Foreword ........................................................ v
Acknowledgements ............................................... xv
Abbreviations, Acronyms and Computer Programs ................. xix
Glossary of Symbols ........................................... xix
1 Introduction ................................................. 1
1.1 Historical development of neutron scattering and key
concepts ................................................ 1
1.2 Inelastic neutron scattering (INS)-a spectroscopic
technique ............................................... 3
1.3 INS spectra ............................................. 5
1.4 Information content of an INS spectrum .................. 7
1.5 When to use neutrons .................................... 8
1.6 A note on units, symbols and chemical names ............. 9
1.6.1 Spectrometers-accuracy and precision of reported
results .......................................... 10
2 The Theory of Inelastic Neutron Scattering Spectroscopy ..... 13
2.1 The atomic cross sections .............................. 15
2.1.1 The coherent and incoherent scattering
strengths ....................................... 15
2.1.2 Spin incoherence ................................ 17
2.1.3 The incoherent approximation .................... 19
2.1.4 Comparison with photon scattering cross
sections ........................................ 20
2.2 Some practical consequences ............................ 21
2.2.1 Effects of deuteration ........................... 22
2.3 Energy and momentum transfer ........................... 23
2.3.1 Worked examples-calculating momentum transfer .... 25
2.4 Thermal ellipsoids ..................................... 27
2.5 The theoretical framework of neutron scattering ........ 29
2.5.1 The scattering law .............................. 31
2.5.2 Powder averaging ................................ 35
2.5.3 Worked example-hydrogendifluoride (bifluoride)
ion [HF2]- ...................................... 41
2.6 Band shaping processes in neutron spectroscopy ......... 45
2.6.1 Vibrational dispersion .......................... 46
2.6.2 Density of vibrational states ................... 49
2.6.3 Phonon wings .................................... 53
2.6.4 Worked example-phonon wings of the bifluoride
ion ............................................. 56
2.6.5 Molecular recoil ................................ 59
2.7 Conclusion ............................................. 64
2.8 References ............................................. 65
3 Instrumentation and Experimental Methods .................... 67
3.1 Neutron sources ........................................ 67
3.1.1 Reactor sources ................................. 68
3.1.2 Spallation sources .............................. 73
3.1.3 Which to use-reactor or spallation source? ...... 79
3.2 Neutron transport ...................................... 81
3.2.1 Neutron beam-tubes .............................. 81
3.2.2 Neutron guides .................................. 82
3.3 Neutron detection and instrument shielding ............. 83
3.3.1 Detection ....................................... 84
3.3.2 Instrumental shielding .......................... 87
3.4 Neutron spectrometers .................................. 89
3.4.1 Triple axis spectrometers ....................... 89
3.4.2 Indirect geometry instruments ................... 91
3.4.3 Direct geometry instruments .................... 111
3.4.4 Choosing the optimal technique ................. 120
3.5 Sample handling ....................................... 122
3.5.1 Sample quantity and multiple scattering ........ 123
3.5.2 Cryogenics ..................................... 126
3.5.3 Conventional samples ........................... 128
3.5.4 Temperature, pressure and magnetic field ....... 129
3.5.5 Catalysts and in situ experiments .............. 130
3.5.6 Safety ......................................... 132
3.6 References ............................................ 134
4 Interpretation and Analysis of Spectra using Molecular
Modelling .................................................. 137
4.1 Modelling-the classical and ab initio approaches ...... 137
4.1.1 The Born-Oppenheimer approximation .............. 138
4.2 Normal mode analysis of molecular vibrations .......... 139
4.2.1 Vibrations in molecules ........................ 140
4.2.2 Calculation of vibrational frequencies and
displacements .................................. 141
4.2.3 The quantum problem ............................ 145
4.2.4 The energy levels of the harmonic oscillator ... 146
4.2.5 Worked example-vibrational frequencies of the
bifluoride ion ................................. 147
4.2.6 Comparison with experiment-sodium bifluoride ... 153
4.2.7 A molecular modelling example-adamantane ....... 155
4.3 The vibrational problem in the solid state ............ 156
4.3.1 The solid state-crystals ....................... 156
4.3.2 Vibrations in one-dimensional crystal-one
atom per unit cell ............................. 156
4.3.3 Vibrations in one-dimensional crystal-two
atoms per unit cell ............................ 159
4.3.4 The three-dimensional crystal .................. 162
4.3.5 Example of a simple system-lithium hydride ..... 164
4.3.6 Calculation of the scattering law .............. 165
4.3.7 The-k-space grid-computational and
instrumental aspects ........................... 167
4.3.8 Comparison with experiment-sodium bifluoride ... 168
4.4 Calculations that avoid solving the dynamical
matrix ................................................ 170
4.4.1 Molecular dynamics ............................. 170
4.4.2 The velocity autocorrelation function .......... 171
