Probability factor nearest neighbor sites

Here (O) is the probability that a site is occupied by an oxygen atom =0o), (OO) is the probability that two neighboring sites are both occupied by oxygen, t is time, W es is the rate constant for desorption, and the factor 6 is the coordination number. For desorption in CO/Rh(100) including nearest-neighbor interactions we get the exact rate equation... 

Calculate the correlation factor for tracer self-diffusion by the vacancy mechanism in the two-dimensional close-packed lattice illustrated in Fig. 8.22. The tracer atom at site 7 has just exchanged with the vacancy, which is now at site 6. Following Shewmon [4], let p. be the probability that the tracer will make its next jump to its kth nearest-neighbor (i.e., a 7 — k jump). 6k is the angle between the initial 6 —> 7 jump and the 7 —> k jump. The average of the cosines of the angles between successive tracer jumps is then... 

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