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(adsbygoogle = window.adsbygoogle || []).push({});

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

[tex]C_{N}^n = \frac{N!}{n!(N-n)!}[/tex]

I think the number of state should be

[tex]\Omega = C_{N}^n = \frac{N!}{n!(N-n)!}[/tex]

but the example just put

[tex]\Omega = \left(C_{N}^n\right)^2 = \left(\frac{N!}{n!(N-n)!}\right)^2[/tex]

without saying why. Do you think it is a mistake?

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# Don't understand state number

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