1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.8.1
1.8.2
1.8.3
i.91.10
1.11
1.12
1.13
1.13.1
1.14
1.14.1
1.14.2
1.14.3
1.15
1.15.1
1.15.2
I 1.15.3
1.15.4
CHAPTER 1
INTRODUCTION
RAMAN SCATTERING
INFRARED ABSORPTIQN
NORMAL MODES OF VIBRATION
SELECTION RULES FOR INFRARED AND RAMAN SPECTRA
ANHARMONICITY
FERMI RESONANCE
POLARIZATION OF RAMAN LINES
SOLID STATE EFFECTS Site symmetry effect
Correlation field effect
Internal-External vibrational coupling
HYDROGEN BONDING
SINGLE CRYSTAL RAMAN SPECTRA
FACTOR GROUP ANALYSIS
SAMPLE HANDLING TECHNIQUES
PHASE TRANSITIONS
Soft modes
INSTRUMENTATION
Laser Raman spectrometer
Variable temperature Raman cell
Infrared spectrophotometer
REVIEW OF EARLIER WORKS
Selenates
Sulphates
Pyrophosphates
Cyclohexaphosphates
REFERENCES
FIGURES
. r
Vibrational spectroscopy provides a very powerful
tool in molecular structure determination. In condensed
phases, lattice dynamics constitute one of the pioneering
fields of study especially in the solid state physics of
crystalline materials. Knowledge of the phonon spectrum is
an important pre�requisite to the understanding of a whole
host of phenomena such as heat capacity, thermal
conductivity, ferroelectricity, superconductivity,
vibronic coupling, phonon-assisted electronic transitions
etc.
Infrared and Raman measurements have a significant
position among those physical methods which have been used
for investigating molecular structure and properties.
These complementary techniques have not only been of great
help in the interpretation of the spectroscopic behaviour
of the solid state but also in the understanding of
intermolecular forces. Significant information concerning
the geometry of the molecules, types of chemical bonding,
the internal and intramolecular interactions and the
crystal field effects can be obtained from the number and
frequency of the bands in conjunction with a group
theoretical analyses. In particular, the dependence of the
vibrational properties of the crystals on the anisotropic
part of the intermolecular potential has given a wealth of
information in terms of the interaction
intensities and polarization of spectral
the structural details of the electron
molecule.
3
potential. The
bands reflects
cloud of the
with the advent of modern and reliable· laser
sources and the subsequent development of optical
spectrometers and new detection techniques, solid-state
physicists have rapidly realized that Raman spectroscopy
is an extremely useful non-destructive tool for
characterization purposes. Raman spectroscopy has enjoyed
a spectacular resurgence in popularity because of the
universality of the phenomenon and the convenience of the
experimental technique. It enables one to obtain an
insight into the ultimate molecular structure.
1.1 RAMAN SCATTERING
Raman spectroscopy is concerned with the
phenomenon of a change of frequency when light is
scattered by molecules. When electromagnetic radiation
interacts with a molecule, most of the photons are
scattered elastically (Rayleigh scattering), but a few
undergo inelastic scattering (Raman scattering). The
frequency difference between the exciting line and the
4
band that arises due to the inelastic scattering is
referred to as Raman shift. The Raman shift is independent
of the frequency of the exciting line. The frequency
·shifts are the frequencies of oscillation of the
chemically bonded atoms of a molecule and thus depends on
the geometry of the molecule and· the forces of chemical
affinity. The intensity of the scattered radiation varies
with the fourth power of the frequency of the incident
radiation. The inelastic light scattering phenomenon was
theoretically predicted by Smekal in 1923 [1] and later
experimentally observed by C.V. Raman and K.S. Krishnan in
1928 [2,3].
The theory of light scattering is based on the
fact that the incident light wave induces an oscillating
dipole moment p = a E cos (2 1t Vt) in the molecules whereo
the electric vector and a represents the
polarizability given by a = ao + a l cos 21t VIt, a is theo
polarizability in the equilibrium configuration and a1
the maximum change of polarizability when the atoms
vibrate
p = (et o +al
cos 21t»lt) [Eo cos (2 1t j)t)] (1 )
Thus the induced electric moment can be regarded as a
superposition of three periodically changing moments
5
having frequencies Y, ( P + J\) and (;) - J)1) respectively.
They radiate light of corresponding frequencies which
constitute the Rayleigh line, the anti-Stokes Raman line
and the Stokes-Raman lines respectively, Stokes lines
being more intense than the anti-Stokes lines
(Figure 1.1). Thus the polarizability of a molecule gives
rise to Rayleigh scattering, it is the changes of
polarizability during molecular motion that are
responsible for the Raman effect. The components of the
induced dipole moment vector are related to the electric
vector as
p = (l E + a X xx X
p = a yx E + y X
p = a E + z zx X
where the coefficients
E + (l Exy y xz z
(lyy E + ayz E y z
a zy E + ay zz z
a a etc. are thexx' yy
of the polarizabili ty tensor and a - a xy - yx'
a = a . The Raman transition yz zy is allowed,
a - a xz - zx'
if one or
another component of polarizabili ty tensor is different
from zero. If the polarizability of a molecule is not
spherically symmetric the induced moment will depend on
the orientation of the molecule and the anisotropic part
of the polarizability is alone responsible for the
rotational Raman effect.
6
If a vibration of the atoms which constitute a
molecule introduces a corresponding periodic change in its
polarizability, the scattered radiation will contains the
sum and difference of the incident frequency and the
molecular vibration frequency. This is the vibrational
Raman effect. If the vibrations of the molecule are
purely harmonic, each vibration will contribute
independently to the electric moment and will appear in
the Raman spectrum. The intensity of any vibrational Raman
line is determined by the displacement belonging to the
corresponding normal vibration. Besides the fundamental
frequencies of vibrations, overtones and combinations
often appear in the spectra due to anharmonicity [4-7].
1.2 INFRARED ABSORPTION
Infrared spectroscopy is generally concerned with
the absorption of radiation. Inorder to absorb infrared
radiation, a molecular vibration must cause a change in
the dipole moment of the molecule. The intensity of an
infrared absorption band is proportional to the square of
the change in dipole moment caused by the molecular
vibrations giving rise to an absorption band. If a
molecule in its equilibrium configuration has a center of
symmetry, then vibrations during which the center of
symmetry is retained will be infrared inactive [8,9].
7
A change in dipole moment may be only a change in
the direction with respect to a co-ordinate system fixed
in space. In harmonic oscillator approximation only the
fundamentals produce a change in dipole moment and
therefore are IR active. But when the anharmonicity is not
negligible the selection rules permit overtones,
combination and difference bands.
Absorption of electromagnetic radiation with
varying frequency in the IR region leads to a transition
of the molecule from vibrational ground state, with all
vibrational quantum numbers having zero values to excited
states with higher quantum numbers of the normal modes.
A characteristic infrared absorption band of a
group is found to occur at about the same frequency
irrespective of the molecule in which the group is
present. The essential constancy of group frequency
results from the constancy of bond force constants from
molecule to molecule. This makes infrared spectroscopy a
unique and powerful tool in structural analysis [10].
1.3 NORMAL MODES OF VIBRATION
Normal modes of vibration of any molecule are
internal atomic motions in which all the atoms move in
phase with the same frequency,
8
but with different
ampli tudes. The various displacements of the atoms in a
given normal mode of vibration, V. may be represented by1
a linear combination of displacements of all atoms, which
is known as the normal co-ordinate Q.. Thus for a1
non-linear molecule there are 3N-6 (3N-5 for linear
molecules, since there is no rotation about the bond axis)
normal co-ordinates [11].
