introduction 1.3.2 selection rule for raman spectra...

Chapter 1

INTRODUCTION

1.1 Raman Spectroscopy

1.2 Infrared Spectra

1.3 Selection Rules for Raman and IR Spectra

1.3.1 Selection rule for IR

1.3.2 Selection rule for Raman spectra

1.4 Group Frequencies

1.5 Normal Modes of Vibration

1.5.1 Internal and external vibrations

1.6 Solid State Effects

1.6.1 Site symmetry effects (static fieldsplitting)

1.6.2 Correlation field splitting

1.7 Hydrogen Bonding

1.8 Structural Features of Hydrated Crystals

1.9 Combinations and Overtones

1.10 Fermi Resonance

1.11 Theoretical Methods of Vibrational Analysis

1.11.1 Unit cell approach

1.11.2 Site group analysis

1.12 Polarization of Raman Lines

1.13 Effect of Temperature on Raman Spectra

1.14 Sulphates, Phosphates and Molybdates A Short Review

1.14.1 Sulphates

1.14.2 'Phosphates

1.14.2a PyrophosphateS

1.14.2b Cyclohexaphosphates

1.14.3 Molybdates

ReferencesFigures

L

2

Raman spectroscopy is concerned with vibrational and

rotational transitions and in this respect, it is similar to infrared

spectroscopy. Since the selection rules for the two are dif ferent,

the information obtained from Raman spectrum often complements that

obtained from an infrared study and provides valuable structural

information. To get a complete knowledge of the energy levels of a

system, a simultaneous study of both IR and Raman spectra is

required. Thus, infrared and Raman spectroscopy together serves as a

powerful tool for investigating the structure of molecules, nature of

hydrogen bonding and rotational and vibrational levels of molecules.

They are to be regarded as complementary rather than alternative

methods.

1.1 Raman Spectroscopy

When light passes through a transparent medium, a small

fraction of it is scattered by the molecules. This scattering is

composed of two parts namely, Rayleigh scattering and Raman

scattering. In Rayleigh scattering, light is elastically scattered in

all directions. Raman scattering is the weaker of the two effects.

The light is inelastically scattered and when examined with a

spectrometer, a series of emission lines are seen on either side of

the parent line. The strongest line which appears at the frequency of

3

the exciting monochromatic line is due to Rayleigh scattering. The

weaker lines seen symmetrically on either side of the Rayleigh line

are the Raman lines (Fig.l.l). The Raman lines on the low frequency

side are called Stokes lines and are of higher intensity compared to

that of the anti-Stokes lines, which are on the higher frequency side

of the Rayleigh line. The shift of these lines from Rayleigh line is

found to be corresponding to the frequencies of the molecular

vibratiens and independent of the exciting radiation. For, a

molecular vibration to be Raman active, there must be a change in the

polarizability of the molecule during this vibration. This change can

be considered as being a change in the shape of the electron cloud

surrounding the molecule. The theory of Raman scattering shows that

the amount of Raman scattering from a molecule is directly

proportional to the intensity of the incident light and also to the

fourth power of the frequency of the excitation radiation. In a

molecule without any symmetry elements, all the normal vibrations are

accompanied

frequencies

by polarizability

appear in the Raman

changes and

spectrum.

the

But in

corresponding

a symmetric

molecule, some of these vibrations may not produce any change in

polarizability and the corresponding normal frequencies are not

observed. Such vibrations are Raman inactive [1-17].

Raman spectrum gives information about molecular symmetry

which can then be used to determine the molecular configuration.

4

Studies of vibration-rotation Raman bands yield the value of the

rotation constant. Structural deductions based on symmetry properties

are. of particular importance in the study of compounds which exist in

several molecular forms or conformations, which are of closely

similar energies and cannot be separated. A good example is the study

of rotational isomers of a flexible molecule. The first experimental

evidence for the existence of such isomers has been from the Raman

studies of the alkali halides [18]. Thus, the Raman scattering method

of investigation afford an extraordinarily easy and convenient way of

mapping the vibration and rotation spectra of chemical compounds and

open up a wholly new field of the study of molecular structure.

The various chemical problems which have been successfully

solved with the help of Raman spectra are the composition and

structure of molecules, molecular interaction, the nature of the

chemical bonds constitution, tautomerism, isomerism, electrolytic

dissociation, association, polymerization, solvent effects exchange

interactions, hydrogen bonding, spectra-structure correlation,

kinetics of fast reduction etc. [1].

Both Rayleigh and Raman scattering

inefficient processes. Only about 10-3 of the

are relatively

intensity of the

incident exciting frequency will appear as Rayleigh scattering and

only 10-6 as Raman scattering. Hence, very intense sources are

required for Raman measurements. Laser beams provide the required

5

intensity and produce very good spectra even with very small amount

of samples. A schematic representation of a modern Laser

Spectrometer is given in Fig. 1.2.

1.2 Infrared Spectra

According to classical electrodynamics, a system

radiation by virtue of periodic changes in its electric dipole

moment, the frequency of the emitted radiation being the same as that

of the dipole oscillations. Absorption is the inverse of emission,

and the system is able to absorb radiation as it is able to emit. The

absorption or emission spectra originating from the vibrational and

rotational motion of a molecule which is not electronically excited

are mostly in the infrared region. A change in the dipole moment may

only be a change in the direction with respect to a coordinate system

fixed in space.

Infrared spectroscopy is generally concerned with the

absorption of radiation incident upon a sample. It finds widespread

applications to qualitative and quantitative analysis.

The infrared region encompasses radiation with wavenumbers

ranging from about 12800 to -110 cm , or wavelengths from 0.78 to

1000 ~m. For the sake of convenience, this region can be further

divided into three namely; near-IR, middle-IR and far-IR. Near IR

region covers 12800 to 4000 cm-1 (0.78 to 2.5 J.1m), middle IR region

-1 1covers 4000 to 200 cm (2.5-50 J.1m) and far-IR covers 200 to 10 cm-

(50 to 1000 J.1m).

6

For the absorption of infrared radiation, a molecule must

undergo a net change in its dipole moment as a result of its

vibrational or rotational motions .. According to the selection rules

of harmonic oscillator, any transition corresponding to A V = +1 in

vibrational levels is allowed. At room temperature, majority of the

molecules are at ground state. Therefore, under ordinary conditions,

only transitions from V = 0 to V = 1 in the electronic ground state

can be observed. However, the number of allowed transitions in a

polyatomic molecule will be greatly reduced due to the symmetry of

the molecule. The intensity of an infrared band is proportional to

the square of the rate of change of dipole moment with respect to the

displacement of the atom [4,6,19-30].

