# [Pw_forum] the problem about eigndisplacement of phonon?

Tue Jun 6 07:59:12 CEST 2006

```Dear Professor Stefano Baroni :
Thank you give me answers. i will give you a clear question.i have calculate the phonon of PbTiO3 at q=0. there is the eignvector of atoms under every phonon.
for example,omega( 1) =      -4.221301 [THz] =    -140.808368 [cm-1], eignvector of Pb atom is  -0.092855  -0.004178  0.001020.now i want to calculte the eigndisplacement of Pb atom under this phonon. i have konw eigndisplacement |u> =M^(-1/2) | v>. |v> is eignvector. i donnot know how to select M mass of Pb atom. in your letter, M should be 207.2 amu.namely, for Pb atom,  eigndisplacement |u> =207.2^(-1/2) | v>. is my opinion true?

there is  phonons of PbTiO3 as below:
omega( 1) =      -4.221301 [THz] =    -140.808368 [cm-1]
( -0.092855  0.000000 -0.004178  0.000000  0.001020  0.000000 )
( -0.185613  0.000000 -0.008352  0.000000  0.002040  0.000000 )
(  0.598322  0.000000  0.026924  0.000000 -0.005371  0.000000 )
(  0.598322  0.000000  0.021990  0.000000 -0.006576  0.000000 )
(  0.488678  0.000000  0.026924  0.000000 -0.006576  0.000000 )
omega( 2) =      -4.221301 [THz] =    -140.808368 [cm-1]
(  0.000638  0.000000  0.008439  0.000000  0.092568  0.000000 )
(  0.001275  0.000000  0.016869  0.000000  0.185040  0.000000 )
( -0.004108  0.000000 -0.054377  0.000000 -0.487170  0.000000 )
( -0.004108  0.000000 -0.044413  0.000000 -0.596476  0.000000 )
( -0.003356  0.000000 -0.054377  0.000000 -0.596476  0.000000 )
omega( 3) =      -4.221301 [THz] =    -140.808368 [cm-1]
( -0.004254  0.000000  0.092476  0.000000 -0.008401  0.000000 )
( -0.008503  0.000000  0.184856  0.000000 -0.016794  0.000000 )
(  0.027409  0.000000 -0.595882  0.000000  0.044214  0.000000 )
(  0.027409  0.000000 -0.486685  0.000000  0.054134  0.000000 )
(  0.022386  0.000000 -0.595882  0.000000  0.054134  0.000000 )
omega( 4) =      -0.669952 [THz] =     -22.347350 [cm-1]
( -0.041557  0.000000 -0.005329  0.000000  0.392444  0.000000 )
( -0.052468  0.000000 -0.006728  0.000000  0.495474  0.000000 )
( -0.047053  0.000000 -0.006034  0.000000  0.440840  0.000000 )
( -0.047053  0.000000 -0.005986  0.000000  0.444344  0.000000 )
( -0.046682  0.000000 -0.006034  0.000000  0.444344  0.000000 )
omega( 5) =      -0.669952 [THz] =     -22.347350 [cm-1]
( -0.169027  0.000000  0.356408  0.000000 -0.013059  0.000000 )
( -0.213403  0.000000  0.449978  0.000000 -0.016488  0.000000 )
( -0.191381  0.000000  0.403543  0.000000 -0.014670  0.000000 )
( -0.191381  0.000000  0.400360  0.000000 -0.014787  0.000000 )
( -0.189872  0.000000  0.403543  0.000000 -0.014787  0.000000 )
omega( 6) =      -0.669952 [THz] =     -22.347350 [cm-1]
(  0.354218  0.000000  0.169447  0.000000  0.039810  0.000000 )
(  0.447213  0.000000  0.213933  0.000000  0.050262  0.000000 )
(  0.401063  0.000000  0.191857  0.000000  0.044720  0.000000 )
(  0.401063  0.000000  0.190344  0.000000  0.045075  0.000000 )
(  0.397900  0.000000  0.191857  0.000000  0.045075  0.000000 )
omega( 7) =       3.378427 [THz] =     112.692954 [cm-1]
( -0.224846  0.000000 -0.197313  0.000000 -0.001099  0.000000 )
(  0.706263  0.000000  0.619778  0.000000  0.003451  0.000000 )
