Neutron Scattering and Other Nuclear Techniques for Hydrogen in Materials (eBook)

Contents 6
Contributors 8
Chapter 1: Introduction 10
Chapter 2: Neutron Scattering: Introduction 15
2.1 Introduction 15
2.2 Production and Detection of Neutrons 19
2.2.1 Production of Neutrons 19
2.2.2 Detection of Neutrons 22
2.3 Interaction of Neutrons with Matter 24
2.3.1 Introduction 24
2.3.2 Scattering Length 24
2.3.3 Scattering and Absorption Cross Section 26
2.3.4 Reflection and Refraction 27
2.4 Coherent and Incoherent Scattering 28
2.4.1 Coherent and Incoherent Scattering Cross Sections 28
2.4.2 The Double-Differential Scattering Cross Section 29
2.4.3 Magnetic Scattering 32
2.5 Elastic, Inelastic, and Quasielastic Neutron Scattering 33
2.5.1 Elastic Scattering: Bragg Diffraction 33
2.5.2 Inelastic Neutron Scattering: Phonons, Magnons 35
2.5.3 Quasielastic Neutron Scattering 36
2.6 Summary 37
References 37
Chapter 3: Neutron Powder Diffraction 38
3.1 Introduction 38
3.2 Principles of Powder Diffraction 41
3.2.1 Crystal Structure 41
3.2.2 Neutron Diffraction 43
3.2.3 Magnetic Neutron Scattering on Crystals with Ordered Magnetic Moments 46
3.3 Information in a Powder Diffraction Pattern 46
3.3.1 Phase Identification: Qualitative Phase Analysis 47
3.3.2 Quantitative Phase Analysis 47
3.3.3 Peak Width 48
3.4 Instrumentation 49
3.4.1 Reactors 50
3.4.2 Spallation Sources 50
3.4.3 Neutron Powder Diffractometer 51
3.4.3.1 Constant Wavelength (CW) Techniques 51
3.4.3.2 Time-of-Flight Techniques 52
3.4.3.3 Comparison CW vs. ToF 54
3.4.4 Sample 54
3.4.5 Materials Containing Hydrogen 55
3.5 Rietveld Method 56
3.5.1 Principle of Rietveld Refinement 56
3.5.2 Recording and Calculating Powder Pattern 57
3.5.2.1 Calculated Pattern 58
3.5.2.2 Scale Factor 59
3.5.2.3 Multiplicity of the Reflection hkl 60
3.5.2.4 Absorption Factor 60
3.5.2.5 Displacement Factor 62
3.5.2.6 Lorentz Factor 62
3.5.2.7 Preferred Orientation 63
3.5.2.8 Structure Factor 64
3.5.2.9 Profile Function 65
3.5.2.10 Background 67
3.5.2.11 Validation of Refined Crystal Structure 67
3.5.2.12 Refinement Strategy 70
3.6 Localizing Hydrogen by NPD 72
3.6.1 Ti-V-Mn Alloy 74
3.6.2 Ti-V-Cr Alloy 76
3.6.3 La1.5Mg0.5Ni7 Alloy 77
3.6.4 Structure of NaAlD4 and LiAlD4 81
3.6.5 beta-Yttrium Borohydride Y(BH4)3: X-rays vs. Neutrons 85
3.6.6 Mg6Co2H11: Weak Superstructure Induced by Hydrogen 87
3.7 In-Situ Experiments 87
3.7.1 Cell Design 89
3.7.2 Palladium 90
3.7.3 Zircaloy-4 91
References 91
Chapter 4: Total Neutron Scattering 97
4.1 Introduction 97
4.2 The Total Neutron Scattering Technique 98
4.2.1 Principles 98
4.2.2 Instrumentation 100
4.2.3 Data Reduction and Analysis 101
4.3 Total Neutron Scattering Investigations of Hydrogen Storage Materials 105
4.3.1 Crystalline Metal Hydrides 105
4.3.2 Amorphous and Nano-sized Metal Hydrides 111
4.3.3 Complex Hydrides 114
4.4 Conclusion 117
References 117
Chapter 5: Neutron Reflectometry 120
5.1 Introduction 121
5.2 Principles of the Method 122
5.2.1 Unpolarized Neutrons 122
5.2.2 Polarized Neutrons 125
5.2.3 Determination of Hydrogen and Deuterium Content 127
5.2.3.1 Single Layers 127
5.2.3.2 Multilayers 128
5.3 Instrumentation 130
5.3.1 Typical Setup at a Reactor Source 130
5.3.2 Typical Setup at a Spallation Source 131
5.3.3 Sample Environment 133
5.4 Difference Between Bulk and Thin Film Samples 133
5.5 Hydrogen Absorption of Mg-Based Thin Films 135
5.5.1 Binary Mg-Al Alloys 135
