[Pw_forum] Some questions about IFC from PWSCF

[Stefano de Gironcoli]

dear Zhou Bo
   the  IFC between atoms  in cell L and L' only depends on L-L' hence 
the answer to 1) is yes.
   2) for any given L , na,nb F_alpha,beta is a 3x3 matrix but when you 
apply symmetry you must not oly rotate alpha and beta but also L,na and 
nb... so ... yes: symmetry determines the structure of the matrix but .. 
no: it's not the global  symmetry of the crystal but the one of the pair 
of atoms.
   3) think of a simple cubic system with a nearest neighbor spring:  if 
you displace the atom in the origin in the x direction this gives a 
certain (big) force in the x direction to the first n.n. atom in the x 
direction ... and a  different (smaller) force to n.n. atoms in y and z 
directions. If you move the atom in the y direction the big force will 
be on the y direction on atom n.n. along y while on atoms along x and z 
the force will be smaller...

stefano

john Bob wrote:
> Dear Stefano:
>
> Thank you very much for the answers. I lernt much from those. In some
> textbook the force constant matrix are
>                   (   L       L' )
> F                (               )
>   alpha,beta (   K      K' )         L is the index of cells, K index of
> different atoms.
>
> (1) Can I rewrite the F_(alpha,beta)^(na,nb)(R) as
>                    (   0       L'  )
> F                (                )            while L' is L(a,b,c)
> L(R)       ?
>   alpha,beta (  na      nb )
>
> (2) F_{alpha,beta} matrix is 3X3 matrix. And It acts like other two rank
> tensor ( dielectric tensor, electric conductivity tensor) under symmetry
> operations ?  The independent parameters can be decided by group theory ?
> one for cubic system.
>
> (3) I pick up the
> " x  x   1  1
>  2 1  1   x.xxxx "
> lines
> ================
>    1   1   1   1
>    1   1   1   4.30811843056E-02
>    2   1   1   1.49655475926E-02
>    1   2   1   1
>    1   1   1   0.00000000000E+00
>    2   1   1   0.00000000000E+00
>    1   3   1   1
>    1   1   1   0.00000000000E+00
>    2   1   1   0.00000000000E+00
>    2   1   1   1
>    1   1   1   0.00000000000E+00
>    2   1   1   0.00000000000E+00
>    2   2   1   1
>    1   1   1   4.30811843056E-02
>    2   1   1   2.68996333333E-03
>    2   3   1   1
>    1   1   1   0.00000000000E+00
>    2   1   1   0.00000000000E+00
>    3   1   1   1
>    1   1   1   0.00000000000E+00
>    2   1   1   0.00000000000E+00
>    3   2   1   1
>    1   1   1   0.00000000000E+00
>    2   1   1   0.00000000000E+00
>    3   3   1   1
>    1   1   1   4.30811843056E-02
>    2   1   1   2.68996333333E-03
> ==========================
> why Fxx /=  Fyy = Fzz ?
>
> I am sorry for my poor english. Also sorry for so many annoying question,
> self-teaching is a hard and careful work.
>
>
> Dr  Zhou Bo
>
> Norhwest University Xi'an China
>
>   
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