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[Yong Liu <occupierliu@yahoo.com.cn>]

Dear Hamann:

        Thank you for your answers.

        Since I have checked the calculation of structural relaxtion for PTiO3 superstructure again, I found that the the final rprim is not consist with the initial symmetry as following,

             -6.9104342826E-01  6.9104344962E-01  2.1193850757E-01
              6.9104342826E-01 -6.9104344962E-01  2.1193850757E-01
              6.9104342826E-01  6.9104344962E-01 -2.1193850757E-01

while the spacegroup 87 need the rprim(0,0) = -rprim(0,1). Why did this happen?

        Now I repeat the GS calculation with a bigger ecutsm to check the conv! ergence.

        Thank you again.

"D. R. Hamann" <drh@bell-labs.com> 写道：

Dear Yong,

I'm replying to both this and your later Forum inquiry about the
negative elastic constants of your 4-formula-unit PbTiO3 supercell.

Using the DDB file you sent me privately for this tetragonal structure,
I calculated the phonons with anaddb both with and without the acoustic
sum rule (a summary is attached). Without asr, there are 3 negative
(unstable) frequencies at qpt=0 0 0. These could be small violations of
the asr causing the 3 acoustic modes to have small negative values
instead of zero, although your values are large. (I note that the asr =
0 results from anaddb duplicate the phonon frequencies in your abinit
output file.) When asr is imposed, these 3 modes ! should be forced very
close to zero. However, as you can see in the attached, imposing asr
gives 7 unstable modes with large negative eigenvalues. Since the
elastic constants are calculated with the asr, the negative relaxed-atom
Cij are a correct representation of an unstable structure. The warning
in your original anaddb output about large asr violations was in fact
the problem.

For your 4-unit PtTiO3 superstructure, your basic abinit output has 11
unstable modes, so I am not surprised that even your rigid-ion diagonal
elastic constants all come out negative for this highly unstable
structure. I'm surprised that you seem to have been able to relax the
structure in the first place.

Now, why the problem? Abinit has been used successfully for phonon and
elastic constant calculations for a number of ferroelectric and
paraelectric perovskites. While your ecut=45 looks quite large, the
psp's you are using have very localized states. In particular,
Psps_for_tests/22ti.psp.mod treats the 3s and 3p semicore states as
valence. All I can suggest is further convergence studies to get the
phonons of the basic cell converged with at most small asr errors and no
unstable optic modes.

Incidentally, with ecut=45, ecutsm=0.5 is much too small (see the
technical discussion of ecutsm in the input variable list to understand
why) and could produce spurious errors in the elastic constants even
with good phonon convergence. I'd suggest ecutsm = 0.05 * ecut,
approximately.

Good luck,

Don Hamann

Yong Liu wrote:

> Dear Abinitors:
> I've done the RF calculation about the elastic constants of tetragonal
> PbTiO3, Cij consists with the previous results of experiments and
> simulations except for C12, C44, and C66. Consindering the error
> induced from the k-point grid (involving 115 k-points) and numerical
> error (ecut 45hartree), the p! ositive C12 and C66 are acceptable. But
> the negative C44 totally confused me. Or this negative elastic
> constant has some physical means?
> P.S.
> Cij (Relaxed ion, GPa)
> 2.4239904 1.5071663 0.7684601 0.0000000 -0.0000001 0.0000000
> 1.5071663 2.4239877 0.7684603 0.0000000 0.0000001 0.0000000
> 0.7684603 0.7684601 0.5754473 0.0000000 -0.0000001 0.0000000
> 0.0000000 0.0000000 0.0000000 -0.5976210 0.0000003 0.0000000
> -0.0000001 0.0000001 -0.0000001 0.0000003 -0.5976204 0.0000000
> 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.0505907
> Results from Journal of materials research, 12:2623-2627(1997)
> c11 = 237Gpa, c33 = 60Gpa, c44 = 69Gpa
> c66 = 144Gpa, c12 = 90Gpa, c13 = 70Gpa
>
>
> Sincerely.
> Yong Liu
>
> -------------------------------------------------------------------------------------
> Yong Liu,
> Institute of Inorganic Materials,
> Department of Materials Science and Engineering,
> Zhejiang University,PR China
> Doctoral student
>
> ------------------------------------------------------------------------
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--
D. R. Hamann Phone: 908-582-4454
Director, Theoretical Materials Fax: 908-582-4868
Physics Research (retired) email: drh@bell-labs.com
Bell Laboratories
Lucent Technologies
700 Mountain Ave, Room 1D-371
Murray Hill, NJ 07974-0636 USA

-outvars9: echo values of input variables ----------------------

Flags :
elaflag 3
instrflag 1
Miscellaneous information :
chneut 1
First list of wavevector (reduced coord.) :
nph1l 1
qph1l
0.00000000E+00 0.00000000E+00 0.00000000E+00 1.000E+00

Phonon wavevector (reduced coordinates) : 0.00000 0.00000 0.00000
Phonon energies in Hartree :
-7.023109E-04 -7.023109E-04 -6.750167E-04 1.545292E-04 1.545292E-04
3.871682E-04 5.365783E-04 8.008861E-04 8.008861E-04 1.097496E-03
1.097496E-03 1.331143E-03 2.188541E-03 2.188541E-03 2.820736E-03



-outvars9: echo values of input variables ----------------------

Flags :
elaflag 3
instrflag 1
Miscellaneous information :
asr 2
chneut 1
First list of wavevector (reduced coord.) :
nph1l 1
qph1l
0.00000000E+00 0.00000000E+00 0.00000000E+00 1.000E+00

Phonon energies in Hartree :
-5.573373E-03 -5.265437E-03 -4.493790E-03 -3.079270E-03 -1.679307E-03
-1.277654E-03 -1.014457E-03 -5.438577E-04 7.192503E-04 1.024782E-03
2.225236E-03 2.586592E-03 3.904726E-03 4.464320E-03 4.605258E-03
Phonon frequencies in cm-1 :



-outvars9: echo values of input variables ----------------------

Flags :
elaflag 3
instrflag 1
Miscellaneous information :
asr 1
chneut 1
First list of wavevec! tor (reduced coord.) :
nph1l 1
qph1l
0.00000000E+00 0.00000000E+00 0.00000000E+00 1.000E+00


Phonon wavevector (reduced coordinates) : 0.00000 0.00000 0.00000
Phonon energies in Hartree :
-5.573373E-03 -5.265437E-03 -4.493790E-03 -3.079270E-03 -1.679307E-03
-1.277654E-03 -1.014457E-03 -5.438577E-04 7.192503E-04 1.024782E-03
2.225236E-03 2.586592E-03 3.904726E-03 4.464320E-03 4.605258E-03

Sincerely.
Yong Liu

-------------------------------------------------------------------------------------
Yong Liu,
Institute of Inorganic Materials,
Department of Materials Science and Engineering,
Zhejiang University,PR China
Doctoral student

---

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