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CHAPTER 1

INTRODUCTION TO CRYSTAL GROWTH AND

CHARACTERIZATION TECHNIQUES

1.1 HISTORICAL INTRODUCTION

Crystals are the unacknowledged pillars of modern technology. In

the past few decades, there has been a growing interest on crystal growth

processes, particularly in view of the increasing demand of materials for

technological applications (Brice 1986, Nalwa and Miyata 1997). Crystal

growth is an interdisciplinary subject covering physics, chemistry, materials

science, chemical engineering, metallurgy, crystallography, mineralogy, etc.

The growth of single crystals is both scientifically and technologically

important, and the applications of such crystals today range from electronics

to thermal management to synthetic gemstones.

Fundamental aspects of crystal growth had been derived from early

crystallization experiments in the 18th and the 19th century (Elwell and Scheel

1975 and Scheel 1993). Theoretical understanding started with the

development of thermodynamics in the late 19th century and with the

development of nucleation and crystal growth theories and the increasing

understanding of the role of transport phenomena in the 20th century. The

phenomena of undercooling and supersaturation and the heat of crystallization

were already recognized in the 18th century.

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The rates of nucleation and crystallization in glasses were the

foundation to nucleation theories. The work of separation of crystal units as

repeatable steps as the basis of the first crystal-growth theories. With the

understanding of facet formation as a function of the entropy of fusion

(Jackson 1958) and depending on the density of bonds in the crystal structure

(Hartman and Perdok 1955) the role of screw dislocations as continuous step

sources in the formation of growth hillocks (Frank and Van der Merwe 1949),

and with the generalized crystal growth theory of Burton (Burton et al 1951),

many growth phenomena could be explained.

In the growth of crystals from a fluid medium (melt, solution, gas

phase) the heat and mass transport phenomena also play a significant role, as

was observed early by Rouelle (1745). The diffusion boundary layer defined

by Noyes and Whitney (1897) was used in the growth-rate equation of

Nernst (1904) and confirmed by interferometric measurements of

concentration profiles around growing crystals. Forced convection was

recognized to be beneficial for diffusion-limited growth. The growth of

inclusion-free crystals from the melt can be accomplished by observing the

principles of “diffusional undercooling” (Ivantsov 1951) and “constitutional

supercooling” (Tiller et al 1953). Formation of inclusions, i.e. growth

instability, can be prevented in growth from solutions by sufficient flow

against or along the crystal facets developed an empirical theory which was

utilized by Scheel and Elwell (1972) to derive the maximum stable growth

rate and optimized programming of supersaturation for obtaining large

inclusion-free crystals.

Microscopic and macroscopic inhomogeneities in doped crystals

and in solid solutions are caused by segregation phenomena, which are related

to mass and heat transfer. Based on the derivation of effective distribution

coefficients for melt growth by Burton et al (1953) and by van Erk (1982) for

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growth from solutions, the theoretical and experimental conditions for growth

of striation-free crystals could be established (Rytz and Scheel 1982, Scheel

and Sommerauer 1983, Scheel and Swendsen 2001).

There have been remarkable developments with respect to size and

perfection of crystals, with silicon, sapphire, alkali and earth alkali halides

reaching diameters up to 0.5 m and weights of nearly 500 kg. These advances

in Czochralski, Kyropoulos, heat-exchanger method, and

Bridgman–Stockbarger growth were accompanied by numerical simulations

which have become increasingly powerful to predict the optimized conditions.

However, further advances in computer modelling and in the reliability of the

used physico-chemical data are required in order to increase the efficiency

and precision of computer simulations and to allow the prediction of the best

crystal-growth technology including growth parameters for the growth of new

large and relatively perfect crystals.

1.2 TECHNIQUES USED TO GROW CRYSTALS

Nowadays crystal growth technology is largely used to grow

crystals such as NLO crystals, piezo-electric crystals, Ferro-electric crystals,

sensitive crystals and crystalline films. Preparation of single crystals of such

materials has resulted in growing realization for the importance of crystal

growth, in the theoretical and experimental aspects. The preparation of single

crystal is mainly based on the availability and nature of the starting materials

and their physico-chemical properties. Crystal growth concept has been

fundamental to many areas of science and technology.

Crystals can be grown in any one of the following four

transformations (Pamplin 1975).

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1. Solid-state reaction involving solid-solid phase transition.

2. Solution growth process involving Liquid-solid phase transition.

3. Vapour growth process involving vapour-solid phase transition.

4. Melt growth process involving liquid- solid phase transition.

The general condition for all the above mentioned processes is that

the growing crystals must have lower free energy than the initial state of the

system.

Growth of crystal ranges from a small inexpensive technique to a

complex sophisticated expensive process and crystallization time ranges from

minutes, hours, days and to months. The method of growing crystals is very

wide and mainly dictated by the characteristics of the material and their size

(Buckley 1951, Mullin 1976). Accordingly the basic growth methods are

1. Growth from melt

2. Growth from solution and

3. Growth from vapour

1.2.1 Growth from Melt

All materials can be grown in single crystal form, from the melt

provided they melt congruently without decomposition at the melting point

and do not undergo any phase transformation between the melting point and

room temperature. Depending on the thermal characteristics, techniques are

classified as

(i) Bridgman technique

(ii) Czochralski technique

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(iii) Kyropoulous technique

(iv) Zone melting technique

(v) Verneuil technique

1.2.2 Growth from Solution

Materials, which have high solubility and have variation in

solubility with temperature, can be grown easily by solution method. There

are two methods in solution growth depending on the solvents and the

solubility of the solute. They are

1. Low temperature solution growth

2. High temperature solution growth (or) Flux growth

1.2.2.1 Low temperature solution growth

Growth of crystals from aqueous solution is one of the ancient

methods of crystal growth. The method of crystal growth from low

temperature aqueous solutions is extremely popular in the production of many

technologically important crystals. It is the most widely used method for the

growth of single crystals, when the starting materials are unstable at high

temperatures (Pamplin 1975) and also which undergo phase transformations

below melting point (Hooper et al 1980). The growth of crystals by low

temperature solution growth involves weeks, months and sometimes years.

Though the technology of growth of crystals from solution has been well

perfected, it involves meticulous work, much patience and even a little

amount of luck. A power failure or a contaminated batch of raw material can

destroy months of work.

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Materials having moderate to high solubility in temperature range,

ambient to 100°C at atmospheric pressure can be grown by low-temperature

solution method. The mechanism of crystallization from solutions is

governed, in addition to other factors, by the interaction of ions or molecules

of the solute and the solvent which is based on the solubility of substance on

the thermodynamical parameters of the process; temperature, pressure and

solvent concentration (Chernov 1984). The advantages of crystal growth from

low temperature solution nearer the ambient temperature results in the simple

and straight forward equipment design which gives a good degree of control

of accuracy of ± 0.01ºC. Due to the precise temperature control,

supersaturation can be very accurately controlled. Also efficient stirring of

solutions reduces fluctuations to a minimum. The low temperature solution

growth technique is well suited to those materials which suffer from

decomposition in the melt or in the solid at high temperatures and which

undergo structural transformations while cooling from the melting point and

as a matter of fact numerous organic and inorganic materials which fall in this

category can be crystallized using this technique. The low temperature

solution growth technique also allows variety of different morphologies and

polymorphic forms of the same substance can be grown by variations of

growth conditions or of solvent (Hooper et al 1979). The proximity to

ambient temperature reduces the possibility of major thermal shock to the

crystal both during growth and removal from the apparatus.

