CHAPTER 1

GENERAL INTRODUCTION AND REVIEW OF LITERATURE

ABSTRACT

General introduction and review of literature deals with the characteristics of

lanthanide ions, free-ion and crystal-field levels, glassy materials, glass transition

temperatures and structure of glass and crystalline materials. The advantages of

amorphous materials over crystalline materials have been discussed. To analyze the

absorption and emission spectra theoretical models have been outlined. Energy level

scheme through free-ion Hamiltonian model, intensities of spectral lines and radiative

properties of excited states using Judd-Ofelt analysis have been presented. Using

Inokuti-Hirayama and Yokota-Tanimoto models the multipolar interactions, energy

transfer processes have been discussed.

1.1 Objectives and scope of research

Spectroscopy is a branch of physics that deals with the study of interaction of

electromagnetic radiation with matter. The tremendous advancement of Science and

Technology is giving raise to the continuous appearance of new spectroscopic

techniques. Spectroscopy finds applications in the fields of physics, chemistry,

medicine, forensic, industry, agriculture, defense, telecommunications, biology,

geology, astronomy etc [1-7].

Different spectroscopic techniques are rooted in a basic phenomenon: “the

absorption, reflection, emission or scattering of radiation by matter in a selective

range of frequencies under certain conditions”.

Optical spectroscopy is an excellent tool to study the electronic structure of

absorbing or emitting centers like molecules, atoms, ions, defects etc., their lattice

locations and their environments. In other words optical spectroscopy allows us to

“look inside” of matter by analyzing the interacted electromagnetic radiation. For the

last several decades, tremendous breakthrough has been achieved in the development

of trivalent lanthanide (Ln3+

) doped materials for potential applications in photonics

[8-12]. The chemical composition of glass network former and modifier results a wide

range of variation in the optical properties of Ln3+

ions in glass environment. The

study of the optical properties of the Ln3+

ions in glass materials provides fundamental

data that includes transition positions and cross-sections, transition probabilities,

radiative life times, branching ratios, line widths etc., for the excited states. This data

is essential to estimate/design optical devices such as lasers, up converters, fiber

amplifiers, color displays, light emitting diodes (LEDs) and so on. In this direction, in

order to identify new optical devices, devices for specific utility or devices with

enhanced performance, active work is being carried out by selecting appropriate new

hosts doped with Ln3+

ions [13].

Among the most popular solid state media the rare earth (RE) ions doped laser

crystals, glasses and ceramic media have attracted the researchers with increasing

interest. Comparing with crystalline media, glasses are favorable hosts due to their

broad inhomogeneous band width, possibility of tuning the wave length, large doping

capability and easy to mould and shape in larger sizes as well [14]. Multi component

glasses which typically consist of network formers and modifiers provide wide range

of excellent optical properties for new applications by selecting and tailoring the

chemical composition. Borate glasses doped with various RE ions offer many

commercial and technological applications. Borate glasses are commonly used in a

wide range of photonic applications such as optical amplifiers, lasers, photosensitive

materials and Faraday rotators [15,16]. In lead containing glasses the non-linearities

are primarily from the Pb2+

ions, as they are highly polarizable due to the presence of

6s2

electrons. These glasses possess a large non-linear optical properties which make

them suitable for potential applications in non-linear optical devices such as power

limiters, ultra fast switches and broad band optical amplifiers [15,17]. The important

properties required for a laser medium are high gain, high energy storage capability

and low optical losses, which depend on stimulated emission cross- section,

fluorescence life-time and optical efficiency [15, 17-20].

Heavy metal oxide (HMO) glasses find their importance as host matrices for good

lasing candidates because of their low phonon energy, high mechanical and thermal

stability, corrosion resistance and good solubility of rare earth ions [15,21-23]. The

incorporation of HMOs such as PbO or Bi2O3 into the borate glass matrix leads to an

increase in its luminescence quantum efficiency [21]. The effect of lead-borate,

bismuth-borate and lead-bismuth-borate glasses on the optical properties of Nd3+

ion

have been reported [21,23-25]. Motivated by these works, in the present work, lead-

bismuth-aluminum-borate glasses, doped with Nd3+

and Pr3+

ions have been prepared

and the physical and optical properties were studied, especially the suitability of the

samples prepared as the core material for optical fiber and active medium for solid

lasers, with concentration variation of RE ions and host variation.

1.2 HOST MATERIAL

GLASSES: Glasses have a long and interesting history. The primitive cave

dwellers used the chipped pieces of obsidian, a natural volcanic glass, for tools and

weapons like scrapers, knives, axes and heads for spears and arrows [26]. The

techniques of production of colored glasses were also known to them and passed on to

the next generations as family secrets. With the advent of modern technology now a

days fine glasses are produced. Most of the glasses are transparent to the visible

light. This makes the glasses for use in sculptures in art museums and in chandeliers

aesthetically pleasing. Glass is one of the useful and versatile materials, which has

also been the focus point for intensive modern research particularly in the fields of

telecommunications and optical fibers.

Inorganic glasses have been used as optical materials for a long time due to their

isotropy and high transparency over a wide spectral range from ultraviolet (UV) to

infrared (IR). With the advent of modern technology a series of new glass forming

systems have been developed to meet the demands of the expanding field of optics

and optoelectronics. In oxide glass systems, besides traditional silicate, borate,

phosphate, tellurite, germanate glasses, new glass forming systems have also been

expanded to non-oxide glasses such as halide and chalcogenide glasses.

1.2.1 Definition of glass

Glasses are essentially non-crystalline solids obtained by freezing super cooled

liquids which exhibit short range order. According to the ASTM (American Society

of Testing Materials) standards, „glass is an inorganic product of fusion which has

been cooled to a rigid condition without crystallization‟ [27]. This definition would

exclude splat quenched glasses, glass made under high pressure, sol-gel and sputtered

glasses. In AD 1968 glass was redefined as “an amorphous solid which exhibits a

glass transition”. Glasses have two common characteristics namely absence of long

range periodic atomic arrangement and presence of time dependent behavior known

as glass transformation behavior over temperature range known as glass

transformation region[27,28]. Accordingly a glass can formally be defined as an

amorphous solid completely lacking long range periodic structure and exhibiting a

region transformation behavior [29].

1.2.2 Classification of glasses

1.2.2.1 Natural glasses: When molten lava reaches the surface of the earth‟s crust

and is cooled rapidly, natural glasses such as obsidians, pechsteins, pumice etc., can

be formed. Natural glasses can also be formed by the sudden increase in temperature

following strong shock waves e.g., tectites [30]. Glass formation is also rarely be

possible by biological process. The skeleton of some deep water sponges consists of

a large rod of vitreous SiO2 [31].

1.2.2.2 Artificial glasses: The formation of the artificial glasses takes place in various

diverse classes of materials but only some of them are of practical value. Artificial

glasses are classified as follows.

(i) Oxide glasses: Oxide glasses are the most important among the inorganic

glasses eg silicate (SiO2), phosphate (P2O5), borate (B2O3) and germinate

(GeO2) glasses.

Oxide glasses find photonic applications such as lasing material and core

material for optical fibers.

(ii) Halide glasses: BeF2 is a glass network former whose structure is based on

BeF4 tetrahedra. Fluorozirconate , fluoroborate and fluoro phosphate glasses

are the best candidates for high power lasers for thermonuclear fusion

applications.

(iii) Chalcogenide glasses: Chalcogenide glasses are formed when group VI

(S, Se and Te) elements are combined with group IV (Si and Ge) and group V

(P, As, Sb and Bi) elements. These glasses do not contain oxygen and so are

interesting due to their infrared optical transmission and electrical switching

properties. Vitreous Se possesses photoconductive properties and is used in

photocopiers (Xerography). Ge-As-Si glasses have opto-acoustic applications

and are used as modulators and deflectors for IR rays.

(iv) Metallic glasses: These are of two types viz, metal-metalloid alloys and

metal-metal alloys. These glasses have the properties of extremely low

magnetic losses, zero magnetostriction, high mechanical strength and

hardness, resistance to radiation and chemical corrosion. These materials are

used as cores in moving magnets, recording cartridges, amorphous heads for

audio and computer tape recording and high frequency power transformers.

1.2.3 Glass preparation methods

Glassy materials can be prepared by various techniques like melt quenching, gel

desiccation, thermal evaporation, chemical reaction, chemical vapor deposition,

electrolytic deposition, reaction amorphization, shear amorphization, sputtering,

glow-discharge decomposition, irradiation and shock-wave transformation. Among

these methods, melt quenching and gel desiccation techniques are widely used in the

preparation of glasses.

1.2.4 Properties of the glasses

The physical properties of a glass matrix may depend upon the previous history of

the specimen. The surface pre-treatment of the specimen has decisive importance.

