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In the present work transition metal ions incorporated into alkaline earth
zinc borate glasses have been characterized by X-ray diffraction (XRD),
Electron paramagnetic resonance (EPR), Optical absorption and FT-IR
spectroscopic techniques. A brief introduction to glasses is presented in this
chapter. The necessary theory of EPR, Optical absorption spectra and FT-IR is
also described.
1.1 Introduction
Over the last few decades, great importance has been attached to glasses
doped with transition-metal or rare earth ions because of the interesting
spectroscopic properties of their 3dn and 4fn electrons, respectively. Glass
products are widely varied including windows, bottles, mirrors, chemical
operators, building blocks, thermal and electrical insulation, automobile and
aircraft bodies. They also find potential applications in the development of new
tunable solid state lasers, luminescent solar energy concentrators and fiber optic
communication devices. Moreover, in applications ranging from new optical
material research to optoelectronic and integrated optical devices, there has been
considerable demand for glasses due to lower production costs.
Glass has many advantages over crystalline materials. It can be cast in a
variety of forms and sizes from small fibers to meter sized pipes. Tremendous
flexibility in choosing glasses and laser properties is offered by the ability to
vary the glass composition over large ranges. Glass is also relatively inexpensive
because of the shorter time required for its manufacture and the use of
inexpensive chemical products. Further, large pieces of laser glasses can be
made with excellent homogeneity, uniformly distributed dopant concentrations,
low birefringence and can be finished easily even in larger sizes. The only major
drawback of glass is its low thermal conductivity, which limits its applicability
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in high average power systems. Depending on its compositions, it can be made
stronger than steel [1] or soluble in water.
1.2 Definition of Glass
There have been several attempts to give technological definitions to
glass.
(i)
In 1930, glass was defined as an amorphous solid, i.e., a structureless
solid [2].
(ii)
In 1938, it was redefined as an inorganic substance in a condition
which is continuous with and analogous to the liquid state of that
substance. As a result of reversible change in viscosity during cooling,
it attains high degree of viscosity that for all practical purposes it may
be treated as rigid [3].
(iii)
In 1949, The American Society for Testing and Materials (ASTM)
defined as: “An inorganic product of fusion that has cooled to a rigid
condition without crystallizing” [4].
(iv)
The classic definition: Glass is a supercooled liquid.
1.3 Difference between Crystalline and Amorphous Solids
On the basis of atomic arrangement, solids may be broadly classified into
two categories, (i) crystalline and (ii) amorphous.
In crystalline solids, both long-range and short-range order exists in the
arrangement of atoms while in amorphous solids only short-range order exists.
Fig. 1.1(a&b) represents the schematic representation of the ordered crystalline
form and random network amorphous form of the same composition. Due to the
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short-range periodicity in the atomic arrangement, the degree of disorder will be
greater in an amorphous solid than its crystalline counterpart and it will be
having a higher entropy compared to the crystalline phase. Therefore amorphous
state is a non-equilibrium state. So, on cooling from liquid phase to the solid
phase, a crystalline solid is obtained as a transformation from one equilibrium
state to another while in amorphous solid, the transformation is from an
equilibrium state to a non-equilibrium state. Due to the random arrangement of
atoms, amorphous materials exhibit isotropic properties while crystalline solids
exhibit anisotropic properties.
(a)
(b)
Fig. 1.1: Schematic representation of (a) ordered crystalline form and
(b) random network amorphous form of the same composition.
1.4 Glassy state
Non-crystalline or amorphous materials are those which possess
randomness to some degree. Randomness can occur in several forms viz., (a)
Topological (b) Spin (c) Substitutional and (d) Vibrational disorders. These
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types of disorders are illustrated in Fig. 1.2. A brief description of four types of
disorders is given below.
Fig. 1.2: Types of disorders in amorphous materials, (a) Topological
disorder, (b) Spin disorder, (c) Substitutional disorder,
(d) Vibrational disorder.
(a) Topological disorder
Topological or geometric disorder is a form of randomness in which there
is no translational periodicity as shown in Fig. 1.2(a). Nevertheless there are
‘degrees’
of
topological
disorder.
Certain
amorphous
materials
have
considerable short-range. However all amorphous or glassy solids are
distinguished by their lack of periodicity.
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(b) Spin disorder
The case of a spin disordered solid is shown in Fig.1.2(b). This disorder is
characterized by an underlying perfect crystalline lattice, but each atomic site
possesses a spin or magnetic moment which is oriented randomly.The materials,
which are topologically disordered and possess randomly oriented spins are
known as spin glasses. Hence one should not be confused between “Glasses”
and “Spin Glasses”.
(c) Substitutional disorder
A further kind of randomness is substitutional disorder and is shown in
Fig. 1.2(c). Here although the underlying crystalline lattice is preserved, the
material is in fact, an alloy (say Cu-Au) with one type of the atom randomly
substituting for the other in the lattice. These systems are of great importance in
metallurgy and other branches of material science.
(d) Vibrational disorder
The final category of randomness considered here is vibrational disorder
of a crystalline lattice (Fig. 1.2 (d)). Here, the concept of a perfect crystal is valid
at the absolute zero only (ignoring the zero-point motion 0 K). At any finite
temperature, the random motion of atoms about their equilibrium positions
destroys the perfect periodicity.
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1.5 Preparation of amorphous materials (glasses)
The amorphous phase is less thermodynamically stable than the
corresponding crystalline form. This means that amorphous phase possesses a
greater free energy.
Hence the preparation of amorphous materials can be
considered as the addition of excess of free energy to the crystalline polymorph.
There are numerous techniques to prepare amorphous materials. Below given are
the twelve widely used techniques for preparing materials in amorphous state.
1) Melt Quenching
2) Sputtering
3) Glow Discharge Decomposition
4) Chemical Vapour Deposition
5) Thermal Evaporation
6) Gel Desiccation
7) Electrolytic Deposition
8) Chemical Reaction
9) Reaction Amorphization
10) Irradiation
11) Shock-wave transformation
12) Shear Amorphization.
Among these techniques ‘Melt-quenching’ and ‘Gel-desiccation’ were
frequently used for preparing glasses. Since the present thesis deals with glasses
prepared by melt-quenching method, more emphasize is given to this technique.
1.6 Melt-Quenching Technique
The oldest method of producing amorphous solid is to cool the matter
form of the material at sufficiently faster rates. The distinguishing feature of this
process is that the amorphous solid is formed by the continuous hardening of the
melt. On the other hand, crystallization of the melt occurs as discontinuous
solidification. Hence the formation of glass is strongly dependent on the cooling
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rate of the melt, the cooling rate should be high enough to bypass the crystal
nucleation and growth. As the crystallization phase is more thermodynamically
stable than the amorphous phase, crystal growth will dominate over the
formation of amorphous phase, if allowed to take place freely.
