[Article] A Classification of Quadratic Vector Functions by Hitchcock F.L.

By Hitchcock F.L.

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This is true in particular for optical modes that address directly a local physical property, that is, the bond force constant, and as such are highly sensitive to the local atom arrangement. In fact, the loss of translational symmetry shows itself via partial release of the Raman and infrared q $ 0 selection rules. Another effect is that the IR and Raman linewidths are generally broader in glasses than in crystals. 4. Brillouin modes are much less affected. As they correspond to vibrations with long characteristic wavelength, that is, of the crystal taken as a whole, they are much less sensitive to disorder and most often the Brillouin lines are comparable in a crystal and in the glass of same composition.

1). In fact, the same expression of er can be obtained just by writing P à à as N(Ze) u þ ne y, that is, directly in terms of the effective charges (macroscopic à scale), which allows to skip a treatment of the local field Ee, but (Ze) should satisfy v2L Àv2T ¼ NðZeÞ Ã2 me0 e1 ðer ¼ 0Þ ð2:13Þ Ã and also, the electronic susceptibility x1, as given by ne y ¼ e0 x1E, should be formulated as e1 ¼ 1 þ x1 : ð2:14Þ The latter relation simply expresses that at pulsations well beyond those of optical modes, the polarization of the crystal is all due to electrons.

In a classical description, these behave as oscillating dipoles Pe, and as such scatter light in all directions – but the oscillating one – according to the Hertz mechanism. Most of the light is scattered quasielastically, which is referred to as Rayleigh scattering. Less probably (106–1012 times less) part of the incident energy is taken to set one optical phonon in motion, or on the contrary one optical phonon is consumed during the light/matter interaction. The pulsation of the scattered light (vs) is accordingly shifted with respect to the incident one (vi) – downward for a Stokes process and upward for an anti-Stokes one – of the pulsation of the optical phonon (V) brought into play.

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