Preface page xiii
Acknowledgments xv
Symbols and notations xvi
Introduction
What is scattering? 1
An overview of the field of neutron scattering 2
Matters of general significance 6
1 About neutrons
1.1 The neutron as an elementary particle 10
1.2 Neutron interactions 12
1.3 Neutrons as waves 16
1.4 Neutrons as particles 20
1.5 The neutron transport equation 22
1.6 The diffusion equation 24
1.7 Transport theory results 26
1.8 Thermal neutron diffusion theory results 28
1.9 Slowing-down theory: neutrons slowing down in a medium 31
1.10 Time-dependent slowing-down 37
1.11 The Maxwellian thermal-neutron energy distribution 43
1.12 The angular distribution at the surface of a moderator
– the Fermi approximation 46
1.13 Summary 47
Further reading 48
2 Neutron production, moderation, characterization of sources
2.1 Primary neutron sources 50
2.2 Moderators and moderation of fast neutrons 71
2.3 Characterization of sources 77
2.4 Conclusion 86
Further reading 86
3 Scattering theory: nuclear
3.1 Scattering of slow neutrons from a single spinless nucleus 87
3.2 The Fermi pseudopotential 95
3.3 Scattering by simple objects: form factors 96
3.4 Scattering cross sections and scattering length density 101
3.5 Double differential scattering cross section and the Fermi
golden rule 103
3.6 Coherent and incoherent scattering 107
3.7 Scattering functions and correlation functions 116
3.8 Dynamical susceptibility and linear response theory 118
3.9 Elastic scattering cross sections, total scattering, and static
approximation 124
3.10 Total scattering and multiple scattering 128
3.11 Examples of correlation functions and the Gaussian
approximation 131
3.12 Concluding remarks 137
Further reading 138
4 Scattering theory: magnetic
4.1 The magnetic moment of the neutron 139
4.2 Magnetic scattering of neutrons from electrons 143
4.3 The scattering function, the dynamic correlation function, and
the generalized magnetic susceptibility 148
4.4 Magnetic scattering from atomic electrons in crystalline solids 149
4.5 Polarized neutrons 151
4.6 Neutron spin-dependent nuclear scattering: coherent and
spin-incoherent scattering 153
4.7 Magnetic scattering from identical paramagnetic spins 155
4.8 Separation of nuclear coherent, spin-incoherent, and magnetic
scattering from a paramagnetic powder 156
4.9 Polarization analysis of field-induced magnetic form factors 158
4.10 Examples 160
4.11 Concluding remarks 164
Further reading 164
5 Neutron-scattering instruments: diffractometers and reflectometers
5.1 Introduction and early neutron diffraction 165
5.2 Powder diffractometers 169
5.3 Single-crystal diffractometers 173
5.4 Small-angle diffractometers 179
5.5 Neutron reflectometers 197
Further reading 202
6 Neutron-scattering instruments: spectrometers
6.1 Chopper spectrometers 206
6.2 Inverse geometry spectrometers 214
6.3 Triple-axis spectrometers 225
6.4 Spin-echo spectrometers 232
7 Devices
7.1 Collimators 237
7.2 Mirrors and neutron guides 247
7.3 Lenses 259
7.4 Rotating devices 262
7.5 Crystal monochromators 276
7.6 Reference scatterers 279
7.7 Polarizing filters and spin-manipulation devices 279
7.8 Conclusions 279
8 Detectors
8.1 Conversion reactions for slow-neutron detectors 281
8.2 Gas detectors 286
8.3 Scintillation detectors 298
8.4 Semiconductor detectors 306
8.5 Integrating detectors 307
8.6 Microchannel neutron detectors 310
8.7 Resonance capture gamma-ray neutron detectors 312
8.8 Detector development needs 313
9 Nuclear scattering: crystal structures
9.1 Coherent elastic scattering from a perfect crystal: the Laue
condition, Bragg’s law, and the Ewald sphere 316
9.2 The crystallographic unit-cell structure factor and the
phase problem 319
9.3 The total elastic coherent scattering cross-section of a single