The thermal expansion and viscosity of glass also depend to some extent on the

history of the specimen. The importance of these factors has been emphasized by

Dale and Starwort [32]. In Ad 1945 Douglas [33] has given a valuable review of the

physical properties of glass.

The basic properties of glasses are:

(i) Glass is transparent but non-crystalline, a major paradox in the physics

of condensed matter.

(ii) Glass has very high resistance to water and atmospheric agencies.

(iii) Glass is electrically insulating at normal temperatures but becomes

conducting at very high temperatures.

(iv) Glass usually breaks in a direction at right angles to the direction of

maximum tensile stress.

(v) Glass is hard and yet brittle. When it cracks it shatters at the speed of

sound. It breaks suddenly when subjected to a stress exceeding its

elastic limit. Glass obeys Hooke‟s law accurately within the elastic

limit.

(vi) The coefficient of linear thermal expansion is almost constant, for

most types of glasses up to the temperature ranging 400-600 0C,

depending on the chemical constitution of the glass.

1.2.5 Glass network formers and modifies

Glasses can be prepared using different types of materials. The ability of a

substance to form a glass matrix does not depend upon any particular physical or

chemical property. It is now generally agreed that almost any substance, if cooled

sufficiently fast, could be obtained in the glassy state although in practice

crystallization intervenes in many substances.

B2O3, P2O5, SiO2, GeO2 all of which come from a certain area of the periodic table

readily form glasses on their own when their melts are cooled sufficiently fast and are

commonly known as „glass formers‟. These elements are sufficiently electro positive

to form ionic structures such as MgO and NaCl, and are not sufficiently

electronegative to form covalently bonded small molecular structures such as CO2.

Instead, bonding is usually a mixture of ionic and covalent and the structures are best

regarded as three-dimensional polymeric structures. AS2O3 and Sb2O3 produce glass

on their own when cooled very rapidly. TeO2, SeO2, MeO3, WO3, Bi2O3, Al2O3,

Ga2O3 and V2O5 will not form glasses on their own, but each will do so when melted

with a suitable quantity of certain other non-glass forming oxide. Hence they are

known as „conditional glass formers‟.

Some oxides like PbO, CaO, K2O, Na2O and Li2O produce drastic changes in the

properties (melting point, conductivity etc) of the glass network forming oxides when

added in small quantities. These oxides also modify the network structure of the glass

and hence they are termed as „network modifiers‟. Anions like halogens and oxygen

become non-bridging when they bridge two network former cations. Network

modifier cations, such as alkali, alkaline-earth and higher valance state ions are

accommodated randomly in the network in close proximity to non-bridging anions.

Glass formers, modifiers and intermediates are listed in Table 1.1. Average phonon

frequencies (ћω) of some of the network formers in glasses are given in Table1.2.

Table1.1: Glass formers, modifiers and intermediates

Glass former Modifier Intermediate

SiO2 Li2O Al2O3

GeO2 Na2O PbO

B2O3 K2O ZnO

P2O5 CaO CdO

TeO2 BaO TiO2

As2O3

As2O5

1.2.6 Differences between crystalline and amorphous solids

Basing on the atomic arrangement, solids may be broadly classified into two

categories i.e. (1) crystalline and (2) amorphous solids.

In crystalline solids both short-range and long-range order exists in the atomic

Table: 1.2 Average phonon frequencies (ћω) of some of the

network formers in glasses.

_______________________________________

Matrix ћω (cm-1

)

_______________________________________

Borate 1400

Phosphate 1200

Silicate 1100

Germanate 900

Tellurite 700

LaF3 (Crystal) 350

______________________________________

arrangements where as in amorphous solids only short-range order exists. Figure 1.1

shows the schematic representation of (a) ordered crystalline form and (b) random

network amorphous form, of the same composition.

The degree of disorder will be greater in an amorphous solid than its crystalline

counterpart. Entropy of amorphous solid is greater than that of crystalline solid.

Hence amorphous state is a non-equilibrium state. On cooling, from liquid phase to

the solid phase, a crystalline solid is obtained as a transformation from one

equilibrium state to another while amorphous solid is obtained as a transformation

from an equilibrium state to a non-equilibrium state. Amorphous materials which

melt over a range of temperature are isotropic where as crystalline materials which

have well defined melting point are anisotropic.

(a) (b)

Figure 1.1 Molecular arrangements in (a) crystal and (b) glass.

The following are the advantages of glass materials over crystalline materials in many

optical device applications.

(i) Flexibility of choosing glass composition over a wide range,

(ii) A disordered ion environment that can broaden fluorescence band width,

(iii) Uniform (isotropic) optical properties over a wide range of composition,

(iv) Ease of fabrication into complex shapes,

(v) Low fabrication cost and

(vi) Useful in producing large active lasers with good optical quality.

1.2.7 Glass transition

The transition from a viscous liquid to a solid glass is called “ glass transition” and

the corresponding temperature is known as the glass transition temperature, Tg. When

the glass is heated to a temperature above Tg, glass to viscous liquid transformation

takes place. Glass formation is due to the increase of viscosity depending on cooling

rate. Figure 1.2 represents the enthalpy–temperature characteristics for crystal, liquid

and glass. When a liquid solidifies into a crystalline state there is abrupt discontinuity

in the enthalpy at a well defined temperature called the „melting point‟, Tm , of the

material. In the case of glass formation the enthalpy of the liquid decreases at about

the same rate as in crystalline formation until there is a decrease in the expansion

coefficient in a range of temperature called „glass transformation range‟.

The liquid–glass cooling curve does not show any discontinuity. Slope of the

curve changes at Tg. Below this temperature, the glass structure does not relax at the

cooling rate used.

Fig.1.2: The effect of temperature on the enthalpy (or volume) of a glass forming

melt.

The expansion coefficient for the glassy state is usually about the same as that for

the crystalline state. Tg is a function of cooling rate and is not well defined. Slower

the rate of cooling, lower value of Tg. However, Tg cannot be lower than a particular

minimum temperature called the „ideal glass transition temperature‟, To. This can be

explained by considering the relative heat capacities and entropies of liquid and

crystalline phases of the same composition. The glass transition temperature can be

determined by differential thermal analysis (DTA) or differential scanning

calorimetry (DSC).

1.2.8 Structural features of glass

There is no single experimental technique which could produce a direct mapping

of the glass network structure due to the absence of long-range order. Hence the

elucidation of glass structure involves many different experimental and theoretical

methods. These methods yield different, often complementary, information which

can be combined to a structural model of a certain glass system.

For studying the glass structure, diffraction and spectroscopic techniques are used.

The short-range order, thereby the structural information of glasses can be obtained

by X-ray diffraction (XRD). In electron and neutron diffractions, the beam

encountering the atoms results in scattering and the structure of the order region will

be obtained. These methods lack resolution and provide the statistical average of the

spatial distribution of atoms in one-dimension. The work of Wong and Angel [28]

includes an extensive bibliography on spectroscopic studies of glasses.

Zachariasen [34] concluded that the atoms in a glass are linked together by the

same forces as in crystals. Basing on this he proposed a structure consisting of an

extended three-dimensional network made up of well defined small „structural units‟

which are linked together in a random way. According to the Zachariasen‟s rule for

the formation of the glass

(i) An oxygen atom should be linked to not more than two glass forming cations,

(ii) The number of oxygen atoms around a glass forming cation must be small,

(iii) The oxygen polyhedral share corners but not edges or faces,

(iv) In three-dimensional network, at least three corners in each polyhedral should

be occupied by anions, with cations at the centers.

The violation of any of these rules means the glass formation will be energetically

less favorable. Planar AO3 triangles are the structural units in both the cases. The

randomness of the glass phase is due to the variations of angles and distances mainly

between the structural units and to a minor extent within the structural units. The

work of Cooper [35] based on topological arguments supported Zachariasen‟s ideas.

Cooper combined Zachariasen‟s rules (iii) and (iv) and gave modified statement that

each oxygen polyhedron must be connected directly to at least three other oxygen

polyhedra. Hence, tetrahedra that share an edge and two opposite corners are no

longer excluded.

Zachariasen gave the name „network forming cations‟ for cations which form the

random network of glasses in association with oxygen. The term „network former‟ is

attributed to the oxides capable of forming glass. Oxygen ions act as bridges between

the structural units and so are called „bridging oxygens (BOs). The oxides which do

not participate in forming the glass network structure and present in the glass are

called „network modifiers‟. The three principal actions of network modifiers in

glasses for an A2O3 glass are as follows.

(i) Breaking of A-O-A bonds and creation of non-bridging oxygen,

(ii) Increasing the oxygen co-ordination of cation and

(iii) A combination of both.

The breaking of A-O-A bonds leads to the creation of non-bridging oxygen, shown

in Fig:1.3 .

Fig.1.3 Creation of non-bridging oxygens.

