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) La morale est une logique de l'action comme la logique est une morale de la pens?e - Jean Piaget Please, if possible, don't send me MS Word or PowerPoint attachments Why? See: http://www.gnu.org/philosophy/no-word-attachments.html -------------- next part -------------- An HTML attachment was scrubbed... URL: http://www.democritos.it/pipermail/pw_forum/attachments/20080510/a40fc97b/attachment.htm
