Powder diffraction experiment

Bragg-Brentano Powder Diffractometer. A powder diffraction experiment differs in several ways from a single-crystal diffraction experiment. The sample, instead of being a single crystal, usually consists of many small single crystals that have many different orientations. It may consist of one or more crystalline phases (components). The size of the crystaUites is usually about 1—50 p.m in diameter. The sample is usually prepared to have a fiat surface. If possible, the experimenter tries to produce a sample that has a random distribution of crystaUite orientations. 

In the powder diffraction technique, a monochromatic (single-frequency) beam of x-rays is directed at a powdered sample spread on a support, and the diffraction intensity is measured as the detector is moved to different angles (Fig. 1). The pattern obtained is characteristic of the material in the sample, and it can be identified by comparison with a database of patterns. In effect, powder x-ray diffraction takes a fingerprint of the sample. It can also be used to identify the size and shape of the unit cell by measuring the spacing of the lines in the diffraction pattern. The central equation for analyzing the results of a powder diffraction experiment is the Bragg equation... 

The crystal lattices of a series of ternary alkali metal-silver acetylenediide [M Ag(C=C)] (M1 = Li 161, Na, K 162, Rb, Cs 163) have been analyzed by Ruschewitz and co-workers using X-ray powder diffraction.209 Neutron powder diffraction experiments have also been performed on 161-163 for obtaining precise bond lengths. It has been found that for 161 and 162, the [Ag(C C)] chains were packed parallel to each other, whereas for 163, they were aligned in layers that were rotated by 90° with respect to each other (see Figure 51). 

Although a great many intercalation compounds of LDHs have been prepared and characterized, there have been few studies of the kinetics and mechanism of the intercalation process. In their chapter, O Hare and colleagues describe how detailed information about these aspects may be obtained by means of time-resolved in situ X-ray powder diffraction experiments. 

Staykova, D.K. Kuhs, W.F. Salamatin, A.N. Hansen, T. (2003). Formation of Porous Gas Hydrates from Ice Powders Diffraction Experiments and Multistage Model. J. Phys. Chem. B, 107 (37), 10299-10311. 

FIGURE 2.4 (a) Cones produced by a powder diffraction experiment (b) experimental arrangement for a Debye-Scherrer photograph. 

X-ray diffraction (XRD) is a routine method for determining crystal lattice parameters and molecular structure. The application of XRD to modified electrodes has been limited, particularly for actual molecular structure determination. First, such experiments presuppose a single-crystal electrode substrate. Second, the small amount of sample present in a thin film on an electrode surface means that the scattered intensities will be restrictively low, at least for commonly available x-ray sources [67]. However, if one is fortunate enough to have access to a synchrotron, such experiments are quite feasible. For details, the reader is directed to an excellent review by Toney and Melroy [68]. On the other hand, powder diffraction experiments with Cu or Mo Ka anode sources are straightforward, and can yield lattice-constant data in situ. For example, Ikeshoji and Iwasaki measured lattice constants for Prussian blue films (discussed earlier) on gold electrode surfaces [69]. 

TABLE 3 Case studies of powder diffraction experiments under catalytic conditions. 

However, it is often very difficult to grow single crystals of suitable size for a successful diffraction experiment and the researcher has to resort to powder diffraction experiments on a polycrystalline sample. Powder patterns are fingerprints of the solid materials and are therefore used to identify polymorphs. In the pharmaceutical industry, and in associated laboratories, it is becoming common practice to accompany the routine quality control analyses on the production fine with the measurements of powder patterns. 

The applicability of this system in the development of a crystalline SO2 sensor was studied in greater detail. While binding of gaseous substrates by nonporous crystalline materials may lead to the destruction of the long crystalline order, this did not happen in the case of 26. The crystallinity of the sensor material is maintained during the uptake and release of SO2, as was shown by time-resolved powder diffraction experiments (Figure 8). 

Electron paramagnetic resonance experiments also support the existence of ferromagnetic iron particles. X-ray powder diffraction experiments, electron microscopy, and surface analysis measurements show the existence of both metals on the surface before and after reduction. We know the particle size again is quite large, although there is a wide digtribution in these samples, ranging from 30 A to about 150 A. 

Usually, low-temperature or high-pressure single-crystal or powder diffraction experiments provide a set of cell parameters as a function of T or... 

X-ray powder diffraction experiments were performed on a Phillips x-ray diffractometer with a Diano interface as described earlier (15). Mossbauer spectroscopy studies were all done at 77K with a homebuilt spectrometer consisting of an Elscint transducer, a Canberra amplifier and multichannel analyzer, and a Nal Harshaw... 

Figure 13 Paris-Edinburgh cell used for high-pressure neutron powder diffraction experiments. On the right neutron time-of-flight data of the high-pressure monoclinic form of cristobalite are shown...

In cases where it is difficult to obtain large crystals, chemists may logically conclude that powder diffraction experiments offer a suitable alternative. However, powder diffraction experiments " are usually restricted to large samples of smaller unit cells than those commonly involved in a typical organometallic structure. In addition, because the nature of the diffraction data is one-dimensional (rather than three-dimensional in a single-crystal experiment), peak overlap is a serious problem. This difficulty is largely alleviated by the use of the Rietveld method, " in which the overall profile of the diffraction pattern is essentially scanned stepwise to yield hundreds of individual intensity measnrements. Fnr-thermore, deuteration is almost always necessary in a powder... 

Both collimation methods shown in Figure 2.9 are commonly used in powder diffractometers that are employed for routine powder diffraction experiments. High resolution and low-angle scattering diffractometers require better and therefore, more complex eollimation, which to some extent overlaps with the monochromatization described below, but otherwise will not be considered in this book. ... 

A position sensitive detector (PSD) employs the principle of a gas proportional counter, with an added capability to detect the location of a photon absorption event. Hence, unlike the conventional gas proportional counter, the PSD is a line detector that can measure the intensity of the diffracted beam in multiple (usually thousands) points simultaneously. As a result, a powder diffraction experiment becomes much faster, while its quality generally remains nearly identical to that obtained using a standard gas proportional counter. ... 

Assuming that the diffracted intensity is distributed evenly around the base of each cone (see the postulations made above), there is usually no need to measure the intensity of the entire Debye ring. Hence, in a conventional powder diffraction experiment, the measurements are performed only along a narrow rectangle centered at the circumference of the equatorial plane of the Ewald s sphere, as shown in Figure 2.32 and indicated by the arc with an... 

The intensity, Ihu, scattered by a reciprocal lattice point hkl) corresponds to the integrated intensity of the matching Bragg peak. For simplicity, it is often called intensity . What is actually measured in a powder diffraction experiment is the intensity in different points of the powder pattern and it is commonly known as profile intensity. Profile intensity is usually labeled F/, where / is the sequential point number, normally beginning from the first measured data point (i = 1). 

Preferred orientation effects are addressed by introducing the preferred orientation factor in Eq. 2.65 and/or by proper care in the preparation of the powdered specimen. The former may be quite difficult and even impossible when preferred orientation effects are severe. Therefore, every attempt should be made to physically increase randomness of particle distributions in the sample to be examined during a powder diffraction experiment. The sample preparation will be discussed in Chapter 3, and in this seetion we will discuss the modelling of the preferred orientation by various functions approximating the radial distribution of the crystallite orientations. 

The expression for harmonic factors is complex and is defined azimuthally by means of a Lagrange function. Sample orientation in routine powder diffraction experiment is fixed and so is the corresponding harmonic factor k y), which simplifies Eq, 2.82 to ... 

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