Debye-Scherrer geometry

Thompson, P., and Wood, I. G. X-ray Rietveld refinement using Debye-Scherrer geometry. J. Appl. Cryst. 16, 458-472 (1983). 

Only for the Bragg-Brentano geometry, the Dollase-March texture multiplier has a simple expression. For any other diffraction geometry the integral over m cannot be removed. In the Debye-Scherrer geometry C = 0, = 0, then from... 

Reduction from the two-dimensional form to the one-dimensional equatorial form was a requirement of the equatorial diffractometer geometries utilizing point detectors or at most linear position sensitive detectors. Importantly, this correction is neither applicable to the Bragg-Brentano nor to the flat transmission geometry, but is only valid for the Debye-Scherrer geometry. 

In the range of 10 kbar, a gas-filled bomb with beryllium windows suffices. Since 1949, a number of miniature pressure vessels have been designed in which both the bomb and sample are bathed in the X-ray beam. Polycrystalline beryllium, single-crystal beryllium, and singlecrystal diamond containers have been used for X-ray. transparency. More recently, diamond and WC anvils have permitted pressures of 200-500 kbar, respectively. Details of such instrumentation have been reviewed by Klement and Jayaraman. These techniques employ the Debye-Scherrer geometry and use mostly film recording, though counter tubes have been used in some of the anvil procedures. Cell dimension accuracy is limited to about 0.5 % under these conditions and structure refinements are hampered by the difficulties associated with intensity measurement. 

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. 

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. 

Fig. 6-2 Geometry of the Debye-Scherrer method, diffraction cone.

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. 

These laboratory parallel geometry configurations lead to average angitlar resolutions, but have the advantage of requiring limited acquisition times. Therefore, they are used for apphcations where the acquisition speed is a key factor. From this point of view, they constitute an alternative to the Debye-Scherrer and Hull systems with a curved position sensitive detector, for example, when conducting thermodiffraction measurements. 

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