International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. C. ch. 2.5, p. 84

Section 2.5.1.1. Recording of powder diffraction spectra

B. Burase‡ and L. Gerwardb

2.5.1.1. Recording of powder diffraction spectra

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In XED powder work, the incident- and scattered-beam directions are determined by slits (Fig. 2.5.1.1[link]). A powder spectrum is shown in Fig. 2.5.1.2[link]. The Bragg equation is [2d\sin \theta _0=\lambda =hc/E,\eqno(2.5.1.1a)]where d is the lattice-plane spacing, [\theta_0] the Bragg angle, λ and E the wavelength and the photon energy, respectively, associated with the Bragg reflection, h is Planck's constant and c the velocity of light. In practical units, equation (2.5.1.1a[link]) can be written [E({\rm keV})\,d(\,\AA)\sin \theta_0=6.199.\eqno (2.5.1.1b)]The main features of the XED powder method where it differs from standard angle-dispersive methods can be summarized as follows:

  • (a) The incident beam is polychromatic.

    [Figure 2.5.1.1]

    Figure 2.5.1.1| top | pdf |

    Standard and conical diffraction geometries: 2θ0 = fixed scattering angle. At low scattering angles, the lozenge-shaped sample volume is very long compared with the beam cross sections (after Häusermann, 1992[link]).

    [Figure 2.5.1.2]

    Figure 2.5.1.2| top | pdf |

    XED powder spectrum of BaTiO3 recorded with synchrotron radiation from the electron storage ring DORIS at DESY-HASYLAB in Hamburg, Germany. Counting time 1 s. Escape peaks due to the Ge detector are denoted by e (from Buras, Gerward, Glazer, Hidaka & Olsen, 1979[link]).

  • (b) The scattering angle [2\theta_0] is fixed during the measurement but can be optimized for each particular experiment. There is no mechanical movement during the recording.

  • (c) The whole energy spectrum of the diffracted photons is recorded simultaneously using an energy-dispersive detector.

The scattering angle is chosen to accommodate an appropriate number of Bragg reflections within the available photon-energy range and to avoid overlapping with fluorescence lines from the sample and, when using an X-ray tube, characteristic lines from the anode. Overlap can often be avoided because a change in the scattering angle shifts the diffraction lines to new energy positions, whereas the fluorescence lines always appear at the same energies. Severe overlap problems may be encountered when the sample contains several heavy elements.

The detector aperture usually collects only a small fraction of the Debye–Scherrer cone of diffracted X-rays. The collection of an entire cone of radiation greatly increases the intensities. Also, it makes it possible to overcome crystallite statistics problems and preferred orientations in very small samples (Holzapfel & May, 1982[link]; Häusermann, 1992[link]).

References

First citation Buras, B., Gerward, L., Glazer, A. M., Hidaka, M. & Olsen, J. S. (1979). Quantitative structural studies by means of the energy-dispersive method with X-rays from a storage ring. J. Appl. Cryst. 12, 531–536.Google Scholar
 First citation Häusermann, D. (1992). New techniques for new sources: a fresh look at energy-dispersive diffraction for high-pressure studies. High Press. Res. 8, 647–654.Google Scholar
 First citation Holzapfel, W. B. & May, W. (1982). Improvements in energy dispersive X-ray diffraction with conical slit and diamond cell. High-pressure research in geophysics, edited by S. Akimoto & M. H. Manghnani, pp. 73–80, and references therein. Dordrecht: Reidel.Google Scholar








































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