For a crystal containing n primitive unit cells,
each with N atoms there is 3nN degrees of freedom arising
from the motion of the atoms. Since the primitive
translations are treated as identical operations, 3N
degrees of freedom are only considered. Of the 3N degrees
of freedom, three are acoustic modes and the rest 3N-3
are optic modes. The symmetry species of the acoustic wave
functions are the same as those of translational vectors
aligned with the same axes and are therefore obtained
directly from the character table. Acoustic modes are not
normally active, since no dipole moment change is
associated with them. Depending on the factor group and
its site symmetry the 3N-3 optic modes mayor may not be
optically active.
9
The optic modes can be classified into internal
and external modes. The internal modes involve stretching
and bending vibrations of the chemical bonds within the
molecule. The external modes (lattice modes) involve
partial rotations (librations) and translations of
molecules as a whole in the crystal lattice [12].
1.4 SELECTION RULES FOR INFRARED AND RAMAN SPECTRA
All the vibrational transitions need not be Raman
or IR active, some may even be inactive in both. When a
transition is active in both, the intensity factors may
make it easier to observe in one effect than in the other.
For molecules having center of symmetry Raman active
vibrations will be IR inactive and vice versa. A study of
both techniques are essential for a complete knowledge of
the energy levels of a system [13-17].
The intensity of a transition is proportional to
the square of the relevant transition moment [13]. Hence,
a transition is allowed if the corresponding moment does
not vanish. For a fundamental transition from vibrational
state m to n, the transition moment induced by the
electric field E of the incident radiation is given by
where <X is the molecular polarizability which is a
10
function of the normal co-ordinate Q of the vibrational
mode. The integral is to be extented over the whole
co-ordinate range. For non-isotropic molecules the tensor
(a) has six components axx
' ayy
' a22
, axy
' ayz
and azx
Symmetry considerations based on group theory lead to the
conclusion that a fundamental is permitted in Raman
scattering only if its species is the-same as that of at
least one of the components of the polarizabili ty. The
polarizability component can be expanded in a Taylor
series with respect to the normal co-ordinate as
a . .1]
where ( a .. ) is the value of a. . at the equilibriumlJ O l]
configuration, Q •••• are normal co-ordinates m
associated with vibrational frequencies w •••
and the summations are overall normal co-ordinates. Thus
for a vibrational mode with frequency wk to be Raman
active, the derivative of the polarizability tensor with
respect to the corresponding normal co-ordinate at the
equilibirium position must not vanish.
The quantum mechanical formulation of
11
the
selection rule for IR is that if a molecule changes from a
vibrational state m to a state n light can only be emitted
or absorbed if00
M =! ljJ )l ljJ dT_00 m n
is not equal to zero. The quality )l represents the dipole
moment change involved in the transition from state m
to n [18].
1.5 ANHARMONICITY
In polyatomic molecules, anharmonicity leads
to the appearance of overtone and combination bands. The
transi tions corresponding to 6 v .= ±.2 or ±.3 in addition to
that of6Y= ±,l lead to the appearance of overtone bands of
frequencies approximately two or three times that of the
fundamental band.
Anharmonicity is of two types, mechanical and
electrical. Mechanical anharmonicity is a consequence of
the deviation from the harmonic potential whereas the
electrical anharmonicity is due to higher order terms in
the polarizability. If the molecular motion is
anharmonic, the dipole moment will oscillate with the
fundamental frequency and integral multiples thereof.
12
These are called the fundamental, first overtone, second
overtone etc [9].
The main effects of anharmonicity are the shift of
the phonon frequencies and the finite lifetime of the
phonon states. While the latter effect is directly
observable in the infrared and Raman spectra, being
connected to the band width, the former can only be
determined with difficulty owing to the fact that
overtones and combination bands of the lattice vibrations,
are observed only in rare cases in the spectra of
molecular crystals. However both effects are temperature
dependent, and measurements of phonon frequencies and band
widths as a function of the temperature can be easily
made. Anharmonicity effects can also be studied
conveniently through the shape and intensity of
multiphonon bands [19].
The intensity of an overtone absorption is also
dependent on the amount of anharmonicity in the vibration.
The intensity of an overtone band is usually about
one-hundredth of that of the fundamental band [20]. The
absorption bands due to anharmonicity are usually broad
[21]. The lower intensity of these bands in the Raman
spectra than that in the infrared spectra is probably due
13
to the fact that electrical anharmonicity is more
significant in infrared absorption [22].
Another phenomenon associated with anharmonicity
is the appearance of the hot bands [23]. These are
transitions in which molecules, originally in an excited
state, absorb a further quantum. Thus, the quantum number
changes by +1, but because of anharmonicity the frequency
of this transition is less than that of the fundamental.
Since the appearance of hot bands depends on the
population of an excited state, hot bands are usually
observed at lower wavenumbers.
1.6 -FERMI RESONANCE
Fermi resonance is a phenomena which occur when
two vibrational levels, usually one fundamental and one
overtone have nearly the same energy and are symmetrically
placed. In such cases the overtone borrows intensity from
the fundamental and become as strong as the fundamental.
The two levels repel each other and the one with greater
energy moves to higher frequency and the one with lower
energy moves to lower frequency [24,25].
Whenever a sharp vibrational transition of low
intensity falls within the energy range of a much broader
14
and more intense transition of the same symmetry species
Fermi resonance interaction may occur resulting in unusual
features recognized as Evans holes or negative absorption.
When the sharp feature is close to the center of the broad
absorption band, a transmission window may form at the
frequency of the sharp band. The intensity of the missing
band is redistributed by resonance repulsion in to the
absorption region on both sides of the transmission
window. This transmission window has been observed in a
variety of strongly hydrogen bonded systems [26,27].
1.7 POLARIZATION OF RAMAN LINES
A unique feature of Raman scattering is that each
line has a characteristic polarization, and polarization
data provide additional information related to molecular
structure. Polarization study is an ideal technique for
understanding the crystal field effects in the vibrational
levels of molecules or polyatomic
crystals [20].
ions in single
p =
The state of polarization of the Raman scattering
yields valuable information concerning the molecular
vibrations. The degree of polarization is defined as
I.L
III
15
where I is the intensity of scattered light polarized.L
perpendicular to the direction of observation and 1" is
the intensity of scattered light polarized parallel to
the direction of observation.
The polarizability is the sum of two components
a (isotropic) and Y (anisotropic)
cx=.!.(a + a + a)3 xx yy zz
+ 6 [a2 + a 2 + a2!. ]xy yz xz
Averaging over all molecular orientations the
polarization ratio is found to be
f =
Using i~cident plane polarized radiation it is shown that
(?J =
whereCX' and Y' are the derivatives of ex and y.
If ~ = 6/7 , the line is said to be depolarized if
r< 6/7 the line is said to be polarized. For the
symmetric vibrations the size of the ellipsoid changes and
16
hence the line must be polarized, but the Raman lines due
to anti symmetric vibrations are depolarized [9].
1.8 SOLID STATE EFFECTS
The molecular vibrations in gas phase are
subjected to constraints based on molecular symmetry. In a
crystal it is controlled by symmetry restrictions arising
out of the crystalline environment. The new bands seen in
crystal spectra which do not appear in gas phase spectra
are due to translational and rotational motions of rigid
units, splitting of internal modes, lifting of degeneracy
of modes and coupling between internal and external
modes [28].
1.8.1 Site symmetry effect
The symmetry of the site occupied by the molecule
is considered for studying changes in spectra. In most
cases, molecular groups in a crystal occupy sites of lower
symmetry than the free ion symmetry and the point group
for the site will be a subgroup of the ionic point group.
The effects of lower site symmetry are (i) changes in
selection rules, that is a vibration which is inactive in
a free molecule may become active (ii) lifting of
17
degeneracies of degenerate modes (iii) non-degenerate
internal vibration may get shifted in frequency.
1.8.2 Correlation field effect
This occurs due
internal vibrations of
to the interaction between the
molecules in one unit cell.
