[Wien] 2 ways to calculate bindning energy

[B. Yanchitsky]

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

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