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<DIV><FONT face=Arial size=2>I agree with Stefano:</FONT></DIV>
<DIV><FONT face=Arial size=2>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, a</FONT><FONT face=Arial
size=2>nd 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.</FONT></DIV>
<DIV><FONT face=Arial size=2>Fernando</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=baroni@sissa.it href="mailto:baroni@sissa.it">Stefano Baroni</A>
</DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=pw_forum@pwscf.org
href="mailto:pw_forum@pwscf.org">pw_forum@pwscf.org</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Wednesday, June 14, 2006 2:56
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [Pw_forum] how to find out
the stable structure under high pressure</DIV>
<DIV><BR></DIV>Nicola: here, I beg to differ. For two reasons.
<DIV><BR class=khtml-block-placeholder></DIV>
<DIV>First: even if there was a minimum such as discrebed in the question,
this would be a _local_ and not necessarily a global one.</DIV>
<DIV><BR class=khtml-block-placeholder></DIV>
<DIV>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.</DIV>
<DIV><BR class=khtml-block-placeholder></DIV>
<DIV>Hope to have been not too confusing.</DIV>
<DIV><BR class=khtml-block-placeholder></DIV>
<DIV>Stefano</DIV>
<DIV><BR class=khtml-block-placeholder></DIV>
<DIV> </DIV>
<DIV><BR>
<DIV>
<DIV>On Jun 14, 2006, at 5:01 AM, Nicola Marzari wrote:</DIV><BR
class=Apple-interchange-newline>
<BLOCKQUOTE type="cite">
<DIV style="MIN-HEIGHT: 14px; MARGIN: 0px"><BR></DIV>
<DIV style="MARGIN: 0px">Yes,</DIV>
<DIV style="MIN-HEIGHT: 14px; MARGIN: 0px"><BR></DIV>
<DIV style="MARGIN: 0px"><SPAN class=Apple-tab-span
style="WHITE-SPACE: pre"></SPAN><SPAN class=Apple-tab-span
style="WHITE-SPACE: pre"></SPAN><SPAN class=Apple-tab-span
style="WHITE-SPACE: pre"></SPAN>nicola</DIV>
<DIV style="MIN-HEIGHT: 14px; MARGIN: 0px"><BR></DIV>
<DIV style="MIN-HEIGHT: 14px; MARGIN: 0px"><BR></DIV>
<DIV style="MARGIN: 0px">li yan wrote:</DIV>
<BLOCKQUOTE type="cite">
<DIV style="MARGIN: 0px">Dear all,</DIV>
<DIV style="MARGIN: 0px"><SPAN class=Apple-converted-space>
</SPAN>I found soft modes in a system under pressure. Is it
true that<SPAN class=Apple-converted-space> </SPAN></DIV>
<DIV style="MARGIN: 0px">there must be a global energy miniumu in the
subspace spanned by the<SPAN
class=Apple-converted-space> </SPAN></DIV>
<DIV style="MARGIN: 0px">eignevectors of the soft modes?<SPAN
class=Apple-converted-space> </SPAN>And by searching this munimum,
can i<SPAN class=Apple-converted-space> </SPAN></DIV>
<DIV style="MARGIN: 0px">find the stable high-pressure strucure? <SPAN
class=Apple-converted-space> </SPAN></DIV>
<DIV style="MIN-HEIGHT: 14px; MARGIN: 0px"><BR></DIV>
<DIV style="MIN-HEIGHT: 14px; MARGIN: 0px"><BR></DIV>
<DIV style="MARGIN: 0px">best regards</DIV>
<DIV style="MIN-HEIGHT: 14px; MARGIN: 0px"><BR></DIV>
<DIV
style="MARGIN: 0px">__________________________________________________</DIV>
<DIV style="MARGIN: 0px">赶快注册雅虎超大容量免费邮箱?</DIV>
<DIV style="MARGIN: 0px"><A
href="http://cn.mail.yahoo.com">http://cn.mail.yahoo.com</A></DIV>
<DIV style="MIN-HEIGHT: 14px; MARGIN: 0px"><BR></DIV></BLOCKQUOTE>
<DIV style="MIN-HEIGHT: 14px; MARGIN: 0px"><BR></DIV>
<DIV style="MIN-HEIGHT: 14px; MARGIN: 0px"><BR></DIV>
<DIV style="MIN-HEIGHT: 14px; MARGIN: 0px"><BR></DIV>
<DIV style="MIN-HEIGHT: 14px; MARGIN: 0px"><BR></DIV>
<DIV style="MARGIN: 0px">--<SPAN
class=Apple-converted-space> </SPAN></DIV>
<DIV
