XRD

In X-ray diffraction (XRD), X-rays are diffracted by electrons surrounding the nuclei in atoms in a crystalline or polycrystalline solid. 

The wavelength of X-rays ( 10 °m, i.e. 100pm) is of the same order of magnitude as the intemuclear distances in molecules or non-molecular solids. As a consequence of this, diffraction is observed when X-rays interact with the electrons in an array of atoms in the crystalline solid. 

The angle 6 in eq. 4.23 is half of the diffraction angle (Fig. 4.31), and diffraction data are often referred to in terms of an angle 20. Scattering data are collected over a wide range of 0 (or 20) values and for a range of crystal orientations. Each setting results in a different diffraction pattern as discussed below. 

X-ray diffraction uses the elastic scattering of X-rays from structures that have long-range order. Diffracted waves from different atoms in the structure can interfere with each other 

Two types of diffraction measurements are typically made on cosmochemical samples. Powder diffraction, where a sample powder is mounted on the end of a fiber and placed in the X-ray beam, is most commonly used. The term powder in this usage means that the crystal lattice domains are randomly oriented. Powder diffraction is used to identify unknown materials and to determine their basic crystal structure. Single-crystal X-ray diffraction is used to solve the complete structure of crystalline materials. For more details, see Cullity (1978). 

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For bulk structural detemiination (see chapter B 1.9). the main teclmique used has been x-ray diffraction (XRD). Several other teclmiques are also available for more specialized applications, including electron diffraction (ED) for thin film structures and gas-phase molecules neutron diffraction (ND) and nuclear magnetic resonance (NMR) for magnetic studies (see chapter B1.12 and chapter B1.13) x-ray absorption fine structure (XAFS) for local structures in small or unstable samples and other spectroscopies to examine local structures in molecules. Electron microscopy also plays an important role, primarily tlirough unaging (see chapter B1.17). 

With XRD applied to bulk materials, a detailed structural analysis of atomic positions is rather straightforward and routine for structures that can be quite complex (see chapter B 1.9) direct methods in many cases give good results in a single step, while the resulting atomic positions may be refined by iterative fitting procedures based on simulation of the diffraction process. 

From the above descriptions, it becomes apparent that one can include a wide variety of teclmiques under the label diffraction methods . Table Bl.21.1 lists many techniques used for surface stmctural detemiination, and specifies which can be considered diffraction methods due to their use of wave interference (table Bl.21.1 also explains many teclmique acronyms commonly used in surface science). The diffraction methods range from the classic case of XRD and the analogous case of FEED to much more subtle cases like XAFS (listed as both SEXAFS (surface extended XAFS) and NEXAFS (near-edge XAFS) in the table). 

One fiirther method for obtaining surface sensitivity in diffraction relies on the presence of two-dimensional superlattices on the surface. As we shall see fiirtlrer below, these correspond to periodicities that are different from those present in the bulk material. As a result, additional diffracted beams occur (often called fractional-order beams), which are uniquely created by and therefore sensitive to this kind of surface structure. XRD, in particular, makes frequent use of this property [4]. Transmission electron diffraction (TED) also has used this property, in conjunction with ultrathin samples to minimize bulk contributions [9]. 

In tenns of individual techniques, table B1.2T1 lists tlie breakdown totalled over time, counting from the inception of surface stmctural detennination in the early 1970s. It is seen that LEED has contributed altogether about 67% of all stmctural detenninations included in the database. The annual share of LEED was 100% until 1978, and has generally remained over 50% since then. In 1979 other methods started to produce stmctural detenninations, especially PD, ion scattering (IS) and SEXAFS. XRD and then XSW started to contribute results in the period 1981-3. 

As the table shows, a host of other teclmiques have contributed a dozen or fewer results each. It is seen that diffraction teclmiques have been very prominent in the field the major diffraction methods have been LEED, PD, SEXAFS, XSW, XRD, while others have contributed less, such as NEXAFS, RHEED, low-energy position diffraction (LEPD), high-resolution electron energy loss spectroscopy (HREELS), medium-energy electron diffraction (MEED), Auger electron diffraction (AED), SEELFS, TED and atom diffraction (AD). 

The diffraction pattern observed in LEED is one of the most connnonly used fingerprints of a surface structure. Witii XRD or other non-electron diffraction methods, there is no convenient detector tliat images in real time the corresponding diffraction pattern. Point-source methods, like PD, do not produce a convenient spot pattern, but a diffrise diffraction pattern that does not simply reflect the long-range ordermg. 

