Nearest-available-neighbour

The accuracy of the Kirkwood superposition approximation was questioned recently [15] in terms of the new reaction model called NAN (nearest available neighbour reaction) [16-20], Unlike previous reaction models, in the NAN scheme AB pairs recombine in a strict order of separation the closest pair in an initially random distribution is removed first, then the next one and so on. Thus for NAN, the recombination distance R, e.g., the separation of the closest pair of dissimilar particles at any stage of the recombination, replaces real time as the ordering variable time does not enter at all the NAN scheme. R is conveniently measured in units of the initial pair separation. At large R in J-dimensions, NAN scaling arguments [16] lead rapidly to the result that the pair population decreases asymptotically as cR d/2 (c... 

Brown (62) has recently shown that the presently available theory for the interpretation of EXELFS data is inadequate. In his study of the layered BN structure he found that whereas the distances to first nearest neighbours could be satisfactorily extracted from EXELFS data, second nearest-neighbour distances could not. The way ahead (62), here, is for the theory to be extended and tested against several known structures composed of light elements. 

In layer structures, the number and availability of bonds to the nearest neighbours is decided by the electrons available as stipulated by valence theory. Layer structures based on linked polyhedra are the most common ones in catalysis. Some of these are described below. 

It is noteworthy that in mercury each atom has six nearest neighbours in formal agreement with the 8-n rule, and this is also the case in zinc and cadmium owing to the fact that the hexagonal closest packing is strongly deformed in these elements. There can, however, be no question of the formation of an octet, since there are only two valence electrons available per atom. 

A subset may involve all basis functions on an atom or on a molecular fragment, all basis functions on atom or on a molecular fragment of a particular S5mmetry, all basis functions on an atom and its nearest neighbours (in this case some of the subsets may overlap), or may consist of all available basis functions. 

Figures 3.20a and b stem from work by Fraser et al.. (In fig. 20a the open and filled circles are taken from refs. and 1.) This was a MC simulation of 408 discs where a special geometrical device, the so-called Voronoi tesselatlon was Invoked to keep track of nearest neighbours. The available area and the reduced surface pressure n/hT are expressed in units of the hard sphere area, and respectively. From fig. 20a it can be read that this simulation is of just sufficient quality to allow us to observe a hint of an incipient fluid-ciystalline transition. Figure 20b. shows a distribution of neighbours. With increasing pressure this distribution becomes more narrow at the highest pressure the co-ordination is purely hexagonal.

Focusing our interest towards special sites available for adsorption, W g(Ar) for a nearest-neighbour vector Ar directly yields the fraction of (two-fold) bridge-sites between unlike atoms. Unfortunately, A(Ar) or W gCAr) do not directly yield the number of three-fold or four-fold hollow sites neighbouring, e.g., only atoms of type A. Nevertheless, we will see that the value of also gives an indication whether such sites are more or less common than in a random alloy surface. 

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