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["Yong Liu" <yongliu.yl@gmail.com>]

Dear Don Hamann,

 

    I have check the output files of elastic calculation for diamond Si. Yes, the internal strains do have non-zero part even it only contributes to the c44, c55, and c66. I admit that I make a mistake to say that only one independent structural parameter will lead to zero internal strain contribution. But for cubic PbTiO3, the internal strain contribution is exactly zero according to the output file. I guess it relates to the different the symmetry. So I want to figure it out that the relationship between the independent structural parameters and the internal strains. Would you mind give me some clue? Thank you in advance.

 

Best regards,

LY

2008/9/18 D. R. Hamann <drhamann@mat-simresearch.com>

Dear Mozhgan,

Here's a follow-up having just read the Liu paper.

They use Abinit and report the rigid-ion elastic constants for cubic PbTiO3 from a DFPT calculation using cutoffs similar to yours.  If everything is converged in both calculations, the only reasonable source of difference could be the choice of pseudopotentials.

As to the instability  issue discussed in my last response below, their paper contains the statement that because there is only one independent structural parameter, the internal strain contribution is zero.  This is in general not true.  For example there are non-zero internal strain parameters for diamond-structure Si and an atomic-relaxation  correction to the elastic constants.  I suspect that the same is true for cubic perovskites, but you will have to look at these parameters in the .out file to be sure.  Assuming some are non-zero, the unstable phonons indicating the ferroelectric instability will most probably lead to elastic instabilities, and the rigid-atom results will be rather academic, not related to  the high-temperature cubic phase in which the phonons are stabilized by anharmonic effects.

Don Hamann

D. R. Hamann wrote:

Dear Mzahgan,

Let's keep this discussion on the forum so others may benefit.

Your input file looks good in a quick scan.  A few things to look for in your output file are whether the first-order wave function calculations converged within your 100-iteration limit, and whether there were non-zero terms in the list of internal strain parameters at the end.  The issue here is that I believe the cubic structure of PbTiO3 is unstable relative to a ferroelectric distortion.  If there are non-zero internal strain terms that means that atomic relaxation makes contributions to the elastic constants.  However if there are unstable phonon modes, trying to calculate the relaxed-atom elastic constants using anaddb will fail, indicating (probably) that the cubic structure is unstable with respect to one or more strain distortions.  I don't have access to the Liu paper at the moment, so I don't know what they did, but if the problem is ill-defined, it's unclear what the comparison of results means.

Don Hamann

Mozhgan Amini wrote:

Hi,
 I have done the "Elastic properties" tutorial, and here is my full input file.
Thanks a lot in advance.
#PbTiO3
#Response function calculation for:
#    * rigid-atom elastic tensor
#    * rigid-atom piezoelectric tensor
#    * interatomic force constants at gamma
#    * Born effective charges
  ndtset   3
# Set 1 : Initial self-consistent run
   iscf1   5
 kptopt1   1
 tolvrs1   1.0d-18  #need excellent convergence of GS quantities for RF runs

# Set 2 : Calculate the ddk wf's - needed for piezoelectric tensor and
#         Born effective charges in dataset 3
 getwfk2  -1
   iscf2  -3        #this option is needed for ddk
 kptopt2   2        #use time-reversal symmetry only for k points
   nqpt2   1        #one wave vector will be specified
    qpt2   0 0 0    #need to specify gamma point
 rfelfd2   2        #set for ddk wf's only
  rfdir2   1 1 1    #full set of directions needed
 tolwfr2   1.0d-20  #only wf convergence can be monitored here
# Set 3 : response-function calculations for all needed perturbations
 getddk3  -1
 getwfk3  -2
   iscf3   5
 kptopt3   2        #use time-reversal symmetry only for k points
   nqpt3   1
    qpt3   0 0 0
 rfphon3   1        #do atomic displacement perturbation
 rfatpol3   1 5      #do for all atoms
 rfstrs3   3        #do strain perturbation
  rfdir3   1 1 1    #the full set of directions is needed
 tolvrs3   1.0d-10  #need reasonable convergence of 1st-order quantities
#Common input data

