Principles and Applications of X-ray, Light and Neutron Scattering

Preface
Contents
1 General Introduction
1.1 Basic Concepts Underlying Relationship Between the Scattering and Structures
1.2 Various Structures Characterized by Scattering Methods
References
Part I Fundamentals of X-ray, Light and Neutron Scattering
2 Scattering Mechanism of X-ray, Light and Neutron Scattering
2.1 Principle of Scattering Experiments
2.2 X-ray and Light
2.3 Neutrons
2.4 Comparison of Scattering Mechanism
2.4.1 X-ray Scattering and Light Scattering
2.4.2 Neutron Scattering
References
3 Scattering of Schrödinger Wave: Interference of Scattered Waves and Born Approximation
3.1 Field Theory (Optical Theory) of Scattering
3.2 Schrödinger’s Wave Equation
3.3 Wave Equation in Free Space: Plane Wave and Spherical Wave
3.4 Wave Equation in Potential Field: Born Hypothesis in Scattering of Schrödinger Wave
3.5 Criteria for the Born Hypothesis
3.6 Differential Scattering Cross-Section of Schrödinger Wave
3.7 Notes of This Chapter
References
4 Scattering of X-ray and Visible Light
4.1 Maxwell’s Equations of Electromagnetic Wave
4.2 Fundamentals of Electromagnetic Wave
4.3 Fundamental Equations in Scattering of Electromagnetic Wave
4.4 Born Hypothesis in Scattering of Electromagnetic Wave: Scattering from Oscillating Dipoles
4.5 Notes of This Chapter
Further Reading
5 Response of Electrons to X-ray and Visible Light: Thomson Scattering and Rayleigh Scattering
5.1 Frequency Response of Electrons
5.2 X-ray Scattering: Scattering from Free Electrons
5.3 Scattering of Visible Light: Scattering from Bound Electrons
5.4 Differential Scattering Cross-Section and Scattering Length
5.4.1 Differential Scattering Cross-Section for X-ray, Light and Neutron Scattering
5.4.2 Scattering Length and Scattering Length Density
5.5 Notes of This Chapter
Further Reading
6 Polarization of Scattered Electromagnetic Wave and Light Scattering from Optically Anisotropic Scattering Elements
6.1 Scattering with Polarized Incident Wave
6.2 Scattering with Unpolarized Incident Wave
6.3 Light Scattering from Optically Anisotropic Scattering Elements and Depolarized Light Scattering
6.3.1 Induced Dipole Moment of Optically Anisotropic Scattering Elements
6.3.2 Optically Isotropic Scattering and Optically Anisotropic Scattering
7 Rayleigh–Gans–Born–Debye Scattering from Large Particles
7.1 Physical Basis of Rayleigh–Gans–Born–Debye Scattering
7.2 Interference of Scattered Waves from Scattering Elements
7.3 Scattering Structure Amplitude and Structure: Reciprocal Space (Fourier Space) and Real Space
7.4 Scattering Structure Factor and Autocorrelation Function: Mathematics of Fourier Transform and Physics of Reciprocal Phenomena
7.5 Intraparticle Interference and Interparticle Interference
Further Reading
8 Physics of Reciprocal Phenomena
8.1 Introduction
8.2 Scattering from Very Small Particles: p(z) = δ(z)
8.3 Scattering from Homogeneous Matters: p(z) = p0(Constant)
8.4 Scattering from Matters with Finite Size
8.5 Scattering from Periodic Structure: Diffraction from Crystal Lattice
8.6 Shape Anisotropy of Structures and Anisotropy of Scattering Patterns
8.7 Notes of This Chapter
9 Scattering Structure Factor: Spectral Intensity Distribution of Fourier Modes of Structure
9.1 General Concept
9.2 Example: Scattering Structure Factor of Lamellar Microdomains in Block Copolymers
9.3 Coupled Internal Structures of Matters in r-Space Are Decoupled in q-Space
9.3.1 Dilute, Isolated Systems
9.3.2 Systems with Finite Particle Concentrations
References
Part II X-ray and Neutron Scattering: Isotropic Scattering
