Coupling of the Binding Energy

In the preceding section we have seen that the chemical potential could be expressed in terms of g R) provided we also know the dependence of g R) on either T or p. We now derive a third expression due to Kirkwood, which employs the idea of a coupling parameter The ultimate expression for the chemical potential would be an integral over both R and involving the function g R, ). 

Associated with f/( ( ) we also define an auxiliary configurational partition function by 

The expression (5.9.10) for the chemical potential can be rewritten using the above notation as 

The formal steps in (5.9.26) are very similar to those in section 5.8 and there is no need to go through them in detail. The only new feature in (5.9.26) is the appearance of the parameter employed throughout in the distribution functions. 

We now combine (5.9.26) with (5.9.25) to obtain the final expression for the chemical potential  

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Note, however, that within the assumption of pairwise additivity of the total potential energy, the quantity UN is unaffected by this coupling of the binding energy of the newly added particle. 

The same vibration leads to a periodical shift of the surface-state energy levels via the exchange coupling of the surface spin to the bulk magnetization. Bovensiepen and coworkers observed this oscillation of the binding energy, which with the aid of DFT calculations they translated to the interlayer spacing in picometer scale [20,23],... 

With Eq. (3.25), p. 42, we have already indicated that the distribution function of the binding energy for the distinguished solute in the actual, fiilly-coupled system (e) = 8 e — tkUa)) is related to the distribution function of Eq. (3.5),... 

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