Camera Debye-Scherrer

X-ray powder diffraction studies are perfonned both with films and with counter diffractometers. The powder photograph was developed by P Debye and P Scherrer and, independently, by A W Hull. The Debye-Scherrer camera has a cylindrical specimen surrounded by a cylindrical film. In another commonly used powder... 

Data taken with a 143.2-mm diameter Debye-Scherrer camera using Cu Ka radiation (X 1.5418 A). 

X-Ray Powder Patterns. Samples for x-ray pattern determinations were sealed in 0.2-mm. glass capillary tubes under an atmosphere of argon. The samples were then exposed to nickel-filtered, CuKa radiation in an 11.459-cm. Debye-Scherrer camera for 18 to 20 hours. 

The preceding setup allows both X-ray diffraction (32) and absorption experiments (33, 34). The capillary geometry was used until about 30 years ago for ex situ XRD studies in connection with the placement of Lindemann tubes in powder Debye-Scherrer cameras. At that time, films were used to detect the diffracted X-rays. Today, this cumbersome technique has been almost completely replaced as modern detectors are used. 

Powder photographs were taken with a 57.3-mm radius Debye-Scherrer camera and nickel-filtered Cu Ka radiation (Xmean = 1.5418 A). For intensity work, the multiple-film technique was used. The lattice constant, derived from 23 reflections from 42.56° to 73.47° 20 and corrected for film shrinkage with a parallel film of a reference substance, was Oo = 15.02 A with an estimated standard deviation of 0.01 A. 

Fig. 1 a Photograph and b schematic drawing of the large Debye-Scherrer camera at SPring-8 BL02B2... 

The X-ray powder data were measured by the large Debye-Scherrer camera at SPring-8 BL02B2 using solvent-free (Sc2C2) C84 powder sample. The exposure time on the IP was 80 min. The wavelength of incident X-rays was 0.75 A. The... 

The compound layer formed in the transition zone between nickel and bismuth was investigated metallographically, by X-rays and electron probe microanalysis (EPMA). X-ray patterns were taken both from the cross-sections in the planes parallel to the initial Ni-Bi interface (after successive removal of the specimen material and polishing its surface) and the powdered phases using Cu Ka radiation. Two methods of obtaining X-ray patterns were employed. Firstly, X-ray photographs were obtained in a 57.3 mm inner diameter Debye-Scherrer camera. Secondly, use was made of a DRON-3 diffractometer to record X-ray diffractograms. 

X-ray Powder Diffraction. Photographs were taken on products in quartz capillaries using Debye-Scherrer cameras. 

Figure 3.2. Debye-Scherrer camera without a cover showing cylindrical sample, collimator, incident beam trap, and the location of the x-ray film.

Figure 3.3. Two Debye-Scherrer cameras with covers, which have been loaded with x-ray film and installed on the x-ray generator, ready for collecting powder diffraction data.

Cylindrical samples, which are common in the Debye-Scherrer cameras Figure 3.2), are also used in powder diffractometry. Similar to flat transmission samples, small amounts of powder are required in the cylindrical specimen geometry. This form of the sample is least susceptible to the non-random distribution of particle orientations, i.e. to preferred orientation effects. 

The x-ray spectrometer can also be used as a tool in diffraction analysis. This instrument is known as a diffractometer when it is used with x-rays of known wavelength to determine the unknown spacing of crystal planes, and as a spectrometer in the reverse case, when crystal planes of known spacing are used to determine unknown wavelengths. The diffractometer is always used with monochromatic radiation and measurements may be made on either single crystals or polycrystalline specimens in the latter case, it functions much like a Debye-Scherrer camera... 

Fig. 6-1 Debye-Scherrer camera, with cover plate removed. (Courtesy of Philips Electronic Instruments, Inc.)...

The resolving power, or ability to separate diffraction lines from planes of almost the same spacing, is therefore twice that of a Debye-Scherrer camera of the same radius. In addition, the exposure time is much shorter, because a much larger specimen is used (the arc AB of Fig. 6-7 is of the order of 1 cm) and diffracted rays from a considerable volume of material are all brought to one focus. The Seemann-Bohlin camera is, therefore, useful in studying complex diffraction patterns, whether they are due to a single phase or to a mixture of phases such as occur in alloy systems. 

There is an optimum specimen thickness for the transmission method, because the diffracted beams will be very weak or entirely absent if the specimen is either too thin (insufficient volume of diffracting material) or too thick (excessive absorption). As will be shown in Sec. 9-8, the specimen thickness which produces the maximum diffracted intensity is given by l/ i, where /t is the linear absorption coefficient of the specimen. Inspection of Eq. (1-10) shows that this condition can also be stated as follows a transmission specimen is of optimum thickness when the intensity of the beam transmitted through the specimen is 1 /e, or about j, of the intensity of the incident beam. Normally this optimum thickness is of the order of a few thousandths of an inch (0.1 mm). There is one way, however, in which a partial transmission pattern can be obtained from a thick specimen and that is by diffraction from an edge (Fig. 6-13). Only the upper half of the pattern is recorded on the film, but that is all that is necessary in many applications. The same technique has also been used in some Debye-Scherrer cameras. 

