Chapter 3 Lattice vibration and crystal thermal properties Shuxi Dai Department of Physics Unit 4 : Experimental measurements of Phonons

Dispersion curves ω as a function are measured by inelastic diffraction If the atoms are vibrating then diffraction can occur with energy loss or gain by scattering particles In principle, can use any particle –neutrons from a reactor, X- rays, photon, … Photon scattering Neutron scattering Content:

3.4.1 Photon scattering Interaction of photons with crystal phonon Inelastic scattering “+”absorb a phonon “-”generate a phonon Interaction of photons with phonons in crystal With conservation laws of momentum, energy An inelastic collision between the incident photon and phonon and   : Wave vector and energy of incident photon

when absorbs a phonon when generates a phonon Inelastic light scattering can be medicated by many different types of elementary excitations in a crystal such as phonons, magnons or plasmons. Inelastic light scattering from phonons is subdivided as: Raman scattering: scattered from optical phonons; Brillouin scattering: scattered from acoustic phonons Phonon absorption and emission

General principles of inelastic light scattering Inelastic light scattering can be subdivided into two types: Stokes scattering: emitting a phonon or other excitation; Anti-Stokes scattering: absorbing a phonon. The light is shifted down in frequency – Stokes; The light is shifted up in frequency – anti-stokes. Conservation of energy: Conservation of momentum: Raman scattering is mainly used to determine the frequency of LO and TO modes near the Brillouin zone centre

Neutrons are most useful for vibrations For λ~ atomic size, energies ~ vibration energies Neutron scattering Interaction of Neutrons with crystal phonon Inelastic scattering Interaction of Neutrons with phonons in crystal With conservation laws of momentum, energy Wave vector and energy of incident photon “+”absorb a phonon “-”generate a phonon

Measure momentum,energy We can fix the momentum of incident neutrons Method: Experimental setup: we can determine the frequency of the emitted or absorbed phonon

8 Measure for phonons  (10 12 Hz) k(2  /a) A triple axis neutron spectrometer at Brookhaven Na T=90K [100] [110] [111]

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