As said above, the cooling rate plays a dominant role in the glass
formation. Further, the cooling rate required for glass formation depends on the
constituents of the melt. For certain easy glass-formers, such as B2O3, very slow
cooling rates (e.g., 1 Ks-1) are sufficient to form glass while certain other
materials (such as metallic glasses) require very high cooling rates (~105 Ks-1).
In preparing the glasses with easy formers, a batch of finely powdered
chemicals (~10 g) taken in a porcelain crucible will be placed in a furnace
maintained at high temperatures. The melt will be stirred uniformly to get
homogeneous liquid. After some time, the crucible will be taken out and the melt
will be poured on a plate having good thermal conductivity (e.g., Brass or
Copper). Another plate will be placed over the melt so that heat will be removed
quickly from the melt. A cooling rate of the order of 10 Ks-1 will be achieved by
this method and is sufficient for preparing most of the glasses.
For certain other materials, especially metallic glasses cooling rates
produced in the above method are insufficient for producing glasses. Still higher
cooling rates are required for such cases and these can be achieved by the use of
a ‘chill-block’. Klemant [5] were the first to use the “splat cooling technique”,
where quenching rate of the order of 105 Ks-1 can be achieved. This technique
employs a method of projecting small droplets of liquid on a copper sheet.
Table 1.1 lists the various quenching techniques used to prepare glasses and their
cooling rates. The conventional annealing technique is also included in the table
to have a comparison between this and the different quenching techniques.
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Table 1.1: Different quenching Techniques and their rates of Cooling.
Technique
Cooling rate Ks-1
Annealing
10-5 - 10-2
Air quenching
1 - 10
Liquid quenching
102 -103
Chill Block splat cooling
105
Melt spinning or Melt extraction
106 -108
1.7 Properties of Glasses
Glasses have excellent properties as given belows,
1. Glass is inert. This depends on the environment. It is nearly true if the glass
is a silicate and essential if it is going to contain radioactive waste, but not all
glasses are inert. Bioglass is designed not to be inert.
2. Glass is homogeneous. This depends on how the glass was formed and its
composition. We can process glass to make it inhomogeneous.
3. Glass can be reshaped. This is generally true and is the reason why glass is
so recyclable. Some glasses are designed so that they can be modified by
light, by diffusion, by irradiation, etc.
4. Glass has a small expansion coefficient. This is usually true, but not all
glass is Pyrex.
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5. Glass is transparent. This is essential for optical fibers, but we can make it
translucent or opaque. Most early glasses were not very transparent because
they contained impurities and inclusions.
6. Glass is cheap. This is true for window glass since the invention of the floatglass process.
7. Glass is a bulk material. This is true unless we grow it as a thin film or it is
present as an intergranular film (IGF) or pocket in, or on, a crystalline
ceramic.
8. They have great resistance to corrosion. This is largely due to the fact that
they are fully oxidized chemical substance, being mixtures of one, two or
more oxides.
9. Glasses have been stable for a long time or in other words they show good
chemical durability.
10. The great ranges of composition and properties, which can be covered by
different glasses, depend upon the fact that they are mixtures of solutions
rather than exact chemical compounds.
11. The internal energy of a glass is always greater than that corresponding to a
crystalline phase of the same composition.
12. The response to temperature is typical.
They do not possess a distinct
melting point, but on elevation of temperature they progressively soften and
transform into a liquid.
13. Their characteristic mechanical properties are progressively modified and
they pass without discontinuity from elastic solid to a viscous liquid.
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1.7 Glass Transition
A glass is defined as ½an inorganic product of fusion which has been
cooled to a rigid condition without crystallization″. The main distinction
between glass and crystals is the presence of long range order in the crystal
structure [6]. The transition from a viscous liquid to a solid glass is called ½glass
transition½ and
the
corresponding
temperature
is
Tg.
The
reversible
transformation from a glass to a viscous liquid takes place if the glass is heated
to a temperature above Tg. Since the glass transition occurs as a result of the
increase of viscosity and the rate of viscosity increase is dependent on cooling
rate, the glass transition temperature, Tg, is not always the same. If the chemical
composition is the same, Tg usually depends on the cooling rate of a liquid. A
volume-temperature diagram showing the cooling behavior of a typical glassforming melt is provided in Fig. 1.3.
(a)
(b)
Fig.1.3: (a) Volume-temperature relationship of glass-forming liquid and
non glass-forming liquid. (b) Temperature dependence of
nucleation rate I and crystal growth rate U.
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A slow cooling allows enough time for a viscous liquid to alter its local
atomic arrangement to attain the minimum free energy at the corresponding
temperature, whereas a rapid cooling causes an increase of viscosity that is too
quick for the local atomic arrangement to follow and results in a transition into a
glass at a higher temperature. The structure of a rapidly cooled glass is more
open than that of a slowly cooled one because the “freezing-in” of the atomic
arrangement occurs at a higher temperature. The properties of a glass are
therefore different from glass to glass, depending on the thermal history, even if
the chemical composition is the same.
A glass whose atomic arrangement lacks regularity over a long range has
higher configurational entropy and hence higher free energy, than a crystalline
material of the same composition. Therefore a glass is a thermodynamically
metastable material. The transformation of a glass to a crystal proceeds via
nucleation and crystal growth under the driving force of the difference in free
energy between crystal and glass ∆Gí, which increases with the increase of
supercooling ∆Tr. When a solid forms in a liquid there an interface is created.
The surface free energy is associated with this interface. As the solid grows, the
total surface free energy increases. With decreasing temperature there are two
competing effects: the increased difference in free energy between crystals and
liquid favors crystallization; the increasing viscosity reduces the tendency to
crystallization.
1.9 Different Types of Glasses
(a) Natural Glasses
They are formed when molten lava reaches the surface of the earth’s crust
and cooled rapidly, e.g., obsidians, pechsteins, pumice etc. Natural glasses can
also be formed by the sudden increase in temperature following strong shock
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waves e.g., tektites [7]. Biological process can in some rare cases lead to glass
formation. The skeleton of some deep-water sponges (monoharpis) consists
large rod of vitreous SiO2 [8].
(b) Artificial Glasses
The artificial formation of glasses occurs in very diverse classes of
materials. Although many substances can be used to form glasses, only some of
them are of practical value. For example, they are oxide glasses, halide glasses,
chalcogenide glasses and metallic glasses.
According to their chemical composition and their type of bond (Table
1.2) glasses may be broadly classified into different groups as follows.