# acell  COPY RELAXED RESULT FROM PREVIOUS CALCULATION
# Here is a default value, for automatic testing : suppress it and fill the previous line
 acell  3*3.863 angstrom
   rprim   1.0  0.0  0.0   #hexagonal primitive vectors must be
         0.0  1.0  0.0   #specified with high accuracy to be
         0.0  0.0  1.0   #sure that the symmetry is recognized
                         #and preserved in the optimization
                         #process
#Definition of the atom types and atoms
 ntypat   3
 znucl   82 8 22
 natom   5
 typat   1 3 2 2 2
#Starting approximation for atomic positions in REDUCED coordinates
#based on ideal tetrahedral bond angles
# xred  COPY RELAXED RESULT FROM PREVIOUS CALCULATION
# Here is a set of default values, for automatic testing : suppress it and fill the previous line
 xred  0.0    0.0    0.0
       0.5    0.5    0.5
       0.5    0.5    0.0
       0.5    0.0    0.5
       0.0    0.5    0.5

#Gives the number of bands, explicitely (do not take the default)
 nband   13             # For an insulator (if described correctly as an
                        # insulator by DFT), conduction bands should not
                        # be included in response-function calculations
#Definition of the plane wave basis set
  ecut   45.0            # Maximum kinetic energy cutoff (Hartree)
 ecutsm   0.5            # Smoothing energy needed for lattice paramete
                        # optimization.  This will be retained for
                        # consistency throughout.
#Definition of the k-point grid
 kptopt   1              # Use symmetry and treat only inequivalent points
 ngkpt   6 6 6          # 4x4x4 Monkhorst-Pack grid
nshiftk   1              # Use one copy of grid only (default)
 shiftk   0.5 0.5 0.5    # This choice of origin for the k point grid
                        # preserves the hexagonal symmetry of the grid,
                        # which would be broken by the default choice.
#Definition of the self-consistency procedure
 diemac   6.0            # Model dielectric preconditioner
  iscf   5              # Use conjugate-gradient SCF cycle
 nstep   100            # Maxiumum number of SCF iterations


--- On *Wed, 9/17/08, D. R. Hamann /<drhamann@mat-simresearch.com>/* wrote:

   From: D. R. Hamann <drhamann@mat-simresearch.com>
   Subject: Re: [abinit-forum] calculation of elastic constants for
   PbTiO3
   To: forum@abinit.org
   Date: Wednesday, September 17, 2008, 5:40 AM

   Dear mozhganamini,

   Your input file does not look like an elastic-constants input file.      Have you done the "Elastic properties" tutorial?  Without the full
   input     file that gave these results, it is hard to diagnose your problem.  I     see no "tol..." input variables, and the convergence criteria to get     good elastic constant (and other response function) results are much     tighter than the defaults that your attached ground-state file     apparently would get.

   Don Hamann

   mozhganamini@yahoo.com wrote:
   > Dear all,
   > I'm trying to calculate the elastic constants of PbTiO3 for comparing
   the
   > results with:  " Y. Liu et al. , Materials Science and Engineering A
   472(2008)
   > "
   > but my results are approximately twice the results in this article!?
   > Thanks a lot in advance
   >
   > my results for elastic          results in article
   > C11: 629 (GPa)                     383
   > C12: 192                     151     > C44: 116                     120
   >
   > my input file:
   >
   >  acell    3*3.863 angstrom
   >  rprim 1.0  0.0  0.0     >        0.0    1.0  0.0       >        0.0    0.0  1.0          > #Definition of the atom types and atoms
   >  ntypat   3     >  znucl     82 8 22
   >  natom     5
   >  typat     1 3 2 2 2
   >
   >   xred    0.0    0.0    0.0
   >     0.5    0.5    0.5
   >     0.5    0.5    0.0
   >     0.5    0.0    0.5
   >     0.0    0.5    0.5
   >
   >  nband     13         >               > #Definition of the plane wave basis set
   >    ecut   45.0         >  ecutsm   0.5             >                  > #Definition of the k-point grid
   >  kptopt   1             > ngkpt    6 6 6      > nshiftk   1               >  shiftk   0.5 0.5 0.5      >            > #Definition of the self-consistency procedure
   >  diemac   6.0         >    iscf   5          >   nstep   100              >
   >      --     D. R. Hamann
   Mat-Sim Research LLC    | Deptartment of Physics
   P.O. Box 742            |  and Astronomy
   Murray Hill, NJ 07974   | Rutgers University
   phone: 908-370-8079     | 732-445-4381

   email: drhamann@mat-simresearch.com


           

--
D. R. Hamann
Mat-Sim Research LLC    | Deptartment of Physics
P.O. Box 742            |  and Astronomy
Murray Hill, NJ 07974   | Rutgers University
phone: 908-370-8079     | 732-445-4381

email: drhamann@mat-simresearch.com

--
Best regards.

-------------------------------------------------------------------------------------
Liu, Yong, Ph D
Institute of Inorganic and nonmetal Materials,
Department of Materials Science and Engineering,
Zhejiang University,PR China