These oxygen ions carry a partial negative charge and are connected to the glass

network at one end only. The resulting network gets loose and by decreasing the

connectivity a larger flexibility of the structure is obtained.

1.3 RARE EARTHS

1.3.1 SIGNIFICANCE OF LANTHANIDE IONS

The rare earth ions are divided into two series of elements, the lanthanides and the

actinides. The neutral forms of these elements have an electronic configuration made

up by progressively filling the 4f electronic shells for the lanthanides and the 5f

electronic shell for the actinides. The group of elements having atomic numbers (Z)

57 to 71 are usually classified as lanthanides (Ln) and very often referred as rare

earths (REs). They were originally extracted from oxides for which ancient name was

„earth‟ and which were considered to be „rare‟ hence the name „rare earths‟. The name

„lanthanides‟ has been derived from lanthanum which is the prototype of lanthanides.

A feature common to all the elements in the lanthanide series is xenon (Z=54)

based electronic configuration with two (6s2) or three (5d

16s

2) outer electrons.

Neutral lanthanides possess the electronic configuration [Xe] 4f n 5d

m 6s

2 where n is

the number of 4f electrons ranging from 2 for cerium to 14 for ytterbium with m=0,

with an exception of zero for lanthanum, 7 for gadolinium and 14 for lutetium where

m= 1. All the lanthanide elements have common „trivalent state‟ attained by losing

three electrons, one from 5d or 4f and two from 6s orbitals. Therefore the trivalent

lanthanide ions having most stable oxidation state have xenon core electronic

configuration [Xe] 4 f n

where n is an integer varying zero for La3+

to 14 for

Lu

3+.

Table 1.3 shows the electronic configurations of lanthanide ions along with their

ground states and valences.

The filling of 4f shell can be explained by the Hund‟s rule according to which the

term with highest quantum number S has the lowest energy and if there are several

terms with same S, the one with highest angular momentum quantum number L has

the lowest energy. Furthermore, because of spin–orbit coupling, the terms 2s+1

L split

into (2s+1)

LJ levels with J= L+S, L+S-1,…,|L-S|, where for less than half- filled shells,

the term with the smallest J lies lowest in energy. The 4f electrons are effectively

shielded by the 5s and 5p electrons, Fig. 1.4.

Hence they do not play any role in chemical bonding and so the

chemical properties of the lanthanides are much alike [33]. That is why the trivalent

lanthanides are sometimes referred to as „triple positively charged noble gases‟.

Among the 4 f n

configuration, 4 f 0 (empty f-shell), 4 f

7 (half-filled f-shell) and 4 f

14

(completely filled f-shell) are the most stable ones. Therefore, besides the trivalent

state some ions also occur in divalent and tetravalent states. Examples are Ce4+

(4 f 0),

Sm2+

(4 f 6), Eu

2+ (4 f

7), Tb

4+(4 f

7) and Yb

2+ (4 f

14).

Table 1.3: The electronic configurations of lanthanides along with their

ground states and valences.

Lanthanide Atomic Neutral atom Possible Trivalent atom

element number electronic valence Electronic Ground

configuration state configuration state

Lanthanum (La) 57 [Xe] 4f0

5d1 6s

2 3 [Xe] 4f

0

1S0

Cerium (Ce) 58 [Xe] 4f2 6s

2 3, 4 [Xe] 4f

1

2F5/2

Praseodymium (Pr)59 [Xe] 4f36s

2 3 [Xe] 4f

2

3H4

Neodymium (Nd)60 [Xe] 4f4 6s

2 3 [Xe] 4f

3

4I9/2

Promethium (Pm) 61 [Xe] 4f5 6s

2 3 [Xe] 4f

4

5I4

Samarium (Sm) 62 [Xe] 4f6 6s

2 2, 3 [Xe] 4f

5

6H5/2

Europium (Eu) 63 [Xe] 4f7 6s

2 2, 3 [Xe] 4f

6

7F0

Gadolinium (Gd) 64 [Xe] 4f7 5d

1 6s

2 3 [Xe] 4f

7

8S7/2

Terbium (Tb) 65 [Xe] 4f9 6s

2 3, 4 [Xe] 4f

8

7F6

Dysprosium (Dy) 66 [Xe] 4f10

6s2 3 [Xe] 4f

9

6H15/2

Holmium (Ho) 67 [Xe] 4f11

6s2 3 [Xe] 4f

10

5I8

Erbium (Er) 68 [Xe] 4f12

6s2 3 [Xe] 4f

11

4I15/2

Thulium (Tm) 69 [Xe] 4f13

6s2 3 [Xe] 4f

12

3H6

Ytterbium (Yb) 70 [Xe] 4f14

6s2 2, 3 [Xe] 4f

13

2F7/2

Lutetium (Lu) 71 [Xe] 4f14

5d1 6s

2 3 [Xe] 4f

14

1S0

Fig. 1.4. Approximate charge distributions of electrons in different orbitals for

Ln3+

ions demonstrating the shielding of unpaired 4f electrons

by outer filled 5s2 and 5p

6 shell electrons.

Lanthanide group ions differ in the number of electrons in the 4f shell. The

ground state electronic configuration is 4 f n

and the first excited state configuration is

4 f n-1

5d. The relative location and energy extent of these two configurations for the

rare earth ions (RE 3+

) are shown in Fig. 1.4. Due to the shielding of 4f orbitals by the

filled in 5s2

5p6

orbitals, the 4f electrons are only weakly perturbed by the charge of

the surround ligands. The spectra of RE compounds are sharp and similar to the

atomic spectra. Shielding effect also causes the unique optical properties of RE ions

[36]. John Hopkins group, under the direction of Dieke [37], generated the complete

set of energy level assignments for all RE3+

ions in an hydrous tri chlorides.

1.3.2 Free-ion crystal-field levels

An ion isolated from any interactions with its environment is known as free-ion

and its electronic energy levels are determined by the coulomb interaction between

each electron and the nucleus of the ion. The coulomb exchange and the spin-orbit

interactions among all the 4f electrons produce the multiple terms denoted by 2s+1

LJ

known as Russell-Saunders coupling. Since the free-ion is in a physical environment

having completely spherical symmetry, these interactions determine both the radial

extent and the shape of the orbital with both the energy and angular momentum being

quantized. The results of these considerations provide a set of electronic states with

significant amount of degeneracy.

Applying any type of external perturbations to this system that has a specific

spatial symmetry (electric field, magnetic field, uniaxial stress etc) can lift some of

the degeneracy, resulting in a splitting of the free-ion energy levels. The cumulative

effects of the lattice charges in the surrounding of the ion cause a perturbation that

splits the ionic energy levels into sub levels. By splitting, it is meant that the (2J+1)

fold degeneracy is partially removed which is the well known „Stark effect‟. The

perturbation that causes the splitting is an electrostatic field known as the „crystal–

field (CF)‟. Hence the multiplet terms denoted by 2S+1

LJ split into fine structure by

the strength of CF and the symmetry of the site accommodating the Ln3+

ion. The

thirty two crystallographic point groups can be divided into four general symmetry

classes as follows:

(i) Cubic: Oh, O, Td, Th, T

(ii) Hexagonal:D6h, D6, C6v, C6h, C6, D3h, C3h, D3d, D3, C3v, S6, C3

(iii)Tetragonal: D4h, D4, C4v, C4, D2d, S4

(iv)Lower symmetry: D2h, D2. C2v, C2h, C2, Cs, S2, C1

As the interaction between the 4f n

electrons and the crystal- field is low, only a

small splitting of the order of a few hundred cm-1

occurs as shown in Fig.1.5.

__________________________________________________________________

2S+1

L J(µ)

2S+1

LJ

2S+1

L 102 cm

-1

103 cm

-1

fn

104 cm

-1

SPIN-ORBIT CRYSTAL-

COULOMB FIELD

Fig. 1.5 . Schematic diagram of the splitting of RE3+

energy levels due to the

coulomb, spin-orbit and crystal-field interactions.

However, in reality, general ligand field theory gives a more accurate picture.

According to this theory, covalent bonding plays an additional role since the electrons

of the ion are partially shared with the surrounding ions or ligands. The shielding of

4f electrons reduces this effect. Ligand field theory is more appropriate to systems of

transition metal ions, which are not shielded from the surrounding environment.

Therefore CF theory is a more accurate approximation when applied to Ln3+

ions.

If the above suppositions are correct then the fact that transitions between 4f Stark

levels are forbidden for electric-dipole (ed) radiation by the parity selection rule,

which states that ed transition can only occur between levels of opposite parity. There

must be a mechanism that changes the parity of some of the levels. According to Van

Vleck [38] the CF, apart from splitting the energy levels by removing the (2J+1)

degeneracy could also mix higher configurations, such as 4 f n-1

5d, that make some of

the transitions allowed. It should be noted that the magnetic-dipole (md) transitions do

not violate the parity selection rule i.e. they can occur between the states of same

parity.