10 Scattering from Isolated Particles
10.1 Scattering from a Spherically Symmetrical Particle
10.2 Scattering from a Sphere
10.2.1 General Scattering Equation and Its Characteristics
10.2.2 Form Factor Maxima
10.2.3 Asymptotic Behavior at q→0: Guinier’s Law
10.2.4 Asymptotic Behavior at q→∞: Porod’s Law
10.3 Scattering from an Ellipsoid of Revolution
10.3.1 Perfect Orientation
10.3.2 Random Orientation
10.4 Scattering from a Cylinder
10.4.1 Perfect Orientation
10.4.2 Random Orientation
10.4.3 Randomly Oriented Infinitesimally Thin Rod
10.4.4 Randomly Oriented Infinitesimally Thin Disk
10.5 Scattering from a Gaussian Chain
10.5.1 Debye Scattering Function
10.5.2 Asymptotic Behavior at q→0: Guinier’s Law
10.5.3 Asymptotic Behavior at q→∞: Porod’s Law
10.6 Scattering from Particles with Large Aspect Ratios: Asymptotic Behaviors, Radius of Gyration of Cross-Section, and Lorentz Factors
10.6.1 Long Cylinder
10.6.2 Thin Disk
10.6.3 Summary of Asymptotic Behaviors and Crossover Behaviors in q-Dependence of Scattering Intensity Distribution
10.6.4 Lorentz Factor
10.7 Notes of This Chapter
References
11 Scattering from Fluctuations: Statistical Theory of Scattering
11.1 Debye–Bueche Statistical Theory of Scattering from Heterogeneous Matters
11.1.1 General Theory
11.1.2 Spread of Correlation Function in r-Space and Spread of Scattering Function in q-Space
11.2 Experimental Evaluation of Statistical Parameters
11.2.1 Inverse Fourier Transformation
11.2.2 Debye–Bueche Plot
11.3 Relationships Between Structures and Characteristic Statistical Parameters
11.3.1 Mean Square Fluctuations
11.3.2 Correlation Function
11.3.3 Integral Parameters and Differential Parameters of Correlation Function
11.4 Spatial Correlation Function for Assembly of Asymmetric Particles
11.4.1 3D Isotropic Systems Having 3D Correlation Functions
11.4.2 3D Isotropic Systems Having 1D Correlation Function
11.4.3 3D Isotropic Systems Having 2D Correlation Function
11.5 Radius of Gyration
11.5.1 Guinier’s Law
11.5.2 Radius of Gyration for Particles Having Various Shapes
11.6 Scattering from Dilute Polymer Solutions
11.6.1 Description of Scattering Based on Fluctuation Theory and Excess Scattering Due to Concentration Fluctuations
11.6.2 Average Molecular Weight and Average Square of Radius of Gyration
11.6.3 The Second Virial Coefficient and Θ Condition
11.7 Scattering from Ideal Two-Phase Structure and Differential Parameters
11.7.1 Porod’s Theory
11.7.2 Debye–Anderson–Brumberger Theory
11.8 Pseudo Two-Phase Structures: Evaluation of Interphase Structure
11.8.1 Generals
11.8.2 Scattering from Spheres, Cylinders, and Lamellae Having the Interphase with a Finite Interfacial Thickness
11.9 Evaluation of Interface Curvature
11.10 Scattering from Particles Having Internal Heterogeneities
11.10.1 Scattering Model and Theory
11.10.2 Analyses of Scattering Intensity Distributions
11.11 Scattering from Thermal Density Fluctuations and Thermal Diffuse Scattering
11.11.1 Thermal Density Fluctuations in Liquids
11.11.2 Thermal Diffuse Scattering from Solids
11.12 Notes of This Chapter
References
12 Scattering from Thermal Concentration Fluctuations
12.1 Ginzburg–Landau and Cahn–Hilliard Theory for Nonuniform Solutions Having Thermal Concentration Fluctuations
12.2 Scattering Intensity Is(q): Spectral Intensity of Fourier Modes ηq2 and Susceptibility F(q)−1 for Thermodynamically Stable Mixtures
12.3 Critical Scattering
12.4 Random Phase Approximation
12.4.1 Response Function and Structure Factor
12.4.2 RPA for Two-Component Systems
12.4.3 Response Functions of Ideal Chains Sijo(q)
12.4.4 Sijo(q) for Block Copolymers
