GROUP THEORY SYMBOL

GTVibDynamicalMatrix

GTVibDynamicalMatrix[basis, cut off, nshell]
gives the dynamical matrix from a structure with basis and one atom per unit cell. A cluster up to the cut off radius is calculated. nshell shells are taken into account.

DetailsDetails

  • The dynamical matrix is calculated in a central force model. The interaction of atoms are simulated by springs. The model assumes, that each neighbour shell is represented by a certain spring constant. From the interaction potential in this model the force constant matrix is calculated and finally the dynamical matrix is prepared.
  • The mass of the atom is explicitly taken into account, although the spring constants could be renormalized accordingly.
  • Please note, that in GTBandStructure the option GOPhotonic True has to be used, if the phonon spectra are calculated from the dynamical matrix. Similar to the photonics eigenvalue problem omega^2 is calculated as eigenvalue, i.e. the square root has to be taken to get the phonon frequency itself.
  • The following option can be given:
  • GOVerboseFalseControls the output of additional information
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 13.2.1.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package:

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The dynamical matrix is calculated for a simple cubic structure. A cut of radius of 3 is used. Up to next nearest neighbour interactions are taken into account.

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The parameters in the dynamical matrix are set.

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The phonon spectrum is calculated.

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Options  (1)Options  (1)

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