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RAMAN
SCATTERING:
FOUNDATIONS,
TECHNICAL
EVOLUTION
and
APPLICATIONS
Sir Chandrasekhara Venkata Raman
Kariamanickam Srinivasa Krishnan
the two indian researchers that
observed for the first time the
“inelastic light scattering”= Raman
effect
THEORETICAL
FOUNDATIONS
What’s Raman Scattering?
Essentially is...
When light interacts with matter,
the scattered (absorbed and reemitted) light may have
different “colours” (or frequency
or energy – a little bit greater and
a little bit lower of the incident
one).
(The human eyes are not so
sensitive
to
detect
the
differences!!)
Foundations of Raman Scattering:
A - Classical Approach
Remembering about electric field
1) Interaction between electric
charges is done by electric field E:
F = q.E; E = F/q
That is, electric fields apply forces
on electric charges, polarizing
electrically materials...
-q
+q
E
2) What’s light?
Electromagnetic radiation.
From the Maxwell’s equations, we
can obtain wave equations for the
electric and magnetic fields:
∂2E/∂x2 – 1/c2 ∂2 E/∂t 2 = 0
∂2B/∂x2 – 1/c2 ∂2B/∂t2 = 0
Solutions of any wave equation:
periodical functions of space and
time.
Electromagnetic radiation is a
propagating distribution of electric
and magnetic fields (visible light
included, with a frequency ~1014 Hz)
For the electric field E, the time
dependence (a laser light, for
example) can be given by:
E(t) = Eo cos (ω0.t)
Electromagnetic Spectrum:
Light is Only a Small Portion
The eletromagnetic spectrum goes
from gamma rays to radio waves!!
Δλ ~ 1024 !!!
To apply an electric field E on
materials leads always to electric
dipole formation due to the
electrical forces that’s, to an
electric polarization P of matter...
E
P
P and E are related by the third
order
polarizability
tensor
α
(electronic polarization in the Raman
scattering):
P = α.E
If E = E(t) hence P = P(t).
However, α can also be α(t), hence
P(t) = α(t).E(t)
The time dependence of α comes
from the atomic vibrations of a solid
material (or molecular vibrations in
gases or liquids).
The
time
dependence
of
αij
components is given in terms of the
normal coordinates describing the
atomic vibrations (normal modes of
vibration )
q(t) = qk cos(ωk t)
ωk is the frequency of atomic
vibrations.
In the harmonic approximation, the
expansion of αij in Taylor serie
gives:
[αij]k = [αij]0+ [∂αij/∂qk]0 .qk +...
P(t) = [αij(t)]k.E(t)
P(t)= [αij]0E0cos(ω0t)+1/2[∂αij/∂qk]0
E0q0 {cos(ω0-ωk)t+cos(ω0+ωk)t}
+...
cos(a).cos(b)= ½ [cos (a+b)+cos(a-b)]
P(t)=
[αij]0E0cos(ω0t)+
+1/2[∂αij/∂qk]0 E0q0 {cos(ω0-ωk)t}
+ 1/2[∂αij/∂qk]0 E0q0 {cos(ω0+ωk)t}
+...
Since
an
oscilanting
electric
dipole
emits
eletromagnetic radiation
at the dipole oscilation
frequency...
(Classical Electrodynamics, Jackson, pg 272)
# The first term,
[αij]0E0cos(ω0t)
is the radiation (light) emitted at
the same frequency (energy) of the
incident light, called Rayleigh
scattering
or
elastic
light
scattering;
The second term
1/2[∂αij/∂qk]0 E0q0 {cos(ω0-ωk)t}
is the light emitted with
frequency (energy) lower than
the frequency of the incident
light, the Raman scattering or
inelastic light scattering (also
called Stokes “side”);
The third term
1/2[∂αij/∂qk]0 E0q0 {cos(ω0+ωk)t}
is the light emitted with
frequency (energy) higher
than the frequency of the
incident light, the Raman
scattering
(Anti-Stokes
“side”).
At this point we know already the
classical origin of the Raman
scattering.
Since the Rayleigh scattering is
about 106 more intense than the
Raman scattering, we need to
separate the Rayleigh from the
Raman scattering...
How We Can Detect Experimentally
the Raman Scattering ?
Raman Spectrometer
monochromator
sample
detector
laser
Similarity Between a Raman
Spectrometer and FM Radio
1- the laser light is generated in the
laser tube...
