[Pw_forum] Some questions about IFC from PWSCF
Stefano de Gironcoli
degironc at sissa.it
Sat Oct 9 10:23:36 CEST 2010
Dear John Bob,
answer to 1. & 2:
IFC have four indices and depend on a lattice vector :
F_(alpha,beta)^(na,nb)(R)
this is the force in direction alpha (cartesian) on atom na in the unit
cell at the origin when atom nb in the unit cell identified by R is
displaced in direction beta.
The header of each block (the four integers 1 1 1 1 for instance) etc.
are just alpha,beta,na,nb and the subsequent lines contain
i j k F_(alpha,beta)^(na,nb)(R)
where R=(i-1)*a + (j-1)*b +(k-1)*c.
There are 6x6x6 lines in your case because your q-points grid had these
dimensions and a grid of q in the BZ translate in a set of R in real space.
In order to compare individual IFC you must take into consideration the
fact that they are tensorial quantities (matrices) and not scalar
For instance if the system is cubic you expect
F_{xx}{11} (0) = F_{yy}{11}(0) = F_{zz}{11} (0) = something
while
F_{xy}{11}(0) = F_{yx}{11}(0) =F_{yz}{11}(0) =F_{zy}{11}(0)
=F_{xz}{11}(0) = F_{zx}{11}(0) = 0
where the R=0 is the first element (i,j,k=1,1,1) after the header of
each block (alpha,beta,na,nb)
you should have
F_{xx}{11}(2 1 1) = F_{yy}{11}(1 2 1) = F_{zz}{11} (1 1 2)
and also
F_{xx}{11}(2 1 1) = F_{xx}{11}(6 1 1) = F_{yy}{11}(1 6 1) = F_{zz}{11}
(1 1 6)
for your 6x6x6 grid.
and many other relations that links rotations of the linking vector R
and rotations of the alpha,beta indices
answer to 3:
The written vectors are normalized displacements i.e. are eigenvectors
rescaled with the sqrt of the atomic mass and remormalized.
In case of doubts the routine that does that is PH/dyndia.f90 and the
corresponding section (look for "Diagonalizing the " in dyndia.f90)
should be quite transparent
stefano
===
John Bob wrote:
> Dear Pwscf users:
> I have some questions about IFC from pwscf. I have read some threads
> about interatomic force constants in PWSCF maillist. I get confused when
> trying to analysis the IFC of NiTi alloy, and also the example06 AsAl.
>
> 1. F(R) and R=(i-1)*a + (j-1)*b +(k-1)*c. It means F(1 2 1) should equal
> to F(1 1 2) and F(2 1 1) for cubic lattice. But in B2 NiTi alloy ( CsCl
> strucuture) F(1 1 2) = F(1 2 1) /= F(2 1 1). and in example06 F(2 1 1) = F(1
> 1 2) /= F(1 2 1). It seems some extra-things added to some direction. Why?
>
> 2. How to interpret the "1 1 1 1" section, F_{xx}^{1,1}(0). Does it means
> the force along x axis on Atom1 when Atom1 has a small displacement along
> the x direction?
>
> 3. The section after the "diagonalizing the dynamical matrix". I find the
> vectors in xx.dyn file xx.vec file (after matdyn.x) are different, rotated.
> Are these vectors eigen-displacements or just eigen-vector after
> diagonalizing?
>
> Best regards
>
> Dr. Zhou Bo
> Northwest University, Xi'an China
>
> NiTi.fc
>
> ...
