Heinz Haas wrote: >> Lyudmila Dobysheva wrote: >>> Tuesday 11 March 2008 21:02 B. Yanchitsky has written: >>>> Ev_super = E[N-1] - (N-1)*E[1]. (1) >>>> Ev_atom = Ei - E[1]. (2) >>> I cannot quite catch the problem: do you expect these values equal? > > You are absolutely right: > (1) gives you (approximatly) the formation energy of a vacancy, in metal > physics generally described as the energy required to move an atom from > the inner area to the surface. For this reason also the simplistic > argument of B.Y. is not correct. Even in the primitive model of isolated > bonding one would get: Ev_atom = (Ei - E[1]) / 2. > (2) gives you (again very approximately) the formation energy of > the crystal from free atoms. > Heinz Haas >
I agree, a real vacancy is not just a hole in crystal lattice, and effects of distortions are/may be important. I've calculated the difference E[1]-Ei, i.e. difference between energy for an atom in a crystal lattice and in a stretched box Atom name Z E[1]-E[i] (eV) Be(hcp) 4 -4.01952760 Al(fcc) 13 -9.1210168 Cu(fcc) 29 -32.5998664 Au(fcc) 79 -57.3670440 this is just wrong, interatomic potential is something like 0.01-0.1 eV, and been multiplied by number of nearest neighbors, something like 10, gives 0.1-1 eV (1000K-10000K), but not a million of kelvins. I don't think this may be related to DFT, there is some spurious term (electrostatic?) that pushes energy up on large volumes. Regards, -- Bogdan Yanchitsky Institute of Magnetism Vernadsky Blvd., 36-b 03142 Kiev UKRAINE Tel. (+380-44) 444 34 20 Fax. (+380-44) 444 10 20