1.3 Selection Rules for Raman and IR Spectra

Selection rules for Raman scattering characteristics such as

intensity of band contours, directional properties and state of

polarization are different from those for IR spectroscopy. All the

transitions may not be active in both IR and Raman spectra. Some may

be active in IR while inactive in Raman or vice versa. Some of the

transitions may be inactive in both IR and Raman spectra. In a

molecule having a centre of symmetry, Raman active transitions are IR

inactive and IR active modes are inactive in Raman.

1.3.1 Selection rule for IR

According to quantum mechanics, the selection rules for the

7

infrared spectrum is determined by the integral

[/-1] I .. = 1$ I (Qa) fl$ .. (Qa) dQv v v v a

Here, J.l is the dipole moment in the electronic ground state. ¢ is

the vibrational eigen function and VI and v.. are the vibrational

quantum numbers before and after the transition respectively.

By resolving the dipole moment into three components in the

x, y and z directions, one gets

[11 ] I .. =! $ I (Qa) }l $ .. (Qa) dQa)'x v v v x v

[r ] I .. = r¢ I (Qa)}l ¢ .. (Qa) dQayvv v y v

If one of these integrals is different from zero, the normal

vibration associated with Qa is infrared active. If all the integrals

are zero, the vibration is infrared inactive [22].

1.3.2 Se1ection rule for Raman Spectra

The molecule interacts with electromagnetic radiation

through the oscillating molecular polarizability. The intensity, I,

L exij ijs

I =

of a scattered radiation, Vs is a function of the polarizability,

a ij' of the molecule

27

'lt5

I o

where Io is the intensity of the incident radiation and ex

ij is an

element of the molecular polarizability tensor ex [29] .

8

When a molecule is placed in an electric field E, the

induced dipole moment is given by

~ -.p = ex E

The electric polarizability <l being a function of all

normal vibrational coordinates, it can be expanded as a Taylor

series.

Here, higher powers are neglected. <l is the polarizabilityo

at the equilibrium configuration and ( 6 ex) is the derived6Qk 0

polarizability for the kth normal mode at the equilibrium position.

The transition moment associated with a transition between

the levels nand m is given by

where *n and *m are the independent wave functions. On substitution

of P

pnm

Because of the mutual orthogonality of the eigen functions,

the integral in the first term vanishes unless * = * , and when theyn m

are equal, it is unity. Thus, this term stands for Rayleigh

9

scattering for which there is no frequency change. The second term

accounts for the Raman scattering. The kth summand represents the

thcontribution of the k normal mode to Raman spectrum. Hence, it

follows that a particular normal vibration shall be permitted or

forbidden in the Raman effect depending on the factor (-.6..S!) in theSQk 0

second term of the above equation.

If (%Q:) 0 is different from zero during a certain vibration,

it will be active in the Raman spectrum. If (6 ex) = 0 for a(;Qk 0

particular vibration, it ,nil be forbidden in the Raman spectrum.

Also, it can be shown that for the integral of the second

term to be non-vanishing, the following conditions must be satisfied:

(1) For all modes except

identical, i.e., n = m.

the the two states should be

(2) thFor the k mode, the vibrational quantum number must change

only by unity [20].

1.4 Group Frequencies

Characteristic frequencies exhibited by a group of common

atoms in different molecules, regardless of the rest of the molecules

are called group frequencies. The concept of group frequency rests on

the assumption that the vibrations of a particular group are

relatively independent of those of the rest of the molecules. The

relative constancy of band positions of group frequencies depends on

10

the masses of the atoms, symmetry and force constants of bonds

between atoms and the interaction of vibrations. The internal factors

like change in atomic mass, vibrational coupling, resonance, crystal

field effects, hydrogen bonding, coordinations, bond angle strain

etc. can affect these frequencies appreciably. Also, they are

sensitive to external parameters, like temperature and physical state

(gas, liquid, solid, solution, solvent and concentration) of the

system. These group frequencies are very helpful in chemical

analysis. The changes of these frequencies from the standard values

give an insight into the internal structure of the molecules [19,22].

1.5 Normal Modes of Vibration

For any molecule containing N nuclei, three relations

between the 3N nuclear displacement coordinates are required to

account for the translational motion. For a non-linear molecule, i.e.

for one with non-vanishing moment of inertia about each of its three

principal axis, a further three relationships are required to account

for rotational motions. For a linear molecule, the line of the

nuclei is a principal axis and the moment of inertia of the molecule

with respect to it is zero. The rotation about this axis cannot

contribute anything to the kinetic energy and therefore, such

rotations can be excluded. It follows that the number of independent

coordinates for the description of the internal motions of the linear

molecule is now 3N-S, as compared to 3N-6 for a non-linear molecule.

Each of these (3N-S) or (3N-6) vibrations is called normal modes

[20] .

11

The normal vibrations or normal modes are independent,

self-repeating displacements of the atoms that preserve the centre

of mass. In a normal vibration all the atoms vibrate in phase and

with the same frequency. The motion of the atoms of a molecule in

different normal modes can be represented by a set of normal

coordinates.

The number of observed bands in the spectra may be less than

the number of normal modes, due to various reasons:

1. The symmetry of the molecule is such that no change in dipole

moment results from a particular vibration.

2. The energies of two vibrations may be identical or nearly

identical.

3. The intensity may be so low as to be detected by ordinary means.

4. The vibrational energy may be in a frequency range beyond the

range of the instrument.

The characteristic of a vibration changes as a result of the

coupling with another vibration. These couplings are influenced by

many factors:

1. Strong coupling between two stretching vibrations occurs only

when there is a common atom to the two vibrations.

2. Interaction between two bending vibrations requires a common bond

between the vibrating groups.

12

3. Coupling between stretching and bending vibrations is possible if

the stretching bond forms one side of the angle that varies in

the bending vibration.

4. If the individual groups have identical energy, the· interaction

will be large.

5. Little or no interaction is possible between groups which are

separated by two or more bonds.

