By I. (editor) Prigogine

ISBN-10: 0470143576

ISBN-13: 9780470143575

ISBN-10: 0470699167

ISBN-13: 9780470699164

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. jam-packed with state-of-the-art learn mentioned in a cohesive demeanour now not came upon somewhere else within the literature, each one quantity of the *Advances in Chemical Physics* sequence serves because the ideal complement to any complicated graduate category dedicated to the learn of chemical physics.

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**Example text**

Finally, there may be further conditions involved in the statement of the type of disorder present and not already implicit in Eqs. (70)-(73) above. For example, for Frenkel disorder in a one-component system of neutral atoms one must specify that the number of interstitials is equal to the number of vacancies. (For Frenkel disorder in an ionic crystal however this yields nothing not already given by Eqs. (70373)). By taking the minimum in Eq. (69) subject to the restrictions specified and using Lagrange undetermined multipliers (see, for example, Ref.

A term of given composition in the summand is the sum over all configurations of the sum of the products of q-bonds which correspond to every arrangement of the n, vertices within the chain, like vertices being treated as indistinguishable. To carry out the chain summations we therefore require the quantity defined by the equation By considering the Fourier transform of this sum and again using the properties of IR” which we considered in detail above, it is straightforward to show* that For the simple two-defect system introduced in the preceding section it is found that f 8, I- ek a% - + wa8 (142) 1 - (wau wBB) f Waaw86 - WaBwBa In terms of the chain sum mi,, the sum S@)is found from Eqs.

Is the number of ways of choosing the sets m k-1 and nl, n2,. , npfrom the set (m n). M(am)is the number V + of times the prototype am occurs in the sum S. I n chain number k like defects may be interchanged in n, ! ways. Equation (135) can therefore be written as where The double prime on the summation over S(n) signifies that it is over every arrangement of vertices in each of the q-bond chains when only vertices corresponding to different defect species are distinguishable. The summation over n gives terms corresponding to every possible composition of each of the Y chains.

### Advances in Chemical Physics, Volume 11 by I. (editor) Prigogine

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