The main disadvantages of the low temperature solution growth are

the slow growth rate in many cases and the ease of solvent inclusion into the

growing crystal. Under the controlled conditions of growth the solvent

inclusion can be minimized and the high quality of the grown crystal can

compensate the disadvantage of much longer growth periods. After many

modifications and refinements, the process of solution growth now yields

good quality crystals for a variety of applications. Growth of crystals from

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solution at room temperature has many advantages over other growth methods

though the rate of crystallization is slow. Since growth is carried out at room

temperature, the structural imperfections in solution grown crystals are

relatively low (Brice 1973).

Among the various methods of growing single crystals, solution

growth at low temperatures occupies a prominent place owing to its versatility

and simplicity. In the low temperature solution growth, crystals can be grown

from solution if the solution is supersaturated, that is it contains more solute

than it can be in equilibrium with the solid. Three principal methods are used

to produce the required supersaturation:

i. Slow cooling of the solution

ii. Slow evaporation of the solvent

iii. The temperature gradient method

Low temperature solution growth is a well-established technique

due to its versatility and simplicity. It is possible to grow large crystals of

high perfections as the growth occurs close to equilibrium conditions

(McArdle and Sherwood 1987). It also permits the preparation of different

morphologies of the same materials by varying the growth conditions.

1.2.2.1.1 Slow cooling technique

It is the best way to grow single crystals by solution technique. The

Main limitation is the need to use a range of temperature. The possible range

of temperature is usually small so little amount of the solute remains in the

solution at the end of the run. To compensate this effect, large volumes of

solution are required. The use of a range of temperatures may not be desirable

because the properties of the grown material may vary with temperature. Even

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though the method has technical difficulty of requiring a programmable

temperature control, it is widely used with great success. The temperature at

which such crystallization can begin is usually within the range 45-75°C and

the lower limit of cooling is the room temperature.

1.2.2.1.2 Slow evaporation method

This method is similar to the slow cooling method in view of the

apparatus requirements. The temperature is fixed constant and provision is

made for evaporation. With non-toxic solvents like water, it is permissible to

allow evaporation into the atmosphere. Typical growth conditions involve

temperature stabilization to about ± 0.05°C and rates of evaporation of a

few ml/hr. The evaporation techniques of crystal growth have the advantage

that the crystals grow at a fixed temperature. But inadequacies of the

temperature control system still have a major effect on the growth rate. This

method is the only one, which can be used with materials, which have very

small temperature coefficient of stability.

1.2.2.1.3 Temperature gradient method

This method involves the transport of the materials from a hot

region containing the source material to be grown to a cooler region where the

solution is supersaturated and the crystal grows. The main advantages of this

method are that

(a) Crystal grows at a fixed temperature

(b) This method is insensitive to changes in temperature provided

both the source and the growing crystal undergo the same

change.

(c) Economy of solvent and solute.

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On the other hand, changes in the small temperature differences

between the source and the crystal zones have a large effect on the growth

rate.

1.2.2.2 High temperature solution growth (or) Flux growth

The greatest advantage of crystal growth from high temperature

solutions (or flux growth) is that one can crystallise materials, which

cannot be obtained in single crystal form by any other method. Flux

growth methods, which allow the crystals to grow before the melting

temperature is reached, are used when the crystals melt incongruently or when

there is a phase transition before melting. The components of the final desired

materials are dissolved in a solvent. This method is based on the concepts of

solubility and supersaturation. At a given temperature, a limited amount of a

substance dissolves in a particular solvent. The amount dissolved defines the

solubility at that temperature. If a saturated solution is prepared at a certain

temperature and then cooled to a lower temperature, it contains more salt than

is permitted by the solubility at the lower temperature. The same happens if

some of the solvent is allowed to evaporate, the solution is now in the

supersaturated state, which is a metastable state and, with a slightest

induction, the extra salt precipitates.

If a seed crystal is introduced into the solution, the substance

precipitating from the solution grows around the seed crystal to form a larger

single crystal. In the absence of a seed, even dust particles provide a nucleus

for crystal growth. Crystallisation can be performed in air or any other

suitable atmosphere. Crystal growth is possible even if very little is

known about the crystallization conditions. For this reason, this method is

used as a preliminary one, to obtain new materials for the first time in

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single crystal form, so that their physical and chemical properties can be

investigated.

1.2.3 Growth from Vapour

The growth of single crystal material from the vapour phase is

probably the most versatile of all crystal growth processes. Crystals of high

purity can be grown from vapour phase by sublimation, condensation and

sputtering of elemental materials. To obtain single crystals of high melting

point materials this method is used. The most frequently used method for the

growth of bulk crystals utilizes chemical transport reaction in which a

reversible reaction is used to transport the source material as a volatile species

to the crystallization region. Finding a suitable transporting agent is a

formidable, problem in this technique. It is rarely possible to grow large

crystals because of multi-nucleation.

The commercial importance of vapour growth is the production of

thin layers by chemical vapour deposition (CVD), where usually irreversible

reactions e.g. decomposition of silicon halides or of organic compounds are

used to deposit materials epitaxially on a substrate. Doping can be achieved

by introducing volatile compounds of dopant elements into the reaction

region. The thickness of the doped layer can be controlled.

1.3 SANKARANARAYANAN-RAMASAMY (SR) METHOD

Sankaranarayanan-Ramasamy method is one of the solution growth

methods. To grow high quality crystal with a reasonable yield, the

investigation of a possible single crystal growth technique is needed. Further,

growth of organic or inorganic crystal with specific orientation has

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tremendous value in terms of its significance towards device application.

From this point of view, a novel Sankaranarayanan-Ramasamy crystal growth

method has more advantages when compared to conventional solution growth

techniques (Sankaranarayanan and Ramasamy 2005) and this can be

employed to grow unidirectional crystal from solution. Figure 1.1 shows the

schematic representation of SR method apparatus. It consists of heating coils,

seed-mounting pad, growth portion and top portion (made up of glass).

Heating coil is placed at the top of the crucible and it is directly connected to

thermostat to maintain the heater voltage. Heater voltage plays a major role in

this novel unidirectional SR method and this is used for solvent evaporation

of the growth solution. The entire SR method crucible was placed inside a

constant temperature bath (CTB) (accuracy ± 0.01°C) for avoiding

temperature fluctuations in the growth portion. Growth condition of this

method depends on the temperatures of heating coils. Once the growth

condition is optimized, it is easy to grow the crystals with different

orientations.

Figure 1.1 Schematic of experimental set up of SR method

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The advantages of Sankaranarayanan-Ramasamy method are as

follows:

(i) Can grow single crystal with specific orientation from solution

(ii) Room temperature growth is possible

(iii) Solute-crystal conversion efficiency is almost 100 percent.

(iv) Simple experiment setup

1.4 GEL GROWTH

It is an alternative technique to solution growth with controlled

diffusion and the growth process is free from convection. Gel is a two-

component system of a semisolid rich in liquid and inert in nature.

