[Pw_forum] Too low speed of sound in quartz

[Stefano Baroni]

Dear Mikhail,

I have only faint memories of things done long ago, but I kind of remember that making elastic constants (EC) calculated from sound velocities match with those obtained by "frozen strain" calculations is a far-from-trivial task. The reason is, when you try to convert one expression into the other, you realize that ECs can actually be expressed as some moments (don't remember exactly which one) of the interatomic force constants (IFC). This means that the former are very sensitive to the long-range behavior of the latter. This imply, in turn, that in order to have good ECs you have to have many (and accurate) IFCs, which can only be obtained from a correspondingly fine grid of wave-vectors at which the phonon frequencies are sampled.

The factor of five that you find in the difference between the two calculations seems to me a bit too large to be explained by the above arguments, and you may want to cross-check all of your algebra, but once you are sure that the algebra is OK, the above considerations are worth considering and understanding in somewhat more detail than I have given. Before proceeding you may want to give your mastering of the whole subject a final check by calculating the elastic constants of, say, bulk silicon, which is a case you can treat with arbitrary accuracy on any laptop ...

HTH - good luck!
SB

On Jan 8, 2012, at 11:13 PM, Гриша Гончаровский wrote:

> Dear QE developers and users,
> 
> I've calculated phonon dispersion for alpha-quartz. It gives for acoustic branches at Gamma --- A direction:
> 
> q (2*pi/a_0)       omega_1   omega_2   omega_3 (cm^(-1))
> ------------------------------------------------------------------
> 0.00000000       -1.1614      -0.8602       -0.7608
> 0.045470455      9.2277      18.1443     24.0697
> 0.09094091       21.8192     34.5505     47.4024
> . . .
> 
> Differentiating these dispersion relations I found that the speed of the "fastest" sound waves is about 1000 m/sec, while the simple mechanical calculation (as well as reference data) gives at least a five times larger value.
> 
> My scf input:
> 
> &control
> calculation='scf',
> restart_mode='from_scratch',
> prefix='sio2',
> pseudo_dir = '/home/user/espresso/pseudo',
> outdir='/home/user/espresso/tmp'
> /
> &system
> ibrav=4,
> celldm(1)=9.289897331,
> celldm(3)=1.099552482,
> nat= 9, ntyp= 2,
> ecutwfc = 20.0
> ecutrho = 150.0
> /
> &electrons
> electron_maxstep=1000
> mixing_mode = 'plain'
> mixing_beta = 0.7
> conv_thr = 1.0d-8
> /
> ATOMIC_SPECIES
> Si 28.086 Si.pw91-n-van.UPF
> O 15.999 O.pw91-van_ak.UPF
> ATOMIC_POSITIONS crystal
> Si 0.465976452 0.000000000 0.000000000
> Si -0.000045477 0.465778133 0.666710600
> Si -0.465823610 -0.465778133 0.333289400
> O 0.410406470 0.274336629 0.112688982
> O -0.274215479 0.135800008 0.779283047
> O -0.136110820 -0.409868933 0.446516439
> O 0.273758113 0.409868933 0.553483561
> O -0.410015489 -0.135800008 0.220716953
> O 0.136069841 -0.274336629 -0.112688982
> K_POINTS automatic
> 4 4 4 0 0 0
> 
> 
> Phonon input:
> 
> phonons of SiO_2
> &inputph
> tr2_ph=1.0d-12,
> prefix='sio2',
> ldisp=.true.,
> nq1=2, nq2=2, nq3=2
> amass(1)=28.086,
> amass(2)=15.999,
> outdir='/home/user/espresso/tmp',
> fildyn='sio2.dyn',
> /
> 
> 
> Does anyone know the origin of such discrepancy? 
> 
> Regards,
> Mikhail Goncharovskii,
> postgraduate student, Omsk State University, Russia
> 
> 
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---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center - Trieste
http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

La morale est une logique de l'action comme la logique est une morale de la pensée - Jean Piaget

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