Disordered solid

However, one can proceed beyond this zeroth approximation, and this was done independently by Guggenheim (1935) with his quasi-chemicaT approximation for simple mixtures and by Bethe (1935) for the order-disorder solid. These two approximations, which turned out to be identical, yield some enliancement to the probability of finding like or unlike pairs, depending on the sign of and on the coordmation number z of the lattice. (For the unphysical limit of z equal to infinity, they reduce to the mean-field results.)... 

The standard analytic treatment of the Ising model is due to Landau (1937). Here we follow the presentation by Landau and Lifschitz [H], which casts the problem in temis of the order-disorder solid, but this is substantially the same as the magnetic problem if the vectors are replaced by scalars (as the Ising model assumes). The themiodynamic... 

Even for a single radical tire spectral resolution can be enlianced for disordered solid samples if the inliomogeneous linewidth is dominated by iimesolved hyperfme interactions. Whereas the hyperfme line broadening is not field dependent, tire anisotropic g-matrix contribution scales linearly with the external field. Thus, if the magnetic field is large enough, i.e. when the condition... 

The present paper is devoted to the theoretical formulation and numerical implementation of the NDCPA. The dynamical CPA is a one-site approximation in which variation of a site local environment (due to the presence, for example, of phonons with dispersion) is ignored. It is known from the coherent potential theory for disordered solids [21], that one can account in some extension the variation of a site local environment through an introduction of a nonlocal cohcn-cnt potential which depends on the difference between site... 

Some of the distinctions that we shall have to examine in more detail before proceeding much further are the considerations of order versus disorder, solid versus liquid, and thermodynamics versus kinetics. These dualities are taken up in the next section. With those distinctions as background, we shall examine both the glassy and crystalline states from both the experimental and modelistic viewpoint. 

J. L. Harden, D. Andelman. Thermal fluctuations of thin wetting films on disordered solids. Langmuir 5 2547-2551, 1992. 

Figure 1 Intrinsic stacking fault energy for chemically disordered solid solution Al-X (where X=Cu or Mg) as a function of composition.

As expected, the entropy of the disordered solid is higher than that of the perfectl) ordered solid. 

A compound which displays liquid crystal properties is referred to as a mesogen and said to exhibit mesomorphism. Liquid crystals may be considered either as disordered solids or ordered liquids, and their properties are very dependent on temperature and the presence or absence of solvent. In thermotropic liquid crystals the phases of the liquid crystals may be observed to change as the temperature is increased. In lyotropic liquid crystals the ordered crystalline state is disrupted by the addition of a solvent, which is very commonly water. For these systems temperature changes may also be... 

Before dealing with reinforcement of elastomers we have to introduce the basic molecular features of mbber elasticity. Then, we introduce—step-by-step—additional components into the model which consider the influence of reinforcing disordered solid fillers like carbon black or silica within a rabbery matrix. At this point, we will pay special attention to the incorporation of several additional kinds of complex interactions which then come into play polymer-filler and filler-filler interactions. We demonstrate how a model of reinforced elastomers in its present state allows a thorough description of the large-strain materials behavior of reinforced mbbers in several fields of technical applications. In this way we present a thoroughgoing line from molecular mechanisms to industrial applications of reinforced elastomers. 

Equation (12.6) is in the shape predicted by the tunnelling theory for the amorphous materials [38,39] and 8 of eq. (12.7) is within the range of values obtained for other disordered solids [40]. 

Taking into account thatiVAA = /VBB and Nm =zN - /VAA - NBB the energy of the disordered solid solution becomes... 

K. Binder, and W. Kob, Glassy Materials and Disordered Solids, World Scientific, Singapore,... 

Some of the major areas of activity in this field have been the application of the method to more complex materials, molecular dynamics, [28] and the treatment of excited states. [29] We will deal with some of the new materials in the next section. Two major goals of the molecular dynamics calculations are to determine crystal structures from first principles and to include finite temperature effects. By combining molecular dynamics techniques and ah initio pseudopotentials within the local density approximation, it becomes possible to consider complex, large, and disordered solids. 