The material, which decomposes before melting, can be grown in this

medium by counter diffusing two suitable reactants. Crystals with dimensions

of several mm can be grown in a period of 3 to 4 weeks. The crystals grown

by this technique have high degree of perfection and fewer defects since the

growth takes place at room temperature.

1.5 HYDROTHERMAL GROWTH

Hydrothermal implies conditions of high pressure as well as high

temperature. Substances like calcite, quartz are considered to be insoluble in

water but at high temperature and pressure, these substances are soluble. This

method of crystal growth at high temperature and pressure is known as

hydrothermal method. Temperatures are typically in the range of 400°C to

600°C and the pressure involved is large (hundreds or thousands of

atmospheres). Growth is usually carried out in steel autoclaves with gold or

silver linings. Depending on the pressure the autoclaves are grouped into low,

medium and high-pressure autoclaves. The concentration gradient required to

produce growth is provided by a temperature difference between the nutrient

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and growth areas. The requirement of high pressure presents practical

difficulties and there are only a few crystals of good quality and large

dimensions are grown by this technique. Quartz is the outstanding example of

industrial hydrothermal crystallization. One serious disadvantage of this

technique is the frequent incorporation of OH- ions into the crystal, which

makes them unsuitable for many applications.

1.6 NUCLEATION

Nucleation is an important phenomenon in crystal growth and is the

precursor of the overall crystallization process. Nucleation is the process of

generating within a metastable motherphase, the initial fragments of a new

and more stable phase capable of developing spontaneously into gross

fragments of the stable phase. Nucleation may occur spontaneously or it may

be induced artificially. These are referred to as homogeneous and

heterogeneous nucleations respectively. Both these nucleations are called

primary nucleation and occur in systems that do not contain crystalline matter.

On the other hand, nuclei are often generated in the vicinity of crystals present

in the supersaturated system. This phenomenon is referred to as secondary

nucleation (Mullin 1972). Growth of crystals from solutions can occur if some

degree of supersaturation or supercooling has been achieved first in the

system. There are three steps involved in the crystallization process.

(i) Achievement of supersaturation or supercooling

(ii) Formation of crystal nuclei

(iii) Successive growth of crystals to get distinct faces

All the above steps may occur simultaneously at different regions

of a crystallization unit. However an ideal crystallization process consists of

a strictly controlled stepwise program.

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1.7 OSTWALD’S DIAGRAM

The relationship between the concentration and temperature is

schematically shown in Figure 1.2 (Meirs and Issac 1987). Meirs carried out

extensive research into the relationship between supersaturation and

spontaneous crystallization. The lower continuous line is the normal solubility

curve for the salt concerned. Temperature and concentration at which

spontaneous crystallization occurs are represented by the upper broken curve,

generally referred to as the supersolubility curve. The whole concentration-

temperature field is separated by the saturated-solution line (solubility curve)

into two regions, unsaturated and supersaturated solutions. Saturated solutions

are those mixtures, which can retain their equilibrium indefinitely in contact

with the solid phase with respect to which they are saturated. The solubility of

most substances increases with temperature (the temperature coefficient of the

solubility is positive) and crystals can be grown only from supersaturated

solutions, which contain an excess of the solute above the equilibrium value.

The diagram is divided into three zones, which are termed as region I, II and

III respectively.

(i) The stable (undersaturated) zone, where crystallization is not

possible

(ii) The second region is a metastable zone, between the solubility

and supersolubility curves, where spontaneous crystallization

is improbable. However, if a crystal seed is placed in such a

metastable solution, growth would occur on it

(iii) Third region is the unstable or labile (supersaturation) zone,

where spontaneous crystallization is more probable

If the solution whose concentration and temperature represented by

point A in the Figure 1.2, is cooled without loss of solvent (line ABC)

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spontaneous crystallization cannot occur until conditions represented by

point C are reached. At this point, crystallization may be spontaneous or

seeding, agitation or mechanical shock may induce it. Further cooling to some

point D may be necessary before crystallization can be induced, especially

with very soluble substances such as sodium thiosulphate.

Figure 1.2 Solubility diagram showing different levels of saturation

The evaporation of solvent from the solution may also result in

supersaturation. Line AB’C’ represents an operation carried out at constant

temperature. Penetration beyond the super solubility curve into the labile zone

rarely happens, as the surface from which evaporation takes place is usually

supersaturated to a greater degree than the bulk of the solution. Crystals,

which appear on this surface eventually fall into the solution and seed it.

In practice, a combination of cooling and evaporation as represented by the

line AB”C” in (Figure 1.2) is adopted.

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1.8 EXPRESSION FOR SUPERSATURATION

The supersaturation of a system may be expressed in a number of

ways. The basic units of concentration as well as temperature must be

specified. The concentration driving force (∆C), the supersaturation ratio (S)

and relative supersaturation (σ) are related to each other as follows:

The concentration driving force ∆C = C – C* (1.1)

where C is the actual concentration of the solution at a given temperature and

C* is the equilibrium concentration at a given temperature.

Supersaturation ratio S = C / C* (1.2)

Relative supersaturation σ = (C - C*) / C*

σ = S – 1 (1.3)

If the concentration of a solution can be measured at a given

temperature and the corresponding equilibrium saturation concentration is

known, then, it is easier to calculate the supersaturation.

Growth of good quality single crystals by slow evaporation and

slow cooling techniques require optimized conditions. The same may be

achieved with the help of the following criteria: (i) material purification,

(ii) solvent selection, (iii) solubility, (iv) solution preparation, (v) seed

preparation, (vi) agitation, (vii) crystal habit and (viii) cooling rate.

1.9 CHOICE OF SOLVENT AND SOLUBILITY

Growth from aqueous solution provides information on the

fundamental process applicable to both low and high temperature solution

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growth methods (Bordui et al 1987). Water is a popular solvent for the

growth of a variety of inorganic and organic compounds. It is not toxic and is

less volatile than organic solvents, which are, in general, toxic, volatile and

flammable. In comparison with organic solvents, it is also easily available in

the pure state and is cheap. Because of its higher boiling point than most of

the organic solvents commonly used for growth, it provides a reasonably wide

range for the selection of growth temperature. Moreover, it is chemically inert

to a variety of glasses, plastics and metals used in crystal growth equipment.

However, water is not a reversible solvent for some materials. It hydrolyses

some materials and introduces water of crystallization to others which may be

desired in the anhydrous form. Therefore, for the growth of crystals of a

compound from solution, the selection of a solvent is critical.

A simple rule of thumb in the proper selection of a solvent is

chemical similarity between the solvent and the compound to be grown. For

example, crystals of nonpolar organic compounds can be grown easily from

nonpolar organic solvents. Chemical similarity also determines solute

solubility in the solvent. Experiments reveal that a solvent in which the

compound has solubility between 10 and 60% at a given temperature is

economically suitable for crystal growth. Very low and very high solubility of

a solute provide low growth rates due to low solute concentration and

increased viscosity, respectively. Therefore, in both of these cases it is

desirable to use additives to change the solute solubility in a solvent or

solution viscosity. Additives not only change the properties of solutions, but

also lead to changes in the growth habits of crystals (Buckley 1951).

