International Tables for Crystallography Volume E: Subperiodic groups

572 Pages·2002·15.439 MB·English

by  V. Kopský, D. B. Litvin (auth.), V. Kopský, D. B. Litvin (eds.)

INTERNATIONAL TABLES
FOR
CRYSTALLOGRAPHY
International Tables for Crystallography
Volume A: Space-Group Symmetry
Editor Theo Hahn
First Edition 1983, Fifth Edition 2002
Volume B: Reciprocal Space
Editor U. Shmueli
First Edition 1993, Second Edition 2001
Volume C: Mathematical, Physical and Chemical Tables
Editors A. J. C. Wilson and E. Prince
First Edition 1992, Second Edition 1999
Volume E: Subperiodic Groups
Editors V. Kopsky´ and D. B. Litvin
First Edition 2002
Volume F: Crystallography of Biological Macromolecules
Editors Michael G. Rossmann and Eddy Arnold
First Edition 2001
Forthcoming volumes
Volume D: Physical Properties of Crystals
Editor A. Authier
Volume A1: Symmetry Relations between Space Groups
Editors H. Wondratschek and U. Mu¨ller
INTERNATIONAL TABLES
FOR
CRYSTALLOGRAPHY
Volume E
SUBPERIODIC GROUPS
Edited by
V. KOPSKY´ AND D. B. LITVIN
Published for
THE INTERNATIONAL UNION OF CRYSTALLOGRAPHY
by
KLUWER ACADEMIC PUBLISHERS
DORDRECHT/BOSTON/LONDON
2002
AC.I.P.Catalogue record for this book
isavailable from the Library ofCongress
ISBN1-4020-0715-9(acid-free paper)
Published byKluwerAcademic Publishers,
P.O.Box 17,3300AADordrecht, The Netherlands
Soldand distributed in North, Central and South America
by Kluwer Academic Publishers,
101 Philip Drive, Norwell, MA02061,USA
Inall other countries, sold and distributed
by Kluwer Academic Publishers,
P.O.Box 322,3300AHDordrecht, The Netherlands
Technical Editors: N.J.Ashcroft and G.F.Holmes
# International Union ofCrystallography 2002
Short extracts may be
reproduced without formality, provided that the
source is acknowledged, but substantial portions
may not be reproduced by any process
without written permissionfrom the
International Union ofCrystallography
Printed in Denmark by P.J.Schmidt A/S
Dedicated to
Mary
V.Kopsky´
Tikva ( ) and Professor W. Opechowski,
may their memories be blessed.
D. B. Litvin
Contributing authors
V. Kopsky´: Department of Physics, University of the South D. B. Litvin: Department of Physics, The Eberly College of
Pacific, Suva, Fiji, and Institute of Physics, The Academy of Science, Penn State – Berks Campus, The Pennsylvania State
Sciences of the Czech Republic, Na Slovance 2, PO Box 24, University, POBox 7009, Reading, PA19610–6009, USA
18040 Prague 8,Czech Republic
vi
Contents
PAGE
Preface .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ix
PART 1. SUBPERIODIC GROUP TABLES: FRIEZE-GROUP, ROD-GROUP AND LAYER-GROUP
TYPES .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1
1.1.SymbolsandtermsusedinParts1–4 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 2
1.2.Guidetotheuseofthesubperiodicgrouptables .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 5
1.2.1.Classificationofsubperiodicgroups .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 5
1.2.2.Contentsandarrangementofthetables .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 7
1.2.3.Headline .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 7
1.2.4.International(Hermann–Mauguin)symbolsforsubperiodicgroups .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 7
1.2.5.Pattersonsymmetry .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 8
1.2.6.Subperiodicgroupdiagrams .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 8
1.2.7.Origin .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 13
1.2.8.Asymmetricunit .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 14
1.2.9.Symmetryoperations .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 15
1.2.10. Generators .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 15
1.2.11. Positions .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 16
1.2.12. Orientedsite-symmetrysymbols .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 16
1.2.13. Reflectionconditions .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 16
1.2.14. Symmetryofspecialprojections .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 16
1.2.15. Maximalsubgroupsandminimalsupergroups .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 17
1.2.16. Nomenclature .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 22
1.2.17. Symbols .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 22
References .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 27
PART 2. THE 7 FRIEZE GROUPS .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 29
PART 3. THE 75 ROD GROUPS .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 37
PART 4. THE 80 LAYER GROUPS .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 219
PART 5. SCANNING OF SPACE GROUPS .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 391
5.1.SymbolsusedinParts5and6 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 392
5.2.Guidetotheuseofthescanningtables .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 393
5.2.1.Introduction .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 393
5.2.2.Thebasicconceptsofthescanning .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 394
5.2.3.Thecontentsandarrangementofthescanningtables .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 398
5.2.4.Guidelinesforindividualsystems .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 402
5.2.5.Applications .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 410
References .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 415
PART 6. THE SCANNING TABLES .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 417
Authorindex .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 561
Subjectindex .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 562
vii