12.4.5 Sijo(q) for Polymer Mixtures
12.4.6 Scattering from Polymer Mixtures and Block Copolymers
12.4.7 Comparisons of Scattering: A-b-B versus A/B
12.4.8 Phase Transitions of Polymer Mixtures and Block Copolymers
12.5 Notes of This Chapter
References
13 Interparticle Interference in Liquids
13.1 General Description
13.2 Scattering from Linearly Linked Particles
13.2.1 Chain of Spherical Particles Having a Fixed Nearest-Neighbor Distance
13.2.2 Chain Composed of Rod-Like Particles Linked by Flexible Joints
13.2.3 A Pair of Spherical Particles
13.3 Interparticle Interference in Simple Liquids: Zernike−Prins and Debye−Menke Equation
13.4 Debye’s Hard Spheres
13.5 Amorphous Matters
13.6 Percus–Yevick Equation for Hard Spheres
13.7 Sticky Hard Spheres
13.8 Notes of This Chapter
References
14 Interparticle Interference in Solids: Diffraction from Paracrystal Lattice and Superlattice
14.1 Distortion of Lattice
14.1.1 The First-Kind Lattice Distortions
14.1.2 The Second-Kind Lattice Distortions
14.2 Debye–Waller Factor: Effect of Thermal Motions
14.3 Diffraction from Paracrystal Lattice
14.3.1 Statistical Description of Paracrystal Lattice
14.3.2 Paracrystal Lattice Factor Z(q)
14.4 1D Paracrystal
14.4.1 Lattice Factor Kk(q)
14.4.2 Fk(q): Scattering Structure Amplitude for Unit Cell with Fundamental Paracrystal Lattice Vector overlineak
14.4.3 Zero-Order Scattering, δKk (q), and Paracrystal Lattice Factor, mathcalRmathfrake{(1 + Fk)/(1 - Fk)}
14.5 3D Paracrystal Lattice Factor: Z(q)
14.6 Diffraction Intensity Distribution from 3D Paracrystal Lattice and Superlattice
14.7 Broadening of Diffraction Profiles for Infinitely Large Paracrystal
14.8 Broadening of Diffraction Profiles due to the Coupled Effects of the Second Kind Lattice Distortion and Finite Size in Paracrystal
14.9 Application of Paracrystal Diffraction Theory
14.10 Notes of This Chapter
References
15 Scattering from Fractals
15.1 Scattering from Mass Fractals
15.2 Scattering from Surface Fractals
References
16 Combined Small-Angle Scattering Methods for Analyses of Hierarchical Structures
16.1 Combined Small-Angle Scattering Methods
16.2 Phenomenological Analyses of Hierarchically Self-Organized Nanoparticles
16.2.1 Analyses Based on Unified Guinier-Law/Power-Law Approach
16.2.2 Research Background for Nanoparticle/Polymer Composites
16.2.3 Hierarchical Structures of CB Powders
16.2.4 Hierarchical Structures of SBR/CB(20) and PI/CB(20) Composites after Cross-Linking
16.2.5 Partially Interdigitating Mass Fractal Agglomerates
16.2.6 Shape Anisotropy of Clusters as Building Blocks of Mass Fractal Agglomerates
16.2.7 Roughened Filler Surface via Formation of Bound Polymer Layer before and after Cross-Linking
16.2.8 Cascade Self-Organization of Dissipative Structures into Ordered Structures of Nanocomposites under Imposed Stress Field
16.3 In Situ Combined Small-Angle Scattering Analyses of Acetobacter Xylinum
16.3.1 Acetobacter Xylinum and Simplified Scattering Model
16.3.2 Preparation of Living AX Specimens in Deuterated and Non-Deuterated Water
16.3.3 Experimental Results and Analyses of the Combined USANS, PFUSANS, and Pinhole SANS
References
17 Statistical Mechanical Analyses of Hierarchically Self-Organized Nanoparticles Based on Scattering Methods
17.1 Research Backgrounds: Bottom-Up Preparation of Nanocomposites with Hierarchically Self-Organized Dispersion Structure of Metal Nanoparticles
17.2 Theoretical Background Based on Statistical Mechanics of Simple Liquids
17.2.1 Generalized Zernike–Prins Scattering Equation and Percus–Yevick Equation
