Line Broadening and Crystal Imperfections

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. 

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Magnetic resonance line shape for nuclei of Van Vleck ions The essential sources of the NMR line broadening for VV ions are (a) imperfections of a crystal structure (b) dipole-dipole interactions of VV ions with each other, with nuclei of diamagnetic ligands, with electronic moments of impurity ions and (c) unresolved fine structure of the NMR spectra for ions with spin I >. ... 

For half-integral spins (7=3/2, 5/2,...) the frequency of the central line (-t- - —5) is unchanged to first order, since the expression for Vq vanishes if M/ = 5 the other two lines appear as symmetrical satellites (Figure 7). The intensities are in the ratio 3 4 3 for spin 3/2, 5 8 9 8 5 for spin 5/2, and so on. The satellites are broadened by molecular motions or crystal imperfections, and for large splittings may disappear out of the observable range. 

Color centers in alkali halide crystals are based on a halide ion vacancy in the crystal lattice of rock-salt structure (Fig. 5.76). If a single electron is trapped at such a vacancy, its energy levels result in new absorption lines in the visible spectrum, broadened to bands by the interaction with phonons. Since these visible absorption bands, which are caused by the trapped electrons and which are absent in the spectrum of the ideal crystal lattice, make the crystal appear colored, these imperfections in the lattice are called F-centers (from the German word Farbe for color) [5.138]. These F-centers have very small oscillator strengths for electronic transitions, therefore they are not suited as active laser materials. 

Early experiments with positrons were dedicated to the study of electronic structure, for example Fermi surfaces in metals and alloys [78,79], Various experimental positron annihilation techniques based upon the equipment used for nuclear spectroscopy underwent intense development in the two decades following the end of the Second World War. In addition to angular correlation of the annihilation of y quanta, Doppler broadening of the annihilation line and positron lifetime spectroscopy were established as independent methods. By the end of the 1960s, it was realised that the annihilation parameters are sensitive to lattice imperfections. It was discovered that positrons can be trapped in crystal defects i.e., the wavefunction of the positron is localised at the defect site until annihilation. This behaviour of positrons was clearly demonstrated by several authors (e.g., MacKenzie et al. [80] for thermal vacancies in metals, Brandt et al. [81] in ionic crystals, and Dekhtyar et al. [82] after the plastic deformation of semiconductors). The investigation of crystal defects has since become the main focus of positron annihilation studies. 

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