An Introduction to Neutron Scattering - Spallation Neutron Source

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In NSE*, Neutron Spins Precess Before and After Scattering & a y Polarization Echo is Obtained if Scattering is Elastic z x π/2 F S π/2 π Initially, neutrons are polarized along z F Rotate spins into x-y precession plane Final Polarization, P S Allow spins to precess around z: slower neutrons precess further over a fixed path-length = cos( φ − Rotate spins through π about x axis 1 φ2 ) Elastic Scattering Event Rotate spins to z and measure polarization Allow spins to precess around z: all spins are in the same direction at the echo point if ∆E = 0 * F. Mezei, Z. Physik, 255 (1972) 145
For Quasi-elastic Scattering, the Echo Polarization depends on Energy Transfer • If the neutron changes energy when it scatters, the precession phases before & after scattering, φ 1 & φ 2, will be different: 1 2 2 using hω = m( v1 − v2 ) ≈ mvδv 2 2 3 ⎛ 1 1 ⎞ γBd γBdhω γBdm λ ω φ1 −φ 2 = γBd ⎜ − ≈ δv ≈ = 2 3 2 v1 v ⎟ ⎝ 2 ⎠ v mv 2πh • To lowest order, the difference between φ 1 & φ 2 depends only on ω (I.e. v 1 – v 2) & not on v 1 & v 2 separately • The measured polarization, , is the average of cos(φ 1 - φ 2) over all transmitted neutrons I.e. P = ∫∫ I r λ) S( Q, ω) cos( φ1 −φ ) dλdω r I( λ) S( Q, ω) dλdω ( 2 ∫∫
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y Roger Pynn Los Alamos National La
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Why do Neutron Scattering? • To d
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The Neutron has Both Particle-Like
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Thermal Neutrons, 8 keV X-Rays & Lo
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Brightness & Fluxes for Neutron & X
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Scattering by a Single (fixed) Nucl
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Coherent and Incoherent Scattering
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so or ie Coherent Elastic Scatterin
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Neutrons can also gain or lose ener
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Magnetic Scattering • The magneti
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Ene rgy Trans fe r (me V) 10000 100
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References • Introduction to the
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Overview 1. Essential messages from
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What Do We Need to Do a Basic Neutr
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About 1.5 Useful Neutrons Are Produ
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The ESRF* & ILL* With Grenoble & th
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Neutron Sources Provide Neutrons fo
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Proton Radiography 800-MeV Linear A
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Components of a Spallation Source A
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Simultaneously Using Neutrons With
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The Actual ToF Gain From Source Pul
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Why Isn’t There a Universal Neutr
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• Uncertainties in the neutron wa
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Typical Neutron Scattering Instrume
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Most Neutron Detectors Use 3 He •
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Rotating Choppers Are Used to Tailo
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3. Diffraction Next Lecture 1. Diff
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2. Diffraction This Lecture 1. Diff
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Neutron Diffraction • Neutron dif
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For Periodic Arrays of Nuclei, Cohe
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We would be better off if diffracti
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Powder - A Polycrystalline Mass All
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Measuring Neutron Diffraction Patte
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Time-of-Flight Powder Diffraction U
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There’s more than meets the eye i
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How good is this function? Protein
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High-resolution Neutron Powder Diff
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Texture Measurement by Diffraction
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Definitions of Stress and Strain
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Why use Metal Matrix Composites ? F
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Neutron Diffraction Measures Mean R
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Deformation Mechanism in U/Nb Alloy
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Obtaining the Pair Distribution Fun
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Effect of Doping on the Octahedra
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Surface Reflection Is Very Differen
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What Is the Neutron Wavevector Insi
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Only Those Thermal or Cold Neutrons
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What do the Amplitudes a R and a T
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Fresnel’s Law for a Thin Film •
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Reflection by a Graded Interface io
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Direct Inversion of Reflectivity Da
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4 R*Q z 10 -7 10 -8 10 -9 1.3% PEG
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Polarized Neutron Reflectometry (PN
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Reflection from Rough Surfaces z z
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fi fi fi Q =kf -ki Qx-Qz Transforma
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Observation of Hexagonal Packing of
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This Lecture 5. Small Angle Neutron
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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: The Principles of NSE are Very Simp
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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