<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; "><BR><DIV><DIV>On May 30, 2006, at 11:40 PM, Lijun Zhang wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><DIV class="MsoNormal" style="MARGIN: 0cm 0cm 0pt"><SPAN lang="EN-US" style="FONT-SIZE: 12pt"><FONT face="Times New Roman">Dear all,<O:P></O:P></FONT></SPAN></DIV> <DIV class="MsoNormal" style="MARGIN: 0cm 0cm 0pt"><SPAN lang="EN-US" style="FONT-SIZE: 12pt"><FONT face="Times New Roman">I am doing some calculations on the phase transition induced by lattice </FONT></SPAN></DIV> <DIV class="MsoNormal" style="MARGIN: 0cm 0cm 0pt"><SPAN lang="EN-US" style="FONT-SIZE: 12pt"><FONT face="Times New Roman">instability. With increasing pressures, I found that a Raman active phonon </FONT></SPAN></DIV> <DIV class="MsoNormal" style="MARGIN: 0cm 0cm 0pt"><SPAN lang="EN-US" style="FONT-SIZE: 12pt"><FONT face="Times New Roman">softens to zero, the same as behaviors in the ferroelectricity. <SPAN style="mso-spacerun: yes"> </SPAN>An elastic </FONT></SPAN></DIV> <DIV class="MsoNormal" style="MARGIN: 0cm 0cm 0pt"><SPAN lang="EN-US" style="FONT-SIZE: 12pt"><FONT face="Times New Roman">instability also appears upon compression, signaled by a sound velocity </FONT></SPAN></DIV> <DIV class="MsoNormal" style="MARGIN: 0cm 0cm 0pt"><SPAN lang="EN-US" style="FONT-SIZE: 12pt"><FONT face="Times New Roman">going to zero. However, the former extremely precedes the latter, thus I </FONT></SPAN></DIV> <DIV class="MsoNormal" style="MARGIN: 0cm 0cm 0pt"><SPAN lang="EN-US" style="FONT-SIZE: 12pt"><FONT face="Times New Roman">conclude that the phase transition is driven by the phonon instability. Is it </FONT></SPAN></DIV> <DIV class="MsoNormal" style="MARGIN: 0cm 0cm 0pt"><SPAN lang="EN-US" style="FONT-SIZE: 12pt"><FONT face="Times New Roman">right? <BR></FONT></SPAN></DIV></BLOCKQUOTE><DIV><BR class="khtml-block-placeholder"></DIV>NO, it is not. For two reasons, which are somewhat related to one another. First, the phonon instability is usually coupled to the phonon instability, so that the phase transformation usually results from a distortion pattern which involves both the shape of the unit cell (elastic) and the atomic positions within the unit cell (phonon). As a consequence of this, the transition is usuall first-order, i.e. it occurs before any mode (either phonon-like or elastic) actually softens. Phonon or sound-velocity softening just signal the onset of an instability. In order to study the structural stability of the crystal as a function of pressure, you should study how the enthalpy (E+PV) of the systems depends on the "order parameters" of the transition for different values of the pressure. Good order parameter would obviously be the atomic distortion patterns corresponding to the soft phonon mode and the components of the strain corresponding to the vanishing sound velocity.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>I am sure this is discussed in many different places. The references were what I have understood in this business is explained is:</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">M. Buongiorno Nardelli, S. Baroni, and P. Giannozzi, Phys. Rev. B <B>51</B>, 8060 (1995). </DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">M. Buongiorno Nardelli, S. Baroni, and P. Giannozzi, Phys. Rev. Lett., <B>69</B>, 1069 (1992). </DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Hope this helps</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">SB</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="3"><SPAN class="Apple-style-span" style="font-size: 12px;"><BR class="khtml-block-placeholder"></SPAN></FONT></DIV><DIV><BR><BLOCKQUOTE type="cite"><DIV class="MsoNormal" style="MARGIN: 0cm 0cm 0pt"><SPAN lang="EN-US" style="FONT-SIZE: 12pt"><FONT face="Times New Roman">If true, how to search for the stable high pressure phase through the </FONT></SPAN></DIV> <DIV class="MsoNormal" style="MARGIN: 0cm 0cm 0pt"><SPAN lang="EN-US" style="FONT-SIZE: 12pt"><FONT face="Times New Roman">eigenvectors of the unstable mode?</FONT></SPAN></DIV> <DIV class="MsoNormal" style="MARGIN: 0cm 0cm 0pt"><SPAN lang="EN-US" style="FONT-SIZE: 12pt"><FONT face="Times New Roman">Any reply will be appreciated. <SPAN style="mso-spacerun: yes"> </SPAN><SPAN style="mso-spacerun: yes"> </SPAN></FONT></SPAN></DIV> <DIV class="MsoNormal" style="MARGIN: 0cm 0cm 0pt"><SPAN lang="EN-US" style="FONT-SIZE: 12pt"><FONT face="Times New Roman"><SPAN style="mso-spacerun: yes">Lijun Zhang</SPAN></FONT><O:P></O:P></SPAN></DIV><DIV> <BR class="khtml-block-placeholder"></DIV><HR size="1"><A href="http://music.yahoo.com.cn/?source=mail_mailbox_footer" target="blank"> Mp3疯狂搜-新歌热歌高速下 </A> </BLOCKQUOTE></DIV><BR><DIV> <SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 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-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 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-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 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="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; ; font-size: 12px; "><BR style="; font-size: 12px; "></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 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-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 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="color: rgb(0, 35, 233); font-size: 12px; -khtml-text-decorations-in-effect: underline; "><SPAN class="Apple-style-span" style="color: rgb(0, 35, 233); font-size: 12px; -khtml-text-decorations-in-effect: underline; ">http://www.gnu.org/philosophy/no-word-attachments.html</SPAN></SPAN></SPAN></FONT></A></DIV><DIV><BR class="khtml-block-placeholder"></DIV><BR class="Apple-interchange-newline"></SPAN></SPAN></SPAN> </DIV><BR></BODY></HTML>