Frédéric Datchidatchi@impmc.upmc.fr

IMPMC, CNRS, Université Paris 6, 140 rue de Lourmel, 75015 Paris, France

Nanomat NP427

Introduction to Raman spectroscopy

quasielastic

phonon

valence electron

excitations

plasmon Compton profile

core-electron excitation

Spectrum of excitations in condensed-matter

IR

Vibrational spectroscopies

Infrared

Raman Linear effect / widely used

Brillouin

Hyper-Raman Non-linear

Coherent anti-Stokes Raman effects /

Impulsive stimulated Brillouin Less used

…..

Inelastic X-ray/neutron scattering - Requires large facilities (neutron or synchrotron sources)

Identification of molecular species and bondingtypes

Information about:

The intra/intermolecular potential

Crystalline structure

Elasticity

Electronic structure (resonance effect)

…

What is vibrational spectroscopy useful for ?

Introduction to Raman spectroscopy

• The Raman effect was discovered by the Indian physicist C. V. Raman for which he was awarded the Nobel Prize in Physics in 1930.

• Raman spectroscopy is now a widely used technique which enables to probe vibrational modes (or phonons) of a material in the range of optical frequencies (THz)

•The Raman effect originates from the interaction of a electromagnetic (EM) wave with the vibrations of a material.

A molecule with N atoms has 3N-6 vibrational degrees of freedom (3N-5 for a linear molecule)

In the harmonic approximation, these degrees of freedom can be represented by « normal modes » of vibration: each vibrational state may then be expressed as a combination of these normal modes.

The total vibrational energy is the sum of independent harmonic oscillators of energy:

Symmetric stretching1

3657 cm-1

Antisymmetric stretching 3

3756 cm-1

Bending 2

1595 cm-1

H2O molecule

)2/1( kkk nhE

Molecular vibrations

Normal modes of a crystal

In a crystal with N atoms, the 3N degrees of freedom gives rise to 3N normal modes of vibrations, or phonons. 3 are acoustic modes (GHz) and 3N-3 are optic modes (THz)

A phonon in the crystal can bedescribed by a plane wave of wavevector q, a set of displacementvectors un and a pulsation=2=2c/

In 1D, 2 atoms/unit cell:

q un

+

-

Normal modes of a crystal

qun

Acoustic modes

Optic modes

q

TO

LO

Opticbranches

Acousticbranches

First Brillouin zone

q

Incident light

(I0 ,0 )

Reflected light

(IR ,0 )

Transmitted light

(IT ,0 )

Scattered light

(IS ,S )

Rayleigh

(S = 0 )

Elastic scattering

IS~10-3 I0

Brillouin Raman

(S = 0 ± Δ )« Acoustic » « Optic »

vibrations vibrations

Δ ~ 30-300 GHz Δ ~ 3-30 THz

IS~10-6-10-9 I0

Light scattering

Classical description of the Raman effectA. Origin of the Raman effect (1)

Classical description of the Raman effectA. Origin of the Raman effect (2)

dQ

Classical description of the Raman effectA. Origin of the Raman effect (3)

3 scattered radiations:

Stokes wave Anti-Stokes waveRayleigh wave

Elastic: =0Inelastic: =0v

Classical description of the Raman effectB. Selection rules. Comparison with IR spectroscopy

Raman selection rule :

IR absorption selection rule:

Classical description of the Raman effectB. Selection rules. Comparison with IR spectroscopy

Classical description of the Raman effectB. Selection rules. Comparison with IR spectroscopy

Classical description of the Raman effectB. Selection rules. Comparison with IR spectroscopy

Classical description of the Raman effectB. Selection rules. Comparison with IR spectroscopy

Classical description of the Raman effectC. Scattered Raman Intensity

Classical description of the Raman effect

Classical theory does not explain:

– Raman scattering from rotational vibrations, since it does not assign discrete frequencies to rotational transitions

– The resonnance Raman effect when 0 is close to an electronic absorption of the molecule

– Surface enhanced Raman scaterring

– ….

D. Classical vs quantum theory

Classical description of the Raman effect

Stokes/anti-Stokes intensity ratio:

– Classical theory: IS/IAS1 and does not depend on T

– Quantum theory:

Where

This relation can be used to measure T

D. Classical vs quantum theory

Raman effect in a crystal (classical theory)

Raman effect in a crystal (classical theory)

In addition to the elastic scattered wave, we thus again obtain twoscattered waves at different frequencies:

The Stokes wave with and

The anti-Stokes wave with and

Both frequency and wavevectors are conserved in the scattering process

Raman probes zone-center phonons

Since kAS/S=k0q, |q| 2 |k0 |=2 n.0 /c=2n/0 . For a visible laser, ~500 nm. Using n=3, |q| 4.105 cm-1

.

|q |<< |Kmax,BZ|=2/a 108 cm-1 (a~5 Å)

q is very close to the Brillouin zone center (q0).

K

Defect-induced Raman modes

When the crystal is not perfect, such as in the presence of defects, the translational symmetry is violated and so is the conservation rule of wavectors.

