Please enable JavaScript.
Coggle requires JavaScript to display documents.
Lattice Vibration, image - Coggle Diagram
Lattice Vibration
Lattice Vibration IV
Real Crystal System
- a 3D crystal, the atoms vibrate in three dimensions
- obtain simultaneous equations
- three different dispersion relations or three dispersion curves
Transverse mode
- degenerate on only special high-symmetry direction
- two transverse modes and one longitudinal mode all have different frequencies
- distinction between longitudinal and transverse waves no longer
Number of branches
- three branches are acoustic and remaining ( 3z - 3 ) optical
- allowed k-values in any single branch is N
- 3z different vibrational
-
-
-
-
Photon Momentum
- phonon of wavevector k will interact with particles
- phonon does not carry physical momentum
- the center of mass of the crystal does not change
- elastic scattering of crystal is governed by wavevector selection rule K'=K+G
-
Lattice Vibration I
Hooke's Law
- Extension of the spring is directly proportional to the pulling force
Inelastic Limit
- permanent deformation occurs
- will not return to its original size and shape
Proportional Limit
- deformation no longer directly proportional to the applied force
Sample Periodic Motion
- motion which body moves back and forth
- return to each position and velocity
Definition
- periodic motion in the absence of friction and produced by restoring force and directly proportional to displacement and oppositely directed
-
-
-
Heat Capacity
Definition
- the amount of heat needed to raise an unit amount substance by unit in temperature
Heat capacity constant volume
Heat capacity constant pressure
Classical gas theory
Kinetic energy
Models Lattice Vibration
-
Debye Model
- recovers the Dulong-Petit law at high temperature
- The maximum vibration frequency determined by Debye frequency
-
- exact at low and high temperature and an interpolation formula in between
Born Von Karman Model
- periodic boundary condition which impose the restriction that wave function must be periodic on a certain Bravais lattice
Lattice Vibration III
-
Normal mode
- two atoms in a molecule vibrate with respect to each other
- atom make small displacement, minima of bond potentials can be approximated as parabolas
- possible motion of a spring system
Definition:
- pattern of motion which all parts of the system move in a sinusoidal fashion, with the same frequency
- 2N normal mods of vibration as this is the total number of atoms
-
-
-