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Umfang: XX, 418 p. 148 illus. , online resource.

Ausgabe: 1st ed. 2022.

ISBN: 9783031110771

Serie: Springer Series in Materials Science, 326

Inhalt: This book provides a detailed, self-contained description of automatic indexing of crystal diffraction patterns, considering both ab initio indexing and indexing of patterns originating from known structures. Introductory chapters equip the reader with the necessary basic knowledge of geometric crystallography, as well as kinematic and dynamic theories of crystal diffraction. Subsequent chapters delve and describe ab initio indexing of single crystal diffraction patterns and indexing of patterns for orientation determination. The book also reviews methods of indexing powder diffraction and electron spot-type patterns, as well the subject of multigrain indexing. Later chapters are devoted to diffraction by helical structures and quasicrystals, as well as some aspects of lattice parameter refinement and strain determination. The book is intended equally for materials scientists curious about 'nuts and bolts' of diffraction pattern indexing and orientation mapping systems, as well as interdisciplinary researchers from physics, chemistry, and biology involved in crystallographic computing. It provides a rigorous, yet accessible, treatment of the subject matter for graduate students interested in understanding the functioning of diffraction pattern indexing engines.

Anmerkung: Geometric crystallography -- Basic aspects of crystal diffraction -- Diffraction of high energy electrons -- Cartesian reference frames in diffractometry -- Indexing of single crystal diffraction patterns -- Ab-inito indexing of Laue patterns -- Indexing of powder diffraction patterns -- Indexing for orientation determination -- Indexing of spot-type diffraction patterns -- Complications in indexing -- Multigrain indexing -- Beyond diffraction by periodic crystals -- Quasicrystals -- Strain determination.

In: Springer Nature eBook

Weitere Ausg.: Printed edition: ISBN 9783031110764

Weitere Ausg.: Printed edition: ISBN 9783031110788

Weitere Ausg.: Printed edition: ISBN 9783031110795

Sprache: Englisch

DOI: 10.1007/978-3-031-11077-1

URL: https://doi.org/10.1007/978-3-031-11077-1

URL: Volltext  (URL des Erstveröffentlichers)

URL: lizenzpflichtig

UID:

Umfang: XX, 418 Seiten , Illustrationen

ISBN: 9783031110771 , 9783031110764

Serie: Springer series in materials science Volume 326

Weitere Ausg.: Erscheint auch als Druck-Ausgabe ISBN 978-3-031-11078-8

Weitere Ausg.: Erscheint auch als Online-Ausgabe ISBN 978-3-031-11077-1

Sprache: Englisch

Schlagwort(e): Kristall ; Streifenbild

UID:

Umfang: 1 online resource (427 pages)