(i) Oxide glasses (silicates, borates, phosphates, etc.).
(ii) Chalcogenide glasses.
(iii) Metallic glasses.
Table 1.2: Classification of glass forming materials in terms of chemical
bonding.
Bond type
Covalent
Glass-forming materials
Oxide glasses (silicates, borates, Phosphates
etc), chalcogenides, organic high polymers.
Hydrated ionic
Aqueous salt solutions
Ionic
Halides, nitrides, sulphates
Molecular or vander Waals
Splat-cooled alloys
or metallic
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(i) Oxide glasses
Silicate glasses: Among oxide glasses, commercially important and
extensively studied are the silicate glasses (SiO2 based glasses). In silicate
glasses SiO2 is the glass former and the study of its structure and properties has
been very important in understanding the chemically more complex silicate
glasses. These glasses have immense applications in various fields due to its
chemical and weathering stability.
Borate glasses: Boron trioxide is a significant component of glasses,
enamels and glazes. It is very rarely added to the raw material mixtures in the
form of oxide, more frequent use being made of H3BO3 or Na2B4O7. Boron
oxide (B2O3) usually occurs in the glassy form which is virtually incapable of
direct crystallization. The crystalline forms of B2O3 can only be prepared by
special procedure. Although borate glasses are of little commercial importance
because they are water soluble, B2O3 is an important constituent of borosilicate
glasses such as Pyrex. In contrast to SiO2 and silicate glasses in which the silicon
is present as SiO4 tetrahedra, B2O3 glasses contain BO3 triangular units and BO4
tetrahedra depending on the composition. Addition of alkali oxide to glassy B2O3
gives rather different results from those obtained in the corresponding alkali
silicates. The structure of borate glasses are explained in detail in section 1.10.
(ii)
Chalcogenide glasses
Chalcogenides (elements of group 6A in the periodic table) like sulphur
and selenium give viscous liquids on melting which rapidly form glasses on
cooling. Glassy or amorphous semiconductors can be made from the chalcogens
either alone or in combination with other elements. In this type of glasses, the
bonding is fairly covalent and the melt contain rings and chains of sulphur and
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selenium atoms. The chalcogenide based glasses are semiconductors and usually
have electronic conductivities in the range 10-3 to 10-I3 ohm-1 cm-1. These glasses
are used as optical elements in the instruments for the infrared region, where
they transmit radiation of considerably longer wavelengths than oxide glasses;
however they show very strong absorption in the visible region.
(iii) Metallic glasses
Usually, liquid metals do not form glasses, but recently certain
compositions have been shown to do so. Some particular metallic compositions
may be quenched very fast to yield glasses and usually, at least two elements
must be present in the melt composition. One of these is a conventional metal,
eg., a transition-metal element such as iron or palladium and the other is an
element on the metal insulator border line. In order to prepare glassy metals,
special ultra rapid quenching techniques like splat quenching or roller quenching
are necessary. The cooling rates are usually of the order of l06 to 108 K/sec.
1.10 Structure of borate glasses
B2O3 is never used alone to form glass because of its hygroscopic nature.
But it is incorporated in several industrial glasses. In spite of their ability to
absorb moisture, borate glasses are being used for technological applications
such as high refractive index rare earth borates, lead borate glasses in plasma
soldering. The behavior of ZnO in borate systems generates special interest
owing to their applications in different fields of electronic products. The addition
of alkali [M+] or the alkaline earth [M2+] cations act as network modifiers in the
glass structure, breaking bridging oxygen bonds to form non-bridging oxygens
(NBO) [9,10] and extends their scope of applications to radiation dosimetry,
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vaccum ultraviolet (VUV) optics, phosphors and solar energy converters, etc.
[11-13].
Borate glass contains a mixture of BO3 triangles and BO4 tetrahedra
depending on composition. An important constituent of vitreous B2O3 is boroxol
group (Fig. 1.4). It is a planar, six memebered ring of alternate boron and oxygen
atoms which are randomly connected in a three-dimensional network by sharing
all the three oxygen atoms with adjacent BO3 units. However, with the planar
coordination of boron, in comparison with the tetrahedral coordination of silicon
in SiO2, glassy B2O3 has a rather open structure. Molten B2O3 is also more fluid
than molten SiO2. Using X-ray diffraction and various spectroscopic studies, the
triangular coordination of boron in B2O3 glass can be deduced.
Fig. 1.4: Schematic model of boroxal group which is linked by shared
oxygen in B2O3 glass.
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The addition of alkali oxide to glassy B2O3 gives rather different results
than those obtained in the corresponding alkali silicates and an effect known as
the boron oxide anomaly is observed. It was shown that a gradual change in the
coordination number of boron from three to four occurs as alkali oxide is added.
By combining Raman scattering studies and the NMR investigations with the
available crystallographic data, structural groups present in these glasses have
been clearly identified. Fig. 1.5 shows the several structural groups present in
various borate compounds.
Fig. 1.5: Structural groupings in borate glasses
Pure B2O3 (1.6) consists of planar BO3 units which are randomly
distributed in a three-dimensional network by sharing all the three oxygen atoms
with adjacent BO3 units. The planar BO3 unit presumably involved in sp2
hybridization, with the third orbital being vacant and extending in direction
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perpendicular to the BO3 plane. This vacant orbital accepts an electron from the
unpaired electrons from the oxygen atoms, forming a partial double bond.
Fig. 1.6: 3D structure of boron trioxide
The following modifications in the network can be enhanced by the
addition of network modifying oxides. (a) Boron-oxygen-boron bonds may be
broken by oxygen anions (as in the case of the breakdown of silica network) to
form non-bridging atoms. (b) a filled orbital of an oxygen anion may overlap
with an empty p-orbital of a boron atom resulting in a change of hybridization of
the boron atom to the sp3 tetrahedra arrangement leading to BO4 tetrahedron
with three bridging and one non-bridging oxygen, (c) an oxygen atom may
contribute an electron pair to two BO3 units changing the coordination of the two
borons from sp2 to sp3 hybridization and with no nonbridging oxygen.
Several attempts [14] were made to explain the structure of borate glasses
on the basis of a number of imaginative structural models, all of which were
built around the relatively unique ability of boron to exist in two distinct
coordination states. However NMR studies [15,16] showed that the four
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coordinated boron varies smoothly as x/(l-x) where x varied from 0 to 30 mol%
modifier oxide without any unusual behaviour in the critical range 15-20 mol%
of modifier oxide. The BO4 groups are bonded to the rest of the structure in four
directions and the structure is therefore tied together in three dimensions rather
than two. This will produce a marked increase in the strength and tightness of
the Structure.
