[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)
Please, if possible, don't send me MS Word or PowerPoint attachments
Why? See: http://www.gnu.org/philosophy/no-word-attachments.html
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