GroupTheory`
GroupTheory`

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.

Details and Options

  • 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:
  • GOVerbose FalseControls 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.

Examples

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Basic Examples  (1)

First load the package:

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.

The parameters in the dynamical matrix are set.

The phonon spectrum is calculated.

Options  (1)

GOVerbose  (1)

Additional information about the construction of the dynamical matrix is given.