Woran liegt es dass nicht unendlich viele phononen angeregt werden können
Weil kristalle endlich gross sind und ihre wellenlänge in diese größe passen muss. D.h. es sind nur bestimmte energien erlaubt. Gleichzeitig ist die anzahlung von phononen pro energie durch die bose statistik begrenzt (phononen sind bosonen)
Wodurch wird sichergestellt, dass der Körper auf denn die Kraft angewandt wird nicht rotiert?
σ_ij=σ_ji
Hooke’s law als Summe über die Komponenten
σ_ij=Σ_kl C_ijkl ɛ_kl
Ist σ > 0 tension oder compression?
tension
Für was steht σ?
stress
Für was steht C?
elasticity tensor
Wie sieht die Dispersionsrelation von phononen in einem kubischen kristall aus?
Was bedeuten die Indizes bei σ_xy?
x: direction of force
y: direction of area normal to which the force is applied
Was bedeutet σ_xy mit x ungleich y
Shear stress
Was bedeutet σ_xy mit x=y
Normal stress
typical speed of sound in solids
5000 m/s
Wie viele unabhängige Komponenten hat der Elasticity Tensor im kubischen Kristall?
3
Für was steht ɛ?
Strain
Wie sieht dieser Tensor in der Voigt Notation aus?
How can we measure sound velocity in solids?
By applying a pulse on one end and record the swinging of the solid in longitudinal or transversal direction, e.g. with piezo crystals
What is the young’s modulus?
The tensor that scales between stress and strain
Why does the Young’s modulus contain 81 components? Why is the number of independent components smaller?
Since it scales between two 3x3 matrices, meaning that it relates 9 numbers with 9 other numbers -> 9x9=81.
The symmetry of the problem (allowing no rotation or translation) reduces the modulus to 36 components.
By applying certain crystal symmetries, this can get even smaller, e.g. cubic young’s modulus only has three independent components.
Why is the first Billouin zone sufficient when looking at the dispersion relation?
The neighbouring brillouin zones are physically not different, they feature higher orders of waves that fit in between the atoms.
What is the dispersion relation of a photon in vacuum?
c=lambda nu = 2 pi /k nu = omega/k
omega = c * k
What are the consequences of periodic or fixed boundary conditions?
The quantization of possible q-vectors.
What limits the phonon lifetime?
Scattering with either other phonons or defects or the sample surface or other particles
What would happen to phonons if there would not be any anharmonicity in the potential energy of the atoms?
They would never decay because they cannot interact with other phonons (why?)
No thermal expansion
Which type of optical spectrometers is used in Brillouin scattering experiment?
3-axis neutron spectrometer
ore sometimes x-rays, but much harder
What is the difference between Raman and Brillouin scattering?
Raman occurs at high omega, using optical phonons.
Brillouin occurs at low omega, using acoustic phonons.
What is the difference between Raleigh, Stokes and Antistokes?
Raleigh doesn’t involve phonons.
Stokes is scattering under phonon creation, Antistokes is scattering under phonon annihilation.
What peak is bigger, Stokes or Antistokes? Why?
What peak is at higher energies, Stokes or Antistokes?
Stokes has a bigger peak at lower energies, since a phonon is created, using up parts of the original photon frequency. The peak is bigger than Antistokes since the elimination of a phonon requires it to exist, which is more unlikely.
What is the difference between Raman absorption and infrared absorption?
In Raman absorption, the dipolar moment of the lattice or molecule changes.
In IR absorption, the polarizability changes.
A material can only perform one of the two.
What happens to the Brillouin/Raman scattering peaks if temperature changes?
For lower T, they get smaller, AS might even vanish.
What effect appears when light is scattered by a phonon?
The Doppler effect: the light experiences the phonon as moving wavefronts, creating a shift in photon frequency.
Why is inelastic neutron scattering the method of choice for measuring phonon dispersions
Because the phonon causes energy differences that can be easily observed in the neutrons, \Delta E/E is quite big.
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