crystal and a powder: the time-of-flight Laue method 320
9.4 Diffraction methods using monochromatic incident neutrons 322
9.5 Kinematical approximation and other wavelength- and
geometry-dependent factors 323
9.6 Implications of crystallographic symmetry 324
9.7 The Patterson function and Patterson symmetry 325
9.8 Data collection and crystal structure refinement 326
9.9 Crystal structure refinement 330
9.10 An example of structural refinement 333
9.11 Neutron protein crystallography 336
9.12 Surface crystallography 339
9.13 Concluding remarks 344
10 Nuclear scattering: lattice dynamics
10.1 Theoretical framework 347
10.2 Phenomenological models, microscopic theories, and
molecular-dynamics simulations 352
10.3 Group-theoretical analysis of the phonon dispersion
relation 353
10.4 Neutron measurements of phonon dispersion curves and
density of states 354
10.5 Phonon-related physics and thermodynamic properties 361
10.6 Examples 365
10.7 Studies of phonons in disordered and amorphous solids 367
10.8 Concluding remarks 368
Further reading 369
11 Nuclear scattering: chemical spectroscopy
11.1 A simple classical liquid: a qualitative discussion of the
neutron scattering functions 371
11.2 Single-particle motion in a liquid: microscopic dynamics
at short time 375
11.3 Single-particle motion in a liquid: diffusion dynamics
at long time 378
11.4 The generalized frequency distribution function 380
11.5 Coherent quasielastic scattering and de Gennes narrowing 381
11.6 Fast sound measurements by neutron Brillouin scattering and
momentum distribution by deep inelastic scattering 382
11.7 Hydrogen motion in crystalline lattices 384
11.8 Rotational spectroscopy in molecular solids 391
11.9 The elastic incoherent structure factor 393
11.10 Inelastic scattering from molecular rotation:
librational-torsional oscillations and tunneling 393
11.11 Concluding remarks 399
12 Magnetic scattering: structures
12.1 Magnetic diffraction using unpolarized neutrons 402
12.2 The magnetic moment basis vector and propagation vectors 405
12.3 Single-k, multi-k, higher harmonics of k, and domain
structures 410
12.4 Scattering cross sections of magnetic diffraction from
single-crystal and powder samples 410
12.5 Data collection: some practical considerations 413
12.6 Solving magnetic structures 414
12.7 Classification of magnetic structures according to magnetic
space groups 422
12.8 Study of magnetic structures using polarized neutrons 422
12.9 Beyond spin-ordered structures and concluding remarks 428
13 Magnetic scattering: excitations
13.1 Excitations from low-lying states of a single ion: the
crystal-field effect 432
13.2 Excitation spectra of spin pairs coupled by the Hiesenberg
exchange interaction 434
13.3 Single molecular magnets 437
13.4 Spin waves of Heisenberg magnets 441
13.5 Itinerant electron magnetism 446
13.6 Concluding remarks 450
Further reading 450
14 Disordered and large structures
14.1 Basic distribution functions obtained from
diffraction experiments 452
14.2 Experimental details and data correction 455
14.3 Data interpretation and structure models 459
14.4 Diffuse scattering from local disorder 461
14.5 The PDF method for analysis of local structures 465
14.6 Small-angle scattering from structures containing large
particles 467
14.7 SANS from dilute systems 472
14.8 Characterization of individual particles 473
14.9 Interparticle interactions: the structure factors 477
14.10 Experimental setup and SANS data analysis 481
14.11 Practical examples of structural parameters obtainable from
SANS experiments 482
14.12 Concluding remarks 484
Appendices
A.1 Physical constants and numerical relationships 485
A.2 Dirac delta functions 489
A.3 Laplace transforms 493
References 497
Index 511