By I. (editor) Prigogine
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Extra resources for Advances in Chemical Physics, Vol.11 (Interscience, 1967)
Thus every node is multiply connected. ) It should be noted that f$) is zero when i and j coincide (cf. Eq. (44)). We now consider the contribution of all diagrams involving 12-bonds to Eq. (49). From Eq. (50) it is seen that corresponding to every diagram consisting of n F2)-bondsdistributed among k nodes and occurring in the nth semi-invariant, whether the diagram is unlinked, linked reducible, or irreducible, there is additionally in the same semi-invariant the set of all possible diagrams which can be formed from it by adding 12-bonds among the nodes present, with the provisos that only one h-bond can directly link any pair of nodes already directly linked by one or more P2)bonds and that the h-bonds are only between defects on the same sublattice.
R. ALLNATT which are of kinds s and Y respectively. n-th nearest neighbours. +,(sr) is the number of lattice sites of the kind occupied by a defect of type r which are n-th nearest neighbours to a site of the kind occupied by defects of type s. The subscripts 'u and i denote vacancies and interstitials respectively. Only nearestneighbour interactions will be retained unless otherwise stated. A. Dilute Single-Defect Systems The systems we have in mind here are pure monatomic solids such as metals and inert gas solids which contain only one kind of defect in a single electronic state.
Consider first the evaluation of terms not involving h functions. The diagrams may be classified according to their topology into 3 22 A. R. l~ts~~), multiply connected (the definition is taken to include the graph of a single line between two nodes). Examples of the three types of graph arising in M 3 are shown in Fig. 2. It is readily shown c t (b) (0) (d) (C) Fig. 2. Some of the diagrams occurring in Ma. Articulation points are indicated by arrows. (a) and (b) are irreducible diagrams; (c) and (d) are linked reducible and unlinked respectively.