Diffractometer errors

W. N. Schreiner and C. Surdowski, Systematic and random powder diffractometer errors relevant to phase identification, Norelco Rep., 1983, 30 IX, 40 4. 

Blessing, R.H. (1989) DREADD - data reduction and error analysis for single-crystal diffractometer... 

As with most instruments, erroneous results may be obtained if the high resolution diffractometer is not correctly set up. In modem instmments this is greatly assisted by the manufacturers, by prealigned components, permanent alignment on installation and by automated algorithms for specimen alignment. The primary errors to be considered are... 

Friedel-opposite reflections, hkl and — h, — k, — / (or, eventually, symmetry-equivalents thereof26), should always be measured. Several potential sources of systematic error can be minimized by measuring hkl at diffractometer setting angles of 20. a, q>. followed immediately by — h, — k, — at — 20, to — 20, X- [Pg.386]

X-ray graphical investigations were performed on an automatic assembly including a diffractometer DRON-UM-1 (Cu K -cmission) and the managing computer. The error of definition of interplanar spacing did not exceed 0.0005 nm. 

The proper extrapolation function depends on the type of diffractometer used for the measmements. Generally such functions are provided in the software provided with the instrument. Several somces of error need to be taken into account to insme that they are dealt with before undertaking the measmements. 

Displacement of the sample from the diffractometer axis. This is usually the largest error so care must be taken to properly place the sample. 

In modem diffractometers both scanning modes result in nearly identical quality of experimental data. A step scan is usually considered as the one with less significant positioning errors, which could be important in experiments where the maximum lattice parameter precision is essential. Continuous scans are used most often for fast experiments, whereas step scans are usually employed in overnight or weekend experiments. 

In problems 4-8, the data were collected on a powder diffractometer with Bragg-Brentano geometry using Cu Ka radiation. Errors in (/-spacing should not exceed 0.02 A for (/ > 3 A, otherwise they should be less than 0.01 A. 

In ideal conditions, an X-ray beam focuses on a specimen and the intensity of diffraction from the specimen is detected accurately at the 26 angle. The focusing arrangement in a diffractometer, however, cannot ensure true focusing due to features of the X-ray source and specimen. Thus, errors due to parafocusing always exist. The errors of parafocusing are referred... 

Figure 2.17 System aberrations of the X-ray diffractometer due to axial-divergence and flat-specimen errors. (Reproduced with permission from R. Jenkins and R.L. Snyder, Introduction to X-ray Powder Diffractometry, John Wiley Sons Inc., New York. 1996 John Wiley Sons Inc.)...

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. 

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