<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><div>On Aug 11, 2012, at 7:47 AM, Alex Mariani wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div><div style="color:; background-color:; font-family:times new roman, new york, times, serif;font-size:12pt"><div><span><br></span></div><div><br></div> <div style="font-family: times new roman, new york, times, serif; font-size: 12pt;"> <div style="font-family: times new roman, new york, times, serif; font-size: 12pt;"> <br>
<meta http-equiv="x-dns-prefetch-control" content="off"><div id="yiv551715428"><div><div style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; position: static; z-index: auto; "><div>Dear all</div><div><span id="yiv551715428result_box" class="yiv551715428" lang="en"><span class="yiv551715428hps">I</span> <span class="yiv551715428hps">want</span> <span class="yiv551715428hps">to calculate</span> <span class="yiv551715428hps">the</span> <span class="yiv551715428hps"></span></span>piezoelectric constant for PbTio3.</div><div><span id="yiv551715428result_box" class="yiv551715428" lang="en"><span class="yiv551715428hps">How</span> <span class="yiv551715428hps">do </span><span class="yiv551715428hps"></span><span class="yiv551715428hps">using</span> the QE <span class="yiv551715428hps">code</span><span>?</span><br> <span class="yiv551715428hps">What is</span> <span class="yiv551715428hps">the</span> <span class="yiv551715428hps">procedure</span><span>?</span><br></span></div></div></div></div></div></div></div></div></blockquote><div><br></div><div>Simple solution: Perform a set of finite-field calculations and plot the stress as a function of the applied electric field. The slope at zero field gives you the piezoelectric coefficient(s).</div><div><br></div><div>A more elegant solution (which requires some coding, though) is described in: S. de Gironcoli et al. PRL <b>62</b>, 2853 (1989), <span style="color: rgb(50, 50, 50); font-family: arial, helvetica, sans-serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display: inline !important; float: none; "><a href="http://link.aps.org/doi/10.1103/PhysRevLett.62.2853">http://link.aps.org/doi/10.1103/PhysRevLett.62.2853</a></span></div><div><span style="color: rgb(50, 50, 50); font-family: arial, helvetica, sans-serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display: inline !important; float: none; "><br></span></div><div><span style="color: rgb(50, 50, 50); font-family: arial, helvetica, sans-serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display: inline !important; float: none; ">SB</span></div><div><font class="Apple-style-span" color="#323232" face="arial, helvetica, sans-serif"><br></font></div></div><div>
<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-size: 14px; "><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-size: 14px; "><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-size: 14px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "><a href="http://stefano.baroni.me/">http://stefano.baroni.me</a> [+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></span></div></div></div>
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