ISBN: 9783031110771

Serie: Springer Series in Materials Science ; v.326

Anmerkung: Includes index. , Intro -- Preface -- Contents -- Preliminaries -- Points and Vectors in Space -- Index Notation -- List of Selected Symbols -- NIST Values of Physical Constants -- 1 Elements of Geometric Crystallography -- 1.1 Linear Oblique Coordinate Systems -- 1.1.1 Component-free Tensor Notation -- 1.1.2 Frames-Overcomplete Sets of Vectors -- 1.2 Lattices -- 1.2.1 Lagrange-Gauss Reduction -- 1.2.2 Buerger- and Niggli-Reduced Bases -- 1.2.3 Delaunay Reduction -- 1.2.4 Sublattices and Superlattices -- 1.2.5 Centerings and Non-Primitive Lattice Cells -- 1.3 Crystal Symmetry Groups -- 1.3.1 Euclidean Group -- 1.3.2 Finite Point Groups -- 1.3.3 Crystallographic Point Groups -- 1.3.4 Space Groups -- 1.3.5 Crystal Systems -- 1.3.6 Bravais Types -- 1.3.7 Symmetry of the Reciprocal Lattice -- 1.3.8 Bravais Type from Niggli Character or Delaunay Sort -- 1.4 Conventional Crystallographic Settings -- 1.5 Indices of Directions and Planes -- 1.5.1 Direction and Miller Indices -- 1.5.2 Generalized Indices of Directions and Planes -- 1.6 Families of Equivalent Stacks of Planes -- 1.7 Comparison of Lattices and Bravais-class Determination -- 1.7.1 Lattice Symmetry from Distribution of Two-fold Axes -- 1.7.2 Method Based on Metric Tensor -- 1.8 Crystal Orientation -- 1.9 Homogeneous Strain -- 1.9.1 Change of Lattice Metric -- 1.9.2 Effect of Lattice Transformation on Its Reciprocal Lattice -- 1.9.3 Strain Tensor in the Crystal Reference System -- 1.9.4 Strain Tensor in Cartesian Reference System -- 1.10 Lattice and Fourier Transformation -- 1.11 Appendix: Fourier Transformation -- 1.11.1 Fourier Series and Fourier Transformation -- 1.11.2 Distributions -- 1.11.3 Convolution -- 1.11.4 Fourier Transform of Dirac Comb -- 1.11.5 Projection-Slice Theorem -- References -- 2 Basic Aspects of Crystal Diffraction -- 2.1 Scattering of Waves in Solids -- 2.1.1 Coherence. , 2.1.2 Diffraction Theories -- 2.2 Geometry of Crystal Diffraction -- 2.2.1 Laue Equation -- 2.2.2 Ewald Construction -- 2.2.3 Bragg's Law -- 2.3 Geometries of Selected Diffraction Techniques -- 2.3.1 X-ray Diffractometry -- 2.3.2 Planar Detector -- 2.3.3 Geometry of K-lines -- 2.3.4 Electron Spot Patterns -- 2.3.5 Geometry of Laue Patterns -- 2.4 Structure Factor -- 2.4.1 Introduction -- 2.4.2 X-ray Form Factors -- 2.4.3 Electron Atomic Scattering Factors -- 2.5 Formal Approach to Crystal Diffraction -- 2.5.1 Fourier Transform of the Transfer Function of an Unbounded Crystal -- 2.5.2 Crystal of Finite Dimensions -- 2.6 Intensities of Reflections -- 2.6.1 Systematic Absences -- 2.6.2 Friedel's Law -- 2.7 Other Factors Affecting Intensities -- 2.7.1 Absorption -- 2.7.2 Occupancy and Thermal Vibrations -- 2.8 Appendix: A Note on the Diffraction of Light -- 2.8.1 Pattern at the Focal Plane of a Converging Lens -- References -- 3 Diffraction of High Energy Electrons -- 3.1 Introduction to Dynamical Diffraction -- 3.1.1 Bloch Waves -- 3.2 Wave equation for a Single Electron in an Electrostatic Potential -- 3.2.1 Solutions for an Unbounded Crystal -- 3.2.2 Two-Beam Centro-Symmetric Case -- 3.3 Bloch Waves in Semi-Infinite and Plate-Like Crystals -- 3.4 Intensities on TEM Diffraction Patterns -- References -- 4 Cartesian Reference Frames in Diffractometry -- 4.1 X-ray Diffractometer -- 4.2 Crystal Orientation in Transmission Electron Microscope -- 4.2.1 Tilt Angles and Specimen Orientation -- 4.2.2 Crystal Orientation with Respect the Microscope Axis -- 4.2.3 Tilting a Crystal to a Given Zone Axis -- 4.2.4 Determination of `Magnetic' Rotation Angle -- 4.3 Orientation in Scanning Microscope -- References -- 5 Ab Initio Indexing of Single-Crystal Diffraction Patterns -- 5.1 Indexing in General -- 5.2 Ab Initio Indexing for Structure Determination. , 5.3 Experimental Single-Crystal Techniques -- 5.4 The Problem of Indexing Single-Crystal Data -- 5.4.1 Basics -- 5.4.2 Indexing Error-Free Data -- 5.4.3 Impact of Errors -- 5.4.4 Some Objective Functions -- 5.5 Real-Space Indexing -- 5.5.1 Obtaining Test Vectors -- 5.5.2 Interpretations of t- .4 cdoth- .4 n -- 5.6 Period Detection -- 5.6.1 Domains -- 5.6.2 Test Periods -- 5.6.3 Period Determination Without Binning the Data -- 5.6.4 Folding -- 5.6.5 Correlations with Other Functions -- 5.6.6 One-Dimensional Fourier Transformation -- 5.6.7 Rayleigh Test -- 5.6.8 Lomb-Scargle Periodogram -- 5.6.9 Combining Various Techniques -- 5.7 Difference Vectors -- 5.8 Indexing via Three-Dimensional Fourier Transformation -- 5.9 Clustering in Reciprocal Space -- 5.10 Directions of Zone Axes from Difference Vectors -- 5.11 Constructing a Three-Dimensional Lattice -- 5.12 An Example Indexing Program Ind_X -- 5.12.1 Method -- 5.13 A Bird's Eye View on Ab