International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2013 |
International Tables for Crystallography (2013). Vol. D, ch. 2.4, pp. 350-351
Section 2.4.4.2. Scattering cross section^{a}Laboratoire des Verres, Université Montpellier 2, Case 069, Place Eugène Bataillon, 34095 Montpellier CEDEX, France |
The power , scattered from the illuminated volume V in a solid angle , where and are measured inside the sample, is given by where is the incident light intensity inside the material, is the appropriate elastic constant for the observed phonon, and the factor results from taking the fluctuation–dissipation theorem in the classical limit for (Hayes & Loudon, 1978). The coupling coefficient M is given by In practice, the incident intensity is defined outside the scattering volume, , and for normal incidence one can write Similarly, the scattered power is observed outside as , and again for normal incidence. Finally, the approximative relation between the scattering solid angle , outside the sample, and the solid angle , in the sample, is Substituting (2.4.4.9a,b,c) in (2.4.4.7), one obtains (Vacher & Boyer, 1972) where the coupling coefficient is In the cases of interest here, the tensor is diagonal, without summation on i, and (2.4.4.11) can be written in the simpler form
References
Hayes, W. & Loudon, R. (1978). Scattering of light by crystals. New York: Wiley.Vacher, R. & Boyer, L. (1972). Brillouin scattering: a tool for the measurement of elastic and photoelastic constants. Phys. Rev. B, 6, 639–673.