable species e.g., ion exchange), but as we have discussed, it can be applied as well to multicomponent systems with competitive Langmuir isotherms by introducing a fictitious species. Since the theory of Rhee et al. [10] is based on the use of the characteristics and the shock theories, its results are comprehensive e.g., the characteristics of the components that are missing locally are supplied directly by this theory, while in the /i-transform they are obtained as trivial roots, given by rules and definitions. 

In the isothermal cycle described above, the net work produced in the irreversible cycle was negative, that is, net work was destroyed. This is a fundamental characteristic of every irreversible and therefore every real isothermal cyclic transformation. If any system is kept at a constant temperature and subjected to a cyclic transformation by irreversible processes (real processes), a net amount of work is destroyed in the surroundings. This is in fact a statement of the second law of thermodynamics. The greatest work effect will be produced in a reversible isothermal cycle, and this, as we have seen, is Wcy = 0. Therefore we cannot expect to get a positive amount of work in the surroundings from the cyclic transformation of a system kept at a constant temperature. 

Kinetic and hydrodynamic analyses, and methods for the calculation of the parameters of industrial reactors are sufficiently developed today [2-6]. Computer simulation is also popular because if we know the kinetic and hydrodynamic parameters of processes and the principles of reactor behaviour, it is not a problem to calculate process characteristics and final product performance. This principle is an adequate tool for the description of low and medium rate chemical transformations with uniform concentration fields and isothermic conditions which are easy to achieve. In this case, it is easy to calculate and control all the characteristics of a chemical process under real conditions. 

The basic idea is to develop expressions for common thermodynamic quantities in terms of fluctuations in a system open to all species. The key lies in the fact that the fluctuating quantities characteristic of the grand canonical ensemble can then be transformed into expressions, which provide properties representative of the isothermal isobaric ensemble. Using an equivalence of ensembles argument, one can then consider these fluctuations to represent properties of small microscopic local regions of the solution of interest. This approach can be used to understand many properties of isobaric, isochoric, or osmotic systems in terms of particle number (and energy) fluctuations. 

From Equation 2.91 and Equation 2.92, it is clear that for every pair of values for X andp (i.e., for every point on the adsorption isotherm), there is a corresponding pair of values of and W (i.e., a point on the characteristic curve). Because , the adsorption potential, is independent of temperature, the characteristic curve will correspond to points on adsorption isotherms for a given vapor on a given adsorbent for all temperatures. This means that the equivalence of adsorption isotherms for a given vapor on a given adsorbent at different temperatures can aU be transformed, point by point, to a single characteristic curve. Alternatively we can say that from a known characteristic curve, which can be obtained from the isotherm measured for a single temperature, it is possible to obtain isotherms at any other arbitrary... 

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