Powder diffraction techniques

A typical powder diffraction apparatus is shown in Fig. 14. The desirable requirements of high beam intensity and high resolution are rather incompatible and conventional instruments often have fairly poor resolution. This is advantageous in experiments where peaks are well separated as count rates can be high, and was the situation for example, in the measurements on Mn2+ and Ni2+ rock-salt compounds (56, 61) and Cr2+, Fe + and Mn + oxide perovskites (62), where only a few low-angle peaks were measured. High resolution is essential in profile analysis refinement, however, or when many intensities must be measured to 

Because the observed covalent spin reductions are of the order of only 5—15%, with an intensity reduction of 10—30%, it is clear that data of high quality are required if the reduction is to be measured with any accuracy, particularly if the spin is relatively low as for Cr +(S=3/2) and Ni2+(S = 1) so that the magnetic intensities are low in the first place. For this reason it is important to eliminate as many other potential uncertainties as possible. Measurement is preferably carried out at 4.2K or lower to achieve magnetic saturation and a simple magnetic structure is desirable to avoid uncertainties in 

The principal uncertainty with these, and all other determinations on anti-ferromagnets lies in the estimation of the zero-point spin deviation. Even at zero 

18) The scattering length of the calibrant must of course be accurately known, as must those of the sample if an internal calibration is being made. This was well discussed by Hutchings and Guggenheim 82) in estimating the errors associated with the covalency parameter for Ni2+—F determined in KNiFs. 

Such a refinement program was very useful in these cases but is in general of limited application, for it is only with very simple structures (both nuclear and magnetic) that a sufficient number of nuclear intensities can be accurately resolved at 4.2K to provide a basis for refinement and the determination of the scale factor. A more general refinement procedure has been recently introduced (69) which fits the measured profile of the powder diffraction pattern rather than individual intensities or structure factors. With data of high resolution obtained over a wide 

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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... 

FIGURE 1 In the powder diffraction technique, a sample is spread on a flat plate and exposed to a beam of monochromatic (single-frequency) x-rays. The diffraction pattern (inset) is recorded by moving the detector to different angles. 

In addition to the decreased polarizability of the heavier metals, their larger radii require higher metal coordination numbers to achieve steric saturation. As a result, extensive aggregation, frequently coinciding with rather limited solubility in non-donor solvents, and occasionally even in donor solvents, complicates the characterization of these species in solution and the solid state. In fact, several structural characterizations of organoalkali species have relied on recent advances in powder diffraction techniques using synchrotron radiation.1 ... 

The physical properties of parent lithium cyclopentadienyl are those of a typical sait22-24 [MeLi]4 (1), it is insoluble in hydrocarbons, has a high melting point and a low volatility. Developments in powder diffraction techniques just recently enabled the structure determination of [CpLijoo (38). 

X-ray diffraction has been a part of the physical chemistry laboratory curriculum for a long time, but mostly using the relatively simple powder diffraction technique. However a new experiment introduces the more complex method of single crystal X-ray diffraction (80). Another new experiment uses the technique to investigate the structure of alloys (81). 

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. 4). The pattern obtained is characteristic of the material in the sample, and it can... 

The simplicity and advantages of the routine application of powder diffraction techniques for the chemical analysis and identification of polycrystalline materials were pointed out by Hull [9], who stated "that every crystalline substance gives a pattern that the same substance always gives the same pattern," and by the pioneering work of Hanawalt et al. [10]. 

The samples used were a standard Na-A zeolite and five nitrogeneous types of zeolite A, or N-A.(18) The N-A zeolites are siliceous analogues of zeolite A, synthesized with tetramethyl-ammonium cation. The Si Al ratio varied from 0.94 (NaA) to 3.54 for the most siliceous N-A sample.t The ratios were determined by wet chemical analysis, and the structure type and absence of impurity phases were confirmed by X-ray powder diffraction techniques. Adsorption measurements (oxygen, -183°C) showed a zeolite A content of greater than 90%. 

Perhaps the first application of this technique directly to polymorphic systems was by Ripmeester (1980), and Threlfall (1995) has more recently reviewed the subject in addition to references cited above. For the study of polymorphic systems SSNMR has a number of advantages. The signal is not influenced by particle size which may eliminate the complications of possibie polymorphic transformations due to the grinding required in, say IR and X-ray powder diffraction techniques. The intensity of the signal is directly proportional to the number of nuclei producing it, so that... 

X-ray Bragg-Brentano powder diffraction technique (XRD) was applied to investigate the atomic structure of PbS nanoparticles. The diffraction pattern was measured with a Philips X Pert diffractometer using a 2.2 kW copper tube... 

