Contributors ................................................... xi
Volumes in Series ............................................ xiii
Preface ...................................................... xvii
Symbols ....................................................... xxi
1 An Introduction to Neutron Scattering ...................... 1
David L. Price and Felix Fernandez-Alonso
1.1 Fundamentals ............................................... 2
1.1.1 Why Are Neutrons so Unique? ......................... 2
1.1.2 Thermal Neutrons for Condensed Matter Research ...... 5
1.1.3 Conservation Laws .................................. 11
1.1.4 The Structure of Materials ......................... 11
1.1.5 Adding Motion: Dynamics and Spectroscopy ........... 16
1.2 Scattering Foundations .................................... 22
1.2.1 The Master Formula and Fermi's Golden Rule ......... 22
1.2.2 Nuclear Scattering ................................. 25
1.2.3 The Double Differential Cross Section in the Time
Domain ............................................. 26
1.2.4 Farewell to Nuclear Physics ........................ 27
1.2.5 Coherent and Incoherent Scattering ................. 28
1.2.6 Scattering Functions ............................... 30
1.3 Canonical Solids .......................................... 31
1.3.1 Normal Modes of Vibration .......................... 31
1.3.2 Scattering Under the Harmonic Approximation ........ 32
1.3.3 Purely Elastic Events .............................. 33
1.3.4 Inelastic (One-Phonon) Scattering .................. 35
1.3.5 Multiphonon Scattering ............................. 39
1.3.6 Beyond Harmonic Vibrations ......................... 41
1.4 Beyond Canonical Solids ................................... 42
1.4.1 Space-Time (Van Hove) Correlation Functions ........ 42
1.4.2 Pair Distribution Functions ........................ 43
1.4.3 Properties of the Dynamic Structure Factor ......... 47
1.4.4 From Order to Disorder: Diffuse Scattering ......... 58
1.4.5 Stochastic Diffusion ............................... 61
1.4.6 Beyond Atoms and Molecules: Large-Scale
Structures ......................................... 75
1.5 Magnetic Structure and Polarized Neutrons ................. 82
1.5.1 Basic Principles ................................... 82
1.5.2 Polarized Neutrons ................................. 88
1.5.3 Magnetic Bragg Scattering .......................... 95
1.5.4 Diffuse Scattering from Magnetic Disorder .......... 97
1.5.5 Large-Scale Magnetic Structures ................... 101
1.6 Spin Dynamics ............................................ 106
1.6.1 Generalized Susceptibility ........................ 106
1.6.2 Spin Waves ........................................ 108
1.6.3 Crystal Fields and Magnetic Clusters .............. 111
1.6.4 Spin Fluctuations ................................. 114
1.6.5 Interband Transitions ............................. 115
1.6.6 Critical Scattering ............................... 117
1.7 Nuclear Spin: Order and Disorder ......................... 120
1.7.1 A Closer Look at Nuclear Spins .................... 121
1.7.2 Scattering Cross Sections ......................... 121
1.7.3 Uncorrelated and Correlated Spin Ensembles ........ 123
1.8 Outlook .................................................. 125
References ............................................... 127
2 Neutron Sources .......................................... 137
Francisco J. Bermejo and Fernando Sordo
2.1 Scope .................................................... 138
2.2 Useful Neutron Production Reactions ...................... 140
2.2.1 Fission ........................................... 141
2.2.2 Direct and Stripping Reactions .................... 142
2.2.3 Bremsstrahlung .................................... 144
2.2.4 Spallation Reactions .............................. 146
2.3 Neutron Slowing Down and Moderators ...................... 153
2.3.1 Moderators ........................................ 158
2.4 Basic Building Blocks of Accelerators to Drive Neutron
Sources .................................................. 166
2.4.1 Beam Injectors .................................... 167
2.4.2 Targets ........................................... 178
2.5 Accelerator-Driven Sources: Some Predecessors ............ 197
2.6 State-of-the-Art Accelerator Drivers for Neutron
Sources .................................................. 199
2.6.1 Last-Generation Megawatt-Range Sources ............ 199
2.6.2 Medium-Power (100 kW) Sources ..................... 205
2.6.3 Compact, Accelerator-Driven Sources ............... 209
2.7 Research Reactors ........................................ 212
2.7.1 Core Designs ...................................... 213
2.7.2 Reactor Vessel .................................... 217
2.8 Future Prospects ......................................... 219
