Temperature dependence of integrated thermal diffuse scattering

Abstract

The temperature dependence of the integrated thermal diffuse scattering (T.D.S.) surrounding Bragg reflexions is discussed, with particular reference to cryogenic applications. Detailed calculations of the T.D.S. and its ratio to the Bragg intensity are presented for NaCI over the range 0 to 800°K. The T.D.S. includes not only the one-phonon contribution but also multiphonon processes. The temperature dependence of the T.D.S.-to-Bragg ratio is shown to fall off more quickly at low temperatures than the Debye-Waller exponent values. Some insight is gained into the importance of multiphonon processes, and it is concluded that there is much to be gained both in the reduction of T.D.S. and in the increase in intensity of higher-order reflexions by cooling to liquid-nitrogen temperatures.

Investigation of a silicon single crystal by means of the diffraction of Mössbauer radiation

“…Robertson & Reid (1979) calculated the total phonon cross section for different reflections of silicon using the experimentally obtained B value of for an illuminated volume of 1/4000 of the Brillouin zone. Taking into account the experimental geometry by the formula given by Reid (1973) good agreement was only obtained for a small interval of the scan length (Figs. 5, 6).…”

X-ray scattering intensities from a shell model for silicon

“…Table 2 shows the phonon scattering which would be detected from a spherical region occupying 1/4000 of the Brillouin zone centred around the lower Bragg peaks along the principal symmetry directions. The scattering is expressed as a ratio to the corresponding kinematic Bragg intensity and, as explained by Reid (1973), can be used as an estimate of the diffuse scattering seen by a counter of finite width as it is scanned through the peak. tours agree well with the experimental data of Bonefa6i6 (1969), except of course in the region around 222.…”

The calculation and interpretation of multiphonon X-ray scattering - example of cubic zincblende structure compounds

“…calculation taking the observed volume as 1/256th of the Brillouin zone. The results can be scaled to other volumes following Reid (1973). A somewhat different interpretation of what scattering processes are happening close to Bragg pea.ks is provided by the observation made earlier that the zerophonon term cancels the zerophonon contribution to the Debye-Waller factor.…”

“…Multiphonon processes seen by such a counter are also included, but less accurately. Table 2 gives a quantitative illustration for some reflections from GaAs at 295 and 700 K of values for the Bragg intensity (IB), the one-phonon intensity (as a percentage of Is) and the multiphanon intensity Im (also as a percentage), the Reid (1973).…”