[Pw_forum] IFCs and supercell

[stefano de gironcoli]

dear Alexander,

     the grid correspond to a 8x8x8 supercell (or rather to the FFT of a 
8x8x8 q-point grid ... which is the same)

     atomic pairs are specified by the indices of the two atoms in the 
unit cell plus the direct lattice vector connecting the two cells in 
which they are located with two important details to be considered
     1) the origin is the 1,1,1 element of the list
     2) the IFC are obtained by a FFT from the dynamical matrices of the 
q-point grid and are therefore written assuming  8 8 8 periodicity (in 
the present case)
      the corresponding relevant real space vectors vectors are 
therefore given by
r(i) = (n1-1)*at(i,1)+(n2-1)*at(i,2)+(n3-1)*at(i,3) + their periodic 
refolding to points nearest the origin
a few examples should clarify:
      1 1 1  -> r =    0
      2 1 1  -> r =  a1
      8 1 1  -> r = -a1

      the routine weight play the fundamental role of trimming the 
vector in such a way the only the points inside the wigner-seitze
cell of the supercell contribute
      weight (r) = 1 if r is inside the WS cell
      weight (r) = 0 if r is ouside the WS cell
      weight (r) = 1/(n+1) if r is on the surface of the WS cell where n 
is the number of planes that pass through it

stefano

On 11/06/2014 06:14 PM, Kvasov Alexander wrote:
>
> Dear All,
>
> My question is: how the supercell (which is used by q2r and matdyn) is 
> specified? If anybody has any information about this I would highly 
> appreciate.
>
> “fltau” option of matdyn gives atomic positions only for 1 cell and 
> not for N1xN2xN3 supercell.
>
> Apparently, there are some tricks… for example, here one has some IFCs 
> for 8x8x8 grid of SrTiO3
>
> ...
>
> 8   8   8
>
> 1   1   1   1
>
> 1   1   1   5.72142674655E-02
>
> 2   1   1  -1.06343912107E-02
>
> 3   1   1   1.01649714042E-04
>
> 4   1   1   4.15611567060E-06
>
>    5   1   1  -6.46046533014E-06
>
>    6   1   1   4.15611567060E-06
>
>    7   1   1   1.01649714042E-04
>
> 8   1   1  -1.06343912107E-02
>
> ...
>
> 1. first, IFC values decries with N1 and then increase, so they have 
> to be shuffled
>
> 2. second, it seems SUBROUTINE setupmat and frc_blk is the right place 
> to look for this
>
> …
>
> DO na=1, nat
>
> DO nb=1, nat
>
> total_weight=0.0d0
>
> DO n1=-2*nr1,2*nr1
>
> DO n2=-2*nr2,2*nr2
>
> DO n3=-2*nr3,2*nr3
>
> !
>
> ! SUM OVER R VECTORS IN THE SUPERCELL - VERY VERY SAFE RANGE!
>
> !
>
> DO i=1, 3
>
> r(i) = n1*at(i,1)+n2*at(i,2)+n3*at(i,3)
>
> END DO
>
> …
>
> but summation goes from -2N to 2N, which is not clear for me.
>
> 3. what is “weight”  in SUBROUTINE setupmat and frc_blk
>
> If anybody could explain what is going on here it would be great!
>
> Sincerely yours,
>
> Alexander Kvasov
>
> Scientist
>
> Ceramics Laboratory (LC)
>
> École Polytechnique Fédérale de Lausanne (EPFL)
>
> Phone: +41 21 693 5805
>
> Address:
>
> EPFL STI IMX LC
>
> MXD 220 (Bâtiment MXD) Station 12
>
> 1015 Lausanne, Switzerland
>
>
>
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