Interaction between molecules of different unit cell can
also contribute to this effect. Correlation field effect
may lead to the splitting of both non-degenerate and
degenerate modes. One fundamental vibration can be split
into a number of bands depending on the number of ions in
the primitive unit cell. However, all these bands may not
be IR or Raman active [12].
In ionic solids, site symmetry splitting seems to
be greater than correlation field splitting whereas in
covalent substances the two have the same order of
splitting. In strongly hydrogen bonded systems large
correlation field splitting is also observed [12].
1.8.3 Internal-External vibrational coupling
Coupling between internal and external modes may
also lead to splitting of degenerate fundamentals. If the
frequency difference between the internal and external
modes is large, the coupling is possible only if the
18
square of the irreducible representation of the
degenerate internal mode contains the irreducible
representation of the external mode, provided the internal
mode is not affected by totally symmetric external
modes [12]. If the frequency difference is small, coupling
can occur and it leads to the mixing of internal and
external vibration which belong to the same irreducible
representations.
1.9 HYDROGEN BONDING
Hydrogen bonding is an important form of molecular
association and can be intramolecular or intermolecular.
Hydrogen bonding occurs between a proton donor group A-H
and a proton acceptor group B and is usually represented
as A-H •••B. Atoms A and B have electronegativity values
greater than H. The strength of A••• B is identical ~ith
the dissociation energy of the A-H •.• B complex. Hydrogen
bonds can be either symmetrical or asymmetrical depending
on the symmetry of the energy surface for the proton
between A and B. Hydrogen bonding plays an important role
in the ferroelectric phase transition of crystals [29].
The distinguishing feature of H-bonding is the
involvement of a specific H atom of a proton donor group
with a localized site of high electron density in the same
19
or another molecule. This corresponds to the formation of
intramolecular and intermolecular H bonds respectively. It
is an association phenomenon and causes a decrease in the
total number of free molecules and an increase in the
average molecular weight. These bonds are distinctly
directional and linear. It is more localized than any
other type of weak intermolecular interaction. The H bond
is much weaker than a covalent bond.
The major spectral changes that occur when a
hydrogen bond is formed are:
(1) the A-H stretching frequency decreases due to the
weakening of the force cosntant for this mode and
bands become broader [30].
( 2 ) the band width and band intensity of the
stretching frequency increases [31]. However,
corresponding overtones decrease slightly
intensity.
A-H
the
in
frequency increases
bonds constraints
( 3 ) the A-H
formation
vibrations
bending
of H
which in turn increases
because the
the bending
the force
constants.
( 4) New vibrational modes corresponding to
stretching and deformations are found at
frequencies [32,33].
20
H • • • B
low
Hydrogen bonds can be represented by a potential
function with two minimum energy positions of the proton
(Pigue 1.2). With decreasing distance between the two
minima, the separating barrier also decreases, until it
completely disappears in the limiting case of symmetrical
hydrogen bond with single minimum in which case there will
-1 be no OH stretching band above 1700 cm [33,34]. If the
separating barrier is sufficiently small, proton tunneling
can occur which produces a splitting of the vibrational
levels resulting in the A and B bands.
The stretching bands of strongly hydrogen bonded
systems are usually broad and are built up of a number of
unresolved components [35,36]. The broadening of these
bands is due to the strong interaction between the proton
vibration and V(O .•. O) vibration [37]. If the broad band
is in Fermi-resonance with the overtones of cf (OH) and
Y(OH) modes, it splits into trio (ABC) bands, a
characteristic of hydrogen bonded systems [38,39]. The
trio bands are expected in strongly hydrogen bonded
systems with X(:O).OH grouping, (X= Se, s, P, As and C) in
the regions 2800-2400
-11720-1600 cm (C).
-1cm (A) I
1.10 SINGLE CRYSTAL RAMAN SPECTRA
2350-1900 -1
cm ( B)
21
and
Selection of appropriate scattering geometries
allows the recording of six independent spectra that
correspond to the six independent components of the
scattering tensor. In majority of cases, Raman experiments
are carried out with the 90°
scattering geometry and with
single crystals. The directions of the incident and
scattered beams coincide with two crystal axes or with two
principal optical axes.
The symmetry of a scattering molecule and its
vibrations determine which components of the derived
polarizability tensor and how many distinct non-zero
components the tensor will contain. Generally the pattern
of entries in the derived polarizability tensor is
characteristic of a particular symmetry class. Thus the
experimental determination of the magnitudes of tensor
components from the directional properties of oriented
single .crystal can yield information regarding the
symmetry properties of the molecules and their normal
modes of vibration.
22
The notation i(kl)j can be used [40,41] to
represent the experimental orientations. Letters i and j
represent the direction of propagation of the incident and
scattered radiations respectively, and the letter k and 1
represent the directions of polarization of the electric
vectors of the incident and scattered radiations. The
symbol within the bracket defines the component of the
scattering tensor being measured.
In monoclinic system the unique axis of the
crystal is chosen as 'b'. As this may coincide with one of
the axes of the elliptic section of the indicatrix formed
in a birefringent crystal, only a and c axes are used as
propagation direction [7].
1.11 FACTOR GROUP ANALYSIS
Group theoretical methods can be used for
classifying the allowed vibrations in a crystal. The
symmetry and geometry of the molecular model can be used
to determine the number of fundamental frequencies, their
degeneracies and the selection rules for the infrared and
Raman spectra. In factor group analysis only those atoms
which are translationally invariant ( k = 0) in a crystal
23
are considered. This will be the number of molecules or
formula uni ts in the Bravais unit cell. Bravais cell is
identical with the crystallographic unit cell if it is
primitive and smaller if it is non-primitive.
In Bhagavantam and Venkatarayudu [ 42] method the
symmetry properties of the vibrations are determined by
observing the effect of each symmetry operation of factor
group on each atom or group in the primitive unit cell.
In the site group analysis [43] one molecular
subunit in a unit cell is considered at a time and the
atoms and molecules other than the one considered are
kept at their equilibrium positions. The atom or molecule
under consideration is assumed to vibrate in an
environment of fixed symmetry given by its site group,
which refers to the specific position or site of each atom
in the unit cell.
The correlation method developed by Fateley et al.
[ 44] is a generalization of the site group analysis of
Halford and Hornig [45]. This involves the correlation of
molecular symmetry group to the factor group symmetry of
the crystal through its site symmetry. The same result can
also be obtained by correlating the site group of each
atom to the factor group of the crystal. In the analysis
24
of the spectra in this thesis the correlation method
developed by Fateley et al. is made use of.
1.12 SAMPLE HANDLNG TECHNIQUES
For Raman spectral studies, powdered samples are
taken in capillary tubes. In polarization studies the
single crystal is fixed on a goniometer for selecting
different scattering geometries. Raman spectra of coloured
samples and high absorbing substances are obtained by
rotating pellet method [6]. For optically dense materials
back scattering geometry may be used [ 46]. The quantum
yield in Raman spectroscopy is less than one millionth of
that in fluorescence, which can mask the Raman spectra.
Fluorescence can be reduced by [6] the following method:
(i) drench-quench method in which the sample is exposed
to blue or red laser radiation for a long time.
(ii) using different laser frequencies.
(iii) adding a quenching agent to the sample
recrystallization.
during
(iv) distillation, recrystallization and sublimation of
the sample.
25
(v) using filtration, gas chromatography, thin layer
chromatography
modifications.
and certain instrumental
An efficient optical system combined with a
powerful laser source and a highly sensitive detector
permit Raman spectra of high quality to be recorded. This
non-destructive method requires samples smaller than those
employed in IR spectroscopy.
Two different techniques are employed in recording
the IR spectra of solids the pellet technique and mull
technique.
In pellet technique, a fine powder of the
substance is mixed with suitable matrix material like KBr,
CsBr etc. and the mixture is pressed into a transparent
disc. Mull technique involves dispersing of the fine
powder of the substance in a mulling agent like nujol,
fluorolube etc. to get a slurry or mull of the substance.
