Dear Yukihiro,
I have several suggestions for you.
1) You seem to be following Test_v4/t66.in as a model. The finite-
difference d/dk calculation is used here for reasons explained in
the README file, and is not a good choice as it converges very slowly
with zone sample size. The response-function d/dk as in t65.in and
t67.in are much preferred (except for certain testing purposes).
2) The convergence limits in the tests are much too loose (for timing
reasons), as stated in the README. I suggest tolvrs=1.0E-18 in datasets
1 and 3 and tolwfr=1.0E-20 in dataset 2 (t65 structure).
3) Your relaxed-atom results seem most sensitive to the change in
pseudopotential. Since you say your Born effective charges look OK,
the interatomic force constants must be responsible for the large
differences. Looking at your data file, it appears that you are
not using fully relaxed atomic positions and lattice constants.
This could invalidate your results, so I suggest your relax these
fully and then do your response-function calculation with the same
psp's, cutoffs, etc. Even with this, if your structure is near one
of the perovskite structural instabilities, a strong psp dependence
could persist. This would be a basic limitation of the theory.
You should look directly at your Q=0 phonon frequencies (ignoring
the 3 acoustic modes) and see how consistent they are.
4) The biggest issue in experimental comparisons could be the
difference between the "proper" piezoelectric tensor calculated
by abinit/anaddb and the "improper" one which is probably what is
quoted in your experimental reference. See the discussion following
Eq. (30) in abinit_4.4.2/Infos/Theory/vanderbilt-anaddb-notes.pdf
and Reference 17 of that document.
5) Finally, I don't know if the tetragonal phase of PbTiO3 you are
using is the stable low-temperature phase or not and at what temperature
the measurements were performed, but perovskite phonon frequencies
and hence interatomic force constants often have very large temperature
dependencies.
I hope these comments help.
Don Hamann
yukihiro_okuno@fujifilm.co.jp wrote:
Dear ABINIT Users.
I'm now calculating the piezoelectric coefficient , elastic constant
of the PbTiO3,(PT) by Density functional perturbation theory, (DFPT).
I found the Born effective charge are
calculated reasonably good vaule, but
the piezoelectric coefficient is far from the experiments and
other calculate values ( PRL vol(80) p4321).
I'm informed in this mailing list that the reason is possibly due to
the pseudopotential I used.
I used Teter's extended norm conserved pseudo potential which is downloaded
from the ABINIT Home Page. I also check the TM norm conserved potentials which are generated fhi98PP code. I check two
TM norm conserved pseudo potential one of which is
made by myself, and other is downloaded from the ABINIT web site.
The value of poezoelectric tensor from the Teter's pseudo potential
whici is down loaded from the web site,
================================================================================
Calculation of the piezoelectric tensor
-begin at tcpu 0.037 and twall 0.117sec
Proper piezoelectric constants(clamped ion)(Unit:c/m^2)
0.00000000 0.00000000 0.33709523
0.00000000 0.00000000 0.33709521
0.00000000 0.00000000 -0.73010205
0.00000000 0.14564668 0.00000000
0.14564654 0.00000000 0.00000000
0.00000000 0.00000000 -0.00000002
phonon modes warning- :
accoustic sum rule violation met:the eigenvalues of accoustic mode
are too large at Gamma point
increase cutoff energy or k-points sampling.
the three eigenvalues are: -9.481483E-03 3.209976E-03 -9.481370E-03
phonon modes warning- :
unstable eigenvalue detected in force constant matrix at Gamma point
the system under calculation is physically unstabale.
Proper piezoelectric constants(relaxed ion)(Unit:c/m^2)
0.00001074 0.00001665 3.66885153
0.00001320 0.00001685 3.66884157
0.00002883 0.00007794 15.60848674
0.00000405 -2.89251432 0.00001611
-2.89249871 0.00000253 0.00001237
0.00000000 0.00000000 0.00000095
================================================================================
The piezoelectric tensor which is calculated the pseudopotential which is generated by Fhi98PP code. ( In this case , the ground state
calculation is conserved by nband = 26, or iscf = 3)
================================================================================
Calculation of the piezoelectric tensor
-begin at tcpu 0.037 and twall 0.241sec
Proper piezoelectric constants(clamped ion)(Unit:c/m^2)
0.00000000 0.00000000 -0.34997886
0.00000000 0.00000000 -0.34997886
0.00000000 0.00000000 0.82928878
0.00000000 -0.09788078 0.00000000
-0.09788078 0.00000000 0.00000000
0.00000000 0.00000000 0.00000000
phonon modes warning- :
accoustic sum rule violation met:the eigenvalues of accoustic mode
are too large at Gamma point
increase cutoff energy or k-points sampling.