From combinational theory, the number of possible states for any given atom can

be calculated from [39, 40]

Ck

f =Ck14 =

𝟏𝟒!

𝐧! (𝟏𝟒−𝐧) …(1.1)

where n is the number of electrons present in a particular valence state of the specific

Ln3+

ion. Table 1.4 gives details of number of degeneracy states which arise from the

4f n

configuration.

The ionic radii of the Ln3+

ions are shown in Fig. 1.6 [41]. The large radii

mean that the charge to radius ratio (ionic potential) is relatively low which results in

a very low polarizing ability. This reflects the predominant ionic character of the

metal-ligand bonds and the co-ordination number of the Ln complexes.

Table 1.4: Degeneracy of 4 f n

configurations (The numbers shown in parentheses for 2S+1

𝑳 terms indicate the number of times that

particular term repeats.)

Configurations Ln3+ Terms(2S+1 L) Number of Number of Maximum number of

Terms J levels 2S+1LJ Crystal- Field Levels

f1, f13 Ce3+, Yb3+ 2F 1 2 14

f2, f12 Pr3+, Tm3+ 1SDGI 3PFH 7 13 91

f3,f11 Nd3+,Er3+ 2PD(2)F(2)G(2)H(2)IKL 4SDFGI 17 41 364/2

f4,f10 Pm3+,Ho3+ 1S(2)D(4)FG(4)H(2)I(3)K(2)LN 5SDFGI 3P(3)D(2)F(4)G(3)H(4)I(2)K(2)LM 47 107 1001

f5, f9 Sm3+, Dy3+ 2P(4)D(5)F(7)G(6)H(7)I(5)K(5)L(3)M(2)NO6PFH 4SP(2)D(3)F(4)G(4)H(3)I(3)K(2)LM 73 198 2002/2

f6,f8 Eu3+, Tb3+ 1S(4)PD(6)F(4)G(8)H(4)I(7)K(3)L(4)M(2)N(2)Q 3P(6)DF(9)G(7)H(9)I(6)K(6)L(3)M(3)NO 119 295 3003

5SPD(3)F(2)G(3)H(2)I(2)KL 7F

f7 Gd3+ 2S(2)P(5)D(7)F(10)G(10)H(9)I(9)K(7)L(5)M(4)N(2)OQ 4S(2)PD(2)F(6)G(5)H(7)I(5)K(5)L(3)MN 119 327 432/2

6PDFGHI 8S

Fig. 1.7 shows the Dieke diagram which gives the energy level structure of the multiplets of

the Ln3+

ions [37]. Because of the shielding effect of the outer shell electrons, these energy levels

change only slightly from host to host.

Fig.1.6. Ionic radius of trivalent lanthanides ions

1.3.3 Characteristics of the lanthanide ions

The Lanthanides exhibit a number of features in their chemistry which differentiate them

from the d-block metals. The reactivity of the elements is greater than that of the transition

metals, similar to the Group II metals.

Fig. 1.7. Dieke diagram (energy levels of free RE3+

ions up to 42000 cm−1

).

The following are the characteristics of lanthanides.

1. Lanthanides are relatively soft metals. Their hardness slightly increases with atomic

number,

2. They have wide range of co-ordination numbers (generally 6-12, but numbers of 2,3 or 4

are also known),

3. Co-ordination geometries are determined by ligand steric factors rather than CF effects,

4. Unless complex agents are present, insoluble hydroxides precipitate at neutral pH,

5. They do not form multiple bonds like Ln = O or Ln ≡ N, known for many transition

metals and certain actinides,

6. They possess high melting and boiling points and they act as strong reducing agents,

7. Except La3+

and Lu3+

, lanthanide compounds are strongly paramagnetic,

8. The f→f transitions have small homogeneous line widths,

9. Due to well shielding of 5s2

and 5p6

orbitals, their spectroscopic and magnetic properties

are almost uninfluenced by the ligand field,

10. They have small CF splitting and very sharp electronic spectra in comparison with the d-

block metals,

11. There are many possible three and four level lasing schemes as the electronic states of the

ground 4 f n configuration provide rich optical energy level structure and

12. There are several excited states suitable for optical pumping. These excited states decay

nonradiatively to meta stable states having high radiative quantum efficiencies.

1.3.4 Color of the rare earth ions

Due to the internal transitions of 4f electrons occurring in the visible region of the spectrum,

the RE3+

ions have their characteristic colors. Main- Smith [42] tried to correlate the color

sequence in rare earth series with the 4f electronic configuration of the RE3+

ions. Table1.5 gives

similarity between the ions having 4 f n

and 4f 14-n

configurations. However, the non tri- positive

ions show wide divergence in color compared to the iso -electronic tri-positive ones. Thus the

colors of the non tri-positive rare earth ions are : Ce4+

(4f 0) - orange, Sm

2+ (4 f

6)- reddish brown,

Eu2+

(4 f 7)- straw yellow and Yb

2+ (4 f

14)- green.

Table: 1.5 Color sequence of the RE3+

ions

4fn

color 4f14-n

La (4f0) → Colorless ← Lu(4f

14)

Ce(4f1) → Colorless ← Yb(4f

13)

Pr (4f2) → Green ← Tm (4f

12)

Nd (4f3) → Pink ← Er (4f

11)

Pm (4f4) → Orange ← Ho (4f

10)

Sm (4f5) → Yellow ← Dy (4f

9)

Eu (4f6) → Pale Pink ← Tb (4f

8)

Gd(4f7) → Colorless

__________________________________________

1.3.5 General properties of rare earth ions

The following are the general properties of the rare earth ions.

(i) Rare earths are silvery-white metals which tarnish when exposed to air,

(ii) They possess high melting and boiling points,

(iii) They can burn easily in air,

(iv) They are relatively soft,

(iv) Their hardness slightly increases with increase in atomic number,

(v) Their compounds are generally ionic,

(vi) They are strong reducing agents and

(vii) They react with water to liberate hydrogen (H2) slowly in cold and quickly upon

heating.

1.3.6 Optical properties of rare earth ions

RE3+

ions are favorable candidates for luminescent device fabrication due to the following

optical properties.

(i) Luminescence of RE3+

ion spreads in various spectral ranges,

(ii) They have long emission lifetimes,

(iii) They have small homogeneous line widths,

(iv) They possess high refraction with relatively low dispersion and

(v) There are several excited states suitable for optical pumping.

1.3.7 Applications of rare earth ions in glasses

The following are some of the scientific and technological applications of RE3+

doped glasses.

(i) Communication fibers and glass lasers,

(ii) LED and color television phosphors,

(iii) Optical glasses, filters and lenses,

(iv) Light sensitive and photo chromic glasses,

(v) Coloring and discoloring agents,

(vi) Glass polishing agents,

(vii) pH Electrodes and

(viii) X-ray and γ-ray absorbing glasses.

1.4 SPECTROSCOPIC INVESTIGATIONS OF RARE EARTH IONS.

Optical absorption and fluorescence spectroscopy are the important techniques in the study of

Ln3+

doped systems because they allow the determination of natural frequencies of Ln3+

ions.

The 4f →4f transitions are very sharp due to very effective shielding of the 4f electrons by the

filledin 5s and 5p shells having higher energies than the 4f shell [41, 43, 44].

1.4.1 Absorption spectrum

The 4f electronic orbitals in Ln3+

ions are incompletely filled. So the ions absorb

electromagnetic radiation in the spectral regions of ultraviolet, visible and the near-infrared [41].

The intra–4f n

transitions, the inter- 4f n→

4f

n-1 5d

1 transitions or charge transfer transitions occur

in these regions. Also it is possible to correlate the positions of these 4f→5d transitions with the

standard (III-II) and (IV-III) reduction potentials for the lanthanides [45,46]. An easily oxidized

ligand is bound to Ln3+

ion, which can be reduced to the divalent state or when the ligand is

bound to one of the tetravalent ions then charge transfer bands result [47]. The standard

lanthanide (III-II) and (IV-III) reduction potentials have also been correlated with the energy of

the first charge transfer band [45,46]. The electrostatic interaction yields 2s+1

L terms with

separation of the order of 104

cm-1

. The spin-orbit interaction then splits these terms into J states

with typical splitting of 103 cm

-1. Finally the „J’ degeneracy of the free-ion state is partially or

fully removed by the crystalline electric field. The magnitude of the crystal field splitting

usually extends over several hundred cm-1

. In glasses the amount of splitting is of the order of

magnitude of the inhomogeneous broadening as a result of multiplicity of RE3+

ion sites.

The intra-4f n transitions are the most useful transitions in the spectra of the Ln complexes

[48]. These transitions are formally Laporte-forbidden and as a result tend to be very weak. In

addition to this the transitions that do not occur within the ground multiplet may be spin-

forbidden. Because of the shielding of the 4f electrons, the transitions that are observed are very

sharp and line like. These spectra are quite different from those of the d-transition elements.