To get good result with mull technique the sample
particles must be reduced to a size of less than minimum
wavelength of radiation they are to transmit.
The advantages of pellet technique include high
resolution of the spectra, lower scattering losses,
26
absence of interfering bands, better control over
concentration and homogeneity of the sample, ease in
examining small samples and possibility of storage of the
specimens for further studies. In this thesis, the IR
spectra of the compound are recorded using the KBr pellet
technique.
1.13 PHASE TRANSITIONS
Phase transitions are the subject of considerable
interest in many branches of chemistry and physics, and
the literature on the subject is extensive. The successful
detection of phase transition is dependent upon the
sensitivity of the investigative technique to the changes
which characterize the transitions.
One of the most sensitive probes for the study of
phase transitions is Raman scattering from vibrational
modes involved in the phase transition at various
temperatures. Raman spectroscopic studies are useful for
molecular structure studies of high temperature species,
study of structural changes with temperature,
identification of hot bands etc. A temperature-dependent
vibrational spectroscopic study can provide information
27
about not only the potential energy environment of the
mobile ion but also information concerning dynamical
processes in the crystal which couple the ionic motion
and affect the behaviour of the ion.
A structural phase transition can be described in
terms of an order parameter T) whose appearance at the
curie point breaks the symmetry of the high symmetry phase
[47]. The order parameter measures the extent to which the
atomic configuration in the less symmetrical phase departs
from the configuration of the more symmetrical phase.
T) vanishes above T and is non-zero below the curie point.c
In order-disorder transition T) measures the amount of long
range ordering of permanent dipoles whereas in displacive
transitions it measures the long range ordering of induced
dipoles.
The first order phase changes are characterized by
discontinuous changes in thermodynamic quantities such as
energy and entropy I while the second order phase changes
are characterized by continuous changes in these
quantities. When a crystal changes the structure it always
has either one symmetry or another. Such a phase change
may occur discontinuously through a sudden rearrangement
of the" atoms in the crystal giving a first order phase
28
change. However, the symmetry may also be changed by an
arbitrarily small displacement of the atoms from their
lattice points resulting in a phase transition of second
order. At a first-order phase transition two different
states are in equilibrium, but there is no predictable
symmetry relationship between them. By contrast, in second
order phase transitions the states of the two phases are
the same at the transition point, and it follows therefore
that the symmetry of the body at the transition point must
contain all the symmetry elements of both phases. The
theory of symmetry restrictions on second-order phase
transitions has been developed originally by Laudan [48].
1.13.1 Soft modes
Certain solids undergo structural phase
transitions at some critical temperature T ,c and often
this transition is connected with a transition to .some
ordered state such as ferroelectricity. It is found that
as one aproaches Tc ' certain modes go "soft", that is,
their frequency tends to zero as T--> T. The soft modec
theory explains a continuous structural phase transition
as arising from a dynamical instability of the crystal
against a particular normal mode of vibration.
A simple understanding of soft modes can be
obtained in the case of ferroelectricity. This is a
29
phenomenon characterized by a spontaneous polarization
below a critical temperature T • Above T the dielectric C C
! constant obeys a Curie-Weiss law
Hochli
E.. 0
and
= €. + 00
Scott
T - T C
have investigated the displacive
transition in quartz below its a - f3 phase transition near
580°
c. This is the system where soft modes were first seen
by Raman in 1940 [49].
1.14 INSTRUMENTATION
1.14.1 Laser Raman Spectrometer
In the present work a Spex 1401 Raman spectromete�
equipped with a Specta Physics model 165.08 argon ion
laser is used for recording the Raman spectra of majority
of the samples. Both 514. 5 nm and 488. 0 nm lines of the
laser have been used for the study. A detailed optical
diagram of a Raman spectrometer is given in
Figurel.3 [50].
The sample illuminator is equipped with a
dielectric or aluminium coated mirror to direct the laser
beam on to the sample. A beam expander expands the laser
light by a factor of four and passes through a Claassen
filter which is used to disperse the light from the laser
and to filter out plasma lines. The radiation is focussed
30
on to the sample by a condensing lens. Two spherical
mirrors, above and behind the sample, increases the energy
density on the sample. Collection lens assembly collects
the light scattered at 90 0 from the sample and image it on
the entrance slit of the spectrometer. It is followed by a
polarization analyser and a scrambler that scrambles the
polarization of light entering the spectrometer. The
dispersing system consists of a double monochromator
(Czerny-Turrer type) with optical bridging system which
helps to obtain double resolution, luminosity and better
signal to noise ratio. Two holographic gratings with
1800 groves/em are used in the monochromator. Grating Gl
is rotated by the scanning drive and G2 follows through
its linkage. Four slits 8 1 , 8 2 , 83
and 8 4 are bilaterally
adjustable to continuously vary the width. The light
leaving the exit slit of the monochromator is focussed on
the cathode of a photomultiplier tube where it is
converted to an electric signal. By having many dynodes in
a chain, a cascade process develops until the change
arriving at the anode consists of a pulse of 107
electrons. A DPC-2 digital photometer amplifies it and
converts the output of the photomultiplier tube into
digital signals. Output from DPC-2 is fed to a recorder to
record the spectrum in synchronisation with the
spectrometer scanning drive.
31
Raman spectra of a few polycrystalline samples
presented in this thesis were recorded using a Z24 Dilor
spectrometer.
1.14.2 Variable Temperature Raman Cell
A variable temperature cell for Raman
spectroscopic studies of crystals has been designed and
fabricated in the laboratory (Figure 1.4). It contains a
double walled metallic container, the space between which
can be evacuated. The inner hollow cylinder is made up of
copper. The lower portion of the outer wall is of
rectangular shape with four optically perfect glass
windows, so that it can be fixed to a Spex Ramalog 1401
instrument. The laser beam can be sent through the window
oat the bottom and Raman spectra can be recorded at 90
geometry. The lower part of the inner cylinder is a copper
block (cold junction) to which the crystal can be fixed in
any particular orientation. For low temperature studies
liquid nitrogen is filled in the inner copper cylinder.
The sample temperature can be controlled by adjusting the
current throgh a heater coil wound over the copper block.
A specially designed RTD pt 100 is used for sensing the
sample temperature, and it is connected to a relay for
controlling the temperature. The inner cylinder can be
rotated to any desired position to select different
scattering geometries. The cell is designed for recording
the Raman spectra in a temperature range 77-620 K with an
accuracy of ~ 1 K.
1.14.3 Infrared Spectrophotometer
An infrared spectrophotometer consists of a high
intense infrared source, a monochromator and an infrared
detector (thermopile) along with signal handling
electronics. In double beam instruments, two equivalent
beams of radiant energy from the source pass through the
sample and reference paths of the cell compartment. After
passing through an attenuator, the two beams are combined
in space but separated in time with the help of a rotating
sector mirror acting as a beam switch. This mirror
either reflects the reference beam or transmits the sample
beam through a system of mirrors to focus at the entrance
slit of the monochromator. The spectrum is scanned across
the exit slit by rotation of a suitable compartment of the
monochromator. The scanning mechanism is linked to the
chart drive mechanism and to the wavenumber scale
(Figure 1.5).
1.15. REVIEW OF EARLIER WORKS
1.15.1 Selenates
32
Selenates
compounds as they
are
have
spectroscopically
diverse physical and
important
chemical
properties
33
leading to structural phase transitions.
Compounds containing sed; ions have been studied by many
investigators [51-54]. The infrared and polarized Raman
spectra of RbHSeO 4 and CsHSeO 4 have confirmed that the
internal vibrations of seo~- ions are similar while the
hydrogen bond systems are different in both of these
crystals [27,55].
single
The polarized Raman spectral studies of Li 2Seo4
2crystal show vibrational coupling between seo4
internal vibrations and lithium translatory modes [56].