6. Coupling occurs between vibrations of same symmetry species [6].

1.5.1 Internal and external vibrations

Normal modes are generally classified as internal modes and

external modes. Stretching and bending vibrations come under internal

modes, while translational and librational modes of the molecule come

under external modes. External modes appear in the low frequency

region. The stretching vibrations involve a continuous change in the

interatomic distances along the axis of the bond between two atoms

and bending vibrations, a change in the angle between two bonds.

Bending vibrations are of four types viz., scissoring, rocking,

wagging and twisting vibrations.

A crystal containing N unit cells and each unit cell

containing n. atoms can be treated as a system of Nn particles. On

solving the vibrational problem for such a system, one obtains 3n

frequencies as a function of the wave vector k = 2n/A ; k can take N

13

values. Of these, three frequencies tend to zero as k tends to zero

and form the acoustic branch and the rest belong to the optic branch.

Since the wavelength of the exciting radiation in Raman and infrared

spectra is large compared to that of phonons at the Brillouin zone

boundaries, the wave vector conservation allows only the phonons near

the centre of the Brillouin zone (k =0) to be observed in the first

order spectra. At the centre of the Brillouin zone, the vibration of

the corresponding atoms in all the unit cells will be in phase and it

is sufficient to consider only 3n-3 optic modes.

1.6 Solid State Effects

The molecules in crystalline solids have a relatively fixed

orientation with respect to the crystal axes. Due to this fixed

orientation, the spectra of a solid differ much from the gas-phase or

liquid-phase spectra:

1. Gas-phase fundamental vibration can be split into a number of

bands depending on the degeneracies of the vibrational modes.

2. There can be changes in the shape and intensity of the bands.

3. In the low frequency region, a number of new bands can appear due

to the translational and rotational motions. These are known as

external vibrations. This is a characteristic property of the

solid state spectra.

4. Due to anharmonic coupling between the external and internal

modes, combination bands can appear.

14

5. Hydrogen bonds may be formed in solids leading to large changes

in frequencies of fundamental vibrations.

6. The size, nature and orientation of the crystal can have an

important effect on the observed spectra. The single crystal

spectra provide more information than those of powdered samples.

7. The defects and disorders in crystal may give a large number of

additional frequencies.

8. Application of stress to a crystal can cause changes in the

spectra [6].

1.6.1 Site symmetry effects (static fie1d sp1itting)

In a crystal, all molecular groups occupy a site of lower

symmetry than the free ion symmetry. The point group for the site

will be a subgroup of the ionic point group. Then the surrounding

lattice in its equilibrium configuration will exert a field on the

molecule leading to static field splitting of fundamental modes. In a

site of lower symmetry, a vibration which is inactive for a free ion

may become acti,ve. Also, the nondegenerate internal vibrations can be

shifted in frequency and the degeneracies of the degenerate internal

vibrations can be lifted.

1.6.2 Corre1ation fie1d sp1itting

Correlation field splitting known also as Davydov or

dynamical field splitting is due to the interactions with internal

15

vibrations of other molecules in the unit cell. They are also known

as factor group splitting. Due to this effect, additional splitting

can occur in both degenerate and non-degenerate modes. If there are n

molecules in the unit cell, due to correlation field splitting, each

fundamental vibration can give n bands. However, all these n bands

may not be observed, because some of them may even be degenerate.

In most ionic compounds, site symmetry splitting seems to be

greater than the correlation field splitting. In covalent bonded

substances, the two have the same order of splitting. In strongly

hydrogen bonded systems, large correlation field splitting can be

observed due to strong interaction through hydrogen bonding between

internal modes [7].

1.7 Hydrogen Bonding

Hydrogen bonding is an important form of molecular

association. It can be intermolecular or intramolecular and in both

cases, there will be marked effects on group frequencies involved.

Hydrogen bond is much weaker than a covalent bond and their energies

are of the order of 3 to 5 Kcal per mole. Therefore, it can cause a

-1frequency shift of the order of 100 cm [19].

A hydrogen bond exists when a hydrogen atom H is bonded to

more atoms. The hydrogen bond is directed through a hydrogen atom,

and it has some characteristic angular properties. If the H atom is

16

formed between two atoms, X and Y, the two bonds of H to X and to Y

may have different strengths. The stronger bond is usually termed as

normal X-H bond. The strength of the weak bond H•.• Y is identical

with the dissociation energy of X-H .•• Y complex. H-bonds can be

either symmetrical or asymmetrical, depending on the symmetry of the

energy surface for the proton between X and Y. When an H-bond is

formed, a dimer is created. One of the translational degrees of

freedom of the monomer becomes the hydrogen bond stretching mode.

Similarly, the other modes are also affected.

R-OH + OR' -) R - OH ..• OR'

The ROH deformation mode becomes ~ (OH •••0) in the plane and ROH

torsion becomes out-of-plane ¥(O-H •.. O). Because of these

fundamental changes in the nature of the vibrations, their frequency

will also be changed. The range of vibrational frequencies is

correlated with the H-bond geometries such as 0 •..0 distance [R(OO)]

and the O-H distance [r(OH)]. The R(OO) value decreases from a

maximum value abouto 0

2.8 A to a minimum of about 2.4 A and r (OH)ci

increases from 1.0 to 1.2 A. The possible hydrogen vibrational

potentials for different H-bond strengths are given in fig.1.3 [31].

Vibrational analysis of different crystals at different

temperatures reveals that strength of hydrogen bonding increases at

low temperature, possibly due to the overall contrac·tion of the

crystal structure on cooling [32].

17

The atoms usually invovled in the formation of H-bond have

very high electronegativities. The higher the acidity of the X-H

group, the stronger will be X-H ....Y hydrogen bond. If Y atom has

higher electron donor ability, the hydrogen bond formed will be very

strong. Hydrogen bonds have a key role in the ferroelectric phase

transition in crystals [33,34).

The marked effects on the infrared and Raman spectra of

crystals due to hydrogen bonds are:

1. X-H stretching bands shift to lower wavenumbers. The amount of

shifting depends on the strength of hydrogen bonds formed.

Formation of hydrogen bonds weakens the force constant for this

mode.

2. X-H stretching bands gains intensity and becomes broader.

However, the corresponding overtones decrease slightly in

intensity.

3. X-H bending bands will be shfited to higher wavenumbers. This is

because, the force constants for this modes are increased as a

result of hydrogen bond formation.

4. New vibrational modes corresponding to X-Y stretching and

deformation, are observed at low frequencies.

