The ABINIT Users Mailing List ( CLOSED )

[yukihiro_okuno@fujifilm.co.jp]

Dear Abinit Users.

I'm now calculationg the piezoelectric tensor of PbTiO3.
I use the Densyty Functional Perturbation Theory (DFPT) 
by ABINIT and anaddb. 
The calculation is conversed by Pen4 3.0G within 24 hours.
and for  example, calculated Born Effective charge is good value
like below,


Atom Zxx Zyy Zzz
Pb 3.839 3.839 3.51   (3.52)
Ti 6.741 6.741 5.69   (5.18)
O1 -2.54/(-5.61) -2.54/-5.61 -2.23  (-2.16)
O3 -2.42  -2.42 -4.72  (-4.38)

( here () value is Cohen's calculated values PRL vol(80) p4321 )


But the result of the piezoelectric tensor is too far from 
the experimental vaule. (anaddb output files)

 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


 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


This is far from the experimental and the FLAPW calculated value by Cohen's
(Physical Review Letter vol(11) 4321 (1998) ) Paper's Table IV

Cohen's calculated values (c/m^{2})

                     e_{15}    e_{31}     e_{33}           
Proper homogeneous   1.99       -1.72    -0.88
Internal Strains     1.16       0.79     4.11
Proper total        3.15        -0.93    3.23

Experimental^{a}    3.92        -0.98    3.35
Experimental^{b}    2.96        0.46     6.50 


The Anaddb output file has the warnings like 

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.

Is it the difference of my calculation due to this warnings? 

Sincerely.

Yukihiro Okuno. 


My Input file of ABINIT and anaddb is below.


# Here ABINIT input file

# 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     0.454644985500 
    3.686500000000     3.686500000000     4.136562666000 
    3.686500000000     3.686500000000    -0.138984736500 
    3.686500000000     0.000000000000     3.663072292500 
    0.000000000000     3.686500000000     3.663072292500 

ecut 40
ixc 3
ngkpt 6 6 6
nband 22
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 
  
# 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


##############################################
here the anabbd files


dieflag 3
elaflag  3  !the flag for the elastic constant
piezoflag 3
instrflag 1  !the flag for the internal strain tensor

#the effective charge part

asr 1
chneut  1

#Wavevector list number 1

#number of phonons in list 1
nph1l 1 
qph1l  0.0 0.0 0.0 1.0 !the Gamma point