This can be explained by examining the magnitude of the perturbations acting on the two types

of electrons [49].

In d-transition metal complexes

Inter electronic repulsions ≈ crystal–field >>spin-orbit coupling > thermal energy

In f-transition metal complexes

Inter electronic repulsions >> spin – orbit coupling > crystal–field ≈ thermal energy

This order means that the CF in the lanthanides is acting to remove some of the degeneracy

contained in the individual values of the J quantum number. This additional splitting is generally

in the order of 200 wave numbers whereas in the d-transition elements it is in the order of 10-30

thousand wave numbers.

In comparison of the spectrum of a complex Ln3+

ion with that of aquo ion three effects are

observed: (1) there are small changes usually toward longer wave lengths,(2) the bands undergo

additional (or at least different) splitting and (3) there is a significant change in the molar

absorptivity of the individual bands. These are due to the changes in the strength and symmetry

of the CF produced by the ligands. The shifts in the barycenters of the peaks in the spectra of Ln

complexes relative to the aquo–ion are caused by what has been termed as the „Nephelauxetic

effect‟ by Jorgensens [50]. These are related to the decrease in the inter-electronic repulsion

parameters in the complex. Numerous attempts have been made to relate this effect to weak

covalence effects.

Optical properties of RE3+

ions in a solid matrix are affected by changes in the environment of

the Ln3+

ion and its interaction with ligands. According to the Judd-Ofelt (JO) theory [51,52]

intensities of a set of absorption lines for a particular Ln3+

ion in any matrix is characterized by

three intensity parameters Ωλ (λ=2, 4 and 6) which depend on the symmetry of CF at the RE3+

site and the strength of covalence of the RE ion-ligand bond. Therefore it is of interest to study

the variation of these intensity parameters with the host glass composition. From these

parameters, several important optical properties such as radiative transition probabilities,

radiative life times (τR) of the excited states and branching ratios can be estimated [53, 54].

1.4.2 Fluorescence spectrum

The fluorescence spectrum can be analyzed by essentially the same procedure as for the

absorption spectrum except that the nature of the emission process will generally yield additional

information concerning the ground multiplet of the ion. When photons of electromagnetic

radiation are used for exciting the molecule, atom or ion then the emission of electromagnetic

radiation takes place while the molecule, atom or ion return to its normal level from excited level

and may result in fluorescence. Fluorescence involves optical transition between electronic states

which is the characteristic of the radiating substance. Depending upon the type of fluorescing

ion and its environment the radiation life time of the excited electronic states varies from 10-10

to

10-1

s. In the case of RE3+

ions the most striking feature of the fluorescent emission is that it

occurs in the spectral region where the crystal or glass is non-absorbing.

RE3+

ions act as very good fluorescing centers in a matrix. The fluorescence of an active

RE3+

ion is influenced by the asymmetry of the surrounding binding forces. The parameters

position (λp) intensity full width at half maximum of the emission band (∆λp) and the life time

(τR) of the fluorescing state are affected by the structure of the solid matrix. The stimulated

emission cross-section, σ(λp), one of the important parameters which determine laser

characteristics of a given transition of RE3+

ion, can be evaluated from the emission studies. The

experimental branching ratios, (βR), equal to the relative intensities of the emission bands of the

transitions with same ground level, can also be evaluated from the emission studies. All these

parameters are used to compare the theoretical branching ratios predicted from the JO theory

[51, 52]. For a given RE3+

ion, all these parameters can be varied over a wide range by changing

the composition of the material.

1.5 THEORITICAL MODELS

When a 4f ion is embedded in a solid matrix, the effect of ligand environment is minimum on

the 4f shell due to its effective shielding by the closed 5s and 5p shells. This weak perturbation

is responsible for the rich electronic spectra which provide detailed fingerprint information about

the surrounding arrangement of atoms and their interactions with the 4f electrons. Hence, it is

the prime task to evaluate the electronic energy level structure of RE3+

ions in any given solid

matrix to understand their fluorescence properties.

1.5.1 ELECTRONIC ENERGY LEVEL ANALYSIS- Hamiltonian model

The Eigen states of a system are described in terms of the wave functions of the different

electron orbitals. The energy levels of the electronic states can be found by calculating the

matrix elements of Hamiltonian between the eigen states of the system. The three types of

physical interactions described by the Hamiltonian have different magnitudes. The energy levels

of the electronic states can be found in successive steps using the techniques of perturbation

theory. The wave functions for the electronic states of the ion can be approximated by linear

combinations of products of single-electron wave functions. The physical condition is enforced

mathematically by constructing a wave function that is anti symmetric with respect to an

interchange of the electrons in two orbitals since the electrons obey Fermi-Dirac statistics and

thus must obey Pauli exclusion principle. If two of the spin-orbitals are identical the wave

function vanishes due to anti symmetry.

1.5.1.1 Free-ion Hamiltonian

In any host matrix, each interaction experienced by the Ln3+

ion can be described with the aid

of effective operators and their effect can be parameterized by using phenomenological models

[44,55,56]. The effective Hamiltonian for free-ion (HFI) is given by

Ĥ= EAVG + ∑k F

k fk + 𝜉4f Aso+ 𝛼 L(L+1)+ 𝛽 G(G2)+ 𝛾 G(R7)+ ∑iT

i ti+ ∑kP

k pk+ ∑jM

jmj

…(1.2

)

where k=2,4,6; i=2,3,4,6,7,8 and j=0,2,4. The free-ion Hamiltonian includes two body

electrostatic interactions (Fk), spin-orbit interaction (𝜉4f), two body configuration interactions

(𝛼, 𝛽, 𝛾 ), three body configuration interactions (Ti), electrostatically correlated spin-orbit

interaction (Pk) and spin-other orbit interaction(M

j). The energy of the entire configuration is

shifted by the parameter EAVG [57]. The Slater integral, Fk (k=2,4 and 6), describes the

coulombic interaction between the 4f electrons. Standard least-square methods can be used in a

semi empirical fitting approach to the 4f n

electronic energy levels structure. The quality of the fit

is estimated by rms (root-mean-square) deviation given by [58]

σrms= (𝑬𝒊

𝒆𝒙𝒑−𝑬𝒊

𝒄𝒂𝒍)𝟐𝒏𝒊=𝟏

𝒏

…(1.3)

where 𝑬𝒊𝒆𝒙𝒑

and 𝑬𝒊𝒄𝒂𝒍 are experimental and calculated energies for level i respectively and n is

the total number of energy levels considered.

1.5.1.2 Crystal-field Hamiltonian

The Ln3+

ion present in a solid matrix experiences an inhomogeneous electrostatic field

produced by the surrounding charges. The crystal field Hamiltonian, ĤCF, is expressed in

Wybourne‟s notation [55] as

ĤCF= 𝑘 𝐵𝑞𝑘𝐶𝑞

𝑘𝑞 …(1.4)

where 𝑩𝒒𝒌 =(-1)

q (𝑩𝒒

𝒌 − 𝒊𝑺𝒒𝒌 ) are the coefficients representing the functions of the radial

distances which can be varied in order to match experimental and calculated CF levels. The 𝑪𝒒(𝒌)

are the tensor operators of rank „k‟ closely related to the spherical harmonics that can be obtained

exactly [41, 55]. By the symmetry selection rules for the point symmetry at the Ln3+

ion site, the

number of HCF parameters is greatly reduced. Any surrounding that breaks the spherical

symmetry of the free ion can lead to shift and splitting of the energy levels. Hence these

conditions apply to glass materials also. The Hamiltonian for a multi electron atom is given by

Ĥ = ĤFI + ĤCF …(1.5)

where ĤFI represents the isotropic parts of Ĥ and ĤCF represents non-spherically symmetric

components of the crystal field with even parity.

1.5.2. Intraconfigurational f - f transitions

Generally transitions in the absorption spectra of Ln3+

ions are of the forced electric-dipole

type. The transitions gather intensity by mixing in states having opposite parity although

formally Laporte-forbidden. In a few cases, particularly in Eu3+

, magnetic-dipole transitions with

selection rule |∆J|= 0, ±1 but not 0↔0 have been observed. The md character has been confirmed

from the polarization properties. The spin selection rule is relaxed by spin-orbit coupling and so

the transitions that are md in origin are generally at least an order of magnitude weaker than

those that are ed in origin [59].

1.5.2.1. Induced electric–dipole transitions

An ed transition is the consequence of the interaction of the optically active ion with the

electric field vector through an ed. Such a transition has odd parity. This type of

intraconfigurational ed transitions are forbidden by the Laporte selection rule. Non-

centrosymmetrical interactions allow the mixing of electronic states of opposite parity giving

rise to weaker transitions and are called as induced ed transitions which are much weaker than

the ordinary ed transitions. The selection rules for the induced ed transitions are ∆l = ± 1, ∆τ =

0, ∆S=0, |∆L|≤ 6, |∆J|≤6, |∆J|=2,4,6 if J=0 or J’ =0.

