Line narrowing direct observation, shape

X-Ray diffraction has an important limitation Clear diffraction peaks are only observed when the sample possesses sufficient long-range order. The advantage of this limitation is that the width (or rather the shape) of diffraction peaks carries information on the dimensions of the reflecting planes. Diffraction lines from perfect crystals are very narrow, see for example the (111) and (200) reflections of large palladium particles in Fig. 4.5. For crystallite sizes below 100 nm, however, line broadening occurs due to incomplete destructive interference in scattering directions where the X-rays are out of phase. The two XRD patterns of supported Pd catalysts in Fig. 4.5 show that the reflections of palladium are much broader than those of the reference. The Scherrer formula relates crystal size to line width ... 

Even if perfectly narrow spectral lines are not available, we may take a clue from this approach and measure a spectral line of known shape. De-convolution should then yield the instrument function. This technique does indeed work (Chapter 2, Section II.G.3). Some of the information needed to generate the known line shape can even be obtained directly from the observed data. 

The theory of line shapes of systems involving one or more molecules starts from the same relationships mentioned in Chapter 5. We will not repeat here the basic developments, e.g., the virial expansion, and proceed directly to the discussion of binary molecular systems. It has been amply demonstrated that at not too high gas densities the intensities of most parts of the induced absorption spectra vary as density squared, which suggests a binary origin. However, in certain narrow frequency bands, especially in the Q branches, this intensity variation with density q differs from the q2 behavior (intercollisional effect) the binary line shape theory does not describe the observed spectra where many-body processes are significant. In the absence of a workable theory that covers all frequencies at once, even in the low-density limit one has to treat the intercollisional parts of the spectra separately and remember that the binary theory fails at certain narrow frequency bands [318],... 

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