Bray has shown [17,18] using B11 NMR spectroscopy that a gradual
change in the coordination number of boron from three fold to four occurs as
alkali oxide is added to B2O3. By the time about 30 mol% has been added,
approximately 40 per cent of the borons would have changed to tetrahedral
coordination and this is independent of the nature of the alkali. In triangular
coordination, the B11 nucleus shows strong quadrupole coupling with a broad
resonance line whereas in tetrahedral coordination, the quadrupole coupling is
weak and the resonance is narrow. Extensive investigations have been carried
out on crystalline and glassy borates by Krough-Moe [19] who proposed a new
model for the structure of borate glass. Krough-Moe suggested that borate
glasses are not merely a random network of BO3 triangles and BO4 tetrahedra
joined at the corners, but, they actually contain well-defined and stable groups as
segments of the disordered frame work. These borate groups which are included
in the glass structure should be indentical with the groupings which occur in
crystalline borates. From the experimental results of thermodynamic [20] and
infrared [21] studies, the structural groupings in borate glasses can be classified
into four different groupings. viz., boroxol , pentaborate, triborate and diborate
groups (Fig. 1.5). The pentaborate and triborate groups will always occur in
pairs and these pairs are referred to as tetraborate groups.
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1.11 Electron Paramagnetic Resonance
Electron Paramagnetic Resonance (EPR) and Electron Spin Resonance
(ESR) are synonymous terms. It is a branch of absorption spectroscopy. It
describes the resonant absorption of microwave radiation by paramagnetic ions
or molecules in static magnetic field.
Eversince the discovery of EPR by
Zavoisky [22] in 1945, it has been developed as the important branch of
spectroscopy and has become a powerful tool in all branches of science
whenever systems containing unpaired electrons are to be investigated. This
technique has been proved to be a powerful tool to study the paramagnetic
defects in materials [23], concentration defects, dating and geological sample
[24]. The EPR study of free radicals was widely used in biological systems [25].
This technique has been proved to be a powerful tool to probe the site of a
paramagnetic center and determine its symmetry, describe the ground state and
the effect of the nearest neighbours and the energy levels of the species and to
map the crystal field.
1.11.1 Resonance condition
Whenever a system possessing resultant angular momentum and magnetic
moment is placed in an external magnetic field, magnetic energy level
separations can be observed [26, 27] by supplying electromagnetic field of
appropriate frequency to the system. When the magnitude of pumping the
electromagnetic frequency exactly matches the magnetic energy level separation,
energy absorption takes place in the system. This phenomenon is known as
magnetic resonance. If the system is electronic in origin it is known as electron
spin resonance.
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A free electron with spin angular momentum S, possesses a magnetic
moment µe given by,
µe = -ge â S
------ (1.1)
where ge is the spectroscopic splitting factor of the free electron (ge = 2.0023), â
is Bohr magneton (â = 0.927X10-23 J/T).
In the absence of external magnetic field, the free electrons are randomly
oriented and possess a zero resultant spin. If an external magnetic field
H (or B) is applied, then the degeneracy of the electronic spin levels
corresponding to the magnetic spin quantum numbers Ms = + 1/2 is lifted. Thus
an electron can have two possible energies given by,
E1 = + ½ g â H
------ (1.2)
E2 = - ½ g â H
------ (1.3)
The separation between these levels depends on the strength of the
external magnetic field. The resonance between these levels can be induced by
quanta of frequency í such that,
hí=gâH
------ (1.4)
This is the resonance condition to observe the EPR signals. The selection
rules for the allowed transitions are ∆Ms= +1; in practice, the resonance is
observed by varying magnetic field at constant microwave frequency. This is
because the variation of microwave frequency is technically not easy. The
principle of EPR is shown schematically in Fig 1.7. In general EPR spectra will
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be recorded as a first derivative of absorption curve. A detailed insight of the
technique can be had from the pioneering books by many authors [28-32].
Fig.1.7: The principle of Electron Paramagnetic Resonance.
1.11.2 General spin-Hamiltonian
In EPR spectroscopy, the transitions can be observed between the energy
levels of ground state. In order to get the eigen values and eigen functions, we
need to solve the Schrödinger’s time-dependent equation applied on Hamiltonian
operator. For a Hamiltonian consisting of more than one term, the easier way to
solve the equation is by perturbation theory. Here the eigen value is found by
taking the strongest interaction and then the next interaction will be treated as a
perturbation of the levels obtained in the first case. This procedure is repeated
until the weakest interaction is included. This method suffers with a draw back
that various interactions should differ from one another by at least one or two
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orders of magnitude. Incidentally, this condition is satisfied in EPR
spectroscopy.
The Hamiltonian, which describes various interactions of unpaired
electrons with the static magnetic field and that of the surrounding environment,
can be formalized in terms of spin operators. The coefficient of spin operators is
called spin-Hamiltonian parameters, which can be obtained from the EPR
measurements.
The concept of Hamiltonian was originally developed by Pryce [33] and
Abragam and Pryce [34] to interpret the observed resonance of ions in the first
transition series. The concept was subsequently extended by Elliott and Stevens
[35] to interpret the paramagnetic behaviour observed for the rare earth ions.
The terms in the general Hamiltonian for an ion in a crystalline environment can
be written as [36],
H = H E + H LS + H SI + H Q + H V + H SH + H 1H
------ (1.5)
where the symbols indicate the type of interaction to which Hamiltonian applies
and have the following meaning.
i) HE is a composite term expressing the total kinetic energy of the electrons, the
Coloumbic attraction between the electrons and the nuclei and the repulsion
among the electrons,
HE
 Pi 2
Ze 2 
 


ri 
i  2m
e2
ij r
ij
22
------ (1.6)
where Pi is the momentum of ith electron, ri is the distance of the electron from
the nucleus, rij is the distance between ith electron and jth electron and Ze is the
nuclear charge.
These terms are summed over all the electrons and yield the unperturbed
electronic levels before considering the interaction between spin and orbital
angular momenta. The separations will be of the order 105 cm-1 .
ii) HLS represents the spin-orbit coupling and may be written in the form,
HLS = ∑ ij . li . s
------ (1.7)
where l is the orbital angular momentum of the individual electron, ‘s’ is the spin
angular momentum of the individual electron and ëij is the spin - orbit coupling
constant. This can be written in a simple form as,
HLS = ë L . S
------ (1.8)
where L and S are the total orbital angular momentum and the spin angular
momentum of free ion respectively. The magnitude of this interaction lies
between 102 to 103 cm-1.
iii) H
SI
describes the magnetic interaction between each electron and the
nucleus,
HSI = ∑ ai . Ji . Ii
------ (1.9)
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where Ji is the total angular momentum of the ith electron and Ii is the nuclear
spin. The magnitude of this interaction will be of the order of 10-2 cm-1.
iv) HQ represents the nuclear quadrupole interactions, which are even smaller
than HSI (~10-4 cm-1 ) and may be neglected. For nuclei with spin I > ½, these
interactions shift the hyperfine levels by a small amount,
HQ= ∑ Ii. QI. Ii
------ (1.10)
v) HV represents the effect of crystal field, which can be written as
HV = ∑ ei V(ri)
------ (1.11)
where V(ri) is the electrostatic potential at the ion with which each electron
interacts.