1.5.2.2 Magnetic – dipole transitions

A md transition is caused by interaction of the spectrally active ion with the magnetic field

component of the light through an md. The intensity of the induced md transitions are weaker

than ed transitions. An md transition has even parity and allows transitions between the states of

equal parity (intraconfigurational transitions). Selection rules are given by ∆τ= ∆S =∆L= 0, ∆J=

0, ±1 but 0 ↔ 0 is forbidden.

1.5.2.3 Electric-quadrupole transitions

An electric-quadrupole transition arises from the displacement of charge with quadrupolar

nature. An electric-quadrupole has even parity. Electric–quadrupole transitions are much weaker

than induced ed and md transitions. So far, no experimental evidence exists for the occurrence of

quadrupole transitions in Ln3+

spectra. However, hypersensitive transitions are considered

as pseudo-quadrupole transitions because these transitions obey the selection rules of quadrupole

transitions (|∆S|=0, |∆L|= < 2 and |∆J|= < 2).

1.5.2.4 Hypersensitive transitions

The intensities of a few of the induced ed transitions in RE3+

ions are very sensitive to the

environment. These are called „hypersensitive transitions‟ and obey the selection rules of

quadrupole transitions, |∆S|=0, |∆L| < 2 and |∆J| < 2. In almost all RE3+

ions hypersensitive

transitions have been observed and are given in Table 1.6. The possible mechanism for the

occurrence of hypersensitivity was given by Jorgensen and Judd [60]. They argued that the

inhomogenety in the dielectric medium surrounding the RE3+

ion could enhance the intensity of

the hypersensitive transitions.

1.5.3 Intensity analysis of optical spectra

1.5.3.1 properties of spectral lines – Oscillator strengths

The properties of radiative transitions are manifested in absorption and emission

spectroscopy. The strength of a spectral line is characterized by a dimensionless parameter

called „oscillator strength‟ or „f number‟. The concept of oscillator strength was first introduced

by Ladenburg [61]. The ratio of the actual intensity to the intensity radiated by an electron

oscillating harmonically in three dimensions gives the oscillator strength of a transition. The

oscillator strength of an absorption transition (ƒexp) is directly proportional to the area under the

absorption curve and is given by [62, 63]

exp= 𝟐.𝟑𝟎𝟑𝒎𝒄𝟐

𝑵𝝅𝒆𝟐 𝜺(𝝊)𝒅𝝊 = 𝟒. 𝟑𝟏𝟖 ⤬ 𝟏𝟎−𝟗 𝜺(𝝊)𝒅𝝊 …(1.6)

where 𝑚 and 𝑒 are the mass and charge of an electron, c is the velocity of light, N is the

Avogadro‟s number, 𝜀(𝜐) is the molar absorptivity of a band at a wave number 𝜐 (cm-1

). The

integral value in the above equation corresponds to the area under the absorption curve. The

value of oscillator strength is obtained in cgs units.

The molar absorption coefficient 𝜺(𝝊) at a given energy 𝝊 (cm-1

) is obtained from Beer-

Lambert‟s law:

𝜺(𝝊)= (1/C𝒍) log (I0/I) …(1.7)

where C is the concentration of Ln3+

ions in mol/lit, 𝑙 is the optical path in the absorbing medium

and log (I0/I) is the absorptivity or optical density (OD) . The order of oscillator strengths of

magnetic and induced ed transitions is 10-6

.

The shape of the spectral line is also important in addition to the strength of a transition. The

sum of the initial and final energy levels of transitions determines the shape of the spectral line.

Lorentzian, Gaussian and Voigt are the three types of line shapes. The physical process that has

the same probability of occurrence for all atoms of the system produces a Lorentz line shape and

is known as homogeneous broadening. Lorentzian broadening is also known as lifetime

broadening because of the shortened lifetimes of the energy levels involved in the transition.

This type is associated with the Heisenberg uncertainty relationship relating time and energy.

This contribution is referred to as the natural line width for a transition. The process that has a

random distribution of occurrence for each atom produces a Gaussian line shape and is known as

inhomogeneous broadening. The line shape is called as Voigt profile when both the broadening

processes are present.

In determining laser characteristics the difference between Lorentzian and Gaussian line

shapes are important. In Lorentzian shapes all of the ions participate in laser emission at a

specific frequency and so single longitudinal mode operation can be obtained. In Gaussian line

shapes, several subsets of ions may laze simultaneously and so multimode operation will take

place. „Spectral hole burning‟ is exhibited by inhomogeneous broadened lines and „spatial hole

burning‟ is exhibited by homogeneouly broadened lines. The broadening line magnitude

generally depends on concentration of ions and temperature.

1.5.3.2 Mixed electric- and magnetic- dipole line strengths

The majority of 4f n

intraconfigurational transitions are induced ed type. There are certain

transitions which are neither pure electric-dipole nor pure magnetic-dipole. They contain major

„ed‟ contribution and partial „md‟ contribution [53]. The „ed‟ and „md‟ oscillator strengths are to

be calculated separately. The line strength of the electric-dipole transition can be obtained from

the expression [63-65]

𝑆𝑒𝑑 (𝛹𝐽, 𝛹′𝐽′) = 𝑒2 𝛺𝜆𝜆=2,4,6 𝛹𝐽 𝑈𝜆 𝛹′ 𝐽′ 2 …(1.8)

where Judd-Ofelt parameters 𝜴𝝀 ( 𝛌 = 𝟐, 𝟒 𝐚𝐧𝐝 𝟔) represent the square of the charge

displacement due to induced ed transition and are host dependent. The host independent doubly

reduced matrix elements 𝑼(𝝀) 𝟐 are evaluated in the intermediate coupling approximation for

the transition 𝜳𝑱 ⟶ 𝜳′𝑱′ [66].

𝑆𝑚𝑑 𝛹𝐽, 𝛹′ 𝐽′ =𝑒2ℎ2

16𝜋2𝑚2𝑐2 𝛹𝐽 (𝐿 + 2𝑆) 𝛹′𝐽′ 2 …(1.9)

The non-zero matrix elements will be those of the diagonal in the quantum numbers 𝛼, 𝑆 and 𝐿.

The selection rule ∆J= 0, 1 gives three different cases for the magnetic dipole elements. (i)

𝑱′ = 𝑱

𝜳𝑱 (𝑳 + 𝟐𝑺) 𝜳′𝑱′ = 𝒈[ 𝑱 𝑱 + 𝟏 𝟐𝑱 + 𝟏 ] 𝟏/𝟐 …(1.10)

where the Lande‟s factor 𝑔 is given by

𝒈 = 𝟏 +𝑱 𝑱+𝟏 +𝑺 𝑺+𝟏 −𝑳(𝑳+𝟏)

𝟐𝑱(𝑱+𝟏) …(1.11)

The effective magnetic momentum of an atom or an electron in which the orbital (𝐿) and

spin(𝑆) angular momenta combine to give total angular momentum( 𝐽) is given by the Lende‟s

factor.

(ii) 𝑱′ = 𝑱 − 𝟏

𝛹𝐽 (𝐿 + 2𝑆) 𝛹′𝐽′ = 1

4𝐽 𝑆 + 𝐿 + 𝐽 + 1 𝑆 + 𝐿 + 𝐽 − 1 𝐽 + 𝑆 − 𝐿 (𝐽 + 𝐿 − 𝑆)

1/2

…(1.12)

(iii) 𝑱′ = 𝑱 + 𝟏

𝜳𝑱 (𝑳 + 𝟐𝑺) 𝜳′𝑱′ = 𝟏

𝟒 𝑱+𝟏 𝑺 + 𝑳 + 𝑱 + 𝟐 𝑺 + 𝑱 + 𝟏 − 𝑳 𝑳 + 𝑱 + 𝟏 − 𝑺 (𝑺 + 𝑳 − 𝑱)

𝟏/𝟐

…(1.13)

Before computation of the magnetic dipole contribution the matrix elements must be transformed

into the intermediate coupling scheme.

