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