MPB Users & Steven,
I have a question about calculating bandstructures for supercells.
Starting with an primitive FCC unit cell with a basis of one, I calculate
the freqs for 10 bands and find the gap between the 8th and 9th bands
(inverted FCC using silicon as the interstitial material, air for the
spheres). Now if a double the primitive unit cell dimensions and fill in
the other 7 lattice points in the cell with spheres, I would have to
calculate atleast 65 bands, since the 8th band times n^3 where n=2 is
8x8=64, in order to see the gap. Obviously if I increase the supercell
size, the number of bands I have to calculate goes up significantly.
Now my specific problem is more complicated. In my supercell I have
asymmetric shaped particles (ellipsoids) all randomly oriented on their
lattice sites. This is called a rotator phase (particles positioned on a
lattice but with orientation disorder) and I'm trying to calculate the band
structure for it. I do this by making a super-"primitve" FCC unit cell of n
x n x n larger than the primitve unit cell of FCC and filling in the lattice
sites with randomly oriented particles. Obviously the larger the supercell
the more "random" the structure is and it will model the actual real
structure more accurately. My question is, how many bands, assuming the gap
still exists, would I have to calculate for this structure? Would it:
1) follow the same principle as the spheres? Or,
2) since the particles are all different, I would just define my supercell
edges as the lattive vectors and the particles inside of it as one huge
basis for this larger crystal?
Would option two allow me to calculate less bands, or would I still have
to calculate many bands in order to see gaps. I'm just trying to figure out
how to handle such a super cell calculation, were the particles are all on
lattice sites, but due to the random orientation it is not a true crystal,
and so I need to define a much larger periodic cell in order to do the
calculations.
Any thoughts or suggestions could be appreciate.
Thanks,
Ian
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