<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><br><div><div>On May 9, 2008, at 2:29 PM, penghua wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div> <div> <span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-family: 宋体">Dear Professor Baroni,</span></div></div></blockquote><div><br></div>Peng Hua:</div><div><br><blockquote type="cite"><div><div><span lang="EN-US" style="FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-family: 宋体; mso-bidi-font-size: 10.5pt"><o:p></o:p></span><div style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 0pt; margin-left: 0cm; text-align: left; "><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-family: 宋体; mso-bidi-font-size: 10.5pt"> I wrote a letter to you last week and received your letter which gave me a lot of help about third derivative of energy related to the phonon life calculation. Thank you very much!</span></div><div style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 0pt; margin-left: 0cm; text-align: left; "><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-family: 宋体; mso-bidi-font-size: 10.5pt"> Since I am a mew one in this domain ,I do not understand something in (A. Debernardi, S. Baroni, and E. Molinari, Phys. Rev. Lett. 75, 1819 - 1822 1995).In the formula(1)of the article ,the N is the number of unit cells in crystal. But I think N is infinite in crystal, thus the inverse lifetime becomes 0. Is what I thought is wrong? </span></div></div></div></blockquote><div><br></div>this is like saying that the density (=N/V) of any material is zero, because the volume is infinite - do you see the point? </div><div><br></div><div>The equation you are referring to gives the lifetime as the ratio between two quantities that diverge in the thermodynamic (N->infinity) limit, while the ratio tends to a well defined limit (not an unusual situation indeed). In your particular case, the denominator contains a N^3 tem. N^2 compensates the square of the third-order derivative of the energy [which, being an extensive quantity, is linear in the system size, i.e. N (E=N times energy per cell)]. The other factor N is the standard normalization factor for the number of k-points in the BZ. </div><div> </div><div><blockquote type="cite"><div><div><div style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 0pt; margin-left: 0cm; text-align: left; "><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-family: 宋体; mso-bidi-font-size: 10.5pt">How can i get N? Could you give me some explanation?</span></div></div></div></blockquote><div><br></div>In other terms, if you substitute the energy per cell for E in Eq. (1), you have just to divide by the number of special k-points you use to evaluate the sum (N^3 -> N_kpoints).</div><div><br><blockquote type="cite"><div><div><div style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 0pt; margin-left: 0cm; text-align: left; "><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-family: 宋体; mso-bidi-font-size: 10.5pt"> <o:p></o:p></span></div><div style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 0pt; margin-left: 0cm; text-indent: 12pt; text-align: left; "><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-family: 宋体; mso-bidi-font-size: 10.5pt">Beside if I want to calculate the inverse lifetime using the output of d3.x, should I programmer according to the formula (1)? I really appreciate your help.</span></div></div></div></blockquote><div><br></div>this is what we did befoe d3.x was available. no idea whatsoever about what d3.x actually calculates (the third derivatives appearing in Eq. 1, I guess, but I do not know any details of the input, etc.)</div><div><br><blockquote type="cite"><div><div><div style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 0pt; margin-left: 0cm; text-indent: 12pt; text-align: left; "><span lang="EN-US" style="FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-family: 宋体; mso-bidi-font-size: 10.5pt"><o:p></o:p></span></div><div style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 0pt; margin-left: 0cm; text-align: left; "><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-family: 宋体; mso-bidi-font-size: 10.5pt">Thanks again for reading this mail.</span></div></div></div></blockquote><br></div><div>Hope this helps</div><div>Stefano</div><div><br></div><div> <span class="Apple-style-span" style="border-collapse: separate; 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; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; 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; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; 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; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><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></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; ">Stefano Baroni - SISSA</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">&</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">DEMOCRITOS National Simulation Center - Trieste</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; ">[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)</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: normal normal normal 12px/normal Helvetica; min-height: 14px; font-size: 12px; "><span class="Apple-style-span" style="font-size: 14px; "><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; ">La morale est une logique de l'action comme la logique est une morale de la pensée - Jean Piaget</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; "><br></span></font></div></span></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; ">Please, if possible, don't</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">send me MS Word or PowerPoint attachments</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; ">Why? See:</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" color="#0023E9" size="3"><span class="Apple-style-span" style="font-size: 12px; "><a href="http://www.gnu.org/philosophy/no-word-attachments.html">http://www.gnu.org/philosophy/no-word-attachments.html</a></span></font></div><div><font class="Apple-style-span" color="#0023E9" size="3"><span class="Apple-style-span" style="font-size: 12px; "><br class="webkit-block-placeholder"></span></font></div></div></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"> </div><br></body></html>