thank you for the explanation, it is really helpfull bahadir
On 02/27/2012 07:24 AM, Stefano Baroni wrote: > Dear Bahdir: > >> i just tried a quick calculation for my curiosity on this. i just >> optimized a fcc structure under 100GPa pressure also under 0GPa >> i calculated bulk modulus for 0GPa system by changing equilibrium >> celldm(1) in range of -10% and +10% and calculatin energy. and used >> ev.x for fitting. fiiting curve is an U-shaped plot > > +/- 10% may be too large a variation to estimate the second derivative > by finite differences, but assuming that you know what you are doing, > I would say that the procedure is correct. No surprise that you find a > "U-shaped" curve, given that you calculate points on that curve near > the minimum (the "bottom of the U") >> >> then i did the same procedure for 100GPa system by calculating energy >> for the celldm(1) values -10% to +10%. first thing is: alatt vs >> energy plot is not U-shaped. > > why should it? at such a large pressure, you would probably be rather > far from the minimum ... > >> and if i extend the range from +-10% >> to +-20% a get an equilibrium energy but obviously it is the same as >> that of 0GPa's result. >> >> that is the point that i am getting confused by. >> and still curious about, what should i do to calculate a bulk modulus >> for a system under 100GPa? > > I maintain that you are probably fooled by names. If you want to > calculate the second derivative of the E(V) curve, just do it: the > second derivative has well defined value even far from the minimum, > where the curve is not "U-shaped". Just do what any text in numerical > analysis tells you to do in the chapter on numerical differentiation ... > > Let's now come to names. Strictly speaking, the bulk modulus is the > second derivative of the energy (or free energy) *as a function of > volume*. It is therefore a function of volume, not of pressure. Of > course, once you have the bulk modulus as a function of volume, > B=B(V), you can always use the equation of state, V=V(P), to formally > write it as a function of pressure, by a simple change of variable: > B(P) "=" B(V(P)). Note the quotation marks that mean: "the bulk > modulus at the volume corresponding to the pressure P". I think that > some algebraic gymnastics would allow you to obtain this quantity from > the second derivative of the enthalpy (which is the appropriate > thermodynamical potential that depends on pressure as an independent > variable). It all depends on what you need: if you need the second > derivative of "A" with respect to "B", then just calculate it, > whatever the name of that second derivative is ... > > HTH - SB > > --- > Stefano Baroni - SISSA&DEMOCRITOS National Simulation Center - Trieste > http://stefano.baroni.me <http://stefano.baroni.me/> [+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 > -- Dr.Bahadir Altintas * Dept. of Chemistry SUNY Buffalo NY,USA * Abant Izzet Baysal University Dept. of Computer Education Bolu,Turkey -------------- next part -------------- An HTML attachment was scrubbed... URL: http://www.democritos.it/pipermail/pw_forum/attachments/20120227/8cea2549/attachment.htm
