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["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