[Pw_forum] The choice of Acoustic Sum Rule for crystal

[naivebamboo Huang]

Dear PWscf users,
       I am trying to calculate the phonon eigen modes of Bi2Te3 crystal at 
gamma point. The fraction of one Te atom has two different reported values 
in the literature (x1=0.792, x2=0.7905). I want to know which value is more 
appropriate. I calculated the energy of the cell and found the configure 
with x=0.7905 has a very slightly lower energy(0.001% lower, does this mean 
the well is flat?). I also calculated the frequency. Both of the 
configurations give 14 positive frequencies and 1 negative frequency 
(totally 15 modes). I just thought this may be due to the acoustic sum rule. 
I impose asr='simple' and used dynmat.x to get the frequency. Only x=0.792 
gives 12 positive frequencies and 3 zero frequency. But if I set 
asr='crystal', both configures can produce 12 positive frequencies and 3 
zero frequency. After checking with the gamma point of  experimental 
dispersion curve at 300 K, the configure x=0.792 and asr='crystal' give the 
best results. My questions are
          (1) which ASR  should I use, since the different ASR give 
different frequencies (10% difference for x=0.792 configure)
           (2) how can I trust the results I calculated? Does the positive 
eigen frequency indicate a stable structure? I guessed at 300 K, the 
frequencies should be different from those of the relax structure.

Thanks very much

Baoling

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