[Pw_forum] negative value of polarization and Z* for Pb in Tetragonal PbTiO3 and discrepancy in calculation of

sathya subramanyan sathya_sheela1985001 at rediffmail.com
Fri Jun 27 11:51:12 CEST 2008


  
Dear Developers,
                I am trying to calculate the Berry Phaze Polarization and effective charge on Pb(with the displacement of .01*ao) for PbTiO3(tetragonal) but am getting a negative value, using quantum espresso ver 4.0.

                When I run the example 10 for cubic phase the polarization and the Z* comes out to be alright. But, when I try for tetragonal phase, I am getting negative ionic phase leading to negative polarization for Pb. 
                If I compare the out put file for both cubic and tertragonal phase, to my surprise in the cubic phase the total ionic phase comes out to be positive (actually, if you sum it is negative), where as in the case of tetragonal phase the ionic phase comes out to be negative (but, it is positive if you sum the same way as for the cubic). 
                I do not understand this differrent summing rule for different phases. I am attaching both the input and out files for cubic and tetragonal phases. I would appreciate any useful suggestions to clear this point.
I am very sorry for the long mail and data files.

INPUT FILE FOR CUBIC PbTiO34
      &control
    calculation  = 'nscf'
    pseudo_dir    = '/home/nbaski/espresso-4.0/pseudo/'
    outdir        = '/home/nbaski/tmp/'
    lberry        = .true.
    gdir          = 3
    nppstr        = 7
/
&system
    ibrav        = 1
    celldm(1)    = 7.3699
    nat          = 5
    ntyp          = 3
    nbnd          = 22
    ecutwfc      = 30.0
    occupations  = 'fixed'
    degauss      = 0.00
/
&electrons
    conv_thr      = 1e-5
    mixing_beta  = 0.3
/
ATOMIC_SPECIES
  Pb  207.2      Pb.vdb.UPF
  Ti    47.867    Ti.vdb.UPF
  O    15.9994  O.vdb.UPF
ATOMIC_POSITIONS
  Pb    0.000    0.000    0.010
  Ti    0.500    0.500    0.500
  O    0.000    0.500    0.500
  O    0.500    0.500    0.000
  O    0.500    0.000    0.500
K_POINTS {automatic}
  4 4 7  1 1 1

THE O/P FILE FOR CUBIC PbTiO3   (as it is a very big file am attaching only the ionic phase calculation section)


  ==================================================
                            POLARIZATION CALCULATION
                        !!! NOT THOROUGHLY TESTED !!!
              --------------------------------------------------


                    K-POINTS STRINGS USED IN CALCULATIONS
                    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

      G-vector along string (2 pi/a):  0.00000  0.00000  1.00000
      Modulus of the vector (1/bohr):  0.85255
      Number of k-points per string:  7
      Number of different strings  :  3


                              IONIC POLARIZATION
                              ~~~~~~~~~~~~~~~~~~

        Note: (mod 1) means that the phases (angles ranging from
        -pi to pi) have been mapped to the interval [-1/2,+1/2) by
        dividing by 2*pi; (mod 2) refers to the interval [-1,+1)

  ============================================================================
    Ion    Species    Charge              Position                Phase
  ----------------------------------------------------------------------------
    1        Pb      14.000      0.0000  0.0000  0.0100    0.14000 (mod 2)
    2        Ti      12.000      0.5000  0.5000  0.5000    0.00000 (mod 2)
    3        O        6.000      0.0000  0.5000  0.5000    -1.00000 (mod 2)
    4        O        6.000      0.5000  0.5000  0.0000    0.00000 (mod 2)
    5        O        6.000      0.5000  0.0000  0.5000    -1.00000 (mod 2)
  ----------------------------------------------------------------------------
                                              IONIC PHASE:  0.14000 (mod 2)
  ============================================================================


                            ELECTRONIC POLARIZATION
                            ~~~~~~~~~~~~~~~~~~~~~~~

        Note: (mod 1) means that the phases (angles ranging from
        -pi to pi) have been mapped to the interval [-1/2,+1/2) by
        dividing by 2*pi; (mod 2) refers to the interval [-1,+1)

  ============================================================================
  Spin    String    Weight      First k-point in string        Phase
  ----------------------------------------------------------------------------
    up        1      0.250000      0.1250  0.1250 -0.5000    -0.05427 (mod 1)
    up        2      0.500000      0.1250  0.3750 -0.5000    -0.04876 (mod 1)
    up        3      0.250000      0.3750  0.3750 -0.5000    -0.05048 (mod 1)
  ----------------------------------------------------------------------------
  down      1      0.250000      0.1250  0.1250 -0.5000    -0.05427 (mod 1)
  down      2      0.500000      0.1250  0.3750 -0.5000    -0.04876 (mod 1)
  down      3      0.250000      0.3750  0.3750 -0.5000    -0.05048 (mod 1)
  ----------------------------------------------------------------------------
                                        Average phase (up):  -0.05057 (mod 1)
                                      Average phase (down):  -0.05057 (mod 1)
                                          ELECTRONIC PHASE:  -0.10114 (mod 2)
  ============================================================================


                              SUMMARY OF PHASES
                              ~~~~~~~~~~~~~~~~~

                          Ionic Phase:  0.14000 (mod 2)
                    Electronic Phase: -0.10114 (mod 2)
                          TOTAL PHASE:  0.03886 (mod 2)