In an external magnetic field H, the terms HSH and HIH must be added to
represent the interaction of the angular momentam of electrons and nuclei
respectively with the magnetic field.
HSH = . ( L + ge S) . H
------ (1.12)
HIH = h / 2
------ (1.13)

 i. Ii. H
i
where i is the gyromagnetic ratio of the ith nucleus and the latter terms (about
10-4 cm-1) may be neglected except in considering second order effects in the
nuclear hyperfine interaction.
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1.11.3 Hyperfine structure
The most important feature of EPR spectra is their hyperfine structure. In
general spectroscopy, the term ‘hyperfine structure’ means the structure of the
spectrum due to interactions of the electrons with nucleus, other than as a result
of the latter point electronic charge. The source of the hyperfine structure in EPR
is the magnetic interaction between electronic magnetic moment and magnetic
moment (both spin and orbital) of the nuclei present in the radical. The hyperfine
structure of an EPR spectrum is a kind of finger print that helps to identify the
radicals present in a sample.
If the nucleus of the paramagnetic ion has a non zero spin I, each EPR
line splits into (2I+1) equally spaced lines as illustrated in Fig 1.8, for the case of
S = 1/2 and I = 3/2 (Cu2+ ions). The magnetic field exerts a negligible effect on
the tiny nuclear magnetic moment so that the allowed transitions are those in
which the magnetic nuclear quantum number (mI) does not change. For Cu2+
ions the spectrum consists of four equally spaced lines.
Fig. 1.8: The hyperfine structure expected for a system with S = 1/2 and
I = 3/2 (Cu2+ ions).
25
At normal temperature, all orientations will have equal probability and
hence the four lines are of equal intensity. However, in practice the hyperfine
lines will not have equal intensity due to various perturbations acting on the
nucleus and the unpaired electrons. A direct determination of the nuclear spin (I)
can be made from the hyperfine structure in the EPR spectrum.
Further,
measurements on the anisotropy of the hyperfine structure not only give
information about the nuclear properties but also help in an understanding of the
electronic state of the unpaired electron in the paramagnetic ion. The hyperfine
structure also gives the information regarding the nature of chemical bonding
between central metal ion and its ligand.
1.11.4 Line shapes
The most commonly observed shape functions in EPR spectroscopy are
Lorentzian and Gaussian, described by the functions given below,
I0
I
------ (1.14)
=
T22 (H  Hr)2 + 1
I
=
I0 exp [ b (H  Hr)2 T22]
------ (1.15)
where I0 is the intensity of the absorption at its center, Hr is the resonant field at
the line center. The constants T22 and b are related to the half width of each of
the two types of curves.
The Lorentzian shape arises due to harmonically bound electron. If the
harmonic motion of the electron is interrupted by some process, then the
distribution of frequencies follow the eqn. (1.15). For an EPR spectrum, the
interruption will be in the form of exchange.
26
Since all the electrons are
equivalent, their interchange between two molecules is quite possible if the
molecules are close enough to each other. If this exchange is so rapid to affect
the phase coherence of the spins, Lorentzian shape results.
On the other hand, Gaussian shape results from the paramagnetic ion
separated from each other by molecules, which are having no unpaired electrons
but possessing magnetic nuclei. Each unpaired electron will experience a local
static magnetic field which will be dominated by how the nuclear spins are
arranged in the nearby host molecules. The observed EPR spectra will be a
superposition of shapes from all the spins with their local fields. Since the local
fields will be randomly distributed, the total line shape results in a Gaussian line
shape according to eqn. (1.14). The characteristic Lorentzian and Gaussian line
shape are shown in the Fig 1.9.
Fig. 1.9: The characteristic Lorentzian and Gaussian line shapes.
27
1.11.5 Line width and Intensities
Generally the EPR signals are recorded as the first derivative of the
absorption curve and hence the area under the EPR signal can be calculated by
numerical double integration method.
In this method, the EPR spectrum is
divided into ‘n’ small intervals each having length‘d’. The height hr of the EPR
signal corresponding to the center of rth interval is noted and the area under the
curve can be calculated from the equation,
A = (1/2) d
2
n
Ó (n  2r+1) hr
r=1
------ (1.16)
Fig.1.10 shows the method of finding the area under the first derivative
absorption curve by numerical double integration method. The accuracy of this
method depends on the number of intervals and complexity of the spectrum.
Using about 8 to 10 intervals per peak, the error in calculating the area will
likely be within 2 to 3% in Gaussian curves. For Lorentzian curves, the error
may be greater due to the presence of long tails.
Fig. 1.10: The method of finding the area under the first derivative
absorption curve by numerical double integration method.
28
For EPR signals, the line widths are measured from the maximum and
minimum line positions at the first derivative curve. The EPR lines always have
a finite width due to electrons interacting magnetically with the environment of
the sample. Hence, from the line width and the rate of build up or decay of the
line intensity, one can obtain the information about the spin environment.
The intensity of EPR signals depends on various factors (i) concentration
of the paramagnetic ion (ii) the microwave frequency (iii) the power of
microwaves (iv) the transition probability and (v) the temperature.
1.11.6 Applications of EPR technique to glasses
The EPR spectra give a large amount of information regarding transition
metal and rare earth ions in the materials.
A list of applications of EPR
technique are given below.
1. From the fine structure and hyperfine structure of EPR spectrum one can
obtain the spin state of both of the paramagnetic ion and its nucleus.
2. It can be used to estimate the concentration of the paramagnetic
impurities in a sample.
3. This method is unique to determine zero field splitting parameter [37].
4. On analyzing the hyperfine splitting constant (A), the interaction of
electron spin with the nuclear spin can be studied.
5. The coupling constant (J) can be calculated from the temperature
variation of the relative intensity.
In addition to the above, the results of EPR in combination with that of
optical absorption data give us the information regarding the nature of the
29
bonding between the central metal ion and its surrounding ligands. Some of the
basic principles necessary to understand and interpret the optical absorption
spectra are explained in the subsequent sections.