2.8.1 Accelerators ...................................... 219
2.8.2 Hybrid Systems .................................... 225
2.8.3 Reactors .......................................... 226
2.9 Nonneutron-Scattering Uses of Neutron Sources ............ 227
2.9.1 Isotope Production, In-Vessel Irradiation,
y-Radiation, and Neutron Activation Analysis ...... 228
2.9.2 Nuclear Physics and Engineering: Astroparticle
Physics, Nuclear Structure and Reactions, and
Transmutation of Nuclear Waste .................... 228
2.9.3 Hadron Physics: Neutrino-Related Phenomena ........ 229
2.9.4 Fundamental Physics: Foundations of Quantum
Mechanics, Effects of Gravity on Isolated
Particles, Search for Dark Matter Using
Ultracold Neutrons, Tests, and Validations of
the Standard Model of Particle Physics ............ 230
2.9.5 Use of Muon Beams for Condensed Matter and
Fusion Research ................................... 231
Acknowledgments .......................................... 231
Appendix A Some Basic Relationships ...................... 232
Appendix В The Transport Equation for Neutrons ........... 234
References ............................................... 237
3 Experimental Techniques .................................. 245
Masatoshi Arai
3.1 Introduction ............................................. 246
3.2 Scattering Measurements .................................. 247
3.2.1 Cross Section ..................................... 247
3.2.2 Integrated Intensity and the Lorentz Factor ....... 249
3.3 Useful Neutrons for Condensed Matter Science ............. 254
3.3.1 Neutron Flux from Moderators ...................... 254
3.3.2 Pulse Peak Structure .............................. 255
3.3.3 Pulse Peak Width .................................. 257
3.3.4 Choice of Parameters in Spallation Sources ........ 257
3.3.5 High-Energy Neutron Background .................... 259
3.4 Diffraction Techniques ................................... 261
3.4.1 Powder Diffraction ................................ 262
3.4.2 Single-Crystal Diffractometers .................... 271
3.5 Inelastic Scattering Techniques .......................... 275
3.5.1 Triple-Axis Spectrometer .......................... 275
3.5.2 Chopper Instruments ............................... 277
3.5.3 Inverted-Geometry Instrument ...................... 288
3.6 Instruments for Semi-Macroscopic Structures .............. 293
3.6.1 Small-Angle Neutron Scattering Instruments ........ 293
3.6.2 Neutron Spin-Echo Spectrometers ................... 296
3.7 Neutron Detectors ........................................ 300
3.7.1 3He-Gas Detectors ................................. 301
3.7.2 Scintillation Detectors ........................... 301
3.8 Beam Transport and Tailoring ............................. 305
3.8.1 Neutron Optics .................................... 305
3.8.2 Choppers .......................................... 313
References ............................................... 318
4 Structure of Complex Materials ........................... 321
Silvia C. Capelli
4.1 Introduction ............................................. 321
4.2 Useful Properties of Neutrons ............................ 324
4.2.1 Neutron Scattering Length ......................... 324
4.2.2 A Particle with a Mass ............................ 324
4.3 What can be Learnt from Neutron Diffraction
Experiments? ............................................. 326
4.3.1 Hydrogen Bonding .................................. 326
4.3.2 Proton Migration .................................. 329
4.3.3 Transition Metal Hydrides ......................... 332
4.3.4 Porous Materials .................................. 333
4.3.5 Diffuse Scattering ................................ 335
4.4 Outlook .................................................. 339
4.4.1 Neutron Sources ................................... 339
4.4.2 Neutron Optics .................................... 340
4.4.3 Detectors ......................................... 341
4.4.4 Samples and Sample Environment .................... 342
4.4.5 Software .......................................... 347
4.5 Conclusions .............................................. 348
References ............................................... 349
5 Large-Scale Structures ................................... 353
Jeffrey Penfold and Ian M. Tucker
5.1 Introduction ............................................. 353
5.2 Experimental Details ..................................... 356
5.2.1 Fundamentals of Neutron Reflectivity .............. 356
5.2.2 Fundamentals of Small-Angle Neutron Scattering .... 358
5.2.3 Experimental Details for Neutron Reflection ....... 361
5.2.4 Experimental Details for SANS ..................... 363
5.3 Thin Films, Interfaces, and Solutions .................... 365
5.3.1 Adsorption at the Air-Solution Interface .......... 365