Kroupa et ale have carried out an analysis of the
far-infrared spectra of NH 4HSe0 4 and have found that the
seo 4 tetrahedra is distorted more in NH 4Hse0 4 than that in
RbHse0 4 [57].
On the basis of the Raman spectroscopic
investigation, Gupta et ale have studied the solid state
effects of selenate vibrations in yttrium and a few other
rare earth selenates [58]. Infrared and Raman spectral
studies of the paraelectric and superionic phase
transition in ammonium hydrogenoselenate have identified a
new intermediate phase on cooling [59]. Raimbault et al.
have carried out the Raman and infrared study of
structural phase transitions in and
(ND4)3D(Seo4)2 crystals. They have found the
3-a non-centrosymmetric (Se04Hseo4)
34
existence of
dimer in
[ 60]. The existence of five
structural phases in the temperature range 20-400 K have
also been spectroscopically characterized. A decrease in
temperature leads to a progressive ordering of the
+ d 2- . . d 1 th f 1 . h VNH4 an Seo4 entities an on y e erroe ectr1c p ase
is found to be fully ordered.
The polarized infrared and Raman spectra of
CsHSeo4 and CsDSeo4 single crystals have been analysed by
assuming strong coupling between the vibrations of two
shortest Se-0 bonds and an intermediate Se-0 bond [61]. A
temperature dependent vibrational analysis of the same
compound by Colomban et al. suggests that the structural
disorder increases progressively with increasing
temperature [62]. Pham-Thi et al. have carried out the
phase transition studies in super ionic protonic
conductors CsHso4 and CsHSeo4 using calorimetry, infrared
and Raman spectroscopy and inelastic neutron scattering in
the 100-500 K temperature range. Three phases have been
shown to exist in CsHS04 and four phases in CsHSeo4 [63].
Spectroscopic results show that heating induces a
progressive structural disorder in these crystals.
35
Analysis of the infrared and Raman spectra of
certain selenate
significant change
pentahydrates has
takes place in the
shown that no
spectra in the
temperature range 10-298 K, other than a sharpening of the
peaks [64].
An investigation of NH4
Hseo4
and ND4
oseo4
crystals
is carried out by Aleksandrova et al. to study their phase
diagrams, structures of various phases and dynamics of
their transformation using X-ray, neutron diffraction,
calorimetry, nuclear magnetic resonance and infrared and
Raman spectroscopy. A new phase diagram is proposed and
two different phase sequences and their transition
mechanisms are discussed with particular attention
paid to the incommensurate, ferroelectric and superionic
phase [65].
Baran et al. [66] have studied the structure and
polarized IR and Raman spectra 6f Na2
seo4
.H2
seo3
.H2
o
crystal and the internal vibrations of the selenate anions
are discussed in terms of a site and factor group effect.
Vibrational spectroscopic studies of trivalent
hexa-aqua-cations in CsAl(Seo4
)2
.12H2
o have been reported
by Best et al. [67].
36
1.15.2 Su1phates
In solid sulphates it has been observed that the
symmetric stretching frequency of the sulphate ion
decreases linearly with increasing cation radius for the
et ale have confirmed this from the Raman spectroscopic
studies of the sulphates M2so4 (M=Li, Na, K, Rb and Cs).
Berenblut et ale have investigated the effect of water of
crystallization on the symmetric stretching mode and it
has been observed that the presence of water leads to a
frequency decrease [69]. The relative intensity of the
symmetric stretching mode for various sulphates in aqueous
solution has been investigated [70,71].
Durie et ale have obtained the infrared spectra of
certain anhydrous alkali metals at ambient temperature
[72]. The characteristic absorption frequencies of two
high temperature phases of Na 2so4
have also been
identified. The reorientation dynamics of sulphate ions
and superconductivity of CSDS0 4 crystal are obtained using
the Raman scattering spectra of oriented crystals [73]. In
a related study Botto has described the vibrational and
thermal analysis of an ordered mixed-oxo salt
37
Lemos et al. have obtained the polarized Raman
spectra of lithium ammonium sulphate crystal and the
number of zone-centre modes of each symmetry are deduced
using a correlation method [75]. A complete polarized IR
and Raman studies of BaSO 4 have been made by Dawson et al.
and various observed k = 0 modes have been assigned
according to symmetry type [76].
Infrared spectra of certain double sulphates of
ammonium and rare earth sulphates have been reported
[ 77, 78] and the existence of different types of water
molecules and structural variations of the sulphate ions
in these compounds have been established. Among the double
sulphates, infrared and Raman studies of Tutton salts have
been carried out by many investigators [79-83].
Ananthanarayanan has recorded the Raman spectra of
K2M(S04)2.6H2o (M = Mg, Zn, Ni and Co) and has assigned
six fundamental frequencies of metal-aqua complex in
K2co(so4)2.6H2o [84]. Brown and Ross [85] have carried out
the infrared spectral studies of 64 Tutton salts and have
interpretted them on the basis of the site group and
factor group approximation.
In a correlation of the infrared modes of 10 I II I II Tutton salts M2 M (S04)2.6H20 (M = NH4,K and M ::: Ni,
38
Co, Fe, Cu, Zn and Mn) with the known S-0 bond lengths
Gupta et al. have found two types of so!- ions in the unit
cell of K2cu(so4)2.6H2o [86].
Campbell et al. (87] have studied the IR spectra
of 18 Tutton salts and have found that the MI cation has
more influence on the spectra than the MII cation. The IR
and polarized Raman spectra of K2Mg ( SO 4) 2• 6H2o crystal
reveal that the angular distortion of the sulphate ion is
greater than the bond distortion [88].
Single crystal Raman and IR study of
Xavier Mathew et al. have identified
the presence of two crystallographically distinct sulphate
ions in the crystal with stronger S-0 bonds than a free 2- .
so4 ion (89]. The Raman spectra of oriented single
crystals of cerium sulphate enneahydrate and that of its
fully deuterated analogue are reported by Torres et al.
(90]. The role of the two types of lattice water molecules
has been determined, consistent with optimum interactions
with their surroundings. Baran et al. have obtained the
vibrational spectrum and space group of K2In(OH)(so4)2
(91]. Two distinct sulphate groups in NH4Pr(so4)2 and
NH4La(so4)2 are identified by Pradip et al. (92].
P.K. Acharya et al. have carried out
39
the
vibrational analysis of certain ferroelectric sulphates
and have shown that proton occupies off-centric positions
along the O-H .•. O hydrogen bond giving rise to the HS04ion [93]. A study of far infrared reflectivity and Raman
spectra of the phases of (NH4)3H(S04)2 crystals are
reported by Srivastava et al. [94]. The effects of the
increased anharmonicity and the ordering of coupled
motions of cations and anions are witnessed in the Raman
spectrum of the ferroelectric phase.
A vibrational analysis of LiNH30HS0 4 and
LiND 30DS0 4 compounds reveals the existence of strong
hydrogen bonds in the protonated compound [95]. The
vibrational study of LiRbS0 4 suggests the possibility of
resonance interaction between sulphate ions in the unit
cell [96]. Botto et al. have reported the vibrational
spectra of some crystalline sulphates of the type
IM3 In(s04)3 [97].
Polarized infrared and Raman spectra of a CsHSO 4
single crystal recorded by Baran show the breakdown of the
selection rules for the ~-ray determined C2h factor group
[98]. The polarization features of HSO~ ion vibration are
predicted assuming that the longest S-OH bond vibrates
independently of the s03 group vibrations.
40
The temperature dependent Raman spectra of a
ferroelectric langbeinite Rb2
cd2
(so4
)3
reveal that the
splitting of the lines of internal vibrations at the phase
transition is due to the appearance of nonequivalent so4
groups [99].
1.15.3 Pyrophosphates
Depending upon the nature and degree of
condensation, the symmetry of the P04
tetrahedra changes
from one compound to another.
