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MIND MAP 3, SHARIFAH AZRA BT ABDUL KADIR - Coggle Diagram

- - - - To calculate the forces it is necessary to determine the wavefunctions and energies of the electron within the crystals
  - - - One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far
      - That linear dependence of displacement upon stretching force is called Hooke's Law .
      - Elastic Region ends is called the inelastic
        limit, or the proportional limit
      - The inelastic Limit is the point at which permanent deformation
        occurs and The Proportional Limit is the point at which the deformation is no longer directly proportional to the applied force
  - - - In a solid, the energy associated with this vibration and perhaps also with the rotation of atoms and molecules is called as thermal energy
  - - - The energy given to lattice vibrations is the dominant contribution to the heat capacity in most solids. In non-magneticinsulators, it is the only contribution.
        
        In metals are from the conduction electrons
        
        In magnetic materials are from magneting ordering.
      - Classical Gas Theory from From Boltzmann distribution
  - - - The maximum vibration frequency is determined by Debye
        frequency, Wd
      - Just like the Einstein model, it also recovers the Dulong–Petit
        law at high temperatures.
    - - Born–von Karman boundary conditions are periodic boundary conditions which impose the restriction that a wave function must be periodic on a certain Bravais lattice
    - - High temperature limit
      - Low temperature limit
- - - - The force to the right
      - The force to the left
  - - - There is a minimum possible wavelength, given by twice the equilibrium separation a between atoms
      - Shorter wavelengths are physically identical with some longer wavelength. That means the configuration of the system will look the same
- - - - Quanta of lattice vibrations
        -Energies of phonons are quantized -
    - - -Quanta of electromagnetic radiation
        -Energies of photons are quantized as well
    - - Piezoelectric
      - Thermal Excitation
      - Electron Tunnelling
- - - - Equation of motion for mass M (nth):
        mass x acceleration = restoring force
      - Equation of motion for mass m (n-1)th
      - ω versus k relation for diatomic chain
  - - - Transverse optical mode for diatomic chain
      - Transverse acoustical mode for diatomic chain