Phase transformation rate temperature dependence

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. 

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. 

There is a small thermal hysteresis of the transition temperature, which depends on many parameters such as the rate of temperature change, mechanical stresses or crystal imperfections. From a crystal chemical view, the Ba-O framework evokes an interstitial for the central Ti4+ ion which is larger than the actual size of the Ti4+ ion. As a result, the serie of phase transformations takes place to reduce the Ti cavity size. Certainly, the radii of the ions involved impact the propensity for forming ferroelectric phases thus both PbTi03 and BaTi03 have ferroelectric phases, while CaTi03 and SrTi03 do not [5]. 

Most solid state work published in recent years has dealt primarily with a molecular analysis of product formation that seems to arise from the intuitive appeal of the topochemical postulate. Problems associated with phase changes can sometimes be neglected if reactions are carried out to sufficiently low conversion values. However, since preferential reactions at defect sites may be a problem, the involvement of nontopochemical reactions at defect sites should be experimentally documented and avoided. Changes in reaction rates and product selectivity have also been associated with internal stress [54], with sample melting, or with surface effects [62]. In contrast, the mechanisms and consequences of phase transformation have been studied much less. Phase changes depend on the properties of the ensemble and, as suggested in Scheme 5, they are affected by composition, temperature, pressure and whether or not equilibrium is achieved throughout the reaction. 

However, even though this transformation is thermodynamically favored, the diamond allotrope still exists at high pressures and over long time periods. That is, if a particular phase transformation is predicted as spontaneous, the acmal rate of that process will depend on the kinetics of the transformation. Since the sp carbon bonds in diamond are extremely strong, the kinetics governing the migration of carbon atoms between diamond-graphite is extremely slow at normal temperatures and... 

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