Quantitative diffraction

The advantage of being able to record diffraction intensities over a range of incident beam directions makes CBED readily accessible for comparison with simulations. Thus, CBED is a quantitative diffraction technique. In past 15 years, CBED has evolved from a tool primarily for crystal symmetry determination to the most accurate technique for strain and structure factor measurement [16]. For defects, large angle CBED technique can characterize individual dislocations, stacking faults and interfaces. For applications to defect structures and structure without three-dimensional periodicity, parallel-beam illumination with a very small beam convergence is required. 

The general expression underlying quantitative diffraction analysis was presented by Alexander and Klug 3... 

Alexander LE, Klug HP. 1948. Basic aspects of X-ray absorption in quantitative diffraction analysis of powder mixtures. Anal. Chem. 20 886-894. 

Unfortunately, now that such methods have become available, such as the Time Of Flight Diffraction (TOFD) technique, this revolution does not happen. What we see instead is a much slower process towards quantitative NDT, in combination with adapted acceptance criteria for weld defects. 

X-Ray Methods. In x-ray fluorescence the sample containing mercury is exposed to a high iatensity x-ray beam which causes the mercury and other elements ia the sample to emit characteristic x-rays. The iatensity of the emitted beam is directly proportional to the elemental concentration ia the sample (22). Mercury content below 1 ppm can be detected by this method. X-ray diffraction analysis is ordinarily used for the quaUtative but not the quantitative determination of mercury. 

X-rays provide an important suite of methods for nondestmctive quantitative spectrochemical analysis for elements of atomic number Z > 12. Spectroscopy iavolving x-ray absorption and emission (269—273) is discussed hereia. X-ray diffraction and electron spectroscopies such as Auger and electron spectroscopy for chemical analysis (esca) or x-ray photoelectron spectroscopy are discussed elsewhere (see X-raytechnology). 

Quantitative Phase Analysis. Once the identity of the components in a sample are known, it is possible to determine the quantitative composition of the sample. There are several different methods for doing a quantitative analysis, but the most rehable method is to use mixtures of known composition as standards. The computer can determine quantitatively the relative amounts of each component in the unknown sample. For accurate calculations of relative amounts in the unknown sample, it is necessary that the sample and standards have uniform distributions of crystaUites. Often the sample and standards are rotated during data collection to provide a more even distribution of crystaUites which diffract. 

Trialkyl- and triarylarsine sulfides have been prepared by several different methods. The reaction of sulfur with a tertiary arsine, with or without a solvent, gives the sulfides in almost quantitative yields. Another method involves the reaction of hydrogen sulfide with a tertiary arsine oxide, hydroxyhahde, or dihaloarsorane. X-ray diffraction studies of triphenylarsine sulfide [3937-40-4], C gH AsS, show the arsenic to be tetrahedral the arsenic—sulfur bond is a tme double bond (137). Triphenylarsine sulfide and trimethylarsine sulfide [38859-90-4], C H AsS, form a number of coordination compounds with salts of transition elements (138,139). Both trialkyl- and triarylarsine selenides have been reported. The trialkyl compounds have been prepared by refluxing trialkylarsines with selenium powder (140). The preparation of triphenylarsine selenide [65374-39-2], C gH AsSe, from dichlorotriphenylarsorane and hydrogen selenide has been reported (141), but other workers could not dupHcate this work (140). 

The physical data index summarizes the quantitative data given for specific compounds in the text, tables and figures in Volumes 1-7. It does not give any actual data but includes references both to the appropriate text page and to the original literature. The structural and spectroscopic methods covered include UV, IR, Raman, microwave, MS, PES, NMR, ORD, CD, X-ray, neutron and electron diffraction, together with such quantities as dipole moment, pX a, rate constant and activation energy, and equilibrium constant. 

XRD offers unparalleled accuracy in the measurement of atomic spacings and is the technique of choice for determining strain states in thin films. XRD is noncontact and nondestructive, which makes it ideal for in situ studies. The intensities measured with XRD can provide quantitative, accurate information on the atomic arrangements at interfaces (e.g., in multilayers). Materials composed of any element can be successfully studied with XRD, but XRD is most sensitive to high-Z elements, since the diffracted intensity from these is much lar r than from low-Z elements. As a consequence, the sensitivity of XRD depends on the material of interest. With lab-based equipment, surface sensitivities down to a thickness of -50 A are achievable, but synchrotron radiation (because of its higher intensity)... 

