Powder diffraction experimental methods

By determining the mass loss due to dehydration (rfwi and dm2 in Fig. 4), it is possible to quantitatively determine the phase composition of mixtures of crystal hydrates provided it was qualitatively ascertained by some other method (for instance, by X-ray powder diffraction). This method has been used to determine the influence of various experimental parameters on the phase composition of calcium oxalate precipitates. Several examples are given in Figs. 5-9. 

The Rietveld Fit of the Global Diffraction Pattern. The philosophy of the Rietveld method is to obtain the information relative to the crystalline phases by fitting the whole diffraction powder pattern with constraints imposed by crystallographic symmetry and cell composition. Differently from the non-structural least squared fitting methods, the Rietveld analysis uses the structural information and constraints to evaluate the diffraction pattern of the different phases constituting the diffraction experimental data. 

The most important experimental task in structural chemistry is the structure determination. It is mainly performed by X-ray diffraction from single crystals further methods include X-ray diffraction from crystalline powders and neutron diffraction from single crystals and powders. Structure determination is the analytical aspect of structural chemistry the usual result is a static model. The elucidation of the spatial rearrangements of atoms during a chemical reaction is much less accessible experimentally. Reaction mechanisms deal with this aspect of structural chemistry in the chemistry of molecules. Topotaxy is concerned with chemical processes in solids, in which structural relations exist between the orientation of educts and products. Neither dynamic aspects of this kind are subjects of this book, nor the experimental methods for the preparation of solids, to grow crystals or to determine structures. 

Recent developments and prospects of X-ray powder diffraction methods. In the preceding paragraph a few comments have been made about diffractometry and its uses in the analysis of materials. However it is not possible to give here an account of this subject its principles and underlying theories, its experimental techniques and... 

In a paper by Albinati and Willis (1982) the application of the Rietveld method in neutron and X-ray powder diffraction was discussed considering the different experimental techniques of obtaining the diffraction patterns. For a detailed description of the method and its applications see a reference publication (Young 1995). See also Jenkins and Snyder (1996). A frequently used calculation program for the... 

Experimental tilt angles have usually an accuracy of at best 3°, leading to an error of about 0.1 A in cell axes. The calculated third cell axis will show a higher deviation. If possible an internal standard should be used for calibration purposes but a higher accuracy will be obtained with a Pawley fit (e.g. fit forP CuPc in Fig. 6) from x-ray powder diffraction data [11]. Especially for packing energy minimization used for simulation methods it is essential to determine the cell parameters as precise as possible. In the case of polymorphism, it is essential to use x-ray powder diffraction to ensure that bulk and investigated nano crystals represent the same modifications. 

The object of this experiment is to determine the crystal structure of a solid substance from x-ray powder diffraction patterns. This involves determination of the symmetry classification (cubic, hexagonal, etc.), the type of crystal lattice (simple, body-centered, or face-centered), the dimensions of the unit cell, the number of atoms or ions of each kind in the unit cell, and the position of every atom or ion in the unit cell. Owing to inherent limitations of the powder method, only substances in the cubic system can be easily characterized in this way, and a cubic material will be studied in the present experiment. However, the recent introduction of more accurate experimental techniques and sophisticated computer programs make it possible to refine and determine the structnres of crystals of low syimnetiy from powder diffraction data alone. 

Because of the general similarities in the diffraction patterns, and the lack of clearly resolvable distinguishing peaks, they employed the Rietveld method (Young 1993). In the Rietveld method, the entire experimental diffraction pattern for each solid phase is used as a basis for comparison. For structure determination using powder diffraction, this comparison is made with a structural model used to generate a calculated pattern. In quantitative analysis of polymorphic phases, the known crystal stmctures are used to generate the standard diffraction patterns and these are then refined against the experimental powder pattern of the mixture to obtain the relative amounts of the polymorphs. 

