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<p>I think what Grimvall is saying is that there has been no
rigorous discussion before, but in their review they make this
discussion, and show how the stability condition for phonons does
not need any correction - the material collapses at the pressure
where the phonon dispersions calculated at the corresponding
volume go negative. Anyhow, they cite a few papers and their
follow-up corrections.<br>
</p>
<p>nic<br>
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<div class="moz-cite-prefix"><br>
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<div class="moz-cite-prefix">On 11/01/2021 11:04, Uri Argaman wrote:<br>
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<blockquote type="cite"
cite="mid:CA+6Rk3wpiU1VzMhgNRBJsoGsEQh07efCb35QEL_uZ+zVQQ9eaA@mail.gmail.com">
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<div dir="ltr">Hi all
<div>In the literature the mechanical stability condition using
elastic constants includes explicitly the pressure:</div>
<div>In cubic symmetry, for example:</div>
<div>C11 <a class="gmail_plusreply"
id="gmail-m_-7814860968767635018plusReplyChip-0"
moz-do-not-send="true">+</a> 2*C12 +P>0; </div>
<div>C44 +P>0;<br>
C11 <a class="gmail_plusreply"
id="gmail-m_-7814860968767635018plusReplyChip-1"
moz-do-not-send="true">+</a> C12 <a class="gmail_plusreply"
id="gmail-m_-7814860968767635018plusReplyChip-2"
moz-do-not-send="true">+</a> 2*P>0;<br>
</div>
<div>from: Grimvall et al. REVIEWS OF MODERN PHYSICS, VOLUME
84, 2012<br>
</div>
<div>In this paper, they write: " There seems to be no rigorous
discussion of this point in papers that have presented ab
initio calculations of phonon dispersion curves under
pressure,..."</div>
<div>The stability condition from phonons: omega>0 for all
modes. It seems that it is not equivalent, because the phonon
condition is at constant volume. Is it known what is the
condition at constant pressure? </div>
<div>Than you very much</div>
<font color="#888888">
<div>Uri Argaman</div>
<div>Ben-Gurion University of the Negev</div>
<div>Israel</div>
</font></div>
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