[Pw_forum] Pw_forum Digest, Vol 31, Issue 2
Stefano Baroni
baroni at sissa.it
Thu Jan 7 00:12:53 CET 2010
Dear Zhen,
all of your very legitimate questions have the same answer: aliasing. Real-space force constants are obtained by discrete Fourier transform (FT) from reciprocal-space dynamical matrices. Discrete FTs are periodic, with period {2\pi\over \Delta q}, with hopefully obvious notation. Periodicity tell you what to do with negative indeces in the force constants. If for some physical reason the force constants are even by parity, this should also explain the symmetry you have observed.
EXERCISE: think about the above and try to answer yourself your questions in as clear a way as you can. I will be glad to read your own explanation on this forum.
Regards - SB
PS: please, always indicate the real subject of your post in the subject field (do not limit yourself to hit "reply" to a digest daily dispatch of the forum's posts)
On Jan 5, 2010, at 4:02 AM, Zhen Huang wrote:
> Dear Prof. Eyvaz Isaev and users-
>
> This is Zhen. Thanks for you information. However, I have couple of uncleared questions to follow up. Below is part of the results a friend of mine provided which are the force constants of Au who has FCC structure. Two things made me confused. First, according to your information R=(i-1)*a + (j-1)*b + (k-1)*c, I found that 2 1 1's force constant and 4 1 1's force constants are the same (marked by a line of @ after below). Why is this? On the other hand, 2 2 1 should represent the force constants of x, x between an atom and its third nearest neighbor (distance is (3/2)^0.5a where a is the lattice constant) atom and 3 1 1 represent the force constant between an atom and its fourth nearest neighbor (2^0.5a) (both are marked by $ below). Why the force constant between the atoms and its third nearest neighbor is smaller than the one between it and its fourth nearest's. Is there a particular reason for it?
>
> On the other hand, how do I find the R= -1*a+x*b+y*c. Seems based on R=(i-1)*a + (j-1)*b + (k-1)*c there will never be a negative index.
>
>
>
> *******************************
> 1 1 2 7.8423629 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
> 1 'Au ' 179527.171937097
> 1 1 0.0000000 0.0000000 0.0000000
> F
> 4 4 4
> 1 1 1 1
> 1 1 1 1.26759193594E-01
> 2 1 1 -1.87445789062E-02 @@@@@@@@
> 3 1 1 1.66957109375E-03 $$$$$$$$$$$$$$
> 4 1 1 -1.87445789062E-02 @@@@@@@@
> 1 2 1 6.90391046875E-03
> 2 2 1 -4.25726562500E-05 $$$$$$$$$$$$$$
> 3 2 1 -4.96455781250E-04
> 4 2 1 -1.87445789063E-02
> 1 3 1 -2.07408906250E-04
> 2 3 1 -4.25726562500E-05
> 3 3 1 1.66957109375E-03
> 4 3 1 -4.25726562500E-05
> 1 4 1 6.90391046875E-03
> 2 4 1 -1.87445789063E-02
> 3 4 1 -4.96455781250E-04
> 4 4 1 -4.25726562500E-05
> 1 1 2 -1.87445789062E-02
> ******************************
>
> Best Regards
> -------
> Zhen (Alex) Huang
> Ph.D. Student
> Nanoscale Transport Research Group
> Laboratory for Computational Methods in Emerging Technologies
> Cooling Technologies Research Center
> School of Mechanical Engineering
> Purdue University
> Tel: 765 237 9733
>
>
> On Sun, Jan 3, 2010 at 2:58 AM, <pw_forum-request at pwscf.org> wrote:
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> 1. Re: A question about force constants calculation output
> (Eyvaz Isaev)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Sat, 2 Jan 2010 09:04:41 -0800 (PST)
> From: Eyvaz Isaev <eyvaz_isaev at yahoo.com>
> Subject: Re: [Pw_forum] A question about force constants calculation
> output
> To: PWSCF Forum <pw_forum at pwscf.org>
> Message-ID: <980073.51698.qm at web65703.mail.ac4.yahoo.com>
> Content-Type: text/plain; charset=iso-8859-1
>
> Dear Zhen,
>
> In order to understand correctly the content of these files you should read a textbook on the lattice dynamics theory of semiconductors. Textbook "Fundamentals of Semiconductors" by Peter Yu and Manuel Cardona is a very good starting point.
>
> --- On Wed, 12/30/09, Zhen Huang <huang87 at purdue.edu> wrote:
>
> > ph.x calculation generated files alas.dynX where X goes from
> > 0 to 8. In the file alas.dyn0 it gives the k points.. Seems
> > in the other dynX files for example .dyn1 it gives force
> > constants of q=(0.0, 0.0, 0.0)? and .dyn2 gives force
> > constants of q=(-0.25?? 0.25? -0.25)
>
> This is correct. 4x4x4 set of q-points gives 8 q-points for which dynamical matrices have to be calculated. These q-points are written in dyn0 file. Files dyn1 - dyn8 are dynamical matrices.
>
> > What is the T matrix? and Matrix 1 and 2 labeled below.
>
> There is no T-matrix at all, "T" means .true., i.e. AlAs, in fact, is semi-conducting.
>
> Next 3x3 matrix is the macroscopic dielectric constants matrix.
>
> "Matrix 1" and "Matrix 2" contain effective Born charges for Al (atom 1) and As (atom 2).
>
> For metals you find "F" (.false.) and no dielectric matrix and Born effective charges.
>
> > Also, the questions are what is 4 4 4 representing the the force
> > constants information part labeled below,? what does the 1 1 1 1 mean > on the second line and also what is the meaning of the index?
> > 2?? 1?? 1? -6.26636620736E-03 (for example), I assume -6.266e-03 is
> > the force constants but what is 2 1 1.
>
> You asked this question before. Please have a look at
>
> http://www.democritos.it/pipermail/pw_forum/2008-September/010099.html
>
> The only correction is that R=(i-1)*a + (j-1)*b + (k-1)*c (thanks Stefano d.G).
>
> > If the forth column is the force constants why it is different from
> > Ph.x calcualtion's output.
>
> Please do not mix dynamical matrix with IFC. The first one is in q-space, and the second one is in R-space.
>
> > One more question, if I want to look at the force constants
> > between a unit cell and its closest nearest neibhor unit
> > cell do I look at the dynX output with k=(0, -1, 0), (-1, 0,
> > 0) and such and second nearest unit cells will be in dynX of
> > k=(0, -.5, 0), (-.5, 0, 0)?
>
> This is unclear what do you mean as IFC is for atoms, but not for unit cells. Just keep in mind in the Linear Response theory all calculations are performed inside the unit cell. To calculate the IFC range see a formula for R given above.
>
> Bests,
> Eyvaz.
>
> -------------------------------------------------------------------
> Prof. Eyvaz Isaev,
> Theoretical Physics Department, Moscow State Institute of Steel & Alloys, Russia,
> Department of Physics, Chemistry, and Biology (IFM), Linkoping University, Sweden
> Condensed Matter Theory Group, Uppsala University, Sweden
> Eyvaz.Isaev at fysik.uu.se, isaev at ifm.liu.se, eyvaz_isaev at yahoo.com
>
>
>
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> End of Pw_forum Digest, Vol 31, Issue 2
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---
Stefano Baroni - SISSA & DEMOCRITOS National Simulation Center - Trieste
http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)
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