1.5.3.3 Judd-Ofelt theory

Judd and Ofelt independently derived expressions for the oscillator strengths of induced

electric dipole transitions of ƒ𝒏 configurations [51,52]. Since their results were similar and

published simultaneously this theory is known as Judd-Ofelt theory. According to J-O theory the

intensity of the forbidden ƒ − ƒ electric dipole transitions can arise from the admixture of

configurations of opposite parity (e.g., 4ƒ𝒏−𝟏𝒏′𝒅′ and 4ƒ𝒏−𝟏𝒏′𝒈′) into the 𝟒ƒ𝒏 configuration. It

was considered that the odd part of the crystal- field potential is the perturbation for mixing

states of different parity into the 𝟒ƒ𝒏 configuration. The experimental oscillator strength is given

by [15, 39, 51, 64, 67]

ƒ𝒆𝒙𝒑 = ƒ𝒆𝒅 + ƒ𝒎𝒅 …(1.14)

The total oscillator strength of an absorption band is obtained from the expression

ƒ𝒆𝒙𝒑 𝜳𝑱, 𝜳′𝑱′ =𝟖𝝅𝟐𝒎𝝂

𝟑𝒉(𝟐𝑱+𝟏)

(𝒏𝟐+𝟐)𝟐

𝟗𝒏𝑺𝒆𝒅 𝜳𝑱, 𝜳′𝑱′ + 𝒏𝟑 𝑺𝒎𝒅(𝜳𝑱, 𝜳′𝑱′) …(1.15)

where n is the refractive index of the medium, m is the electron mass, 𝝂 is the wave number of

the transition in cm-1

, h is the Plank‟s constant, (2J+1) is the degeneracy of the ground state

2S+1LJ,

(𝒏𝟐+𝟐)𝟐

𝟗 is the Lorentz local field correction which accounts for dipole-dipole correction.

The intensities of the magnetic dipole transitions which are weak are relatively independent of

the surrounding Ln ions. Therefore the experimental oscillator strengths are almost equal to the

electric dipole oscillator strengths.

ƒ𝒆𝒙𝒑 = ƒ𝒆𝒅 …(1.16)

Hence the experimental oscillator strengths can be equated to the calculated oscillator strengths.

ƒ𝒆𝒙𝒑 𝜳𝑱, 𝜳′𝑱′ = ƒ𝒄𝒂𝒍 𝜳𝑱, 𝜳′𝑱′ = 𝟖𝝅𝟐𝒎𝝂

𝟑𝒉(𝟐𝑱+𝟏)

(𝒏𝟐+𝟐)𝟐

𝟗𝒏𝑺𝒆𝒅 𝜳𝑱, 𝜳′𝑱′ …(1.17)

The experimental oscillator strengths are evaluated from the obtained spectra and used to find the

J-O intensity parameters Ωλ (𝛌 = 𝟐, 𝟒 𝐚𝐧𝐝 𝟔) by least square fit. The quality of the fit is

determined by the rms deviations between the measured and calculated oscillator strengths.

The intensity of ƒ − ƒ transitions in rare earth complexes is ligand dependent. Hence many

authors tried to correlate the intensity parameters with the chemical nature of ion-ligand bond,

with the properties of the ligand itself or with the structure of the complex. According to Zahir,

Ω2 depends on the asymmetry of the rare earth ligand field [3,15,68,69]. Oomen and van Dogen

suggested that Ω2 depends on the short-range effects i.e., the covalency of the ligand field. It

depends on the structural changes in the vicinity of the lanthanide ion [70]. 𝛀𝟒 and Ω6 follow

the same trend and mainly depend upon long-range effects. These parameters are related to the

bulk properties of the host material and the indicators of viscosity of the rare earth doped glasses

[15, 17, 19, 20]. For the first time Kaminski et al.[71] introduced the parameter, spectroscopic

quality factor (𝝌) ,which is useful for predicting the stimulated emission in any laser active

medium and is given by

𝝌 = 𝜴𝟒

𝜴𝟔 …(1.18)

1.5.4 Radiative properties

The radiative properties of excited states of RE3+

ion are predicted by the J-O parameters

using refractive index. For the transition 𝜳𝑱 ⟶ 𝜳′𝑱′ the radiative transition probability can be

obtained from the equation [54, 63,72, 73]

𝑨𝑹 𝜳𝑱, 𝜳′𝑱′ =𝟔𝟒𝝅𝟒𝝂𝟑

𝟑𝒉(𝟐𝑱+𝟏) 𝒏(𝒏𝟐+𝟐)𝟐

𝟗𝑺𝒆𝒅 𝜳𝑱, 𝜳′𝑱′ + 𝒏𝟑𝑺𝒎𝒅(𝜳𝑱, 𝜳′𝑱′) …(1.19)

The total radiative transition probability is given by

𝑨𝑻 𝜳𝑱 = 𝑨𝑹 𝜳𝑱, 𝜳′𝑱′ 𝜳′ 𝑱′

…(1.20)

The radiative lifetime of an excited state is obtained from the expression

𝛕𝑹 𝜳𝑱 = 𝛕𝒄𝒂𝒍 𝜳𝑱 =𝟏

𝑨𝑻 𝜳𝑱 …(1.21)

Strong emission probabilities and more number of transitions from an energy level result

shorter lifetimes due to faster decay. The difference between the predicted and experimental

lifetimes is due to the non-radiative process (WNR) either by multiphonon relaxation rate (WMPR)

or energy transfer rate (WET). The quantum efficiency can be estimated from the expression

η=𝛕𝒎

𝛕𝑹=

𝑨𝑹

𝑨𝑹+𝑾𝑵𝑹 …(1.22)

The experimental branching ratios are obtained from the relative areas of the emission bands.

The branching ratios corresponding to the emission from an excited level 𝛹𝐽 to its lower level

𝜳′𝑱′ is given by [74-76]

𝛃𝑹 𝜳𝑱, 𝜳′𝑱′ =𝑨𝑹 𝜳𝑱,𝜳′ 𝑱′

𝑨𝑻 𝜳𝑱 …(1.23)

The peak stimulated emission cross-section, σp 𝜳𝑱, 𝜳′𝑱′ between the states 𝜳𝑱 𝐚𝐧𝐝 𝜳′𝑱′

can be obtained from the equation

σp 𝜳𝑱, 𝜳′𝑱′ =𝛌𝑷𝟒

𝟖𝝅𝒄𝒏𝟐∆𝝀𝒆𝒇𝒇𝑨𝑹 𝜳𝑱, 𝜳′𝑱′ …(1.24)

where λP peak wave length of the transition and ∆𝝀𝒆𝒇𝒇 is its effective line width. The large values

of stimulated emission cross-sections indicate the good lasing transitions.

1.5.5. Excited State Decay

The study of excitation and relaxation of RE ions due to intra 4f electronic transitions gives a

deeper insight into mechanisms involved in excitation. Fig.1.8 shows a typical time-resolved

intensity spectrum. The curve is described by integral solutions to appropriate rate equations

which account for the possible excitation and de-excitation mechanism. An excited RE3+

ion

may relax to the initial ground state through radiative transition, phonon emission, by

transferring its excess energy to a nearby RE3+

ion or by a combination.

The fluorescence decay curves can be fitted to a single exponential function at very low

concentrations of doped ions, where the interaction between the RE3+

ions is negligible. A

perfect single exponential decay indicates that the energy transfer between luminescent ions is

not dominant and the lifetime of the excited level can be simply determined by finding the first

e-folding times.

Fig.1.8: A typical time-resolved excitation and de-excitation curve of RE3+

ions.

The fluorescence intensity as a function of time is given by

𝑰 𝒕 = 𝑰𝒐 𝒆−𝒕/𝛕 …(1.25)

where 𝑰𝒐 is the fluorescence intensity when t=o or τ represents the lifetime of the excited state

and is reciprocal to the probability of a spontaneous emission from the excited state to the ground

state. A logarithmic plot of the intensity versus time helps to determine lifetime. It is evident

from Fig.1.8 that after time t= τ the intensity of the excited state becomes 𝑰𝒐 /e.

1.5.6. Nonradioactive relaxation

An excited RE3+

ion may relax to the lower energy state via a non- radioactive process. The

deviation from a single exponential decay is due to non-radiating energy transfer to the 4f

electron system provided only a single local environment is present. The energy transfer

between different RE3+

ions by cross-relaxation and excitation migration between the same

types of RE3+

ions are typical examples. Another example is the population of a multiplet by

another multiplet, which is energetically located above, but within the same ion.

The total decay rate is given by

𝟏/( 𝝉𝒎 ) = AR + WNR …(1.26)

where τm denotes the measured lifetime of the emitting state and (AR) and (WNR ) are the

radiative and non-radiative decay rates respectively.

The quenching of lifetime is mainly influenced by the non-radiative decay rates. There are

mainly four non-radiative decay processes contributing to the reduction of measured lifetime of

the emitting level.

WNR= WMPR+ WET+ WCQ+ WOH …(1.27)

where WMPR, WET , WCQ and WOH denote the non-radiative decay rates corresponding to the

multi-phonon relaxation (MPR), energy transfer between donor to donor or donor to acceptor,

concentration quenching (CQ)and hydroxyl (OH-) groups respectively.

