The ABINIT Users Mailing List ( CLOSED )

["D. R. Hamann" <drhamann@mat-simresearch.com>]

Hi,

You can also calculate the bulk modulus directly by using density
functional perturbation theory to calculate the elastic tensor. See the
"Elastic Properties" tutorial. This is typically more accurate than
finite-difference or fitting methods, especially for systems where there
is relaxation of internal atomic coordinates. In the limit in which
everything is well converged, all methods should yield identical results.

Best regards,
Don Hamann

Anglade Pierre-Matthieu wrote:
> Hi,
>
> As long as your formula are correct they will give the exact same
> result in the limit that your computation is perfectly converged. You
> can test very easily the convergence by increasing your k-point
> samplign and ecut. If the two computation of bulk modulus tend to the
> same result when you increase absolute convergence then your formula
> are correct. Ottherwise you can be sure there is a flaw.
>
> regards
>
> PMA
>
>
> 2008/7/12 zhaohscas <zhaohscas@yahoo.com.cn>:
>   
>> Hi forks,
>>
>> I use the abinit to compute bulk modulus of BaHfO_3, I obtaibed the the 
>> volume and energy under zero pressure first, then I compute the several 
>> volume and energy dataset of BaHfO_3 under 2.5GPa, 5.0GPa, 7.5GPa, 10GPa, 
>> 20GPa, and 30GPa respectively.
>>
>> Then, I use the dataset to compute bulk modulus.  Due to the formulae of  
>> P-V and E-V Birch�CMurnaghan equation of state are all can be used to do 
>> this, in order to comparison, both the P-V and E-V Birch�CMurnaghan 
>> equation of state are used.  But, I found that there're  great difference 
>> between the result obtained from fitting P-V Birch�CMurnaghan equation of 
>> state and that of the E-V Birch�CMurnaghan equation of state.  I also 
>> found that the result from P-V fitting is more close to the reports value 
>> in the literatures.
>>
>> Furthermore, I also have a puzzle about the form of the formulae of  P-V 
>> and E-V Birch�CMurnaghan equation of state, in detail, I've read from the 
>> different literatures that there are two forms of the P-V Birch�CMurnaghan 
>> 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?
>>
>> As for the E-V Birch�CMurnaghan equation of state, I read the following 
>> form:
>>
>> E(V) = E_0  + \frac{{9V_0 B_0 }}{{16}}\left\{ {\left[ {\left( {\frac{{V_0 
>> }}{V}} \right)^{\frac{2}{3}}  - 1} \right]^3 B_0^'  + \left[ {\left( 
>> {\frac{{V_0 }}{V}} \right)^{\frac{2}{3}}  - 1} \right]^2 \left[ {6 - 
>> 4\left( {\frac{{V_0 }}{V}} \right)^{\frac{2}{3}} } \right]} \right\}
>>
>> Is this right or not?
>>
>> Who can give me some hints?
>>
>> Sincerely yours,
>> --------------
>> Hongsheng Zhao <zhaohscas@yahoo.com.cn>
>> Xinjiang Technical Institute of Physics and Chemistry
>> Chinese Academy of Sciences
>> GnuPG DSA: 0xD10849
>> 2008-07-12
>>
>>     
>
>
>
>   

-- 
D. R. Hamann
Mat-Sim Research LLC    | Deptartment of Physics
P.O. Box 742            |  and Astronomy
Murray Hill, NJ 07974   | Rutgers University
phone: 908-370-8079     | 732-445-4381

email: drhamann@mat-simresearch.com