Hi Andrei and Akshu
> My excuses,
> I strongly disagree with Roberto's opinion:
>
Well, not that much ;-)
>> The closest thing to bulk modulus in hcp is obtained by varying
>> all the cell dimensions simultaneously and homogeneously and
>> monitoring the pressure while doing that. Then P = B \delta V / V.
>
> The definition of bulk modulus (B) known to me is
> B = -V dP/dV.
> As the structure is not cubic, varying cell dimensions simultaneously
> will introduce stress (the relaxed cell won't like to have the same
> c/a for different volumes). I think the right thing to do is
> to vary TARGET PRESSURE, let cell parameters free and monitor the VOLUME,
> then use the formula above.
> Or - probably better - you extract elastic constants,
> checking back their definition in hcp, as indepent parameters.
> Because they may behave differently; the bulk modulus is just
> some averaged combination of them, and won't tell you much,
> for a serious test.
>
The formula I quoted, P = B \delta V / V, will give you just that
average of elastic modulii Andrei's mentioning
B = 1/9 {2C11+2C12+4C13+C33}
This, I seem to recall, is called Voigt's average. Namely one where
an average deformation is imposed.
Andrei's point of view is an alternative possibility that corresponds
to impose an average stress (currently a pressure, Reuss average).
Clearly, the former method requires fixed cell while the latter
variable cell. I believe, however, that my method is a bit better
for numerical calculations, because it is easier (or more exact) to
control lattice dimensions than pressure.
>>> should i fix the atomic positions?
>>
>> No. The hcp 2-atoms cell possesses inner degrees of freedom,
>
> How's that??? I always thought there is something like
> (0 0 0) and (1/3 2/3 1/2), no internal coordinates.
> These relative coordinates should not change
> (they will in fact, slightly, due to lack of symmetry constraint
> in Siesta).
>
A distortion of the basal plane will generally produce a relative
displacement between the two atoms of the cell.
This is because the atomic positions are not centrosymmetric.
I agree though, that for a uniform expansion/contraction this will
not happen.
Best,
Roberto