style="MARGIN: 0px">---------------------------------------------------------------------</DIV>
<DIV style="MARGIN: 0px">Prof Nicola Marzari <SPAN
class=Apple-converted-space> </SPAN>Department of Materials Science
and Engineering</DIV>
<DIV style="MARGIN: 0px">13-5066 <SPAN class=Apple-converted-space>
</SPAN>MIT <SPAN class=Apple-converted-space> </SPAN>77 Massachusetts
Avenue <SPAN class=Apple-converted-space> </SPAN>Cambridge MA
02139-4307 USA</DIV>
<DIV style="MARGIN: 0px">tel 617.4522758 fax 2586534 marzari@mit.edu <A
href="http://quasiamore.mit.edu">http://quasiamore.mit.edu</A></DIV>
<DIV
style="MARGIN: 0px">_______________________________________________</DIV>
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<DIV style="MARGIN: 0px"><FONT class=Apple-style-span size=3><SPAN
class=Apple-style-span style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px">---</SPAN></SPAN></SPAN></FONT></DIV>
<DIV style="MARGIN: 0px"><FONT class=Apple-style-span size=3><SPAN
class=Apple-style-span style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px">Stefano Baroni -
SISSA</SPAN></SPAN></SPAN></FONT><FONT class=Apple-style-span size=3><SPAN
class=Apple-style-span style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"> </SPAN></SPAN></SPAN></FONT><FONT
class=Apple-style-span size=3><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px">&</SPAN></SPAN></SPAN></FONT><FONT
class=Apple-style-span size=3><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"> </SPAN></SPAN></SPAN></FONT><FONT
class=Apple-style-span size=3><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px">DEMOCRITOS National Simulation Center -
Trieste</SPAN></SPAN></SPAN></FONT></DIV>
<DIV style="MARGIN: 0px"><FONT class=Apple-style-span size=3><SPAN
class=Apple-style-span style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px">[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni
(skype)</SPAN></SPAN></SPAN></FONT></DIV>
<DIV style="MIN-HEIGHT: 14px; MARGIN: 0px; FONT: 12px Helvetica"><BR
style="FONT-SIZE: 12px"></DIV>
<DIV style="MARGIN: 0px"><FONT class=Apple-style-span size=3><SPAN
class=Apple-style-span style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px">Please, if possible,
don't</SPAN></SPAN></SPAN></FONT><FONT class=Apple-style-span size=3><SPAN
class=Apple-style-span style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"> </SPAN></SPAN></SPAN></FONT><FONT
class=Apple-style-span size=3><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px">send me MS Word or PowerPoint
attachments</SPAN></SPAN></SPAN></FONT></DIV>
<DIV style="MARGIN: 0px"><FONT class=Apple-style-span size=3><SPAN
class=Apple-style-span style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px">Why? See:</SPAN></SPAN></SPAN></FONT><FONT
class=Apple-style-span size=3><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"><SPAN class=Apple-style-span
style="FONT-SIZE: 12px"> </SPAN></SPAN></SPAN></FONT><A
href="http://www.gnu.org/philosophy/no-word-attachments.html"><FONT
class=Apple-style-span color=#0023e9 size=3><SPAN class=Apple-style-span
style="FONT-SIZE: 12px; COLOR: rgb(0,35,233); khtml-text-decorations-in-effect: underline"><SPAN
class=Apple-style-span
style="FONT-SIZE: 12px; COLOR: rgb(0,35,233); khtml-text-decorations-in-effect: underline"><SPAN
class=Apple-style-span
style="FONT-SIZE: 12px; COLOR: rgb(0,35,233); khtml-text-decorations-in-effect: underline">http://www.gnu.org/philosophy/no-word-attachments.html</SPAN></SPAN></SPAN></FONT></A></DIV>
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