Space groups – the final frontier: a tutorial guided tour of some entries in International Tables for Crystallography Volume A

Abstract

After an introductory section providing some basic foundation, definitions, and terminology regarding space group symmetry in crystal structures, three particular examples are selected to demonstrate the information given for each space-group type in the standard reference book International Tables for Crystallography Volume A (current sixth edition). The format and layout of the information is explained, and the most important items of the content are described, together with some practical applications. This treatment should enable readers unfamiliar with the tables to use them confidently in understanding and interpreting crystal structures belonging to these and other space-group types.

KEYWORDS:

• Symmetry
• space groups
• space-group types
• point groups
• International Tables for Crystallography
• symmetry element
• geometric element
• symmetry operation
• crystal systems
• asymmetric unit
• general position
• special position
• crystal class
• Laue class
• multiplicity
• reflection conditions
• polar axis

Acknowledgements

I thank John Wiley & Sons Ltd for permission to reproduce four pages of International Tables for Crystallography, Volume A, 6th edition, as Figures 1–4. This work has not received any specific funding support.

Disclosure statement

No potential conflict of interest was reported by the author.

Subject index

Asymmetric unit, 7, 10

Cambridge Structural Database, 11, 15

Centred unit cell, 4, 15

Chiral, 10, 11, 13

Crystal class, 4, 7, 8

Crystal systems, 5, 7

Geometric element 3, 5, 7

Enantiomorphous, 4, 15

Friedel’s Law, 7

General position, 8, 10, 11, 13, 15

Glide plane, 4, 8, 12, 13

Hermann-Mauguin (international) notation, 3, 5

Identity operation, 3, 11

Improper rotation, 3

Inversion, 3, 6, 7, 8, 13, 14

International Tables for Crystallography, Volume A, 2, 8, 17

IUCr online dictionary, 3

Lattice, 3, 4, 5, 6

Laue class, 7, 8, 15

Multiplicity, 11, 14

Non-primitive, 11, 15

Origin, 7, 9, 13, 15, 17

Point group, 4, 5, 7

Point-group type, 5

Polar axis, 17

Proper rotation, 3, 4

Reflection, 3, 4, 6, 13, 14

Reflection conditions, 11, 14, 17

Schoenflies notation, 3, 4, 8

Screw axis, 4, 8, 9, 10, 14, 15

Site symmetry, 8, 11, 13, 15, 17

Space group, 2,4, 5, 6, 7

Space-group type, 5

Special position, 8, 10, 13, 14, 15, 17

Symmetry elements, 2, 3, 4, 6, 7, 9, 11, 15

Symmetry operations, 2, 3, 4, 5, 10, 11, 13, 15

Systematic absences, 11

Translation symmetry, 2, 3, 4, 5, 7, 10

Unit cell, 2, 4, 5, 6, 7, 11

Wyckoff letter, 11, 13, 14, 15, 17