[Pw_forum] how to find out the stable structure under high pressure

Stefano Baroni 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:

> Yes,
> 			nicola
> 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
>> __________________________________________________
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> -- 
> ---------------------------------------------------------------------
> Prof Nicola Marzari   Department of Materials Science and Engineering
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Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
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