[Pw_forum] how to find out the stable structure under high pressure
baroni at sissa.it
Wed Jun 14 08:56:55 CEST 2006
Nicola: here, I beg to differ. For two reasons.
First: even if there was a minimum such as discrebed in the question,
this would be a _local_ and not necessarily a global one.
Second: there would be such a minimum if there was not any coupling
between the soft modes and any other (phonon or elastic) modes. In
practice, this is seldom the case, so that the low-simmetry phase
seldom results from the distortion of soft modes alone. I would
advise Li Yan to browse into a book dealing with the Landau theory of
phase transitions, where these questions should be thoroughly
discussed. Unfortunately, the only title that occurs to me right now
is in French ("Symétries brisées", by Boccara and Boccara - an
English translation may exist). In any case, these texts are usually
rather awkward and, when I needed to work with these concepts, I
preferred to "rediscover" what I needed from scratch. My own efforts
in mastering the subject are witnessed in the papers: Phys. Rev.
Lett., 69, 1069 (1992) and Phys. Rev. B 51, 8060 (1995). What is true
(and what Nicola most probably actually meant) is that if you start
an energy minimization from a configuration characterized by a non-
vanishing amplitude of the soft mode-distortion, then the system will
certainly find a configuration of lower energy. This configuration
may or may not be a local minimum (let alone a global one that you
will never know for sure) according to whether your supercell and the
symmetry of the starting configuration are such as to allow for all
the relevant mode-mode couplings eventually responsible for the
stability of the low-symmetry phase.
Hope to have been not too confusing.
On Jun 14, 2006, at 5:01 AM, Nicola Marzari wrote:
> li yan wrote:
>> Dear all,
>> I found soft modes in a system under pressure. Is it true that
>> there must be a global energy miniumu in the subspace spanned by the
>> eignevectors of the soft modes? And by searching this munimum, can i
>> find the stable high-pressure strucure?
>> best regards
> Prof Nicola Marzari Department of Materials Science and Engineering
> 13-5066 MIT 77 Massachusetts Avenue Cambridge MA 02139-4307 USA
> tel 617.4522758 fax 2586534 marzari at mit.edu http://quasiamore.mit.edu
> Pw_forum mailing list
> Pw_forum at pwscf.org
Stefano Baroni - SISSA & DEMOCRITOS National Simulation Center -
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