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M I N D M A P 3 - Coggle Diagram

- - - - In metals
        
        From thermal energy
        
        From the conduction electrons
      - In non magnetic insulators
        
        From thermal energy only
      - In magnetic materials
        
        From thermal energy
        
        From magnetic ordering
    - - The amount of heat needed to raise a unit amount of substance by a unit in temperature
      - Heat capacity at constant volume
        
        The slope of internal energy vs temperature
      - Heat capacity at constant pressure
        
        The slope of enthalpy vs temperature
    - - The constant value of the heat capacity of most simple solids
      - In 1819, Dulong and Petit found experimentally that Cv for most solids at room temperature is 3R = 25 J/Kmol
  - - - for 3-D
  - - - Periodic boundary condition which impose the restriction that a wave function must be periodic on a certain Bravais lattice
- - - - Force to the right
        
        Force to the left
        
        Total force
  - - - The dispersion relation of the monoatomic for 1D lattice
      - Relationship between frequency and wave number is known as dispersion relation
      - The result is periodic and the only unique solutions are correspond to values in the range,
  - - - The cos forces the group velocity to 0 at the edge of the 1st Brillouin zone
- - - - At A, the two atoms are oscillating in antiphase with their centre of mass at rest
      - At B, the lighter mass m is oscillating and M is at rest
      - At C, M is oscillating and m is at rest
      - At max.acoustical point C, M oscillates and m is at rest
      - At min.optical point B, m oscillates and M is at rest
  - - - If the two masses are equal, the two branches join (become degenerate) at π/a
      - At optical branch,
      - At acoustical branch,
      - The difference between maximum frequency and minimum frequency becomes narrower when both atoms are nearly identical and no longer exist for m=M
- - - - When k lies in the direction of high symmetry, two of the branches as transverse and one is longitudal
    - - In real crystals, two transverse modes degenerate on only in special high-symmetry directions
      - For directions of propagation, these two transverse modes and the one longitudinal mode all have different frequencies
    - - Wigner-Seitz cell of the reciprocal lattice is also called the 1st Brillouin zone
      - Contains all information about the lattice vibrations of the solid
      - For 3D lattices
  - - - Phonon is created, K’+ k = K +G
      - Phonon is absorbed, k' = k + K + G
  - - - Electric field applied to a piezoelectric material (quartz, cadmium sulfide, etc..), strain experienced
      - Oscillating electric field generated, the field then swing the piezoelectric transducer at the same frequency
      - Phonon transmitted by the transducer, into the specimen
      - No suitable for frequencies > 10GHz
    - - Current flows through metal wires causes the electron's temperature to rise
      - The electrons release energy by emitting phonon and photons into the metal and its surrounding
      - Above the threshold frequency, only photons are produced
    - - Thin layer of insulator is placed between two thin layers of metal to form a barrier for the electrons
      - At certain energies, the electron can tunnel through the barrier, and can speed up with additional kinetic energy
        
        Additional energy is released in the form of phonon emission
        
        Phonon is emitted by hot electrons