17.2.2 Structure Factor for Hard Spheres Dispersed in Infinitely Large Space, SHS/inf(q)
17.2.3 Structure Factor for Sticky Hard Spheres Dispersed in Infinitely Large Space, SSHS/inf(q)
17.2.4 Structure Factor for Particles Dispersed in Clusters as a Confined Space
17.2.5 Polydispersity Effects in Cluster Size and Particle Size
17.2.6 Scattering from Mass Fractal Structure Built-Up by Clusters
17.3 Analyses Based on Hard Spheres Dispersed in Infinitely Large Space and in Confined Space
17.4 Analyses Based on Sticky Hard Spheres Dispersed in Infinitely Large Space and in Confined Space
17.5 Effects of Interparticle Interactions on ZP Structure Factor of HS and SHS: Dynamic Aggregates Driven by Attractive Interparticle Interactions
17.6 Scattering from Mass Fractal Structure Built-Up by Clusters
17.7 Notes of This Chapter:
References
Part III Light Scattering
18 Light Scattering from Solids and Condensed Matters
18.1 Characteristics of Light Scattering Methods
18.2 Light Scattering Theory and Criteria for Born Approximation
18.3 Rayleigh-Gans-Born-Debye Scattering from Optically Anisotropic Solids and Condensed Matters
18.4 Light Scattering Patterns from Various Supermolecular Structures
References
19 Experimental Methods and Apparatuses
19.1 Apparatus Using 2D Detector
19.2 Scattered Intensity Measurements with Photomultiplier
19.3 Measurements of Polarized and Depolarized Scattered Light
19.4 Various Correction Factors
References
20 Light Scattering from Fluctuations in Solid and Condensed Matters
20.1 Light Scattering from Density Fluctuations
20.2 Light Scattering from Optical-Anisotropy Fluctuations
20.2.1 Orientation Fluctuations of Optical Axes and Orientation Correlation
20.2.2 Random Assembly of Crystallites: Random Orientation Correlation
20.2.3 Generalization of Orientation Correlation Function
References
21 Light Scattering from Fibrillar Crystalline Superstructures
21.1 Scattering Model
21.2 Light Scattering from Randomly Oriented Optically Anisotropic Cylinders
References
22 Light Scattering from Spherulitic Crystalline Superstructures
22.1 Light Scattering from Ideal, Perfect Spherulites
22.2 Inter-Spherulite Interference Effects on Scattering Patterns
22.3 Light Scattering from Real Spherulites: Effects of Various Deviations from the Ideal Perfect Spherulite on Scattering
22.4 Broken Symmetry in Real Spherulites
22.5 Fluctuations of Optical Anisotropy within Spherulites
22.5.1 Radial Fluctuations of Optical Anisotropy
22.5.2 Tangential Fluctuations of Optical Anisotropy
22.6 Deviations of Shape of Spherulites from Spheres: Sheaves and Truncated Spherulites
22.7 Diffraction Rings from Ringed Spherulites
References
23 Light Scattering from Paracrystal Superlattice Structures of Crystalline Superstructures
23.1 Ultra-Superstructure of Optically Anisotropic Fibrillar Superstructures
23.1.1 Model
23.1.2 Scattering Equations from the Ultra-Superstructure
23.1.3 Theoretical Analyses of Experimental Scattering Patterns
23.2 Ultra-Superstructure of Sheaf-Like Crystalline Superstructures
23.3 Complex Light Scattering Patterns: Spherulitic Scattering at Small Angles and Fibrillar Scattering at High Angles
23.3.1 Experimental Complex Light Scattering Patterns
23.3.2 Model
References
24 Appendices
24.1 Appendix for Sect. 10.3.1: Scattering Structure Amplitude for an Oriented Ellipsoid of Revolution
24.2 Appendix for Sect. 10.3.2: Scattering Intensity for a Randomly Oriented Ellipsoid of Revolution and Its Asymptotic Behavior in a Small q Range
List of Various Proportionality Constants Used to Describe Absolute Scattered Intensity
Glossary of Principal Symbols and Abbreviations
Subject Index