The solvent must be chosen taking into account the following

factors to grow crystals from solution. A solvent of choice is the one with

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(i) A good solubility for the given solute

(ii) A good solubility gradient

(iii) Less viscosity

(iv) Less volatility

(v) Less corrosion

(vi) Non-toxic

If the solubility is too high, it is difficult to grow bulk single

crystals and too small a solubility restrict the size and growth rate of the

crystals. Solubility gradient is another parameter, which dictates the growth

procedure. Neither a flat nor a steep solubility curve will enable the growth of

bulk crystal from solution; while the level of supersaturation could not be

varied by reducing the temperature in the former, even a small fluctuation in

the temperature will affect the supersaturation to a large extent in the later

disabling the growth of good quality bulk crystals in both cases. If the

solubility gradient is very small, slow evaporation of the solvent is the other

option for crystal growth to maintain the supersaturation in the solution.

Growth of crystals from solution is mainly a diffusion- controlled

process; the medium must be less viscous to enable faster transport of the

growth units from the bulk solution by diffusion. Hence a solvent with less

viscosity is preferable (Ohara and Reid 1973). The solubility data at various

temperatures are essential to determine the level of supersaturation. Hence,

the solubility of the solute in the chosen solvent must be determined before

starting the growth process (Christian 1990).

The solubility of the solute may be determined by dissolving the

solute in the solvent maintained at a constant temperature with continuous

stirring. On reaching saturation, the equilibrium concentration of the solute

may be determined gravimetrically. A sample of the clear supersaturated

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liquid is withdrawn by means of a warmed pipette and a weighed quantity of

the sample is analyzed. The solubility curve can then be plotted in this way by

repeating the above for different temperatures.

1.10 NONLINEAR OPTICS

Nonlinear optics is attracting the attention of researchers due to its

wide application in the area of laser technology, optical communication and

data storage technology. Nonlinear optics (NLO) is the interaction of intense

electromagnetic fields with materials to produce modified fields that are

different from the input field in phase, frequency or amplitude (Firdous

Anwar 1988). The light propagates through a crystalline solid, which lacks a

centre of symmetry, generates light at second harmonics of the applied

frequency. This important nonlinear property of noncentro-symmetric crystals

is called second Harmonic generation (SHG) and this phenomenon and the

materials in which it occurs is the subject of intense study (Chemla and Zyss,

1987). In the beginning nonlinear optics is often taken to be discovery of

second-harmonic generation by Franken et al (1961), after the demonstration

of the first working laser by Maiman (1960). Second harmonic generation

observed the ultraviolet light at twice the frequency of a ruby laser light, when

the light was made to traverse through a quartz crystal. Numerous nonlinear

optical phenomena have been discovered since then. The existence of

harmonic light waves at the boundary of a nonlinear dielectric medium was

predicted by Blombergen and Pershan (1962). Some materials change light

passing through them, depending upon orientation, temperature, light

wavelength etc. (red light, lower wavelength) releasing one photon of

accumulated higher energy (blue and green light, higher wavelength). NLO

materials typically have a distinct crystal structure, which is anisotropic with

respect to electromagnetic radiation.

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1.11 THEORY OF NONLINEAR OPTICS

The explanation of nonlinear effects lies in the way in which a

beam of light propagates through a solid. The nuclei and associated electrons

of the atoms in the solid form electric dipoles. The electromagnetic radiation

interacts with these dipoles causing them to oscillate which, by the classical

laws of electromagnetism, results in the dipoles themselves acting as sources

of electromagnetic radiation. If the amplitude of vibration is small, the dipoles

emit radiations of the same frequency as the incident radiations. As the

intensity of the incident radiations increases, the relationship between

irradiance and amplitude of vibrations becomes nonlinear resulting in the

generation of harmonics in the frequency of radiations emitted by oscillating

dipoles. Thus frequency doubling or second harmonic generations (SHG) and

indeed higher order frequency effects occur as the incident intensity is

increased. In a nonlinear medium the induced polarization is a nonlinear

function of the applied field. A medium exhibiting SHG is a crystal composed

of molecules with asymmetric charge distributions arranged in such a way

that a polar orientation is maintained throughout in the crystal. At very low

fields, the induced polarization is directly proportional to the electric field

(Nalwa and Miyata 1997).

P = ε0χ.E (1.4)

where χ is the linear susceptibility of the material, E is the electric field

vector, ε0 is the permittivity in free space.

At high fields polarization becomes independent of the field and the

susceptibility becomes field dependent. Therefore, the nonlinear response is

expressed by writing the induced polarization as a power series in the field.

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P = ε0 χ(1). E + ε0 χ

(2). E. E + ε0 χ(3). E.E.E + … (1.5)

where χ(2), χ(3), … are the nonlinear susceptibilities of the medium.

χ(1) is the linear term responsible for the refractive index,

dispersion, birefringence and absorption. χ(2) is the quadratic term which

describes second harmonic generation, optical mixing and optical parametric

oscillation. χ(3) is the cubic term which is responsible for observing

phenomena such as stimulated Raman scattering, third harmonic generation,

phase conjugation and optical instability. Hence the induced polarization is

capable of multiplying the fundamental frequency to second, third and even

higher harmonics. The coefficients of χ(1), χ(2) and χ(3) give rise to certain

optical effects. The table 1.1 gives the nonlinear optical effects and

applications of materials.

Table 1.1 Optical effects of nonlinear materials

Order Effects Applications

χ(2) Refraction Optical fibers

χ(2) SHG (ω+ω = 2ω

Frequency mixing

(ω1±ω2=ω3)

Pockels effects

(ω+o=ω)

Frequency doubling

Optical parametric oscillators

Electro-optical modulators

χ(3) 4 wave mixing phase gratings

Kerr effect

Optical amplitude

Raman coherent spectroscopy

Real time holography

Ultra high speed optical gates

Amplifiers, choppers etc.

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A noncentrosymmetric crystal, which exhibits the following

properties, is required for nonlinear device fabrication.

(i) High effective nonlinear optical coefficient

(ii) Good optical quality

(iii) Wide transparency region

(iv) Good mechanical and chemical stability

(v) Large birefringence

(vi) Low absorption

(vii) Easy device fabrication

1.12 SECOND HARMONIC GENERATION (SHG)

The first break through of SHG was achieved in 1961, when pulsed

laser beam was sent into a piezoelectric crystal sample. Peter A Franken

(Franken et al 1961) and several coworkers at the University of Michigan

were the first to observe SHG experimentally. They focused a 3 kW pulse of

red ruby laser light onto a quartz crystal, the frequency of the incident light

gets doubled which enables one to extend the range of laser wavelength into

the blue and UV parts of the spectrum. This is called frequency doubling.

Two waves each of frequency ω simultaneously superimposed constructively.

The resulting wave excites an electron from the ground state to a virtual

excited state. On relaxation, one wave of frequency 2ω is emitted.

To optimize SHG effect, one must optimize χ(2). χ(2) is influenced by various

structural features. Crystallographically, the compound must be

noncentrosymmetric by nature. The process of transformation of light with

frequency into light with double frequency is referred as SHG (Tarasov 1981)

(Figure 1.3).

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Figure 1.3 Second harmonic generation

1.13 PARAMETRIC GENERATION (OR) SUM FREQUENCY

GENERATION

The transformation of the light wave with frequency υ into two new

light waves with frequencies υ1

and υ2

is termed as parametric generation

(Tarasov 1981) (Figure 1.4).

