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

International Tables for Crystallography (2006). Vol. C. ch. 2.2, p. 35

Section 2.2.5.2. Crystal setting

J. R. Helliwella

a Department of Chemistry, University of Manchester, Manchester M13 9PL, England

2.2.5.2. Crystal setting

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Setting of the crystal for one zone is carried out in two stages. First, a Laue photograph is used for small molecules or a monochromatic still for macromolecules to identify the required zone axis and place it parallel to the X-ray beam. This is done by adjustment to the camera-spindle angle and the goniometer-head arc in the horizontal plane. This procedure is usually accurate to a degree or so. Note that the vertical arc will only rotate the pattern around the X-ray beam. Second, a screenless precession photograph is taken using an angle of ∼7–10° for small molecules or 2–3° for macromolecules. It is better to use unfiltered radiation, as then the edge of the zero-layer circle is easily visible. Let the difference of the distances from the centre of the pattern to the opposite edges of the trace in the direction of displacement be called δ = DΔ so that for the horizontal goniometer-head arc and the dial: δarc = xRtxLt and δdial = yUpyDn (Fig. 2.2.5.1[link] ). The corrections [\varepsilon] to the arc and camera spindle are given by [\Delta={\delta\over D}={\sin4\varepsilon\cos\bar\mu\over\cos^22\varepsilon-\sin^2\bar\mu}\rm\ in\ r.l.u.,\eqno (2.2.5.1)]where D is the crystal-to-film distance and [\bar\mu] is the precession angle.

[Figure 2.2.5.1]

Figure 2.2.5.1| top | pdf |

The screenless precession setting photograph (schematic) and associated mis-setting angles for a typical orientation error when the crystal has been set previously by a monochromatic still or Laue.

It is possible to measure δ to about 0.3 mm (δ = 1 mm corresponds to 14′ error for D = 60 mm and [\bar\mu\simeq 7 ^\circ] [Table 2.2.5.1[link], based on IT II (1959[link], p. 200)].

Table 2.2.5.1| top | pdf |
The distance displacement (in mm) measured on the film versus angular setting error of the crystal for a screenless precession ([\bar\mu=5^\circ]) setting photograph

Angular correction, [\varepsilon], in degrees and minutes[\Delta] r.l.u Distance displacement (mm) for three crystal-to-film distances
60 mm75 mm100 mm
00000
15′0.01751.11.31.8
30′0.0352.12.63.5
45′0.05263.24.05.3
60′0.0704.25.37.0
1° 15′0.0875.26.58.7
1° 30′0.1056.37.910.5
1° 45′0.1237.49.212.3
0.1408.410.514.0

Alternatively, Δ = δ/D [\simeq\sin4\varepsilon] can be used if [\varepsilon] is small [from equation (2.2.5.1)[link]].

Notes

  • (1) A value of [\bar\mu] of 5° is assumed although there is a negligible variation in [\varepsilon] with [\bar\mu] between 3° (typical for proteins) and 7° (typical for small molecules).

  • (2) Crystal-to-film distances on a precession camera are usually settable at the fixed distance D = 60, 75, and 100 mm.

  • (3) This table should be used in conjunction with Fig. 2.2.5.1[link].

  • (4) Values of [\varepsilon] are given in intervals of 5′ as this is convenient for various goniometer heads which usually have verniers in 5′, 6′ or 10′ units. The vernier on the spindle of the precession camera is often in 2′ units.


References

First citation International Tables for X-ray Crystallography (1959). Vol. II. Birmingham: Kynoch Press.Google Scholar








































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