5.5.1.1 Mg-Al Alloy Composition 135
5.5.1.2 The Importance of the Catalyst Layer 137
5.5.2 Ternary Mg-based Alloys 137
5.5.2.1 Real-Time Measurements 138
5.5.2.2 Comparison of Pure Mg to Mg-Cr-V 139
5.6 Hydrogen Absorption of Polycrystalline and Epitaxial Single-Crystal Nb Films 140
5.6.1 Nb Bulk Properties 140
5.6.2 Fe/Nb Multilayers 142
5.6.3 W/Nb Multilayers 149
5.6.4 Conclusion 150
5.7 In-Situ Electrochemical Measurements 151
5.7.1 Zr Thin Films 151
5.7.2 Ti Thin Films 154
5.8 Exchange-Coupled Multilayers 156
5.8.1 Introduction 156
5.8.2 Fe/Nb Multilayers 157
5.8.3 Fe/V Superlattices 160
References 161
Chapter 6: Small Angle Neutron Scattering 164
6.1 Introduction 164
6.2 Principles of the Method 165
6.2.1 Scattering Vector 165
6.2.2 Interaction Radiation/Sample 166
6.2.3 Form Factor and Particle Correlation 169
6.2.4 Guinier Approximation 171
6.2.5 Porod Law 172
6.2.6 Particle Shape 173
6.2.7 Fractals 174
6.3 Instrumentation 176
6.3.1 Typical Setup at a Reactor Source 176
6.4 Analysis of Data 179
6.4.1 Interacting Particles 180
6.4.2 Contrast Variation and Deuterium Labelling 181
6.4.3 Background Subtraction 183
6.5 SANS and Porous Media 183
6.6 Nano-Scaled and Infiltrated Hydrides 184
6.6.1 Infiltrated Mg(11BD4)2 184
6.6.2 Infiltrated NaAlD4 187
6.6.3 Infiltrated MgD2 188
6.6.4 Li11BD4-Mg(11BD4)2 190
6.7 SANS and SAXS 191
References 196
Chapter 7: Neutron Imaging 197
7.1 Introduction 198
7.2 Basics of Neutron Imaging 198
7.3 Neutron Radiography Experiments 201
7.3.1 Digital Radiography 202
7.3.2 Beam Geometry: A Pinhole Camera 202
7.3.3 Hardware Limit of the Resolution 204
7.3.4 Computed Tomography 205
7.3.5 Other Imaging Methods 206
7.3.5.1 Stroboscopic Neutron Imaging 206
7.3.5.2 Bragg-Edge Neutron Imaging 206
7.3.5.3 Magnetic and Depolarization Measurement 206
7.3.5.4 Linear Phase Contrast and Dark Field Imaging 207
7.3.6 High-Resolution Neutron Imaging Facilities Worldwide 207
7.4 Investigation of Hydrogen in Steel and Iron 208
7.4.1 In Situ Diffusion Measurements 209
7.4.2 In Situ Measurements of Hydrogen Distributions 212
7.5 Investigations of Hydrogen in Zirconium Alloys 215
7.5.1 Introduction 215
7.5.2 Ex Situ and In Situ Investigations of the Hydrogen Uptake During Steam Oxidation of Zirconium Alloys 216
7.5.3 Inspection of Samples from Large-Scale Accident Simulation Tests 223
7.5.4 In Situ Investigations of the Hydrogen Diffusion in Zircaloy-4 225
References 227
Source of Further Information 229
Chapter 8: Incoherent Neutron Scattering 230
8.1 Introduction 231
8.2 Coherent and Incoherent Scattering 231
8.3 Sensitivity of Incoherent Neutron Scattering to Hydrogen in Nuclear Fuels 236
8.4 Determining the Solubility Limit of Hydrogen in Metallic Materials [3] 241
8.5 Conclusion 247
References 247
Chapter 9: Inelastic and Quasi-Elastic Neutron Scattering 248
9.1 Introduction: The Advantages of These Methods 249
9.2 Theory 250
9.2.1 The Basic Theory of Neutron Scattering 250
9.2.2 Quantum Treatment of Inelastic Neutron Scattering 253
9.2.3 Theory of Inelastic Neutron Scattering from Crystals 254
9.2.4 Incoherent Inelastic Scattering from a Proton in a Harmonic Potential Well: The Einstein Oscillator Model 255
9.2.5 Perturbation Analysis of Anharmonic and Anisotropic Effects in Inelastic Incoherent Neutron Scattering from H in Solids 257
9.2.6 Comparison with Ab Initio Calculations 258