1’- (~100 MHz radio wave source)
2- incides on the sample and is
modulated by the atomic vibrations
2’- (radio wave is modulated by the
audio wave using a microphone)
3- the modulated light, colected by
the monochromator, is separated in
Rayleigh (discarded) and Raman
components (saved)
3’- the modulated FM radio wave ,
colected by the receiver, is separated
in radio (discarded) and audio
components (saved – speaker)
Units in Raman Spectroscopy
The Raman Shift is given in cm-1
(wavenumber) relationship to the
laser line considered as zero:
- cm-1 + cm-1
0
Anti-Stokes Laser (0) Stokes
For the argon laser, the most
intense lines are:
488 nm
514 nm
20 492 cm-1
19, 455 cm-1
For the Nd:YAG,
532 nm
18 797 cm-1
For the He-Ne,
633 nm
15 798 cm-1
Most Important Parameters of a
Raman Peak:
# position
# peak width (full width at half
maximum)
# relative intensity
Problem With the Classical
Approach: IST = IAS
Experimentally: IST > IAS e IST/IAS
depends on the temperature!
Below, the Raman spectrum of
silicon single crystal.
Si
Intensity (c/s)
1200
800
400
-600
-400
-200
0
200
-1
Raman Shift (cm )
400
600
Intensity x Temperature (K)
1) Stokes
 2) Anti-Stokes
Foundations of Raman Scattering:
B - Quantum Approach
In the quantum approach, we need to
change ( is the Planck constant/÷2π):
# incident eletromagnetic radiation by
photons, a light particle with energy
and momentum
E = ωi p = ki
# scattered electromagnetic radiation
by photons, a light particle with energy
and momentum
E = ωs p = ks
# lattice vibrations by phonons, a
quasi-particle
with
energy
and
momentum
E = ωp p = kp
The energy levels of a harmonic
oscilator is given by
En= (n+1/2) ωj (n = 0,1,2…)
The population factor is given by
Bose-Einstein statistics:
The intensity of a Raman scattering
process depends on n(ωj)
Since the lower energy vibrational
state is the most populated by
phonons, the transition probability
of the Stokes process is higher than
Anti-Stokes!!!
Sumarizing, the Raman
occurs in three steps:
scattering
# radiation-electron interaction: the
incident photon interacts with the
electron, generating a electron-hole
pair;
# electron-phonon interaction:
the
pair electron-hole is scattered to
another energy state by the emission
(or absorption) of one phonon - Stokes
(anti-Stokes);
# electron-radiation interaction: the
pair
electron-hole
recombines
radiatively, emitting the scattered
photon.
 During
the
photon-phonon
interaction, the energy and
momentum must be conserved,
so
s  i   p
But
Since the phonon momentum is
103 times the photon momentum,
only phonons at the center of the
Brillouin zone can participate.
Relationship Between Raman
Spectrum and Phonon Dispersion
Relation in Crystals
For amorphous materials...
For
amorphous
materials, the Raman
spectrum shows the total
vibrational density of
states,
where
all
vibrational modes of all
Brillouin zone participate
of the scattering process,
leading to broad Raman
bands localized at the
same position of the
EXPERIMENTAL SETUP
and
TECHNICAL EVOLUTION
Remembering: Raman Spectrometer
monochromator
sample
detector
laser
Separating Light: Monochromator
A simplest monochromator:
glass prism
entrance
slit
exit
slit
step motor
closed
box
...or a diffraction grating...
Advantage relationship to prism:
possibility to control the number of
grooves: 600, 1200, 1800, 3200
gr/mm
Improving the “Separation”
Capability: Two, Three, Four
Monochromators in Serie
More recently, highly seletive
optical filters were developed to
eliminate
the
Rayleigh
component,
with
monochromators with only one
diffraction grating
Rayleigh line
ultra low frequency filter
Si
Intensity (c/s)
1200
800
400
-600
-400
-200
0
200
-1
Raman Shift (cm )
400
600
Light Detectors
Photographic films (before ~ 1945)
Photomultiplier tube (after 1945)
CCD - charge coupled device /
diode arrays (1969 up to now)
Light Sources
Solar light (Raman’s experiment)
Arc lamps, gas lamps
Ruby Laser (1960)
He-Ne gas laser: 632,8 nm (1962)
Ar, Ar+Kr: 458 – 700 nm (after 1964)
Nd:YAG: 532 nm
Semiconductors...
Sample Ilumination Systems
1) Macro Raman: laser beam
direct on the sample (spot ~ 1
mm);
2) Micro Raman: use a
microscope to focuses the laser
beam on the sample (d ~ 1 μm).
The time
reached!!!
of
nanostructures
Should
be
the
Raman
spectroscopy condemned by de
Abbe Limite?????? It says that
“Spatial resolution for an optical
microscope is:
d ~ λ/2 ~ 500 nm/2 ~250 nm”
Response: NO!!!!!!!!
Tip Enhanced Raman Scattering
TERS
Coupling Raman and Atomic Force
Microscopies
CERTEV’s RAMAN LAB
Macro-Raman Jobin-Yvon U1000
(doble monochromator) - 1990
Detector: photomultiplier
12
Micro-Raman Jobin-Yvon T64000
(triple monochromador) -1995
Detector: LN2 CCD
35
Raman – AFM
Colocalized
+
Tip Enhanced Raman Scattering
(2014)
63
Optical Coupler Raman - AFM
64
FACILITIES
# Low Temperatures: closed cycle
helium cryostat.
