Basic elements of crystallography

324 Pages·2016·51.786 MB·English

by  Gonzalez Szwacki, Nevill, Szwacka, Teresa

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graduate levels.
Nevill Gonzalez Szwacki
NNeevvilill lG Goonnzazalelez zS Szwzwaackckii
Nevill Gonzalez Szwacki
Teresa Szwacka
TeTereresasa S Szwzwaackckaa
Teresa Szwacka
V455
ISIBSNB NI9S 7B98N7-89 9-89718-8V41--649415863511V--3454V-6755-4165735-6-557-6
ISBN 978-981-4613-57-6
BASIC ELEMENTS OF
CRYSTALLOGRAPHY

BASIC ELEMENTS OF
CRYSTALLOGRAPHY
2nd Edition
Nevill Gonzalez Szwacki
Teresa Szwacka
CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2016 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20160322
International Standard Book Number-13: 978-981-4613-58-3 (eBook - PDF)
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March4,2016 15:39 PSPBook-9inx6in 00-Nevill-Gonzalez-Szwack-prelims
Contents
Preface ix
Abbreviations xi
1 One-andTwo-DimensionalCrystalLattices 1
1.1 Introduction 1
1.2 One-DimensionalCrystalStructures 1
1.3 Two-DimensionalCrystalStructures 5
1.4 CrystallographicPointandSpaceGroupsinTwo
Dimensions 19
1.5 WyckoffPosition 23
2 Three-DimensionalCrystalLattices 43
2.1 Introduction 43
2.2 ExamplesofSymmetryAxesofThree-Dimensional
Figures 44
2.3 RotationAxesofaCube 47
2.4 RotationAxesofaSetofPoints 48
2.5 CrystalSystems 51
2.6 TheRhombohedronandHexagonalPrism 54
2.7 The14BravaisLattices 56
2.7.1 Introduction 56
2.7.2 TheTriclinicSystem 57
2.7.3 TheMonoclinicSystem 57
2.7.4 TheOrthorhombicSystem 59
2.7.5 TheTetragonalSystem 62
2.7.6 TheCubicSystem 62
2.7.7 TheTrigonalandHexagonalSystems 63
2.7.8 SymbolsfortheBravaisLattices 63
2.7.9 FinalRemarks 64
March4,2016 15:39 PSPBook-9inx6in 00-Nevill-Gonzalez-Szwack-prelims
vi Contents
2.8 CoordinationNumber 66
2.9 BodyCenteredCubicLattice 67
2.10FaceCenteredCubicLattice 70
2.11RhombohedralUnitCellinaCubicLattice 74
2.11.1Introduction 74
2.11.2ARhombohedralUnitCellofthescLattice 74
2.11.3SimpleCubicCrystalStructure 76
2.11.4InterpretationofDataforAs,Sb,Bi,andHg 77
2.12RhombohedralLattice 79
2.13TripleHexagonalRCellintheCubicLattice 82
2.14Wigner–SeitzCell 84
2.14.1Introduction 84
2.14.2ConstructionoftheWigner–SeitzCell 84
2.14.3TheWigner–SeitzCellofthebccLattice 85
2.14.4TheWigner–SeitzCellofthefccLattice 86
3 CrystalStructuresofElements 101
3.1 Introduction 101
3.2 PearsonNotationandPrototypeStructure 102
3.3 FillingFactor 103
3.4 SimpleCubicStructure 104
3.5 BodyCenteredCubicStructure 105
3.6 FaceCenteredCubicStructure 108
3.7 Close-PackedStructures 109
3.8 DoubleHexagonalClose-PackedStructure 114
3.9 SamariumClose-PackedStructure 116
3.10SymmetryAxes 119
3.11HexagonalClose-PackedStructure 124
3.12IntersticesinClose-PackedStructures 131
3.13DiamondStructure 138
3.14ArsenicStructure 144
3.15SeleniumStructure 147
3.16GraphiteStructure 149
3.17AtomicRadius 152
4 CrystalStructuresofImportantBinaryCompounds 163
4.1 Introduction 163
4.2 TheIonicRadiusRatioandtheCoordinationNumber 164
March4,2016 15:39 PSPBook-9inx6in 00-Nevill-Gonzalez-Szwack-prelims
Contents vii
