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

[sathya subramanyan]

Dear Sir,
          Thank you for your reply. I do understand that the sum of all the effective charges for a system should be zero but I would like to know why there is a discrepancy in calculating the ionic phase of the cubic( EXAMPLE10 OF ESPRESSO-4.0) and tetragonal PbTiO3 i.e. in cubic phase the total ionic phase should be -1.86 whereas it is 0.14(if it is sum of all the individual ionic phases of the constituent elements).
 
         In the tetra phase the total ionic phase is the sum of the individidual elements which is not so in cubic.I thus would like to know if this is the reason for me getting a negative value of effective charge for Pb for the displacement.I am attaching the ionic phase section for comparison.Please do enlighten me and thank you in advance


FOR CUBIC PHASE

              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)
  ============================================================================



FOR TETRAGONAL PbTiO3
            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)
  ============================================================================


Thanking You


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