The P 2
o7
group is considered as a result of the
decrease in positional symmetry of the P04
tetrahedra
during the condensation and this causes additional
splitting of P04
valence vibrations [100]. Studies on
pyrophosphate have revealed that P 2oi- ion exists as a
discrete unit consisting of two P04
tetrahedra sharing a
common oxygen [101]. Characteristic vibrations of the
pyrophosphates are discussed in terms of the P-0-P bridge
and the terminal Po3
groups. Stegar et al. [102] have
reported the first IR and Raman spectra of pyrophosphates.
Hezel et al. [103] have shown that the
pyrophosphate anion can have six possible symmetries 03d
'
o3h
, o3
, c2v
' Cs
and c2
depending on the linearity of the
41
p-o-P bridge and free rotation of p0 3 group and the nature
of the terminal bond length. If the P-O-P bridge is
non-linear the pyrophosphates do not possess the dihedral
symmetries.
From the vibrational spectroscopic studies of
a and t3-Mg 2P 2°7' Cornilsen and Condrate have concluded
that t3-Mg 2P 207 has a linear P-O-P bridge and the
transition between the two phases is not a second order
process [104]. Their observation have also shown that
a-sr 2p 20 7 is isostructural with a-Ba2p207 and their
spectral difference with a -ca2P207 is related to the
difference in crystal structure [105]. From the intensity
ratio of iJs POP to i)sp03 bands, Cornilsen et al. have
shown that pyrophosphate ion possesses an eclipsed
configuration in a-sr 2p 20 7 and ~ca2P207 [106]. Stanford
et al. have shown that the anion possesses an eclipsed
configuration in a-zn2
p2
07
from the IR spectral studies
[107] •
An empirical correlation between the number of
i) p-o split components and the unit cell size (z) hass
been established from the Raman spectral measurements of
the medically interesting ca2P2°7. 2H 20 by comparing with
pyrophosphates having larger unit cells [108]. O.Sarr
42
et ale [109] have established a linear correlation between
the Y POPas ~ POP and the P-O-P bridge angle ins
crystalline hydrogenopyrophosphates. Partial or total
dehydration do not affect the strength of hydrogen
bonding, which is the same for all the compounds
From the IR and polarized Raman spectra of
4Na 4P20 7 .10H20, Daizy et al [110] have shown that P20 7 ion
possesses a C2v symmetry. Baran et ale [111] have
investigated the vibrational spectra of Fe 2p 20 7 and have
shown a bend POP bridge and a centrosymmetric space
group 1.
The vibrational analysis by Santha et ale [112]
have shown that the POP bridge has a bend configuration
in C0 3Pb(P 20 7 )2 as in Ni 3Pb(P 20 7 )2' The anion possesses a
centrosymmetric structure in both the compounds. Infrared
and Raman studies of three polycrystalline samples
have shown that the anion possesses a non-centrosymmetric
structure [113] in these compounds.
The normal co-ordinate analysis based on the D3h
model has been carried out by Hezel et ale for some
divalent metal pyrophosphates. Spectroscopic analysis
43
shows that the point group of the pyrophosphate ion in
divalent metal pyrophosphate is C2v ' Cs or C2 [103,114].
Correlations between the vibrational spectrum of the X20 7
group and its structure have been established by
Gabelica-Robert [115].
1.15.4 Cyclohexaphosphates
The crystal chemistry of cyclohexaphosphates has
been explored only recently because of the lack of a
convenient starting material. The chemical preparation and
crystal structure of various monovalent and bivalent
cation cyclohexaphosphates have been reported [116-119].
The cyclohexaphosphates, belonging to condensed
phosphates, are built up by six corner-sharing P04
tetrahedra. The basic structural units in these compounds
are the P-O-P
Investigation of
bridges and the
the behaviour
2-P0 2 terminal
6of the P60 18
groups.
anion in
aqueous solutions by means of conductometry, ion exchange
and electrical conductivity has shown that it behaves as a
polyelectrolyte, forming extra spherical complexes with
cations by electrostatic interaction [120-123].
Structural studies of different cyclohexa-
phosphates reveal that the P60 18 anion in different
compounds possesses different internal symmetries. In
44
no internal symmetry [116,124]. However, P60lS ring anion
with 1 internal symmetry is found in M6P6olS.6H2o
[M = Rb,Cs], (NH3NH3)2(NH2NH3)2P601S and some telluric
acid adducts [124-l2S].
In the compounds like M6P6olS.H2o [M = Ag, K],
K6P6olS.2Te(OH)6.3H2o and A93(NH4)3P6olS.H2o the anion
exists with 3 internal symmetry [12S-l30]. A recent review-
of the geometry of P60 lS ring having 1 internal symmetry
[131] has shown that the P6o l8 ring anion is more
distorted, with P-O-P angles ranging from 96.65 to
l44.S7°.
Lazarevski et ale have studied the thermal
conversion of Cu, Co, Ni, Mn, Ba, Cd, Y and Ga
cyclohexaphosphates using thermogravimetry, X-ray phase
analysis, paper chromatography and IR spectroscopy [132].
However, only a few investigations has been reported on
the vibrational analysis of cyclohexaphosphates.
The IR and Raman spectra of M6P6olS.6H2o
[M = Cs,Rb] have been studied by S. Abraham et ale [133].
The observed frequencies are assigned on the basis of
2-characteristic vibrations of p0 2 and P-O-P groups. The
P60 lS anion is found to have Ci symmetry with considerable
distortion. The structure of these compounds is
intermediate between those of chain polyphosphates and
cyclic tetra and trimetaphosphates.
45
REFERENCES
[1] A. Smekal, Naturwiss. II, 873 (1923).
[2] c.v. Raman and K.S. Krishnan, Nature 121, 501 (1928).
[3] C.V. Raman, Indian J. Phys. 2, 387 (1928).
[4] L.J. Radziemski, R.W. Solarz and.J.A. Paisner, 'Laser
Spectroscopy and its Applications', Marcel Dekkar Inc.,
New York (1987).
[5] S.P. Parker, 'Spectroscopy Source Book', Mc Graw-Hill
Company, New York (1987).
[6] S.K. Freeman, 'Applications of Laser Raman Spectroscopy',
Wiley-Interscience, New York (1974).
[7] G.R. Gilson and P.J. Hendra, 'Laser Raman Spectroscopy',
Wiley-Interscience, London (1970).
[8] G. Herzberg, 'Infrared and Raman Spectra of Polyatomic
Molecules', Van Nostrand, New York (1966).
E. Wiberley,
Spectroscopy',
[ 9 ] N.B. Colthup, L.H. Daly and Stephen
, Introduction to Infrared and Raman
Academic Press, London (1964).
[10] S.S. Mitra, Solid State Phys. 13, 66 (1962).
[11] E.F.H. Brittain, W.O. George and C.H.J. Wells,
'Introduction to Molecular Spectroscopy Theory and
Experiment', Academic Press, London (1970).
46
[12] P.M.A. Sherwood, 'Vibrational Spectroscopy of Solids',
Cambridge University Press, London (1972).
[13] Raymond Chang, 'Basic Principles
Mc Graw-Hill, New York (1971).
of Spectroscopy,
[ 14] F. Albert Cotton, 'Chemical Applications of Group
Theory', Wiley-Interscience, New York (1963).
[ 15] D. A. Long, 'Raman Spectroscopy' , Mc Graw-Hill, Great
Britain (1977).
[16] S.D. Ross, 'Inorganic Infrared and Raman Spectra',
Mc Graw-Hill, London (1972).
[17] R.E. Dodd, 'Chemical Spectroscopy', Elsevier Publishing
Company, New York (1962).
[18] H.A. Szymanski, 'Raman Spectroscopy-Theory and Practice',
Vol. 1, Plenum Press, New York (1967).
