International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. B, ch. 5.1, pp. 541-542
Section 5.1.6.1. Absorption coefficient^{a}Laboratoire de Minéralogie-Cristallographie, Université P. et M. Curie, 4 Place Jussieu, F-75252 Paris CEDEX 05, France |
In transmission geometry, the imaginary part of is small and, using a first-order approximation for the expansion of , (5.1.5.1) and (5.1.5.2), the effective absorption coefficient in the absorption case is where is the phase difference between and [equation (5.1.2.10)], the upper sign (−) for the ∓ term corresponds to branch 1 and the lower sign (+) corresponds to branch 2 of the dispersion surface. In the symmetric Laue case (, reflecting planes normal to the crystal surface), equation (5.1.6.1) reduces to
Fig. 5.1.6.1 shows the variations of the effective absorption coefficient with for wavefields belonging to branches 1 and 2 in the case of the 400 reflection of GaAs with Cu Kα radiation. It can be seen that for the absorption coefficient for branch 1 becomes significantly smaller than the normal absorption coefficient, . The minimum absorption coefficient, , depends on the nature of the reflection through the structure factor and on the temperature through the Debye–Waller factor included in [equation (5.1.2.10b)] (Ohtsuki, 1964, 1965). For instance, in diamond-type structures, it is smaller for reflections with even indices than for reflections with odd indices. The influence of temperature is very important when is close to one; for example, for germanium 220 and Mo Kα radiation, the minimum absorption coefficient at 5 K is reduced to about 1% of its normal value, (Ludewig, 1969).
References
Ludewig, J. (1969). Debye–Waller factor and anomalous absorption (Ge; 293–5 K). Acta Cryst. A25, 116–118.Ohtsuki, Y. H. (1964). Temperature dependence of X-ray absorption by crystals. I. Photo-electric absorption. J. Phys. Soc. Jpn, 19, 2285–2292.
Ohtsuki, Y. H. (1965). Temperature dependence of X-ray absorption by crystals. II. Direct phonon absorption. J. Phys. Soc. Jpn, 20, 374–380.