Neutron Diffraction

Since the great discovery made by Laue, x-ray diffraction has become the most im­ portant method for the investigation of atomic structure in condensed matter. Cer­ tain investigations, however, are difficult or totally impossible to conduct using x-rays, for example, the localization of atomic nuclei or atoms having only a few core electrons, and the observation of magnetic moments. The investigation of these important areas is made possible by neutron diffraction. Thus this method has devel­ oped into an important supplement to x-ray investigations. An ever-increasing de­ mand is put on the method by research areas, old and new. Neutron diffraction has completely reformed the subject of solid-state magnetism; especially the area of chemical binding has received a new impetus by the union of x-ray and neutron dif­ fraction. An exchange of different isotopes of the same element gives rise, as a rule, to a change in the strength of the neutron diffraction. Due to this effect itls possible, by means of deuteration, to make visible a single chain in a solid high polymer. Thus neutron small-angle scattering is important in protein research and for the biology of macromolecules. Of equal importance is the application of neu:ron diffraction in metallurgy. There already exist several excellent books which discuss the results obtained by neans of neutron diffraction.

1. Principles of Neutron Diffraction..- 1.1 Introduction.- 1.2 Background.- 1.3 VAN HOVE Theory in the Classical Approximation.- 1.3.1 Neutron Spectroscopy.- 1.3.2 Neutron Diffraction.- 1.4 Interaction of Neutrons with Matter.- 1.4.1 Scattering from the Atomic Nucleus.- 1.4.2 Incoherent Scattering.- 1.4.3 Magnetic Scattering.- 1.5 Optimization of Scattering Experiments.- 1.5.1 Description of the Reactor Spectrum.- 1.5.2 Focusing Methods.- 1.6 Theory of the Neutron Spectrometer.- 1.6.1 Monochromator Crystals.- 1.6.2 Single-Crystal Measurements.- Half-Width of Rocking Curves.- Systematic Errors in the Measurement of Integrated Intensities.- Resolution of Single-Crystal Spectrometers.- Measurement Problems for Crystals with \/ery Large Lattice Constants.- Intensity Measurements Using Fixed Samples.- 1.6.3 Powder Diffractometer.- References.- 2. Polarized Neutrons..- 2.1 Overview.- 2.2 Theoretical Background.- 2.2.1 Definition of a Polarized Neutron Beam.- 2.2.2 Polarization-Dependent Cross Section.- 2.2.3 Neutron Optical Effects.- 2.3 Production and Handling of Polarized Beams.- 2.3.1 Devices Using Field Gradients.- 2.3.2 Polarizing Filters.- 2.3.3 Use of Neutron Optical Effects.- Magnetic’Mirrors and Guides.- Polarizing Multilayer Structures.- 2.3.4 Neutron Spin-Turn Devices.- The Leningrad Flipper.- The MEZEI Spin-Turn Coil.- 2.4 Some Applications of Polarized Neutron Scattering.- 2.4.1 Topological Problems.- 2.4.2 Flipper Choppers.- 2.4.3 Neutron Spin Echo.- 2.4.4 Resonance-Modulated Diffraction.- 2.5 Summary.- References.- 3. Combining X-Ray and Neutron Diffraction: The Study of Charge Density Distributions in Solids..- 3.1 Background.- 3.2 The Electron Distribution in Crystals and the Pertinence of Neutron Diffraction.- 3.2.1 Charge Density Functions.- 3.2.2 The Importance of Neutron Diffraction.- 3.3 Experimental Aspects.- 3.3.1 Survey of Experimental Requirements.- Essential Conditions for Density Analysis.- Desirable Conditions.- 3.3.2 Extinction.- 3.3.3 Multiple Reflection.- 3.3.4 Thermal Diffuse Scattering.- 3.3.5 Differences Between X-Ray and Neutron Thermal Parameters.- 3.4 Statistical Analysis of the Errors in X-N Maps.- 3.5 Survey of Selected Results.- 3.5.1 Analysis of Lone-Pair Densities.- 3.5.2 Analysis of Bond Densities.- 3.5.3 Quantitative Comparison of Theory and Experiment.- 3.6 Results Based Exclusively on X-Ray Data; Can They Replace the X-N Technique?.- References.- 4. The Determination of Magnetic Structures..- 4.1 Magnetic Neutron Scattering: Elementary Treatment.- 4.1.1 Unpolarized Neutrons.- 4.1.2 Polarized Neutrons.- 4.2 Magnetic Structures: Phenomenology.- 4.3 Generating Models.- 4.4 The Application of Magnetic Groups.- 4.4.1 Magnetic Point Groups.- 4.4.2 Magnetic Translation Groups.- 4.4.3 Magnetic Space Groups (SHUBNIKOV Groups).- 4.4.4 The Construction of Models.- 4.4.5 Limitation of the Method and New Developments.- 4.5 Irreducible Representation of Space Groups.