Compound energy formalism

Evidence relevant to the phase stability problem has been given by Massalski (1989). The so-called compound energy formalism was constructed by Hillert and Staffansson (1970) in order to describe models of the thermodynamic properties of phases with two or more sublattices showing a variation in composition, which therefore belong to the class of solution phases. A review of this formalism and a summary of its applications have been recently published by Hillert (2001) and Frisk and Selleby (2001). 

By contrast, the Gibbs energy of an ordered sublattice phase is modeled using what is known as the compound energy formalism. For the simplest sublattice... 

The descriptions of all ternary systems were combined in one dataset to simulate the phase equilibria in the quaternary Si-B-C-N system. The results of the thermodynamic calculations of individual systems are shown in the corresponding sections. Thermodynamic models used are the Redlich-Kister polynomial [39], extrapolations according to Muggianu et al. [40] and the compound energy formalism [41] to describe the solid solution phases )S-boron, SiBn, SiBg, SiBs and B4+ C. 

Together with the assessment of the binary B-C phase diagram the homogeneity range of boron carbide and the other compounds was modeled by means of the Compound Energy Formalism using the following sublattice models (Table 1) where vacancies are denoted as V ... 

The methods can be applied to extremely diverse data sets where linear free energy formalisms ate bound to fail. Inactive compounds can be included in the calculation. 

Molecular Interaction. The examples of gas lasers described above involve the formation of chemical compounds in their excited states, produced by reaction between positive and negative ions. However, molecules can also interact in a formally nonbonding sense to give complexes of very short lifetimes, as when atoms or molecules collide with each other. If these sticky collisions take place with one of the molecules in an electronically excited state and the other in its ground state, then an excited-state complex (an exciplex) is formed, in which energy can be transferred from the excited-state molecule to the ground-state molecule. The process is illustrated in Figure 18.12. 

A variety of acyclic and cyclic S-N compounds decompose at moderate temperatures (100-150°C) with the formal loss of a symmetrical NSN fragment, but this molecule has never been detected. The lowest energy isomer, linear NNS, is generated by flash vacuum pyrolysis of 5-phenyl-1,2,3,4-thiatriazole (Eq. 5.1). ... 

In the introductory chapter we stated that the formation of chemical compounds with the metal ion in a variety of formal oxidation states is a characteristic of transition metals. We also saw in Chapter 8 how we may quantify the thermodynamic stability of a coordination compound in terms of the stability constant K. It is convenient to be able to assess the relative ease by which a metal is transformed from one oxidation state to another, and you will recall that the standard electrode potential, E , is a convenient measure of this. Remember that the standard free energy change for a reaction, AG , is related both to the equilibrium constant (Eq. 9.1)... 

Vibrational spectroscopy has played a very important role in the development of potential functions for molecular mechanics studies of proteins. Force constants which appear in the energy expressions are heavily parameterized from infrared and Raman studies of small model compounds. One approach to the interpretation of vibrational spectra for biopolymers has been a harmonic analysis whereby spectra are fit by geometry and/or force constant changes. There are a number of reasons for developing other approaches. The consistent force field (CFF) type potentials used in computer simulations are meant to model the motions of the atoms over a large ranee of conformations and, implicitly temperatures, without reparameterization. It is also desirable to develop a formalism for interpreting vibrational spectra which takes into account the variation in the conformations of the chromophore and surroundings which occur due to thermal motions. 

It is unlikely that the compound (27) is derived directly from the reaction of an excited benzene with tetrafluorobenzyne even though the compound (27) is formally analogous to the photo-adducts formed by the irradiation of olefins in benzene 74,75) A number of other products derived from the o-iodotetrafluorophenyl radical were also obtained 73>. These results suggest either that the tetrafluoro-o-phenylene di-radical (32) is identical with tetrafluorobenzyne or that if it is produced at a higher energy level it returns rapidly to the groundstate before it reacts with benzene. An alternative and perhaps more likely explanation is that the tetrafluorobenzyne formed arises by the concerted loss of both iodine atoms. 

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