Neutron Scattering with a Triple-Axis Spectrometer

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 11
1.1 Properties of thermal neutrons......Page 13
1.2 Neutron sources......Page 16
1.3 Reciprocal space and scattering diagram......Page 23
1.3.1 Elastic scattering......Page 24
1.3.2 Inelastic scattering......Page 26
1.4.1 Three-axis instrument......Page 27
1.4.2 Time-of-flight (TOF) instrument......Page 28
1.4.3 Backscattering and neutron spin echo (NSE)......Page 29
References......Page 30
2.1 Introduction......Page 32
2.2 Fermi’s Golden Rule and the Born approximation......Page 33
2.3 Coherent vs. incoherent scattering......Page 34
2.4.1 Elastic scattering (Bragg peaks)......Page 35
2.4.2 Inelastic scattering......Page 38
2.4.2.1 Phonons......Page 39
2.4.2.2 Damped harmonic oscillator......Page 41
2.4.2.3 Eigenvector determination......Page 42
2.4.2.4 Brillouin zones and intensity zones......Page 44
2.5 Incoherent nuclear scattering......Page 47
2.6 Coherent magnetic scattering......Page 48
2.6.1 Paramagnetic scattering......Page 50
2.6.2 Magnetic form factors and orbital moments......Page 51
2.6.3 Determination of magnetic structures with unpolarized neutrons......Page 52
2.7.1 Magnons......Page 58
2.7.1.1 Ferromagnet......Page 59
2.7.1.2 Antiferromagnet......Page 60
2.7.2 Diffuse magnetic scattering......Page 61
2.7.2.1 Quasielastic scattering......Page 62
2.7.2.2 Critical scattering......Page 63
References......Page 66
3.1 Shielding......Page 67
3.2 Monochromators......Page 69
3.2.1 Focusing monochromators and analyzers......Page 76
3.2.2 Resolution effects......Page 81
3.2.3 Double monochromators......Page 83
3.3 Collimators......Page 85
3.4 Filters......Page 87
3.4.1 Fast neutron filters......Page 88
3.4.2 Resonance filters......Page 89
3.4.3 Bragg-scattering filters......Page 90
3.6 Spectrometer alignment......Page 96
3.6.2 Experimental alignment......Page 97
3.7.1 Two-circle goniometer......Page 100
3.7.3 Translation of the sample......Page 102
3.7.4 Super holder......Page 103
References......Page 104
4 Inelastic scattering and the resolution function......Page 106
4.1 Notation and definitions......Page 107
4.2 Definition of the resolution function......Page 110
4.3 Constant-Q scans......Page 114
4.4 Focusing......Page 117
4.5 Selection of collimators and energies......Page 122
4.6 Bragg tails......Page 126
4.8 Vertical resolution......Page 127
4.9 Harmonics in the incident beam......Page 129
References......Page 133
5.1 Phonons in copper......Page 135
5.1.2 E-fixed mode......Page 141
5.2 Phonons and magnons in iron......Page 143
5.3 Magnons in MnF2......Page 149
References......Page 156
6.1 Higher-order neutrons......Page 157
6.1.2 Inelastic scattering......Page 158
6.2 Accidental Bragg scattering......Page 160
6.2.1 General case......Page 162
6.2.2 Small q......Page 167
6.3 Elastic streaks at small q......Page 170
6.4.1 Bragg tail......Page 171
6.5.1 Al......Page 172
6.5.2 Air......Page 174
6.5.3 He......Page 175
6.6 Techniques for spotting “spurions”......Page 176
References......Page 179
7.1 Three-axis vs. two-axis instruments......Page 180
7.2 Lorentz factor for a triple-axis spectrometer......Page 182
7.3 Non-uniform lineshapes......Page 184
7.4 Double scattering......Page 189
7.5 Double scattering in structural phase transitions......Page 194
7.5.1 SrTiO3......Page 195
7.5.2 Nb3Sn......Page 197
7.6 Double scattering in magnetic transitions......Page 199
7.6.1 FeTiO3......Page 200
7.6.2 Fe3O4......Page 203
7.6.3 MnF2......Page 204
7.7 Double scattering from twins......Page 206
7.8 Varying resolution by choice of analyzer......Page 207
References......Page 211
8.1.1 Definition of polarization......Page 213
8.1.2 Scattering formulas......Page 214
8.2.1 Polarizing a neutron beam......Page 217
8.2.2 Control of polarization direction......Page 220
8.3 Magnetic form-factor studies......Page 221
8.4.1 Basics of polarization analysis......Page 225
8.4.2 Applications to Bragg diffraction......Page 230
8.4.3 Paramagnetic scattering by the differential technique (HF – VF)......Page 232
8.5 Spherical neutron polarimetry......Page 239
References......Page 241
Appendix 1 Neutron scattering lengths and cross sections......Page 243
References......Page 244
Appendix 2 Crystallographic data......Page 260
Appendix 3 Other useful tables......Page 262
Appendix 4 The resolution function for a triple-axis neutron spectrometer......Page 268
A4.1.1 Derivation of…......Page 269
A4.1.2 Properties of…......Page 273
A4.2 Qualitative analysis of the resolution function......Page 275
A4.3.1 Transformation to a common coordinate system......Page 276
A4.3.2 Integration over…......Page 277
A4.3.4 Special case: elastic scattering......Page 279
A4.3.5 Sample mosaic......Page 280
A4.4 The ellipsoid of constant probability......Page 281
References......Page 282
Index......Page 283