International Tables for Crystallography (2019). Vol. H. ch. 3.1, pp. 224-251
https://doi.org/10.1107/97809553602060000946

Chapter 3.1. The optics and alignment of the divergent-beam laboratory X-ray powder diffractometer and its calibration using NIST standard reference materials

Contents

  • 3.1. The optics and alignment of the divergent-beam laboratory X-ray powder diffractometer and its calibration using NIST standard reference materials  (pp. 224-251) | html | pdf | chapter contents |
    J. P. Cline, M. H. Mendenhall, D. Black, D. Windover and A. Henins
    • 3.1.1. Introduction  (p. 224) | html | pdf |
    • 3.1.2. The instrument profile function  (pp. 224-230) | html | pdf |
    • 3.1.3. Instrument alignment  (pp. 230-235) | html | pdf |
    • 3.1.4. SRMs, instrumentation and data-collection procedures  (pp. 235-238) | html | pdf |
    • 3.1.5. Data-analysis methods  (pp. 238-241) | html | pdf |
    • 3.1.6. Instrument calibration  (pp. 241-250) | html | pdf |
    • 3.1.7. Conclusions  (p. 250) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 3.1.1. A schematic diagram illustrating the operation and optical components of a Bragg–Brentano X-ray powder diffractometer  (p. 224) | html | pdf |
      • Fig. 3.1.2. A schematic diagram illustrating the operation and optical components of a Bragg–Brentano X-ray diffractometer equipped with a position-sensitive detector  (p. 225) | html | pdf |
      • Fig. 3.1.3. A schematic diagram illustrating the geometry of a Johansson incident-beam monochromator  (p. 225) | html | pdf |
      • Fig. 3.1.4. Diagrammatic representations of convolutions leading to the observed XRPD profile  (p. 226) | html | pdf |
      • Fig. 3.1.5. The flat specimen error aberration profile as a function of incident-slit size (R = 217.5 mm)  (p. 227) | html | pdf |
      • Fig. 3.1.6. The flat specimen error aberration profiles for a 1° incident slit as a function 2θ (R = 217.5 mm)  (p. 227) | html | pdf |
      • Fig. 3.1.7. The PSD defocusing error aberration profiles for a silicon strip PSD as a function of window width (R = 217.5 mm, incident slit = 1° and strip width = 75 µm)  (p. 227) | html | pdf |
      • Fig. 3.1.8. Axial divergence aberration profiles shown for several levels of axial divergence  (p. 228) | html | pdf |
      • Fig. 3.1.9. Axial divergence aberration profiles for primary and secondary Soller slits of 2.3° as a function of 2θ (R = 217.5 mm)  (p. 228) | html | pdf |
      • Fig. 3.1.10. Linear attenuation aberration profiles that would roughly correspond to SRMs 676a (50 cm−1), 640e and 1976b (100 cm−1), and 660c (800 cm−1) at 90° 2θ, where the transparency effect is at a maximum (R = 217.5 mm)  (p. 228) | html | pdf |
      • Fig. 3.1.11. The emission spectrum of Cu Kα radiation as provided by Hölzer et al  (p. 229) | html | pdf |
      • Fig. 3.1.12. Illustration of the Kα3 lines and tube-tails contributions to an observed profile on a log scale, shown with two fits: the fundamental-parameters approach, which includes these features, and the split pseudo-Voigt PSF, which does not  (p. 229) | html | pdf |
      • Fig. 3.1.13. Illustration of the effect of the Johansson optic on the Cu Kα emission spectrum  (p. 229) | html | pdf |
      • Fig. 3.1.14. Diagrammatic explanation of the conditions necessary to realize a properly aligned X-ray powder diffractometer  (p. 230) | html | pdf |
      • Fig. 3.1.15. Diagrammatic view illustrating the use of a knife edge to determine the 2θ zero angle  (p. 231) | html | pdf |
      • Fig. 3.1.16. Diagrammatic view of the glass tunnel for determination of θ and 2θ zero angles  (p. 232) | html | pdf |
      • Fig. 3.1.17. Design of experiments using a pinhole optic to align the X-ray source with the receiving slit  (p. 232) | html | pdf |
      • Fig. 3.1.18. Successful results from the pinhole experiment showing variation in profile shape with successive adjustment of tube tilt; the central peak of highest intensity indicates the state of parallelism between the source and the receiving slit  (p. 232) | html | pdf |
      • Fig. 3.1.19. Results from 2θ scans at successive θ angles using the glass tunnel to determine the θ and 2θ zero angles  (p. 233) | html | pdf |
      • Fig. 3.1.20. Diagram of hypothetical results from two zero-angle measurements (Fig  (p. 233) | html | pdf |