(  0.075451  0.000000  0.066211  0.000000  0.000316  0.000000 )
(  0.075451  0.000000  0.056787  0.000000  0.000369  0.000000 )
(  0.064711  0.000000  0.066211  0.000000  0.000369  0.000000 )
omega( 8) =       3.378427 [THz] =     112.692954 [cm-1]
( -0.197127  0.000000  0.224701  0.000000 -0.011833  0.000000 )
(  0.619195  0.000000 -0.705805  0.000000  0.037169  0.000000 )
(  0.066149  0.000000 -0.075402  0.000000  0.003406  0.000000 )
(  0.066149  0.000000 -0.064669  0.000000  0.003971  0.000000 )
(  0.056734  0.000000 -0.075402  0.000000  0.003971  0.000000 )
omega( 9) =       3.378427 [THz] =     112.692954 [cm-1]
( -0.008630  0.000000  0.008170  0.000000  0.298912  0.000000 )
(  0.027108  0.000000 -0.025663  0.000000 -0.938909  0.000000 )
(  0.002896  0.000000 -0.002742  0.000000 -0.086028  0.000000 )
(  0.002896  0.000000 -0.002351  0.000000 -0.100304  0.000000 )
(  0.002484  0.000000 -0.002742  0.000000 -0.100304  0.000000 )
omega(10) =       6.809520 [THz] =     227.142638 [cm-1]
(  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 )
(  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 )
( -0.706639  0.000000 -0.025709  0.000000  0.000000  0.000000 )
(  0.706639  0.000000  0.000000  0.000000  0.000444  0.000000 )
(  0.000000  0.000000  0.025709  0.000000 -0.000444  0.000000 )
omega(11) =       6.809520 [THz] =     227.142638 [cm-1]
(  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 )
(  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 )
( -0.000153  0.000000 -0.008007  0.000000  0.000000  0.000000 )
(  0.000153  0.000000  0.000000  0.000000 -0.707061  0.000000 )
(  0.000000  0.000000  0.008007  0.000000  0.707061  0.000000 )
omega(12) =       6.809520 [THz] =     227.142638 [cm-1]
(  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 )
(  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 )
( -0.025712  0.000000  0.706594  0.000000  0.000000  0.000000 )
(  0.025712  0.000000  0.000000  0.000000 -0.007996  0.000000 )
(  0.000000  0.000000 -0.706594  0.000000  0.007996  0.000000 )
omega(13) =      15.128567 [THz] =     504.638023 [cm-1]
(  0.007689  0.000000 -0.000587  0.000000  0.000000  0.000000 )
(  0.010929  0.000000 -0.000834  0.000000  0.000000  0.000000 )
(  0.362132  0.000000 -0.027649  0.000000  0.000000  0.000000 )
(  0.362132  0.000000  0.065311  0.000000  0.000000  0.000000 )
( -0.855422  0.000000 -0.027649  0.000000  0.000000  0.000000 )
omega(14) =      15.128567 [THz] =     504.638023 [cm-1]
(  0.000587  0.000000  0.007689  0.000000  0.000000  0.000000 )
(  0.000834  0.000000  0.010929  0.000000  0.000000  0.000000 )
(  0.027649  0.000000  0.362132  0.000000  0.000000  0.000000 )
(  0.027649  0.000000 -0.855422  0.000000  0.000000  0.000000 )
( -0.065311  0.000000  0.362132  0.000000  0.000000  0.000000 )
omega(15) =      15.128567 [THz] =     504.638023 [cm-1]
(  0.000000  0.000000  0.000000  0.000000  0.007711  0.000000 )
(  0.000000  0.000000  0.000000  0.000000  0.010961  0.000000 )
(  0.000000  0.000000  0.000000  0.000000 -0.857912  0.000000 )
(  0.000000  0.000000  0.000000  0.000000  0.363186  0.000000 )
(  0.000000  0.000000  0.000000  0.000000  0.363186  0.000000 )

Regards

zhuzhenye

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