Crystallography by Dieter Schwarzenbach

By Dieter Schwarzenbach

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0 cm, 38 cm, 200 cm), mentioned above, fulfill the required inequalities. Of course, the most correct way of calculating the measured counts versus (} is to start from the theoretical annihilation probability for kl to be in dkl and k2 to be in dk2 (see Sect. 1) and sum up all photons hitting both slits, taking into account the detection efficiency of the detectors. Furthermore, all the annihilations in the samples must be added, taking into account the distribution of positron flux, and the scattering probability of the photons, in the sample.

Normally, a rough semiquantitative estimation of the possible errors of the AC measurements will show that the errors are very small. For example, an estimation of the errors caused by the use of finite slit lengths showed that they were much smaller than expected at first sight, partly because the sample length in the direction of the y-axis (Fig. 10]. Several effects contribute to the angular resolution. First, the contribution of the finite slit widths is a triangular resolution curve of fwhm = b I L.

The curves in Fig. 4 are such fitting curves. In PARAFIT the fitting curve is a sum of gaussians and curves made by folding a free-electron parabola with a gaussian. In principle, the analyses of AC spectra are fairly similar to those of LT spectra. However, the resolution curve is not corrected for tn the AC analyses, because the effect of the finite resolution is nonnally much smaller in the AC case. The source correction is not needed either. Furthennore, the number of points in an AC spectrum is lower than in a LT spectrum.

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