The use of a monochromator produces a change in the relative intensities of the beams diffracted by the specimen. Equation (4-19), for example, was derived for the completely unpolarized incident beam obtained from the x-ray tube. Any beam diffracted by a crystal, however, becomes partially polarized by the diffraction process itself, which means that the beam from a crystal monochromator is partially polarized before it reaches the specimen. Under these circumstances, the usual polarization factor (1 - - cos 26)12, which is included in Eqs. (4-19) through (4-21), must be replaced by the factor (1 + cos 2a cos 20)/(l -I- cos 2a), where 2a is the diffraction angle in the monochromator (Fig. 6-16). Since the denominator in this expression is independent of 6, it may be omitted the combined Lorentz-polarization factor for crystal-monochromated radiation is therefore (1 + cos 2a cos 20)/sin 6 cos 6. This factor may be substituted into Eqs. (4-19) and (4-20), although a monochromator is not often used with a Debye-Scherrer camera, or into Eq. (4-21), when a monochromator is used with a diffractometer (Sec. 7-13). But note that Eq. (4-20) does not apply to the focusing cameras of the next section. 

Compared to a Debye-Scherrer camera of the same size, operated directly from the x-ray tube, a Guinier camera provides a much clearer pattern with twice the resolution and about the same exposure time, but any one Guinier camera covers only a limited range of 10. It is best suited to the examination of particular parts of complex patterns. 

Derive an equation for the resolving power of a Debye-Scherrer camera for two wavelengths of nearly the same value, in terms of A5, where 5 is defined by Fig. 6-2. 

A powder pattern of zinc is made in a Debye-Scherrer camera 5.73 cm in diameter with Cu Ka radiation. 

Basically, a diffractometer is designed somewhat like a Debye-Scherrer camera, except that a movable counter replaces the strip of film. In both instruments, essentially monochromatic radiation is used and the x-ray detector (film or counter) is placed on the circumference of a circle centered on the powder specimen. The essential features of a diffractometer are shown in Fig. 7-1. A powder specimen C, in the form of a flat plate, is supported on a table H, which can be rotated about an axis O perpendicular to the plane of the drawing. The x-ray source is S, the line focal spot on the target T of the x-ray tube S is also normal to the plane of the drawing and therefore parallel to the diffractometer axis O. X-rays diverge from this source and are diffracted by the specimen to form a convergent diffracted beam which comes to a focus at the slit F and then enters the counter G. A and... 

This is a very recent development. It involves a side-window position-sensitive proportional counter (Sec. 7-5), a multichannel analyzer, and the rpeasurement of the angular positions of many diffraction lines simultaneously. The anode wire of the counter, which is long and curved, coincides with a segment of the diffractometer circle and is connected, through appropriate circuits, to an MCA. The powder specimen is in the form of a thin rod centered on the diffractometer axis. The geometry of the apparatus therefore resembles that of a Debye-Scherrer camera (Fig. 6-2), except that the curved film strip is replaced by a curved counter. 

The powder pattern of the unknown is obtained with a Debye-Scherrer camera or a diffractometer, the object being to cover as wide an angular range of 20 as possible. A camera such as the Seemann-Bohlin, which records diffraction lines over only a limited angular range, is of very little use in structure analysis. The specimen preparation must ensure random orientation of the individual particles of powder, if the observed relative intensities of the diffraction lines are to have any meaning in terms of crystal structure. After the pattern is obtained, the value of sin 9 is calculated for each diffraction line this set of sin 9 values is the raw material for the determination of cell size and shape. Or one can calculate the d value of each line and work from this set of numbers. 

For reasons to be discussed in Chap. 11, the observed values of sin 6 always contain small systematic errors. These errors are not large enough to cause any difficulty in indexing patterns of cubic crystals, but they can seriously interfere with the determination of some noncubic structures. The best method of removing such errors from the data is to calibrate the camera or diffractometer with a substance of known lattice parameter, mixed with the unknown. The difference between the observed and calculated values of sin 6 for the standard substance gives the error in sin 9, and this error can be plotted as a function of the observed values of sin 6. Figure 10-1 shows a correction curve of this kind, obtained with a particular specimen and a particular Debye-Scherrer camera. The errors represented by the ordinates of such a curve can then be applied to each of the observed values of sin 0 for the diffraction lines of the unknown substance. For the particular determination represented by Fig. 10-1, the errors shown are to be subtracted from the observed values. 

As a simple example, we will consider an intermediate phase which occurs in the cadmium-tellurium system. Chemical analysis of the specimen, which appeared essentially one phase under the microscope, showed it to contain 46.6 weight percent Cd and 53.4 weight percent Te. This is equivalent to 49.8 atomic percent Cd and can be represented by the formula CdTe. The specimen was reduced to powder and a diffraction pattern obtained with a Debye-Scherrer camera and CuKa. radiation. 

The general approach in finding an extrapolation function is to consider the various effects which can lead to errors in the measured values of 0, and to find out how these errors in 6 vary with the angle 6 itself. For a Debye-Scherrer camera, the chief sources of error in 9 are the following ... 

A camera of this kind is preferred for work of the highest precision, since the position of a diffraction line on the film is twice as sensitive to small changes in plane spacing with this camera as it is with a Debye-Scherrer camera of the same diameter. It is, of course, not free from sources of systematic error. The most important of these are the following ... 

Suppose a cubic substance is being examined in a Debye-Scherrer camera. Then Eq. (11-11), namely. 

The pattern may be recorded with a Debye-Scherrer camera, Guinier camera, or diffractometer. Here again, line intensities depend on the apparatus. In particular, absorption effects cause high-angle lines on a Debye-Scherrer pattern to be stronger, relative to low-angle lines, than on a diffractometer recording, as shown m Sec. 4-10. 

When the unknown is a single phase, the search procedure is relatively straightforward. Consider, for example, the pattern described in Table 14-1. It was obtained with Cu Koi radiation and a Debye-Scherrer camera line intensities were estimated. The experimental values of dj, di, and d are 2.82, 1.99, and 1.63 A,... 

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