Xray Powder Diffractometry

All substances are built up of individual atoms, and nearly all substances have some degree of order of periodicity in the arrangement of these atoms. A crystal can be defined as a homogeneous, anisotropic body having the natural shape of a polyhedron. In practical terms, whether a substance is homogeneous or not can only be defined by the means that are available for measuring the crystallinity. In general, the shorter the wavelength, the smaller the crystalline region that can be recognized. Even noncrystalline materials have a degree of order, and each will give some sort of a diffraction pattern. For example, glassy materials and liquids will give diffraction patterns of sorts, generally in the form of one or more broad diffuse peaks or halos. A crystalline substance has a definite form, which is retained no matter what the physical size of the crystal. A certain type of crystal can thus be defined in terms of specific physical characteristics that determine its shape. Since every ordered material is made up of a unique arrangement and number of atoms, every ordered material will give a diffraction pattern that is, to all intents and purposes, also unique.

In X-ray powder diffractometry one is generally dealing exclusively with polycrystalline materials, and the speci-

The instrumentation that is used for powder diffraction measurements has not changed much from the instruments developed in the late 1940s. The major difference found in modern instrumentation is the use of the minicomputer for control, data acquisition, and data processing. Figure 7a shows a photograph of a typical vertical powder diffrac-tometer system, and Fig. 7b illustrates the geometry of the system. This geometric arrangement is known as the Bragg-Brentano parafocusing system and is typified by a diverging beam from a line source F, falling onto the specimen S, being diffracted and passing through a receiving slit R to the detector. Distances FA and AR are equal. The amount of divergence is determined by the effective focal width of the source and the aperture of the divergence slit D. Axial divergence is controlled by two sets of parallelplate collimators (Soller slits) P and RP placed between focus and specimen and between specimen and scatter slit, respectively.

Use of the narrower divergence slit will give a smaller specimen coverage at a given diffraction angle, thus allowing the attainment of lower diffraction angles where the specimen has a larger apparent surface (thus larger values of d are attainable). This is achieved, however, only

FIGURE 7 (a) The vertical diffractometer. A Philips PW1050 vertical goniometer system. (b) Geometry of the Bragg-Brentano diffractometer. The geometrical layout of a typical diffractometer system showing source F, Soller slits P and RP, sample S, divergence slit D, and receiving slit R. The axis of the goniometer is at A.

FIGURE 7 (a) The vertical diffractometer. A Philips PW1050 vertical goniometer system. (b) Geometry of the Bragg-Brentano diffractometer. The geometrical layout of a typical diffractometer system showing source F, Soller slits P and RP, sample S, divergence slit D, and receiving slit R. The axis of the goniometer is at A.

at the expense of intensity loss. Choice of the divergence slit, plus its matched scatter slit, is thus governed by the angular range to be covered. The decision as to whether or not the slit size should be increased at a given angle will be determined by the available intensity. A photon detector, typically a scintillation detector, is placed behind the scatter slit and converts the diffracted X-ray photons into voltage pulses. These pulses may be integrated in a rate meter to give an analog signal on an x/1 recorder. By synchronizing the scanning speed of the goniometer with the recorder, a plot of degrees 29 versus intensity, called the diffractogram, is obtained. A timer/scaler is also provided for quantitative work and is used to obtain a measure of the integrated peak intensity of a selected line(s) from each analyte phase in the specimen. A diffracted beam monochromator may also be used in order to improve signal-to-noise characteristics. The output from the diffractometer is a "powder diagram," essentially a plot of intensity as a function of diffraction angle, which may be in the form of a strip chart or a hard copy from a computer graphics terminal.

The powder method derives its name from the fact that the specimen is typically in the form of a microcrystalline powder, although, as has been indicated, any material that is made up of an ordered array of atoms will give a diffraction pattern. The possibility of using a diffraction pattern as a means of phase identification was recognized by 1935, but it was not until the late 1930s that a systematic means of unscrambling the superimposed diffraction patterns was proposed by Hanawalt, Frevel, and Rinn. Their technique was based on the use of a file of single-phase patterns, characterized in the first stage by their three strongest reflections, and a search technique based on matching strong lines in the unknown pattern with these standard pattern lines. A potential match was then confirmed by a check using the full pattern in question. The identified pattern was then subtracted from the experimental pattern, and the procedure was repeated on the residue pattern until all lines were identified.

Manual techniques for this "search/matching" process have changed little over the years. In the hands of experts manual search/matching is an extremely powerful tool, but for the less experienced user it can be rather time-consuming. Typically 2-4 h may be required for the complete identification of a four-phase mixture. A growing complication is that the file of standard patterns increases by about 2000 each year and currently stands at about 46,000 entries. Most manual methods of search/matching that are used to identify phases in an unknown mixture are similar to that shown in Fig. 8. The three strongest lines in the pattern are used to locate potential matches in the index of standards. Each time a potential candidate is

FIGURE 8 Analytical approach to multiphase diffraction. A flow chart showing the major steps in performing a typical qualitative analysis by X-ray diffraction.

found, a match is made with the complete pattern. If all lines agree, a phase confirmation is assumed and the lines for the match are subtracted from the original pattern. This process is repeated until all significant lines in the pattern are identified.

The two basic parameters being used in this search/ match process are the d values calculated from the measured 20 values in the diffractogram and the relative intensities of the lines in the pattern. Whereas the d value can be accurately measured (with an accuracy of better than 0.5% in routine analysis), the intensities are rather unreliable by comparison and can be subject to error, sometimes running into tens of percent. Because of the unreliable nature of the measured intensities, any search procedure based on the selection of lines by their intensities must be used with caution.

The responsibility for the maintenance of the Powder Data File lies with the International Centre for Diffraction Data (JCPDS), which is a nonprofit organization located in Swarthmore, Pennsylvania. This group is made up of a staff of permanent officers along with a number of academic and industrial scientists who are active in the field of X-ray powder diffractometry. The Powder Data File is a unique assembly of good-quality single-phase patterns and is used by thousands of chemists, geologists, and materials scientists. The automation of the search/match process promises to make the use of the file even more widespread, since this should do much to relieve much of the tedium associated with manual search/matching.

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