Neutron Diffraction

ISBN-13: 9783642812385 / Angielski / Miękka / 2011 / 360 str.

H. Dachs

Opis

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."

Spis treści

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.