Figure 1.4 Optical parametric generation

1.14 APPLICATIONS OF NLO EFFECTS

Various susceptibility functions and frequency arguments with their

applications in various fields (Williams 1984) are given in Table 1.2 for χ (2)

and χ (3).

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Table 1.2 Various susceptibility functions with their applications

Susceptibility Effect Application

χ (2)(0;ω, - ω) Optical rectification Hybrid bistable device

χ(2) (-ω; ω, 0)

Electro-optic (Pockels)

Effect

Modulators, variable phase

retarders

χ(2) (-2ω; -ω, ω) Frequency doubling Harmonic generation device

χ(2) (-ωc; ω

a, ω

b) Frequency mixing Parametric amplifiers, IR up

convertors

χ (3)(-ω; ω, ω, -ω) ac electro-optic effect

ac Kerr effect

Optical bistability

Phase conjugation

χ (3) (-3ω;ω; ω, ω) Frequency tripling Deep UV conversion

1.15 ELECTRO-OPTIC MODULATOR

An Electro-optic modulator is a device with operation based on

electric field controlled change in index of refraction or change in natural

birefringence. Depending on the device configuration, the following

properties of the light wave can be varied in intensity, amplitude, frequency or

direction of propagation of the light. Electro-optic light modulators control

the polarization of light passing through a crystal subjected to an electrical

driving signal. The effect was first described by Pockels in 1893; hence, the

devices are known as Pockels cells. The phenomenon is also called the linear

electro-optic effect, because phase retardation of light transiting the crystal is

directly proportional to the applied electric field. Early attempts to use

Pockels cells were not overly successful, in the absence of a source of well-

collimated, monochromatic light.

25

The electro-optic effect is the change in refractive index resulting

from the application of a DC or low frequency electric field. If the materials

have nonlinear polarization properties then the dielectric displacement (D)

can be related with the applied electric field (E) as

D = Є0χ(1) E + Є0χ

(2) E2 + Є0χ(3) E3 + .......... (1.6)

where χ(1) is the linear susceptibility and χ(2)

, χ(3)

are the second and third order

susceptibilities respectively. The permittivity of the material is defined as:

dD/dE = Є0χ(1) + Є0χ

(2) E + Є0χ(3) E2 +…….. (1.7)

where the first term is a constant and the higher order terms show the change

in permittivity due to applied electric field. Since the refractive index of

materials is directly related to their dielectric constant, it will also change

under electric field due to the nonlinear effect. Based on the change of

refractive index electro-optic effect is classified into two types. They are

Pockels effect (or linear electro-optic effect): Change in the

refractive index linearly proportional to the electric field. Only certain

crystalline solids show the Pockels effect, as it requires lack of inversion

symmetry.

Kerr effect (or quadratic electro-optic effect): Change in the

refractive index proportional to the square of the electric field. All materials

display the Kerr effect, with varying magnitudes, but it is generally much

weaker than the Pockels effect.

26

1.16 TYPES OF OPTICAL MODULATORS

There are different kinds of optical modulators:

(i) Acousto-optic modulators are based on the acousto-optic

effect. They are used for switching or continuously adjusting

the amplitude of a laser beam, for shifting its optical

frequency, or its spatial direction.

(ii) Electro-optic modulators exploit the electro-optic effect in

a Pockels cell. They can be used for modifying the

polarization, phase or power of a beam, or for pulse picking

in the context of ultrashort pulse amplifiers.

(iii) Electroabsorption modulators are intensity modulators, used

for data transmitters in optical fiber communications.

(iv) Interferometric modulators (Mach–Zehnder modulators) are

often realized in photonic integrated circuits for optical data

transmission.

(v) Fiber-optic modulators can exploit various physical

principles. They can be true fiber devices, or contain fiber

pig-tailed bulk components.

(vi) Liquid crystal modulators are suitable for optical displays

and pulse shapers. They can serve as spatial light

modulators, with a spatially varying transmission, for

displays.

27

(vii) Chopper wheels can periodically switch the optical power of

a light beam, as required for certain optical measurements

(lock-in amplifier).

(viii) Micromechanical modulators (which are microelectro-

mechanical systems = MEMS), (silicon-based light valves

and two-dimensional mirror arrays, are particularly useful

for projection displays).

Pockels cells can have two different geometries concerning the

direction of the applied electric field:

1.17 LONGITUDINAL DEVICES

Longitudinal devices have the electric field in the direction of the

light beam, which passes through holes in the electrodes. Large apertures can

easily be realized, as the required drive voltage is basically independent of the

aperture. The electrodes can be metallic rings (Figure 1.5 (a)) or transparent

layers on the end faces (b) with metallic contacts.

(a) (b)

Figure 1.5 Pockels cells with longitudinal electric field

28

1.18 TRANSVERSE DEVICES

Transverse devices have the electric field perpendicular to the light

beam. The field is applied through electrodes at the sides of the crystal. For

small apertures, they can have lower switching voltages. Figure 1.6 shows the

Pockels cells with transverse electric field. On the left is a bulk modulator and

on the right a waveguide modulator.

Figure 1.6 Pockels cells with transverse electric field

1.19 HALF-WAVE VOLTAGE

An important property of a Pockels cell is the half-wave voltage Vπ

which is the voltage required for inducing a phase change of π. In an

amplitude modulator, the applied voltage has to be changed by this value in

order to go from the operation point with minimum transmission to that with

maximum transmission. The half-wave voltage of a Pockels cell with

transverse electric field depends on the crystal material, the electrode

separation, and the length of the region where the electric field is applied. For

larger open apertures, the electrode separation needs to be larger, and hence

also the voltages. For a Pockels cell with longitudinal electric field, the crystal

length does not matter, since a shorter length also increases the electric field

strength for a given voltage. Larger apertures are possible without increasing

the half-wave voltage. Typical Pockels cells have half-wave voltages of

29

hundreds or even thousands of volts, so that a high-voltage amplifier is

required for large modulation depths. Relatively small half-wave voltages are

possible for highly nonlinear crystal materials such as LiNbO3, and

for integrated optical modulators with a small electrode separation, but such

devices have a limited power handling capability.

The voltage required to produce a retardation of π is called half

wave voltage. For a longitudinal modulator the applied electric field is

E = V / L , and the induced phase shift is 3x x

n rVπλ

∆Φ = , which is

independent of L and is linearly related to V. For a transverse

modulator E = V / d and the induced phase shift is 3 ( / )x xn rV L dπλ

∆Φ = ,

which is a function of the aspect ratio L / d and V. The voltage that would

produce an induced phase shift of φ π∆ = is the half-wave voltage.

For longitudinal modulator 3/ xV n rπ λ= (1.8)

For transverse modulator 3( / )( / )xV n r d Lπ λ= (1.9)

where λ is the wavelength, nx is the unperturbed index of refraction, r is the

corresponding Electro-optical coefficient, L is the interaction length and d is

the electrode spacing.

Therefore for the longitudinal modulators, the required magnitude

of the applied electric field for a desired degree of modulation cannot be

reduced by changing the aspect ratio (ratio of the crystal length to the

electrode separation) and it increases with wavelength. Here the electrodes do

not obstruct the light as it passes through the crystal. The induced phase shift

is proportional to the aspect ratio. Therefore, the voltage necessary to achieve

30

a desired degree of modulation can be greatly reduced by reducing the crystal

thickness. However the transverse dimension d is limited by the increase in

capacitance, which affects the modulation bandwidth or speed of the device

and by diffraction for a given length ‘L’, since a beam with finite cross

section diverges as it propagates.

