Phase transformation diagrams isothermal

Figure 4 presents the isothermal phase transformation diagram of the template-free syntheses in which the SiCL/Alo ratio and the time t of crytallization are varied. The Siof/Nafcr and l O/SiCL ratios are 10 and 30, respectively. The pentasil phase could only be synthesized for n = SiC /A O, =30-50 and t = 36 - 72 h. Outside of this area amorphous material, mordenite, sheet structures similar to kenyaite, quartz and crystobalite can be found. For values of n less than 25 the crytalline product is mordenite. For 30 < n < 50 a yield of 95% (related to the SiC content) ZSM-5 type, which was proved by X-ray diffraction pattern, could be found. Depending on n and the crystallization time, t, a more or less large amount of amorphous material is produced. This is shown in Figure 5. A long crystallization time causes recrystallization and is harmful to the yield of ZSM-5 products.

Figure 4. Isothermal phase transformation diagram of the template free syntheses. SS denotes sheet structures.

Fig. 1. Transformation diagram for 1 cured with sulfanilamide showing changes in morphology as a function of the cure time. This particular diagram shows the time at which phase transformations occur when the sample is cured isothermally at a given temperature. I, isotropic LC, liquid crystalline K, crystalline. Reprinted from Ref. 70, Copyright (1994), with permission from Elsevier Science.

Rousset [30] used a model called FEM-TTT. The software, based on a model originally developed for metal solidification [45,46], is able to calculate the kinetics of the phase transformation for any thermal path, using experimental isothermal crystallization kinetics data represented by the time-temperature-transformation (TTT) diagrams and an additivity principle, in a Cartesian bidimensional... 

Figure 14 Schematics of the additivity principles used for a model liquid-solid transformation. (a) The thermal path followed hy the sample is cut into small isothermal plateaus of duration 5f, where the isothermal data of the TTT diagram can be applied. ti d is the induction time, estimated for the transformation using an additivity principle. Once find has elapsed, phase transformation begins. EstimaAon of its progress is presented in (b). (b) Calculation of the evolution offs-fs is known at time step i - 1. The fictitious time tf corresponding to this solid fracAon on the curveis calculated, where /,7 (t) is the isothermal evolution of the solid fraction at the temperature T, of the sample at timestep i. The increment of sohd fracAon at time step i is then given by fs.Ti(f + 0 -fs.T,(tn...

In a eutectic reaction, as found in some alloy systems, a hquid phase transforms isothermally into two different solid phases upon cooUng (i.e., L + /3). Such a reaction is noted on the copper-silver and lead-tin phase diagrams (Figures 9.7 and 9.8, respectively). 

It is important to note that the treatments relating to the kinetics of phase transformations in Section 10.3 are constrained to the condition of constant temperature. By way of contrast, the discussion of this section pertains to phase transformations that occm with changing temperatirre.This same distinction exists between Sections 10.5 (Isothermal Transformatiorr Diagrams) and 10.6 (Continuous-Cooling Transformation Diagrams). 

In summary, isothermal and continuous-cooling transformation diagrams are, in a sense, phase diagrams in which the parameter of time is introduced. Each is experimentally determined for an alloy of specified composition, the variables being temperature and time. These diagrams allow prediction of the microstructure after some time period for constant-temperature and continuous-cooling heat treatments, respectively. 

Phase diagrams provide no information as to the time dependence of transformation progress. However, the element of time is incorporated into isothermal transformation diagrams. These diagrams do the following ... 

However, the situation is different if one considers the total transformation, including the solidus and peritectic type reactions where substantial solid state difflision is needed to obtain complete equilibrium. Unless very slow cooling rates are used, or some further control mechanism utilised in the experiment, it is quite common to observe significant undercooling below the equilibrium temperature of transformation. The following sections will briefly describe determinations of phase diagrams where non-isothermal techniques have been successfully used, and possible problems associated with non-equilibrium effects will be discussed. 

Fig. n.9. Isobaric isothermal ternary phase diagram containing process paths for an asymmetric transformation example. The two enantiomers are labeled R and S, and the solvent is labeled W. 

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