1.12 Optical absorption spectrum
Optical absorption spectroscopy is one of the important tools to get the
information of the excited states. It is well known that at room temperature a
major number of atoms or molecules will occupy the lower energy state (ground
state) relatively to higher energy level (excited state). When such a material
interacts with electromagnetic radiation then the atoms or molecules absorb the
radiation and get excited to one of the higher energy levels, provided the energy
of the electromagnetic radiation is equal to the energy difference between the
two levels. A plot of intensity of absorption against the wavelength or frequency
of the electromagnetic radiation is called the absorption spectrum.
The transition of the outermost electron from ground state of the atom to
one of its excited states is known as atomic spectra or more often it is known as
electronic spectra. Some selection rules will govern the possibility of optical
absorption between two energy levels.
The first group transition metal ions are characterized by their
incompletely filled 3d-orbitals. The d orbitals are five fold degenerate.
In
crystals as well as glasses, the orbital degenercy is lifted due to the presence of
surrounding ligands. The splitting of the 3d-orbitals depends on the nature,
number and the arrangement of the ligands around the transition metal ion.
30
1.12.1 Free ion terms
In the absence of the ligands, the central metal ion in a sample is called
free ion. In atomic spectra, the energy levels are represented by terms. A term is
represented by,
(2S+1)
LJ
where S is the total spin angular momentum quantum number, L is the total
orbital angular momentum quantum number and J is the total angular
momentum quantum number of the system of electrons obtained by Russell
Saunders coupling [37-40]. The subscript (2S+1) is called as multiplicity term
(M). L = 0,1,2,3, ---- corresponds to S,P,D,F ----- states respectively and S = 1/2,
1, 3/2 ---- corresponds the terms singlet, doublet, triplet, quartet etc.,
respectively. The various terms from different dn configurations are given in
Table 1.3.
Table 1.3: The various terms from different dn configuration.
Configuration
d 1, d 9
2
D
8
3
F,3P, 1G, 1D, 1S
d 3, d 7
4
F, 4P, 2H, 2G, 2F, 2D(2), 2P
d 4, d 6
5
D, 3H, 3G, 3F(2), 3D, 3P(2)
1
I, 1G(2), 1F, 1D(2), 1S(2)
6
S, 4G, 4F, 4D, 4P, 2I, 2H
2
G(2), 2F(2), 2D(3), 2P, 2S
1
S
2
d ,d
d5
d10
*
Terms*
The number of times a symbol occurs is given in parenthesis. The first term
is the ground state.
31
The ground state of any configuration can be determined by Hund’s rule.
According to this rule, the term with highest spin multiplicity M and the largest
orbital angular momentum L will occupy the lowest level in any configuration.
If the d orbitals are less than half filled then the value of J will be (L-S) and if
they are more than half filled then the value of J will be (L+S). However, the
order of other terms and their separations from each other and from the ground
term can be determined by the perturbation theory.
For a partially filled n, l shell containing q electrons, the number of states
is,
q
(4l + 2) !
=
4l + 2
.
------ (1.17)
q ! (4l + 2 – q) !
For example, the number of micro states that arise out of a d2
configuration is
2
10 !
=
10
45
.
------ (1.18)
2 ! (8) !
The energy level diagram for d2 configuration with all 45 micro states is
shown in Fig. 1.11. The transitions between these levels are governed by the
selection rules S = 0 and L = + 1, where S and L are the differences in the
respective quantum numbers for ground and excited states.
It is possible to develop the theory of inter electronic repulsion within a
configuration, to give the energies of the terms above the ground term. The
energies are function of two parameters known as Racah parameters (Electronic
repulsion parameters).
32
Fig.1.11 : Schematic representation of the splitting of electronic energy level
for d2 configuration with all 45 microstates.
1.12.2 Ligand field theory
According to crystal field theory developed by Bethe [41] and Van vleck
[42], the ligands are known as point charges and the bond between metal and
ligands are purely ionic. It gives no account of the covalent nature of the metal
ligand bonds. This draw back is rectified by modifying the crystal field theory.
33
The modified crystal field theory is known as ligand field theory or molecular
orbital theory.
This theory starts with the premises that the overlap of atomic orbitals of
the central metal ion and those of the ligands will occur, to some degree,
whenever the condition of energy, overlap and symmetry permit.
The most common complexes of transition metal ions in glasses can have
either octahedral or tetrahedral symmetry. When a transition metal ion is placed
in a crystalline field, the free ion terms corresponding to the ion will be
transformed into electronic energy levels. Bethe [41] and Mulliken [43]
proposed two different notations to represent these energy levels. In a complex,
these electronic energy levels are represented by A1, A2, E, T1 and T2 where A1
and A2 are non degenerate; E is doubly degenerate while T1, T2 are triply
degenerate. Table 1.4 shows the various notations of energy levels used by Bethe
and Mulliken. In the present thesis, the notations fallowed by Mulliken are used.
Table 1.4: Various notations of energy levels used by Bethe and Mulliken.
Bethe [41]
Mulliken [43]
Octahedral
Tetrahedral
Oh
Td
Ã1
A1g
A1
Ã2
A2g
A2
Ã3
Eg
E
Ã4
T1g
T1
Ã5
T2g
T2
34
If the crystal has no center of symmetry, no subscripts are used. When it
has a center of symmetry, depending upon the partiy of the atomic orbital, either
‘g’ or ‘u’ is used as subscript. For atomic orbital with even parity (i.e., s, d and g
orbitals), the subscript ‘g’ is used while for orbitals with odd parity (i.e., p, f and
h orbitals), the subscript ‘u’ is used.
A free d-electron has five fold orbital degeneracy with all the five d
orbitals namely dxy, dyz, dzx, dx2-y2 and dz2 possessing the same energy. Each
orbital has four lobes at right angles.
The dz2 orbital represents a linear
combination of two orbitals, dx2- y2 and dz2- x2. The sign of the wave function of
the lobes in opposite quadrants is identical, but opposite to that of lobes in
adjacent quadrants as shown in Fig.1.12.
Fig. 1.12 : The five d-orbitals (t2g and eg).
35
The five d-orbitals may be divided into two groups on the basis of their
angular distributions. Three orbitals dxy, dyz and dzx have lobes projecting
between the Cartesian axes. Group theory calls these as t2g orbitals where ‘t’
refers to the triply degenerate set; the subscript 2 indicates that the sign of the
wavefunction does not change on rotation about the axes diagonal to the
Cartesian axes. The subscript ‘g’ refers to the fact that the wavefunction does not
change sign on inversion. The other two orbitals dx2-y2 and dz2 have lobes
directed along the Cartesian axes. Group theory designated them as eg where e
refers to doubly degenerate set. All the five d orbitals have symmetric wave
functions.
