An Introduction to Neutron Scattering - Spallation Neutron Source

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Recapitulation of Key Messages From Lecture #1 • Neutron scattering experiments measure the number of neutrons scattered by a sample as a function of the wavevector change (Q) and the energy change (E) of the neutron • Expressions for the scattered neutron intensity involve the positions and motions of atomic nuclei or unpaired electron spins in the scattering sample • The scattered neutron intensity as a function of Q and E is proportional to the space and time Fourier Transform of the probability of finding two atoms separated by a particular distance at a particular time • Sometimes the change in the spin state of the neutron during scattering is also measured to give information about the locations and orientations of unpaired electron spins in the sample
What Do We Need to Do a Basic Neutron Scattering Experiment? • A source of neutrons • A method to prescribe the wavevector of the neutrons incident on the sample • (An interesting sample) • A method to determine the wavevector of the scattered neutrons – Not needed for elastic scattering • A neutron detector Incident neutrons of wavevector k 0 Scattered neutrons of wavevector, k 1 Q k 0 k 1 Sample Detector Remember: wavevector, k, & wavelength, λ, are related by: k = m n v/(h/2π) = 2π/λ
Page 1 and 2: y Roger Pynn Los Alamos National La
Page 3 and 4: Why do Neutron Scattering? • To d
Page 5 and 6: The Neutron has Both Particle-Like
Page 7 and 8: Thermal Neutrons, 8 keV X-Rays & Lo
Page 9 and 10: Brightness & Fluxes for Neutron & X
Page 11 and 12: Scattering by a Single (fixed) Nucl
Page 13 and 14: Coherent and Incoherent Scattering
Page 15 and 16: so or ie Coherent Elastic Scatterin
Page 17 and 18: Neutrons can also gain or lose ener
Page 19 and 20: Magnetic Scattering • The magneti
Page 21 and 22: Ene rgy Trans fe r (me V) 10000 100
Page 23 and 24: References • Introduction to the
Page 25: Overview 1. Essential messages from
Page 29 and 30: About 1.5 Useful Neutrons Are Produ
Page 31 and 32: The ESRF* & ILL* With Grenoble & th
Page 33 and 34: Neutron Sources Provide Neutrons fo
Page 35 and 36: Proton Radiography 800-MeV Linear A
Page 37 and 38: Components of a Spallation Source A
Page 39 and 40: Simultaneously Using Neutrons With
Page 41 and 42: The Actual ToF Gain From Source Pul
Page 43 and 44: Why Isn’t There a Universal Neutr
Page 45 and 46: • Uncertainties in the neutron wa
Page 47 and 48: Typical Neutron Scattering Instrume
Page 49 and 50: Most Neutron Detectors Use 3 He •
Page 51 and 52: Rotating Choppers Are Used to Tailo
Page 53 and 54: 3. Diffraction Next Lecture 1. Diff
Page 55 and 56: 2. Diffraction This Lecture 1. Diff
Page 57 and 58: Neutron Diffraction • Neutron dif
Page 59 and 60: For Periodic Arrays of Nuclei, Cohe
Page 61 and 62: We would be better off if diffracti
Page 63 and 64: Powder - A Polycrystalline Mass All
Page 65 and 66: Measuring Neutron Diffraction Patte
Page 67 and 68: Time-of-Flight Powder Diffraction U
Page 69 and 70: There’s more than meets the eye i
Page 71 and 72: How good is this function? Protein
Page 73 and 74: High-resolution Neutron Powder Diff
Page 75 and 76: Texture Measurement by Diffraction
Page 77 and 78:
Definitions of Stress and Strain
Page 79 and 80:
Why use Metal Matrix Composites ? F
Page 81 and 82:
Neutron Diffraction Measures Mean R
Page 83 and 84:
Deformation Mechanism in U/Nb Alloy
Page 85 and 86:
Obtaining the Pair Distribution Fun
Page 87 and 88:
Effect of Doping on the Octahedra
Page 89 and 90:
Surface Reflection Is Very Differen
Page 91 and 92:
What Is the Neutron Wavevector Insi
Page 93 and 94:
Only Those Thermal or Cold Neutrons
Page 95 and 96:
What do the Amplitudes a R and a T
Page 97 and 98:
Fresnel’s Law for a Thin Film •
Page 99 and 100:
Reflection by a Graded Interface io
Page 101 and 102:
Direct Inversion of Reflectivity Da
Page 103 and 104:
4 R*Q z 10 -7 10 -8 10 -9 1.3% PEG
Page 105 and 106:
Polarized Neutron Reflectometry (PN
Page 107 and 108:
Reflection from Rough Surfaces z z
Page 109 and 110:
fi fi fi Q =kf -ki Qx-Qz Transforma
Page 111 and 112:
Observation of Hexagonal Packing of
Page 113 and 114:
This Lecture 5. Small Angle Neutron
Page 115 and 116:
Two Views of the Components of a Ty
Page 117 and 118:
Where Does SANS Fit As a Structural
Page 119 and 120:
Instrumental Resolution for SANS Tr
Page 121 and 122:
SANS Measures Particle Shapes and I
Page 123 and 124:
Examples of Spherically-Averaged Fo
Page 125 and 126:
Correlations Can Be Measured in Con
Page 127 and 128:
Radius of Gyration Is the Particle
Page 129 and 130:
Contrast & Contrast Matching Water
Page 131 and 132:
Verification of of the Gaussian Coi
Page 133 and 134:
Porod Scattering function. n correl
Page 135 and 136:
ln(I) Typical Intensity Plot for SA
Page 137 and 138:
References • Viewgraphs describin
Page 139 and 140:
We Have Seen How Neutron Scattering
Page 141 and 142:
The Elastic & Inelastic Scattering
Page 143 and 144:
Examples of S(Q,ω) and S s(Q,ω)
Page 145 and 146:
Inelastic Magnetic Scattering of Ne
Page 147 and 148:
Measured Inelastic Neutron Scatteri
Page 149 and 150:
Atomic Motions for Longitudinal & T
Page 151 and 152:
Phonons - the Classical Use for Ine
Page 153 and 154:
The Accessible Energy and Wavevecto
Page 155 and 156:
What Use Have Phonon Measurements B
Page 157 and 158:
Time-of-flight Methods Can Give Com
Page 159 and 160:
Neutron Spin Echo By Roger Pynn* Lo
Page 161 and 162:
• Uncertainties in the neutron wa
Page 163 and 164:
The Underlying Physics of Neutron S
Page 165 and 166:
How does a Neutron Spin Behave when
Page 167 and 168:
The Principles of NSE are Very Simp
Page 169 and 170:
For Quasi-elastic Scattering, the E
Page 171 and 172:
Neutron counts ( per 50 sec) Neutro
Page 173 and 174:
Field-Integral Inhomogeneities caus
Page 175 and 176:
Neutron Spin Echo study of Deformat
Page 177 and 178:
Neutron Spin Phases NRSE spectromet
Page 179 and 180:
The Measured Polarization for NRSE
Page 181 and 182:
Measuring Line Shapes for Inelastic
Page 183 and 184:
“Phonon Focusing” • For a sin
Page 185 and 186:
An NRSE Triple Axis Spectrometer at
Page 187 and 188:
“Tilted” Fields for Diffraction
Page 189 and 190:
Spin Echo SANS using Magnetic Films
Page 191:
Conclusion: NSE Provides a Way to S
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An Introduction to Neutron Scattering - Spallation Neutron Source

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