Mechanisms of phase transitions

An interesting aspect of many structural phase transitions is the coupling of the primary order parameter to a secondary order parameter. In transitions of molecular crystals, the order parameter is coupled with reorientational or libration modes. In Jahn-Teller as well as ferroelastic transitions, an optical phonon or an electronic excitation is coupled with strain (acoustic phonon). In antiferrodistortive transitions, a zone-boundary phonon (primary order parameter) can induce spontaneous polarization (secondary order parameter). Magnetic resonance and vibrational spectroscopic methods provide valuable information on static as well as dynamic processes occurring during a transition (Owens et ai, 1979 Iqbal Owens, 1984 Rao, 1993). Complementary information is provided by diffraction methods. 

Phase transitions in solids are also fruitfully classified on the basis of the mechanism. The important kinds of transitions normally encountered are (i) nucleation-and-growth transitions (ii) order-disorder transitions and (iii) martensitic transitions. 

In the nucleation-and-growth transitions, nuclei of the new phase possessing a critical size have to be first formed in the parent phase. The change in free energy, AG, due to the formation of spherical nuclei is given by 

Empirical relations are often used to analyse kinetic data on nucleation-growth transitions. One of the common relations is that established by Avrami 

Order-disorder transitions are generally associated with (i) positional disordering, (ii) orientational disordering or (iii) disordering of electronic (or nuclear) spin states. The configurational entropy due to disordering is given by 

---

Yeomans Y M 1992 Statistical Mechanics of Phase Transitions (Oxford Oxford University Press)... 

Islands occur particularly with adsorbates that aggregate into two-dimensional assemblies on a substrate, leaving bare substrate patches exposed between these islands. Diffraction spots, especially fractional-order spots if the adsorbate fonns a superlattice within these islands, acquire a width that depends inversely on tire average island diameter. If the islands are systematically anisotropic in size, with a long dimension primarily in one surface direction, the diffraction spots are also anisotropic, with a small width in that direction. Knowing the island size and shape gives valuable infonnation regarding the mechanisms of phase transitions, which in turn pemiit one to leam about the adsorbate-adsorbate interactions. 

Recrystallization. The recrystallization of a solid may result in the production of a higher temperature lattice modification, which permits increased freedom of motion of one or more lattice constituents, e.g. a non-spherical component may thereby be allowed to rotate. Such reorganizations are properly regarded as premelting phenomena and have been discussed by Ubbelohde [3]. The mechanisms of phase transitions have been reviewed by Nagel and O Keeffe [21] (see also Hannay [22]). 

The nature and the mechanisms of phase transitions in solids are still matters of discussion among crystallographers, as nicely summarized in a recent review [20]. The reader is referred to textbooks for a comprehensive overview of this long term debate [98-100]. Here, we summarize the qualitative namre of the main changes that are possible in a solid to solid phase transition. 

The effect of temperature on g is difficult to predict because effects such as solvatation, entropic thermodynamic have to be taken into account. Thus the phase transition of MCM-41 to MCM-48 can not be explained by using the packing parameter g when crystallization temperature increases. Some complementary studies (synthesis at lower and higher temperatures, XRD or SAXS measurements...) should be made to understand and explain the mechanism of phase transition. 

The transformation of c-BN into h-BN was investigated during DTA-analysis [22]. The SEM images show formation of differently textured h-BN at the surface of the c-BN crystallites, which indicates that there is no uniform mechanism of phase transition (Fig. 5). 

J. M. Yeomans, Statistical Mechanics of Phase Transitions , University Press, Oxford 1992. 

The following section treats the one-dimensional aspects and focuses on the importance of fluctuations. Section V treats the two-dimensional regime, and the one after, the three-dimensional situation and the mechanisms of phase transitions. 

There is a fair amount of unity, as seen in Section VI, in the mechanisms of phase transitions of the organic conductors and the oxide superconductors. Correlations, be they inter- or intramolecular, play an important role. Quantum and thermal fluctuations are important in the quasi-one-dimensional solids and, to a lesser extent, in the quasi-two-dimensional conductors. There is a striking richness of phases and unusual phenomena in the organic conductors. These are explored in the following chapters of this book. 

