# [Pw_forum] About the method to obtain the common tangent for determing the phase transition pressure.

Stefano Baroni baroni at sissa.it
Mon Dec 20 15:52:13 CET 2010

On Dec 20, 2010, at 2:07 PM, 红生 赵 wrote:

> Dear all,

Dear Hongsheng,

>
> For the first-order phase transitions, the following criteria should be met: Pressures of the two phases are equal, i.e.,
> P_{eq} = - \frac{{d{E_1}}}{{d{V_1}}} = - \frac{{d{E_2}}}{{d{V_2}}}
>
> In other words, the P_{eq} is gradient of common tangent of the two phases E-V curves obtained from EOS fitting.
> This is a mathematical problem, but for the plot of this common tangent, can someone please give me some hints? What tools/softwares should I use for this purpose? Thanks in advance.

1) plot the curves and find the tangent by hand
2) solve the equation E1(V1(p))+pV1(p)=E2(V2(p))+pV2(p), as a function of the pressure p. V12 is here the volume of the two phases as a function of the pressure.

hope this helps
Stefano

>
> Best regards.
> Hongsheng Zhao
>
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---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center - Trieste
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