4.4.3 Computational considerations ................... 172
4.5 Ab initio methods ..................................... 173
4.5.1 Hartree-Fock method ............................ 173
4.5.2 Density functional theory ...................... 173
4.6 Use offeree fields derived from classical mechanics ... 174
4.7 The ACLIMAX program ................................... 176
4.8 Conclusion ............................................ 177
4.9 References ............................................ 178
5 Analysis of INS spectra .................................... 183
5.1 General considerations-model compounds and the INS
database .............................................. 184
5.2 Ammonium bromide ...................................... 185
5.2.1 Observed INS spectrum of ammonium bromide ...... 188
5.2.2 Molecular recoil ............................... 195
5.3 Benzene ............................................... 197
5.3.1 The internal modes ............................. 197
5.3.2 Impact of the external modes ................... 201
5.4 Molecular systems using a direct geometry
spectrometer .......................................... 205
5.4.1 A special case-liquid helium ................... 206
5.4.2 Rubidium hexahydridoplatinate(IV) .............. 207
5.4.3 Phonon wings ................................... 212
5.4.4 Low momentum transfer spectra .................. 214
5.5 Conclusion ............................................ 215
5.6 References ............................................ 215
6 Dihydrogen and Hydrides .................................... 219
6.1 The rotational motion of diatomic molecules ........... 220
6.1.1 The rotational spectroscopy of dihydrogen ...... 223
6.1.2 Ortho- and para-hydrogen ....................... 223
6.1.3 The angular probability density function,
P(Θ, Φ) ........................................ 225
6.1.4 The scattering law for dihydrogen rotations .... 226
6.1.5 An outline of the INS spectrum of dihydrogen ... 227
6.1.6 Experimental considerations-the conversion to
para-hydrogen .................................. 229
6.2 The INS spectrum of dihydrogen in an anisotropic
potential ............................................. 230
6.2.1 Planar rotor in an attractive field-the 2-D
type ........................................... 231
6.2.2 Upright rotor in an attractive field-the 1-D
type ........................................... 234
6.2.3 Experimental consequences ...................... 235
6.3 Dihydrogen on graphite and carbons .................... 236
6.3.1 Graphite and other carbons and carbon
nanostructures ................................. 237
6.3.2 Alkali metal intercalated graphite ............. 240
6.3.3 См ............................................. 241
6.4 Dihydrogen in microporous oxides including zeolites ... 242
6.4.1 Dihydrogen in a cobalt aluminophosphate ........ 243
6.4.2 Dihydrogen in zeolites ......................... 246
6.4.3 Dihydrogen in Vycor, nickel(II) phosphate and
a zinc complex ................................. 248
6.5 Dihydrogen complexes .................................. 249
6.6 Hydrogen in metals .................................... 258
6.6.1 The spectral characteristics ................... 258
6.6.2 Hydrogen trapping .............................. 262
6.6.3 The hydrogen vibrational potential ............. 264
6.7 Metal hydrides ........................................ 266
6.7.1 Alkali metal hydrides .......................... 267
6.7.2 Ternary metal hydrides ......................... 268
6.8 References ............................................ 277
7 Surface Chemistry and Catalysis ............................. 285
7.1 Vibrations of atoms in surfaces and adsorbed
species ............................................... 285
7.2 Experimental methods .................................. 288
7.3 INS studies of metal catalysts ........................ 289
7.3.1 Metal-hydrogen vibrations and surface
vibrational states ............................. 290
7.3.2 Hydrocarbons on metal catalysts and reference
hydrocarbons ................................... 310
7.3.3 Acetonitrile, CH3CN-binding and
hydrogenation .................................. 329
7.4 Oxides and oxide-supported catalysts .................. 330
7.4.1 Molybdenum(VI) oxide on alumina-chemisorbed
water .......................................... 330
7.4.2 Selective oxidation of ргоретю-the allyl
radical ........................................ 332
7.4.3 Copper zinc oxide catalysts-methanol
synthesis ...................................... 334
7.4.4 Gold on titanium dioxide-the hydrogen-oxygen
reaction ....................................... 335
7.5 Zeolites .............................................. 335
7.5.1 Sodium, ammonium and protonated zeolite Y ....... 337
7.5.2 Ammonium and protonated zeolite rho ............ 338
7.5.3 Hydrated H-mordenite and ZSM-5 ................. 339
7.5.4 Molecules in zeolites .......................... 340
7.6 Metal sulfide catalysts ............................... 345
7.6.1 S-H vibrational modes .......................... 349
7.6.2 Metal-hydrogen vibrational modes ............... 349
7.6.3 Lattice vibrations and hydrogen riding modes ... 350
7.6.4 Computed INS spectra ........................... 350
7.6.5 Adsorbed dihydrogen ............................ 351
7.6.6 Thiophene and related compounds ................ 353
7.7 Conclusion ............................................ 356
7.8 References ............................................ 356
8 Organic and Organometallic Compounds ....................... 367
8.1 Analysis of the INS spectra of organic compounds ...... 367
8.1.1 Group frequencies .............................. 368
