[Pw_forum] example06

Stefano Baroni baroni at sissa.it
Tue Jan 4 21:48:17 CET 2005


Dear Fethi:

disentangling which-is-which in vibrational frequencies (as well as in  
electronic-structure calculations) requires the consideration of the  
vibrational eigenvectors (or, for electronic structure, the  
eigenfunctions), plus some elementary knowledge of group theory.

The distinction between acoustic and optic branches is to much extent  
conventional (acoustic branches are the lowest-lying, i.e.  their  
frequencies vanish in the long-wavelength limit). All the other  
branches (i.e. those whose energy is finite in the q->0 limit) are  
conventionally named "optic".

The term "transverse" or "longitudinal" refers to the polarization of  
the vibration with respect to the direction of propagation of the  
lattice vibration. This is also to some extent conventional. It is not  
for vibrations propagating along high-symmetry wave-vectors in, say,  
cubic materials. In this case, group theory shows that the polarization  
vector is either parallel (for longitudinal modes) or perpendicular  
(for transverse modes) to the phonon wave-vector. For low-symmetry  
crystals, or for low-symmetry directions in high-symmetry materials,  
lattice vibrations may not be longitudinal nor transverse. In any case,  
in general, you cannot tell without examining the phonon eigenvectors.

However, as a first, very crude, hint degeneracy may also help (see  
below).

See below for some more comments

On Jan 4, 2005, at 8:31 PM, Fethi SOYALP wrote:

>  Dear PWSCF user’s
> My question is about example06. in example06 matdyn.x calculate  
> vibration
> modes (for AlAs) at any q-vector from previously calculated IFC’s and  
> save
> results in matdyn.modes
> I can determine some modes but not all. how can I determine vibration
> modes. which ones are LA-TA, which ones are LO-TO. I have need some
> explanations.
>
>
>
> q =       0.0000      0.0000      0.0000
>
> I guess no splitting

You guess? The acoustic mode is 3-fold degenerate. The other three  
modes are split in a singlet (LO) plus a doublet (TO). Why LT and TO  
modes are split would require some more explanation, and I would like  
to urge you to consult any text-book in solid-state physics to  
understant why. If after studying your favorite text you still do not  
understand, please revert to us and we will give further help.


>
> q =       0.1250      0.0000      0.0000
>
> 23.8935   T? (may be TA because  its vibration is small, but Al  
> vibration
> is bigger than As vibration. how can I decide )
>
> 23.8935   TA (because As vibration is bigger than Al)

they are both Acoustic (because the frequency is small) and Transverse  
(because they are doubly degenerate). See below, however, for a more  
detailed explanation
> 43.6837   L? (LA or LO which one?)

L! Bravo! L because it is a singlet. A because it is the lowest singlet.

> 374.1934  TO
> 374.1934  TO
> 411.2102  LO

Perfect!

> q =       0.1250      0.0000      0.0000

according to the output below, this should be 0.25,0,0 ...

> 46.2977   TA
> 46.2977   TA
> 84.7692   L?
> 370.0075  TO
> 370.0075  TO
> 412.4930  LO

Here I am confused. What made you guess (almost) every assignement,  
while you were in doubt for the previous ones .?...

> q =       0.3750      0.0000      0.0000
>
> 65.6812  TA
> 65.6812  TA
> 121.6146  L?
> 363.2877  TO
> 363.2877  TO
> 413.1999  LO
>
> q =       0.5000      0.0000      0.0000
>
> 80.5497
> 80.5497
> 153.5469
> 355.7745
> 355.7745
> 412.6416

as above ...

