Verified Syntheses of Zeolitic Materials
2nd Revised Edition
Product characterization by X-ray powder diffraction
Lynne B. McCusker
Laboratorium für Kristallographie
ETH, Zürich, Switzerland
Different features of a powder diffraction pattern can be exploited in the characterization of a material (see Table 1). Of course, powder diffraction data is most commonly used as a "fingerprint"in the identification of a material, but the other information that can be gleaned from a diffraction pattern should not be forgotten. If possible, the diffraction experiment should be adapted to optimize that feature which provides the information desired.
Table 1. Information contained in a powder diffraction pattern
Peak positions (2θ values)
Unit cell dimensions
Although there are a number of different powder diffractometer geometries on the market, each one with its positive and negative attributes, all have an X-ray source, a specimen holder and a detector, and almost all are capable of recording a respectable powder diffraction pattern. The difficulty arises when one wants to compare data from different instruments or even from the same instrument with different operators. It is not possible to go into detail in the space available here, but the basic considerations and a few common sources of error will be discussed. For more information, the reader is referred to the volume entitled "Modern Powder Diffraction" edited by Bish and Post  or to the article entitled "Practical Aspects of Powder Diffraction Data Analysis‚ by Baerlocher and McCusker .
2. Data Collection
2.1 Peak positions
If the pattern is to be indexed (Miller indices hkl assigned to each of the peaks and thereby the unit cell dimensions extracted from the pattern), it is essential that the peak positions be determined accurately. In this case, the instrument‚s 2θ scale needs to be carefully calibrated using a standard material such as the NIST silicon standard 640b. The sharper a peak, the better its 2θ value can be determined, so the diffractometer should also be adjusted to optimize resolution. As a guide, almost any laboratory instrument can be adjusted to give a full width at half maximum (FWHM) for the Si 111 reflection (28.44°2θ with CuKα1 radiation) of 0.10°2θ or less. The measured 2θ values for the peaks in the standard material‚s pattern should agree with the literature values to within 0.01°2θ .
If the sample is off-center, this will affect the 2θ zeropoint correction, so ideally, the sample should be mixed with a small amount of the standard (that is, measured with an internal standard), so that the 2θ calibration can be done simultaneously. However, if care is taken in positioning of the sample, a 2θ calibration using an external standard is usually sufficient. In reflection mode, thin samples are preferred for peak position determination, so effects of sample transparency can be eliminated.
2.2 Peak intensities
For indexing purposes, the intensities of the peaks are irrelevant, but for identification or for structure analysis, accurate relative intensities are essential. There are three commonly ignored factors which can severely affect the relative peak intensities: 1) sample thickness, 2) preferred orientation, and 3) divergence slit(s).
Bragg-Brentano reflection geometries require an "infinitely thick" sample. That is, it is assumed that the sample is thick enough that all the X-rays interact with the sample (by absorption or diffraction) before they reach the sample holder. In this way, the volume of sample effectively irradiated remains constant as 2θ changes. If this is not the case, the intensities must be adjusted for the transparency of the sample. in general, the relative intensities of the low angle reflections will be too large if the "infinite thickness" criterion is not met. For transmission geometries, on the other hand, the sample must be thin enough that the X-rays are not too strongly attenuated.
Most powder diffraction data analyses assume that the sample consists of millions of randomly oriented crystalhites. If this is not the case, relative intensities will be distorted. For example, if the crystallites have a plate-like morphology, they are likely to lie flat. Assuming that the c-axis is parallel to the short dimension, crystallites aligned in the 001 diffraction condition will be overrepresented, and those In the hk0 diffracting condition underrepresented. This will then lead to a bias in the relative intensities recorded. Various sample preparation techniques have been used to reduce preferred orientation (such as back or side loading of flatplate sample holders, mixing amorphous glass beads with the sample, or spray drying), but none is foolproof. Measurements in transmission mode with the sample loosely packed in a rotating capillary are less susceptible (but not immune) to this problem. An easy way to establish whether or not preferred orientation is present is to measure the diffraction pattern in both reflection and transmission mode. The two measured patterns should be comparable, and if their relative intensities differ significantly (in an hkl-dependent manner), there is probably preferred orientation present in the sample.
At low angles, the X-ray beam is spread over a larger surface of the specimen than it is at high angles. To ensure that the X-rays interact only with the sample (and not the edges of the specimen holder) a slit is inserted between the X-ray source and the sample to confine the beam to the sample (divergence slit). As the 2θ angle increases, this slit can be opened wider to allow more X-rays through and thereby increase the counting rate, but then the resulting data must be corrected for the increased volume of sample irradiated. The slit size can be varied during the measurement either continuously (using an automatic divergence slit) or manually (using a series of calibrated slits). For data comparison purposes, the data should then be transformed to constant sample volume (single constant slit) data. In many laboratories, data are recorded using a relatively wide single slit that is appropriate for higher angle data, but not for the lower 2θ values. In such a measurement, the relative intensities of the low angle peaks will appear to be too low, because only a part of the X-ray beam interacts with the sample.
In a zeolite laboratory, powder diffraction data are most commonly used to identify a newly synthesized material or to monitor the effects of a post-synthesis treatment. In both cases, the measured pattern is compared with an existing one, whether it be a pattern in the Collection of Simulated XRD Powder Patterns for Zeolites , the Powder Diffraction File (PDF) of the ICDD  or an inhouse data file. Such comparisons are not easy for zeolites, especially if the data collection or sample preparation conditions differ. A few practical considerations are presented briefly below.
(1) Intensities are important for identification, so the data should be collected bearing the points discussed in the previous section in mind.
(2) Data should be in the form of a constant volume measurement if the Collection, the PDF or any of the common databases is to be used in a search/match process.
(3) Peak position information is often given in terms of d-values rather than 2θ values, because d-values are independent of the X-ray wavelength (λ ) used. (d=λ /2 sinθ )
(4) The low angle lines are the ones most strongly affected by non-framework species (see Ref.  p. 418). In general, these lines are more intense in the calcined material than in the as synthesized form, and similar materials containing different cations or different organic species may have quite different relative intensities at low angles. However, the intensities of the higher angle reflections are generally dominated by the positions of the framework atoms, so these can be compared quite well.
(5) Different synthesis conditions or different post-syntheses treatments can cause subtle distortions in a zeolite framework structure that can complicate identification. The symmetry may be reduced (and thereby produce many more peaks in the pattern), although the basic framework topology (connectivity) remains unchanged. In such a case, indexing the pattern to obtain the dimensions of the unit cell can facilitate the identification.
 Modern Powder Diffraction, D. L Bish, J. E. Post (eds.), Review in Mineralogy
 Ch. Baerlocher, L B. McCusker, Stud. Surf. Sci. & Catal. 85 (1994) 391
 M. M. J. Treacy, J. B. Higgins, R von Ballmoos, "Collection of Simulated XRD Powder Patterns for Zeolites," Zeolites 16, 1996
 PDF Database (Sets 1-44), Copyright 1994, International Centre for Diffraction Data, 12 Campus Blvd., Newtown Square, PA 19073-3273, USA