Finding Special K-Points in Cubic Structures - mechdude

[Mechdude]

Hi
im looking at a book and for a cubic structure they have stated about 20 special k-points are found, does anyone have a tutorial like resource for how this is done? or can anyone offer some insight?
mechdude.
ps see attached for what I am referring to.

 

[M Quack]

This is not completely clear. How do you get from an unspecified grid (presumably regular) to high-symmetry points?

Usually you look at the Brillouin zone and then look for high-symmetry axes and high-symmetry points on the surface of the BZ. This was of course done decades ago, and all such points and axes carry names (historically). You have to look up books and tables to find the proper nomenclature for your system.

 

[sam_bell]

They are probably referring to so-called "Monkhorst-Pack" special k-points. The regular 4x4x4 grid is first generated from the reciprocal lattice vectors as: (n1/4) b1 + (n2/4) b2 + (n3/4) b3 for ni = 0,1,2,3. Any points outside the 1st BZ are translated back in. Then equivalent points are found by applying all the symmetry operations of the corresponding crystal --48 for a perfect cube, less for the strained lattice. The remaining inequivalent points are the irreducible special k-points.