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

International Tables for Crystallography (2006). Vol. C, ch. 6.2, p. 596

Section 6.2.3. The angular-velocity factor

H. Lipson,a J. I. Langforda and H.-C. Hub

aSchool of Physics & Astronomy, University of Birmingham, Birmingham B15 2TT, England, and bChina Institute of Atomic Energy, PO Box 275 (18), Beijing 102413, People's Republic of China

6.2.3. The angular-velocity factor

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In experiments where the crystal is rotated or oscillated, reflection of X-rays takes place as a reciprocal-lattice point moves through the surface of the sphere of reflection. The intensity is thus proportional to the time required for the transit of the point through the surface, and so is inversely proportional to the component of the velocity perpendicular to the surface. In most experimental arrangements – the precession camera (Buerger, 1944[link]) is an exception – the crystals move with a constant angular velocity, and the perpendicular component of the velocity varies in an easily calculable way with the `latitude' of the reciprocal-lattice point referred to the axis of rotation. If the reciprocal-lattice point lies in the equatorial plane and the radiation is monochromatic – the most important case in practice – the angular-velocity factor is [{\rm cosec}\,2\theta. \eqno (6.2.3.1)]If the latitude of the reciprocal-lattice point is [\varphi], a somewhat more complex calculation shows that the factor becomes [{\rm cosec}\,\theta(\cos^2\varphi-\sin^2\theta){}^{1/2}.  \eqno (6.2.3.2)]For [\varphi=0], the expression (6.2.3.2)[link] reduces to (6.2.3.1)[link]. In some texts, [\varphi] is used for the co-latitude; this and various trigonometric identities can give superficially very different appearances to (6.2.3.2)[link].

References

Buerger, M. J. (1944). The photography of the reciprocal lattice. American Society for X-ray and Electron Diffraction, Monograph No. 1.








































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