International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 2.7, pp. 162-163

Section 2.7.8. Single-crystal data collection

A. Katrusiaka*

aFaculty of Chemistry, Adam Mickiewicz University, Poznań, Poland
Correspondence e-mail: katran@amu.edu.pl

2.7.8. Single-crystal data collection

| top | pdf |

It is essential that a crystal sample is centred precisely on the diffractometer. Optical centring of a crystal is hampered by the limited view of the sample through the DAC windows in one direction only and by the strong refractive index of diamonds. Consequently, diffractometric methods of crystal centring are more precise for DAC centring. Hamilton's method comparing the diffractometer setting angles of reflections at equivalent positions (Hamilton, 1974[link]) was modified for the purpose of the DAC by King & Finger (1979[link]) and then generalized for any reflections, not necessarily at equivalent positions (Dera & Katrusiak, 1999[link]). These methods are very precise, but they require the approximate orientation matrix (UB matrix) of the sample crystal (Busing & Levy, 1967[link]) to be known and the reflections to be indexed. This information was determined at the beginning of an experiment when traditional diffractometers with a point detector were used. However, nowadays diffractometers with area detectors are used, and generally the crystal orientation is not determined before collecting the diffraction data. To meet these requirements, a new efficient and semi-automatic method was devised, whereby the diffractometer measures a sequence of shadows of the gasket on the CCD detector and calculates the required corrections to the DAC position along the goniometer-head translations (Budzianowski & Katrusiak, 2004[link]). Precise centring can only be achieved for very stable goniometer heads that do not yield under the weight of the DAC (Katrusiak, 1999[link]).

The mode of data collection for a sample enclosed in a DAC can affect the data quality considerably. Data for a bare crystal on a four-circle diffractometer with a scintillation point detector were measured in the so-called bisecting mode, where the ω angle [diffractometer-axes positioning angles ω, χ, ϕ and θ of the Eulerian cradle will be used here (Busing & Levy, 1967[link]), unless otherwise noted] was fixed to 0° and not used in the process of crystal positioning. In other words, the shaft ϕ and circle χ lie in the plane bisecting the angle formed by the incident beam and the reflection actually measured. The bisecting mode was optimal for avoiding collisions between the diffractometer shafts and detector, and also minimized absorption effects for most vertically mounted samples. However, these features are irrelevant for samples enclosed in a DAC. It was shown by Finger & King (1978[link]) that the DAC absorption of the incident and reflected beams is a minimum when the Eulerian goniometer ϕ axis is not used and is always set to 0°. Hence, this is called the ϕ = 0° mode. The ϕ = 0° mode also minimizes the effect of the sample being shadowed by the gasket edges (Katrusiak, 2008[link]). Moreover, in the ϕ = 0° mode the DAC axis always lies in the diffraction plane of the diffractometer, which gives maximum access to the reciprocal-lattice nodes (Fig. 2.7.6[link]).

The advent of area detectors facilitated high-pressure experiments considerably and extended the range of attainable conditions to simultaneous very high pressure and temperatures of several thousand kelvin. Single-crystal experiments are easier because the diffraction data can be recorded before the orientation matrix UB of the crystal is determined (Busing & Levy, 1967[link]; Finger & King, 1978[link]). The recorded data can thus be analysed after the experiment and all relevant structural models can be tested. The use of area detectors shortens the data-collection times for both single-crystal and powder diffraction measurements, and this is particularly efficient with the extremely intense X-ray beams provided by synchrotrons. In single-crystal experiments, several or even tens of reflections are partly scanned through or fully recorded in one image. Although these reflections are not each recorded at their optimum diffractometer settings, corresponding to the ϕ = 0° mode setting described above, the redundancy of the data is increased and the intensities can be corrected for the absorption coefficients derived from differences between equivalent reflections. It is also advantageous that simultaneous diffraction events in the sample crystal and in one or both of the diamonds, which occur sporadically and weaken the recorded reflections, can be eliminated by comparing the intensities of the same reflection measured at several ψ angle positions as well as the equivalent reflections. Equivalent reflections measured at different positions are particularly useful for eliminating systematic errors in the data collection.

It is important that the so called `run list', defining the diffractometer setting angles and scan directions for the detector exposures, takes into account the ϕ = 0° mode of the DAC orientations, for which access to the DAC is still on average at its widest and the DAC absorption and gasket-shadowing effects are on average the smallest. Most importantly, such an optimum setting can be executed with a four-circle diffractometer, and cannot be done on simplified diffractometers with the ϕ shaft fixed at a χ angle of about 50°. Even fewer reflections can be accessed when the DAC is rotated about one axis only, which is still the case for some laboratory and synchrotron diffractometers.

References

Budzianowski, A. & Katrusiak, A. (2004). High-pressure crystallographic experiments with a CCD detector. In High-Pressure Crystallography, edited by A. Katrusiak & P. F. McMillan, pp. 101–112. Dordrecht: Kluwer.Google Scholar
Busing, W. R. & Levy, H. A. (1967). Angle calculations for 3- and 4-circle X-ray and neutron diffractometers. Acta Cryst. 22, 457–464.Google Scholar
Dera, P. & Katrusiak, A. (1999). Diffractometric crystal centering. J. Appl. Cryst. 32, 510–515.Google Scholar
Finger, L. W. & King, H. E. (1978). A revised method of operation of the single-crystal diamond cell and refinement of the structure of NaCl at 32 kbar. Am. Mineral. 63, 337–342.Google Scholar
Hamilton, W. C. (1974). International Tables for X-ray Crystallography, Vol. IV, pp. 273–284. Birmingham: Kynoch Press.Google Scholar
Katrusiak, A. (1999). A hinge goniometer head. J. Appl. Cryst. 32, 576–578.Google Scholar
Katrusiak, A. (2008). High-pressure crystallography. Acta Cryst. A64, 135–148.Google Scholar
King, H. E. & Finger, L. W. (1979). Diffracted beam crystal centering and its application to high-pressure crystallography. J. Appl. Cryst. 12, 374–378.Google Scholar








































to end of page
to top of page