Powder diffraction pattern information

Information content in a powder diffraction pattern is reduced as compared to that in single crystal diffraction, due to the collapse of the three dimensional reciprocal space into a one dimensional space where the only independent variable is the scattering angle. The poorer the resolution of the diffraction method, the less the information content in the pattern (Altomare et al. 1995 David 1999). As a consequence, structure of less complex phases can be determined from power diffraction alone (fewer atoms in the asymmetric unit of the unit cell). However, refinement of the structure is not limited so seriously with resolution issues, so powder diffraction data are used in Rietveld refinement more frequently than in structure determination. Electron powder diffraction patterns can be processed and refined using public domain computer programs. The first successful applications of electron diffraction in this field were demonstrated on fairly simple structures. 

F. X-ray Powder Difi action Search System. Compounds that fail to crystallize may still be examined by X-ray diffraction, because non-crystalline materials, as powders, give characteristic diffraction patterns. A collection of powder diffraction patterns proves to be a very effective means by which to identify materials and indeed, one of the very earliest search systems in chemical analysis was based upon such data by Hanawalt (21) over forty years ago. The importance of these data in TSCA can be seen by examining the TSCA Inventory regulations for treatment of confidential chemicals (22). Section 710.7 of these regulations indicates that EPA intends to rely on powder diffraction data to assure the validity and seriousness of a manufacturers request for treating information on a chemical as confidential. 

The last method for producing standard patterns for phases not in the PDF is more involved. In many instances single crystals of unknown phases can be removed from reaction mixtures. If this is the case, a full three dimensional crystal structure analysis will yield the positions of all atoms in the structure. Once the crystal structure is known, it can be used to calculate the X-ray powder diffraction pattern for the phase. This powder diffraction information can then be used with confidence as a standard powder pattern. 

The intent of this chapter is twofold. One is to give brief structural descriptions of many of the copper-oxide superconductors. For in-depth information, the reader is referred to the original publications. The second is to provide detailed crystallographic information (lattice constants, positional and thermal parameters, space groups, etc.), and compositional data on many of the superconductors discussed. Also, calculated x-ray powder diffraction patterns for these same compounds are tabulated. It is hoped that such information will prove useful to the superconductivity researcher. 

Random structure methods have proved useful in solving structures from X-ray powder diffraction patterns. The unit cell can usually be found from these patterns, but the normal single-crystal techniques for solving the structure cannot be used. A variation on this technique, the reverse Monte Carlo method, includes in the cost function the difference between the observed powder diffraction pattern and the powder pattern calculated from the model (McGreevy 1997). It is, however, always necessary to include some chemical information if the correct structure is to be found. Various constraints can be added to the cost function, such as target coordination numbers or the deviation between the bond valence sum and atomic valence (Adams and Swenson 2000b Swenson and Adams 2001). 

Alternatively, when a powdered crystalline solid diffracts monochromatic X-radiation, the diffraction pattern will be a series of concentric rings, rather than spots, because of the random orientation of the crystals in the sample (Fig. 4.2). The structural information in this pattern is limited however, because even solid compounds that have the same structure but different composition will almost inevitably have different d values, each individual solid chemical compound will have its own characteristic powder diffraction pattern. 

During the last five years, a powerful new method of getting crystal structural information from powder diffraction patterns has become widely used. Known variously as the Rietveld method, profile refinement1, or, more descriptively, whole-pattern-fitting structure refinement, the method was first introduced by Rietveld (X, 2) for use with neutron powder diffraction patterns. It has now been successfully used with neutron data to determine crystal structural details of more than 200 different materials in polycrystalline powder form. Later modified to work with x-ray powder patterns (3, X) the method has now been used for the refinement of more than 30 crystal structures, in 15 space groups, from x-ray powder data. Neutron applications have been reviewed by Cheetham and Taylor (5) and those for x-ray by Young (6). 

In spite of the wealth of information contained therein, as of this writing there are no citations to this 1995 compilation of Whitaker, which is a useful resource for reference powder diffraction patterns of many organic colorants, polymorphic and non-polymorphic. This may be due to the fact that it was published in a specialist monograph or that subsequent workers would use and cite the primary sources cited by Whitaker. Whatever the reason, it appeared to be of some benefit and convenience to the reader to compile here those primary references to polymorphic materials that are designated as colourants by the Colour Index, with the primary sources given by Whitaker. Whitaker also presents references for many other related dye materials that have not received such a designation. 

