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LATTICE VIBRATION IV, 1., 2., 3., PHONON, characteristic, definition,…

- - - - hot electrons release energy into the surrounding
        
        by emitting phonon and protons into metal and its surrounding
      - probability to emit phonon is more than photon
      - current flow in metal causing electron temperature to increase
      - above threshold frequency, only photons are produced
    - - electron speed up with additional inetic energy (eV)
      - additional energy is released in the form of phonon emission
      - at certain energies, electron can tunnel through the barrier
      - phonon emitted by hot electron that losses energy when returning to equilibrium
    - - conversion from photon to phonon is inefficient (probability order of =10^-7)
      - electric field applied to material, it will experience strain
      - not suitable frequencies >10 GHz
      - oscillating electric field the piezoelectric transducer at a same frequency
        
        transducer emits phonon into specimen medium
  - - - had momentum ħk
    - - Inelastic scattering
        
        K’= k + K +G
        
        K’+ k = K +G
      - elastic scattering
        
        K= wavevector of the incident photon
        
        K’ = wavevector of the scattered photon.
        
        G = vector in the reciprocal lattice
  - - - frequencies of normal modes of these oscillators will be given by the solution of 3z linear equations
- - - - Non-Symmetry
        
        mixed character
      - High Symmetry
        
        pure longitudinal or pure transverse wave
        
        entire planes of atoms move in phase with their displacements perpendicular to k
    - - Differences
      - EQUATIONS
        
        obtain three simultaneous equations involving Ax, Ay and Az, the components of A.
        
        lead to three different dispersion relations, or three dispersion curves.
  - - - each of these two transverse modes and the one longitudinal mode all have different frequencies.
  - - - interaction of all atoms matter (not limited to nearest neighbour)
      - If sample is polyatom, there are many optical branch
      - force constant may vary- the branches are not degenerate
  - - - There are 6 branches if all three degree of freedom is allowed:
        
        doubly degenerate TA
        
        1LA
        
        doubly degenerate TO
        
        1LO
      - 3 acoustic and (3z-3) optical which (2z-2) are transverse optical phonons and the remaining phonons are longitudinal optical phonons
- - - - The region bounded by all such planes is called the Wigner-Seitz cell and is a primitive unit cell for the lattice.
    - - WS cell of the reciprocal lattice is also called the 1st Brillouin Zone.
        
        BCC direct space will produce FCC reciprocal lattice
        
        FCC direct space will produce BCC reciprocal lattice
      - containing all information about the lattice vibrations of the solid
      - Only the values in the 1st BZ correspond to unique vibrational modes
      - Any outside this zone is mathematically equivalent to a value inside the 1st Brillouin Zone
- - - - ACOUSTICAL BRANCH (Lower branch is due to the -ve sign of the root)
        
        OPTICAL BRANCH (Upper Branch is due to the +ve sign of the root)
    - - TRANSVERSE ACOUSTICAL
        
        give rise to long wavelength vibration -speed of light
      - TRANSVERSE OPTICAL
        
        1) higher energy vibration (frequency higher & certain amount of energy needed to excite this mode)
        
        2) The charges are moving in opposite direction
        
        3) Electromagnetic radiation can be used to excite this mode