Symmetry elements producing systematic absences

Shmueli, U.; Wilson, A. J. C.

doi:10.1107/97809553602060000554

International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

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International Tables for Crystallography (2006). Vol. B. ch. 2.1, pp. 191-192 | 1 | 2 |

Section 2.1.3.1. Symmetry elements producing systematic absences

U. Shmueli^a ^* and A. J. C. Wilson^b ^‡

^a School of Chemistry, Tel Aviv University, Tel Aviv 69 978, Israel, and ^bSt John's College, Cambridge, England
Correspondence e-mail: ushmueli@post.tau.ac.il

2.1.3.1. Symmetry elements producing systematic absences

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Symmetry elements can be divided into two types: those that cause systematic absences and those that do not. Those producing systematic absences (glide planes and screw axes) produce at the same time groups of reflections (confined to zones and rows in reciprocal space, respectively) with an average intensity an integral¹ multiple of the general average. The effects for single symmetry elements of this type are given in Table 2.1.3.1 for the general reflections [hkl] and separately for any zones and rows that are affected. The `average multipliers' are given in the column headed $[\langle I \rangle/\Sigma]$ ; `distribution' and `distribution parameters' are treated in Section 2.1.5. As for the centring, the fraction of reflections missing and the integer multiplying the average are related in such a way that the overall intensity is unchanged. The mechanism for compensation for the reflections with enhanced intensity is obvious.

Table 2.1.3.1 | top | pdf |
Intensity-distribution effects of symmetry elements causing systematic absences

Abbreviations and orientation of axes: A = acentric distribution, C = centric distribution, Z = systematically zero, S = distribution parameter, 〈I〉 = average intensity. Axes are parallel to c, planes are perpendicular to c.

Element	Reflections	Distribution	$[S/\Sigma]$	$[\langle I\rangle/\Sigma]$
$[2_{1}]$	hkl	A	1	1
	hk 0	C	1	1
	00l		1	2
$[3_{1}, 3_{2}]$	hkl	A	1	1
	hk 0	A	1	1
	00l		1	3
$[4_{1}, 4_{3}]$	hkl	A	1	1
	hk 0	C	1	1
	00l		1	4
$[4_{2}]$	hkl	A	1	1
	hk 0	C	1	1
	00l		2	4
$[6_{1}, 6_{5}]$	hkl	A	1	1
	hk 0	C	1	1
	00l		1	6
$[6_{2}, 6_{4}]$	hkl	A	1	1
	hk 0	C	1	1
	00l		2	6
$[6_{3}]$	hkl	A	1	1
	hk 0	C	1	1
	00l		3	6
a	hkl	A	1	1
	hk 0		1	2
	00l	C	1	1
	0k0	A	2	2
C , I	All		1	2
F	All		1	4