In case of the free metal ion, all the five d orbitals are degenerate. But in
the presence of octahedral crystal field, the five-fold orbital degeneracy is lifted
and they split into triply degenerate t2g and doubly degenerate eg orbitals, the
former lying lower than the latter. Since the lobes of the two eg orbitals lie
directly in the path of the approaching ligands, the electrons in these orbitals
experience greater force of repulsion than those in three t2g orbitals, whose lobes
are directed in space between the path of the approaching ligands, i.e. the energy
of the orbitals is increased while that of t2g is decreased as illustrated in the
Fig.1.13. However, in tetrahedral crystal fields, the ‘e’ orbitals lie lower than the
t2 orbitals. The energy separation between these orbitals t2 and e sets is denoted
by ∆ or 10Dq.
When a transition metal ion is embedded in a crystal, three forces act on
its electrons. They are (i) crystal field force (CF) (ii) electronic repulsion force
(e2/rij) and (iii) the force due to spin orbit interaction [ (ã)]. The energy levels of
transition metal ions are more affected by crystal fields. Depending on the
relative strength of the above three forces, three types of crystal fields can be
defined.
36
Fig.1.13 : Diagram showing the relative energies of t2 and e-orbitals
resulting from the splitting of set of d orbitals by octahedral and
tetrahedral environment.
(a) Weak crystal field: In this e2/rij >  (r) > CF. This is normally observed in
Lanthanides and Actinides. In this, the unfilled nf-shell will be well shielded by
the outer (n+1) s, (n+1) p and (n+1) d orbitals. The crystal field splitting will be
of the order of 50-400 cm-1.
(b) Medium crystal field: In this e2/rij > CF >  (r). Generally iron group
transition metal ions will experience medium crystal field. The crystal field
splitting will be of the order 10,000-20,000 cm-1; because of this crystal field, the
free ion term splits into various energy levels which are denoted by irreducible
representation. Table 1.5 lists the transformation of free ion terms to irreducible
representations in octahedral crystal field.
(c) Strong crystal field: In this CF >e2/rij >  (r). Generally Palladium group
(4d), Platinum group (5d) ions and also rarely observed low spin states of the
iron group ions will experience strong crystal fields. The crystal field will be of
37
the same order as e2/rij so that the field effect is considered before or along with
the interelectronic repulsion.
Table 1.5: Irreducible representations of free ion terms in octahedral
symmetry.
Free ion terms
Irreducible representation
S
A1g
P
T1g
D
T2g, Eg
F
A2g, T2g, T1g
G
A1g, Eg, T1g, T2g
H
Eg, 2T1g,T2g
I
A1g, A2g, T1g, 2T2g
1.12.3 Fundamental absorption edge
The study of the fundamental absorption edge helps in calculating the
optical band gap energy (Eopt) and Urbach energy (E). The absorption in the
ultraviolet region may be of two types. One of them is the transition of an
electron from one orbital to another orbital at high energy. In such case, a band
with well defined maxima results. The second one is the transition of the valence
electron from one of the localized orbital to the conduction band, which is
common for all the molecules in the material. In this case, a sharp rise in
absorption coefficient with increasing photon energy results. The rapid rise of
38
absorption coefficient
()
with photon energy
h is referred to as
fundamental absorption edge.
The energy difference between the maximum of the valence band and
minimum of the conduction band is called optical band gap Eopt (optical energy
gap). Depending upon the positions of these extrema, the transitions can be
either of two types; direct or indirect. If the maximum of the valence band and
minimum of the conduction band occurs at the same point in the K-space, then
the transition is said to direct. On the other hand, if these extrema are at different
points in K-space, then the transitions are possible only when assisted by
phonons and are called indirect transitions.
The value of the optical band gap (Eopt) depends on the structure and the
actual values of the pseudo potentials in the materials. It is to be distinguished
from the gap Eg, which is characteristic of the whole absorption band and is
connected with the basic properties of the materials.
A typical fundamental absorption edge in a glass sample is shown in the
Fig 1.14. In this figure, the region A is the high absorption region and the region
B is the exponential absorption region.
The main feature of the absorption edge at lower values of absorption is
an exponential increase in absorption coefficient (í) with photon energy (hí)
according to the relation.
(í) = 0 exp (h/E)
------ (1.19)
39
Fig. 1.14: A typical fundamental absorption edge in a glass sample.
where 0 is a constant, ÄE is the Urbach energy and í is the frequency of
radiation. The absorption coefficient,  (í) can be determined near the edge
using the formula,
(í) = 1/d ln (Io/I) = 2.303 A/d
------ (1.20)
where A is the absorbance of the frequency í and d is the thickness of the glass
sample. For an absorption by indirect transition, the absorption coefficient is
given by the formula,
Eopt = hí  (hí/ B)1/2
------ (1.21)
40
where B is a constant and Eopt is the optical band gap. This relation applies to
many oxide glasses [44]. The optical band gap can be obtained by extrapolating
the linear region of the curve to the hí-axis in (hí) 1/2 versus h graph. From
the slope of ln(á)-hí plot, the Urbach energy can be calculated.
1.13 Infrared spectroscopy
Infrared spectroscopy is an important tool for understanding the structure
and dynamics of materials. IR spectroscopy is used to assign the observed
absorption peaks to the proper vibration of the atoms in geometric grouping. But
in the spectra of solids many variables can affect the absorption peaks and the
assignment of vibration peaks of the atoms is very difficult. Usually, the method
of repeated occurrence is followed in analysing the IR spectrum of solids. The
spectrum of a sample is compared with the spectrum of a large number of'
compounds containing a common atom group or groups. Certain absorption
peaks are common to certain groups and are assigned the vibration characteristic
of these atom groups [45].
The infrared region of the electromagnetic spectrum extends from the red
end of the visible spectrum to the microwave region. Infrared spectroscopy
involves the twisting, bending, rotating and vibrational motions of atoms in a
molecule [46, 47]. Upon interaction with infrared radiation, portions of the
incident radiation are absorbed at particular wavelength. The IR spectrum of a
molecule may be considered as its finger print and can be used for the
identification of the compound. The spectral range of the greatest use is the mid
infrared region which covers the frequency range from 200 to 400 cm-1 (50 to
2.5 m). The absorption of infrared radiation can be expressed either in terms of
wavelength ‘’ or the wavenumber ‘’. Infrared spectroscopy has been
extensively employed over the years to investigate the structure of glasses [48].
41
Borate glasses, in particular have been the subject of numerous infrared studies
because of their structural peculiarities [49-55].