                            VALUES OF POLARIZATION
                            ~~~~~~~~~~~~~~~~~~~~~~

        The calculation of phases done along the direction of vector 3
        of the reciprocal lattice gives the following contribution to
        the polarization vector (in different units, and being Omega
        the volume of the unit cell):

          P =  0.2864184  (mod  14.7398000)  (e/Omega).bohr

          P =  0.0007155  (mod  0.0368220)  e/bohr^2

          P =  0.0409070  (mod  2.1051744)  C/m^2

        The polarization direction is:  ( 0.00000 , 0.00000 , 1.00000 )


              ==================================================






THE I/P FILE FOR TETRAGONAL PbTiO3

&CONTROL
    calculation  = 'nscf'
    pseudo_dir    = '/home/nbaski/espresso-4.0/pseudo/'
    outdir        = '/home/nbaski/tmp/'
    lberry        = .true.
    gdir          = 3
    nppstr        = 7
/
&SYSTEM
    ibrav        = 6
    celldm(1)    = 7.3415
    celldm(3)    = 1.0653
    nat          = 5
    ntyp          = 3
    nbnd          = 22
    ecutwfc      = 30.0
    occupations  = 'fixed'
    degauss      = 0.00
/
&ELECTRONS
    conv_thr      = 1e-5
    mixing_beta  = 0.3
/
ATOMIC_SPECIES
  Pb  207.2      Pb.vdb.UPF
  Ti    47.867    Ti.vdb.UPF
  O    15.9994  O.vdb.UPF
ATOMIC_POSITIONS
  Pb    0.00000    0.00000    0.01000
  Ti    0.50000    0.50000    0.53770
  O    0.50000    0.50000    0.11180
  O    0.00000    0.50000    0.61740
  O    0.50000    0.00000    0.61740
K_POINTS {automatic}
  4 4 7  1 1 1





O/P FILE FOR PbTiO3


==================================================
                            POLARIZATION CALCULATION
                        !!! NOT THOROUGHLY TESTED !!!
              --------------------------------------------------


                    K-POINTS STRINGS USED IN CALCULATIONS
                    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

      G-vector along string (2 pi/a):  0.00000  0.00000  0.93870
      Modulus of the vector (1/bohr):  0.80338
      Number of k-points per string:  7
      Number of different strings  :  3


                              IONIC POLARIZATION
                              ~~~~~~~~~~~~~~~~~~

        Note: (mod 1) means that the phases (angles ranging from
        -pi to pi) have been mapped to the interval [-1/2,+1/2) by
        dividing by 2*pi; (mod 2) refers to the interval [-1,+1)

  ============================================================================
    Ion    Species    Charge              Position                Phase
  ----------------------------------------------------------------------------
    1        Pb      14.000      0.0000  0.0000  0.0100    0.13142 (mod 2)
    2        Ti      12.000      0.5000  0.5000  0.5377    0.05689 (mod 2)
    3        O        6.000      0.5000  0.5000  0.1118    0.62968 (mod 2)
    4        O        6.000      0.0000  0.5000  0.6174    -0.52267 (mod 2)
    5        O        6.000      0.5000  0.0000  0.6174    -0.52267 (mod 2)
  ----------------------------------------------------------------------------
                                              IONIC PHASE:  -0.22735 (mod 2)
  ============================================================================


                            ELECTRONIC POLARIZATION
                            ~~~~~~~~~~~~~~~~~~~~~~~

        Note: (mod 1) means that the phases (angles ranging from
        -pi to pi) have been mapped to the interval [-1/2,+1/2) by
        dividing by 2*pi; (mod 2) refers to the interval [-1,+1)

  ============================================================================
  Spin    String    Weight      First k-point in string        Phase
  ----------------------------------------------------------------------------
    up        1      0.250000      0.1250  0.1250 -0.4694    -0.30118 (mod 1)
    up        2      0.500000      0.1250  0.3750 -0.4694    -0.28922 (mod 1)
    up        3      0.250000      0.3750  0.3750 -0.4694    -0.25437 (mod 1)
  ----------------------------------------------------------------------------
  down      1      0.250000      0.1250  0.1250 -0.4694    -0.30118 (mod 1)
  down      2      0.500000      0.1250  0.3750 -0.4694    -0.28922 (mod 1)
  down      3      0.250000      0.3750  0.3750 -0.4694    -0.25437 (mod 1)
  ----------------------------------------------------------------------------
                                        Average phase (up):  -0.28353 (mod 1)
                                      Average phase (down):  -0.28353 (mod 1)
                                          ELECTRONIC PHASE:  -0.56706 (mod 2)
  ============================================================================


                              SUMMARY OF PHASES
                              ~~~~~~~~~~~~~~~~~

                          Ionic Phase: -0.22735 (mod 2)
                    Electronic Phase: -0.56706 (mod 2)
                          TOTAL PHASE: -0.79441 (mod 2)


                            VALUES OF POLARIZATION
                            ~~~~~~~~~~~~~~~~~~~~~~

        The calculation of phases done along the direction of vector 3
        of the reciprocal lattice gives the following contribution to
        the polarization vector (in different units, and being Omega
        the volume of the unit cell):

          P =  -6.2130096  (mod  15.6417999)  (e/Omega).bohr

          P =  -0.0147393  (mod  0.0371074)  e/bohr^2

          P =  -0.8426689  (mod  2.1214933)  C/m^2

        The polarization direction is:  ( 0.00000 , 0.00000 , 1.00000 )


              ==================================================

Thank you in advance for any help


SATHYA SHEELA.S
Grad. Student
Department of Physics 
National Institute of Technology
Tiruchirapalli - 620015 
India
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