1.20 ASSESSING PROPERTIES OF A GOOD ELECTRO-OPTIC

MODULATOR

Practical electro-optic materials should preferably have the

following properties (Robert Goldstein 1986)

(i) Large electro-optic figure of merit, n3r, (where ‘n’ is the

refractive index and ‘r’ is the relevant electro-optic

coefficient)

(ii) The half wave voltage should be as small as possible

(iii) The crystals should be transparent at frequency at which

they are to be used

(iv) Alternatively the transmission region of the crystal

determines the spectral region available for modulation

(v) The crystal should have highest attainable optical

homogeneity with the minimum amount of absorption or

scattering

(vi) The crystal should lack in the centre of inversion

(vii) The relative dielectric constant must be as low as possible

because the reactive power required to drive the modular

becomes large with increased dielectric constant. But this

requirement is conflicting with the previous requirement

31

since r is directly proportional to the dielectric constant.

Hence one has to compromise between the two, depending

on which parameter is more important for the device

(viii) The presence of any natural birefringes to a larger degree

will affect the performance of the electro-optic device

because firstly, it is a direct function of temperature and

secondly, the emerging rays be collinear on the same axis to

properly recombine

(ix) Dielectric dissipation must be very low

(x) As the strain in the lattice affects the phase relationship, the

crystal should be hard enough to resist strain during cutting

and polishing

(xi) The thermal conductivity of the crystal determines the

deleterious birefringes due to thermal gradients in the crystal

as heated by electrical or optical sources. Hence the thermal

conductivity of the crystal must be as high as possible

(xii) The crystal must be resistive to radiation damage at high

laser powers

(xiii) The crystal should not be optically active and

(xiv) Availability of large and good optical quality single crystals.

1.21 CHARACTERIZATION TECHNIQUES

Characterization of a crystal essentially consists of its chemical

composition, structure, defects and the study of its electrical, mechanical and

optical properties. A brief description of the fundamentals and the procedure

related to each technique is given. The equipment, schematic views and

illustrations of some of the systems used are presented.

32

In the present investigation the grown crystals were characterized

by various techniques. Single crystal and Powder diffraction studies were

carried out to confirm the grown crystals. Some of the grown crystals were

subjected to HRXRD to evaluate the crystalline perfection. The optical

transmittance, optical band gap and refractive index of the grown materials

were evaluated by recording optical transmission spectra. The

photoluminescence (PL), dielectric and Vickers microhardness studies were

performed on the grown crystals. Etching studies carried out revealed the

defects and growth pattern of the crystals. The second harmonic generation

(SHG) and its efficiency were measured using Kurtz-Perry powder method

(Kurtz and Perry 1968).

1.21.1 X-ray Diffraction

X-ray diffraction is now a common technique for the study of

crystal structures and atomic spacing. X-ray diffraction is based on

constructive interference of monochromatic X-rays and a crystalline sample.

X-rays are generated by a cathode ray tube, filtered to produce

monochromatic radiation, collimated to concentrate, and directed towards the

sample. When a crystal is bombarded with X-rays of a fixed wavelength

(similar to spacing of the atomic-scale crystal lattice planes) and at certain

incident angles, intense reflected X-rays are produced when the wavelengths

of the scattered X-rays interfere constructively. In order for the waves to

interfere constructively, the differences in the travel path must be equal to

integer multiples of the wavelength. When this constructive interference

occurs, a diffracted beam of X-rays will leave the crystal at an angle equal to

that of the incident beam. Each rational plane of atoms in a crystal will

undergo refraction at a single, unique angle (for X-rays of a fixed

wavelength). The general relationship between the wavelength of the incident

33

X-rays, angle of incidence and spacing between the crystal lattice planes of

atoms is known as Bragg's Law, expressed as:

n λ = 2dsinθ (1.10)

where n (an integer) is the "order" of reflection, λ is the wavelength of the

incident X-rays, d is the interplanar spacing of the crystal and θ is the angle of

incidence.

1.21.1.1 High-Resolution X-Ray Diffraction (HRXRD)

To evaluate the crystalline perfection of the specimen crystals,

high-resolution X-ray diffraction (HRXRD) analysis was carried out. A

multicrystal X-ray diffractometer developed at National Physical Laboratory

(NPL), New Delhi (Lal and Bhagavannarayana 1989) was used to record

high-resolution rocking or diffraction curves (DCs). Figure 1.7 shows the

schematic of the Multicrystal X-Ray Diffractometer.

In this system, a fine focus (0.4 × 8 mm2; 2 kW Mo) X-ray source

energized by a well-stabilized Philips X-ray generator (PW 1743) was

employed. The well-collimated and monochromated MoKα1 beam obtained

from the three monochromator Si crystals set in dispersive (+,-,-)

configuration has been used as the exploring X-ray beam. This arrangement

improves the spectral purity (∆λ/λ<< 10-5) of the MoKα1 beam. The

divergence of the exploring beam in the horizontal plane (plane of diffraction)

was estimated to be << 3 arc sec. The specimen crystal is aligned in the

(+,-,-,+) configuration. Due to dispersive configuration of the third

monochromator crystal with respect to the second monochromator, the

spectral quality of the diffracted beam emerged from the third monochromator

34

is highly perfect (∆λ/λ ~ 10-5; horizontal divergence >> 3 arc seconds) and

hence though the lattice constant of the monochromator crystal and the

specimen are different, the unwanted experimental dispersion broadening in

the diffraction curve of the specimen crystal (∆FWHM = ∆λ/λ (tanθM −tanθS);

θM and θS are being the Bragg diffraction angles of monochromator and the

specimen crystals) is insignificant. The specimen can be rotated about a

vertical axis, which is perpendicular to the plane of diffraction, with minimum

angular interval of 0.4 arc sec. The diffracted intensity is measured by using a

scintillation counter. The DCs were recorded by changing the glancing angle

(angle between the incident X-ray beam and the surface of the specimen)

around the Bragg diffraction peak position θB (taken zero as reference point)

starting from a suitable arbitrary glancing angle (θ). The detector was kept at

the same angular position 2θB with wide opening for its slit, the so-called ω

scan. The omega scan is very appropriate to record the short range order

scattering caused by the defects or by the scattering from local Bragg

diffractions from agglomerated point defects or due to low angle and very low

angle boundaries. Before recording the diffraction curve, to remove the non-

crystallized solute atoms remained on the surface of the crystal and also to

ensure the surface planarity, the specimens were first lapped and chemically

etched in a non-preferential etchant of water and acetone mixture in 1:2

volume ratio.

35

Figure 1.7 Schematic of the Multicrystal X-Ray Diffractometer Set up

used for the study

1.21.2 Scanning Electron Microscopy (SEM)

Scanning electron microscopy (SEM) is one of the most versatile

and widely used tools allowing the study of structure, morphology and surface

details of the crystals under investigation. By scanning across a specimen

high–resolution images of the morphology or topography of a specimen with

great depth of filed at very low or very high magnification can be obtained.

