Phase stability characterization

The nematic to smectic A phase transition has attracted a great deal of theoretical and experimental interest because it is tire simplest example of a phase transition characterized by tire development of translational order [88]. Experiments indicate tliat tire transition can be first order or, more usually, continuous, depending on tire range of stability of tire nematic phase. In addition, tire critical behaviour tliat results from a continuous transition is fascinating and allows a test of predictions of tire renonnalization group tlieory in an accessible experimental system. In fact, this transition is analogous to tire transition from a nonnal conductor to a superconductor [89], but is more readily studied in tire liquid crystal system. 

Based on the reversibility of their phase transformation behavior, polymorphs can easily be classified as being either enantiotropic (interchange reversibly with temperature) or monotropic (irreversible phase transformation). Enantiotropic polymorphs are each characterized by phase stability over well-defined temperature ranges. In the monotropic system, one polymorph will be stable at all temperatures, and the other is only metastable. Ostwald formulated the rule of successive reactions, which states that the phase that will crystallize out of a melt will be the state that can be reached with the minimum loss of free... 

If we were only interested in bulk copper and its oxides, we would not need to resort to DFT calculations. The relative stabilities of bulk metals and their oxides are extremely important in many applications of metallurgy, so it is not surprising that this information has been extensively characterized and tabulated. This information (and similar information for metal sulfides) is tabulated in so-called Ellingham diagrams, which are available from many sources. We have chosen these materials as an initial example because it is likely that you already have some physical intuition about the situation. The main point of this chapter is that DFT calculations can be used to describe the kinds of phase stability that are relevant to the physical questions posed above. In Section 7.1 we will discuss how to do this for bulk oxides. In Section 7.2 we will examine some examples where DFT can give phase stability information that is also technologically relevant but that is much more difficult to establish experimentally. 

The majority of processes occurring in the condensed phase are characterized by intracellular reactions involving the primary products of the transformation. This impedes the isolation of particular elementary steps from the overall process. These difficulties do not arise for an intermediate stabilized on the solid surface. The low-molecular products of the reactions involving this intermediate (atoms, radicals, or molecules) the zone of transformation through the gas phase can leave without hindrance. The occurrence of intracellular reactions is virtually ruled out, which makes it possible to detect primary steps of the corresponding processes. 

Microemulsions are thermodynamically stable dispersions of oil and water stabilized by a surfactant and, in many cases, also a cosurfactant.1-4 The microemulsions can be of the droplet type, either with spherical oil droplets dispersed in a continuous medium of water (oil-in-water microemulsions, O/W) or with spherical water droplets dispersed in a continuous medium of oil (water-in-oil microemulsions, W/O). The droplet-type microemulsions can be either a single-phase system or part of a two-phase system wherein the microemulsion phase coexists with an excess dispersed phase (an upper phase of excess oil in the case of O/W and a lower phase of excess water in the case of W/O microemulsions). There are also nondroplet-type microemulsions, referred to as middle-phase microemulsions. In this case, the microemulsion phase is part of a three-phase system with the microemulsion phase in the middle coexisting with an upper phase of excess oil and a lower phase of excess water. One possible structure of this middle-phase microemulsion, characterized by randomly distributed oil and water microdomains and bicontinuity in both oil and water domains, is known as thebiccntinuous microemulsion. Numerous experimental studies have shown1 2 4 that one can achieve a transition... 

To discuss the phase stability of polymer blends in more detail one has to specify the free-energy parameter X. This can be done in terms of an equation-of-state theory [8]. Theories that take into account the compressible nature of the pure components as well as that of the mixture are called equation-of-state theories. As basic quantities characterizing the thermodynamic state of a system the reduced temperature (T), volume (V) and pressure (P) are employed and defined by... 

The ra value significantly increases as the stability of the parent carbocation decreases, while the po value remains rather constant for a series of benzylic carbocations. The Tq values are plotted against the relative alkene basicities G(cc)h+ corresponding to the unsubstituted (parent) carbocations in Fig. 32. It is remarkable that the resonance demand parameters characterizing the stabilities of this series of cations are linearly related to the intrinsic gas-phase stabilities of the parent carbocations. 

McHale JM, Auroux A, Perrotta AJ, Navrotsky A (1997) Surface energies and thermodynamic phase stability in nanocrystalline aluminas. Science 277 788-791 Molteni C, Martonak R, Parrinello M (2001) First principles molecular dynamics simulations of pressure-induced stiuctural transformations in silicon clusters. J Chem Phys 114 5358-5365 Murray CB, Norris DJ, Bawendi MG (1993) Synthesis and characterization of nearly monodisperse CdE (E = S, Se, Te) semiconductor nanocrystallites. J Am Chem Soc 115 8706-8715 Onodera A (1972) Kinetics of polymorphic transitions of cadmium chalcogenides under high pressure. Rev Phys Chem Japan 41 1... 

A basic property is the melting temperature since it is known that materials parameters which characterize the deformation behavior are well correlated with the melting temperature (Frost and Ashby, 1982). Examples are the elastic moduli which not only control the elastic deformation, but are also important parameters for describing the plastic deformation, and the diffusion coefficients which control not only the kinetics of phase reactions, but also the kinetics of high-temperature deformation, i.e. creep. Furthermore, the melting temperature is intuitively regarded as a measure of the phase stability since it limits the application temperature range. 

It may be concluded that the phase formation enthalpy may be a better parameter for characterizing bonding strength and phase stability, and for correlating this with the basic properties, e.g. elastic moduli. Formation enthalpies have been determined experimentally (Hultgren, 1963),... 

It has to be concluded that there are physically justified correlations between parameters which characterize the bonding strength and the phase stability on the one hand, and the macroscopic phase behavior on the other. However, such correlations represent complex functional relationships, and thus they are useful only for order-of-magnitude predictions. More quantitative predictions have to consider the character and strength of bonding in a more detailed way, i.e. they have to rely on quantum-mechanical calculations which are cumbersome and time consuming. 

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