If the alloy is quenched so as to preserve some of the high temperature gamma phase which is not ferromagnetic, one observes a single peak at the center in addition to the six-line pattern from the disordered solid... 

The possibility of simulating the actual BWG ordering energy, rather than Cp, using a polynomial approximation was also examined by Inden (1976) using the disordered solid solution as a reference state. The following expression was suggested for a continuous second-order transformation such as A2/B2 ... 

Figure 4.14. Phase diagram, coverage vs. temperature, of N2 physisorbed on graphite. Symbols used fluid without any positional or orientational order (F), reentrant fluid (RF), commensurate orientationally disordered solid (CD), commensurate herringbone ordered solid (HB), uniaxial incommensurate orientation-ally ordered (UlO) and disordered (UID) solid, triangular incommensurate orientationally ordered (lO) and disordered (ID) solid, second-layer liquid (2L), second-layer vapour (2V), second-layer fluid (2F), bilayer orientationally ordered (2SO) and disordered (2SD) solid. Solid lines are based on experimental results whereas the dashed lines are speculative. Adapted from Marx Wiechert, 1996.

Penmans P, Forrest SR (2004) Separation of geminate charge-pairs at donor-acceptor interfaces in disordered solids. Chem Phys Lett 398 27... 

Nucleation and Growth (Round 1). Phase transformations, such as the solidification of a solid from a liquid phase, or the transformation of one solid crystal form to another (remember allotropy ), are important for many industrial processes. We have investigated the thermodynamics that lead to phase stability and the establishment of equilibrium between phases in Chapter 2, but we now turn our attention toward determining what factors influence the rate at which transformations occur. In this section, we will simply look at the phase transformation kinetics from an overall rate standpoint. In Section 3.2.1, we will look at the fundamental principles involved in creating ordered, solid particles from a disordered, solid phase, termed crystallization or devitrification. 

In such an exotic field of materials science as the amorphous (disordered) solids, one of the fundamental problems studied extensively is how to obtain insight into the stracture. Currently, it seems that versatile studies are needed to elucidate the amorphous structure. In other words, in addition to various direct and indirect structural techniques performed under fixed conditions (X-ray diffraction, Raman scattering, infrared absorption, X-ray absorption, to name a few), the investigation of structural modifications introduced by changes in composition, temperature, or pressure or induced by band-gap illumination may prove fruitful. 

As its name suggests, a liquid crystal is a fluid (liquid) with some long-range order (crystal) and therefore has properties of both states mobility as a liquid, self-assembly, anisotropism (refractive index, electric permittivity, magnetic susceptibility, mechanical properties, depend on the direction in which they are measured) as a solid crystal. Therefore, the liquid crystalline phase is an intermediate phase between solid and liquid. In other words, macroscopically the liquid crystalline phase behaves as a liquid, but, microscopically, it resembles the solid phase. Sometimes it may be helpful to see it as an ordered liquid or a disordered solid. The liquid crystal behavior depends on the intermolecular forces, that is, if the latter are too strong or too weak the mesophase is lost. Driving forces for the formation of a mesophase are dipole-dipole, van der Waals interactions, 71—71 stacking and so on. 

A. D. Buckingham. General Introduction - Faraday Symposium 22 on Interaction Induced Spectra in Dense Fluids and Disordered Solids. J. Chem. Soc. Faraday Trans. 2, 83(10) 1743ff, 1987. 

In nonaromatic systems, ionization usually plays a major role, as compared to excitation.301 Whereas, in liquids or highly disordered solids, the electron can be solvated,302 no, or very low yields of, solvated electrons are observed in solid carbohydrates, even at low temperatures.275 This implies that the electron may return to the positive hole (reaction 295). However, it cannot be excluded that ion-molecule reactions (reaction 194) precede this reaction, and that recombination occurs with the resulting ion N+, instead of with the parent ion M+ (reaction 196). Process 194 has been studied with simple alcohols in the gas phase.303,304... 

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