> matdyn MODES
>
>      diagonalizing the dynamical matrix ...
>
>  q =       0.0000      0.0000      0.0000
>   
> *********************************************************************** 
> ***
>      omega( 1) =       0.000000 [THz] =      -0.000009 [cm-1]
>  ( -0.058918   0.000000    -0.055329   0.000000     0.702472    
> 0.000000   )
>  ( -0.058918   0.000000    -0.055329   0.000000     0.702472    
> 0.000000   )
>      omega( 2) =       0.000000 [THz] =      -0.000007 [cm-1]
>  ( -0.428642   0.000002     0.562314  -0.000002     0.008338    
> 0.000000   )
>  ( -0.428642   0.000002     0.562314  -0.000002     0.008338    
> 0.000000   )
>      omega( 3) =       0.000000 [THz] =       0.000001 [cm-1]
>  ( -0.559281   0.000000    -0.425138   0.000000    -0.080393    
> 0.000000   )
>  ( -0.559281   0.000000    -0.425138   0.000000    -0.080393    
> 0.000000   )
>      omega( 4) =      11.258455 [THz] =     375.544117 [cm-1]
>  (  0.000000   0.000000    -0.302638   0.000000    -0.890853    
> 0.000000   )
>  (  0.000000   0.000000     0.108982   0.000000     0.320803    
> 0.000000   )
>      omega( 5) =      11.258455 [THz] =     375.544117 [cm-1]
>  (  0.000000   0.000000    -0.890853   0.000000     0.302638    
> 0.000000   )
>  (  0.000000   0.000000     0.320803   0.000000    -0.108982    
> 0.000000   )
>      omega( 6) =      12.308719 [THz] =     410.577401 [cm-1]
>  (  0.940855  -0.000093     0.000000   0.000000     0.000000    
> 0.000000   )
>  ( -0.338809   0.000034     0.000000   0.000000     0.000000    
> 0.000000   )
>   
> *********************************************************************** 
> ***
>      diagonalizing the dynamical matrix ...


Let's skip this, 'cause this would require some more understanding  
about LO-TO splitting for lattice-periodic vibrations, which I do not  
know if you have (see above)

> q =       0.1250      0.0000      0.0000
>   
> *********************************************************************** 
> ***
>      omega( 1) =       0.716305 [THz] =      23.893534 [cm-1]
>  (  0.000000   0.000000     0.567877  -0.149466    -0.363260   
> -0.149123   )
>  (  0.000000   0.000000     0.534209  -0.309894    -0.345784    
> 0.000000   )

the eigenvectors are given as:
( r-x(1) im-y(1) r-y(1) im-y(1) r-z(1) im-z(1) )
( r-x(2) im-y(2) r-y(2) im-y(2) r-z(2) im-z(2) )
and so on ...

where r- and im- refer to the real and imaginary parts of the  
eigenvector components
xyz are cartesian coordinates
(1) and (2) refers to the first and second atom

in this case, the vibrational eigenvector has non-vanishing yz  
components; the wavevector is directed along x, hence the mode is  
transverse

>      omega( 2) =       0.716305 [THz] =      23.893534 [cm-1]
>  (  0.000000   0.000000    -0.340285   0.195964    -0.582679   
> -0.072865   )
>  (  0.000000   0.000000    -0.299101   0.173508    -0.617587    
> 0.000000   )

same reasoning as above. note the degeneracy. (there are two  
perpendicular directions, and only one parallel)

>      omega( 3) =       1.309595 [THz] =      43.683674 [cm-1]
>  ( -0.580354   0.392046     0.000000   0.000000     0.000000    
> 0.000000   )
>  ( -0.502160   0.507272     0.000000   0.000000     0.000000    
> 0.000000   )

polarization = x => longitudinal. SINGLET!

>      omega( 4) =      11.217963 [THz] =     374.193441 [cm-1]
>  (  0.000000   0.000000     0.254308  -0.116312     0.887037    
> 0.143423   )
>  (  0.000000   0.000000    -0.082315   0.012605    -0.327810    
> 0.000000   )

and so forth and so on ...


Hope this helps

Have fun!
Stefano

---
Stefano Baroni    ---  SISSA  &  DEMOCRITOS National Simulation Center
via Beirut 2-4 34014 Trieste Grignano / 
[+39] 040 3787 406 (tel) -528  
(fax)

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