Reciprocal lattice line broadening

On the other hand, lattice distortions of the second kind are considered. Assuming [127] that ID paracrystalline lattice distortions are described by a Gaussian normal distribution go (standard deviation ay, its Fourier transform Gd (.S ) = exp (—2n2ols2) describes the line broadening in reciprocal space. Utilizing the analytical mathematical relation for the scattering intensity of a ID paracrys-tal (cf. Sect. 8.7.3 and [127,128]), a relation for the integral breadth as a function of the peak position s can be derived [127,129]... 

A diffraction pattern obtained from a large, perfect crystal is expected to consist of a number of extremely sharp diffraction peaks at s coinciding with the reciprocal lattice r kl. The diffraction peaks actually observed with a crystalline sample and especially those observed with a crystalline polymer, however, have finite widths. Three distinct reasons for such line broadening, examined in this section, are (1) instrumental effects, (2) an effect due to the small -crystal size, and (3) effects due to lattice imperfections. 

Fig. 98. Left The Gaussian-broadened Gaussian relaxation fimction (bottom) (explanation see text). ZF pSR asymmetry spectrum in polycrystalline CeCuo2Nio.jSn at 0.08K (top). The dashed line is a fit of the static Gaussian Kubo-Toyabe relaxation function. The solid line is a fit of the static Gaussian-broadened Gaussian function. From Noakes and Kalvius (1997). Right The minimum polarization achieved by the Monte Carlo RCMMV static ZF muon spin relaxation functions, as a function of the reciprocal of the moment-magnitude correlation length, in units of the magnetic-ion nearest-neighbor separation in the model lattice. The horizontal line represents the 1/3 asymptote, above which the minimum polarization cannot rise. The dashed line is a...

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