[19] R.J.H. Clark and R.E. Hester, 'Advances in Infrared and
Raman Spectroscopy', Vol.10, John Wiley
New York (1983).
and Sons,
[20] R.H. Willard, L.L. Merritt Jr. and John A. Dean,
'Instrumental Methods of Analysis', Fifth Edition, Van
Nostrand Company, New York (1974).
[21] H. Ratajczak and W.J. Orville Thomas, 'Molecular
Interaction', Wiley-Interscience, New York (1980).
[ 22] D .A. Skoog, 'Principles of Instrumental Analysis' ,
Hault-Saunders International Edition (1985).
47
[ 23] L.A. Woodward, 'Introduction to the Theory of Molecular
Vibrations and Vibrational Spectroscopy', Oxford
University Press (1972).
[ 24] P. Gans, 'Vibrating Molecules - An Introduction to the
interpretation of Infrared and Raman spectra' , Chapman
and Hall Ltd., London (1971).
[ 25] W .A. Guillery, 'Introduction to Molecular Structure and
Spectroscory', Allyn and Bacon Inc., Boston (1977).
[26] M. Fukai, T. Matuso, H. Suga and M. Ichikawa, Solid State
Commun. 84, 545 (1992).
[27] J. Baran, z. Czapla, M.M. Ilczyszyn and H. Ratajczak,
Acta Physica Pol. A59, 753 (1981).
[28] P. Dawson, M.M. Hargreave and G.R. Wilkinson,
Spectrochim. Acta 33A, 83 (1977).
[29] J. Tomkinson, Spectrochim. Acta 48A, 329 (1992).
[30] A. Novak, Struct. and Bonding 18, 177 (1974).
[31] A. Novak, Croatica. Chem. Acta 55, 147 (1982).
[32] S.N. Vinogradov, R.H. Linne!,
Van Nostrand, New York (1971).
'Hydrogen Bonding',
[33] M.D. Joester, L.J. Schead, 'Hydrogen Bonding', Marcel
Dekker Inc., New York (1974).
[34] L.J. Bellamy, 'The
Molecules', Vol.2,
Infrared
Advances
Spectra of Complex
in Infrared Group
Frequencies', Chapman and Hall Ltd., London (1980).
48
[35] M.F. Claydown and N. Sheppard, Chem. Commun. 1431
(1969).
[ 36] K. Nakamoto, 'Infrared
Co-ordination Compounds' ,
(1970).
Spectra of Inorganic and
2nd edition, Wiley, New York
[37] S. Bratos and H. Ratajczak, J. Chem. Phys. 76, 77
(1982).
[38] J.T. Braunholtz, G.E. Hall, F.G. Mann and N. Sheppard,
J. Chem. Soc. 868 (1959).
[39] C.N.R. Rao, 'Chemical Applications of Infrared
Spectroscopy', Academic Press, New York (1963).
[40] T.C. Darnen, S.P.S. Porto and B. Tell, Phys. Rev. 142,
570 (1966).
[ 41] G. Turrel, 'Infrared and Raman Spectra of Crystals' ,
Academic Press, London (1972).
[42] s. Bhagavantam and T. Venkatarayudu, 'Theory of Groups
and its Applications to Physical Problems', Academic
Press, New York, (1969).
[43] R.S. Halford, J. Chem. Phys. 14, 8 (1946).
[44] W.G. Fateley, F.R. Dollish, N.T. Mc Devitt and
F. F. Bentley, 'Infrared and Raman Selection Rules for
Molecular and Lattice Vibrations The Correlation
Method', Wiley, New York (1972).
49
[45] D.F. Hornig, J. Chern. Phys. 16, 1063 (1948).
[46] R.C.C. Leite and J .F. Scott, Phys. Rev. Lett. 22, 130
(1969).
[47] R. Blinc and B. Zeks, 'Soft Modes in Ferroelectrics and
Antiferroelectrics', North Holland Publishing Company,
Amsterdam (1970).
[48] William Hauges and Rodney Laudan, 'Scattering of Light
by Crystals', John-Wiley and Sons, New York (1978).
[49] Stephen Jacobs, Murray Sargent III, James F. Scott and
Marlon o. Scully, 'Laser Applications to Optics and
Spectroscopy', Addison-Wesley PUblishing Company, London
(1975).
[50] Ramalog 5/6 Instructions, Spex Industries, Inc., USA.
[51] J. Baran, Acta phys. Pol. A76, 815 (1989).
[52] Seung-Bin Kim and Roger Frech, Spectrochim. Acta 43A, 59
(1987).
[53] J. Baran, Acta Phys. Pol. A78, 731 (1990).
[54] C. Caville, V. Fawcett and D.A. Long, J. Raman
Spectrosc. 7, 43 (1978).
[55] J. Baran, Z. Czapla and H. Ratajczak, Acta Phys. Pol.
A70, 389 (1986).
50
[56] Roger Frech and Seung-Bin Kim, Spectrochim. Acta 44A,
1387 (1988).
[ 57] J. Kroupa and Z. Czapla, Phys. Stat. Solidi 64, K17
(1981) •
[58] M.K. Gupta, L. Surendra and G.V. Jere, J. Solid State
Chern. 43, 359 (1982).
[59] B. Pasquier, N. Le Calve, A. Rozycki and A. Novak,
J. Raman Spectrosc. 21, 465 (1990).
[60] G. Raimbau1t, F. Romain and A. Lautie, J~ Raman
Spectrosc. 23, 147 (1992).
[61] J. Baran, J. Mol. Struct. 162, 229 (1987).
[62] Ph. Co1omban, M. Pham-Thi and A. Novak, J. Mol. Struct.
161, 1 (1987).
[63] M. Pham-Thi, Ph. Co1omban, A. Novak and R. B1inc, Solid
State Commun. 55, 265 (1985).
[64] A. Gona1ez De Saja, F. Ru11, J .M. Pastor and J .A. De
Saja, Spectrochim. Acta, 42A, 997 (1986).
[65] I.P. A1eksandrov, Ph. Co1omban, F. Denoyer, N.·Le Calve,
A. Novak, B. Pasquier and A. Rozycki, Phys. Stat. Solidi
114, 531 (1989).
[66] J. Baran, T. Lis, M. Marchewka and H. Ratajczak, J. Mol.
Struct. 250, 13 (1991).
51
[67] S.P. Best, R.S. Armstrong and J.K. Beattie, J. Chern.
Soc. Dalton Trans. 1655 (1982).
[68] S. Montero, R. Schmolz and S. Haussuhi, J. Raman
Spectrosc. 2, 101 (1974).
[69] B.J. Berenblut, P. Dawson and G.R. Wilkinson,
G.R. Wilkinson,
Spectrochim. Acta A29, 29 (1973).
[70] K. Fujita and M. Kimura, J. Raman Spectrosc. II, 108
(1981) •
[71] K.J. Dean and G.R. Wilkinson, J. Mol. Struct. 79, 293
(1982).
[72] R.A. Durie and J .W. Milne, Spectrochim. Acta 34A, 215
(1978).
[73] V.P. Dmitriev, V.V. Loshkarev, L.M. Rabkin, S.B. Roshal
and L.A. Shuvalov, Sov. Phys. Solid State 29, 699
(1987).
[74] I.L. Botto, Thermochim. Acta 132, 279 (1988).
[75] V. Lemos, P.A.P. Gomes, F.E.A. Melo, J. Mendes Filho and
J.E. Moreira, J. Raman Spectrosc. 20, 155 (1989).
[76] P. Dawson, M.M. Hargreave and
Spectrochim. Acta 33A, 831(1977).
[77] V.M. Malhotra, H.A. Buckmaster and H.D. Bist, Can.
J. Phys. 58, 1667 (1980).
52
[78] B. Eriksson, L.O. Larsson, L. Niinisto and U. Skoglund,
Inorg. Chern. 13, 290 (1974).
