By I. (editor) Prigogine
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Extra info for Advances in Chemical Physics, Volume 11
Nj(Rij) = 2 Yi1(RiJY,,(R1J w . * * Ynd(Rmj) (121) can be written in terms of Fourier transforms: x (~'g@(t)&b)(t). . $Z)(t)) (122) P p denotes the set of symbols u , 6, . , p which specify the positions of defects 1, 2, . , n respectively in their unit cells. The convolution theorem may be used to establish the Fourier transform of a summation over a cycle of functions. The cycle sum defined as . +dot . = (1/B) z\ Yii(RiJYi2(R12) * * - YnAj)Yji(RiJ @ +i +A ( 123) can be shown to be where B, is the number of unit cells in the crystal.
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.
74c)). A limiting case of antistructure disorder is provided by the orderdisorder alloys, where the degree of disorder increases rapidly as the temperature is raised to a critical temperature T,. Above T , the separate sublattices are no longer distinguishable. Special methods are available for this famous statistical problem ;20~s0*67 the formalism so far discussed is not meant for such crystals. Similarly, large departures from stoichiometry (see Section I), which are often dealt with by the order-disorder technique^,^^^^ do not lie within its scope.