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Indexing of Crystal Diffraction Patterns 
From Crystallography Basics to Methods of Automatic Indexing


Springer Verlag
2022, XX, 417 p. 142 illus.
ISBN:  978-3-031-11076-4



 
The 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.




Table of contents:

Geometric crystallography 
    Linear oblique coordinate systems
    Lattices
   Crystal symmetry groups
   Conventional crystallographic settings
   Indices of directions and planes
   Families of equivalent stacks of planes
   Comparison of lattices
   Crystal orientation
 
 Homogeneous strain
   Lattice and Fourier transformation

Basic aspects of crystal diffraction
   Scattering of waves in solids
   Geometry of crystal diffraction
   Geometries of selected diffraction techniques
   Structure factor
   Formal approach to crystal diffraction
   Intensities of reflections
   Other factors affecting intensities

Diffraction of high energy electrons 
    Introduction to dynamical diffraction
    Wave equation
    Bloch waves in semi-infinite and plate-like crystals
    Intensities on TEM diffraction patterns

Cartesian reference frames in diffractometry 
    X-ray diffractometer
    Orientation in transmission microscope
    Orientation in scanning microscope

Indexing of single-crystal diffraction patterns 
    Indexing in general
    Ab initio indexing for structure determination
    Experimental single-crystal techniques
    The problem of indexing single-crystal data
    Real-space indexing
    Period detection
    Difference vectors
    Indexing via three-dimensional Fourier transformation
    Clustering in reciprocal space
    Directions of zone axes from difference vectors
    Constructing a three-dimensional lattice
    An example indexing program Ind_X
    A bird’s eye view on ab initio indexing

Ab-inito indexing of Laue patterns 
    Geometry of Laue patterns
    Gnomonic projection of reciprocal lattice nodes
    Gnomonic projection of a cell
    Laue indexing
    Indexing of pink-beam diffraction patterns

Indexing of powder diffraction patterns 
    Link between peaks positions and reflection indices
    Ambiguities
    Figures of merit
    Indexing procedures
    Integrated software packages


Indexing for orientation determination 
    Orientation mapping
    Orientation via pattern indexing
    Formal aspects of end-indexing
    Spurious scattering vectors
    Accumulation in discrete space
    Accumulation in rotation space
    Testing of indexing algorithms
    Figures of merit and other issues
    Orientation determination via direct pattern matching


Indexing of spot-type diffraction patterns 
    Conventional indexing of zone axis patterns
    Automatic orientation determination
    Three-dimensional ab initio indexing
    Note on other TEM-based patterns

Complications in indexing 
    Pseudosymmetry
    Indexing of ‘multi-lattice’ diffraction patterns
    Ambiguities in crystal orientation determination
    Indexing of satellite reflections
    Non-conventional structure determination methods

Multigrain indexing
    Three-dimensional X-ray diffraction
    X-ray diffraction contrast tomography
    Processing of diffraction data
    Other methods of three-dimensional mapping

Beyond diffraction by periodic crystals
    Debye scattering formula
    Single-particle diffraction imaging
    Indexing of diffraction patterns of helical structures

Quasicrystals
    Example one-dimensional quasicrystal
    The strip projection method
    Two-dimensional pentagonal case
    Frame-based tilings
    Indices of reflections
    The decagonal and other axial quasicrystals
    The icosahedral quasicrystal
    Practical aspects of indexing

Strain determination 
    Methods of local strain determination
    CBED-based determination of micro-strains
    Kossel micro-diffraction