Download Elastic Scattering Reflection

Elastic Scattering
Reflection
Refraction
Rayleigh Scattering
Thomson Scattering
MSE 321 Structural Characterization
Reflection
Io
Ir
Io
θi θr
Smooth surface
Rough surface
Law of Reflection:
Angle of incidence (θi) = angle of reflection (θr)
due to
Fermat's principle (light follows path of least time)
MSE 321 Structural Characterization
Refraction
Note: n = µ
Snell’s Law
θ1
µ1 sinθ2
=
µ2 sinθ1
Slow
medium
θ2
µ=c/v
http://www.scribd.com/doc/48705529/Microscope-Basic-and-Beyond
If the angle is too great, the rays do not emerge but yield total internal reflection.
When light passes from glass (µ = 1.515) into immersion oil (µ = 1.515),
the rays are not refracted since the refractive indices are identical.
MSE 321 Structural Characterization
Rayleigh Scattering
Rayleigh scattering refers to the scattering of light off air molecules and
can be extended to scattering from particles up to about a tenth of the
wavelength of the light.
N dipole scatterers
R
θ
observer
MSE 321 Structural Characterization
λ = wavelength
α = polarisability
Thomson Scattering
elastic scattering of EM radiation by a free charged particle
r
2θ
µ0 = 4πx10-7 mkg/C2
e = 1.6022x10-19 C
m = 9.1094x10-31 kg
K = 7.94x10-30 m2
2θ = angle between incident and scattered photon
1.
The scattered wave is elastic, coherent and spherical (symmetric with respect to the scattering angle,
i.e., as much is scattered forwards as backwards).
2.
Electrons have the same Thomson cross-section for polarized and unpolarized light.
3.
The scattered radiation is polarized: 100% in the plane orthogonal to the direction of incident photon and
0% in the direction of the incident photon.
4.
Thomson scattering is one of the most important processes for impeding the escape of photons through
a medium.
MSE 321 Structural Characterization
Inelastic Scattering
Fluorescence
Compton Scattering
Raman Scattering
Absorption
MSE 321 Structural Characterization
Fluorescence
Absorption of light at one wavelength and its re-emission in any direction
at a longer wavelength
Phosphorescence – relaxation occurs via an intermediate state and so is
delayed
hv1
hv2
MSE 321 Structural Characterization
Compton Scattering
Incoherent – no phase relationship between incident and scattered beams
Useless for diffraction – just adds to background
Note: Thomson scattering is just the low-energy limit of Compton scattering (νh << mc2) in which the
electron is too tightly bound to receive momentum from the photon, so the interaction is elastic and
∆λ = 0.
MSE 321 Structural Characterization
Vibrational Spectroscopy
When visible light is scattered, some will undergo a shift in wavelength
(analogous to modified Compton scattering of x-rays)
Rayleigh Scattering – unmodified, due to normal optical properties of atoms
Raman Scattering – modified, due to fluctuations from their normal state
Group frequencies (C=O, C-C, H-R, etc.) make vibrational spectroscopy a valuable analytical tool
Vibrations in direction of bond = stretching
Vibrations perpendicular to bond = bending or deformation
wavenumber [cm-1] = 1 / λ
3657 cm-1
3756 cm-1
1595 cm-1
IR
3N-6 normal modes
H2O - 3 modes
3N – 5 normal modes
for linear molecules
like CO2
Microwave
Far IR
http://www.lsbu.ac.uk/water/vibrat.html
Sir Chandrasekkara Venkata Raman,
1888-1970
Nobel Prize for Physics in 1930
"A new radiation", Indian J. Phys., 2 387 (1928).
MSE 321 Structural Characterization
Vibrational Spectroscopy
Origin of IR and Raman Spectra
IR spectra arise due to a change in electronic dipole moment during the vibration
Raman spectra arise due to a change in the polarisability of the molecule during the vibration
Molecule irradiated by light of frequency ν, then due to electronic polarisation induced in the
molecule, light of frequency ν (Rayleigh scattering) as well as ν ± νν (Raman scattering) is
emitted.
Frequency shifts are independent of ν.
Calcite
ν4
ν1
Intensity
ν2
FTIR
Raman
ν4
ν3
600
800
1000
1200
Wavenumber (cm-1)
MSE 321 Structural Characterization
1400
1600
Raman Spectroscopy
Electric field, E, associated with photon
of frequency ν, amplitude E0
E = E0cos2πνt
Combining equations and collecting terms:
Induced dipole moment, P,
in diatomic molecule
P = αE = αE0cos2πνt
α is the polarisability
P = αEo cos2 πν t

 δα  
=  αo + 
 q  Eo cos2 πν t

 δq  o 
 δα 
 qEo cos 2 πν t
= αoEo cos2 πν t + 
 δq  o
Displacement from equilibrium position
q = q0cos2πννt
νν is molecular vibration frequency
Polarisability
 δα 
 qo cos 2 πν νtE o cos2 πν t
= αoEo cos2 πν t + 
 δq  o
 δα 
α = αo + 
q
 δq 0
 δα 
 qo Eo cos2 πν t cos 2 πν νt
= αoEo cos2 πν t + 
 δq  o
For small vibration amplitudes q0
αo is polarisability at equilibrium position
P = α0E0cos2πνt +
Rayleigh scattering
Anti-Stokes
Stokes
 δα 
 q0E0{cos[2π(ν + νν)t] + cos[2π(ν – νν)t]}
 δq  o
1
2
MSE 321 Structural Characterization
Inelastic Scattering
Absorption
Penetration depth/mean free path determines depth of specimen sampled
Varies with wavelength and material, but typically several microns for x-rays, shorter for electrons
I = I0exp(-µx)
I = I0exp[-(µ/ρ)ρ’x]
µ = linear absorption coefficient (increases as Z increases), units of cm-1
µ/ρ = mass absorption coefficient, independent of physical state, units cm2/g
ρ(Pb) = 13.84 g/cm3
For λ = 0.4 Å, µ/ρ ~ 30 cm2/g
As λ decreases, µ/ρ decreases (photons of higher E pass more easily)
When λ reduced just below the critical value (0.14088 Å for Pb),
µ/ρ rises by a factor of ~ 5. K absorption edge.
Photons/electrons now have sufficient energy to knock out
K electrons – energy converted into K fluorescent radiation.
Just above K edge, 10% of I gets through 832 µm of Pb
Just below K edge, 10% of I gets through just 179 µm of Pb
and only 0.0022% makes it through 832 µm.
“Absorption” = scattering + true absorption
(production of photoelectrons & fluorescence)
MSE 321 Structural Characterization