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[matthieu verstraete <matthieu.jean.verstraete@gmail.com>]

Hello or_pong,

why are you doing the eigenvector stuff by hand? It it is for your
comprehension it is a good idea, otherwise anaddb will do it with
"eivec 1". Your procedure looks fine, as long as you use the true
displacement vectors and not the eigenvectors (differing by a factor
of 1/sqrt(M)), the latter being dimensionless.

Check the book by Born and Huang
http://www.amazon.ca/Dynamical-Theory-Crystal-Lattices-Born/dp/0192670085

You will not find data on S(t) but certainly on U(q) in early
(probably Phys Rev) papers on phonons in Si.


Matthieu

On Mon, Jun 8, 2009 at 4:38 PM, <or_pong@hotmail.com> wrote:
> Dear ABINIT forum,
>
> In order to study vibrational properties of silicon atoms in crystal, simple
> calculations had been performed.
> 1) Optimized structure calculation of silicon crystal.
> 2) Dynamical matrice, Dij(q) of several q-points (include q = 0,0,0) were
> calculated (following Response-Function tutorial 1) .
> 3) Eigen value problem of Dij(q) were solved using Octave.
>
>   [U(q),e(q)] = eig(Dij(q))
>
>   Where U(q) is eigen vector or displacement vector in Fourier space and 
> e(q)
> is eigen value.
> 4) Position of atoms for each time steps had been calculated.
>   S(t) = S_o + U(q) * sin(wt)   ; 0 <= wt < 2*pi
> 5) S(t) were ploted using visualization program, VMD.
>   The results shown acoustical vibration of w~0 3 modes and optical 
> vibration
> of another 3 modes.
>
> Plese give me any comment aboout this simple procedures and I'm also seeking
> some textbooks or pepers to check my S(t) results.
>



-- 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dr. Matthieu Verstraete

European Theoretical Spectroscopy Facility (ETSF)
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