Initio Indexing -- 5.14 Appendix: Auxiliary Tools -- 5.14.1 Obtaining the Scattering Vector from a Kossel Line -- 5.14.2 Linear Optimization Problem -- 5.14.3 Generation of Integer Triplets -- References -- 6 Ab-Inito Indexing of Laue Patterns -- 6.1 Geometry of Laue Patterns -- 6.1.1 Experimentally Accessible Part of the Reciprocal Space -- 6.2 Gnomonic Projection of Reciprocal Lattice Nodes -- 6.3 Gnomonic Projection of a Cell -- 6.4 Laue Indexing -- 6.4.1 Indexing Software -- 6.4.2 An Approach Referring to Direct Space -- 6.4.3 Getting Zone Axes via Integral Transforms -- 6.4.4 Fitting a Consistent Mesh -- 6.4.5 Indexing Limited to Reciprocal Space -- 6.4.6 Using Sextuplets of Points -- 6.4.7 Testing Superlattices -- 6.4.8 Indices of an Individual Reflection -- 6.4.9 Quality of Solution-Figure of Merit -- 6.5 Indexing of Pink-Beam Diffraction Patterns. , 6.5.1 Algorithm for Fitting the Scaling Factor and Orders of Reflections -- References -- 7 Indexing of Powder Diffraction Patterns -- 7.1 Link Between Peaks Positions and Reflection Indices -- 7.2 Ambiguities -- 7.3 Figures of Merit -- 7.4 Indexing Procedures -- 7.4.1 Search in the Continuous Parameter Space -- 7.4.2 Search in the Discrete Index Space -- 7.4.3 Relationships Between Line Positions -- 7.4.4 Metric in Conventional Crystallographic Setting -- 7.4.5 Indexing Based on Complete Pattern -- 7.5 Integrated Software Packages -- References -- 8 Indexing for Crystal Orientation Determination -- 8.1 Orientation Mapping -- 8.2 Orientation via Pattern Indexing -- 8.2.1 Scattering Vectors and Reciprocal Lattice Vectors -- 8.2.2 Vector Magnitudes and Reflection Intensities -- 8.3 Formal Aspects of End-Indexing -- 8.3.1 Basic Relationships -- 8.3.2 Related Solvable Problems -- 8.3.3 Rotations Versus Proper Rotations -- 8.3.4 Computational Context -- 8.4 Spurious Scattering Vectors -- 8.4.1 Accumulation -- 8.5 Accumulation in Discrete Space -- 8.5.1 Triplet Voting -- 8.5.2 Example Implementation -- 8.6 Accumulation in Rotation Space -- 8.6.1 Accumulation at Points of the Rotation Space -- 8.6.2 Accumulation Along Curves in the Space of Rotations -- 8.6.3 Maxima in Rotation Space -- 8.6.4 Other Orientation-Based Algorithms -- 8.7 Testing of Indexing Algorithms -- 8.8 Figures of Merit and Other Issues -- 8.8.1 Three Remarks -- 8.9 Orientation Determination via Direct Pattern Matching -- 8.9.1 Direct Matching Limited by a Detected Reflection -- References -- 9 Indexing of Electron Spot-Type Diffraction Patterns -- 9.1 Conventional Indexing of Zone Axis Patterns -- 9.1.1 180°-Ambiguity -- 9.1.2 Computer-Assisted Conventional Indexing -- 9.2 Automatic Orientation Determination -- 9.2.1 Precession Electron Diffraction. , 9.3 Three-Dimensional Ab Initio Indexing -- 9.3.1 Automatic Recording of Tilt Series -- 9.4 Note on Other TEM-Based Patterns -- References -- 10 Example Complications in Indexing -- 10.1 Pseudosymmetry -- 10.2 Indexing of `Multi-lattice' Diffraction Patterns -- 10.2.1 Twins -- 10.2.2 Types of Twins -- 10.2.3 Diffraction Patterns Originating From Twins -- 10.3 Ambiguities in Crystal Orientation Determination -- 10.4 Indexing of Satellite Reflections -- 10.4.1 Sinusoidally Commensurately Modulated One-Dimensional `Crystals' -- 10.4.2 Modulation Propagation Vector -- 10.4.3 Indexing -- 10.4.4 Incommensurately Modulated Structures -- 10.5 Non-Conventional Structure Determination Methods -- 10.5.1 Indexing Grazing-Incidence X-ray Diffraction Data -- 10.5.2 Serial Crystallography -- References -- 11 Multigrain Indexing -- 11.1 Three-Dimensional X-ray Diffraction -- 11.2 X-ray Diffraction Contrast Tomography -- 11.3 Processing of Diffraction Data -- 11.3.1 Location of a Diffraction Spot as a Function of Grain Position -- 11.3.2 Algebraic Reconstruction Technique -- 11.3.3 Friedel Pairs -- 11.3.4 Indexing and Reconstruction -- 11.4 Other Methods of Three-Dimensional Mapping -- 11.4.1 Laboratory X-ray Diffraction Contrast Tomography -- 11.4.2 Differential Aperture X-ray Microscopy -- 11.4.3 Three-Dimensional Orientation Mapping in TEM -- 11.4.4 Three-Dimensional Mapping Using Neutron Diffraction -- References -- 12 An Excursion Beyond Diffraction by Periodic Crystals -- 12.1 Debye Scattering Formula -- 12.2 Single-Particle Diffraction Imaging -- 12.2.1 Phase Problem -- 12.2.2 Iterative Phase Retrieval Algorithms -- 12.2.3 Single-Particle Imaging With XFEL -- 12.3 Indexing of Diffraction Patterns of Helical Structures -- 12.3.1 Helix -- 12.3.2 Helical Structure -- 12.3.3 Structure Factor -- 12.3.4 Selection Rule -- 12.3.5 Single-Wall Tubes. , 12.3.6 Intensities in Layer Lines.

Weitere Ausg.: Print version: Morawiec, Adam Indexing of Crystal Diffraction Patterns Cham : Springer International Publishing AG,c2022 ISBN 9783031110764

Sprache: Englisch