bulk modulus

[goja25]

Hi Dear
How I wrote earlier I want to calculate bulk modulus of PbTe. I have a question about that. I know that Murnaghan equation of state:
B = - V(dP/dV).
1. First I relaxed my structure and obtained total energy and volume of this system.
2. I took CONTCAR from previous calculation and obtained volume and next I wrote it to the POSCAR file (insted of latice constant).
3. In the INCAR file I fixed that volume using ISIF=4. I obtained total energy.
4. Next I was changing that volume in 10 steps for about 0,001 and calculate total energy. I obtained 10 volumes and 10 energies.
5. I obtained external pressure of my system too. Should I substitute that pressures and volumes to the Murnaghan equation and take its average?
What should I do? Please help.
Margo

[admin]

if you want to use the Murnaghan eqn. of state, please only use the volumes and their related total energies as input. Please note that delta V should be large enough (a few percent +/- (ca 5%) of the equilibrium volume) to obtain a reliable fit (I fear that your steps of 0.001 are a little too small.)

[goja25]

Thanks for replay
I did calculations how you said. First I used the equilibrium volume and I changed it about 5% in 10 steps.
I have one question what you mean by delta V?
How should I obtain the bulk modulus from 10 different volumes and energies? Please tell me, I'm beginner so I don't know this problem.
Margo

[forsdan]

Please have a look at

http://en.wikipedia.org/wiki/Birch-Murn ... n_of_state

Combine (1) and (2) to find B = V*E''(V), where E''(V) denotes the second derivitive of E with respect to V. So just

(i) make any reasonable fit of the curve E(V) (for example using a spline interpolation or polynomial fit)
(ii) evaluate the second derivitive E''(V)
(iii) evaluate the bulk modulus at the equilibrium volume B =V0*E''(V0)

Another alternative is to fit E(V) directly to expression (8) to get the bulk modulus. You should get approximately the same results.

Best regards,
/Dan

<span class='smallblacktext'>[ Edited Thu Oct 23 2008, 04:31PM ]</span>