In strongly hydrogen bonded sytems with xC:O) .OH grouping

(X P, As, S, Se and C), ABC triplets are observed in the region

2800-2400, -12350-1900 and 1720-1600 cm

18

The observation of these

bands indicates strong hydrogen bonding in the compounds. These bands

are formed due to the Fermi resonance of the OH stretching mode with

overtones of ~(OH) and Y(OH) modes [31-37].

1.8 Structural Features of Hydrated Crystals

There is considerable interest to understand the nature and

role of water of crystallisation in hydrated crystals. The

anion-~ater interaction involving hydrogen bonds affords stability to

the structure of these compounds. Crystallographic non-equivalence of

the water molecules may be successfully investigated by vibrational

spectroscopy. Stoichiometric hydrates may be either true hydrates or

pseudo hydrates. In true hydrates, water is present as recognizable

water molecules ego water of crystallisation. In pseudo hydrates -OH

or -H groups are present. Water of crystallisation are of two types:

(1) Water of coordination and (2) lattice water. Water of

coordination forms part of coordination sphere of a cation. Compared

with water of aqueous solution, the water molecule in crystalline

hydrates is considerably more constrained both by the rigidity of the

crystal structure and by the restriction imposed by crystallographic

-1symmetry. Lattice water absorbs at 3550-3200 cm (OH stretching

modes) and at 1630-1600 cm-1 (HOH bending mode). In the low frequency

region, librational modes due to the rotational oscillations of water

molecules, restricted by the interaction with neighbouring atoms

19

appear. They are observed in the 600-300 cm-1

region in the hydrates

of alkali and alkaline earth halides. Coordinated water is expected

to give rocking, wagging and metal-oxygen stretching modes. The

hydroxo group can be distinguished easily from the aqua group,

because the former lacks HOH bending modes near-11600 cm • The

metal-aqua complex [M(H 0) ]2+ occupies lattice positions2 6 as a

single molecular unit in many crystal hydrates and in many cases, is

regarded as a quasi-molecule [22,37,38].

1.9 Combinations and Overtones

Under harmonic oscillator approximation, only fundamentals

contribute to infrared and Raman bands. The deviations of the

potential function from the harmonic potential may result in

mechanical anharmonicity, while the higher order terms of the dipole

moment or polarizability leads to electrical anharmonicity. These

anharmonicities lead to the appearance of combinations or overtones

arising from simultaneous changes of state by two or more quanta of

vibrational energy. The overtones are far weaker than the

fundamentals and successive overtones are progressively still weaker.

Due to mechanical anharmonicity, overtones of active fundamentals and

combinations of at least one active fundamental may appear.

Electrical anharmonicity of the molecule can generate overtones·· and

combinations of inactive fundamentals [4,19]. The combination bands

are obtained as sum or difference of two fundamentals or as sum or

20

difference of an overtone and a fundamental frequency. These

combination bands and overtones are observed in both the infrared and

Raman spectra of molecules. However, the effect of anharmonicity is

found to be more in IR than in Raman. Combinations and overtone bands

sometimes gain intensity due to Fermi resonance.

1.10 Fermi Resonance

In certain molecules, it may be possible that an overtone

2 V2

(or combination of two vibrations) and a fundamental vibration

LJ1

may occur almost at the same frequency. The two vibrations

interact as explained in a quantum mechanical resonance and the

frequency of one (with higher energy) is raised while the frequency

of the other (with lower energy) is lowered. The wave functions

describing these levels correspond to a mixing of the wave functions

of the two vibrational excited states (.v1 and 2 b 2) that arise from

the harmonic oscillator approximation. Such a phenomenon was first

observed in CO2

by Fermi and known as Fermi resonance [39]. For the

Fermi resonance to occur, the two vibrations should be of the same

symmetry type. If there is resonance, energy sharing may also take

place. The combinations and overtones borrow energy from the

fundamentals and their intensity may become equal to that of the

fundamental$. In any case, it is no longer proper to speak of the one

level as being an overtone or combination level and the other a

fundamental level, for both the displaced levels will be partly of

21

the one kind and partly of the other. Since the Fermi resonance

interaction requires that the vibrations involved have nearly the

same frequency, the interaction will be affected if one mode

undergoes a frequency shift due to deuteration or solvent effect

while the other mode does not. Thus, the presence of Fermi resonance

in compounds can be tested by deuterating the sample or by taking the

spectrum in various solvents [4,19,29].

1.11 Theoretical Methods of Vibrational Analysis

Group theoretical methods for analysing molecular vibrations

are well-known. Hornig [40] has shown that the nature of vibrational

potential energy of a crystal can be expressed in the form:

E V + En

n nv i Vnk + Vl + Vln

nfkwhere the four terms represent the potential energies due to internal

vibrations, interactions between internal vibrations, lattice modes

and interactions between lattice modes and internal modes

respectively. The two commonly used methods for analysing the

vibrational spectra are the site group approximation (or site

symmetry approach) and factor group approximation (or the unit cell

approach). The site symmetry approach uses effectively the first term

of the potential energy expression whereas the unit cell approach

consider the first and second terms.

22

1.11.1 Unit ce11 approach

This method first developed by Bhagavantam and Venkatarayudu

[41], elaborated by Hornig [40] and again by Winston and Halford

[42], does recognize coupling between symmetry equivalent molecules

or complexes within a primitive unit cell, whereupon different

selection rules come into play. This method has over the years proven

very useful in the analysis of the vibrational spectra of the

crystals.

In Bhagavantam and Venkatarayudu method, a primitive cell of

a crystal is treated as if it were a single polyatomic molecule. For

a crystal consisting of N unit cells, each containing n atoms there

are 3nN modes of vibrations. Only those modes for which the

equivalent atoms are in phase are active as fundamentals in the

infrared and Raman spectra. The remaining modes may appear as

combinations. Thus, one has to determine only the modes of one unit

cell. This can be achieved by taking the factor group, which may be

taken as a subgroup of the space group. The distribution of the

vibrations among the irreducible representations of the factor group

can be determined by the method of Winston and Halford.

This method is quite difficult for large molecules, as one

has to identify the symmetry qperations to which each atom is

invariant and also the unit cell content. In most of the cases, these

information are not completely available.