In this case, modes with q0 can become active

Raman spectrum of a high-purityAnd defective graphite sample

LO-TO splitting (1)• When a vibrational mode is both Raman and infrared active, the electric field

produced by the vibrating permanent dipole couples with the longitudinalvibrations but not the transverse ones. As a result, the frequency oflongitudinal optical (LO) wave, LO , is larger than the frequency of thetransverse optical (TO) wave, which is unperturbed: TO=q.

• In the Raman spectrum, this translates in two peaks at different frequenciesfor the same mode but different polarizations (L or T). The magnitude of thissplitting depends on the effective charge associated to the vibrational modeand and dielectric permittivity. It will not always be large enough to beresolved.

TO mode: E q E.q=0

LO mode: E // q E.q0 : The E field addsa restoring force

LO-TO splitting (2)

• In a cubic diatomic crystal (e.g. NaCl) it can be shown that the frequencies ofthe LO and TO waves are related by:

𝜔𝐿𝑂𝜔𝑇𝑂

2

=𝜀0𝜀∞

where 𝜀0 and 𝜀∞ are respectively the static and infinite frequency dielectric

constants. This relation is known as the Lyddane-Sachs-Teller relation

• A generalized form of the Lyddane-Sachs-Teller relation holding for any crystalwas proposed by Cochran and Cowley:

𝑖=1

3𝑁−3𝜔𝐿𝑂𝜔𝑇𝑂

2

=𝜀0𝜀∞

Higher order Raman effectSo far we have only considered the first-order Raman effect, produced by the scattering of a single phonon. The second-order Raman effect occurs when light isscattered simultaneously by two phonons. The conservation of energy and wavevectors impose:

• S= 0 ± (q1 + q2)

• kS = k0 ± (q1 +q2)

Since |kS|| k0|, q1 +q2 0: the vavevectors of the two phonons should be opposite, but can have any value in the Brillouin zone. This produces a continuum spectrum, by contrast with the line spectrum of the first-order Raman effect.

Diamond Raman spectrum(0=228.9 nm)

Raman tensor and scattered intensity

Crystal symmetry and the Raman effect

If we neglect the slight difference in frequency of the incident and scattered radiation, then the Raman tensor R is symmetric, like , ie: Rxy=Ryx

The symmetry of the crystal and of the vibrational modes impose constraints on the Raman tensor, such that only some of its components will be non-zero.

The scattered radiation will thus vanish for certain choices of the polarizations e0 and es . These defines additional selection rules for Raman scattering in crystals which are useful for determining the symmetry of Raman active phonons.

A general rule is that the Raman tensor of odd-parity phonons in centrosymmetric crystals must vanish, whereas they are infrared active.

Example: NH3 molecule

Point group C3v

A1 A1 E E

Normal modes

Using symmetry to determine Raman or IR activity (1)

Character table for C3v point group

E 2C3 (z) 3σv translations,

rotations

IR Raman

A1 1 1 1 z Z xx+ yy; zz

A2 1 1 -1 Rz

E 2 -1 0 (x, y) (Rx, Ry) X,Y (xx- yy, xy)

(yz- zx)

C3

v

s

Solid NH3 at high pressure: Phase IV, space group P212121 (D24)

45 Raman active modes:- 21 lattice modes : 6A + 5B1 + 5B2 + 5B3

- 24 internal modes : 4 1 + 4 2 + 8 3 + 8 4

33 IR active mode:- 15 lattice modes : 5B1 + 5B2 + 5B3

- 18 internal modes : 3 1 + 3 2 + 6 3 + 6 4

3 acoustic modes: 1 B1+ 1B2 + 1B3

A

B1

B2

B3

A

A1 (1 2 Tz)

A2 (Rz)

E( 31 3

2 41 4

2TxyRxy)

D2 (P212121)C1C3v

CrystalSiteMolecular symmetry

R

R, IR

R, IR

R, IR

TZ

TY

TX

The number of observed modes constrains the symmetry of the crystal

Using symmetry to determine Raman or IR activity (2)

Polarized Raman scattering uses the fact that Raman scattering from a crystal depends on the direction of polarization of light: one is able to select modes of a given symmetry using the proper scattering geometry

D2 Rxx Ryy Rzz Rxy Rxz Ryz

A a b c 0 0 0

B1 Tz,Rz 0 0 0 d 0 0

B2 Ty,Ry 0 0 0 0 e 0

B3 Tx,Rx 0 0 0 0 0 f

D2 Raman Tensor

e0 // c

e0 // b

LASERa

c

b

This method is extremely powerful to assign vibrational modes of a crystal

Polarizer(choose eS)

Polarized Raman scattering (single crystal)

Experimental aspects

LASER

Beam Splitter

LENSLENS

SpectrometerEntrance Pinhole

Sample

Raman setup (backscattering)

Scattered light

Czerny-Turner Config. .

Triple stage spectrometer (T64000)

Raman and fluorescence

UV Laser

Green Laser

Red Laser

What you will study during the practical

1. Graphite and graphene 2. Quartz single crystal

Two samples