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Finite electric field calculations without fixing ions

Posted: Mon Sep 19, 2011 11:29 am
by Anwar
Hi everybody. I'm a newcomer and an inexperienced user of ABINIT.

I've been trying to calculate the polarization of perovskite BaTiO3 as a function of finite electric field. So, following the tutorial about polarization and electric filed, I calculated the polarization for various electric field (using a structure that I have optimized previously).

The problem I face is that the Polarization vs. Electric Filed curve comes out as a straight-line even for electric fields as high as 0.0001 a.u. Also there is no sign of hysteresis.

So I thought may be the problem is that the nuclear positions are fixed in the tutorial whereas the hysteresis / polarization switching in perovskites is due to the movement of central B atom and the O atoms under electric field.

Is there anyway to to calculate the polarization of a crystal without fixing the ions (i.e. with ionmov = 2 or 6)?

This is my input file:

Code: Select all




#Definition of the elementary cell
#*********************************
   acell 7.5120216890E+00  7.5120216890E+00  7.6915729471E+00 Bohr
   rprim 1 0 0
         0 1 0
         0 0 1

#Definition of the atoms
#***********************
   natom 5
   ntypat 3
   znucl   56 22 08
   typat 1 2 3 3 3
   ixc 11
   xred   0.0000000000E+00  0.0000000000E+00  0.0000000000E+00
                     5.0000000000E-01  5.0000000000E-01  5.1430000000E-01
                     5.0000000000E-01  5.0000000000E-01 -3.0760000000E-02
                     5.0000000000E-01  0.0000000000E+00  4.8422377187E-01
                     0.0000000000E+00  5.0000000000E-01  4.8422377187E-01

#Definition of the SCF procedure
#*******************************
   iscf 5
   nstep 100
   nband 12
   nbdbuf 0


#Definition of the plane wave basis set
#**************************************
   ecut  35
   ecutsm 0.5
   dilatmx 1.15
   ngkpt 6 6 6
   nshiftk 1
   shiftk 0.5 0.5 0.5
         
   toldfe 1.0d-12
   tphysel 300 K
   getwfk  -1

  ndtset  21
! ndtset   3
jdtset  11
        21     22  23  24  25     # The additional 8 values of the field have been suppressed to spare CPU time
        31     32  33  34  35
        41     42  43  44  45
        51     51  53  54  55
                                                                               
berryopt11 -1       rfdir11    1 1 1
                                                                               
berryopt21  4       efield21   0.000002  0.000002  0.000002   
berryopt22  4       efield22   0.000004  0.000004  0.000004   
berryopt23  4       efield23   0.000006  0.000006  0.000006   
berryopt24  4       efield24   0.000008  0.000008  0.000008   
berryopt25  4       efield25   0.000010  0.000010  0.000010   
                                                                               
berryopt31  4       efield31  0.000008 0.000008 0.000008   
berryopt32  4       efield32  0.000006 0.000006 0.000006   
berryopt33  4       efield33  0.000004 0.000004 0.000004   
berryopt34  4       efield34  0.000002 0.000002 0.000002   
berryopt35  4       efield35  0.000 0.000 0.000   





P.S. Another question has been bothering me. When I do the structural optimization run, the energy converges to a very high value (about 50 Ha). My input file for optimization:

Code: Select all


  ndtset   2       # There are 2 datasets in this calculation

# Set 1 : Internal coordinate optimization

  ionmov1   2       # Use BFGS algorithm for structural optimization
   ntime1   7       # Maximum number of optimization steps
  tolmxf1   1.0e-5  # Optimization is converged when maximum force
                    # (Hartree/Bohr) is less than this maximum
  natfix1   3       # Fix the position of two symmetry-equivalent atoms
                    #  in doing the structural optimization
  iatfix1   1 2 3     # Choose atoms 1 and 2 as the fixed atoms (see discussion)
  optcell1  0

# Set 2 : Lattice parameter relaxation (including re-optimization of
#         internal coordinates)

 dilatmx2   1.15    # Maximum scaling allowed for lattice parameters
 getxred2   -1      # Start with relaxed coordinates from dataset 1
  getwfk2   -1      # Start with wave functions from dataset 1
  ionmov2   2       # Use BFGS algorithm
   ntime2   10      # Maximum number of optimization steps
 optcell2   3       # Fully optimize unit cell geometry, keeping symmetry
  tolmxf2   1.0e-5  # Convergence limit for forces as above
 strfact2   100     # Test convergence of stresses (Hartree/bohr^3) by
                    # multiplying by this factor and applying force
                    # convergence test
  natfix2   3       
  iatfix2   1 2 3         

#Common input data

acell   3.992  3.992  4.036  angstrom           #this is a guess, with the c/a
                                        #ratio based on ideal tetrahedral
                                        #bond angles

  rprim  1 0 0   #  primitive vectors must be
         0 1 0   #specified with high accuracy to be
         0 0 1   #sure that the symmetry is recognized
                  #and preserved in the optimization
                  #process

#Definition of the atom types and atoms
 ntypat   3
  znucl   56 22 08
  natom   5
  typat   1 2 3 3 3