(10 – 300 K)
High Temperatures: microfurnace
(300 - 1200K)
# High Hydrostatic Pressure:
diamond anvil cell – DAC
(ambient - 20 GPa)
# Spectrophotometer UV-VIS-IV
# Particule Size Analyser
# Synthesis Lab
RAMAN X TEMPERATURE
“Why change temperature???
Temperature = energy!!
# Strutural Phase Transitions
# Crystallization Processes
# Anharmonic Effects on Phonon
Spectrum (interatomic potential)
Raman x Pressão
Pressure scale of the universe...
P(atm)
10-32 hydrogen pressure in the intergalatic space
10-19 interplanetary space
10-16 best vacum in laboratory
10-1 blood pressure
100 Sea level
103 Deep ocean
104 Si semiconductor- metallic transition
105 Graphite to diamond transformation
107 Earth’s centre
1011 centro do Sun centre
1029 Nêutrons stars
60 order of magnitude!!!!!!!
New properties of materials under
high pressure?
Densification in glasses.
Diamond Anvil Cell - DAC
Diacell B05 Diamond Anvil Cell
The Stainless Steel Gasket
Indented and Drilled Gasket
100 µm hole
(sample+ruby+ methanol-ethanol)
Measuring Pressure into DAC:
Ruby Luminescence
APPLICATIONS
OF
RAMAN
SPECTROSCOPY
What Type of Materials Can We
Study With Raman
Spectroscopy?
ALL!
# Solids (crystals or amorphous)
# Liquids
# Gases
* (metal is very hard, light cannot
penetrate it! )
Raman in BaSi2O5 Glass
(20 to 840 C)
Crystallization in Situ
Linewidth and Crystallization
BS2 crystallization
at 950 C x time
FWHM (cm
-1
)
80
60
40
0
30
60
Time (minutes)
90
120
Thermal Effect on Structural
Disorder: Boson Peak
Raman Intensity (arb. units)
BS2 T increasing
-1
normalized by peak 550 cm )
850 C
400 C
20 C
100
200
300
400
-1
Raman Shift (cm )
500
Qn’s Distribution
800
Q1: 9594/930/40/13%
Q2: 13144/1026/90/18%
Raman Intensity (c/s)
Q3:45609/1072/70/62%
Q4:4621/1186/96/6%
Q3
600
Q1
Q2
400
Q4
900
1000
-1
Raman Shift (cm )
1100
No Phase Transition...
BS2 Temperature
Phase Transition
(decreasing temp.)
Raman Intensity (arb. units)
900 C
850
800
750
700
600
500
450
400
350
300
200
100
20 C
200
400
600
800
-1
Raman Shift (cm )
1000
1200
BS2 crystallized
Details...
Raman Intensity (arb. units)
crystallized BS2
in situ
Alisson
200
400
600
800
-1
Raman Shift (cm )
1000
1200
Differential Scaning Calorimetry - DSC
OTHER MATERIALS:
# SEMICONDUCTORS
# CERAMICS
# MOLECULAR CRYSTALS
(DRUGS)
Applying Non-Hydrotatic Pressure I:
Vickers Indentation in Si
Hardness and plactic flow, extrusion
(guide for machining conditions)
High non-hydrostatic pressures
Transition pressure reduction
Scanning electron micrography of
an indentation
Intensity (arb.units)
Raman Spectra of Different
Regions of an Indentation
m
nm
nm
m
nm
200
300
400
-1
Raman Shift (cm )
500
Raman Spectra with Ddifferent
Exciting Wavelengths
Raman Micrography of the
Stress Field Around and into
Indentation
Applying Non-Hydrotatic Pressure II
Turning Semiconductors
Diamond tool
Machined
surface
Rp
f
t max
ap
Microcracks
Micrography of a Si Machined
Surface
Intensity (arb. units)
Micro-Raman Spectra of Si:
Machined Surface and Pristine
Si-m
Si-nm
200
300
400 -1
Raman Shift (cm )
500
Diamond Turning InSb Fresnel
Micro-Lenses
Raman of InSb Fresnel Micro-Lenses...
Ceramics: PbTiO3 Raman Spectrum
B
Raman Intensity (cts/s)
20000
PbTiO3
15000
10000
5000
0
200
400
600
800
-1
Raman Shift (cm )
1000
1200
Liquid: CCl4
Raman Intensity (arb. units)
Impact Effect on III-V Semiconductors
GaAs
GaSb
InSb
150
300
450
-1
Raman Shift (cm )
B
600
[100]-GaAs
Intensity(c/s)
500
400
300
200
100
0
180
210
240
270
-1
Raman Shift (cm )
300
Pharmacological Materials
Salophen
Temperature and Pressure
Intensity (arb. units)
Quartz Crystallization
650
600
550
200
400
600
800
1000
-1
Raman Shift (cm )
detail
1200
Thank You
For The
Attention