8.1.2 The Wilson GF method ........................... 369
8.1.3 Ab initio methods .............................. 371
8.2 Alkanes and cycloalkanes .............................. 374
8.3 Alkenes and alkynes ................................... 379
8.4 Aromatic and heteroaromatic compounds ................. 379
8.5 Oxygen containing compounds ........................... 381
8.6 Nitrogen containing compounds ......................... 384
8.7 Organometallic compounds .............................. 385
8.8 References ............................................ 385
9 Hydrogen Bonding ........................................... 393
9.1 Spectroscopic consequences of hydrogen bonding ........ 394
9.1.1 General considerations ......................... 395
9.1.2 Symmetric hydrogen bonds ....................... 396
9.2 Water ................................................. 397
9.2.1 Isolated water molecules in mineral lattices ... 398
9.2.2 The protonated species of water ................ 401
9.2.3 Water-water solids-the ices .................... 402
9.2.4 Water at biological interfaces ................. 408
9.3 Proton transfer ....................................... 410
9.3.1 The dicarboxylate model systems ................ 410
9.3.2 Proton conducting materials .................... 418
9.4 Unusual protonic species .............................. 419
9.4.1 The isotropic proton ........................... 419
9.4.2 The free proton ................................ 420
9.5 Conclusion ............................................ 422
9.6 References ............................................ 422
10 Soft Condensed Matter- Polymers and Biomaterials ........... 427
10.1 Crystalline polymers .................................. 428
10.1.1 Polyethylene and the n-alkanes ................. 428
10.1.2 The n-alkanes .................................. 436
10.1.3 Polypropylene .................................. 453
10.1.4 Nylon-6 ........................................ 455
10.1.5 Conducting polymers ............................ 456
10.2 Amorphous polymers ................................... 461
10.2.1 Polydimethylsiloxane ........................... 462
10.2.2 Advanced composites ............................ 464
10.3 Biological systems .................................... 466
10.3.1 Model peptides ................................. 466
10.3.2 Nucleic acids, nucleic acid bases,
nucleotides and nucleosides .................... 470
10.3.3 Amino acids and proteins ....................... 472
10.3.4 Phosphate biominerals .......................... 475
10.4 Conclusions ........................................... 480
10.5 References ............................................ 480
11 Non-hydrogenous Materials and Carbon ....................... 487
11.1 Analysis of spectra ................................... 489
11.1.1 Chlorine ....................................... 490
11.1.2 Minerals ....................................... 492
11.2 Carbon ................................................ 495
11.2.1 Diamond ........................................ 495
11.2.2 Graphite ....................................... 495
11.2.3 C60 and the fullerenes .......................... 498
11.2.4 Amorphous hydrogenated carbon .................. 504
11.2.5 Industrial carbons ............................. 506
11.2.6 Transition metal carbonyls and carbonyl
hydrides ....................................... 510
11.3 Conclusions ........................................... 516
11.4 References ............................................ 517
12 Vibrational Spectroscopy with Neutrons- the Future ......... 523
12.1 References ............................................ 527
Appendix 1 .................................................... 529
Neutron Cross Sections of the Elements ..................... 529
Al.l References ............................................ 539
Appendix 2 .................................................... 541
Inelastic Neutron Scattering Theory ........................ 541
A2.1 The neutron Schrödinger equation ...................... 541
A2.2 Scattering theory ..................................... 542
A2.2.1 The transition rate-Fermi's Golden Rule ........ 544
A2.2.2 The form of the scattering potential ........... 547
A2.2.3 The scattering law ............................. 551
A2.3 Scattering from vibrating molecules ................... 552
A2.4 Debye-Waller factor ................................... 559
A2.5 Powder averaging ...................................... 559
A2.6 References ............................................ 562
Appendix 3 .................................................... 565
The Resolution Function of Crystal Analyser
Spectrometers .............................................. 565
A3.1 The resolution function ............................... 565
A3.1.1 The time dependent term ........................ 566
A3.1.2 The incident flight path dependent term ........ 567
A3.1.3 The final energy dependent term ................ 568
A3.1.4 The final flight path dependent term ........... 570
A3.1.5 The resolution function ........................ 571
A3.2 Design elements ....................................... 573
A3.2.1 Time focusing .................................. 573
A3.2.2 The Marx principle ............................. 575
A3.3 References ............................................ 576
Appendix 4 .................................................... 577
Systems Studied by INS ..................................... 577
A4.1 References ............................................ 603
Index ......................................................... 627
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