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In our laboratory, the version of Raman scattering spectroscopy is SENTERRA R200L (No.

127). It has a frequency resolution of 0.5 cm-1. Figure 3.1 shows the optical setup of Raman

scattering spectroscopy. The instrument is described below in detail :

1. Laser source system :

It has two kinds of laser source. One is the wavelength of 532 nm laser line, which is

excited by diode-pumped solid-state laser (DPSS) with a maximum power of 20 mW. The other

is the wavelength of 785 nm laser line, which is excited by diode laser with a maximum power

of 100 mW. Excitation laser light passes through a microscope objective lens, which is

magnification of x100 (NA = 0.9), of the Olympus BX51 microscopic model for focusing. It has

a spatial resolution of 1 ~ 2 μm. Focused laser light is incident perpendicularly to the sample

surface, and then will generate the scattering light signal. The scattering light signal is detected

by using CCD device.

2. Spectrometer system :

The type of spectrometer is dual grating in our Raman scattering spectroscopy. The grating

has two kinds of raster density. Raster density is based on the replacement of two different laser

wavelengths. If we use the wavelength of 532 nm light source, the spectrometer will use a 400

grooves/mm raster density of grating. If we use the wavelength of 785 nm light source, the

spectrometer will use a 1200 grooves/mm raster density of grating.

3. Detector system :

The number of the equipment is Infinit 1, which is a charge coupled device (CCD). The

detector has a silicon chip with the two-dimensional photonic array of the 1024 × 256 pixel resolution. The best working temperature of the equipment is about -60℃.

The Raman effect was predicted by A. Smekal in 1923 but was first observed by C. V. Raman in

1928. Raman and Krishnan reported the phenomenon obtained by many liquids, some gases, crystals,

and amorphous substances like glass. They reported the appearance of modified lines on either side

of the exciting line, the lines appearing on the longer wavelength (Stokes) side being more numerous

and intense than the ones appearing on the shorter wavelength (anti-Stokes) side. They showed that

the differences between the frequencies of the emitted radiations and the frequencies of the exciting

radiation, closely agreed in many cases with the frequencies of infrared absorption bands of the same

substances. The frequency shifts observed in scattering are the frequencies of oscillation of the

chemically bonded atoms of a molecule, which is dependent on the geometry of the molecule and the

forces of chemical affinity. Pringsheim immediately recognized the importance of Raman's discovery

and christened the new scattering phenomenon the Raman effect and the spectrum of the new lines,

the Raman spectrum [70,71].

Briefly, the Raman effect can be described as the inelastic scattering of light by matter. When a

photon of the visible light, too low in energy to excite an electronic transition, interacts with a

molecule, it can be scattered in one of three ways. It can be elastically scattered and thus retain its

incident energy or it can be inelastically scattered by either giving energy up to, or by removing

energy from, the molecule. Photons undergoing inelastic loss of energy give rise to Stokes scattering

while photons undergoing inelastic gain of energy give rise to anti-Stokes scattering. The energy

gained by the molecule in Stokes scattering appears as vibrational energy and where a molecule has

excess vibrational energy above the ground state, it is the energy which is lost to the anti-Stokes

scattered photons.

The Raman spectroscopy provides extraordinarily easy and convenient way to know the lattice

vibration of the materials and opens up a wholly new field of the study of molecule structure. The

theory of Raman spectroscopy can be divided into classical part and quantum part, described as

follows :

1. Classical theory

The classical approach to a description of the Raman effect regards the scattering

molecules as a collection of atoms undergoing simple harmonic vibrations and takes no account

of quantization of the vibration energy.

When a molecule is placed in an electric field, its electrons are displaced relative to its

nuclei thus developing an electric dipole moment. For small fields, the induced dipole moment

Pi is proportional to the field strength E. The function can be described by

P

i

= α E

, (3.1.1) where α is proportionality constant which is the polarizability of the molecule. It is the case

with which the electron cloud of the molecule can be distorted. A fluctuating electric field will

produce a fluctuating dipole moment of the same frequency. Electromagnetic radiation

generates such an electric field which can be described by

( )

0

cos 2

0

E = E πν t

, (3.1.2) where E0 is the equilibrium field strength and the ν is the angular frequency of the radiation. 0

Therefore, electromagnetic radiation will induced a fluctuating dipole of frequency ν in the 0

molecule. This induced dipole will emit or scattering radiation of frequency ν . The scattering 0

can be called "Rayleigh scattering".

