Phonon dispersion Points/Modes question

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Discussion Overview

The discussion revolves around understanding the phonon dispersion plot from a specific paper, focusing on the interpretation of the high-symmetry points Tau, L, and X on the x-axis and their relation to the wave vector K in the context of solid-state physics.

Discussion Character

  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant seeks clarification on the meaning of the labels Tau, L, and X in the phonon dispersion plot and their correspondence to the components of the wave vector K.
  • Another participant explains that these labels refer to high-symmetry points in the Brillouin zone, with Gamma at the center, X at the edge along the <100> direction, and L at the edge along the <111> direction.
  • A further clarification is provided regarding the k value at point X, indicating it as 2*PI/a, where a is the [100] plane spacing.
  • The original poster expresses gratitude and asks how to determine the elements of the k-vector, assuming a specific plane orientation.
  • In response, a participant confirms the assumption and elaborates that in general, kx, ky, and kz can be expressed as 2PI/a, 2PI/b, and 2PI/c respectively, noting that the k-space vector is perpendicular to the corresponding real space plane.

Areas of Agreement / Disagreement

Participants generally agree on the interpretation of the high-symmetry points in the Brillouin zone and the relationship between the k-vector components and the plane orientations. However, the discussion does not explore any competing views or unresolved issues.

Contextual Notes

The discussion assumes familiarity with concepts such as the Brillouin zone and k-space vectors, but does not delve into the mathematical derivations or specific conditions for different materials.

Jeff_2016
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Perfect, thank you so much!
 
Daz said:
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.
 
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.)
 

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