23

1.11.2 Site group analysis

In site group analysis, developed by Halford [43], the atoms

and molecules, other than one considered are kept in their

equilibrium positions. The molecule under consideration is then

considered to vibrate in an environment of fixed symmetry given by

its site group. The site symmetry will always be lower than the

symmetry of the molecular point group. In general, site group will

be a subgroup of the molecular point group. Here the types of modes

which will lead to the infrared and Raman active modes must be

obtained, on the basis of the site groups. The method has been widely

used and found to be satisfying when weak to moderate intermolecular

forces prevail and when coupling between different vibrators in the

crystal is negligible. However, when this is not so, the site group

analysis generally breaks down [44].

The correlation method developed by Fateley et al. [46] is a

generalisation of both the methods. The irreducible representation

can be obtained by correlating the site symmetry species of

individual atoms in the crystal to its factor group species or by

correlating the molecular free ion symmetry to the factor group

symmetry of the crystal through the molecular site symmetry.

1.12 Polarization of Raman I~nes

Valuable information can be obtained by studying the

polarized components of a Raman line. If a polarized radiation

24

interacts with a molecule that has an isotropic polarizability

tensor, the oscillation induced in the molecule will be in the same

plane as the electric field. Again, in the case of .molecules with

isotropic polarizability a; , the scattered radiation will be

polarized, even though the incident light is non-polarized. However,

the polarizability tensor is usually anisotropic. Hence, the induced

dipole moment will not be coincident with the plane of the electric

field but 'vi11 tend to be oriented in the direction of greatest

po1arizabi1ity. The scattered light vibrates in the same plane as the

induced dipole. Even if the incident radiation is polarized, an

anisotropic polarizability tensor will give rise to scattered

radiation that is depolarized. A totally symmetric vibration mode

gives rise to a polarized scattered line and that a vibration with

lower symmetry is depolarized. This property can be used to confirm

whether or not a vibration has A1

symmetry [29].

The degree of depolarization f is defined as the ratio of

the intensity of the scattered light polarized perpendicular to the

XYplane (1..1. ) to that polarized parallel to this plane (II/ ).

f = I.lIn

Here z axis is taken in the direction of propagation of the incident

light, and the direction of observation is perpendicular to z axis.

The value of f depends on the isotropic part a' and anisotropic part

Y' of the polarizability.

25

For Raman scattering,

The corresponding total intensity (the sum of the intensities of the

2 2two plane polarized components) is proportional to 45(a') + 13(Y;') •

ex' may vanish even without y' vanishing. Therefore, the value of

/ may reach 6/7. When f = 6/7, the Raman line is said to be

depolarized. Any line for which ! < 6/7 is said to be polarized. In

particular, when ! = 0, the line is said to be completely polarized

[4] •

1.13 Effect of Temperature on Raman Spectra

The increase in temperature affects the width and intensity

of the Raman lines. Also, the frequency of the bands will be shifted.

When the temperature is increased, Raman lines shift

towards the exciting line. The low frequency or the lattice lines

show a proportionately greater shift than the high frequency lines or

line arising from the internal oscillation of the group of atoms.

For a line of frequency J.J, ):. is given by

x.=_(l) bLl

<..I ~t

}. is greater for low frequency lines than for the high frequency

ones.

).: - Value for any line varies with temperature, its value

increases rapidly at high temperature and approaches zero as absolute

26

zero is approached. X-value for different lines in the same crystal

are, in general, different. This value does not depend on the

symmetry class to which the vibration belongs. An increase in

temperature causes an increase in the width due to anharmonicity of

vibration. The width versus temperature curve runs parallel to the

frequency shift versus temperature curve. The width of the line is

roughly proportional to the square root of the temperature.

The peak intensity of the Stokes lines decreases as the

temperature increases, though an increase is to be expected by

Placzek's theory. The anti-Stokes lines increase in intensity with

increase in temperature, but not to the same extent as required by

Placzek's theory [47-48].

1.14 Sulphates, Phosphates and Molybdates- A Short Review

1.14.1 Sulphates

The doubly charged tetrahedral molecular anion S04 has been

the subject of study by many investigators. In the solid state alkali

metal sulphates, M2S0

4eM = K, Rb and Cs), it has been observed that

the symmetric stretching frequency decreases linearly with the

increasing cation radius [49]. Later Dean et ale [50] have confirmed

this observation from the Raman spectra of the sulphates M2

S04

eM = Li, Na, K, Rb, Cs). Berenblut et al. [51] have noted the effect

of water of crystallisation in CaSO4 and Ca2

SO4. 2H20. The

polarization behaviour of the Raman lines under different crystal

27

orientations of Cs2so

4has also been investigated [52]. Ishigame [53]

has studied the temperature dependence of the Raman spectra of K2S0 4

in the temperature range 300 K to 117 K. In the IR study of the

mixed crystal system of Na 2S0 4 and (NH4)2S04 [54], it is observed

that the transition point of the phase transition of sodium sulphate

decreases with increase in concentration of the ammonium ions. Carter

[55] has recorded the polarized Raman spectra of (NH4) 2S0 4 and has

discussed the results in comparison with those of the isomorphous

sulphates [49], External modes have been identified in the single

crystal Raman spectroscopic investigation of MS04

(M = Ba, Sr, Pb,

Ca) [56]. Baran has examined the nature of hydrogen bonding in KHS04

and KDS04

[57] and CsHS04

[58] and has explained the ABC structure of

the IR and Raman bands arising from the .u (OH) stretching vibration

on the basis of Fermi resonance, He has carried out a detailed

analysis of the polarized infrared and Raman spectra of these

crystals. The polarization features of the HSO; ion vibrations are

predicted, assuming that the longest S-OH bond vibrates independently

of the S04 group vibrations,

Ananthanarayanan [59] has recorded the Raman spectra of

K2M(S04)2,6H20 (M = Mg, Zn, Ni and Co), known as Tutton's salts and

has assigned six fundamental frequencies of metal aqua complex in

K2Co(S04)2,6H20. Brown and Ross [60] have carried out the infrared

spectral studies of 64 Tutton's· salts and have interpreted them on

the basis of the site group and factor group approximations. Campbell

28

et al." have found that MI cations has more influence than MIl cations

I IIin the infrared spectra of 18 Tutton's salts ~M (S04)2.6H20 [61].

Gupta et al. have correlated

T_II )sulphates viz., MtM (S042· 6H 20

the infrared bands of ten double

[ MI NH K MIl = Ni C F C= 4" , 0, e, u,

Zn and Mn) with the known s-o bond lengths in these salts [62].

