Understanding 3D Si Dispersion Relations & Reciprocal Lattice Vectors

[jacare]

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?

 

[Dr Transport]

Which dispersion relations are you lookong at, energy or phonon?

 

[jacare]

i am looking at phonon dispersion relations

 

[kanato]

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.