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Chapter 3 Lattice vibration and crystal thermal properties
Shuxi Dai
Department of Physics
Unit 4 : Experimental measurements of Phonons
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, …
3.4.1 Photon scattering3.4.2 Neutron scattering
Content:
3.4.1 Photon scattering
hKqkk
ΩΩ
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
k 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.
,21 .21 qkk
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 vibrationsFor λ~ atomic size, energies ~ vibration energies
3.4.2 Neutron scattering
Interaction of Neutrons
with crystal
phonon
Inelastic scattering
Interaction of Neutrons
with phonons in crystal
With conservation laws of momentum, energy
)(22
' 22
qM
P
M
P
nn
hKqPP
'
Wave vector and energy of incident photon
“+”absorb a phonon
“-”generate a phonon
p
nM
PE
2
2
Measure momentum ,energy nM
PE
2
2p )(q
p
nM
PE
2
2
We can fix the momentum of incident neutrons
Method:
Experimental setup:
we can determine the frequency of the emitted or absorbed phonon
8
Measure E and ,'k ,k
qω and q
for phonons
(1012Hz)
k(2/a)A triple axis neutron spectrometer at Brookhaven
Na T=90K
[100]
[110]
[111]