Infrared and polarized Raman spectra of K2Mg(S04) 2' 6H

20 [63] and

(NH4)2Mg(S04)2.6H20 [64] are also reported and the different modes of

metal aqua complex are identified in these compounds. Mathew et al.

have identified strong hydrogen bonds in KMgC1S04

.3H2

0 [65] in a

polarized Raman study.

Infrared spectra of a number of double sulphates of ammonium

and rare-earth sulphates have been reported [65-68] and the existence

of different types of water molecules in these compounds are

established. Mathew et al. [69] have established from the vibrational--

crystallographically distinct water molecules exist in the unit cell.

Two erystallographically distinct sulphate ions are identified in

et al. [72] have investigated the infrared spectra of a number of

rare earth sulphates, containing potassium, KLn(S04)2(Ln = Pr, Nd,

Sm, Tb, Dy, Er, Tm and Yb). Baran et al. have reported the

vibrational spectra of another type of double sulphate,

29

Infrared and Raman spectra of M3H(S04)2 with M = Na, K and

NH4

(74] reveal the structural disorders in the crystals. Kamoun

et ale (75] have investigated the polarized Raman spectra of

(NH4 ) 3H(SO 4) 2 and (ND4) 3 D(SO 4) 2. and have found that the crystal

3-contains the non-centrosymmetric dimer (S04HS04) and strong

asymmetric O.-H •..o hydrogen bonds. A temperature dependent vibrational

reported. A detailed study of the polarized IR and Raman spectra of

Na3H(S04)2 has been reported by Videnova Adrabinska (78]. Kasahara

et al. (79] have observed an anomalous broadening of the 2)2 line

above Tc

in K3D(S04)2 and have explained it with the motional

narrowing theory developed in NMR. Kalevitch et al.(80] have given a

new interpretation to the IR and Raman spectra of RbHS04

and RbDS04

•

2-Distortion of SO 4 ion is examined from a vibrational spec~roscopic

investigation of Te(OH)6.K2S04 [81] and Te(OH)6.X2S04 (X = Tl, Na)

(82].

2Vanderpool et al. (83] have observed two types of S04 anions

in La2(S04)3.8H20 crystal from its Raman spectra. The role of two

types of lattice water molecules has been determined by the polarized

Raman investigations on Ce2(S04)3.9(H,D)20 single crystals (84].

Raman spectra of compounds LiMS04

with M = Rb, Cs, NH4

, N2H

5and Na

are also reported [85-91]. Infrared and polarized Raman spectra of

LiNH2

S03

have been investigated in the temperature range 300-90 K

(92], while Vijay Varma and Rao have investigated the phase

30

transitions in NZH

6so4 crystal [93]. Botto [94] has described the

vibrational and thermal analysis of an ordered mixed-oxo salt

(NH4)ZHZAs04S04. Liu et ale [95] have recorded the Raman spectrum of

CUS04

.5HZO at 90K and have assigned the internal modes of CU(HZO f:complex and differently bonded water molecules.

A high temperature phase transition is followed by the

temperature dependent IR and Raman spectra in CSZH3(S04)4.HZO [96].

Structural phase transitions and lattice vibrations in K4LiH3(SO 4) 4

and Rb4LiH3 (SO 4) 4 crystals [97] are also investigated by the Raman

scattering technique.

1.14.2 Phosphates

Phosphates are broadly classified into two groups namely

orthophosphates and condensed phosphates. Orthophosphates can exist

as tribasic, dibasic or monobasic forms. In tribasic orthophosphates,

there are independent P04

groups with Td

symmetry. In dibasic

orthophosphates, HPa~ ion is formed by attaching one hydrogen atom to

z-one of the oxygen atoms of the P0 4 tetrahedron. HP0 4 ion has a C3v

symmetry. In the monobasic form, two hydrogen atoms are attached to

the oxygen atoms of the P0 4 group to form HZP0 4 ion. It may have free

ion symmetries Cz or C [98].v s

Chapman et ale have investigated the infrared spectra of a

series of compounds containing Poi: HPO~- and H2PO~ and have

31

determind their vibrational modes [98,99]. Schultze et al. [100] have

confirmed these values. Petrov et al.[101] have studied the infrared

spectra of dicalcium phosphate, dicalcium phosphate dihydrate and

octacalcium phosphate and have investigated the nature of hydrogen2-

bonding in HP04

ions. Also, they have investigated the expected

regions of (P)O-H stretching, inplane and out-of-plane P-O-H bending

modes. Two dis tinct water molecules are identified in NaHP04

• 2H2

0

crystals by the vibrational analysis of the compound [102,103].

Casciani et a~.[104,105] have carried out a detailed vibrational

analysis of CaHP04

and CaHP04

.2H2

0 and have established the existe~ce

of two crystallographically distinct water molecules in CaHP04

• 2H2

0

[ 105] .

Single crystal Raman study of SnHP04

proposes a layer

structure for this compound and the intra-layer forces are found to

be stronger than interlayer forces [106]. The different modes of

orthophosphate ions are identified in PbHP04

[107]. Magane Aoki

et al. [l08] have recorded the Raman spectra of CsH2

P04

at various

temperatures and have suggested that the phase transition in the

crystal is of an order-disorder type. At the same time, Fillaux

et al. [109] have identified two types of hydrogen bonds in CsH2

P04

.

Stretching modes originating from the short and long hydrogen bonds

have also been identified from a study of CsH2

P04

and CsD2

P04

[110,111]. Raman spectra of paraelectric and antiferroelectric phases

32

room temperature and at 20 K of (NH4)2HP04 and (ND4)2 DP04 [113] have

also been investigated.

The vibrational investigation of Te(OH) 6· Cs 2HPO 4 crystals

[114] reveals that the H atom is loosely bonded to the oxygen atom of

the phosphate ion. Hence, phosphate ion exists as a distorted PO 42-

tetrahedron rather than a HP04

ion. The multiplicity of bands

observed in the Raman spectrum of KHS0 4 .KH2PO 4 crystal indicates a

distorted structure for the (P,S)04 groups [115,116]. Mathew et al.

have investigated the infrared and Raman spectra of the ion exchanger

a-Zr(HP04)2.H20 and its half and fully exchanged phases ZrKH(P0 4)2

and Zr(NH4P04)2H20 [117]. Two types of water molecules are identified

in the study of vibrational spectra of Y-TiCHP04)2.2H20 and its

deuterated analogue at room temperature and at 453 K [118].

