An Introduction to Neutron Scattering - Spallation Neutron Source

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V(z) One can also think about Neutron Reflection from a Surface as a substrate z 1-d Problem Film Vacuum V(z)= 2 π ρ(z) h 2 /m n k 2 =k 0 2 - 4π ρ(z) Where V(z) is the potential seen by the neutron & ρ(z) is the scattering length density
Fresnel’s Law for a Thin Film • r=(k 1z-k 0z)/(k 1z+k 0z) is Fresnel’s law • Evaluate with ρ=4.10 -6 A -2 gives the red curve with critical wavevector given by k 0z = (4πρ) 1/2 • If we add a thin layer on top of the substrate we get interference fringes & the reflectance is given by: r = r 01 1+ + r r 01 12 r 12 i2k 1z i2k and we measure the reflectivity R = r.r* e e t 1z t 0.01 0.02 0.03 0.04 0.05 • If the film has a higher scattering length density than the substrate we get the green curve (if the film scattering is weaker than the substance, the green curve is below the red one) • The fringe spacing at large k 0z is ~ π/t (a 250 A film was used for the figure) -1 -2 -3 -4 -5 Log(r.r*) 0 1 2 substrate k 0z Film thickness = t
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
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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: What do the Amplitudes a R and a T
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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