Understanding 3D Si Dispersion Relations & Reciprocal Lattice Vectors

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Discussion Overview

The discussion focuses on understanding 3D silicon dispersion relations and reciprocal lattice vectors, specifically addressing the normalization of wave vectors and the dimensions of the first Brillouin zone (BZ) in the context of phonon dispersion relations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses confusion regarding the normalization of wave vectors in dispersion relations, questioning whether the edge of the first BZ is at pi/a or 2pi/a for a diamond lattice.
  • Another participant clarifies that the first edge of the BZ is at pi/a and that the BZ extends from -pi/a to pi/a, making its total size 2pi/a.
  • A participant notes that the reciprocal lattice vector connects equivalent points in different cells and suggests it must be 2pi/a based on the width of each cell.
  • There is a distinction made between energy and phonon dispersion relations, with one participant specifically focusing on phonon dispersion.

Areas of Agreement / Disagreement

The discussion contains some agreement on the dimensions of the first BZ and the nature of the reciprocal lattice vector, but there remains uncertainty regarding the normalization of wave vectors and the specific context of the diamond lattice.

Contextual Notes

Participants have not fully resolved the implications of the normalization of wave vectors and how it relates to the specific lattice structure being discussed.

jacare
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I am trying to understand 3D Si dispersion relations and reciprocal lattice vectors. My confusion is that when I look at dispersion relations the wave vector typically is normalized from 0 to 1 by a/2pi. I thought the edge of the first BZ was pi/a. Is this correct or is it 2pi/a for a diamond lattice? Also, the reciprocal lattice would be 2Npi/a where N is an integer correct?
 
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Which dispersion relations are you lookong at, energy or phonon?
 
i am looking at phonon dispersion relations
 
The first edge of the BZ is at pi/a. The first BZ extends in both directions, from -pi/a to pi/a. So the size of the BZ is 2pi/a. The center point (often called the \Gamma point) is where the pseudomomentum k=0. The reciprocal lattice vector gets you from the Gamma point in one cell to the Gamma pt in another cell (or any other equivalent point). So this has to be 2pi/a because each cell is that wide.
 

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