> 6 6 6
> 1 1 1 1
> 1 1 1 4.30811843056E-02
> 2 1 1 1.49655475926E-02
> 3 1 1 7.47266388889E-04
> 4 1 1 -2.16783699074E-03
> 5 1 1 7.47266388889E-04
> 6 1 1 1.49655475926E-02
> 1 2 1 2.68996333333E-03
> 2 2 1 6.60210833333E-04
> 3 2 1 3.81960555556E-04
> 4 2 1 -2.61037222222E-04
> 5 2 1 3.81960555556E-04
> 6 2 1 6.60210833333E-04
> 1 3 1 -6.84333333333E-06
> 2 3 1 -6.65476851852E-05
> 3 3 1 -2.73466666667E-05
> 4 3 1 -1.06576851852E-04
> 5 3 1 -2.73466666667E-05
> 6 3 1 -6.65476851852E-05
> 1 4 1 4.48548611111E-05
> 2 4 1 -1.11791388889E-04
> 3 4 1 -1.06166666667E-05
> 4 4 1 -2.20306944444E-05
> 5 4 1 -1.06166666667E-05
> 6 4 1 -1.11791388889E-04
> 1 5 1 -6.84333333333E-06
> 2 5 1 -6.65476851852E-05
> 3 5 1 -2.73466666667E-05
> 4 5 1 -1.06576851852E-04
> 5 5 1 -2.73466666667E-05
> 6 5 1 -6.65476851852E-05
> 1 6 1 2.68996333333E-03
> 2 6 1 6.60210833333E-04
> 3 6 1 3.81960555556E-04
> 4 6 1 -2.61037222222E-04
> 5 6 1 3.81960555556E-04
> 6 6 1 6.60210833333E-04
> 1 1 2 2.68996333333E-03
> 2 1 2 6.60210833333E-04
> 3 1 2 3.81960555556E-04
> 4 1 2 -2.61037222222E-04
> 5 1 2 3.81960555556E-04
> 6 1 2 6.60210833333E-04
> 1 2 2 1.07580273148E-03
> 2 2 2 -8.68419537037E-04
> 3 2 2 -1.26556851852E-04
> 4 2 2 4.42628240741E-05
> 5 2 2 -1.26556851852E-04
> 6 2 2 -8.68419537037E-04
> 1 3 2 1.78201250000E-04
> 2 3 2 1.02706111111E-04
> 3 3 2 -6.21652777778E-05
> 4 3 2 1.27609722222E-05
> 5 3 2 -6.21652777778E-05
> 6 3 2 1.02706111111E-04
> 1 4 2 2.77759259259E-06
> 2 4 2 -6.13445370370E-05
> 3 4 2 7.55775925926E-05
> 4 4 2 -1.15009259259E-05
> 5 4 2 7.55775925926E-05
> 6 4 2 -6.13445370370E-05
> 1 5 2 1.78201250000E-04
> 2 5 2 1.02706111111E-04
> 3 5 2 -6.21652777778E-05
> 4 5 2 1.27609722222E-05
> 5 5 2 -6.21652777778E-05
> 6 5 2 1.02706111111E-04
> 1 6 2 1.07580273148E-03
> 2 6 2 -8.68419537037E-04
> 3 6 2 -1.26556851852E-04
> 4 6 2 4.42628240741E-05
> 5 6 2 -1.26556851852E-04
> 6 6 2 -8.68419537037E-04
> 1 1 3 -6.84333333333E-06
> 2 1 3 -6.65476851852E-05
> 3 1 3 -2.73466666667E-05
> 4 1 3 -1.06576851852E-04
> 5 1 3 -2.73466666667E-05
> 6 1 3 -6.65476851852E-05
> 1 2 3 1.78201250000E-04
> 2 2 3 1.02706111111E-04
> 3 2 3 -6.21652777778E-05
> 4 2 3 1.27609722222E-05
> 5 2 3 -6.21652777778E-05
> 6 2 3 1.02706111111E-04
> 1 3 3 -4.81876388889E-05
> 2 3 3 -4.36212962963E-06
> 3 3 3 -5.60238888889E-05
> 4 3 3 4.51591203704E-05
> 5 3 3 -5.60238888889E-05
> 6 3 3 -4.36212962963E-06
> 1 4 3 -2.30238888889E-05
> 2 4 3 -1.50694444444E-06
> 3 4 3 2.35983333333E-05
> 4 4 3 2.81166666667E-06
> 5 4 3 2.35983333333E-05
> 6 4 3 -1.50694444444E-06
> 1 5 3 -4.81876388889E-05
> 2 5 3 -4.36212962963E-06
> 3 5 3 -5.60238888889E-05
> 4 5 3 4.51591203704E-05
> 5 5 3 -5.60238888889E-05
> 6 5 3 -4.36212962963E-06
> 1 6 3 1.78201250000E-04
> 2 6 3 1.02706111111E-04
> 3 6 3 -6.21652777778E-05
> 4 6 3 1.27609722222E-05
> 5 6 3 -6.21652777778E-05
> 6 6 3 1.02706111111E-04
> 1 1 4 4.48548611111E-05
> 2 1 4 -1.11791388889E-04
> 3 1 4 -1.06166666667E-05
> 4 1 4 -2.20306944444E-05
