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

By I. (editor) Prigogine

The Advances in Chemical Physics sequence offers the chemical physics and actual chemistry fields with a discussion board for serious, authoritative reviews of advances in each region of the self-discipline. packed with state of the art learn mentioned in a cohesive demeanour now not came across in different places within the literature, every one quantity of the Advances in Chemical Physics sequence serves because the excellent complement to any complex graduate category dedicated to the examine of chemical physics.

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Respectively. The matrix wij(t) is defined by the equation For a crystal with a different kinds of defects, define a matrix of cu dimensions CI, ,9, . e. S2 multiplied by itself n times, gives a sum of products, each composed of n oii-functions. The terms U correspond to all possible compositions such that C n , = n, and 8=l for each composition the terms present correspond to every assignment of defects to distinguishable sites arranged in a cycle, like defects being treated as indistinguishable.

We require the probability that a set n of defects shall be in a configuration (n) with the restriction that none of the remaining (N - n) defects are on a particular set of sites b out of the total B sites of the crystal. This probability may be written as POINT-DEFECT INTERACTIONS I N SOLIDS 35 The summation is over all configurations of the (N - n) defects on the (B - b) sites, the remaining n defects being fixed in the configuration {n}. The summation may be written as from which we find that In solution theory the specialized distribution functions of this kind should appear in the theory of ion pairs in ionic solutions, and a form of the Bjerrum-Fuoss ionic association theory adapted to a discrete lattice is generally used for the treatment of the complexes in ionic crystals mentioned above.

The first term is a correction to the second arising from the excluded site property. The first term is conveniently added to the terms in the expansion of log Q,’. From Eqs. (39),(54), and (61) together with the analysis following Eq. (57) it is found that log Qc = B 2 cEB, La2 - log (n(c;Je)N”) w B E 1 where B, is defined by f 15. fW %J z + hij (66) The summand of Eq. (65) is of all multiply connected diagrams of f-functions on the vertices of the set k. Using the definitions of Eqs. (65)-(66)we have the set of all multiply connected diagrams among k nodes made up off (2I-bonds and h-bonds, the latter connecting only defects on the same sublattice.

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