the three eigenvalues are: 9.096939E-04 -1.034723E-03 9.098799E-04
Proper piezoelectric constants(relaxed ion)(Unit:c/m^2)
0.00001277 0.00001374 -1.79825769
0.00001491 0.00000232 -1.79824556
0.00001185 0.00004332 -4.39017143
0.00000854 -3.44122842 0.00000877
-3.44126548 0.00000690 0.00000169
0.00000000 0.00000000 0.00000000
================================================================================
Results of these value are different each other
and also both of results are different from the experimental values.
I had checked the pseudo-potential of PbTiO3 by checking the each element pseudo potential reproduce
the lattice constants within the 1% from the experimantal values. ( Pb fcc for Pb pseudo potential
and TiC for Ti pseudo potential).
Is the responce function calculation so sensitive to the pseudo potential in general ? Or we must calculate more
accurately in the step of ground state caluculation than usual
ground state calculation?
Sincerely,
Yukihiro Okuno.
My input file is below, ( I take the experimental atomic coorinate from PRL vol(80) 4321 ).
# Crystalline AlP - rhombohedral distortion imposed
# Piezoelectroc tensor calculation
ndtset 4
#Common Data Definition of the unit cell
acell 7.3730000000 7.3730000000 7.8522450000
rprim 1.000000000000 0.000000000000 0.000000000000
0.000000000000 1.000000000000 0.000000000000
0.000000000000 0.000000000000 1.000000000000
ntypat 3
znucl 82 8 22
natom 5
typat 1 3 2 2 2
xcart
0.000000000000 0.000000000000 0.000000000000
3.686500000000 3.686500000000 4.224507810000
3.686500000000 3.686500000000 0.918712665000
3.686500000000 0.000000000000 4.805573940000
0.000000000000 3.686500000000 4.805573940000
ecut 50
ixc 3
ngkpt 4 4 4
nband 26
nbdbuf 0
occopt 1
nstep 500
prtden 1
prtvol 10
tolwfr 1.0d-12
diemac 12.0
# First dataset : Self-consistent ground state run
iscf1 5
kptopt1 1
# Second dataset : Non-self-consistent run for full k point set
# we recover full 6 6 6 k space (not kptopt1 = 1)
iscf2 -2
kptopt2 3
#use calculated results of dataset 1
getden2 1
getwfk2 1
## Third data set : finite-difference d/dk ground-state calculation
berryopt3 -2
getwfk3 2
getden3 1
iscf3 -2
kptopt3 3
# idir = 1 1 1 is needed because piezoelectric tensor need all d/dk components
rfdir3 1 1 1
# Fourth dataset : electric field and strain responce
getwfk4 2
getddk4 3
iscf4 3
kptopt4 3
#
rfdir4 1 1 1
# only generation of the first-order responce to the electric field
# assuming that the data on derivative of ground state-wave function
# with respect to k is available on disk
rfelfd4 3
# run strain responce function both uniaxial and shear strain
rfstrs4 3
# activate the calculation of the atomic dispacement
rfphon4 1
rfatpol4 1 5
nqpt4 1
qpt4 0.0 0.0 0.0
# run phonon
# strain perturbation is only available for v4.2 or over.
# but still iscf = 2 or iscf = 3 and diemix <= 0.5 is reccomended
diemix4 0.45
diemac4 1.0
--
D. R. Hamann Phone: 908-582-4454
Director, Theoretical Materials Fax: 908-582-4702
Physics Research (retired) email: drh@physics.bell-labs.com
Bell Laboratories
Lucent Technologies
700 Mountain Ave, Room 1D-371
Murray Hill, NJ 07974-0636 USA
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