These two equations are a special case of the corresponding tliree-dimensional definition, connnon in XRD, with the surface nonnal n replacing the third lattice vector c. 

To obtain spacings between atomic layers and bond lengdis or angles between atoms, it is necessary to measure and analyse the intensity of diffraction spots. This is analogous to measuring the intensity of XRD reflections. 

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. 

Uosaki K, Shen Y and Kondo T 1995 Preparation of a highiy ordered Au(111) phase on a poiycrystaiiine goid substrate by vacuum deposition and its characterization by XRD, GiSXRD, STM/AFM and eiectrochemicai measurements J.Phys. Chem. 99 14 117-14 122... 

The first analytical tool to assess tire quality of a zeolite is powder x-ray diffraction. A collection of simulated powder XRD patterns of zeolites and some disordered intergrowths togetlier witli crystallographic data is available from tlie IZA [4o]. Phase purity and x-ray crystallinity, which is arbitrarily defined as tlie ratio of tlie intensity of... 

Treacy M M J, Fliggins J B and von Ballmoos R 1996 Collection of Simulated XRD Powder Patterns for Zeolites 3rd revised edn (London Elsevier)... 

Free Silica. Free siUca down to 1% can be deterrnined with x-ray diffraction techniques (xrd). 

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. 

Analysis. Excellent reviews of phosphate analysis are available (28). SoHds characterization methods such as x-ray powder diffraction (xrd) and thermal gravimetric analysis (tga) are used for the identification of individual crystalline phosphates, either alone or in mixtures. These techniques, along with elemental analysis and phosphate species deterrnination, are used to identify unknown phosphates and their mixtures. Particle size analysis, surface area, microscopy, and other standard soHds characterizations are useful in relating soHds properties to performance. SoHd-state nmr is used with increasing frequency. 

Instrumental Methods for Bulk Samples. With bulk fiber samples, or samples of materials containing significant amounts of asbestos fibers, a number of other instmmental analytical methods can be used for the identification of asbestos fibers. In principle, any instmmental method that enables the elemental characterization of minerals can be used to identify a particular type of asbestos fiber. Among such methods, x-ray fluorescence (xrf) and x-ray photo-electron spectroscopy (xps) offer convenient identification methods, usually from the ratio of the various metal cations to the siUcon content. The x-ray diffraction technique (xrd) also offers a powerfiil means of identifying the various types of asbestos fibers, as well as the nature of other minerals associated with the fibers (9). 

Characterization. Ceramic bodies are characterized by density, mass, and physical dimensions. Other common techniques employed in characterizing include x-ray diffraction (XRD) and electron or petrographic microscopy to determine crystal species, stmcture, and size (100). Microscopy (qv) can be used to determine chemical constitution, crystal morphology, and pore size and morphology as well. Mercury porosknetry and gas adsorption are used to characterize pore size, pore size distribution, and surface area (100). A variety of techniques can be employed to characterize bulk chemical composition and the physical characteristics of a powder (100,101). 

Sample preparation methods vary widely. The very first procedure for characterizing any material simply is to look at it using a low-power stereomicroscope often, a material can be characterized or a problem solved at this stage. If examination at this level does not produce an answer, it usually si ests what needs to be done next go to higher magnification mount for FTIR, XRD, or EDS section isolate contaminants and so forth. 

This chapter contains articles on six techniques that provide structural information on surfaces, interfeces, and thin films. They use X rays (X-ray diffraction, XRD, and Extended X-ray Absorption Fine-Structure, EXAFS), electrons (Low-Energy Electron Diffraction, LEED, and Reflection High-Energy Electron Diffraction, RHEED), or X rays in and electrons out (Surfece Extended X-ray Absorption Fine Structure, SEXAFS, and X-ray Photoelectron Diffraction, XPD). In their usual form, XRD and EXAFS are bulk methods, since X rays probe many microns deep, whereas the other techniques are surfece sensitive. There are, however, ways to make XRD and EXAFS much more surfece sensitive. For EXAFS this converts the technique into SEXAFS, which can have submonolayer sensitivity. 

Besides phase identification XRD is also widely used for strain and particle size determination in thin films. Both produce peak broadenings, but they are distinguishable. Compared to TEM, XRD has poor area resolution capability, although by using synchrotron radiation beam diameters of a few pm can be obtained. Defect topography in epitaxial films can be determined at this resolution. 

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