Phonon dispersion Points/Modes question

[Jeff_2016]

Hey all,

I am trying to recreate the phonon dispersion plot of the paper below

http://ocw.mit.edu/courses/electric...applications-spring-2003/projects/ProjP21.pdf

The problem is I do not know what the Tau, L, and X on the x-axis really mean and how they correspond to the three components of the wave vector K. Any help would be appreciated. Thanks!

 

[Daz]

They're just labels for the high-symmetry points in the Brillouin zone. Gamma is the centre, X is the edge of the BZ along the <100> direction and L is the edge of the BZ along the <111> direction.

Here you go:
https://en.wikipedia.org/wiki/Brill..._system_CUB.281.29.2CFCC.281.29.2C_BCC.281.29
(GaAs is FCC, by the way.)

So for example, the k at point X would be 2*PI/a where a is the [100] plane spacing.

 

[Jeff_2016]

Perfect, thank you so much!

 

[Jeff_2016]

They're just labels for the high-symmetry points in the Brillouin zone. Gamma is the centre, X is the edge of the BZ along the <100> direction and L is the edge of the BZ along the <111> direction.

Here you go:
https://en.wikipedia.org/wiki/Brill..._system_CUB.281.29.2CFCC.281.29.2C_BCC.281.29
(GaAs is FCC, by the way.)

So for example, the k at point X would be 2*PI/a where a is the [100] plane spacing.

Thanks again for replying, I just have one more question. How do I find the elements of the k-vector? I assume if it is in the [1 0 0] plane and K=2pi/a that kx=2pi/a, ky=0, kz=0.

 

[Daz]

That's right. Don't forget that that was just an example. In general you have kx=2PI/a, ky=2PI/b, kz=2PI/c and if [100] is a plane in real space the k-space vector is perpendicular to that plane. (An easy way to get a,b and c is to sketch a little unit cell on a scrap of paper.)