Powder diffraction techniques can be used to study solid-state reactions as a function of timeJ This is done by scanning 26 as a function of diffraction intensity at regular intervals of time, and plotting the result in a manner such as that shown in Figures 18.14 and 18.15. Powder neutron diffraction methods have been used to study orientational order-disorder transitions as a function of time. ... 

Powder diffraction techniques have become increasingly useful as tools for crystal structure determination especially in cases where it is sometimes difficult to get a single crystal of sufficient size and quality for traditional single-crystal studies. The solution of a structure can be considered as a three-step process (i) data collection and indexing, (ii) data preparation and Pawley refinement, and (iii) Monte Carlo simulated annealing and rigid-body Rietveld refinement. 

In this chapter, we consider basic concepts of crystallographic symmetry, which are essential to the understanding of how atoms and molecules are arranged in space and how they form crystalline solids. Furthermore, the detailed knowledge of crystallographic symmetry is important to appreciate both the capabilities and limitations of powder diffraction techniques when they are applied to the characterization of the crystal structure of solids. We begin with the well-established notions of the three-dimensional periodicity... 

The more detailed description of the non-conventional symmetry goes beyond the scope of this book as it has little use in powder diffraction, because even the three-dimensional diffraction from aperiodic crystals is quite complex. When the diffraction picture is projected along one dimension, its treatment becomes too complicated and the crystal structure of aperiodic crystals is rarely, if ever, completely studied by means of powder diffraction techniques beyond simple phase identification. Nevertheless, this section has been included here for completeness, and to give the reader a flavor of recent developments in crystallography. ... 

D.M. Poojary and A. Clearfield, Application of x-ray powder diffraction techniques to the solution of unknown crystal structures, Acc. Chem. 

The fundamental simplicity of the powder diffraction experiment coupled with the sophistication of the available numerical data processing techniques and unsurpassed visual elegance, with which the results of the full profile refinement are represented, have transformed the powder diffraction technique into a modem and exceptionally important experimental tool in structure determination. Without a doubt, the powder method is poised to play a role in stmcture determinations with ever-increasing complexity. A recent example of the successful refinement of the sperm whale Physeter catodon) metmyoglobin stmcture from synchrotron powder diffraction data is an excellent illustration of how far the technique has been already advanced. ... 

Collectively, these major developments resulted in the revolutionary changes and opened new horizons for the powder diffraction technique. Not so long ago, if you wanted to establish the crystal structure of a material at the atomic resolution, virtually the only reliable choice was to grow an... 

Nelmes RJ, Hatton PD, McMahon MI, Piltz RO, Crain J, Cemik RJ, Bushnellwye G (1992) Angle-dispersive powder-diffraction techniques for eiystal-straeture refinement at high-pressure. Rev Sei Instrum 63 1039-1042... 

Powder diffraction techniques are used on a routine basis by many zeolite scientists. Probably the most common application is the use of a powder diffraction pattern as a fingerprint in the identification of synthesis products. Ideally, a laboratory should have a set of standard zeolite patterns measured on the in house instrument for direct comparison. For laboratories without such a set of patterns or for those whose set is incomplete, the Synthesis Commission of the IZA has published experimental patterns for some zeolites in the book entitled Verified Syntheses ofZeolitic Materials [35] (also available on the internet at http //www.iza-synthesis.org/), and the Structure Commission has published a book entitled Collection of Simulated XRD Powder Patterns for Zeolites [36], which contains at least one representative powder diffraction pattern for each known framework type. An up-to-date internet version of the latter that includes data for newly approved framework types, is maintained at http //www.iza-structure.org/databases/. 

In this chapter diffraction and in particular X-ray and neutron diffraction will be described in general, with an emphasis on powder diffraction techniques. The specific properties of X-ray and neutron diffraction and a description of sources and instruments for powder diffraction studies will be presented. Furthermore the use of powder diffraction data, from the simple use for phase identification to structure solution and refinements with the Rietveld methods, will be described. Two examples showing the potential for powder... 

Powder diffraction techniques have developed enormously since 1990. This is partly due to improved X-ray and neutron sources and instrumentation and partly because of improved methods, algorithms and software for structure solution and refinements of experimental data. The more effective computers are also important. 

At very low temperature (5 K), the positions of D2 molecules in the MOFs are relatively static, which allows use of neutron powder diffraction techniques to determine the positions of D2 molecules. The Rietveld profile analysis of... 

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