Transformation, isothermal start

On cooling to an isothermal temperature below the martensite start (Mg) jwint of790 5 °C (1454 9 °F), first some a phase is formed above Mg and then the remaining, predominate portion of the p phase is transformed into a supersaturated hexagonal martensite (a"). Below Mg and above the martensite finish (Mf) temperature of 740 5 °C (1364 9 °F), there remains a residual P phase, which is probably transformed isothermally to a phase. The resulting structure for isothermal reaction is a + a", where the a" phase below 750 °C (1380 °F) decomposes discontinuously into a two-phase a + p structure and a metastable P phase enriched with p-stabilizing elements. 

However, since the kinetics of the phase transformations require a finite time to take place, the location where the phase transformation is finally completed is displaced behind the calculated isotherms. Thus, the calculated isotherms represent the point where the phase transformations can begin to occur the locations where the transformations are complete can be determined by SRXRD measurements. The difference between the calculated isotherms (start locations) and the SRXRD completion locations is related to the kinetics of a given phase transformation. 

Phase transformation j starts when the induction fraction, Sj, is equal to 1. This means that in the case of an isothermal transformation, transformation starts when the elapsed time is equal to the induction time at this temperature. 

The monolayer resulting when amphiphilic molecules are introduced to the water—air interface was traditionally called a two-dimensional gas owing to what were the expected large distances between the molecules. However, it has become quite clear that amphiphiles self-organize at the air—water interface even at relatively low surface pressures (7—10). For example, x-ray diffraction data from a monolayer of heneicosanoic acid spread on a 0.5-mM CaCl2 solution at zero pressure (11) showed that once the barrier starts moving and compresses the molecules, the surface pressure, 7T, increases and the area per molecule, M, decreases. The surface pressure, ie, the force per unit length of the barrier (in N/m) is the difference between CJq, the surface tension of pure water, and O, that of the water covered with a monolayer. Where the total number of molecules and the total area that the monolayer occupies is known, the area per molecules can be calculated and a 7T-M isotherm constmcted. This isotherm (Fig. 2), which describes surface pressure as a function of the area per molecule (3,4), is rich in information on stabiUty of the monolayer at the water—air interface, the reorientation of molecules in the two-dimensional system, phase transitions, and conformational transformations. 

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... 

To effectively determine the start-of-cycle reforming kinetics, a set of experimental isothermal data which covers a wide range of feed compositions and process conditions is needed. From these data, selectivity kinetics can be determined from Eq. (12). With the selectivity kinetics known, Eqs. (17) and (18a)-(18c) are used to determine the activity parameters. It is important to emphasize that the original definition of pseudomonomolecular kinetics allowed the transformation of a highly nonlinear problem [Eq. (5)] into two linear problems [Eqs. (12) and (15)]. Not only are the linear problems easier to solve, the results are more accurate since confounding between kinetic parameters is reduced. 

Let us discuss an L matrix transformation for isothermal and isobaric atomic fluxes when there is one additional electronic species present. We start with the flux equations in which the index j denotes the atomic species and e denotes the electric charge carriers (eg., electrons). 

Isothermal transformation of a 1080 steel. The left-hand line is for the observable start of the reaction and the right-hand line is for the essential completion of the reaction. Data from Atlas of Isothermal Transformation Diagrams (Pittsburgh U.S. Steel, 1951). 

Isothermal Transformation Diagram. To separate the effects of transformation temperature from those of heat flow, it is essential to understand the nature of the transformation of austenite at a given, preselected temperature below the A. Information needed includes the starting time, the amount transformed as a function of time, and the time for complete transformation. A convenient way to accomplish this is to form austenite in specimens so thin (usually about 1-mm thick) that heat flow is not an issue, rapidly transfer the specimens to a Hquid bath at the desired temperature, and foUow the transformation with time. The experiment is repeated at several other transformation temperatures. On the same specimens, the microstmcture and properties of the transformation products can be assessed. These data can be summarized on a single graph of transformation temperature versus time known as an isothermal transformation (IT) diagram or, more usually, a time—temperature—transformation (ITT) diagram. A log scale is used for... 

The basic equations of catalyst layer operation, Eqs. (42-46), are valid under the assumption of isothermal, stationary conditions. Furthermore, variations of the water vapor partial pressure are neglected. The water content in the PFSI fractions and the corresponding proton conductivity are, therefore, independent of x- Upon proceeding along x, starting at x = 0 with /p(X = 0) = jo, proton current is gradually converted into C>2 flux jo2 = (j-p(x) — y o)/4. At x = 1 the transformation is complete, yp = 0, since no protons are admitted to pass the interface to the GDF. 

Experimental time-temperature-transformation (TXT) diagram for Ti-Mo. Xhe start and finish times of the isothermal precipitation reaction vary with temperature as a result of the temperature dependence of the nucleation and growth processes. Precipitation is complete, at any temperature, when the equilibrium fraction of a is established in accordance with the lever rule. Xhe solid horizontal line represents the athermal (or nonthermally activated) martensitic transformation that occurs when the p phase is quenched. 

Method of p-x curves. Ravich s design of the autoclave makes it possible to isolate salt placed under a layer of mercury in a capsule with holes ((7) in Figure 1.9) from water or solution above mercury until the specified temperature at the starting pressure is reached. In the isothermal experiments with either change of composition of initial solution (case 1) with a constant amount of solid phase, or an amount of solid phase (case 2) with a constant amount and composition of initial solution, the resulting p-x curves reveal phase transformation. 

Isothermal TGA data are commonly analyzed in terms of the reaction models. The analysis starts by transforming mass-time to conversion-time plots. For transformation one can use Eq. (3.3) by replacing mr with m, which is the mass in a given moment of time. Figure 3.24 shows an a-t plot for the thermal... 

This behavior is similar to the Langmuir isotherm, except that it starts at 6 = 0.8 at Xb = 0 and it is inverted with respect to the horizontal line 9 = 0.8. If we make the transformation... 

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