Description of the Lattice

The H Reactor lattice is rectangular the vertical spacing is nine Inches and the horizontal spacinsf is eig ht inches The process tubes are xiominal gnarter-inch vall Zlrcalloy-2 2 7-inch I.D tubes. The bt up fueX elements are concentric tubes of metallic uranium enriched to 0 9l(7 /o fuel clad is 

The process tubes pierce the reactor core frdnt-to-rear. A graphite coolant system composed of 6kO, Zlrcalloy-2 tubes runs side tjo si in every filler layer vertically and on l6-inch centers horizontally. These tubes are 0.75 inches 0 D  

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The Kieffer approach uses a harmonic description of the lattice dynamics in which the phonon frequencies are independent of temperature and pressure. A further improvement of the accuracy of the model is achieved by taking the effect of temperature and pressure on the vibrational frequencies explicitly into account. This gives better agreement with experimental heat capacity data that usually are collected at constant pressure [9],... 

Just as in our abbreviated descriptions of the lattice and cell models, we shall not be concerned with details of the approximations required to evaluate the partition function for the cluster model, nor with ways in which the model might be improved. It is sufficient to remark that with the use of two adjustable parameters (related to the frequency of librational motion of a cluster and to the shifts of the free cluster vibrational frequencies induced by the environment) Scheraga and co-workers can fit the thermodynamic functions of the liquid rather well (see Figs. 21-24). Note that the free energy is fit best, and the heat capacity worst (recall the similar difficulty in the WR results). Of more interest to us, the cluster model predicts there are very few monomeric molecules at any temperature in the normal liquid range, that the mole fraction of hydrogen bonds decreases only slowly with temperature, from 0.47 at 273 K to 0.43 at 373 K, and that the low... 

The input data for the model consist of the description of the lattice deformation and the choice of the slip system in the lattice-invariant shear. The model has successfully predicted the observed geometrical features of many martensitic transformations. The observed and calculated habit planes generally have high indices that result from the condition that they be macroscopically invariant. 

Description of the lattice fibres and their demarcation by elastic fibre and collagenous connective tissue by A. Oppel. 

KF, NaF, KI, and Nal) that accurate descriptions of relaxation as a function of temperature are not likely when one uses a poor description of the lattice vibrational spectrum.It was tentatively concluded that a reasonable (but not overly detailed) description of the optic vibrational branch is needed to describe the Ti behaviour as a function of temperature when the mass ratio between the metal and halogen deviates greatly (ca. > 3) from unity, but would not be required when the mass ratio was near one. 

From the above discussion it can be seen that zeolites are unique catalytic materials combining a size and shape selectivity toward organic reactant and product species with high reactivity, as illustrated schematically in Fig. 4 115], and in fact they show many of the characteristics of enzymes. It should be noted that all the chemical reactions in this figure are practical examples. Thus for a complete understanding of the catalytic properties of specific zeolites, a full and detailed description of the lattice frameworks that confer the molecular selec-... 

If the angles a, and y are all different from 90° and from each other the crystal is said to be triclinic. The only simplification that may be possible in describing the structure is to find another set of parallelepipeds with angles closer to 90° that still describe the structure. For certain special values of a, and Y and special relationships among a, b and c it is possible to find other descriptions of the lattice that conform to the symmetry of the structure. A particular example is the face-centred cubic lattice, illustrated in fig. 2.6, in which the cube of edge a clearly exhibits the full symmetry of the structure, but the rhombohedron of edges a/ /2 does not. This parallelepiped is one of the infinite number of possible types of primitive unit cell that can be chosen so as to contain only one lattice point per cell. The cubic unit cell is not primitive there are four lattice points per cubic cell. Care must be taken when describing diffraction from non-primitive cells, which can occur both for polymeric and for non-polymeric crystals. 

To understand the transition to supersonic velocities we also make use of a description of the lattice in terms of both optical and acoustic order parameters. Here, we study a strictly ID model that is a direct map of the fPA structure. However, as far as the properties of the drifting polaron are concerned, the model is more general and quantitatively describes these properties in other polymeric systems, e.g., poly(paraphenylene vinylene) or polythiophene. In the ID model, the displacement of the lattice sites entering Equation 2.14 and Equation 2.16 is described by a single variable u . In the description of the geometry of conjugated polymers, fPA in particular, it is common to study a smoothed atomic displacement order parameter. This optical order parameter is given by... 

With an electric field applied to the polymer chain, the self-localized polaron starts to drift along the chain. After a short acceleration phase the velocity becomes constant and the excess energy is dissipated by creation of lattice vibrations. Since the description of the lattice is classical in our model, the energy is dissipated continuously. 

Since the crystal field on the lanthanide ions is formed mainly by their nearest surroundings, the elastic-continuum approximation, used by Ivanov et al. (1983) for the description of the lattice deformations induced by a point defect, might result in qualitatively incorrect results when calculating the random component of a crystal field, especially if there are quasimolecular complexes in the lattice. 

The foundation of the "rigid-pseudoion" model is the "rigid-ion" description of the lattice dynamics, which was introduced by Nordheim. In this approximation, the ion-core potential of an atom moves rigidly when the atom is displaced from equilibrium. Thus, the potential seen by an electron due to a lattic of such atoms is justr, 24,27,28... 

The relation (2) can also be obtained by solving the 3s-dlmenslonal dynamical equations of motion of a harmonic lattice and are thereby identified as the normal modes of vibrations of the lattice. As is the case in electromagnetic displacements, it is often convenient to replace the normal modes by an equivalent corpuscular description of the lattice displacements. As a result it is usual to associate a phonon with each of the normal modes. 

A DZ description of the lattice ions should involve a noticeable computational effort hardly balanced by a corresponding improvement in the results. It had been already remarked that the minimal basis set wavefunction for NO2 [5], (Roothaan s best atom zetas, BAZ [6]) albeit inadequate for other reasons, represents in a sufficiently correct fashion the electrostatic potential generated by the ion in the surrounding space. This is the reason why we represent both NO2 and Na ions of the lattice by means of BAZ STO wavefunctions. 

As there is only an average structure for the Fe compound, no detailed description of the lattice doubling in the Fe and Co compounds is known. However Fe Mossbauer spectroscopy of the Fe compound, yielding results virtually identical to those of the tetraalkylammonium salts of Fe(mnt)2 [63], provides strong evidence for dimerisation of the M(mnt) units by M-S interactions, as in the above-mentioned salts, that are known to adopt a standard square-pyramidal coordination of the metal. This is further supported by the magnetic susceptibility data (see below). The transport properties discussed below suggest that any dimerisation effects on the perylene chains should be small. 

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