9.2.7 Incoherent Scattering from Systems Analysed Using Lattice Dynamics 259
9.2.8 Neutron Scattering from Systems with Interacting Hydrogen Atoms: Comparison with DFT Simulations 261
9.2.9 Measurement of Amplitude-Weighted Phonon Density of States Curves for Hydrogen for Comparison with the Simulated Data 262
9.2.10 Coherent Inelastic Neutron Scattering from Polycrystals 264
9.2.11 Inelastic Neutron Scattering from Molecular Hydrogen 267
9.3 Quasi-Elastic Neutron Scattering 272
9.3.1 The Theory of Quasi-Elastic Neutron Scattering 272
9.3.2 The Chudley-Elliott Model 274
9.3.3 Diffusion of H in the ? Pd/H System 276
9.3.4 Lattices with More Than One Atom/Unit Cell 276
9.3.5 QENS from an Atom Diffusing in a Lattice with Traps 277
9.4 Conclusions 278
References 278
Chapter 10: Elastic Recoil Detection Analysis 280
10.1 Introduction 280
10.2 Principles of Elastic Recoil 282
10.2.1 Kinematics of Scattering Events 282
10.2.2 Energy Loss and Depth Resolution 283
10.2.3 Hydrogen Concentration Determination 284
10.3 Instrumentation 285
10.3.1 Accelerators and Beam Lines 285
10.3.2 Conventional Detection Setup. Reflection and Transmission Geometry 285
10.3.3 Less-Conventional Detection Setups 286
10.4 Hydrogen Measurements in Metals 287
10.5 Hydrogen Measurements in Ceramics 298
10.6 Hydrogen Measurement in Minerals 303
10.7 Hydrogen Measurements in Thin Films 305
10.8 Conclusion 313
References 314
Chapter 11: Nuclear Reaction Analysis 318
11.1 Introduction 318
11.2 The Principle of the Method 319
11.2.1 Interaction of Ions with Matter 319
11.2.2 Basic Principle of Depth Profiling 320
11.2.3 Determining a Hydrogen Concentration 322
11.2.4 Depth Information 324
11.2.5 Depth Resolution 325
11.2.6 Straggling 327
11.2.7 A Simple and Straightforward Example 328
11.3 More Special Cases and Complications 331
11.3.1 Stability of Samples Under Irradiation 332
11.3.2 High Efficiency gamma-Ray Detection 333
11.3.3 Background 334
11.3.4 Samples with Hydrogen Concentrations Strongly Varying with Depth 336
11.3.5 Example of Low Concentration Detection 337
References 338
Chapter 12: Nuclear Magnetic Resonance 340
12.1 Introduction 340
12.2 Basic Interactions of Nuclear Spins 342
12.3 Experimental Arrangements and Basic Methods 346
12.3.1 Typical Experimental Setup 346
12.3.2 Methods of Spectral Measurements 348
12.3.3 Magic-Angle Spinning 350
12.3.4 Methods of Relaxation Time Measurements and Pulse Sequences 351
12.3.5 Diffusion Measurements by NMR 353
12.4 Structural Information from NMR Measurements 355
12.5 Electronic Properties of Metal-Hydrogen Systems 359
12.6 Hydrogen Mobility 361
12.6.1 Hydrogen Jump Rates: Localized Motion and Long-Range Diffusion 361
12.6.2 Direct Measurements of Hydrogen Diffusion Coefficients 372
12.6.3 Complementarity Between NMR and Quasielastic Neutron Scattering 374
References 375
Chapter 13: Positron Annihilation Spectroscopy (PAS) 380
13.1 Introduction 380
13.2 Principles and Setup of the PAS 382
13.2.1 Positron Lifetime Measurement 382
13.2.2 (Coincidence) Doppler Broadening Measurement 387
13.3 Examples of Positron Annihilation Studies on Lattice Defects 389
13.3.1 Formation of Lattice Defects Upon Hydrogenation in LaNi5-Based Alloys [20] 389
13.3.1.1 Summary 394
13.3.2 Vacancy Formation and Recovery During Hydrogenation of LaNi5Cu [35] 394
13.3.2.1 Summary 400
13.3.3 Hydrogen Embrittlement in Pure Fe [43] 400
13.3.3.1 Summary 403
References 404
Index 406