[Pw_forum] Question on stress in a system with constraints

[Nicola Marzari]

Hi Kostya,


a quick comment - Don Hamann has written a fairly extensive PRB this
year discussing many of these issues: Vol 72, 350105 (2005).

CP stresses are (I hope) a derivative with respect to the strain
tensor - ie.e they do not take into account that
atoms can relax in response to the stress (the paradigmatic case is the
response to a strain in the 111 direction in silicon - the internal
strain parameter measures how the distance between the two atoms
in the unit cell changes in response to the symmetry-breaking stress).
So, you have the bare stress, calculated by CP and/or PWSCF, but you
want the renormalized one "dressed" by the relaxations (mediated by the
inverse of the dynamical matrix, and by the coupling between
displacements and strains). The constraint will allow you to
renormalize appropriately the bare stress, if you have all the response
functions from DFPT (and their correct long-wavelength limit)
but it might be easier to do it by finite differeces of the energy along 
the strain direction, while constraining the atoms.

By the way - the dressing of a perturbation by the ionic relaxations
is very relevant for piezoelectricity (e.g. Stefano de Gironcoli
1989 PRL) or for the interactions in substitutional alloy
(PRL 72 4001 (1994) - some of the issues with the long wavelength limit 
are discussed there).

Best,

			nicola




Konstantin Kudin wrote:

>  Hi there,
> 
>  I have a basic question on the stress tensor.
> 
>  Presumably, the stress tensor computed in the CP implies continuous
> stretching of the underlying system. Is this correct? Is the derivative
> with respect to % of stretch, or is it to extra length in Bohrs, for
> example?
> What are the units of the stress in CP ?
> 
>  If one projected out certain forces (for constrained coordinates),
> then the stress needs to be corrected for the fact that certain forces
> are no longer there. Basically, the original stress was computed as if
> all the forces were present, now, however, some of them are missing.
> This means that if the system were to be stretched, the constrained
> coordinates would still be constrained.
> 
>  My question is how I can correct the stress in a system with
> constraints if this needs to be done.
> 
>  Thanks!
>  Kostya
> 
> 
> 		
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Prof Nicola Marzari   Department of Materials Science and Engineering
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