Tables for
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 2.3, p. 335

Section Experimental aspects

I. Gregoraa*

aInstitute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Prague 8, Czech Republic
Correspondence e-mail: Experimental aspects

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In a scattering experiment on crystals, the choice of the scattering geometry implies setting the propagation directions [{\bf k}{_I}] and [{\bf k}{_S}] and the polarization of the incident and scattered light with respect to the crystallographic axes and defining thus the direction of the scattering wavevector q as well as the particular component (or a combination of components) of the transition susceptibility tensor [{\delta\chi}]. In practice, the incident radiation is almost exclusively produced by a suitable laser source, which yields a monochromatic, polarized narrow beam, with a well defined wavevector [{\bf k}{_I}]. The light scattered in the direction of [{\bf k}{_S}] is collected over a certain finite solid angle [\Delta\Omega]. Its polarization is analysed with a suitable polarization analyser, and the scattered intensity as a function of frequency [\omega{_S}] (or Raman shift [{\omega}]) is analysed using a spectrometer.

To characterize the Raman scattering geometry in a particular experimental arrangement, standard notation for the scattering geometry is often used, giving the orientation of the wavevectors and polarization vectors with respect to a reference Cartesian coordinate system, namely: [{\bf k}{_I}({\bf e}{_I}, {\bf e}{_S}){\bf k}{_S}]. Thus, for example, the symbol [x(zy)z] means that right-angle scattering geometry is used, where the incident beam polarized in the [z=[001]] direction propagates along the [x=[100]] axis, while the scattered beam is collected in the z direction and the polarization analyser is set parallel with the [y = [010]] direction. The measured intensity, being proportional to [|\chi_{zy}|{^2}], gives information on this particular component of the transition susceptibility tensor. By virtue of the momentum conservation, the scattering wavevector q in this case is oriented along the [[10\bar 1]] direction.

In a typical Raman experiment with visible light ([\omega \ll \omega{_I} \approx\omega{_S}]), the magnitudes of the wavevectors [ k{_I}\approx k{_s}= k] are of the order of 105 cm−1, much lower than those of the reciprocal-lattice vectors K ([\approx 10^{8}] cm−1). Consequently, the range of the magnitudes of the scattering wavevectors q accessible by varying the scattering geometry from [{\varphi}= 0]° (forward scattering) to [{\varphi}=180]° (back scattering) is [0 \leq q \leq 2k], i.e. by about three orders of magnitude lower than the usual dimensions of the Brillouin zone. The use of back-scattering geometry is imperative in the case of opaque samples, which show stronger absorption for the exciting (or scattered) light.

It should be noted that the general formula for the spectral differential cross section ([link] applies to the situation inside the crystal. Since in real experiments the observer is always outside the crystal, several corrections have to be taken into account. These are in particular due to refraction, reflection and transmission of the incident and scattered light at the interfaces, as well as absorption of light in the crystal. Attention must be paid in the case of anisotropic or gyrotropic crystals, where birefringence or rotation of the polarization direction of both incident and scattered light may occur on their paths through the crystal, between the interfaces and the scattering volume.

We conclude this section by remarking that, owing to the obvious difficulties in taking all the properties of the experimental setup and the corrections into consideration, measurements of absolute Raman intensities tend to be extremely rare. There exist, however, several crystals for which absolute determination of the cross section for particular excitations has been made with reasonable reliability and which may serve as secondary standards.

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