Choi et al. [119] have observed the ABC triplets in the OR

stretching region, by the polarized Raman study of NaH2P04

at 300 K

and 10 K. Also, they have not observed any phase transition down to

10 K in the crystal.

Infrared spectra of three simple organic phosphates viz.,

trimethyl phosphate, triethyl phosphate and triphenyl phosphate have

been recorded in both liquid and solid samples by Mortimer [120].

Rotational isomerism in them is discussed. Keijiro Taga et al. [121]

have reported the vibrational spectra and normal coordinate analysis

of barium dimethyl, diethyl and ethylmethyl phosphates. Normal

33

coordinate analysis indicates that the phosphate back bone, CO-P02

-OC

takes part in the gauche-gauche conformation in the solid state.

Infrared spectra of three rare earth dimethyl phosphate have also

been reported [122]. In a study of the polarized Raman spectra of

crystals, different ethylenediammonium groups in

them are identified [123,124]. Infrared and Raman spectra of alanine

and glycine phosphates are also reported [125,126].

Tarte et al. [127] have investigated the IR and Raman

spectra of Nasicon type MIM~V(P04)3 phosphates (MI= Li, Na, K, Rb,

IVCs and Tl and M = Ge, Sn, Ti, Zr, Hg). They have observed that the

3- IP0

4stretching frequencies are modified by the nature of both M and

MIV cations. Husson et al. have investigated the vibrational spectra

of a few antimony phosphates [128,129]. The number of bridging and

unshared oxygen a toms in the PO 4 groups are related to the highes t

1) p-o stretching frequencies in the spectra. The vibrationalas

spectra of [NiCH20) 4 ][VOPO4] 2 have been reported by Baran and Lii

[ 130] • Jayakumar et al. [131] have identified two

crystallographically distinct

crystals by a study of the infrared and polarized Raman spectra of

the compound. They have also observed that NHt ions rotate freely in

the crys tal.

IR and Raman

show that both[132],

studies on M(Mo02

)(P04

)2 with M = Pb and Ba

3-PO 4 and MoO6 groups are distorted in both

compounds. Bismayer and Romer [133] have investigated the hard mode

34

Raman spectroscopy and renormalisation phenomenon in diluted lead

phosphate (Pb1_

xMx )/P04 )Z. They have explained the renormalisation

phenomena as a consequence of order parameter coupling with direct

induced conjugated fields. IR and ,Raman spectra of NaCdInZ(P04 )3 and

NaCaCdMgZ(P04)3 are also reported along with their X-ray structural

data [134,135].

Raman spectra of five hypophosphite compounds La(HZP04 )3'

pr(HZP04)3' La(HZP04 )3· HZO, Mg(HZP04)Z.6HZO and VO(HZP04 )Z.HZO [136]

show that the unit cell group coupling between hypophosphite anions

become quenched with increasing water of crystallization content in

the solid.

The phase transitions in MTiOP04

with M = K, Rb and Tl due

to temperature and pressure changes are investigated by Serhime

et ale [137]. In both KTP and RTP, low frequency lines corresponding

to the soft modes in TTP are observed but their softening does not

extrapolate to zero at T , in contrast to the case of TTP. IR andc

Raman spectra of Li3MZ(P04 )3(M = Sc, Fe) in the temperature range

77-670 K [138] reveal that the bands corresponding to the vibrations

of Li+ ion are quenched in the vicinity of a phase transition due to

the disorder of the Li+ ion. Shasikala et a1. [139] have made a

comparative vibrational spectroscopic study of ferroelectric TMP,

its deuterated analogue (DTAAD) and non-ferroelectric TADP. The

temperature variation of the Raman spectra suggests an order-disorder

model for the phase transition.

35

1.14.2a Pyrophosphates

Depending upon the nature and degree of condensation, . the

symmetry of the P04

tetrahedra changes from one compound to another.

The PZ07 group is considered as a result of the decrease in the

positional symmetry of the PO 4 tetrahedra during condensation and

this causes an additional splitting of P04

valence vibrations [140].

4-Studies on pyrophosphates have revealed that PZ07 ion exists as a

discrete unit consisting of two P04

tetrahedra sharing a common

oxygen atom [141]. Stegar et al. [14Z] have been the first to report

the IR and Raman spectra of pyrophosphates.

Hezel and Ross have shown that the pyrophosphate anion can

have six possible symmetries, viz., D3d

, D3h

, D3

, CZv

' Cs

and Czdepending on the linearity of the P-O-P bridge, free rotation of P0

3

group and the nature of the terminal bond length [143]. For a linear

P-O-P bridge, the symmetry can be D3

, D3d

or D3h

• When the bridge is

bent, the symmetry can be CZv

' Cs

and CZ

. For a bent P-O-P bridge

with staggered structure, the possible symmetry is C • When it is ins

an eclipsed configuration, the possible symmetry is CZv

• A study of

n-the Raman and FTIR spectra of X

Z0

7anion with X = P and Cr has been

carried out by Abbas and Davison [144].

From the Raman spectroscopic investigation of a -ZnlZ07, it

4-is established that PZ07 ion has an eclipsed configuration in the

compound [145]. On the basis of the Raman spectra of a-MgzPZ

07

and

36

4-~ -Mg2P207' Cornilsen and Condrate have predicted that the P20

7ion

has a linear bridge in f3-Mg2P207 and a bent bridge in a-Mg2

P20

74-

[146]. They have also observed that the P20

7anion has a bent P-O-P

bridge in a-Sr 2p207 , a-Ba 2P207

and a-Ca2P207 [147]. Raman and mid-IR

spectra of these compounds reveal that the Barium and the strontium

compounds are isostructural.