[79] B. Singh, S.P. Gupta and B.N. Khanna, Pramana 14,509
(1980); 18, 427 (1982).
[80] G. Sekar, V. Ramakrishnan and G. Aru1dhas, J. Solid
State Chern. 74, 424 (1988).
[81] V.S. Jayakumar, G. Sekar, P. Rajagopa1 and G. Aru1dhas,
Phys. Stat. Solidi Al09, 635 (1988).
[82] V. Ananthanarayanan and A. Panti, J. Mol. Struct. 20, 88
(1966).
[83] V. Ananthanarayanan, Z. Phys. Chern. 222, 102 (1963).
[84] V. Ananthanarayanan, Z. Physik 163, 144 (1961).
[85] R.G. Brown and S.D. Ross, Spectrochim. Acta, 26A, 945
(1970).
[86] S.P. Gupta, B. Singh and B.N. Khanna, J. Mol. Struct.
112, 41 (1984).
[87] J.A. Campbell, D.P. Ryan and L.M.Simpson, Spectrochim.
Acta 26A, 2351 (1970).
[88] G. Sekar, V. Ramakrishnan and G. Aru1dhas, J. Solid
State Chern. 66, 235 (1987).
[89] Xavier Mathew, G. Suresh, T. Pradeep and V.U. Nayar,
J. Raman Spectrosc. 21, 279 (1990).
53
[90] A. Torres, F. Ru11 and J.A. De Saja, Spectrochim. Acta
36A, 425 (1980).
[91] E.J. Baran, I.L. Botto and A.C. Garcia, J. Mol. Struct.
143, 59 (1986).
[92] T. Pradip, G. Suresh, V.P. Mahadevan Pi11ai and
V.D. Nayar, J. Raman Spectrosc. 22, 287 (1991).
[93] P.K. Acharya and P.S. Narayanan, Indian J. Pure Apple
Phys. 11, 519 (1973).
[94] J.P. Srivastava, A. Ku1shreshta, W. Ku11mann and
H. Rauh, J. Phys. C. Solid State Phys. 21, 4669 (1988).
[95] V.P. Mahadevan Pi11ai, T. Pradeep, G. Suresh and V.D.
Nayar, J. Raman Spectrosc. 23, 235 (1992).
[96] V. Ramakrishnan, V.D. Nayar and G. Aru1dhas, Infrared
Phys. 25, 607 (1985).
[97] I.L. Botto, E.J. Baran and A.C. Garcia, Ana1es Quim.
B83, 145 (1987).
[98] J. Baran, J. Mol. Struct. 162, 211 (1987).
[99] L.T. Latush, L.M. Rabkin, V.I. Torgashev, Yu. I. Yuzyuk,
L.A. Shuvalov and B. Brezina, Sov. Phys. Crysta11ogr.
29, 557 (1984).
[100] K. Byrappa, 1.1. plyusnina and G.I. Dorokhova, J.
Mater. Sci. 17, 1847 (1982).
[101] B.D. Saxena, Trans. Faraday Soc. 57, 242 (1961).
54
[102] E. steger, Z. Anorg. A11g. Chern. 294, 146 (1958); 296,
405 (1958).
[103] A. Heze1 and S.D. Ross, Spectrochirn. Acta 23A, 1583
(1967) •
[104] B.C. Corni1sen and R.A. Condrate Sr., J. Phys. Chern.
Solids 38, 1327 (1977).
[105] B.C. Cornilsen and R.A. Condrate Sr., J. Solid State
Chern. 23, 375 (1978).
[106] B.C. Corni1sen, J. Inorg. Nuc1. Chern. 1, 602 (1979).
[107] G.T. Stranford, R.A. Condrate Sr. and B.C. Corni1sen,
J. Mol. Struct. 73, 231 (1981).
[108] B.C. Cornilsen, J. Mol. Struct. 117, 1 (1984).
[109] o. Sarr and L. Diop, Spectrochirn. Acta 40A, 1011
(1984); 43A, 999 (1987).
[110] D°. Philip, B.L. George and G. Aru1dhas, J. Raman
Spectrosc. 21, 523 (1990).
[Ill] E.J. Baran, I.L. Botto and A.G. Nord, J. Mol. Struct.
145, 161 (1986).
[112] N. Santha, V.D. Nayar and G. Keresztury, Spectrochirn.
Acta 49A, 47 (1993).
[113] I.H. Joe, G. Aru1dhas and G. Keresztury, J. Raman
Spectrosc. 22, 537 (1991).
55
[114] A. Heze1 and S.D. Ross, Spectrochirn. Acta 24A, 131
(1968) •
[115] M. Gabe1ica-Robert, J. Mol. Struct. 79, 255 (1982).
[116] P.M. Laugt and A. Ourif, Acta Cryst. B30, 2118. (1974).
[117] M.T. Averbuch-Pouchot, Acta Cryst. C47, 930 (1991).
[118] M.T. Averbuch-Pouchot and A. Ourif, Acta Cryst. C47,
932 (1991).
[119] M.T. Averbuch-Pouchot, Z. Anorg. A11g. Chern. 574, 225
(1989).
[120] G. Kura and S. Ohashi, J. Chrornatogr. 56, 111 (1971).
[121] G. Kura, S. Ohashi and C. Kura, J. Inorg. Nuc1. Chern.
38, 1151 (1976); 36; 1605 (1974).
[122] G. Kura and S. Ohashi, J. Inorg. Nuc1. Chern. 34, 3899
(1972).
[123] S. Ohashi, G. Kura, Y. Shimada and M. Hara, J. Inorg.
Nuc1. Chern. 39, 1513 (1977).
[124] M.T. Averbuch-Pouchot and A. ourif, Acta Cryst. C47,
1579 (1991).
[125] M.T. Averbuch-Pouchot and A. Durif, C.R. Acad Sci.
Paris, Series II, 1699 (1989).
[126] A. Ourif and M.T. Averbuch-Pouchot, Acta Cryst. C45,
1884 (1989).
56
[127] M.T. Averbuch-Pouchot and A. Durif, Acta Cryst. C46,
179 (1990).
[128] M.T. Averbuch-Pouchot and A. Durif, Acta Cryst. C47,
1576 (1991).
[129] M.T. Averbuch-Pouchot,
(1989).
Z. Kristallogr. 189, 17
[130] M.T. Averbuch-Pouchot, Acta Cryst. C45, 539 (1989).
[131] G. Sekar, G. Aruldhas and v. Ramakrishnan, Indian J.
Pure Appl. Phys. 26, 570 (1988).
[132] E.V. Lazarevski, L.V. Kobasova, N.N. Chudinova and
I.V. Tananaev, Inorg. Mater. 16, 93 (1980); 17, 327
(1981); 18, 1322 (1982); 18, 1327 (1982).
[133) s. Abraham and G. Aruldhas, J. Raman Spectrosc. 22,
245 (1991).
Anti Stokes~o '} 11'\
etC).......eJc.'
. e.Ji.t::l'
~C>Stokes Cl
11\,
hvohvo h (';0- VI) h(yo
\/
hv'1
\V
Ground state
Figure 1.1 Quantum representation of the energy interchangein the Raman effect.
(a)
(b)
(c)
Figure 1.2 Diagrams of possible hydrogen vibrational potentials
in : (a) a weak H-bond; (b) a moderate H-bond �nd (c) a strong H-bond.
OMPU- ·REGO-DPC2 RIVE RDER
S4
PMT I
M8
G2
M6
M7
MS M
4
G1
M2
Ll
S1
M3
::z:: L
MII
Figure 1.3 Schematic representation of the Laser Raman Spectrometer set-up
Figure 1.4 Variable Temperature Raman cell.
AMPI..I Ii'It~J~I=====+==-r MOTOR
O!i~CTORJ=s===---==-I RECORe!
REFERENCE
SOURCE
SAMPI..E
