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

International Tables for Crystallography (2013). Vol. D, ch. 2.3, p. 345

Section 2.3.4.4. Stress- (strain-) induced Raman scattering

I. Gregoraa*

aInstitute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Prague 8, Czech Republic
Correspondence e-mail: gregora@fzu.cz

2.3.4.4. Stress- (strain-) induced Raman scattering

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Stress-induced Raman scattering is an example of the case when the external `force' is a higher-rank tensor. In the case of stress, we deal with a symmetric second-rank tensor. Since symmetric stress (T) and strain (S) tensors have the same symmetry and are uniquely related via the fourth-rank elastic stiffness tensor (c),[T_{\alpha \beta} = c_{\alpha \beta \mu \nu} S_{\mu \nu},]it is immaterial for symmetry purposes whether stress- or strain-induced effects are considered. The linear strain-induced contribution to the susceptibility can be written as [\Delta \chi _{\alpha \beta } ({\bf S}) = \left({{{\partial \chi _{\alpha \beta } }\over {\partial S_{\mu \nu }}}}\right) S_{\mu \nu }]so that the respective strain coefficients (conventional symmetric scattering) transform evidently as [[{\Gamma}_{\rm PV} \otimes {\Gamma} _{\rm PV}]{_ S} \otimes [{ \Gamma}_{\rm PV} \otimes {\Gamma}_{\rm PV}]{_S}, ]i.e. they have the same symmetry as the piezo-optic or elasto-optic tensor. Reducing this representation into irreducible components [\Gamma(j)], we obtain the symmetry-restricted form of the linear strain-induced Raman tensors. Evidently, their matrix form is the same as for quadratic electric-field-induced Raman tensors. In centrosymmetric crystals, strain-induced Raman scattering (in any order in the strain) is thus allowed for even-parity modes only.








































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