Infrared and Raman spectra of M3HP207

.H20 (M = Na, Cs;

n = 0, 1, 9) have been studied by Sarr and Diop. Brown's correlation

1J P-O-P - J.J P-O-P as a function of P-O-P bridge angle establishedas s

for neutral pyrophosphates has been extended by them to

hydrogenophosphate. A linear relationship between J P-O-P and P-O-P

angle is also established. Further, they have investigated the

vibrational spectra of K3HP2°7. 3H20 and K3HP207 [148]. Vibrational

spectra of a-CaNaP20

7.4H

20, CaNH

4NaP

20

7.3H

20 and CdNH

4NaP20

7.3H20 are

+also reported [149]. It is observed that NH

4ion is rotating freely

in the compounds. Vibrational spectra of Ni 3Pb(P207)2 and

P20;-anions are more distorted in

the cobalt compound. Non-coincidence of Raman and IR bands suggests a

centrosymmetric structure in both the compounds. Baran et al. [151]

have investigated the vibrational spectra of Fe2

P20

7and have shown

that the compound has a bent P-O-P bridge.

37

1.14.2b Cyclohexaphosphates

The cyclohexaphosphates' belonging to condensed phosphates,

are built up by six corner-sharing P04

tetrahedra. The basic

structural unit in these compounds are the P-O-P bridges and the POZ

terminal groups. The structured studies of different

6-cyclohexaphosphates reveal that P6018 anion in different compounds

possesses different internal symmetries. In CU2Li2P6018 and6-

(C2H5NH3)6P6018.4H20, P60 18 ring has no internal symmetry [152],

while P60~; ring anion has a 1 internal symmetry in M6P6018.6H20

(M = Cs, Rb) and in some telluric acid adducts [153,154]. Lazarevski

et al. have studied the thermal conversion of Cu, Co, Ni, Mn, Ba, Cd

and Ga cyclohexaphosphates using thermogravimetry, X-ray phase

analysis, paper chromatography and IR spectroscopy [155]. Only a few

investigations have been reported on the vibrational analysis of

cyclohexaphosphates. The IR and Raman spectra of Cs 6P6°18. 6H20 and

Rb6

P6°18. 6H2

0 are reported by Sunila Abraham et al. [156]. They have

6-observed that P6018 anion has a Ci symmetry and it is distorted

considerably. They have also investigated the infrared and Raman

spectra of Ag6P6018·H20, (NH4)6P6018.H20 and Ag3(NH4)3P6018oH20

[157] .

1.14.3 Molybdates

Molybdates are structurally interesting compounds, since

some of them form octahedral anionic groups. Normal molybdates of

38

type AMo04

and A2

Mo06

crystallize with different structures like

Scheelite, Wolframite, Spinel etc. The Scheelite type structure is

the common among AMo04

type compounds.

Many investigators have studied the vibrational spectra of

Mo04

with tetrahedral symmetries. But there is considerable

disagreement in the early assignments of V2

and ~4 modes. Busey and

Keller [158] have assigned 1)Z mode at a higher frequency than JJ 4

from their study of the Raman spectra of aqueous solutions and the IR

spectra of Nujol mulled samples of several molybdates. From the IR

spectral studies of molybdates having tetrahedral structures Clark

and Doyle [159] and Brown et al. [160] have also favoured the

assignment ilZ

> V4 for the ion. Kaneska et al. [161] have assigned

bands of the IR and polarized Raman spectra of a -MnMo04

. On the

basis of a normal coordinate analysis using valence force field,

lattice vibrations are explained mainly in terms of Mn-O stretching

force constants. By the calculation of the relative intensities of

Raman bands from approximate force fields using Long matrix method

based on Wollkenstein theory, Weinstock et al. [162] have shown that

in Raman spectrum the intensity of lJ1 >V 3 and that of .lJ2

>.u 4.

Muller et al. [163] have convincingly established from a study of

single crystals of molybdates that lJZ

has a higher intensity than

lJ4

in Raman spectrum while 1J4

has a higher intensity in the IR

spectrum.

39

Raman spectra of CaW04

, SrW04

, CaMo04

and SrMo04

are

investigated by Porto and Scott [164]. Infrared and Raman spectra of

gel grown NiMo04

show that this compound is isomorphous to CoMo04

[165]. Vibrational spectra of NaLa(Mo04

)2 and NaLa(Mo04

)2 with

0.5 mole %.3+

Nd doped crystals do not reveal any change in the

vibrational frequencies due to doping [166,167]. The infrared and

Raman spectra of GdTb(Mo04 )3 and Tb1.8EuO.2(Mo04)3 are also reported

[168,169]. Ratheesh et al. [170] have investigated the IR and Raman

spectra of NaNi2

0H(H20) (Mo0

4)2 and NaZn

20H(H

20)(Mo0

4)2 and their

2-partially deuterated analogues. Mo0

4ions are found to be more

distorted in the Ni compound than in the Zn compound. Hanuza et al.

[171.] have investigated the IR and Raman spectra of Ky(Mo04

) 2

crystals down to liquid helium temperatures. The polarized

spectroscopic studies of KDy (MoO4) 2 [ 172] indicate additional

intermolecular interaction due to pair coupling of the molybdate

tetrahedra. This effect, combined with the multilayer crystal

structure is found to restrict the vibrational degrees of freedom,

distributing the selection rules for vibrational transitions.

Recently, infrared and Raman spectra of a-Th(Mo04 )2 and a-Th(W04 )2

are analysed and new assignments are proposed for the internal modes

2- 2-of Mo0

4and W0

4ions [173]. Hanuza et al. have reported the polarized

IR and Raman spectra of scheelite crystals of NaBi(Mo04

)2 and

LiBi(Mo04

)2 [174]. Raman spectra of CsLiW04

and CsLiMo04

recorded at

different temperatures by Shefer et al. [175] reveal that the

40

internal motion of the ions do not play any role in the dynamics of

the phase transitions. The vibrational spectra of triple molybdates,

KMgSc(Mo0 4)3 and KMgLn(Mo0 4)3 with tetrahedral coordination to

molybdenum and octahedral coordination to the cation with high

oxidation states exhibiting super ionic properties have also been

studied [176].

Two phase transitions are observed in CaMo04 by the pressure

dependent Raman study [177]. Jayaraman et al. have carried out the

pressure induced Raman study of SrMo04! They have observed that

these Scheelite type crystals transform to monoclinic lattice near

13GPa [178]. Kourouklis et al. have observed two phase transitions in

Tb2(Mo04)3 crystals by a high pressure Raman study [179].

41

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Figure 1.1 Quantum representation of the energy interchangein the Raman effect.

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Fig .1.3, Diagrams of possible hydrogen vibrational potentialsin :(a) a weak H-bond;( b) a moderate H-bondand (c) a strong H- bond.

introduction 1.3.2 selection rule for raman spectra...

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