Localized distribution function, magnetic

In order to calculate the distribution function must be obtained in terms of local gas properties, electric and magnetic fields, etc, by direct solution of the Boltzmann equation. One such Boltzmann equation exists for each species in the gas, resulting in the need to solve many Boltzmann equations with as many unknowns. This is not possible in practice. Instead, a number of expressions are derived, using different simplifying assumptions and with varying degrees of vaUdity. A more complete discussion can be found in Reference 34. 

Here X = E,M denotes the type of radiation, either electric or magnetic, index j takes the values 1, 2,..., and index m = —j,..., j. The complex field amplitudes are defined in terms of the source functions, describing the local distribution of current and intrinsic magnetization [25], The mode functions in (17) can be represented in the following form [2,26,27] ... 

It is also possible to prepare crystalline electrides in which a trapped electron acts in effect as the anion. The bulk of the excess electron density in electrides resides in the X-ray empty cavities and in the interconnecting channels. Structures of electri-dides [Li(2,l, 1-crypt)]+-e [K(2,2,2-crypt)]+-e, [Rb(2,2,2-crypt)]+-e, [Cs(18-crown-6)2]+ e , [Cs(15-crown-5)2]+-e and mixed-sandwich electride [Cs(18-crown-6)(15-crown-5) e ]6 l8-crown-6 are known. Silica-zeolites with pore diameters of 7 A have been used to prepare silica-based electrides. The potassium species contains weakly bound electron pairs which appear to be delocalized, whereas the cesium species have optical and magnetic properties indicative of electron localization in cavities with litde interaction between the electrons or between them and the cation. The structural model of the stable cesium electride synthesized by intercalating cesium in zeolite ITQ-4 has been confirmed by the atomic pair distribution function (PDF) analysis. The synthetic methods, structures, spectroscopic properties, and magnetic behavior of some electrides have been reviewed. Theoretical study on structural and electronic properties of inorganic electrides has also been addressed recently. ... 

Among the techniques that probe the average or long-range structure, powder X-ray diffraction (PXRD) and neutron diffraction (ND) will be briefly discussed. Techniques that provide local, atomistic information that will be mentioned are nuclear magnetic resonance (NMR) spectroscopy. X-ray photoelectron spectroscopy, X-ray absorption spectroscopy, and pair distribution function (PDF) analysis. A brief introduction to the underlying theory of each technique will be provided along with relevant examples to illustrate the type of information that can be... 

For the former, i.e., diffraction, structural refinement techniques that wholly address both the crystalline and diffuse portions of the scattering profiles would be a tremendous advance. The latter component will entail heavier reliance on a variety of powerful probes of local structure including nuclear magnetic resonance, scanning tunneling microscopy, anomalous scattering methods, and radial distribution function analysis [21 j. As the number of chemical/structural architectures available continues to increase, determining the fundamental nature of the structure-property relationships will become an ever more important issue. 

The muon spin relaxation technique uses the implantation and subsequent decay of muons, n+, in matter. The muon has a polarized spin of 1/2 [22]. When implanted, the muons interact with the local magnetic field and decay (lifetime = 2.2 ps) by emitting a positron preferentially in the direction of polarization. Adequately positioned detectors are then used to determine the asymmetry of this decay as a function of time, A t). This function is thus dependant on the distribution of internal magnetic fields within a... 

Spin relaxation in a nucleus is induced by random fluctuations of local magnetic fields. These result from time-dependent modulation of the coupling energy of the resonating nuclear spin with nearby nuclear spins, electron spins, quadrupole moments, etc. Any time-dependent phenomenon able to modulate these couplings can contribute to nuclear relaxation. The distribution of the frequencies contained in these time-dependent phenomena is described by a correlation function, characterized by a parameter Tc, the correlation time. Its reciprocal can be considered as the maximum frequency produced by the fluctuations in the vicinity of the nuclear spin. If more than one process modulates the coupling between the nuclear spin and its surroundings, the reciprocal of the effective correlation time is the sum of the reciprocals of the various contributions... 

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