KFC
Dec21-08, 03:30 PM
In textbook of statistical mechanics, there is an example considering an idealization of a crystal which has N lattice points and the same number of interstitial positions (places between the lattice points where atoms can reside). Let E be the energy necessary to remove an atom from a lattice site to an interstitial position and let n be the number of
atoms occupying interstitial sites in equilibrium. Now try to find the number of state
It is quite easy to think about this: choose n atoms from N atoms to fill n interstitial positions, number of possible configuration is given by combination
C_{N}^n = \frac{N!}{n!(N-n)!}
I think the number of state should be
\Omega = C_{N}^n = \frac{N!}{n!(N-n)!}
but the example just put
\Omega = \left(C_{N}^n\right)^2 = \left(\frac{N!}{n!(N-n)!}\right)^2
without saying why. Do you think it is a mistake?
atoms occupying interstitial sites in equilibrium. Now try to find the number of state
It is quite easy to think about this: choose n atoms from N atoms to fill n interstitial positions, number of possible configuration is given by combination
C_{N}^n = \frac{N!}{n!(N-n)!}
I think the number of state should be
\Omega = C_{N}^n = \frac{N!}{n!(N-n)!}
but the example just put
\Omega = \left(C_{N}^n\right)^2 = \left(\frac{N!}{n!(N-n)!}\right)^2
without saying why. Do you think it is a mistake?