Table 2.2.3.1

Helliwell, J. R.

doi:10.1107/97809553602060000577

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. 2.2, p. 32

Table 2.2.3.1

J. R. Helliwell^a

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

Table 2.2.3.1 | top | pdf |
Glossary of symbols used to specify quantities on diffraction patterns and in reciprocal space

$[\theta]$	Bragg angle
$[2\theta]$	Angle of deviation of the reflected beam with respect to the incident beam
$[\hat{\bf S}_o]$	Unit vector lying along the direction of the incident beam
$[\hat{\bf S}]$	Unit vector lying along the direction of the reflected beam
s = $[(\hat{\bf S}-\hat{\bf S}_o)]$	The scattering vector of magnitude $[2\sin\theta]$ . s is perpendicular to the bisector of the angle between $[\hat{\bf S}_o]$ and $[\hat{\bf S}]$ . s is identical to the reciprocal-lattice vector d* of magnitude λ/d, where d is the interplanar spacing, when d* is in the diffraction condition. In this notation, the radius of the Ewald sphere is unity. This convention is adopted because it follows that in Volume II of International Tables (p. 175). Note that in Section 2.2.1 Laue geometry the alternative convention (\|d*\| = 1/d) is adopted whereby the radius of each Ewald sphere is 1/λ. This allows a nest of Ewald spheres between $[1/\lambda_{\max}]$ and $[1/\lambda_{\min}]$ to be drawn
$[\zeta]$	Coordinate of a point P in reciprocal space parallel to a rotation axis as the axis of cylindrical coordinates relative to the origin of reciprocal space
$[\xi]$	Radial coordinate of a point P in reciprocal space; that is, the radius of a cylinder having the rotation axis as axis
$[\tau]$	The angular coordinate of P, measured as the angle between $[\xi]$ and $[\hat{\bf S}_o]$ [see Fig. 2.2.3.1(b)]
$[\varphi]$	The angle of rotation from a defined datum orientation to bring a relp onto the Ewald sphere in the rotation method (see Fig. 2.2.3.3)
$[\mu]$	The angle of inclination of $[\hat{\bf S}_o]$ to the equatorial plane
$[\Upsilon]$	The angle between the projections of $[\hat{\bf S}_o]$ and $[\hat{\bf S}]$ onto the equatorial plane
$[\nu]$	The angle of inclination of $[\hat{\bf S}]$ to the equatorial plane
$[\omega,\chi,\varphi]$	The crystal setting angles on the four-circle diffractometer (see Fig. 2.2.6.1). The $[\varphi]$ used here is not the same as that in the rotation method (Fig. 2.2.3.3). This clash in using the same symbol twice is inevitable because of the widespread use of the rotation camera and four-circle diffractometer.

The equatorial plane is the plane normal to the rotation axis.