4.3 ZincBlendeStructure 168
4.4 FluoriteandAnti-FluoriteStructures 171
4.4.1 FluoriteStructure 171
4.4.2 Anti-FluoriteStructure 174
4.5 WurtziteStructure 175
4.6 NickelArsenideRelatedStructures 181
4.6.1 NiAsStructure 181
4.6.2 TiAsStructure 192
4.7 SodiumChlorideStructure 193
4.8 CesiumChlorideStructure 205
5 ReciprocalLattice 215
5.1 Introduction 215
5.2 TheConceptoftheReciprocalLattice 215
5.3 ExamplesofReciprocalLattices 223
5.3.1 Introduction 223
5.3.2 ReciprocaloftheTriclinicLattice 223
5.3.3 ReciprocaloftheSimpleCubicLattice 224
5.3.4 ReciprocaloftheFaceCenteredCubicLattice 225
6 DirectandReciprocalLattices 231
6.1 Introduction 231
6.2 MillerIndices 231
6.3 ApplicationofMillerIndices 237
7 X-RayDiffraction 247
7.1 Introduction 247
7.2 LaueEquations 247
7.3 EwaldConstructionandtheBraggDiffraction
Formula 250
7.4 AtomicStructureFactor 253
7.5 StructureFactor 260
Appendix 267
A.1 SolutionstoExercisesofChapter1 267
A.2 SolutionstoExercisesofChapter2 284
A.3 SolutionstoExercisesofChapter3 292
A.4 SolutionstoExercisesofChapter4 295
March4,2016 15:39 PSPBook-9inx6in 00-Nevill-Gonzalez-Szwack-prelims
viii Contents
A.5 SolutionstoExercisesofChapter5 301
A.6 SolutionstoExercisesofChapter6 304
A.7 SolutionstoExercisesofChapter7 305
References 309
March4,2016 15:39 PSPBook-9inx6in 00-Nevill-Gonzalez-Szwack-prelims
Preface
Ithasbeenfiveyearssincethefirsteditionofthisbook,whichoffers
the readers a friendly look inside crystallography. In the present
edition, we have added a new chapter and updated some of the
existing ones. Especially the first chapter now offers all the basic
concepts of crystallography presented on the example of simple
structures. Most importantly, perhaps, we have provided the book
withsolutionstoalmostallexercises.
Thisnewedition(astheoldone)isintendedtobeacompleteand
clearintroductiontothefieldofcrystallographyforundergraduate
and graduate students and lecturers in physics, chemistry, biology,
materialsandearthsciences,orengineering.Itincludesanextensive
discussion of the 14 Bravais lattices and the reciprocal to them,
basic concepts of point- and space-group symmetries, the crystal
structure of elements and binary compounds, and much more.
Besides that, the reader can find up-to-date values for the lattice
constantsofmostelementsandabout650binarycompounds(half
of them containing rare earth metals). The entire notation in this
bookisconsistentwiththeInternationalTablesforCrystallography.
Wehaveimprovedthequalityofmanyillustrations.Ourpurpose
remains to show rather than describe “using many words” the
structureofmaterialsanditsbasicproperties.Webelievethateven
readerswhoarecompletelynotfamiliarwiththetopic,butstillwant
tolearnhowtheatomsarearrangedincrystalstructures,willfind
thisbookuseful.
Thetextisorganizedintosevenchapters.Chapter1introduces
basicconceptsanddefinitionsinthefieldofcrystallography,starting
with one- and two-dimensional structures. Chapter 2 provides a
detailed descriptionof the14Bravaislattices. Chapter 3describes
themostimportantcrystalstructures oftheelementswithspecial