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thank you for the explanation,<br>
it is really helpfull<br>
<br>
bahadir<br>
<br>
On 02/27/2012 07:24 AM, Stefano Baroni wrote:
<blockquote cite="mid:AE0A8E78-8D48-43A9-B6FD-FC59AA0E9E91@sissa.it"
type="cite">Dear Bahdir:
<div><br>
<div>
<blockquote type="cite">
<div>i just tried a quick calculation for my curiosity on
this. i just optimized a fcc structure under 100GPa
pressure also under 0GPa<br>
i calculated bulk modulus for 0GPa system by changing
equilibrium celldm(1) in range of -10% and +10% and
calculatin energy. and used ev.x for fitting. fiiting
curve is an U-shaped plot<br>
</div>
</blockquote>
<div><br>
</div>
+/- 10% may be too large a variation to estimate the second
derivative by finite differences, but assuming that you know
what you are doing, I would say that the procedure is correct.
No surprise that you find a "U-shaped" curve, given that you
calculate points on that curve near the minimum (the "bottom
of the U")<br>
<blockquote type="cite">
<div><br>
then i did the same procedure for 100GPa system by
calculating energy for the celldm(1) values -10% to +10%.
first thing is: alatt vs energy plot is not U-shaped. </div>
</blockquote>
<div><br>
</div>
why should it? at such a large pressure, you would probably be
rather far from the minimum ...</div>
<div><br>
<blockquote type="cite">
<div>and if i extend the range from +-10%<br>
to +-20% a get an equilibrium energy but obviously it is
the same as that of 0GPa's result.<br>
<br>
that is the point that i am getting confused by.<br>
and still curious about, what should i do to calculate a
bulk modulus for a system under 100GPa?<br>
</div>
</blockquote>
<div><br>
</div>
I maintain that you are probably fooled by names. If you want
to calculate the second derivative of the E(V) curve, just do
it: the second derivative has well defined value even far from
the minimum, where the curve is not "U-shaped". Just do what
any text in numerical analysis tells you to do in the chapter
on numerical differentiation ...</div>
<div><br>
</div>
<div>Let's now come to names. Strictly speaking, the bulk
modulus is the second derivative of the energy (or free
energy) *as a function of volume*. It is therefore a function
of volume, not of pressure. Of course, once you have the bulk
modulus as a function of volume, B=B(V), you can always use
the equation of state, V=V(P), to formally write it as a
function of pressure, by a simple change of variable: B(P) "="
B(V(P)). Note the quotation marks that mean: "the bulk modulus
at the volume corresponding to the pressure P". I think that
some algebraic gymnastics would allow you to obtain this
quantity from the second derivative of the enthalpy (which is
the appropriate thermodynamical potential that depends on
pressure as an independent variable). It all depends on what
you need: if you need the second derivative of "A" with
respect to "B", then just calculate it, whatever the name of
that second derivative is ...</div>
<div><br>
</div>
<div>HTH - SB</div>
<div><br>
</div>
<div>
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</blockquote>
<br>
<br>
<pre class="moz-signature" cols="72">--
Dr.Bahadir Altintas
* Dept. of Chemistry
SUNY Buffalo
NY,USA
* Abant Izzet Baysal University
Dept. of Computer Education
Bolu,Turkey</pre>
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