Short-range order and clustering

The degree of short-range order or clustering may be defined in terms of a suitable parameter, just as long-range order is, and the value of this parameter may be related to the diffraction effects produced. The general nature of these effects is illustrated in Fig. 13-9, where the intensity of the diffuse scattering is 

These effects, however, are all very weak and are masked by the other forms of diffuse scattering which are always present. As a result, the details shown in Fig. 13-9 are never observed in an ordinary powder pattern made with filtered radiation. To disclose these details and so learn something about the structure of the solid solution, it is necessary to use strictly monochromatic radiation and, preferably, single-crystal specimens, and to make allowances for the other forms of diffuse scattering, chiefly temperature-diffuse and Compton modified, that are always present. 

13-1 A Debye-Scherrer pattern is made with Cu Ka radiation of AuCuj quenched from a temperature 7. The ratio of the integrated intensity of the 420 line to that of the 421 

13-3 (a) What is the Bravais lattice of AuCu(I), the ordered tetragonal modification  

A given substance always produces a characteristic diffraction pattern, whether that substance is present in the pure state or as one constituent of a mixture of substances. This fact is the basis for the diffraction method of chemical analysis. Qualitative analysis for a particular substance is accomplished by identification of the pattern of that substance. Quantitative analysis is also possible, because the intensities of the diffraction lines due to one phase of a mixture depend on the proportion of that phase in the specimen. 

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Fig. 13-9 Calculated intensity of diffuse scattering in powder patterns of solid solutions (here, the face-centered cubic alloy Ni4Au) which exhibit complete randomness, short-range order, and clustering. The short-range order curve is calculated on the basis of one additional unlike neighbor over the random configuration, and the clustering curve on the basis of one less unlike neighbor. Warren and Averbach [13.7].

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