Quasi-crystalline approximation

Estimation of effective elastic moduli of nanocomposites was performed by the version of effective field method developed in the framework of quasi-crystalline approximation when the spatial correlations of inclusion location take particular ellipsoidal forms [71] The independent justified choice of shapes of inclusions and correlation holes provide the formulae of effective moduli which are symmetric, completely explicit and easily to use. The parametric numerical analyses revealed the most sensitive parameters influencing the effective moduli which are defined by the axial elastic moduli of nanofibers rather than their transversal moduli as well as by the justified choice of correlation holes, concentration and prescribed random orientation of nanofibers [72]. 

Estimation of effective elastic moduli of nanocomposites was performed by the version of effective field method developed in the framework of quasi-crystalline approximation when the spatial correlations of inclusion location take particular ellipsoidal forms [71]. The independent... 

In Fig. 3.81 we plot Im ifs//co versus concentration for a = 1.047 10 3 pm, m-r = 1.789 and m = 1.0. Computed results using the T-matrix method agree with the quasi-crystalline approximation. It should be observed that both the quasi-crystalline approximation and the quasi-crystalline approximation with coherent potential do predict maximum wave attenuation at a certain concentration. 

With the advance of computing techniques classic LD programs have become more and more sophisticated. The PHONON program, provided from Daresbury Laboratory [69], is one such excellent example. PHONON uses the quasi-harmonic approximation and has a wide range of two body potentials embodied in the code. In addition, angular three-body bending potentials, four-body torsion potentials are also included. The program has been widely used for simulations of a variety of properties, such as dispersion curves, defects and surface phonons of crystalline and amorphous materials. 

A second mechanism for increasing disorder on melting which cannot be conveniently represented by a quasi-crystalline model for the melt involves the formation of association complexes. Quite generally, these can be defined as clusters of the units of structure (e.g., molecules or ions) in the crystal which have approximately the same distance between nearest neighbours as in the crystal lattice, but which need not have the full regularity of crystal packing. As already stated, only one particular form of cluster, the crystal nucleus can normally be extended indefinitely... 

At very high magnification, it is possible to observe directly the internal structure of carbon black primary particles. They are constituted by overlapping graphitic layers that locally present a quasi-crystalline turbostratic structure with an approximately 0.35 nm interlayer spacing, close to pure graphite (-0.332 nm). 

Computation of vibrational frequencies for crystalline phases can be carried out with various methods. Perhaps the most common is the to use the quasi-harmonic approximation in lattice dynamics calculations (see Parker, this volume). Some excellent examples of this type of study are Cohen et al. 1987, Hemley et al. (1989), Wolf and Bukowinski (1987), and Chaplin et al. (1998). In general, however, such calculations serve as a validation of the modeling technique rather than as a method to interpret frequencies. Vibrational modes in crystalline solids are readily assigned because the structure is known from X-ray diffraction studies. In fact, isochemical crystalline solids are used frequently to help interpret spectra of glasses (e.g., McMillan 1984). 

In 8 1 it was shown that equations (14 4)-(14 6) lead to a statistical deduction of the laws of ideal solutions. For this purpose it was supposed that a solid or liquid solution can be approximated by a quasi-crystalline lattice, and also that the A and B molecules are of a sufficiently equal shape and size for them to be interchangeable between the lattice sit without change of lattice structure and without change in the lattice vibrations or the internal states of the molecules. Before mixing there is only one geometrical arrangement and after mixing there are... 

The whole system s entropy is defined here as simply the sum of entropies of all sites. If the characteristic inhomogeneity of the system is of the order of several nanometers, other methods should be applied. This refers, for example, to spinodal decomposition of supersaturated solid solutions, to nucleation of new phases, and to nano-crystalline alloy behavior. The simplest modification of local quasi-equilibrium approximation for strongly inhomogeneous systems implies adding the squared order parameter gradient into the set of local thermodynamic parameters (van der Waals [24, 25], Ginzburg-Landau [26, 27], Hillert [28, 29], Cahn-Hilliard [30, 31], Khachaturyan [32]). 

Of the books published in 1951, those in refs. 31, 33,34, and 38 have stood the test of time particularly well. Findlay s The Phase Rule has had an enormous impact on the understanding of heterogeneous equilibria ever since the appearance of the first edition in 1904. Roberts Heat , like Findlay s Phase Rule , has been revised and brought up to date by later workers. Zemansky s Heat and Thermodynamics has proved to be very popular and has run to several editions, as has Porter s book. Guggenheim s book is chiefly concerned with the theory of non-polar solutions, based on various approximations to the quasi-crystalline model of the liquid phase. The book is rather narrowly conceived in that it deals mostly with successive approximations to the combinatory problem. Allis and Merlin s book deals with both thermodynamic and statistical mechanics, in accord with the title. 

Amorphous Silicon. Amorphous alloys made of thin films of hydrogenated siUcon (a-Si H) are an alternative to crystalline siUcon devices. Amorphous siUcon ahoy devices have demonstrated smah-area laboratory device efficiencies above 13%, but a-Si H materials exhibit an inherent dynamic effect cahed the Staebler-Wronski effect in which electron—hole recombination, via photogeneration or junction currents, creates electricahy active defects that reduce the light-to-electricity efficiency of a-Si H devices. Quasi-steady-state efficiencies are typicahy reached outdoors after a few weeks of exposure as photoinduced defect generation is balanced by thermally activated defect annihilation. Commercial single-junction devices have initial efficiencies of ca 7.5%, photoinduced losses of ca 20 rel %, and stabilized efficiencies of ca 6%. These stabilized efficiencies are approximately half those of commercial crystalline shicon PV modules. In the future, initial module efficiencies up to 12.5% and photoinduced losses of ca 10 rel % are projected, suggesting stabilized module aperture-area efficiencies above 11%. 

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