An Introduction to Neutron Scattering - Spallation Neutron Source

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What Is the Largest Object That Can Be Measured by SANS? • Angular divergence of the neutron beam and its lack of monochromaticity contribute to finite transverse & longitudinal coherence lengths that limit the size of an object that can be seen by SANS • For waves emerging from slit center, path difference is hd/L if d
Instrumental Resolution for SANS Traditionally, neutron scatterers tend to think in terms of Q and E resolution 4π Q = sin θ λ For SANS, ( δλ/ λ) For equal source - sample & sample - detector distances apertures at source and sample of h, δθ The smallest v alue of θ At this δQ rms ~ ( δθ The largest value of θ , angular rms ⇒ / θ min δQ rms Q )Q observable is ~ δθ This is equal to the transvers e coherence length for the neutron and achieves a maximum of about 5 μm at the ILL 40 m SANS instrument using 15 Å neutrons. Note that at the largest va lues of θ , set by the detector size and distance from the sample, wavelengt h resolution 2 2 ~ 5% andθ is small, min = δλ λ 2 determined resolution rms 2 + cos rms 4π / λ ~ ( 2π / λ) h / L object is ~ 2π/ δQ sin dominates. 2 θ. δθ so by the direct dominates rms = 2 θ 2 δQ 2 Q 2 5/ 12h/L. and ~ λh / L . = 0. 0025 of L + and beam size : θ δθ θ equal min 2 2 ~ 1. 5h / L
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y Roger Pynn Los Alamos National La
Page 3 and 4:
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
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: Where Does SANS Fit As a Structural
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
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For Quasi-elastic Scattering, the E
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Neutron counts ( per 50 sec) Neutro
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Field-Integral Inhomogeneities caus
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Neutron Spin Echo study of Deformat
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Neutron Spin Phases NRSE spectromet
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The Measured Polarization for NRSE
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Measuring Line Shapes for Inelastic
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“Phonon Focusing” • For a sin
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An NRSE Triple Axis Spectrometer at
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“Tilted” Fields for Diffraction
Page 189 and 190:
Spin Echo SANS using Magnetic Films
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Conclusion: NSE Provides a Way to S
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An Introduction to Neutron Scattering - Spallation Neutron Source

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