[Pw_forum] Dear Professor

[Stefano Baroni]

On May 9, 2008, at 2:29 PM, penghua wrote:

>
>  Dear Professor Baroni,

Peng Hua:

>    I wrote a letter to you last week and received your letter which  
> gave me a lot of help about third derivative of energy related to  
> the phonon life calculation. Thank you very much!
>  Since I am a mew one in this domain ,I do not understand something  
> in (A. Debernardi, S. Baroni, and E. Molinari, Phys. Rev. Lett. 75,  
> 1819 - 1822 1995).In the formula(1)of the article ,the N is the  
> number of unit cells in  crystal. But I think N is infinite in  
> crystal, thus the inverse lifetime becomes 0. Is what I thought is  
> wrong?

this is like saying that the density (=N/V) of any material is zero,  
because the volume is infinite - do you see the point?

The equation you are referring to gives the lifetime as the ratio  
between two quantities that diverge in the thermodynamic (N->infinity)  
limit, while the ratio tends to a well defined limit (not an unusual  
situation indeed). In your particular case, the denominator contains a  
N^3 tem. N^2 compensates the square of the third-order derivative of  
the energy [which, being an extensive quantity, is linear in the  
system size, i.e. N (E=N times energy per cell)]. The other factor N  
is the standard normalization factor for the number of k-points in the  
BZ.

> How can i get N? Could you give me some explanation?

In other terms, if you substitute the energy per cell for E in Eq.  
(1), you have just to divide by the number of special k-points you use  
to evaluate the sum (N^3 -> N_kpoints).

> Beside if I want to calculate the inverse lifetime using the output  
> of d3.x, should I programmer according to the formula (1)? I really  
> appreciate your help.

this is what we did befoe d3.x was available. no idea whatsoever about  
what d3.x actually calculates (the third derivatives appearing in Eq.  
1, I guess, but I do not know any details of the input, etc.)

> Thanks again for reading this mail.

Hope this helps
Stefano

---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
Trieste
[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

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