- 4.6 Magnetic Neutron Scattering: The General Case.- 4.6.1 Unpolarized Neutrons.- 4.6.2 Polarized Neutrons.- 4.7 Instruments/Measurements/Data Analysis.- 4.8 Nomenclature and Publications.- References.- 5. Disordered Structures..- 5.1 Summary.- 5.2 Scattering Laws.- 5.3 Experimental Techniques.- 5.4 Small-Angle Neutron Scattering (SANS).- 5.5 Diffuse Elastic Scattering by Nonmagnetic Crystals.- 5.6 Scattering by Disordered Magnetic Systems.- References.- 6. Phase Transitions and Critical Phenomena..- 6.1 Overview.- 6.2 Theory of Phase Transitions.- 6.2.1 The Mean Field Theory, Introduction of Critical Exponents.- Simple Example.- 6.2.2 The Landau Expansion.- Range of Validity of the Landau Theory.- The Dimensionality n of the Order Parameter.- 6.2.3 Competing Order Parameters and Multicritical Points.- 6.2.4 Phase Transitions in Random Systems.- Spin-Glass and Order in Amorphous Material.- Competing Magnetic and Quadrupolar Order Parameters.- 6.3 Theories of Critical Phenomena.- 6.3.1 Series Expansions.- 6.3.2 Scaling and Renormalization Group Theories.- 6.3.3 Crossover Phenomena and the Critical Equation of State.- 6.3.4 First-Order Transitions.- 6.3.5 The Correlation Function in the Critical Region.- Spatial Anisotropic Critical Scattering.- 6.4 The Neutron Scattering Cross Section.- 6.5 Critical Phenomena at a Second-Order Phase Transition.- 6.5.1 One-Dimensional Systems (d = 1).- 6.5.2 Two-Dimensional Systems (d = 2).- 6.5.3 Three-Dimensional Systems (d = 3).- 6.6 Phase Diagrams: Multicritical Points and First- and Second-Order Transitions.- 6.6.1 Uniform Magnetic Systems.- 6.6.2 Other Transitions.- 6.6.3 Mixed Systems and Alloys with Competing Order Parameters.- 6.6.4 Spin-Glass Order.- 6.7 Discussion and Outlook.- References.- 7. Application of Neutron Diffraction to Biological Problems..- 7.1 Background.- 7.1.1 The Ambition of Molecular Biology.- 7.1.2 Structure.- 7.1.3 Why Neutron Diffraction is an Attractive Technique in Biology.- 7.2 Theory.- 7.2.1 Contrast Variation.- 7.2.2 Low Angle Scattering from Solution.- 7.2.3 The Interpretation of the Scattering Curves at Higher Angles.- 7.2.4 Selective Deuteration.- 7.3 Single-Crystal Analysis.- 7.3.1 Proteins.- 7.3.2 Hydrogen Atoms in Proteins.- 7.3.3 Very High Resolution.- 7.3.4 Phase Determination.- 7.3.5 Crystals of Large Complexes at Low Resolution.- 7.4 Oriented Systems.- 7.4.1 Myelin.- 7.4.2 Oriented Systems.- 7.4.3 Disorder.- 7.4.4 Artificial Ordering.- 7.4.5 Model Membranes.- 7.4.6 Retinal Rod Outer Segment (ROS) Membranes.- 7.4.7 Calcified Tendon.- 7.5 Particles in Solution.- 7.5.1 Spherical Viruses.- 7.5.2 Ribosomes Studied by Contrast Variation.- 7.5.3 Ribosomes Studied by Triangulation.- 7.6 Conclusions.- References.- 8. Liquid Structure Investigation by Neutron Scattering..- 8.1 Overview.- 8.2 The Basic Equations.- 8.2.1 Van Hove Scattering Law.- 8.2.2 The Static Approximation and the Structure Factor.- 8.2.3 Polyatomic Systems and Partial Structure Factors.- 8.2.4 Molecular Systems.- 8.2.5 Relation Between Structure Factor and Thermodynamics.- 8.3 Neutron Scattering Experiment.- 8.3.1 The Machines.- 8.3.2 How to Optimize an Experiment.- 8.3.3 Data Analysis.- 8.4 Monatomic Liquids.- 8.5 Binary Systems.- 8.5.1 The Normalization and the Thermodynamic Limit.- 8.5.2 The Isotopic Substitution Method.- 8.5.3 The Concentration Method - The “Zero Alloys”.- 8.5.4 Magnetic Systems.- 8.5.5 Conclusion.- 8.6 Molecular Liquids.- 8.6.1 The Angular Correlation Function.- 8.6.2 The Inelasticity Correction.- 8.6.3 The Intramolecular Structure Factor Determination.- 8.6.4 The Spherically Symmetric Part of the Molecular Correlation Function.- 8.6.5 The Orientational Correlation Function.- 8.7 Solutions.- References.- 9. Dynamical Neutron Diffraction and Its Application..- 9.1 Basic Equations.- 9.1.1 One-Beam Approximation.- 9.1.2 Two-Beam Approximation.- 9.2 Solution for a Plane Slab.- 9.2.1 Laue Case.- 9.2.2 Bragg Case.- 9.2.3 The Directions of the Neutron Current.- 9.3 Spatial Intensity Profiles and the Spherical Wave Theory.- 9.3.1 Ray Considerations.- 9.3.2 Spherical Wave Theory.- 9.4 Influence of Absorption.- 9.5 Magnetic Crystals.- 9.6 Applications.- 9.6.1 High Angular- and Energy-Resolution Experiments.- 9.6.2 Vibrating Crystals.- 9.6.3 Neutron Topography.- 9.6.4 Neutron Interferometry.- References.