An Introduction to Neutron Scattering - Spallation Neutron Source

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Inelastic neutron scattering measures atomic motions The concept of a pair correlation function can be generalized: G(r,t) = probability of finding a nucleus at (r,t) given that there is one at r=0 at t=0 G s (r,t) = probability of finding a nucleus at (r,t) if the same nucleus was at r=0 at t=0 Then one finds: 2 ⎛ d σ ⎞ ⎜ d dE ⎟ ⎝ Ω. ⎠ 2 ⎛ d σ ⎞ ⎜ d dE ⎟ ⎝ Ω. ⎠ coh inc = b = b where r 1 S( Q, ω) = 2πh 2 coh 2 inc ∫∫ k' r NS( Q, ω) k k' r NSi ( Q, ω) k r G( r, t) e r r i( Q. r −ωt) r drdt and (h/2π)Q & (h/2π)ω are the momentum & energy transferred to the neutron during the scattering process r 1 Si ( Q, ω) = 2πh ∫∫ G s r ( r, t) e r r i( Q. r −ωt ) r drdt Inelastic coherent scattering measures correlated motions of atoms Inelastic incoherent scattering measures self-correlations e.g. diffusion
Magnetic Scattering • The magnetic moment of the neutron interacts with B fields caused, for example, by unpaired electron spins in a material – Both spin and orbital angular momentum of electrons contribute to B – Expressions for cross sections are more complex than for nuclear scattering • Magnetic interactions are long range and non-central – Nuclear and magnetic scattering have similar magnitudes – Magnetic scattering involves a form factor – FT of electron spatial distribution • Electrons are distributed in space over distances comparable to neutron wavelength • Elastic magnetic scattering of neutrons can be used to probe electron distributions – Magnetic scattering depends only on component of B perpendicular to Q – For neutrons spin polarized along a direction z (defined by applied H field): • Correlations involving B z do not cause neutron spin flip • Correlations involving B x or B y cause neutron spin flip – Coherent & incoherent nuclear scattering affects spin polarized neutrons • Coherent nuclear scattering is non-spin-flip • Nuclear spin-incoherent nuclear scattering is 2/3 spin-flip • Isotopic incoherent scattering is non-spin-flip
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: Neutrons can also gain or lose ener
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 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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