An Introduction to Neutron Scattering - Spallation Neutron Source

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dσ dΩ ⎛ ⎜ ⎝ Q = dσ ⎞ ⎟ dΩ ⎠ where the i, j From Lecture 1: number of neutrons scattered through angle 2θ per second into dΩ number of incident neutrons per square cm per second coh k 0 = k’ ∑ b coh i b coh j e r r r r i( k −k ') . ( R −R wavevector transfer 2θ Incident neutrons of wavevector k 0 0 i j ) = ∑ i, j b coh i b coh j r Q is defined by e r r r −iQ. ( R −R i r r r Q = k '−k For elastic scattering k 0 =k’=k: Q = 2k sin θ Q = 4π sin θ/λ Sample 2θ j ) 0 Detector Scattered neutrons of wavevector, k’
Neutron Diffraction • Neutron diffraction is used to measure the differential cross section, dσ/dΩ and hence the static structure of materials – Crystalline solids – Liquids and amorphous materials – Large scale structures • Depending on the scattering angle, structure on different length scales, d, is measured: 2π / Q = d = λ / 2sin( θ ) • For crystalline solids & liquids, use wide angle diffraction. For large structures, e.g. polymers, colloids, micelles, etc. use small-angle neutron scattering
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 and 26: Overview 1. Essential messages from
Page 27 and 28: What Do We Need to Do a Basic Neutr
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: 2. Diffraction This Lecture 1. Diff
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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