The morphology and the structure of crystal were examined using the Quanta

200 FEG scanning electron microscope (SEM) which is a versatile high

resolution scanning electron microscope.

1.21.3 Energy Dispersive X–ray Analysis (EDX)

Energy dispersive X-ray spectroscopy is an analytical technique

used for the elemental analysis or chemical characterization of a sample. It is

one of the variants of X-ray fluorescence spectroscopy which relies on the

investigation of a sample through interactions between electromagnetic

36

radiation and matter, analyzing X-rays emitted by the matter in response to

being hit with charged particles. Its characterization capabilities are due in

large part to the fundamental principle that each element has a unique atomic

structure allowing X-rays that are characteristic of an element's atomic

structure to be identified uniquely from one another. During EDX Analysis,

the specimen is bombarded with an electron beam inside the scanning

electron microscope. The bombarding electrons collide with the specimen

atoms' own electrons, knocking some of them off in the process. A position

vacated by an ejected inner shell electron is eventually occupied by a higher-

energy electron from an outer shell. To be able to do so, however, the

transferring outer electron must give up some of its energy by emitting an

X-ray.

The amount of energy released by the transferring electron depends

on which shell it is transferring from, as well as which shell it is transferring

to. Furthermore, the atom of every element releases X-rays with unique

amounts of energy during the transferring process. Thus, by measuring the

amounts of energy present in the X-rays being released by a specimen during

electron beam bombardment, the identity of the atom from which the X-ray

was emitted can be established. Output of an EDX analysis is an EDX

spectrum. The EDX spectrum is just a plot of how frequently an X-ray is

received for each energy level. An EDX spectrum normally displays peaks

corresponding to the energy levels for which the most X-rays had been

received. Each of these peaks is unique to an atom, and therefore corresponds

to a single element. The higher a peak in a spectrum, the more concentrated

the element is in the specimen.

37

1.21.4 Fourier Transformation Infra-Red (FT-IR) Spectroscopy

Infrared light from a suitable source passes through a scanning

Michelson interferometer and its Fourier transformation gives a plot of

intensity versus frequency. IR spectroscopy is one of the most widely used

tools for the detection of functional groups in pure compounds and mixtures,

and for the comparison of compounds. IR region of the electromagnetic

spectrum extends from 400 to 4000 cm-1. There are two types of IR

spectrometers characterised by the manner in which IR frequencies are

handled. In the first type called the dispersive type, the IR light is dispersed

into individual frequencies using a grating monochromator whereas in the

second called the Fourier transform IR where, the IR frequencies interact to

produce an interference pattern and this pattern is then analyzed

mathematically using Fourier Transform to determine the individual

frequencies and their intensities (Silverstein and Webster 1998).

When a sample is placed in the path of the beam, it absorbs the

characteristic frequencies so that their intensities are reduced in the

interferometer and the ensuing Fourier transform is the infrared absorption

spectrum of the sample. The scan time for the moving mirror dictates the

speed with which the IR spectrum can be recorded. Digitalization of the data

calculation of the Fourier Transform takes few seconds more, but the

information which constitutes the spectrum, can be acquired in exceedingly

short time even in a few milliseconds. The FT-IR spectra of samples were

recorded using perkin Elmer FT-IR spectrometer in the range 400-4000 cm-1

by KBr pellet technique for the present work.

38

1.21.5 UV- Visible studies

A double beam UV-Visible NIR spectrophotometer consists of

deutrium lamp which gives continuous radiation and a tungsten as required.

A narrow bandwidth was selected with the help of band pass filters. Then the

radiation lamp which produces visible range. The instrument has an

arrangement for switching on either radiation source was passed through the

cells of the given solution and solvent alternatively and respectively. This

process is called double beam process and it eliminates the fluctuations of

intensity of radiation scattering effect and solvent effect. The two rays were

combined and differences in intensities of those two radiations are measured

electrically. The movement of monochromators and the recorder were

synchronized and adjusted so that the record shows the intensity of

appropriate radiation. In the transmission study the intensity was recorded in

terms of percentage of transmittance (%) along Y-axis and the wavelength

(nm) along X-axis.

In this investigation, PerkinElmer double beam UV-VIS-NIR

Spectrometer was used to study the optical quality of the grown crystals in the

wavelength range of 200 to 1100 nm at room temperature.

1.21.6 Photoluminescence Spectroscopy

Photoluminescence spectroscopy (PL) is the direct emission of light

from an excited medium rather than the scattering of light and, as such,

involves real rather than virtual excitations of electrons. In PL, an excitation

source optically pumps a material. Typically, this excitation source is greater

in energy than the band gap of the material, in order to promote electrons to

excited states. After a relaxation period, electrons that fall back to lower states

through radiative recombination pathways emit photons, as shown

39

schematically in Figure 1.8. Because of the thermal relaxation, the emitted

photons have no correlation with the excitation process.

Figure 1.8 Photoluminescence process

1.21.7 Thermal Studies

Thermal studies involve the measurement of various properties of

materials subjected to dynamical change in environment. Thermogravimetric

analysis (TGA) determines the weight gain or loss of a phase due to gas

absorption or release as a function of temperature under a controlled

atmosphere. This technique provides information about the purity of the

sample, as well as its water, carbonate and organic content. It is also useful

for studying decomposition reactions, both thermal and mass transfers of the

sample are measured simultaneously. These analyses were made at the

Netzsch Thermal Analyzer, which make it possible to differentiate between

endothermic/exothermic transitions with (e.g. degradation) and without

weight change.

40

Differential Thermal Analysis (DTA) can be defined formally

as a technique for recording the difference in temperature between a

substance and a reference material against either time or against

temperature as the two specimens are subjected to identical temperature

regimes in an environment that is heated or cooled at a controlled rate. In

DTA, the difference in temperature between a reactive sample and a non-

reactive reference is determined as a function of time and temperature.

This provides useful information about the temperatures, thermodynamics and

kinetics of reactions. The key features in differential thermal analysis

equipment are a sample holder comprising thermocouples, sample

containers and a ceramic or metallic block, a furnace, a temperature

programmer and a recording system. The sample holder consists of one

thermocouple for the sample and one for the reference, generally

surrounded by a block to ensure heat is evenly distributed.

The furnaces should provide a stable and sufficiently large

hot-zone and must have a low response time in order to accurately follow

the thermal program. To obtain constant heating rates, a temperature

programmer is essential. The recording system must have a low inertial to

faithfully reproduce variations in the experimental set-up. Care must be taken

when selecting the experimental parameters. For example, specimen

environment, composition, size and surface-to-volume ratio all affect

powder decomposition reactions but may not affect solid-state phase

changes. Experiments are frequently performed on powders, so the data

obtained may not be representative of bulk samples, where the

transformations can be controlled by the build-up of strain energy.

The packing state of any powder sample is important in decomposition

reactions and can lead to large variations between apparently identical

samples. The information provided by the equipment differentiates between

endothermic or exothermic events.

41

1.21.8 Dielectric Measurement

The science of dielectrics, which has been pursued for well over

one hundred years, is one of the oldest branches of physics and has close links

to chemistry, materials, and electrical engineering. The term dielectric was

first coined by Faraday to suggest that there is something analogues to current

flow through a capacitor structure during the charging process when current

introduced at one plate (usually a metal) flows through the insulator to charge

another plate (usually a metal). The important consequence of imposing a

static external field across the capacitor is that the positively and negatively

charged species in the dielectric become polarized. Charging occurs only as

the field within the insulator is changing. Electrical measurements to evaluate

the dielectric behaviour of materials are usually made with cells having two

identical electrodes applied to the faces of a sample in the form of a pellet.