Preface
By V. Kopsky´ and D. B. Litvin
This volume is divided into two sections. The first, covered in of domain walls and twin boundaries. Thus, work began on the
Parts1–4,canbeconsideredasanextensionofVolumeA:Space- relationships between space groups and subperiodic groups and
Group Symmetry, in this series of International Tables for standardsfor the subperiodic groups.
Crystallography. As Volume A treats one-, two-, and three- Itisoursubsequentcollaborationwhichhasledtothematerial
dimensional space groups, this Volume treats the two- and presented in this volume. In the many decisions concerning the
three-dimensional subperiodic groups. That is, it treats the frieze choice of symbols, origins, and settings for the subperiodic
groups, two-dimensional groups with one-dimensional transla- groups, the final choices were made based on relationships
tions, the rod groups, three-dimensional groups with one- between space groups and subperiodic groups. While these
dimensional translations, and layer groups, three-dimensional relationships are not all explicitly given here, they have been
groupswithtwo-dimensionaltranslations. Areader familiarwith implicitly used.
VolumeAshouldreadilyrecognizetheformatandcontentofthe As with any major work as this, there are those who we must
tables of Parts 1–4 of this volume. The information presented giveourthanks:toDrE.Woodsforherencouragementduringthe
aboutthesubperiodicgroupsisinthesameformatandconsistsof initial stage of this work. Dr Th. Hahn has provided advice,
thesamecontentasthatprovidedinVolumeAforspacegroups. comments,andencouragementdatingbackto1983.Constructive
A relationship between space and subperiodic groups is feedbackonreadingpartsofthisworkwerereceivedfromDrTh.
considered in Parts 5 and 6: given a crystal of a specific space- Hahn, Dr H. Wondratschek and Dr V. Janovec. The drawings in
group symmetry and a plane transecting the crystal, one can Parts1–4ofthisvolumeweredonebyStevenErb,aMechanical
enquireastowhatisthelayersubgroupofthespacegroupwhich Engineering Technology student at the Berks Campus of the
leavesthisplaneinvariant.Thephysicalmotivationforanswering PennsylvaniaStateUniversity.ThedrawingsinParts5and6were
this question is discussed in Chapter5.2. Thisisfollowed bythe donebyV.Kopsky´Jr,abiologystudentatCharlesUniversity.We
‘Scanning Tables’ in which the layer symmetries of ‘sectional’ also thank M. I. Aroyo, P. Konstantinov, E. Kroumova and M.
planesaretabulatedforallcrystallographicorientationsandforall GateshkiforconvertingthecomputerfilesofParts2,3and4from
positions (locations) of these planes. These tables also contain WordPerfect to LATEXformat.
explicitly the orbits of these planes and implicitly, via the so- The financial support received from various organizations
called‘scanninggroups’,informationabouttherodsymmetriesof duringwhichworkwasperformedleadingtoandforthisvolume
straight lines which penetrate through the crystal. fromaNationalAcademyofScience–CzechoslovakAcademyof
The history of this work dates back to 1972 when one of us Science Exchange Program (1984), the United States National
(DBL) was asked by a fellow post doc, John Berlinsky, if there Science Foundation (INT-8922251), the International Union of
existed International-like tables to classify arrays of hydrogen Crystallography, and the Pennsylvania State University is grate-
molecules on a surface with the molecules not constrained to be fully acknowledged by us. In addition, for their major additional
‘in-plane’.Tablesforthelayergroupsweresubsequentlyderived support DBL thanks the United States National Science Founda-
in the content and format of the International Tables for X-ray tion (DMR-8406196, DMR-9100418, DMR-9305825 and DMR-
Crystallography, Volume 1 (1952). It was later pointed out by a 9510335) and VK the University of the South Pacific (Fiji)
referee of Acta Crystallographica that such tables had already (Research Committee Grant 070-91111), under which a major
been published by E. Wood in 1964. Work on these tables portion of this work was completed in an idyllic setting, and the
remaineddormantuntil1983withthepublicationofVolumeAof Grant Agency of the Czech Republic (GACR 202/96/1614).
the International Tables for Crystallography, and the extensive As to the dedication, we would like to point out, to quell any
addition of new features in the description of each space group. rumorstothecontrary,thatMaryandTikva( Þare
Work began then on including these new features into tables for our respective wives. Their unending patience and constant
the layer groups. encouragement are indeed due recognition. The parenthetical
During this same time one of us (VK) was asked by Dr V. Hebrew means ‘may her memory be blessed’, and Professor W.
Janovectoinvestigatethegrouptheoreticalaspectsoftheanalysis Opechowski isincluded asDBL’sscientific ‘father’.
ix