A successfid indexing of the powder diffraction pattern, which can often be done automatically, yields the unit cell dimensions and information on possible space groups. The chemical analysis and sorption data indicate the framework density, or number of tetrahedra per unit cell. The challenge is then to position these tetrahedra within the unit cell such that (1) they fully interconnect in a sensible manner and (2) the necessary analytical data are reproduced. These structural constraints are quantified in an energy expression and simulated annealing [33,34] is employed as the global optimization approach. 

Of all the methods available for the physical characterization of solid materials, it is generally agreed that crystallography, microscopy, thermal analysis, solubility studies, vibrational spectroscopy, and nuclear magnetic resonance are the most useful for characterization of polymorphs and solvates. However, it cannot be overemphasized that the defining criterion for the existence of polymorphic types must always be a non-equivalence of crystal structures. For compounds of pharmaceutical interest, this ordinarily implies that a non-equivalent X-ray powder diffraction pattern is observed for each suspected polymorphic variation. All other methodologies must be considered as sources of supporting and ancillary information, but cannot be taken as definitive proof for the existence of polymorphism by themselves. 

The use of detectors, collimators and monochromators in different powder diffractometers is discussed in Chapter 3, while the reminder of this chapter is dedicated to theory of diffraction, understanding the origin of the powder diffraction pattern, and a brief description of how structural information can be extracted from powder diffraction data. 

The very existence of the powder diffraction pattern, which is an experimentally measurable function of the crystal structure and other parameters of the specimen convoluted with various instrumental functions, has been made possible by the commensurability of properties of x-rays and neutrons with properties and structure of solids. As in any experiment, the quality of structural information, which may be obtained via different pathways (two possibilities are illustrated in Figure 2.62 as two series of required steps), is directly proportional to the quality of experimental data. The latter is usually achieved in a thoroughly planned and well executed experiment as will be detailed in Chapter 3. Similarly, each of the data processing steps, which were described in this chapter and are summarized in Figure 2.62, requires knowledge, experience and careful execution, and we will describe them in practical terms in Chapters 4 through 7. 

The powder diffraction experiment is the cornerstone of a truly basic materials characterization technique - diffraction analysis - and it has been used for many decades with exceptional success to provide accurate information about the structure of materials. Although powder data usually lack the three-dimensionality of a diffraction image, the fundamental nature of the method is easily appreciated from the fact that each powder diffraction pattern represents a one-dimensional snapshot of the three-dimensional reciprocal lattice of a crystal. The quality of the powder diffraction pattern is usually limited by the nature and the energy of the available radiation, by the resolution of the instrument, and by the physical and chemical conditions of the specimen. Since many materials can only be prepared in a polycrystalline form, the powder diffraction experiment becomes the only realistic option for a reliable determination of the crystal structure of such materials. 

The x-ray powder diffraction method dates back to Debye and Scherrer who were the first to observe diffraction from LiF powder and succeeded in solving its crystal structure. Later, HulF suggested and Hanawalt, Rinn and FreveP formalized the approach enabling one to identify crystalline substances based on their powder diffraction patterns. Since that time the powder diffraction method has enjoyed enormous respect in both academia and industry as a technique that allows one to readily identify the substance both in a pure form and in a mixture in addition to its ability to provide information about the crystal structure (or the absence of crystallinity) of an unknown powder. 

Early data analysis attempted to extract values of the individual structure factors from peak envelopes and then apply standard single crystal methods to obtain structural information. This approach was severely limited because the relatively broad peaks in a powder pattern resulted in substantial reflection overlap and the number of usable structure factors that could be obtained in this way was very small. Consequently, only very simple crystal structures could be examined by this method. For example, the neutron diffraction study of defects in CaF2-YF3 fluorite solid solutions used 20 reflection intensities to determine values for eight structural parameters. To overcome this limitation, H. M. Rietveld realized that a neutron powder diffraction pattern is a smooth curve that consists of Gaussian peaks on top of a smooth background... 

The computer based identification of crystalline phases in powder diffraction patterns normally requires two separate components (a) a powder diffraction database containing reference information and (b) a search-match program that loads the diffractogram and accesses the database to attempt to match the diffraction data to known phases in the database. 

The powder diffraction pattern contains a wealth of information in addition to the pure crystal structure, as can be seen in Figure 1. 

Figure 1 General information content of a powder diffraction pattern.

---