Phase transitions in overlayers or surfaces. The structure of surface layers may undergo a transition with temperature or coverage. Observation of changes in the diffraction pattern gives a qualitative analysis of a phase transition. Measurement of the intensity and the shape of the profile gives a quantitative analysis of phase boundaries and the influence of finite sizes on the transition. ... 

Measurements of surface disorder require a high resolving power (the ability to distinguish two close-lying points in the diffraction pattern). Quantitative measurements of surface disorder are limited in the following manner, the worse the resolving power, the smaller the maximum scale of surface disorder that can be detected. For example, if the maximum resolvable distance of the diffractometer is 100 A, then a surface that has steps spaced more than 100 A apart will look perfect to the instrument. The theoretical analysis of disorder is much simpler than that for atomic positions. 

Solid state NMR is a relatively recent spectroscopic technique that can be used to uniquely identify and quantitate crystalline phases in bulk materials and at surfaces and interfaces. While NMR resembles X-ray diffraction in this capacity, it has the additional advantage of being element-selective and inherently quantitative. Since the signal observed is a direct reflection of the local environment of the element under smdy, NMR can also provide structural insights on a molecularlevel. Thus, information about coordination numbers, local symmetry, and internuclear bond distances is readily available. This feature is particularly usefrd in the structural analysis of highly disordered, amorphous, and compositionally complex systems, where diffraction techniques and other spectroscopies (IR, Raman, EXAFS) often fail. 

As with other diffraction techniques (X-ray and electron), neutron diffraction is a nondestructive technique that can be used to determine the positions of atoms in crystalline materials. Other uses are phase identification and quantitation, residual stress measurements, and average particle-size estimations for crystalline materials. Since neutrons possess a magnetic moment, neutron diffraction is sensitive to the ordering of magnetically active atoms. It differs from many site-specific analyses, such as nuclear magnetic resonance, vibrational, and X-ray absorption spectroscopies, in that neutron diffraction provides detailed structural information averaged over thousands of A. It will be seen that the major differences between neutron diffraction and other diffiaction techniques, namely the extraordinarily... 

Good semi-quantitative agreements are found in diffraction patterns and proposed models obtained by molecular-dynamics[14], because the results of the ex-periments[31-34] are consistent with the atomic models proposed by us[14]. However, in the present state of high-resolution electron microscopy, taking into account, moreover, the number of sheets and the complicated geometry of the helix, it seems unlikely to directly visualize the pentagon-hexagon pairs. 

H2 could be quantitatively removed at room temperature either by partial evacuation or by sparging the solution with argon. Definitive confirmation that the complexes did indeed contain 7J--H2 came from X-ray and neutron diffraction studies on the bisftri t-propylphosphine) analogue at —100°, which revealed the side-on coordination of H2 as shown in Fig. 3.2. During the past decade many other such compounds have been prepared and studied in great detail, and the field has been well reviewed. ... 

The quantitative assessment of the degree of crystallite orientation by x-ray examination is not free of ambiguity. From a comparative analysis [23] in which results obtained from the consideration of (105) and from three different variations of equatorial reflection were compared, the conclusion was that the first procedure can lead to underrated results, i.e., to the underestimation of the orientation. However, it can be assumed that this does not result from an incorrect procedure, but from ignoring the fact that the adjacent (105) reflex can overlap. The absence of the plate effect of the orientation is characteristic of the orientation of crystallites in PET fibers. The evidence of this absence is the nearly identical azimuthal intensity distributions of the diffracted radiation in the reflexes originating from different families of lattice planes. The lack of the plate effect of orientation in the case of PET fiber stretching has to do with the rod mechanism of the crystallite orientation. 

Analyses performed may include conventional wet chemistry, coupled with atomic absorption spectroscopy or other metal-scan techniques to provide a quantitative elemental assay, plus X-ray diffraction to determine the major crystalline constituents. 

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