[Pw_forum] how to find out the stable structure under high pressure
Fernando A Reboredo
reboredofa at ornl.gov
Thu Jun 15 17:43:17 CEST 2006
I agree with Stefano:
While it is true that 1) in matematical terms ALL the phonon modes of a crystal are a compete basis where any posible atomic displacement can be decomposed, and also 2) any new structure with the same number of atoms can be though as a displacement from the old one (it could be big), the set of soft modes are incomple basis and thus they can only describe a subset of arbitrary structure transitions.
----- Original Message -----
From: Stefano Baroni
To: pw_forum at pwscf.org
Sent: Wednesday, June 14, 2006 2:56 AM
Subject: Re: [Pw_forum] how to find out the stable structure under high pressure
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:
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?
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
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