XRD methods

Because x-rays are particularly penetrating, they are very usefiil in probing solids, but are not as well suited for the analysis of surfaces. X-ray diffraction (XRD) methods are nevertheless used routinely in the characterization of powders and of supported catalysts to extract infomration about the degree of crystallinity and the nature and crystallographic phases of oxides, nitrides and carbides [, ]. Particle size and dispersion data are often acquired with XRD as well. 

Both ultrasonic and radiographic techniques have shown appHcations which ate useful in determining residual stresses (27,28,33,34). Ultrasonic techniques use the acoustoelastic effect where the ultrasonic wave velocity changes with stress. The x-ray diffraction (xrd) method uses Bragg s law of diffraction of crystallographic planes to experimentally determine the strain in a material. The result is used to calculate the stress. As of this writing, whereas xrd equipment has been developed to where the technique may be conveniently appHed in the field, convenient ultrasonic stress measurement equipment has not. This latter technique has shown an abiHty to differentiate between stress reHeved and nonstress reHeved welds in laboratory experiments. 

In these structures, the cupf assumes its typical chelating coordination pattern and is nearly symmetrically bound to the [Me2Sn(IV)] center. In complex (4) a pentagonal bypiramidal (PBP) geometry containing C2SnOs moiety was found by XRD method. The Bu2Sn(IV)-cup complex proved to be... 

It is possible to make conclusion about the absence of noticeable structural changes based on comparison of structural parameters of graphite in the beginning and at the end of cycling, using the XRD method. 

X-ray diffraction uses X-rays of known wavelengths to determine the lattice spacing in crystalline structures and therefore directly identify chemical compounds. This is in contrast to the other X-ray methods discussed in this chapter (XRF, electron microprobe analysis, PIXE) which determine concentrations of constituent elements in artifacts. Powder XRD, the simplest of the range of XRD methods, is the most widely applied method for structural identification of inorganic materials, and, in some cases, can also provide information about mechanical and thermal treatments during artifact manufacture. Cullity (1978) provides a detailed account of the method. 

At this point it is important to realize that from single crystals the full crystallographic information is usually obtained by XRD methods (space group, lattice parameters and atomic coordinates) but that for thin films this is hardly the case, because of the physical limitation imposed by the substrate, in particular when the microcrystals are oriented, in which case only a reduced number of reflections are available. Hence only partial information is obtained with conventional diffraction methods. Removing the microcrystals, e.g., by scratching, in order to perform XRD measurements from the powder is not always possible and handling such small and fragile microcrystals with the usual tools is almost impossible. 

Data obtained by the XRD method were equally confusing. Many equations for the expression of Xp have been reported in the literature. The most recent results apparently still indicate thatXo is a step function of Xps (Stimpfl et al., 1999) For Xps between 0.19 and 0.75, Xq depends on temperature as follows ... 

Another example is a mineral named nasonite, which was not suspicious because of its luminescent properties, but gave unexpected results after routine LIBS checking (Fig. 9.2a), where the characteristic fines of Pb were absent, while the emission fines of Ca and Na were very strong. The Raman spectrum (Fig. 9.2b) was also different from those of nasonite. Subsequent analyses by EDX and XRD methods revealed that it is a mixture of two minerals prehnite and pectolite. 

It may be argued whethere these examples, which have usually employed X-ray diffraction analysis of previously UV irradiated crystals, fall within the domain of the X-ray photodiffraction methods or solid state photochemistry, and whether the term X-ray photodiffraction should be reserved only for time-dependent studies. Although that in the original publications many of these examples have not been labeled as such, because they involve application of XRD methods to study photochemical reactions, we believe that they should he considered as part of the X-ray photodiffraction method in its broadest definition. 

To date, mainly two groups have been responsible for the development of the combined EXAFS/XRD methods, namely the group of Clausen, Topspe, Niemann, and co-workers, who developed the combined EXAFS/ XRD and QEXAFS/XRD techniques, and the group of Thomas, Greaves, and co-workers, who developed the DEXAFS/XRD method. In the following, some of the developments are discussed briefly. 

Yen et al. (1961) examined the structure of isolated petroleum asphaltenes by using XRD. From the diffraction pattern they were able to calculate the aromaticity, defined as the number of aromatic carbon atoms over the total carbon atoms. The aromaticity ranged from 0.26 to 0.53 for petroleum asphaltenes. In addition, the characteristic dimensions of an asphaltene were obtained by the XRD method. The asphaltene model developed by Yen et al. (1961) from these observations is presented in Fig. 6 with characteristic molecular dimensions. The model consists of... 

In the following sections we shall focus on the structure and properties of the two-dimensional phases formed by the bent-core liquid crystals. In Sect. 2 we describe the structure studies by the X-ray diffraction (XRD) method, optical studies, and the response of different structures to the external electric field. In Sect. 3 we give theoretical models of the director and layer structure in 2D modulated phases and discuss how to reconstruct electron density maps from XRD data. 

Silicon is a constituent of the main phase as well as of the most common impurities SiC, free Si, Si2N20, Si02, FeSix. Therefore, besides the determination of the total amount of Si, additional methods are needed to determine the amounts of free Si and the other compounds. Quantitative X-ray diffraction (XRD) is often used with modern XRD methods less than 0.1 wt.% free Si [232] and 0.2 wt.% Si2N20 [228] are detectable. The accuracy for SiC is somewhat lower due to the overlapping of the main peak of SiC with / -Si3N4. Free Si can be determined also with volumetric methods [225]. 

X-ray diffraction (XRD) methods are arguably the most significant for both qualitative and quantitative analyses of solid materials in forensic soil science. Extremely minute sample quantities or tiny sample areas as well as large quantities can be successfully analyzed using XRD. The critical... 

XRD is easily used but does not directly provide the dispersion information while TEM is an expensive and difficult method to use. With TEM, however, direct information, although qualitative, about the dispersion of clay (and other nanoadditives) in the matrix polymer can be obtained. The XRD method is usually used together with the TEM technique to characterize the morphology of the resulting PCNs. Attempts have been made to quantify the information that has been obtained through TEM technique,78 but it seems to be not so successful in current practice, particularly for describing the dispersion of clays. 

In Equation 4.1, the factor fiF(0) is included, which is the peak profile function, that describes particle size broadening and other sources of peak broadening. The XRD method can be used as well for the measurement of the crystallite size of powders by applying the Scherrer-Williamson-Hall methodology [4,35], In this methodology, the FWHM of a diffraction peak, p, is affected by two types of defects, that is, the dislocations, which are related to the stress of the sample, and the grain size. It is possible to write [35]... 

Initiation of Zeolite Crystallization. An induction period (tj) is always observed at zeolite crystallization, and is accepted to be the period necessary for the formation of zeolite nuclei (20). The inverse value of induction period, 1/t, is called the rate of nucleation. The crystallization curves were plotted as the degree of crystallization (estimated by the XRD method) versus synthesis time. The values of tj were obtained by extrapolating the time when crystal growth started. 

Even when XRD data are obtained with samples in reactive atmospheres, the data must be complemented by results of other experimental techniques to compensate for the inherent weaknesses of the XRD methods. One approach (Bruckner, 2003 Weckhuysen, 2003) is to combine XRD with, for example, EXAFS spectroscopy (Clausen et al., 1993 ... 

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