1.13.1 Fundamental vibrations of infrared spectroscopy
The number of fundamental vibrational modes that can be responsible for
the absorption of the infrared light of a non-linear and linear molecules
containing n-atoms will be (3n-6) and (3n-5) respectively. In order for a
particular vibration to result in the absorption of infrared energy, that vibration
must cause a change in the dipole moment of the molecule, which means that the
vibration should produce temporary displacement of the electrical center of
gravity. The transition electric-dipole moment integral nm is given by,
nm =  n* (d/dr)q  d
------ (1.22)
where n and m are the upper and lower vibrational wavefunctions,  is the
electric dipole moment and q = r - re, where re is the equilibrium bond distance.
Vibrational motion will change as a result of the change of bond length if the
molecule has a permanent dipole moment to start with. The above relation
immediately excludes all homonuclear diatomic molecules for IR studies. If a
molecule has a center of symmetry then any vibration that is active in IR, is
inactive in Raman and vice versa.
The atoms constituting a molecule are not stationary. They are
continuously rotating and vibrating in a number of ways. Two atoms joined by a
covalent bond may undergo a stretching vibration. Three atoms can undergo a
variety of stretching and bending vibrations. Bending vibrations require less
energy and occur at lower wave numbers than stretching vibrations. Stretching
vibrations are found to occur in the order of bond strength and the masses of the
42
atom involved and force constant (k). The approximation relation between
stretching frequency (in cm-1), masses of the two atoms (mx and my) involved,
velocity of light (cm/sec) and force constant k (dynes/cm) is given as,
 = (1/2) c [ (k ( mx + my ) ) / mx my ]1/2 .
------ (1.23)
1.13.2 Correlation of infrared spectra with molecular structure
The infrared spectrum of a compound is essentially the superposition
bands of specific functional groups, yet subtle interactions with the surrounding
atoms of the molecule impose the stamp of individuality on the spectrum of each
compound. For qualitative analysis, one of the best features of an infrared
spectrum is that the absorption or the lack of absorption in specific frequency
regions can be correlated with specific stretching and bending motions and, in
some cases, with the relationship of these groups to the remainder of the
molecule. Thus, by interpretation of the spectrum, it is possible to state that
certain others are absent. With this one datum, the possibilities for the unknown
can be sometimes narrowed so sharply that comparison with a library of pure
spectra permits identification.
(i) Near-infrared region
In the near-infrared region, which meets the visible region at about
12,500 cm-1 (0.8 m) and extends to about 4000 cm-1 (2.5 m), are found many
absorption bands resulting from harmonic overtones of fundamental bands and
combination bands often associated with hydrogen atoms. Thicker sample layers
(0.5-10 mm) compensate for lessened molar absorptivities. The region is
accessible with quartz optics and this is coupled with greater sensitivity of near43
infrared detection and more intense light sources. The near-infrared region is
often used for quantitative work.
(ii) Mid-infrared region
This region is divided into the “group frequency” region, 4000-1300 cm-1
(2.5-8 m) and the “fingerprint” region, 1300-650 cm-1 (8.0-15.4 m). In the
group frequency region, the principal absorption bands may be assigned to
vibration units consisting of only two atoms of a molecule; that is, units which
are more or less dependent only on the functional group giving the absorption
and not on the complete molecular structure.
(iii) Far-infrared region
The region between 667 and 10 cm-1 (15 and 1000 m) contains the
bending vibrations of carbon, nitrogen, oxygen and fluorine with atoms heavier
than mass 19 and additional bending motions in cyclic or unsaturated systems.
The low-frequency molecular vibrations found in the far-infrared are particularly
sensitive to changes in the overall structure of the molecule. Moreover, this
region is particularly well suited to the study of organometallic or inorganic
compounds whose atoms are heavy and whose bonds are inclined to be weak.
1.13.3 Requirements for absorption of infrared radiation
Those molecules which fulfill the following conditions, absorb infrared
radiations.
44
(i) Correct wavelength of radiation
Only those molecules can absorb radiations in which the natural
frequency of vibration of some part is the same as the frequency of incident
radiation. The IR radiation that is absorbed causes the molecule to vibrate at
increased amplitudes.
(ii) Electric dipole
Only those molecules can absorb IR radiations, in which, such absorption
produces same changes in the electric dipole of the molecule. In the vibration of
a molecule, the continual fluctuation of the charge distribution sets up an
alternating electric field which interacts with the electric vector of the impinging
radiation. The molecule has a natural vibration which involves a periodic
variation of the dipole moment, and also provides the frequency of the
impinging light which is the same as this natural molecular frequency. The light
will strongly excite those specific vibrations, lose energy in the process and an
absorption band will be observed. The vibrations, which involve an oscillation of
the dipole moment, will record themselves in the infrared spectrum.
1.13.4 Theory of IR absorption spectroscopy
The atoms constituting a molecule are not stationary and are continuously
rotating and vibrating in a number of ways. Two atoms joined by a covalent
bond may undergo a stretching vibration. In this type of vibration the two atoms
move back and forth as if joined by a spring.
45
(a) Stretching vibration
This type of vibrations arises because of stretching and contracting bonds
without producing any change in bond angles.
Two types of stretching vibrations are (i) Symmetric stretching
(ii) Asymmetric stretching.
(i)
Symmetric stretching
In this type of stretching, the movement of atoms with respect to a
particular atom in a molecule is in the same direction (Fig .1.15a ).
(ii) Asymmetric stretching
In this type of stretching one atom approaches the central atom whereas
the other atoms move away from it (Fig. 1.15b).
(b) Bending vibrations or Deformations
In case of bending vibrations there is a deformation of bond angles and
there is no change in bond lengths.
Once again these vibrations are classified as (Fig. 1.16)
(i) Scissoring (ii) Rocking (iii) Wagging and (iv) Twisting.
46
(i) Scissoring : In this type of vibration, the two atoms approach each
other in the same plane.
(ii) Rocking : In this type of vibration, the movement of atoms occur in
the same direction as also in the same plane.
(b) Asymmetric stretching
(a) Symmetric stretching
(iii) Wagging : The two atoms move up and down the plane with respect
to the central atom.
(iv) Twisting :
One of the atoms moves up the plane and other moves
down the plane with respect to the central atom.
47
(ii) Rocking
(i) Scissoring
+
_
_
+
+
_
or
(iii) Wagging
(iv) Twisting
Fig.1.16
In the present work, the author analyzed the EPR, Optical absorption and
FT-IR spectroscopic techniques of VO2+, Cr3+, Mn2+ and Cu2+ ions embedded in
strontium alkaline earth zinc borate glasses.
48
1.14 References
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49
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