5.3.2 Adsorption at the Liquid-Solid Interface .......... 374
5.3.3 Structure of Biological Membranes ................. 378
5.3.4 Micelles .......................................... 382
5.3.5 Lamellar Phases and Vesicles ...................... 385
5.3.6 Colloidal Particles ............................... 392
5.3.7 Polymers in Solution, Melt, and Thin Films ........ 394
5.3.8 Proteins and Biomacromolecules in Solution and
at Interfaces ..................................... 404
5.4 Summary and Future Prospects ............................. 409
References ............................................... 409
6 Dynamics of Atoms and Molecules .......................... 415
Mark R. Johnson and Gordon J. Kearley
6.1 Introduction ............................................. 416
6.2 Brief Review of Theoretical Concepts ..................... 418
6.3 Modeling ................................................. 419
6.3.1 Mapping Potential Energy Surfaces ................. 419
6.3.2 Molecular Dynamics Simulation ..................... 420
6.3.3 Empirical and Ab Initio Energy Calculation ........ 420
6.4 Instrumentation .......................................... 422
6.4.1 Three-Axis Spectrometers .......................... 422
6.4.2 Time of Flight .................................... 422
6.4.3 Neutron Compton Scattering Spectrometers .......... 423
6.4.4 Molecular Spectrometers ........................... 424
6.4.5 Backscattering Spectrometers ...................... 425
6.4.6 Neutron Spin-echo Instruments ..................... 426
6.4.7 The Measured Neutron-Scattering Signal ............ 427
6.5 Oscillatory Motion, Incoherent Scattering ................ 427
6.5.1 Molecular Vibrations of Benzene ................... 429
6.5.2 Hydrogen-Bonded Systems ........................... 430
6.5.3 Complex Hydrides .................................. 431
6.5.4 Polymers .......................................... 433
6.6 Oscillatory Motion, Coherent Scattering .................. 434
6.6.1 Classic Phonons and Soft Modes in SrTiO3 .......... 435
6.6.2 Negative Thermal Expansion ........................ 435
6.6.3 Nanostructured Materials .......................... 438
6.6.4 Oxygen-Ion Conductors—Brownmillerites ............. 439
6.6.5 Thermoelectrics—Skutterudites ..................... 441
6.6.6 Pnictides ......................................... 442
6.6.7 Strontium Gallium Oxides .......................... 443
6.6.8 Deoxyribonucleic acid ............................. 445
6.7 Tunneling ................................................ 446
6.7.1 Rotational Tunneling .............................. 446
6.7.2 Translational Tunneling ........................... 453
6.8 Stochastic Relaxation/Dynamics ........................... 453
6.8.1 Complex Diffusion ................................. 455
6.8.2 Ligand Water Rotation ............................. 456
6.8.3 Coherent QENS, Rotation ........................... 456
6.8.4 Dynamical Transitions from Elastic Scans .......... 457
6.8.5 Diffusion of Coherent Scatterer CO2 ............... 459
6.8.6 Water and Complex Diffusion ....................... 460
6.8.7 Ionic Liquids ..................................... 463
6.9 Conclusion and Perspectives .............................. 464
References ............................................... 466
Appendix: Neutron Scattering Lengths and Cross Sections ....... 471
Javier Dawidowski, José R. Granada, Javier R. Santisteban,
Florencia Cantargi, and Luis A. Rodriguez Palomino
A.1 Introduction ............................................. 471
A.2 Theoretical Background ................................... 472
A.2.1 Scattering Length ................................. 472
A.2.2 Spin-Dependent Scattering Lengths ................. 476
A.2.3 Neutron-Atom Interactions ......................... 477
A.3 Methods of Measurement of Scattering Lengths ............. 482
A.3.1 Transmission ...................................... 482
A.3.2 Bragg Diffraction ................................. 484
A.3.3 Dynamical Diffraction ............................. 486
A.3.4 Prism Refraction .................................. 488
A.3.5 Christiansen Filter ............................... 489
A.3.6 Neutron Gravity Refractometer ..................... 490
A.3.7 Neutron Interferometry ............................ 491
A.3.8 Small-Angle Scattering ............................ 492
A.3.9 Total Reflection .................................. 493
A.3.10 Pseudomagnetic Method ............................. 493
A.3.11 High-Energy Experiments ........................... 494
A.4 Tables of Neutron Scattering Lengths and Cross Sections .. 495
References ............................................... 527
Index ......................................................... 529
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