Sivia D.S., Elementary Scattering Theory For X-ray And Neutron Users

Oxford University Press, 2011. — 214 p.
The opportunities for doing scattering experiments at synchrotron and neutron facilities have grown rapidly in recent years and are set to continue to do so into the foreseeable future. This text provides a basic understanding of how these techniques enable the structure and dynamics of materials to be studied at the atomic and molecular level. Although mathematics cannot be avoided in a theoretical discussion, the aim has been to write a book that most scientists will still find approachable. To this end, the first two chapters are devoted to providing a tutorial background in the mathematics and physics that are implicitly assumed in other texts. Thereafter, the philosophy has been one of keeping things as simple as possible.I Some preliminaries
1 Studying matter at the atomic and molecular level
1.1 Length scales and logarithmic axes
1.2 Resolution, magnification and microscopy
1.3 Structure, dynamics and spectroscopy
1.4 Atomic building blocks and interactions
1.4.1 The basic structure of the atom
1.4.2 The fundamental forces of nature
1.4.3 Probing matter by scattering particles
1.5 Energy, length and temperature scales
1.6 A table of useful constants
2 Waves, complex numbers and Fourier transforms
2.1 Sinusoidal waves
2.1.1 The direction of propagation
2.1.2 The principle of superposition
2.2 Complex numbers
2.2.1 Definition
2.2.2 Basic algebra
2.2.3 The Argand diagram
2.2.4 The imaginary exponential
2.3 Fourier series
2.3.1 Orthogonality and the Fourier coefficients
2.3.2 The complex Fourier series
2.4 Fourier transforms
2.4.1 Convolution theorem
2.4.2 Auto-correlation function
2.5 Fourier optics and physical insight
2.5.1 Young’s double slit
2.5.2 A single wide slit
2.5.3 A diffraction grating
2.5.4 The convolution theorem in action
2.5.5 Multi-dimensional generalization
2.6 Fourier data analysis
2.6.1 The phase problem
2.6.2 Truncation effects and windowing
2.6.3 Noise and probability theory
2.7 A list of useful formulae
2.7.1 Dimensional analysis
II Elastic scattering
3 The basics of X-ray and neutron scattering
3.1 An idealized scattering experiment
3.1.1 Elastic scattering and momentum transfer
3.1.2 The differential cross-section
3.1.3 Elastic versus total scattering
3.2 Scattering by a single fixed atom
3.2.1 Nuclear scattering lengths
3.2.2 Atomic form factors
3.2.3 Magnetic form factors
3.2.4 Scattering cross-sections
3.3 Scattering from an assembly of atoms
3.3.1 Scattering density and Fourier transforms
3.3.2 Temperature and Debye–Waller factors
3.3.3 Coherent and incoherent scattering
3.3.4 Mixed scattering events
3.4 X-rays and synchrotron sources
3.4.1 Wigglers and undulators
3.5 Reactors and pulsed neutron sources
3.5.1 The time-of-flight technique
4 Surfaces, interfaces and reflectivity
4.1 Reflectivity and Fourier transforms
4.1.1 Substrate only
4.1.2 One uniform layer
4.1.3 A short multilayer
4.1.4 A phaseless Fourier ambiguity
4.2 Reflectivity and geometrical optics
4.2.1 Refractive index
4.2.2 A single boundary
4.2.3 Multiple boundaries
4.3 X-rays, neutrons and other techniques
5 Small-angle scattering and the big picture
5.1 Diffraction and length scales
5.2 Size, shape and molecular form factors
5.2.1 Absolute intensities
5.2.2 The Guinier approximation
5.2.3 Porod’s law
5.2.4 Polydispersity
5.3 Assemblies and correlations
5.3.1 Orientational alignment
5.3.2 Positional correlation
5.4 Pair-distribution function
6 Liquids and amorphous materials
6.1 The middle phase of matter
6.2 Radial distribution functions
6.3 Structure factors
6.3.1 Partial structure factors
6.4 Comparison with small-angle scattering
6.5 The Placzek correction
7 Periodicity, symmetry and crystallography
7.1 Repetitive structures and Bragg peaks
7.1.1 Atomic planes and Bragg’s law
7.1.2 Simple consequences and applications
7.2 Patterns and symmetries
7.2.1 Reality and Friedel pairs
7.2.2 Centrosymmetry and reality
7.2.3 Space groups and systematic absences
7.2.4 Geometry and space groups
7.2.5 Symmetry and statistics
7.3 Circumventing the phase problem
7.3.1 Patterson maps
7.3.2 Heavy atoms and partial structure
7.3.3 Isomorphous replacement
7.3.4 Direct methods and prior knowledge
7.4 Powdered samples
7.4.1 Texture
7.4.2 Twinning
7.4.3 Fibre diffraction
7.5 Magnetic structures
III Inelastic scattering
8 Energy exchange and dynamical information
8.1 Experimental considerations
8.1.1 The partial differential cross-section
8.1.2 Triple-axis spectrometer
8.1.3 Time-of-flight instruments
8.2 Scattering from time-varying structures
8.2.1 Elastic scattering
8.2.2 Space–time correlation function
8.2.3 Total scattering
8.2.4 Coherent and incoherent scattering
8.3 A quantum transitions approach
9 Examples of inelastic scattering
9.1 Compton scattering
9.1.1 The impulse approximation
9.1.2 Single particle wave function
9.2 Lattice vibrations
9.2.1 Heat capacities
9.2.2 Spin waves
9.3 Molecular spectroscopy
9.3.1 Quasi-elastic scattering
9.3.2 Energy resolution and time-scales
A Discrete Fourier transforms
B Resonant scattering and absorption