I o
I r
θ i
θ r
Smooth surface
I o
Rough surface
Law of Reflection:
Angle of incidence ( θ i
) = angle of reflection ( θ r
) due to
Fermat's principle (light follows path of least time)
MSE 421/521 Structural Characterization
Note: n = µ
µ
1
µ
2
= sin θ
2 sin θ
1
µ = c / v
θ
1
Slow medium
θ
2 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 421/521 Structural Characterization

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
λ = wavelength
α = polarisability
θ observer
R
MSE 421/521 Structural Characterization
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
MSE 421/521 Structural Characterization

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 = I
0 exp(µ x ) I = I
0 exp[-( 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 cm 2 /g
ρ (Pb) = 13.84 g/cm 3
For λ = 0.4 Å, µ / ρ ~ 30 cm 2 /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 µ m of Pb
Just below K edge, 10% of I gets through just 179 and only 0.0022% makes it through 832 µ m.
µ m of Pb
“Absorption” = scattering + true absorption
(production of photoelectrons & fluorescence)
MSE 421/521 Structural Characterization
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
H
2
O - 3 modes
3N – 5 normal modes for linear molecules like CO
2
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 421/521 Structural Characterization

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 emitted.
ν (Rayleigh scattering) as well as ν ± ν
ν
(Raman scattering) is
Frequency shifts are independent of ν .
Calcite
ν
4
ν
1
ν
2
FTIR
Raman
ν
4
600 800 1000 1200
Wavenumber (cm -1 )
MSE 421/521 Structural Characterization
ν
3
1400 1600
Electric field, E , associated with photon of frequency ν , amplitude E
0
E = E
0 cos2 πν t
Combining equations and collecting terms:
Induced dipole moment, P , in diatomic molecule
P = α E = α E
0 cos2 πν t
α is the polarisability
P = α



E o o
+ cos2



δα
δ q
πν


 o t q



E o cos2 πν t
Displacement from equilibrium position = α o
E o cos2 πν t +


δα
δ q

 o qE o cos 2 πν t q = q
0 cos2 πν
ν t
ν
ν is molecular vibration frequency
Polarisability
α = α o
+
 δα

δ q


0 q
= α o
E o cos2 πν t +


δα
δ q
= α o
E o cos2 πν t +



δα
δ q


 o


 o q q o o cos 2
E o
πν cos2
ν tE
πν t o cos2 cos 2
πν
πν
ν t t
For small vibration amplitudes q
0
α o is polarisability at equilibrium position
P = α
0
E
0 cos2 πν t
Rayleigh scattering


δα
δ q

 q o
Anti-Stokes
0
E
0
{cos[2 π ( ν + ν
Stokes
ν
) t ] + cos[2 π ( ν – ν
ν
) t ]}
MSE 421/521 Structural Characterization