Quinn PJ. Measurement of kinetics and mechanisms of phase transitions in lipid-water systems. J. Appl. Crystallogr. 1997 30 733-738. 

Wrack, B., Salje, E.K.H., Graeme-Barber, A. (1991) Kinetic rate laws derived from order parameter theory IV kinetics of Al, Si disordering in Na feldspars. Phys Chem Minerals 17 700-710 Yeomans, J.M. (1992) Statistical Mechanics of Phase Transitions. Clarendon Press, Oxford, UK Ziman, J.M. (1979) Models of Disorder. Cambridge University Press Cambridge, UK... 

One of the most difficult and intriguing aspects of ice physics is the behavior of defects. Although defects have little effect on the statics of phase transitions, they are the key to understanding the dynamics and mechanism of phase transitions. For example, ice-Ih must be doped with hydroxide to catalyze the transition to ice-XI. The mechanism by which hydroxide (OH ) catalyzes the ice-Ih/XI transition is not understood. In fact, it is not even clear that hydroxide defects have significant mobility in this temperature range near 70/v. The structure and transport properties of defects is relevant to problems in environmental and atmospheric science " and glaciology. In this work, we introduce techniques applicable to the study of ionic defects, and OH , and neutral defects, such as the OH radical, in ice. 

The statistical mechanics of phase transitions is briefly reviewed, with an emphasis on surfaces. Flat surfaces of crystals may act as a substrate for adsorption of two-dimensional (d = 2) monolayers and multilayers, offering thus the possibility to study phase transitions in restricted dimensionality. Critical phenomena for special universality classes can thus be investigated which have no counterpart in d = 3. Also phase transitions can occur that are in a sense in between different dimensionalities (e.g., multilayer adsorption and wetting phenomena are transitions in between two and three dimensions, while adsorption of monolayers on stepped surfaces allows phenomena in between one and two dimensions to be observed). 

The molecular packing and the mechanism of phase transition of the cubic phases have been attracting much research interest worldwide. 

Insofar as the dynamics and mechanism of phase transitions are concerned, TRXRD provides two important pieces of information 1) transition kinetics obtained by following the relaxation of the system in response to an applied perturbation and 2) details of intermediates that form in the process. These data provide a basis for formulating, evaluating and refining transition mechanisms (See Ref. [16] as an example). Since kinetics is the primary focus of this review, mechanistic aspects of lipid phase transitions will not be discussed here. 

Theories and Mechanism of Phase Transitions, Heterophase Polymerizations, Homopolymerization,... 

In summary, we calculate that the low clinoenstatite is not stable under hydrostatic conditions and enstatite has a comparatively small stability field. The energy differences are so small that they are within the reliability of the simulations and thus the precise positions of the phase boundaries are not well located. The primary reason for this problem is the reliability of the potential models. Hence, calculating phase relationships represents the most difficult challenge for free energy minimization techniques. However, the simulations do provide valuable insights into the mechanisms of phase transitions and the effect of pressure and/or temperature on the crystal structures and the relative phase stabilities. 

The phase structures in Figure 6 were obtained from a 75% SAN composition. Because this composition is far from the critical composition, one should expect unequal distribution of phase volumes. In fact, the minor phase constitutes approximately 10% of total volume. Hence, it is not possible to prove conclusively that one particular mechanism of phase transition produced the observed structure. This structure could have formed by nucleation and... 

Hunkeler, D., F. Candau, et al. (1994). Heterophase polymerizations a physical and kinetic comparison and categorization Theories and mechanism of phase transitions, heterophase polymerizations, homopolymerization, addition polymerization, Springer, Berlin/Heidelherg 115-133. 

THE MECHANISM OF PHASE TRANSITIONS AND THE BOUNDARIES OF THE LIQUID STATE. 

The mechanisms of phase transitions of l-myristoyl-2-stearoyl-sn-glycero-3-phosphatidylcholine (MSPC) and l-stearoyl-2-myristoyl-sn-glycero-3-phosphatidylcholine (SMPC) have been characterized by Jones et al using DSC, X-ray and NMR measurements in order to characterize their behavior in natural membranes. 

---