phys 590 1 - iowa state universitycanfield.physics.iastate.edu/course/phys_590_1.pdfinelastic x-ray...
TRANSCRIPT
Scattering
Alan Goldman
1
Section Outline
• March 31 Introduction to Scattering (Goldman)
• April 2 e-beam measurements (Kramer)
• April 4 Advanced e-beam measurements (Kramer)
• April 7 Single crystal x-ray and neutron diffraction (Goldman)
• April 9 Magnetic neutron and x-ray diffraction (Kreyssig)
• April 11 Powder diffraction methods (Jesche)
• April 14 Inelastic neutron scattering (Tucker)
2
• atoms pack in periodic, 3D arrays• typical of:
Crystalline materials...
-metals-many ceramics-some polymers
What is the atomic scale structure?
• atoms have no “regular” packing• occurs for:
Noncrystalline materials...
-complex structures-rapid cooling
"Amorphous" = Noncrystalline
Distance between atoms ~ Å (10-9 m)
Si Oxygen
crystalline SiO2
noncrystalline SiO2Adapted from Fig. 3.18(b),Callister 6e.
Adapted from Fig. 3.18(a),Callister 6e.
3
Interference of two waves Double slit diffraction
2 slits 2 slits and 5 slits
You can also do this with light (as well as neutrons and electrons)!
Diffraction
4
Visible light
X-rays
Resolution ~ wavelength
So, 10-9 m resolution Requires λ ~ 10-9 m
How do we use x-rays to study crystal structures?
5
Length scales
6
What are the atomic scale dynamics?
Transverse acoustic mode
Lynn, et al., Phys. Rev. B 8, 3493 (1973).
Linear spin waves
Perring et al., Phys. Rev. Lett. 77, 711 (1996).
Ferromagnetic
7
Dynamical (time) scalesFa
ster
pro
cess
es
Shorter length scales
Elasticscattering
Cold neutrons
Thermal neutrons
Epithermalneutrons
8
How are these changed by….
• Temperature• Magnetic Field• Electric Field• Pressure
9
Different probes
10
Different probes
NEUTRONS X-RAYS ELECTRONS
Wavelength range 0.4 - 10 Å 0.1 - 5 Å 0 .04 - 0.2 Å
Energy range 0.001 - 0.5 eV 3000 - 100000 eV 6000 - 120000 eV
Cross-section 10-25 barns 10-25 Z2 barns ~10-22 barns
Penetration depth ~ cm ~ m - mm ~ nm
Typical flux 1011 s-1 m-2 1024 s-1 m-2 1026 s-1 m-2
Beam size mm-cm m-mm nm-m
Typical sample Any bulk sample Small crystals, powders, surfaces
Surfaces, thin films, grains, gases
TechniquesDiffraction
Inelastic scatteringReflectivity
DiffractionPhoton absorption
PhotoemissionInelastic scattering
MicroscopyDiffraction
Emission spectroscopyEELS
Phenomena
Magnetic/crystal structurescollective excitations
(phonons, spin waves)electronic excitations (crystal-
field, spin-orbit)
Crystal structures, electronic transitions
(photoemission, absorption)
microstructurecrystal structures
electronic transitions
11
Atomic scattering cross-sections
Abundance (%)
Cross-section (bn)
Absorption (bn)
Gd --- 180 49700152Gd 0.2 13 735154Gd 2.1 13 85155Gd 14.8 66 61100156Gd 20.6 5 1.5157Gd 15.7 1044 259000158Gd 24.8 10 2.2160Gd 21.8 10.52 0.77
Neutrons Random with Z Depends on isotope Depends on nuclear spin Absorption can be problem
X-rays: Atomic form factor means that scattering decreases with scattering angle.Neutrons: constant scattering as a function of scattering angle
12
Why neutrons??
Penetration ~ centimeters, bulk probe Sensitivity to low-Z Isotopic contrast Wavelength range ~ interatomic spacing (1-2 Å) → diffraction
interacts with nuclei Interacts with magnetic moment of unpaired e-
Can measure crystal and magnetic structures Thermal neutron energies are comparable to elementary
excitations → natural probe for atomic-scale dynamics
13
Neutron magnetism
Spin-1/2 particle Magnetic moment n
14
Nuclear (lattice) excitations
Commonly studied excitations Phonons Librations and vibrations in molecules Diffusion Collective modes in glasses and liquids
Neutron scattering measures simultaneously the wavevector and energy of collective excitations dispersion relation, (q)In addition, local excitations can of course be observed
Excitations can tell us about Interatomic potentials & bonding Phase transitions & critical phenomena (soft modes) Fluid dynamics Momentum distributions & superfluids (eg. He) Interactions (eg. electron-phonon coupling)
15
Spin excitations
Spin excitations Spin waves in ordered magnets Paramagnetic & quantum spin fluctuations Crystal-field & spin-orbit excitations
Magnetic inelastic scattering can tell us about Exchange interactions Single-ion and exchange anisotropy (determine Hamiltonian) Phase transitions & critical phenomena Quantum critical scaling of magnetic fluctuations Other electronic energy scales (eg. CF & SO) Interactions (eg. spin-phonon coupling)
16
Why x-rays??
Easily accessible in the laboratory Penetration ~ microns to millimeters (tuned with energy)
Low-energies can be used to probe surface and near surface regions High energies can probe the bulk of a sample
High flux at National Facilities Allows you to throw a lot of photons away → high energy and
momentum resolution Is highly polarized and highly collimated Is continuously tunable across a wide range of energies (1 keV →
200 keV) Wavelength range ~ interatomic spacing (1-2 Å) → diffraction
interacts with electrons Magnetic interactions are higher order
17
Single-crystal diffraction
Wide angle diffraction: Get an overview of everythingSingle-crystal: more detail than powders
18
Powder diffraction
For powder: Qhkl = 2kisin
ki = 2/ 2Qhkl
ki
kf
ki
kf
2
Qhkl = 2/dhkl
19
X-ray resonant magnetic scattering***
Magnetic structures of neutron absorbing materials with very high resolution
Pump-probe experiments Dynamics on picosecond to millisecond timescales
Inelastic x-ray scattering Approaching neutron energy resolution
X-ray absorption Spectroscopy***
Studies of local atomic environments and chemistry
Circular magnetic x-ray dichroism***
Element specific magnetization measurements
More than “just diffraction”
20
Small–angle scattering Studying mesoscopic-scale structures
X-ray radiography and tomography 3D views of structural features with submicron resolution
Surface scattering Studies of both solid and liquid surfaces
Coherent x-ray diffraction Probing coherence effects on the atomic scale
More than “just diffraction”
21
Producing neutrons
SpallationParticle accelerator
FissionNuclear reactor
neutrons
Moderators →Cold-EpithermalModerators →Cold-Thermal
22
Neutrons by reactor fission
High flux isotope reactor - ORNL
NIST
23
24
Neutrons by pulsed spallation
Spallation Neutron Source (ORNL)
25
Target-moderator system
SNS liquid Hg target
26
27
Production of x-rays
X-ray tube Rotating anode
28
Synchrotron radiation
Static charge ---- Electric field Charge moving at constant v ---- Magnetic field Accelerating charge --- Electromagnetic radiation
v
a
v << c v ≈ c
Synchrotron radiation is highly collimated highly linearly polarizedhighly brilliantcontinuous wavelength distribution (beyond Cu, Mo, etc..) 29
Advanced Photon Source
Synchrotron
30
31
Insertion Devices
32
Main Undulator Line
33
Places to go
HFIRSNS
MURR
LANSCEEurope
AMES
NISTSSRL
APSNSLS
34