1.5.6.1. MULTI-PHONON RELAXATION

The non-radiative processes competing with luminescence are energy loss due to the local

vibrations of surrounding atoms and electronic states of atoms in the vicinity, such as energy

transfer, which may be resonant or phonon assisted. The other type of energy loss is given by

the exponential energy gap law[17]

WMPR = B exp (-α ΔΕ) …(1.28)

where ∆E is the energy gap between the luminescent level 𝑱 and the closest lower level 𝑱′ and

the parameters B and α are host dependent and independent on the chosen RE ion. Several lattice

phonons are emitted in order to bridge the energy gap if the energy gap between the excited and

the next lower electronic levels is larger than the phonon energy. The most energetic vibrations

are responsible for the non-radiative decay which conserves energy in the lowest order.

The stretching vibrations of the glass network polyhedral are the most energetic vibrations.

These distinct vibrations are active in multiphonon process, rather than the less energetic

vibrations of RE ion- ligand bond. The less energetic vibrations may participate in cases when

the energy gap is not bridged totally by the high energy vibrations. It was found that the

logarithm of the multiphonon decay rate decreases linearly with the energy gap. The average

phonon frequencies ( ħ𝝎 ) of some of the network formers [17] are presented in Table 1.7.

Table: 1.7. Average phonon frequencies ( ħ𝜔 ) of some of the network formers in glasses.

______________________________

Matrix ħ𝝎 (cm-1

)

Borate 1400

Phosphate 1200

Silicate 1100

Germanate 900

Tellurite 700

LaF3 (Crystal) 350

_________________________________

1.5.6.2. Energy transfer

An excited center can also relax to the ground state by non-radiative energy transfer to a

second nearby center. Non-radiative energy transfer is often used in practical applications such

as to enhance the efficiency of phosphors and lasers. Some interaction mechanism is needed to

allow energy transfer from the excited donor D* to the acceptor A. The rate of energy transfer

from the donor centers to the acceptor centers is given by [77, 78]

WDA = 𝟐𝝅

ħ 𝝍𝑫𝝍𝐀∗ 𝑯𝒊𝒏𝒕 𝝍𝐃∗𝝍𝑨

𝟐 𝙜𝑫 (𝝂)𝙜𝑨 (𝝂) 𝒅𝝂 …(1.29)

where 𝜓D and 𝜓 D* refer the wave functions of the donor center in the ground and excited states

respectively, 𝝍A and 𝝍 A* are the wave functions of the acceptor center in the ground and

excited states respectively and Hint is the donor - accepter interaction Hamiltonian.

The overlap between the normalized donor emission line-shape function gD (𝝂) and the

normalized acceptor absorption line-shape function gA (𝝂) is represented by the integral in

Eq.1.28. This term is needed for energy conservation being a maximum when D and A are

centers with coincident energy levels, a case that is called resonant energy transfer, Fig 1.9(a).

However, when D and A are different centers, it is usual to find an energy mismatch

between the transitions of the donor and acceptor ions, Fig 1.9 (b). In this case lattice phonons

of appropriate energy ( ħ𝝎 ) assist the energy transfer process which is known as phonon-

assisted energy transfer. This electron-phonon coupling must also be taken into account together

with the interaction mechanism responsible for this energy transfer.

Fig 1.9. The energy level schemes of donor (D) and acceptor (A) centers for (a) Resonant

energy transfer and (b) phonon-assisted energy transfer.

The interaction Hamiltonian (Hint ) in Eq 1.28 possesses different types of interactions namely

multipolar (electric and/or magnetic) interactions and /or a quantum mechanical exchange

interaction. The dominant interaction strongly depends on the spacing of the donor and acceptor

ions and on the nature of their wave functions. So far, the experiments on REs have been

interpreted mostly in terms of electric multipolar interactions between the ions.

The energy transfer mechanism for electric multipolar interactions can be classified into three

types basing on the character of the involved transitions of the donor and acceptor centers.

When all the transitions in D and A are of electric dipole character then electric dipole-dipole (d-

d) interactions occur and they correspond to the long range order and the transfer probability

(a)

D* A*

D A

(b)

D* …………….. ħω

A*

D A

varies with 1/R6 where R is the spacing of D and A. The dipole-quandrupole (d-q) interaction

varies as 1/R8 while quandrupole-quandrupole (q-q) interaction varies as 1/R10 .

In the similar way as in multipolar electric interactions, energy transfer probabilities due to

multipolar magnetic interactions also behave. Hence the transfer probability for a magnetic

dipole-dipole interaction varies with 1/R6 . The higher order magnetic interactions are influenced

at short distances only. In any case, the multipolar electric interactions are stronger than

magnetic interactions. The basic theory for energy transfer proposed by FÖster [77] and Dexter

[78] was modified by Inokuti and Hirayama [79] to account for energy transfer between 4f shells

of RE3+

ions. According to them the luminescence intensity decay is obtained from

𝑰 𝒕 = 𝑰𝒐 𝒆𝒙𝒑 −𝒕

𝝉𝒐− 𝑸

𝒕

𝝉𝒐 𝟑/𝑺

…(1.30)

where t is the time after excitation, 𝝉𝒐 is the intrinsic decay time of the donors in the absence of

acceptors and Q is the energy transfer parameter given by

𝑸 = 𝟒𝝅

𝟑𝜞 𝟏 −

𝟑

𝑺 𝑵𝒂𝑹𝒐

𝟑 …(1.31)

Q depends on S and the Euler‟s function 𝜞 which is equal to 1.77 for dipole-dipole (S=6),

1.43 for dipole-quadrupole (S=8) and 1.30 for quadrupole-quadrupole (S=10) interactions. Na is

the concentration of the acceptors, which is almost equal to total concentration of lanthanide

ions. Ro is the critical transfer distance, defined as the donor-acceptor separation for which the

rate of energy transfer to the acceptors is equal to the rate of intrinsic decay of the donors. CDA is

the dipole-dipole interaction parameter which describes an elementary energy transfer of direct

donor-acceptor interaction between RE3+

ions at the distance R0 and is given by

𝑪𝑫𝑨 =𝑹𝒐

𝑺

𝝉𝒐 …(1.32)

Yokota-Tanimoto [80] proposed an alternative theoretical approach to explain the energy

transfer mechanism at higher concentrations. They have obtained a general solution for the donor

decay function (migration) which includes both diffusion within the donor system and donor-

acceptor energy transfer via dipole-dipole (S=6), dipole-quadrupole(S=8) and quadrupole-

quadrupole (S=10) coupling.

1.5.6.3. Concentration quenching

In principle, when the concentration of luminescence centers increases there will be increase

in the absorption efficiency resulting an increase in the emitted light intensity. This is true up to

critical concentration of the luminescent centers. Above this concentration, the luminescence

intensity starts decreasing. This process is known as “concentration quenching” of

luminescence.

In general, luminescence concentration quenching arises due to efficient energy transfer

among the luminescent centers. At a certain concentration, the average distance between the

luminescent centers favors energy transfer and so the quenching starts. Two mechanisms are

generally invoked to explain the luminescence concentration quenching.

The excitation energy can migrate about a large number of centers before being emitted due

to efficient energy transfer. These centers can relax to their ground state by multi-phonon

emission or by infrared emission. Thus, they act as an energy sink within the transfer chain and

so the luminescence concentration quenching takes place.

Luminescence concentration quenching also takes place when the excitation energy is lost

from the emitting state via cross relaxation mechanism, by the resonant energy transfer between

two identical adjacent centers, due to particular energy-level structure of these centers. A simple

possible energy level scheme involving cross-relaxation is shown in Fig.1.10. We suppose that

for isolated centers radiative emission E3 E0 dominates. When there are two nearby similar

centers, a resonant energy transfer mechanism may occur. In this, one of the centers (donor)

transfers part of its excitation energy (E3 - E2) to the other center (acceptor). This resonant

transfer becomes possible when the energy for the transition E3 E2 is equal to that of the

transition Eo E1. As a result of this cross-

E3

E2

E1

E0

Fig 1.10. Cross-relaxation between pairs of centers.

relaxation, the donor center will be in the excited state E2 while the acceptor center will be in the

excited state E1. Then from these states a non-radiative relaxation or emission of photons with

energy other than E3 - E0 will occur; in any case the emitted energy is less than (E3 - E0) i.e., E3

E0 emission is quenched.

1.5.6.4. EFFECT of OH group

The effect of the OH group can be estimated by the infrared transmittance spectra. When

RE3+

concentration increases the OH group contents also increase and the possibility of the

interaction between OH and RE3+

ions increases. Hence the influence of OH group increases.

The presence of OH groups decreases the radiative lifetime of RE3+

ions due to energy

transfer form RE3+

to its nearby OH groups. The energy transfer rate, WHO , is proportional to the

acceptor and donor concentrations [81]. The effect of the OH group can be minimized if the

glasses are prepared under dry O2 atmosphere [82].