      • Fig. 3.1.21. Final results from a θ–2θ scan using the glass tunnel, indicating the correct determination of θ and 2θ zero angles  (p. 233) | html | pdf |
      • Fig. 3.1.22. Figures found within the instructions for a Siemens D500 incident-beam monochromator in a Huber 611 monochromator housing, illustrating image formation and movement for correct and incorrect settings of tilt and azimuth angles (reproduced with verbal permission from Huber)  (p. 234) | html | pdf |
      • Fig. 3.1.23. The X-ray powder diffractometer designed and fabricated at NIST, in conventional divergent-beam format  (p. 237) | html | pdf |
      • Fig. 3.1.24. The NIST-built powder diffractometer configured with the Johansson incident-beam monochromator and a position-sensitive detector  (p. 237) | html | pdf |
      • Fig. 3.1.25. Diagrammatic representation of a powder-diffraction line profile, illus­trating the metrics Δ(2θ) and half-width-at-half-maximum (HWHM)  (p. 238) | html | pdf |
      • Fig. 3.1.26. Δ(2θ) curve using SRM 660b illustrating the peak-position shifts as function of 2θ  (p. 239) | html | pdf |
      • Fig. 3.1.27. Simulated and actual FWHM data from SRM 660b using the two Voigt PSFs with (`with Caglioti') and without constraints  (p. 239) | html | pdf |
      • Fig. 3.1.28. Left and right HWHM data from SRM 660b using the split pseudo-Voigt PSF fitted with uniform weighting  (p. 239) | html | pdf |
      • Fig. 3.1.29. Comparison of Δ(2θ) curves determined with profile fitting of SRM 660b data without the use of any constraints, as a function of 2θ  (p. 242) | html | pdf |
      • Fig. 3.1.30. Δ(2θ) curves from SRM 660b determined with profile fitting using the Caglioti function and the unconstrained split pseudo-Voigt PSF with uniform weighting  (p. 242) | html | pdf |
      • Fig. 3.1.31. FWHM data from SRM 660b using various split PSFs fitted without constraints  (p. 242) | html | pdf |
      • Fig. 3.1.32. Fits of the split pseudo-Voigt PSF to the low-angle 100, mid-angle 310 and high-angle 510 lines from SRM 660b illustrating the erroneous peak position and FWHM value reported for the 100 and 510 lines, respectively  (p. 243) | html | pdf |
      • Fig. 3.1.33. FWHM data from fits of the split pseudo-Voigt and split Pearson VII PSFs to simulated low- and high-resolution data  (p. 244) | html | pdf |
      • Fig. 3.1.34. Fits of a split Pearson VII PSF to data from SRM 660b collected using a Johansson IBM  (p. 245) | html | pdf |
      • Fig. 3.1.35. Δ(2θ) curves from the NIST machine configured with a Johansson IBM, illustrating a comparison of results from second-derivative and various profile-fitting methods  (p. 245) | html | pdf |
      • Fig. 3.1.36. FWHM data from SRM 660b collected using the NIST machine configured with a Johansson IBM, illustrating a comparison of results from various profile-fitting and data-collection methods  (p. 245) | html | pdf |
      • Fig. 3.1.37. FWHM data from SRM 660b collected using the NIST machine configured with a Johansson IBM and PSD, illustrating the contribution to defocusing at low angles with increasing window width  (p. 246) | html | pdf |
      • Fig. 3.1.38. FWHM data from SRMs 640e, 1976b and 660c collected with the IBM and PSD (4 mm window) and fitted using the split Pearson VII PSF with uniform weighting  (p. 246) | html | pdf |
      • Fig. 3.1.39. Fits of three SRM 660b lines obtained with a Rietveld analysis using the Thompson, Cox and Hastings formalism of the pseudo-Voigt PSF and the Finger model for asymmetry  (p. 247) | html | pdf |
      • Fig. 3.1.40. Fits of SRM 676a obtained from a Rietveld analysis using GSAS with the Thompson, Cox and Hastings formalism of the pseudo-Voigt PSF and the Finger model for asymmetry  (p. 248) | html | pdf |
      • Fig. 3.1.41. Fit quality realized with a fundamental-parameters-approach analysis of SRM 660b peak-scan data using TOPAS  (p. 248) | html | pdf |
      • Fig. 3.1.42. Δ(2θ) data from the 20 data sets collected for the certification of SRMs 660c and 640e, determined via FPA analyses using TOPAS  (p. 249) | html | pdf |
      • Fig. 3.1.43. Qualification of a machine using SRM 1976b  (p. 250) | html | pdf |
    • Tables
      • Table 3.1.1. Aberrations comprising the geometric component of the IPF  (p. 226) | html | pdf |
      • Table 3.1.2. Run-time parameters used for collection of the data used for certification of SRM 660b  (p. 238) | html | pdf |