[Pw_forum] cutoff convergence of sapphire for elastic properties

[Jörg Buchwald]

Am Mon, 7 May 2012 14:22:58 -0400
schrieb Mike Mehl <rcjhawk at gmail.com>:

> To follow up on Nicola's point, the bulk modulus of sapphire is 240
> GPa or 2400 kbar
> (http://www.mt-berlin.com/frames_cryst/descriptions/sapphire.htm). So
> a 1 kbar error corresponds to a very small change in volume.
> 
> If we use the quick and dirty Birch equation of state:
> 
> P(V) = 3/2 K0 [ (V0/V)^(7/3) - (V0/V)^(5/3)]
> 
> with K0 = 2400 kbar and ask what volume will produce a 1 kbar change
> in pressure we get
> 
> delta V/V0 = +/- 0.0004
> 
> Considering the normal errors in DFT, it's not worth trying to
> converge the stress to the 1 kbar accuracy you're trying to achieve.

But to get the elastic constants in the elastic regime, i would
like then apply strains of serveral per mill, which is of the same
order of magnitude, i.e. also corresponds to changes of the stress
tensor of the order of 1 kbar, which means that errors in the kbar
range would be too high.
An alternative could be the calculation of the elastic constants using
the second derivative of the energy. But this won't work for big
supercells due to the computation time and the number of measuring
points needed.


> 
> On Mon, May 7, 2012 at 10:07 AM, Nicola
> Marzari<nicola.marzari at epfl.ch> wrote:
> 
> >
> > How much does 1 kbar error translates into an error in lattice
> > parameter? (keep atoms fixed, using relative coordinates, cutoff
> > fixed, and expand celldm(1) by 0.3% - what's the change in stress?
> > that change should be very well converged)
> >
> > --
> Michael Mehl
> US Naval Research Laboratory
> Washington DC
> (Home email)