My Community

hellow,
if I generate k points using
8x8x1
0
Monkhorst
8 8 1
0 0 0
for lattice cell (SLAB in Z ):
8.8800001139999996 0.0000000000000000 0.0000000000000000
4.4400000569999998 7.6903052330000001 0.0000000000000000
0.0000000000000000 0.0000000000000000 33.9020000000000010

I expect k-points filling hexagonal Brillioun zone however a get ~squre

as can be seen on imge http://metamind.wikispaces.com/file/view/k8x8x1.png


k points are
0.06 0.06 0
0 0.06 0
0.06 0 0
0.19 0.06 0
0.13 0.19 0
0.06 0.13 0
0.13 0.06 0
0.06 0.19 0
0.19 0.13 0
0.31 0.06 0
0.25 0.31 0
0.06 0.25 0
0.25 0.06 0
0.06 0.31 0
0.31 0.25 0
0.44 0.06 0
0.38 0.44 0
0.06 0.38 0
0.38 0.06 0
0.06 0.44 0
0.44 0.38 0
0.44 0.06 0
0.5 0.44 0
0.06 0.5 0
0.5 0.06 0
0.06 0.44 0
0.44 0.5 0
0.31 0.06 0
0.38 0.31 0
0.06 0.38 0
0.38 0.06 0
0.06 0.31 0
0.31 0.38 0
0.19 0.06 0
0.25 0.19 0
0.06 0.25 0
0.25 0.06 0
0.06 0.19 0
0.19 0.25 0
0.06 0.06 0
0.13 0.06 0
0.06 0.13 0
0.19 0.19 0
0 0.19 0
0.19 0 0
0.31 0.19 0
0.13 0.31 0
0.19 0.13 0
0.13 0.19 0
0.19 0.31 0
0.31 0.13 0
0.44 0.19 0
0.25 0.44 0
0.19 0.25 0
0.25 0.19 0
0.19 0.44 0
0.44 0.25 0
0.44 0.19 0
0.38 0.44 0
0.19 0.38 0
0.38 0.19 0
0.19 0.44 0
0.44 0.38 0
0.31 0.19 0
0.5 0.31 0
0.19 0.5 0
0.5 0.19 0
0.19 0.31 0
0.31 0.5 0
0.19 0.19 0
0.38 0.19 0
0.19 0.38 0
0.31 0.31 0
0 0.31 0
0.31 0 0
0.44 0.31 0
0.13 0.44 0
0.31 0.13 0
0.13 0.31 0
0.31 0.44 0
0.44 0.13 0
0.44 0.31 0
0.25 0.44 0
0.31 0.25 0
0.25 0.31 0
0.31 0.44 0
0.44 0.25 0
0.31 0.31 0
0.38 0.31 0
0.31 0.38 0
0.44 0.44 0
0 0.44 0
0.44 0 0
0.44 0.44 0
0.13 0.44 0
0.44 0.13 0

I'm using vasp 4.6




Is it somehow OK, or I missed something?

It's recommended to use a gamma-centered k-point mesh for hexagonal lattices, since it tends to converge more rapidly and also the even Monkhorst-Pack grid will not have the full symmetry of the cell. This is also stated in the manual:

http://cms.mpi.univie.ac.at/vasp/vasp/node55.html

under "hexagonal lattices". So you can try to switch to a gamma-centered mesh.

EDIT: Please also have a look at http://cms.mpi.univie.ac.at/vasp-worksh ... points.pdf (page 30), where the difference between a even Monkhorst-Pack and a Gamma grid is illustrated for a hexagonal lattice.

Cheers,
/Dan




<span class='smallblacktext'>[ Edited Tue Jul 21 2009, 07:57PM ]</span>

I tried Generation of gamma centred grid, however still it fills rectangular region instead of hexagonal
means - some of these k-points are probably outside of first Brillioun zone

these 1252 k-points is generated using
50x50x1
0
Gamma
50 50 1
0 0 0

http://metamind.wikispaces.com/file/view/k50x50x1.png

Are you sure that you are plotting the correct thing? It seems that you plotting the direct coordinates of the k-points and not the coordinates in reciprocal space. If I regard the values for the k-points in your first post as direct coordinates and multiply with the reciprocal lattice vectors:

b1 = 2*pi/a*[1, -1/sqrt(3), 0]
b2 = 2*pi/a*[0, 2/sqrt(3), 0]
b3 = 2*pi/c*[0, 0, 1]

where a = 8.88, c = 33.902, I get something that looks very reasonable. The grid doesn't have the full symmetry of the cell but at least it has a hexagonal-like structure as it should. So please check what you actually are plotting.


Best regards,
/Dan Fors



<span class='smallblacktext'>[ Edited Fri Jul 24 2009, 09:45AM ]</span>

Yes, sorry my fault , as you say, it was in direct coordinates, in cartesian coordinates it looks right like half of reciprocal cell (my cell has no symmetry so just time reversal symmetry is applied).

however I expected hexagonal shape (first brilioun zone, voronoi ) not just rhombic shape of reciprocal cell

The shape you're seeing should be the irreducible Brillouin zone, which is the first Brillouin zone reduced by all of the symmetries in the point group of the lattice (after symmetrization of the k-point grid). So with the given grid you will obviously obtain a rhombic irreducible Brillouin zone, due to a threefold rotation symmetry.

/Dan
<span class='smallblacktext'>[ Edited Fri Jul 24 2009, 11:24AM ]</span>

you are right, it should be rhomb with 3-fold symetry but in different position in respect to gamma (zero) i think

there is a picture of what I think:
http://metamind.wikispaces.com/file/view/k-hex.jpg

a] cartoon of rhom in hexagonal BZ
b] cartoon of rhomb covered by my k-points
c] firure of x,y positions my k-points

may be it's ok, but I don't know the reason