> 5 1 4 -1.06166666667E-05
> 6 1 4 -1.11791388889E-04
> 1 2 4 2.77759259259E-06
> 2 2 4 -6.13445370370E-05
> 3 2 4 7.55775925926E-05
> 4 2 4 -1.15009259259E-05
> 5 2 4 7.55775925926E-05
> 6 2 4 -6.13445370370E-05
> 1 3 4 -2.30238888889E-05
> 2 3 4 -1.50694444444E-06
> 3 3 4 2.35983333333E-05
> 4 3 4 2.81166666667E-06
> 5 3 4 2.35983333333E-05
> 6 3 4 -1.50694444444E-06
> 1 4 4 -9.10425462963E-05
> 2 4 4 2.44929629630E-05
> 3 4 4 -1.40046296296E-06
> 4 4 4 1.51428240741E-05
> 5 4 4 -1.40046296296E-06
> 6 4 4 2.44929629630E-05
> 1 5 4 -2.30238888889E-05
> 2 5 4 -1.50694444444E-06
> 3 5 4 2.35983333333E-05
> 4 5 4 2.81166666667E-06
> 5 5 4 2.35983333333E-05
> 6 5 4 -1.50694444444E-06
> 1 6 4 2.77759259259E-06
> 2 6 4 -6.13445370370E-05
> 3 6 4 7.55775925926E-05
> 4 6 4 -1.15009259259E-05
> 5 6 4 7.55775925926E-05
> 6 6 4 -6.13445370370E-05
> 1 1 5 -6.84333333333E-06
> 2 1 5 -6.65476851852E-05
> 3 1 5 -2.73466666667E-05
> 4 1 5 -1.06576851852E-04
> 5 1 5 -2.73466666667E-05
> 6 1 5 -6.65476851852E-05
> 1 2 5 1.78201250000E-04
> 2 2 5 1.02706111111E-04
> 3 2 5 -6.21652777778E-05
> 4 2 5 1.27609722222E-05
> 5 2 5 -6.21652777778E-05
> 6 2 5 1.02706111111E-04
> 1 3 5 -4.81876388889E-05
> 2 3 5 -4.36212962963E-06
> 3 3 5 -5.60238888889E-05
> 4 3 5 4.51591203704E-05
> 5 3 5 -5.60238888889E-05
> 6 3 5 -4.36212962963E-06
> 1 4 5 -2.30238888889E-05
> 2 4 5 -1.50694444444E-06
> 3 4 5 2.35983333333E-05
> 4 4 5 2.81166666667E-06
> 5 4 5 2.35983333333E-05
> 6 4 5 -1.50694444444E-06
> 1 5 5 -4.81876388889E-05
> 2 5 5 -4.36212962963E-06
> 3 5 5 -5.60238888889E-05
> 4 5 5 4.51591203704E-05
> 5 5 5 -5.60238888889E-05
> 6 5 5 -4.36212962963E-06
> 1 6 5 1.78201250000E-04
> 2 6 5 1.02706111111E-04
> 3 6 5 -6.21652777778E-05
> 4 6 5 1.27609722222E-05
> 5 6 5 -6.21652777778E-05
> 6 6 5 1.02706111111E-04
> 1 1 6 2.68996333333E-03
> 2 1 6 6.60210833333E-04
> 3 1 6 3.81960555556E-04
> 4 1 6 -2.61037222222E-04
> 5 1 6 3.81960555556E-04
> 6 1 6 6.60210833333E-04
> 1 2 6 1.07580273148E-03
> 2 2 6 -8.68419537037E-04
> 3 2 6 -1.26556851852E-04
> 4 2 6 4.42628240741E-05
> 5 2 6 -1.26556851852E-04
> 6 2 6 -8.68419537037E-04
> 1 3 6 1.78201250000E-04
> 2 3 6 1.02706111111E-04
> 3 3 6 -6.21652777778E-05
> 4 3 6 1.27609722222E-05
> 5 3 6 -6.21652777778E-05
> 6 3 6 1.02706111111E-04
> 1 4 6 2.77759259259E-06
> 2 4 6 -6.13445370370E-05
> 3 4 6 7.55775925926E-05
> 4 4 6 -1.15009259259E-05
> 5 4 6 7.55775925926E-05
> 6 4 6 -6.13445370370E-05
> 1 5 6 1.78201250000E-04
> 2 5 6 1.02706111111E-04
> 3 5 6 -6.21652777778E-05
> 4 5 6 1.27609722222E-05
> 5 5 6 -6.21652777778E-05
> 6 5 6 1.02706111111E-04
> 1 6 6 1.07580273148E-03
> 2 6 6 -8.68419537037E-04
> 3 6 6 -1.26556851852E-04
> 4 6 6 4.42628240741E-05
> 5 6 6 -1.26556851852E-04
> 6 6 6 -8.68419537037E-04
> 1 1 1 2
> 1 1 1 -8.74218916667E-03
> 2 1 1 -8.74218976551E-03
> 3 1 1 -2.35019119479E-03
> 4 1 1 -7.60084259259E-05
> 5 1 1 -7.60088052061E-05
> ...
>
>
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