Section 2.3.1.1.3. Alignment and angular calibration

It is essential to align and calibrate the diffractometer properly. Failure to do so degrades the performance of the instrument, leading to a loss of intensity and resolution, increased background, incorrect profile shapes, and errors that cannot be readily diagnosed. Procedures and devices for this purpose are often provided by the manufacturer. The principles and mechanical devices to aid in making a proper alignment have been described by Parrish & Lowitzsch (1959) and the general procedure by Klug & Alexander (1974, p. 280).

The alignment requires setting the diffractometer axis of rotation to the selected X-ray tube take-off angle at a distance equal to the radius of the diffractometer. The long axes of the X-ray tube focal line, entrance, receiving, and antiscatter slits must be centred, be parallel to the axis of rotation, and lie in the same plane when the instrument is at 0°. The slits are made parallel to the axis of rotation in the manufacture of the diffractometer, and these steps require positioning of the instrument with respect to the line focus. The parallel-slit foils must also be normal to the rotation axis. A flat fluorescent screen made as a specimen to fit into the diffractometer specimen post is used to centre the primary beam by small movements of the ES and/or diffractometer. The diffracted beam can be centred on the curved monochromator with a narrow slit placed at the centre of the monochromator position (with the monochromator removed). The detector arm is then moved to the highest intensity. The procedure is repeated with the receiving slit in position. This is very close to the 0° position described below.

The angular calibration of the diffractometer is usually made by accurately measuring the 0° position to establish a fiducial point. It assumes that the gear system is accurate and that the receiving-slit arm moves exactly to the angle indicated on the scale at all 2θ positions. The determination of the angular precision of the gear train requires special equipment and methods; see, for example, Jenkins & Schreiner (1986). It is essential that the setting of the worm against the gear wheel be adjusted for smooth operation. In practice, this is a compromise between minimum backlash and jerky movement. The backlash can be avoided by scanning in the same direction and running the diffractometer beyond the starting angle before beginning the data collection. Incremental angle encoders have been used when very high precision is required.

The 0° position of the diffractometer scale, 2θ₀, can be determined with a pinhole placed in the specimen post as shown in Fig. 2.3.1.6(a) (Parrish & Lowitzsch, 1959). The receiving slit is step scanned in 0.01° or smaller increments and the midpoints of chords at various heights are used to determine the angle. To avoid mis-centring errors of the pinhole, two measurements are made with the specimen post rotated 180° between measurements. The median angle of the two plots is the 0° position as shown in Fig. 2.3.1.6(b) and the diffractometer scale is then reset to this position. The shape of the curves is determined by the relative sizes of the pinhole and the receiving-slit width. With care, the position can be located to about 0.001°. The 2θ₀ position can be corrected by using it as a variable in the least-squares refinement of the lattice parameter of a standard specimen.

Figure 2.3.1.6| top | pdf | Zero-angle calibration. (a) XRT X-ray tube anode, ψ take-off angle, O axis of rotation, PH pinhole, RS receiving slit. Intensity distribution at right. (b) 0° position is median of two curves recorded with 180° rotation of PH.

Another method measures the peak angles of a number of reflections on both sides of 0°, which is equivalent to measuring 4θ. This method may be mechanically impossible with some diffractometers.

The θ–2θ setting of the specimen post is made with the diffractometer locked in the predetermined 0° position and manually (or with a stepping motor) rotating the post to the maximum intensity. A flat plate can be used as illustrated in Fig. 2.3.1.7(a) . The setting can be made to a small fraction of a degree. Fig. 2.3.1.7(b) shows the effect of incorrect θ–2θ setting, which combines with the flat-specimen aberration to cause a marked broadening and decrease of peak height but no apparent shift in peak position (Parrish, 1958). The effect increases with decreasing θ and could cause systematic errors in the peak intensities as well as incorrect profile broadening.

Figure 2.3.1.7| top | pdf | (a) θ–2θ setting at 0°. Flat plate or long narrow slit is rotated to position of highest intensity. (b) and (c) Profiles obtained with correct θ–2θ setting (solid profile) and 1 and 2° mis-settings (dashed profiles) at (b) 21° and (c) 60° (2θ).