#Starting approximation for atomic positions in REDUCED coordinates
#based on ideal tetrahedral bond angles
   xred   0.0 0.0  0.0
          0.5 0.5  0.5143
          0.5 0.5 -0.03076
          0.5 0.0  0.4814
          0.0 0.5  0.4814
#Gives the number of bands, explicitely (do not take the default)
  nband   15           # 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   50          # Maximum kinetic energy cutoff (Hartree)
 ecutsm   0.5            # Smoothing energy needed for lattice paramete
                         # optimization.  This will be retained for
                         # consistency throughout.
ixc = 11                 !GGA, Perdew-Burke-Ernzerhof GGA functional
tphysel 300 K
#Definition of the k-point grid
  ngkpt   6 6 6          # 6 6 6 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   4000           # Model dielectric preconditioner
   iscf   7              # Pulay mixing of the potential
  nstep   40             # Maxiumum number of SCF iterations
 tolvrs   1.0d-18        # Strict tolerance on (squared) residual of the
                         # SCF potential needed for accurate forces and
                         # stresses in the structural optimization, and
                         # accurate wave functions in the RF calculations



The etotal and fcart are:

Code: Select all


           etotal1  -5.3094090418E+01
           etotal2  -5.3094307091E+01
            fcart1  -0.0000000000E+00 -0.0000000000E+00 -6.9446291206E-03
                    -0.0000000000E+00 -0.0000000000E+00 -2.4101663245E-02
                    -0.0000000000E+00 -0.0000000000E+00  3.1042348651E-02
                    -0.0000000000E+00 -0.0000000000E+00  1.9718573189E-06
                    -0.0000000000E+00 -0.0000000000E+00  1.9718573189E-06
            fcart2  -0.0000000000E+00 -0.0000000000E+00 -6.7464332558E-03
                    -0.0000000000E+00 -0.0000000000E+00 -1.9553866581E-02
                    -0.0000000000E+00 -0.0000000000E+00  2.6297646773E-02
                    -0.0000000000E+00 -0.0000000000E+00  1.3265321034E-06
                    -0.0000000000E+00 -0.0000000000E+00  1.3265321034E-06


Re: Finite electric field calculations without fixing ions

Posted: Mon Sep 19, 2011 12:27 pm
by jzwanzig
It is possible to compute structural relaxation in the presence of a finite electric field. You can use ionmov 2 for example. I don't think you can use optcell different from zero though (that is, you can't allow the cell size to vary, only the ion positions).

Re: Finite electric field calculations without fixing ions

Posted: Mon Sep 19, 2011 2:34 pm
by Anwar
Thank you Professor. I shall append ionmov 2 to my input file. I hope allowing the structure to relax (by moving ions) will be reflected at the calculated wavefunction and subsequently, in the berry polarization.

Re: Finite electric field calculations without fixing ions

Posted: Mon Sep 19, 2011 2:40 pm
by jzwanzig
I have successfully computed \epsilon_\infty (clamped ions) and \epsilon_0 (relaxed ions) using this method. Don't forget that with ionmov 2 you are doing a structural relaxation so you also have to set ntime, tolmxf, and ecutsm.

Re: Finite electric field calculations without fixing ions

Posted: Mon Sep 19, 2011 2:45 pm
by Anwar
jzwanzig wrote:I have successfully computed \epsilon_\infty (clamped ions) and \epsilon_0 (relaxed ions) using this method. Don't forget that with ionmov 2 you are doing a structural relaxation so you also have to set ntime, tolmxf, and ecutsm.


Once again I'm at your debt. I'm actually trying to calculate the optical dielectric tensor (as a function of changing electric field) for ferroelectrics. I can breath easier knowing it is not impossible :) . I'll add the appropriate commands to my input and let you know as soon as I get results. Since I'm not doing calculations in parallel, that may take a while.

Re: Finite electric field calculations without fixing ions

Posted: Mon Feb 26, 2018 2:09 pm
by sevket simsek
Dear Abinit user,

Is there anyone who has calculated the hysteresis curve for a ferroelectric material?
I calculated, but I got a straight line, I could not get the hysteresis curve.

Re: Finite electric field calculations without fixing ions

Posted: Mon Feb 26, 2018 3:28 pm
by ebousquet
Dear Sevket,
What about Fig.5.c of:
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.84.115107
Done for PbTiO3?
Best wishes,
Eric

Re: Finite electric field calculations without fixing ions

Posted: Mon Feb 26, 2018 10:11 pm
by sevket simsek
Dear Eric,
Thank you very much for your reply before anything else.
I think you're talking about figure 5b.
I have calculated for tetragonal BaTiO3 and obtained a result as you indicated in Figure 5b.
but I want to get a curve like the one below.
if you share your advice and suggestion in this matter, I am delighted.
Best wishes

Re: Finite electric field calculations without fixing ions

Posted: Wed Feb 28, 2018 10:51 am
by ebousquet
Dear Sevket,
Humm, what you want is beyond static 0K DFT, the experimental hysteresis involves a much more complex dynamical process with domains, defects, leakage, etc, which give "imperfect" hysteresis (see for example the discussion in http://iopscience.iop.org/article/10.1088/0953-8984/20/02/021001/meta at the experimental side).
As it is now, you get somehow the "hysteresis" of a perfect monodomain crystal at 0K. Going a bit further requires to make an effective Hamiltonian or atomic potential model.
Best wishes,
Eric

Re: Finite electric field calculations without fixing ions

Posted: Wed Feb 28, 2018 12:53 pm
by sevket simsek
Dear Eric,

I thank you for useful discussions.

Best wishes.