In spite of these caveats, there is intense activity in the application of these methods to polymorphic systems and considerable progress has been made. Two general approaches to the use of these methods in the study of polymorphism may be distinguished. In the first, the methods are utilized to compute the energies of the known crystal structures of polymorphs to evaluate lattice energies and determine the relative stabilities of different modifications. By comparison with experimental thermodynamic data, this approach can be used to evaluate the methods and force fields employed. The ofher principal application has been in fhe generation of possible crystal structures for a substance whose crystal structure is not known, or which for experimental reasons has resisted determination. Such a process implies a certain ability to predict the crystal structure of a system. However, the intrinsically approximate energies of different polymorphs, the nature of force fields, and the inherent imprecision and inaccuracy of the computational method still limit the efificacy of such an approach (Lommerse et al. 2000). Nevertheless, in combination with other physical data, in particular the experimental X-ray powder diffraction pattern, these computational methods provide a potentially powerful approach to structure determination. The first approach is the one applicable to the study of conformational polymorphs. The second is discussed in more detail at the end of this chapter. 

Prior to the definitive X-ray powder diffraction characterization of HZ, the true structure of the aggregate remained elusive because of its limited solubility. HZ was soluble only in NaOH, which completely degraded the structure and prevented any attempt to determine the intramolecular atomic interactions. The insolubility of the product rendered useless many standard experimental methods for the characterization of bioinorganic systems. This aspect of the biomineral s identification undoubtedly contributed to Ridley s description of HZ as a black insoluble mass of material that can be soul-destroying to work with (31). 

Our experience with applications of the powder method in diffraction analysis was for the most part, conceptual, and in the remainder of this book, we will discuss key issues that arise during the processing and interpretation of powder diffraction data. Despite the apparent simplicity of onedimensional diffraction patterns, which are observed as series of constructive interference peaks (both resolved and partially or completely overlapped), created by elastically scattered waves and placed on top of a nonlinear background noise, the complexity of their interpretation originates from the complexity of events involved in converting the underlying structure into the experimentally observed data. Thus, nearly every component of data processing in powder diffraction is computationally intense. 

Given the nature of the powder diffraction method, the resultant experimental data can be employed to obtain and/or confirm the following information ... 

Recently the ICDD Powder Diffraction File underwent a substantial and useful upgrade calculated patterns based on single crystal data from the ICSD file have been included into the PDF-2/PDF-4 Full File calculated patterns of structures stored in the CSD file, have been included into the PDF-4 Organics (see Table 4.3). These additions make it possible to conduct searches and find matches with computed digitized powder patterns in addition to experimentally measured powder diffraction data, thus improving automation, simplifying phase identification process and considerably expanding the applicability of the powder method for a qualitative phase analysis. 

The reference intensity ratio method is based on the experimentally established intensity ratio between the strongest Bragg peaks in the examined phase and in a standard reference material. The most typical reference material is corundum, and the corresponding peak is (113). The reference intensity ratio k) is quoted for a 50 50 (wt. %) mixture of the material with corundum, and it is known as the corundum number . The latter is commonly accepted and listed for many compounds in the ICDD s Powder Diffraction File. Even though this method is simple and relatively quick, careful account and/or experimental minimization of preferred orientation effects are necessary to obtain reliable quantitative results. 

It is worth noting that practically all non-traditional methods for solving crystal structures have been initially developed for both powder and single crystal diffraction data to manage intrinsic incompleteness or poor quality that cannot be improved experimentally. Despite a variety of structure solution approaches, traditional direct phase determination methods appear to be the most common and successful when powder diffraction data are adequate. Patterson methods also work quite well but they require the presence of a heavy atom and, perhaps, more extensive crystallographic expertise. The non-traditional methods are generally employed when other techniques fail and their use is somewhat restricted by both the complexity and limited availability of computer codes. 

T. Wessels, Ch. Baerlocher, L. B. McCusker, and W.I.F. David, Experimental methods for estimating the relative intensities of overlapping reflections, in Structure determination from powder diffraction data. lUCr monographs on crystallography 13. W. I. F. David, K. Shankland, L.B. McCusker, and Ch. Baerlocher, Eds., Oxford University Press, Oxford, New York (2002). 

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