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The Advances in Chemical Physics sequence presents the chemical physics and actual chemistry fields with a discussion board for serious, authoritative reviews of advances in each zone of the self-discipline. packed with state-of-the-art study mentioned in a cohesive demeanour now not came upon in different places within the literature, each one quantity of the Advances in Chemical Physics sequence serves because the ideal complement to any complex graduate category dedicated to the research of chemical physics.
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A similar expression can be written for the contribution of every other simple irreducible graph and its derivative graphs in higherorder semi-invariants. After carrying out the summations in Eq. (B), adding together the contributions from all graphs derived 24 A. R. ALLNATT from simple graphs with K distinguishable nodes of composition k, and summing the resultant expression over all possible compositions of the nodes, the total contribution of all full-line graphs to Eq. JB‘; C, = e=l cL8 (57) We have used the fact that for fixed k in the limit as N, -+ 00 with c, fixed.
Eqs. (70) and (71)) (W N,, = ZI NL + c Nit (au) Nau = 2 NL (W t (82) and the various relationships arising from crystal structure, electrical neutrality, and defect structure noted above, the numbers of sets Nl and N, can be eliminated in favour of the thermodynamic variables of No and Naand the resulting equation compared with the equation to obtain the relationship between the Gibbs chemical potentials and the defect chemical potentials. For example, for the systems described by Eqs. (74) it is found that for both (a) and (b) POM = P l M (a) 32 A.
Interest therefore has centred on the interpretation of non-equilibrium properties. Equation (106) has been used to calculate ck, generally counting only nearest neighbours as complexes. sa Perhaps the most detailed application of the theory was made by I,idiard,S1 who analysed the conductivity measurements of Etzel and Maurer for the system (NaC1 CdCl,). The “simple association theory” in which Eq. (106) is used with yo = 1 has been much more extensively used (see Refs. 5 and 53 for further references).