Commonality between nearest neighbors

It was Ioffe (1951) who first pointed out that the basic electronic properties of a solid are determined primarily by the character of the bonds between nearest neighbors rather than by the long-range order. The chemical bond approach enabled Welker (1952) to predict many of the semiconducting properties of the III—V compounds. Mooser and Pearson (1956, 1960) expanded the chemical approach to semiconductivity into a systematic survey of different compounds and crystal classes. Although in the case of crystals this approach has been replaced by band structure calculations, several properties common to large classes of amorphous semiconductors become plausible if one understands their chemical bonding. 

The one-dimensional plasma must therefore be regarded as a somewhat fictitious system. Nevertheless it does have one very important feature in common with its three-dimensional counterpart, and that is the presence of long-range forces. It is these forces which make the statistical mechanics of pleismas and electrolyte solutions so extraordinarily difficult to treat. Where charged particles are involved it is not even approximately correct to consider only interactions between nearest neighbors—the interaction of every pair of particles must be taken into account. The one-dimensional plasma, where this can be done exactly, should thus serve as a useful testing-ground for approximations developed to treat the three-dimensioneil ceise. 

Figure 7.12 tests these concepts using data for symmetrical polymer mixtures for N —M and N = 256, in the framework of the bond fluctuation model with interactions between nearest-neighbor effective monomers." For chains not too long N < 64) there is indeed a common intersection point, and Tc can be estimated with high accuracy ksTc/e = 9.9261). 

Extended X-ray absorption fine structure (EXAFS) on the other hand, is due to the interference of electron waves between atoms, and provides local structure information that is limited to a few interatomic distances. Here, we talk about the distance and the number of nearest and next-nearest neighbors of atoms in the catalyst. The more uniform the environment is through the catalyst, the more meaningful is the EXAFS information. Related to this method is X-ray absorption near edge spectroscopy (XANES), which deals with the detailed shape of the absorption edge, and yields important information on the chemical state of the absorbing atom. Commonly, one uses nowadays the acronym XAFS to include both EXAFS and XANES. 

After a distance function is defined, the diversity of a compound collection can be measured in a number of ways. Minimum intermolecular dissimilarity (9) (where is the distance between the tth and yth compounds in the collection C), and average nearest neighbor distance, (10), are two common examples of distance-based diversity measures. Figure 1 illustrates examples of compound subsets using a nearest-neighbor design metric. 

The oxides of iron are of broad interest because of their importance in such diverse fields as corrosion, catalysis, geochemistry and magnetism. Despite their different structures and metal oxidation states, the oxides of iron — FeO, Fe304, and a- and y-Fe203 - have in common a close-packed plane of oxygen anions in the (111) orientation in which the nearest-neighbor distances are rather similar (within 5%). The various phases differ in the distribution of Fe within the cation planes that lay between the oxygen planes. FeO is rocksalt, whereas... 

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