Transformation rate temperature dependence

Temperature plays an important role in the rate of the austenite-to-pearlite transformation. The temperature dependence for an iron-carbon alloy of eutectoid composition is indicated in Figure 10.12, which plots S-shaped curves of the percentage transformation versus the logarithm of time at three different temperatures. For each curve, data were collected after rapidly cooling a specimen composed of 100% austenite to the temperature indicated that temperature was maintained constant throughout the course of the reaction. 

It is accepted that, at normal pressures, mtile is the thermodynamically stable form of titanium dioxide at all temperatures. Calorimetric studies have demonstrated that mtile is more stable than anatase and that brookite and Ti02 (ii) have intermediate stabiHties, although the relative stabiHties of brookite and Ti02(ii) have not yet been defined. The transformation of anatase to mtile is exothermic, eg, 12.6 KJ/mol (9), although lower figures have also been reported (63). The rate of transformation is critically dependent on the detailed environment and may be either promoted or retarded by the presence of other substances. For example, phosphoms inhibits the transformation of anatase to mtile (64). 

First-order phase transitions exhibit hysteresis, i.e. the transition takes place some time after the temperature or pressure change giving rise to it. How fast the transformation proceeds also depends on the formation or presence of sites of nucleation. The phase transition can proceed at an extremely slow rate. For this reason many thermodynamically unstable modifications are well known and can be studied in conditions under which they should already have been transformed. 

It has been found that both the anhydrous Form III and dihydrate phases of carbamazepine exhibit fluorescence in the solid state [78]. The fluorescence intensity associated with the dihydrate phase was determined to be significantly more intense than that associated with the anhydrate phase, and this difference was exploited to develop a method for study of the kinetics of the aqueous solution-mediated phase transformation between these forms. Studies were conducted at temperatures over the range of 18 40 °C, and it was found that the phase transformation was adequately characterized by first-order reaction kinetics. The temperature dependence in the calculated rate constants was used to calculate activation energy of 11.2 kCal/ mol (47.4 cal/g) for the anhydrate-to-dihydrate phase conversion. 

Temperature dependence and simulation of H 148 NMR were used for determining the rates and activation energies of conformational transformations. Bridged tetraarylstannanes 26-28 can adopt either Z>2 or S4 symmetry. From calculations it was shown that the achiral form S4 has a higher energy level. It was proposed that transitions between one D2 form to its antipodal proceed through the S4 form 3. 

The main environmental factors that control transformation processes are temperature and redox status. In the subsurface, water temperature may range from 0°C to about 50°C, as a function of climatic conditions and water depth. Generally speaking, contaminant transformations increase with increases in temperature. Wolfe et al. (1990) examined temperature dependence for pesticide transformation in water, for reactions with activation energy as low as lOkcal/mol, in a temperature range of 0 to 50°C. The results corresponded to a 12-fold difference in the half-life. For reactions with an activation energy of 30kcal/mol, a similar temperature increase corresponded to a 2,500-fold difference in the half-life. The Arrhenius equation can be used to describe the temperature effect on the rate of contaminant transformation, k ... 

If kepi, k-epi are much larger than the rates k, ki of substitution, the enantiomeric ratio Hepi-1 is similar to kxjk (path C, dynamic kinetic resolution . Both mechanisms are performing when the rates of the two steps are similar. Since rates and equilibrium are temperature-dependent, enhancement of stereoselectivities can be achieved by sophisticated protocols (see Section m.E). The equilibrium 6/epi-6 is determined by the difference of free energy A AG. This effective energy difference is enlarged if it can be coupled with a second order transformation such as the selective crystallization of one diastere-omer dynamic thermodynamic resolution ). In fact, this applies to the first successful (—)-sparteine-mediated deprotonation (Section FV.C.l). 

The origin of the pyroelectric effect, particularly in crystalline materials, is due to the relative motions of oppositely charged ions in the unit cell of the crystal as the temperature is varied. The phase transformation of the crystal from a ferroelectric state to a paraelectrlc state involves what is called a "soft phonon" mode (9 1). In effect, the excursions of the ions in the unit cell increase as the temperature of the material approaches the phase transition temperature or Curie temperature, T. The Curie temperature for the material used here, LiTaO, is 618 C (95). The properties of a large number of different pyroelectric materials is available through reference 87. For the types of studies envisaged here, it is preferable to use a pyroelectric material whose pyroelectric coefficient, p(T), is as weakly temperature dependent as possible. The reason for this is that if p(T) is independent of temperature, then the induced current in the associated electronic circuit will be independent of ambient temperature and will be a function only of the time rate of change of the pyroelectric element temperature. To see this, suppose p(T) is replaced by pQ. Then Equation U becomes... 

Temperature dependence of pearlite nucleation and growth rates in a 0.78% C, 0.63% Mn steel of ASTM grain size 5.25. Data from R. F. Mehl and A. Dube, Phase Transformations in Solids (New York Wiley, 1951), 545. Reprinted with permission of John Wiley Sons, Inc. 

The mathematical models of chemical kinetics just referred to are, in what follow, the mathematical descriptions that permit us to obtain the dependence of the chemical transformation rate on the reaction parameters (temperature, reactant concentrations, etc.). It is the sole purpose of those models specified as kinetic models [26]. 

Davidson et al. (1978a) also used first-order kinetics for nitrogen transformations, but they considered that some of the transformation rate coefficients were dependent on several factors including environmental ones The rate for nitrification was empirically adjusted for water suction. Overall, most of the nitrogen models assume first-order kinetics. Some of them also consider the effects of temperature on rate coefficients. 

Fig. 7.3. The mutual transformation in system (>Si = 0 + C0<-> >Si + C02). (a) The temperature dependence of rate constant for direct reaction (b) the temperature dependence of rate constant for reverse reaction (c) the calculated structure of the TS for this reaction.

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