Description of the Solid State

By contrast, the macroscopic atom model of Miedema (Miedema et al. 1975) starts with a descriptions of the solid state which is then modified to describe the liquid state (Boom et al. 1976a, 1976b). In their model the enthalpy of formation at 0.5 mole fraction, Hc=o.s is given to a first approximation by ... 

The formula of Nb3lj can be written as Nb3lg Ig 2- Explain how this can be translated into a description of the solid state structure of the compound. 

As a starting point for considering the effect of impurity and solvent on crystallization, the growth and interaction process is examined in the framework of the fundamental solid-state, interfacial, and liquid phase (solute-solvent-impurity) chemistry. The solid-state chemistry is specific to a given crystalline material and the nature of the bonds (e.g., ionic, covalent, van der Waals, etc.) that hold the crystal structure together. A complete description of the solid-state aspects of crystal growth is beyond the scope of this... 

FIGURE 3.3 Schematic description of the solid-state polycondensation. 

The complete transition sequence is characterized by the description of the solid state (Sec. 5.1), the liquid crystalline transitions (Sec. 5.2) and the clearing parameter (Sec. 5.3). 

The chapter summarizes the results of recent studies from our laboratories aiming at the development of a chemist-oriented approach to the description of the structures and bonding of the solid state. The main motivation for these efforts originates from the fact that traditional physicist s approach to the description of the solid state in terms of band theoiy considerably differs from tbe more intuitive but remarkably... 

It is probably true that many of the descriptions of physical and solid state reaction mechanisms now existing in the literature are only partially correct. It would appear that part of the frontier of knowledge for Chemistry of The Solid State wiU lie in measurement of physical and chemical properties of inorgcuiic compounds as a function of purity. 

Secondly, for some crystalline systems, the structure obtained by diffraction techniques may be incomplete. For example, in some cases the diffraction data may not reveal dynamic aspects of the solid-state structure (as in the case of fluxional organo-metallics) and in others it may not be possible to distinguish clearly between different atoms (as for example 27A1 and 29Si in zeolites) and a combination of the NMR and x-ray data will yield a more complete and meaningful description of the structure. 

As a starting point in the description of the solid intermetallic phases it is useful to recall that their identification and classification requires information about their chemical composition and structure. To be consistent with other fields of descriptive chemistry, this information should be included in specific chemical and structural formulae built up according to well-defined rules. This task, however, in the specific domain of the intermetallic phases, or more generally in the area of solid-state chemistry, is much more complicated than for other chemical compounds. This complexity is related both to the chemical characteristics (formation of variable composition phases) and to the structural properties, since the intermetallic compounds are generally non-molecular in nature, while the conventional chemical symbolism has been mainly developed for the representation of molecular units. As a consequence there is no complete, or generally accepted, method of representing the formulae of intermetallic compounds. 

Notice especially that of the total heat released in this example, only 13-9% comes from lowering the temperature. Most of the heat comes from the two transformations of state—condensation and crystallization. For Fi20, the fact that the heat of condensation is almost 7 times greater than the heat of crystallization may be interpreted as meaning that the molecular description of the liquid state is much more like the solid than the gas. 

The models described so far provide a qualitative illustration of the viscoelastic behaviour of polymers. In that respect the Maxwell element is the most suited to represent fluid polymers the permanent flow predominates on the longer term, while the short-term response is elastic. The Kelvin-Voigt element, with an added spring and, if necessary, a dashpot, is better suited to describe the nature of a solid polymer. With later analysis of the creep of polymers, we shall, therefore, meet the Kelvin-Voigt model again in more detailed descriptions of the fluid state the Maxwell model is being used. 

This still leaves an important error in the matrix elements. It can be shown by symmetry that matrix elements between certain wave functions vanish c.g., the matrix clement of d/dx between two band states of T i symmetry is zero just as it is for d/dx between two s states in the free atom. Such dependence on band and wave number could also be readily incorporated by using the decomposition of each state into hybrids or atomic orbitals, again, if one desired, with a single-parameter description of the remaining matrix elements. It would be interesting to see how adequate a description of the spectrum, made entirely in terms of the parameters of the Solid State Table, this would produce. Certainly the main features of the spectrum would be predicted, and a more complete calculation, such as that which is illustrated in Fig. 4-1, can very accurately produce the real spectrum. 

These results corroborate the experimentally measured data and predict torsional barriers. Furthermore, the calculations provide a detailed picture at the molecular level of the available isomeric states and show that the mobility of the side chains at temperatures below Tg should differ from that at temperatures above Tg for some cases. Additional experiments will test our conclusion. The theoretical description of the isomeric states provides grounds for predicting the crystalline and amorphous forms of the polymeric materials in the solid and liquid states. 

According to this definition, A is the difference between the two energy states. This kind of definition will play an important role in the description of the solid-liquid interface. Substituting Eqs. (6.52) into (6.51) one obtains ... 

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