Consider the particular case of the diatomic molecule, which vibrates with a frequency ν . ν

If it performs simple harmonic vibrations, then a coordinate Qν along the axis of vibration at

time t, is expressed as

( )

0

cos 2

Q

ν

= Q πν

ν

t

. (3.1.3) If the polarizability changes during the vibration, its value for a small vibrational amplitude will

be given by

Substitution of Eq. (3.1.3) in Eq. (3.1.4) yields Eq. (3.1.5)

( )

If incident radiation of frequency ν interacts with the molecule then from Eq. (3.1.1) and Eq. 0

(3.1.2) :

( )

0cos 2 0

i t

P = α E = α E

πν . (3.1.6) Substitution of Eq. (3.1.5) in Eq. (3.1.6) yields Eq. (3.1.7)

( ) ( ) ( )

The function can be rewritten as Eq. (3.1.8)

The first term in Eq. (3.1.8) describes the Rayleigh scattering and the remaining terms describe

the anti-Stokes and Stokes Raman scattering. This equation indicates that light will be scattered

with frequencies of Rayleigh, anti-Stokes, and stokes scattering. Figure 3.2 shows the schematic

diagram of an energy transfer model of Rayleigh, anti-Stokes, and stokes scattering.

( ) ( )

0 : Rayleigh scattering; 0 ν : Anti-Stokes scattering; and 0 ν : Stokes scattering

ν ν ν+ ν ν−

In addition, Eq. (3.1.8) shows that Raman scattering occurs as

0

Qν 0

 ∂α  ≠

∂ 

  . (3.1.9)

Above equation to indicate the polarizability of the molecule must change during a vibration if

that vibration is to be Raman active.

2. Quantum theory

The quantum theory approach to Raman scattering recognizes that the vibrational energy

of a molecule is quantized. A non-linear molecule will have 3N - 6 normal vibrations and a

linear molecule will have 3N - 5, where N is the number of atoms in the molecule. The energy

of each of these vibrations will be quantized according to the relationship : 1

h n 2

E

ν

=

ν  + , (3.1.10) where ν is the frequency of the vibration and n is the vibrational quantum number

controlling the energy of that particular vibration and having values of 0, 1, 2, 3... etc.

Perturbation theory is used to introduce quantization into the Raman scattering theory. Put

simply this approach applies perturbations to the ground state molecular wavefunctions until

new functions are obtained which describe the vibrational excited state. The transition from

ground state can then be regarded as being achieved via a perturbing wavefunction, having a

corresponding energy and giving us a useful pictorial description of Raman scattering with the

vibrational transitions occuring via this virtual energy level.

The Rayleigh scattering arises from transitions that start and finish at the same vibrational

energy level. Stokes Raman scattering arises from transitions that start at the ground state

vibrational energy level and finish at a higher vibrational energy level, whereas anti-Stokes

Raman scattering involves a transition from a higher to a lower vibrational energy level. At

room temperatures, most molecular vibrations are in the ground state, n=0 state and thus the

anti-Stokes transitions are less likely to occur than the Stokes transitions resulting in the Stokes

Raman scattering being more intense. This greater relative intensity becomes increasingly

greater as the energy of the vibrations increases and the higher vibrational energy levels become

less populated at any given temperature. For this reason, the Stokes Raman scattering is

routinely studied and implied in Raman spectroscopy.

3. Resonant Raman scattering

It is a well established fact that when the exciting frequency approaches that of an

absorption band, a considerable enhancement of the intensities of some of the lines in the

Raman spectrum is encountered. The theory of the resonant Raman effect is quite interesting

and has been discussed by Shorygin and in particular by Behringer and also by Rea. The total

light intensity of the scattering can be described by

( ) ( )

is the different of electronic state; and

( )

αij nm is the polarizability tensor of the electronic states, which indicates the intensity of a Raman band is related to the polarizability tensor.

Using time-dependent perturbation theory, the following expression for the polarizability tensor

can be described as

( ) ( )

exciting radiation. The damping terms which prevent the denominator going to zero as ν 0

approaches ν have been omitted. It is clear from Eq. (3.1.12) that as the frequency of the e

exciting radiation ν approaches 0 ν then the value of the polarizability tensor components e

will increase rapidly. This is the resonance condition and results in increases in Raman intensity

of several orders of magnitude.