The ABINIT Users Mailing List ( CLOSED )

[Xavier Gonze <gonze@pcpm.ucl.ac.be>]

Dear Mustafa,

As mentioned by Mikami-san, one has to do something beyond
usual ABINIT capabilities. Several groups actually feed in a model
Hamiltonian the coefficients  that were obtained by linear-response
(dynamical matrices, Born effective charges, elastic constants ...)
complemented with higher-order coefficients (esp. fourth order,
mentioned by Mikami-san). You should make a litterature survey,
look for "Model Hamiltonian" with the following author names :
Rabe, Waghmare, Vanderbilt, Ghosez, Bellaiche ...
First papers along this line appeared in the mid-nineties.

Xavier




On 08 Feb 2006, at 02:32, Masayoshi Mikami wrote:

> Hi, Mustafa,
>
> As written in the error message, it cannot be computed...
> The dielectric properties should be computed with
> the most stable phase without negative phonon modes.
>
> I just thought of  the cubic BaTiO3 (above 406K)...
> In principle, frequency dependent dielectric properties
> can be experimentally examined.
> In this case, we need to think of the non-linear term
> higher than 2nd order (with respect to atomic position delta_x)
> to keep the BaTiO3 cubic.
> e.g. suppose the 4th term,
>         b (delta_x)^4 = b (delta_x)^2 * (delta_x)^2
> from the thermodynamics (remember "1/2 kT" rule),
> one (x^2) term may be approximately replaced with c (T).
> Thus the 4th-order may contribute as B (delta_x)^2
> (B: a phenomenological coefficient), thus the negative
> coefficient of (delta_x)^2 may be positive from
> the contribution of the 4th-order term (when T is high enough).
>
> Such phenomenological term should contribute
> to keep the BaTiO3 cubic above 406K, so that
> the experiment about dielectric properties may be conducted.
> Such discussion(implementation) would be possible
> in the Density Functional Perturbation Theory in future ... ??
>
> Regards,
> Masayoshi
>
> On 2006/02/08, at 8:52, Mustafa Uludogan wrote:
>
> > Hi,
> > I try to calculate the frequency dependent dielectric
> > coefficients  for a typical cubic ABO3 ferroelectric
> > compound
> > by anaddb variables
> >  dieflag   1     ! 2=> electronic dielectric tensor
> > only
> >  nfreq     100
> >  frmin     0.0
> >  frmax     0.008
> > . I hav egotten the following output.
> > If there are unstable modes present in the system, is
> > there a way to calculate these properties?
> >
> > Yours
> > Mustafa Uludogan
> >
> >
> >
> >
> > Relaxed ion dielectric tensor
> >
> > phonon modes warning- :
> > unstable eigenvalue detected in force constant matrix
> > at Gamma point
> > the system under calculation is physically unstabale.
> >     -80.36253001      0.00013084      0.00008454
> >       0.00013084    -80.35369361     -0.00006049
> >       0.00008454     -0.00006049    -80.36250426
> >
> >  diel9 : ERROR -
> >   The lowest mode appears to be a "true" negative
> > mode,
> >   and not an acoustic mode. This precludes the
> > computation
> >   of the frequency-dependent dielectric tensor.
> >   Action : likely there is no action to be taken,
> > although you,
> >   could try to raise your convergence parameters (ecut
> > and k-points).
> >  For your information, here are the four lowest
> > frequencies :
> >  -7.95442387E-04 -7.95418229E-04 -7.95418229E-04
> > 0.00000000E+00
> >
> >  leave_new : decision taken to exit ...
> >
> >
> > Mustafa Uludogan
> > Chemical Engineering Department
> > Texas A&M University
> > College Station, TX 77843
> >
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