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Truecrimson
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Homework Statement
Please look at P9 in http://panda.unm.edu/pandaweb/graduate/prelims/SM_S09.pdf
"Now consider a metal surface in which the M adhesion sites are comprised of equal populations of sites of two different types..."
Homework Equations
The entropy and the chemical potential of a metal surface with a single type of adhesion site are shown in P7 and P8 respectively.
The Attempt at a Solution
Use the expression [tex]\mu=-\Delta-kT\ln \left(\frac{M-N}{N}\right)[/tex] separately for each type of adhesion sites A and B, so that [tex]\mu_A=-\Delta_A-kT\ln \left(\frac{N-A}{A}\right)[/tex] and [tex]\mu_B=-\Delta_B-kT\ln \left(\frac{N-(N-A)}{N-A}\right)=-\Delta_B+kT\ln \left(\frac{N-A}{A}\right)[/tex] where A is the occupation of sites A.
Then if I assume that the two types of sites are in chemical equilibrium i.e. [tex]\mu_A=\mu_B[/tex], then I can solve for A in terms of the temperature and the difference in binding energy easily. However, I'm not sure if I can assume that, but I can't think of any other way to do this. (I thought of deriving the entropy of a metal surface with two types of sites, and work out the chemical potential from that. But there were some unclear steps. If my proposed solution doesn't work then maybe I'll post that later.) Any suggestion would be appreciated.