logo of Phonon Example of phonon animations

Animations of normal-mode vibrations  corresponding to selected points on the phonon dispersion curves of primitive cubic crystal AB, with atoms A and B at positions (0,0,0) (blue) and (1/2,1/2,1/2) (red).  The high-symmetry directions Gamma -X, X-M, M-Gamma and Gamma-R connect the high-symmetry points Gamma=(0,0,0), X=(1/2,0,0,), M=(1/2,1/2,0), R=(1/2,1/2,1/2) of the primitive cubic Brillouin zone. The force constants for A and B atoms are assumed to be the same, while the masses are different, and MA = 1.5 MB. Vibrational amplitudes are much larger then in the real crystal, except the last file, which shows realistic vibrations corresponding to T=300K.
File  Phonon type
  Wave vector k
  Frequency w (THz)
 LA
  longitudinal acoustic
  (1/10,0,0)
              3.1
 TA
  transverse acoustic
  (1/10,0,0)
              1.8
 LO
  longitudinal optic
  (1/10,0,0)
            11.4
 TO
  transvers optic
  (1/10,0,0)
            11.1
 Optic at X
  optic at X-point
  (1/2,0,0)
            10.3
 Optic at M
  optic at M-point
  (1/2,1/2,0,)
              7.1
 Optic at M
  optic at M-point
  (1/2,1/2,0)
              8.8
 Optic at R
  optic at R-point
  (1/2,1/2,1/2)
              9.0
 All
 superposition of many phonons
 in equilibrium at T=300K
  many k equally distributed
 over Brillouin zone
        all allowed

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