Measuring crystals for absorption

Maslen, E. N.

doi:10.1107/97809553602060000602

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

pdf | chapter contents | chapter index | related articles

International Tables for Crystallography (2006). Vol. C. ch. 6.3, p. 608

Section 6.3.3.6. Measuring crystals for absorption

E. N. Maslen^a ^‡

^a Crystallography Centre, The University of Western Australia, Nedlands, Western Australia 6009, Australia

6.3.3.6. Measuring crystals for absorption

| top | pdf |

In general, A depends both on the shape of the crystal and on its orientation with respect to the incident and diffracted beams. To measure the shape of the crystal, a measuring microscope is mounted in the xy plane, and the crystal rotated about the z axis at right angles to that plane. A rotation about the z axis changes the orientation of the crystal x and y coordinates with respect to those (X and Y) for the measuring device. The x axis is directed from crystal to microscope when the angle of rotation about the z axis ( $[\varphi]$ ) is zero. During rotation, each face will at some stage be oriented with its normal $[N({\bf S})]$ perpendicular to the line of view, i.e. in the XY plane for instrument coordinates. If the angle of rotation at that orientation is denoted $[\varphi_N]$ , the appearance of a typical face ABCD will be as indicated in Fig. 6.3.3.4.

Figure 6.3.3.4| top | pdf |

Crystal oriented with the normal N(S) to the face ABCD in the plane of view.

The equation for the plane is $[x\sin\varphi_N+y\cos\varphi_N+z\tan\chi=Y]$ or, equivalently, $[(x\sin\varphi_N+y\cos\varphi_N)\cot\chi+z=Z.]$

For a crystal oriented on an Eulerian cradle, it is necessary to specify the orientation of the crystal, i.e. the angles $[\Omega,\chi,\varphi]$ in which the measurements of the diffraction intensities are made. In a reflecting position, the reciprocal-lattice vector S, which is normal to the Bragg planes, bisects the angle between the incident and diffracted beams, as shown in Fig. 6.3.3.5.

Figure 6.3.3.5| top | pdf |

Geometry of the Eulerian cradle in the bisecting position.

If the crystal is rotated about the reciprocal-lattice vector S, varying the angle ψ, the crystal remains in a reflecting position. That is, there is a degree of freedom in the scattering experiment that enables the same reflection to be observed at different sets of Ω, χ, $[\varphi]$ values. The path length varies with ψ, except for spherical crystals. In order to calculate an absorption correction, the value of ψ and its origin must be specified. For a crystal mounted on an Eulerian cradle, the bisecting position, with Ω = θ, is usually chosen as the origin for ψ.

References

International Tables for Crystallography (2006). Vol. C. ch. 6.3, p. 608