Rotating-crystal method

Gałdecka, E.

doi:10.1107/97809553602060000597

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

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International Tables for Crystallography (2006). Vol. C. ch. 5.3, pp. 508-509

Section 5.3.2.3.1. Rotating-crystal method

E. Gałdecka^a

^a Institute of Low Temperature and Structure Research, Polish Academy of Sciences, PO Box 937, 50-950 Wrocław 2, Poland

5.3.2.3.1. Rotating-crystal method

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The rotating-crystal method – the simplest of the moving-crystal methods – determines the identity period I along the axis of rotation (or oscillation), $[{\bf r}=u{\bf a}+v{\bf b}+w{\bf c}]$ , from the formula $[I(uvw)=n\lambda/\sin \nu, \eqno (5.3.2.1)]$ in which n is the number of the layer line and ν is the angle between the directions of the primary and diffracted beams.

The angle ν is determined from the measurement of the distance [l_n] between two lines corresponding to the same layer number n from the equation $[\tan \nu=l_n/R, \eqno \eqno (12)]$ where R is the camera radius.

All the lattice parameters may be determined from separate photographs made for rotations of the crystal along different rotation axes, i.e. the system axis, plane and spatial diagonals (Evans & Lonsdale, 1959), without indexing the photographs. In practice, however, this method is rarely used alone and is most often applied together with other photographic methods (for example, the Weissenberg method), but it is a useful preliminary stage for other methods. In particular, the length of a unit-cell vector may be directly determined if the rotation axis coincides with this vector.

Advantages of this method are:

(a) simple equipment (only rotation of the crystal is required, since the film is stationary);
(b) immediate determination of direct-cell parameters (photographs obtained with other cameras afford information about reciprocal-lattice parameters only);
(c) indexing of the photographs is unnecessary.

Drawbacks of the method are:

(a) poor precision and accuracy of the measurement $[(|\delta d|/d\approx10^{-2})]$ ;
(b) small amount of information from a single photograph (one parameter only);
(c) necessity of taking several photographs in the case of a lower-symmetry system if this method is the only one used.

References

Evans, H. T. Jr & Lonsdale, K. (1959). Diffraction geometry. International tables for X-ray crystallography, Vol. II, Chap. 4. Birmingham: Kynoch Press.Google Scholar

International Tables for Crystallography (2006). Vol. C. ch. 5.3, pp. 508-509