[Pw_forum] Compute bulk modulus by using the formulae of P-V and E-V Birch–Murnaghan equation of state.

[Paolo Giannozzi]

On Jul 12, 2008, at 17:09 , zhaohscas wrote:

> I've read from the different literatures that there are two forms  
> of the P-V Birch–Murnaghan equation of state:
>
> a)  P(V) = \frac{{3B_0 }}{2}\left[ {\left( {\frac{{V_0 }}{V}}  
> \right)^{\frac{7}{3}}  - \left( {\frac{{V_0 }}{V}} \right)^{\frac{5} 
> {3}} } \right]\left\{ {1 + \frac{3}{4}\left( {B_0^'  - 4} \right) 
> \left[ {\left( {\frac{{V_0 }}{V}} \right)^{\frac{2}{3}}  - 1}  
> \right]} \right\}
>
> b)  P(V) = \frac{{3B_0 }}{2}\left[ {\left( {\frac{{V_0 }}{V}}  
> \right)^{\frac{7}{3}}  - \left( {\frac{{V_0 }}{V}} \right)^{\frac{5} 
> {3}} } \right]\left\{ {1 + \frac{3}{4}\left( {4 - B_0^'} \right) 
> \left[ {\left( {\frac{{V_0 }}{V}} \right)^{\frac{2}{3}}  - 1}  
> \right]} \right\}
>
> Where, the B_0 and the B_0^' are the bulk modulus and its pressure  
> derivative respectively. Which of the above is correct?

the one that is obtained by derivation of the Birch-Murnaghan  
equation of state
E(V). I cast my vote for a), since this is what I used once upon a  
time in a routine
that calculates P(V)

Paolo
---
Paolo Giannozzi, Dept of Physics, University of Udine
via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222