1.21.9 Mechanical Studies

Hardness of a material is the resistance it offers to indentation by a

harder body. An important use of micro hardness studies is the possibility of

making indirect estimate of other mechanical characteristics of materials

having a specific correlation with their hardness. The hardness depends not

only on the properties of the material under test but also largely on the

conditions of measurements. Hardness is an important factor in the choice of

ceramics for abrasives, tool bits, bearings and wear resistant coatings and it

generally correlates with both micro and macro and macro plastic deformation

and with ease of machining. It may be termed as a measure of the resistance

against lattice destruction or the resistance offered to permanent deformation

or damage.

42

1.21.9.1 Vicker’s microhardness studies

In order to study the mechanical properties, microhardness

measurements were carried out on the smooth surface of the crystals. The

static measurements were carried out at room temperature using Reichert MD

4000E ultra microhardness tester fitted with a Vicker’s diamond pyramidal

indenter. The loads varying from 5-50g were applied over a fixed interval of

time (10 seconds). Vicker’s microhardness values were calculated from the

formula

HV = 1.8544 P/d2 kg/mm2 (1.11)

where

HV = Vicker’s microhardness number in kg/mm2

P = applied load in g

d = average diagonal length in micro meter

The Meyer's index number was calculated from the Meyer's law,

which relates the load and indentation diagonal length.

nP k d= (1.12)

log P = logk + nlogd (1.13)

where, k is the material constant and n is the Meyer's index. The plot between

log P and log d, is a straight line and the slope of this straight line gives the

value of n. Hv should increase with the increase of P if n > 2 and decrease if

n < 2. According to Onitsch (Onitsch 1947) n should lie between 1 and 1.6 for

harder materials and above 1.6 for softer materials. For a crystal with

43

well-defined cracks, the resistance to fracture indicates the toughness of a

material. According to Ponton and Rawling (Ponton and Rawling, 1989)

fracture toughness Kc is dependent on the ratio of c/a, where c is the crack

length and a is the half-diagonal length of the square indentation as shown in

Figure 1.9.

Figure 1.9 Schematic diagram of the microindentation on the polished

surface of crystal

For c/a ≥ 2.5, the cracks are developed with median crack system

and the fracture toughness c/a is calculated using the equation

3/ 2c

kPK

c= (1.14)

where the constant k = 1/7 for the Vickers indenter.

For c/a ≤ 2.5, the cracks have the Palmqvist conguration and Kc is

obtained by the relation

1/ 2c

kPK

al= (1.15)

44

where l = c − a is the mean Palmqvist crack length. The brittleness index Bi is

calculated using the relation

vi

c

HB

K= (1.16)

From the hardness values, the Yield strength σy can be calculated

and it is defined as the stress at which the material begins to deform

plastically and depends on Meyer's index n. For n > 2, the yield strength σy

may be calculated using the expression

( )2

12.5 23

2.9 3

n

y v

nnH

nσ

−− −

= −

(1.17)

For n < 2, the yield strength is calculated using the relation

3v

y

Hσ = (1.18)

1.21.10 Etching Studies

The study of the identification, origin and characteristic of

crystalline defects such as boundaries, slip planes, dislocation and plastic flow

relies heavily on etching phenomena (Sangwal 1987). Etching is the selective

dissolution of the crystal, a reverse phenomenon of growth. When a crystal

phase is exposed to a solvent, dissolution begins by the nucleation of unit pits

of one molecular depth which then grows in the size by the retreating steps

across the crystal surface.

45

Etching is however a surface technique and care must be exercised

in the interpretation of etching studies, since defect densities and properties in

the surface and bulk regions of crystals frequently show a marked difference.

For any defect etchant, it is essential to assess the extent to which a

correspondence exists between etch features and dislocations. In general, it

should be noted that not all etch pits are necessarily formed at emergent

dislocations and that not all dislocations give rise to etch features.

An etchant is a solvent of the testing sample. But all the solvents

are not the best etchants for the same sample. An etchant should satisfy the

following requirement: continued etching of a surface should, in general

result in no net change in the number of pits other than where pits are

associated with, for example, dislocation loops. In such cases, the pits should

appear or disappear in pairs. The occurrence of etch pits is an illustration of

the enhanced chemical reactivity of dislocation, while in this case the

different etch pit shapes on the same crystal face demonstrate the dependence

of this behaviour upon dislocation character. This technique requires only

very basic equipment and yields much valuable information, particularly

about mechanical properties.

There are different methods to obtain preferential dislocation on a

crystal surface such as Chemical etching, Thermal etching, Ionic etching and

Electrolytic etching. In chemical etching the growth spiral could be removed

by observing the impressions of the depressions that are left behind.

The three important parameters for performing chemical etching of

a material are;

(i) Etchant

(ii) Temperature of Etching

(iii) Time of Etching

46

1.21.11 Second Harmonic Generation (SHG) Efficiency in Powder

The SHG is produced when monochroromatic light passes through

a non-centrosymmetric crystal. For a single crystal, only certain orientations

in respect to incoming photons will produce SHG. However, by grinding the

single crystal or using a polycrystalline powder, one arrives to a large number

of randomly oriented small crystallites whose SHG does not depend on the

incoming light direction. This simplifies both qualitative and quantitative

SHG measurements, as first described by Kurtz and Perry.

Kurtz and Perry (1968) demonstrated that it was possible to

perform second harmonic generation (SHG) studies on microcrystalline

powders to predict the phase matching direction in crystals and determine

their averaged nonlinear efficiency. The SHG intensity generated by a powder

in a solid angle of 360º depends on the averaged nonlinear efficiency of the

material but also on the particle size and the total number of small crystals

irradiated by the incident beam. The basic assumptions made by Kurtz and

Perry were that the powder particles were small crystals of almost identical

size, randomly orientated and densely packed. These assumptions mean that

form factors, polycrystallinity, and voids are avoided. Taking these

assumptions into account the small crystals were powdered and graded with

standard sieves to obtain a uniform particle size between 5 and 20 µm. Then,

they were uniformly packed in a capillary tube. Figure 1.10 shows the

schematic of experimental set-up used to make the measurements.

47

Figure 1.10 Schematic of Experimental set up used to measure SHG

efficiency in powder

To irradiate the sample, an Nd: YAG laser emitting at 1.064 µm

wavelength was used. The fundamental power at 1.064 µm reflected by the

sample was measured using a silicon photodiode. The beam generated by

the sample was focused with a lens to a silicon photodiode and an

interferometric filter to eliminate the non-doubled portion of the incident

power. Signals were collected and analysed using a digital oscilloscope. The

SHG efficiency of grown crystals was compared with standard material KDP

and urea.

1.22 THE CONTENT OF THESIS

The synthesis and growth of 1H-Benzimidazolium hydrogen

L-tartrate dihydrate (BT) single crystal by solution growth technique are

presented. Grown crystal characterized by Single crystal XRD confirms that

BT crystallizes in the monoclinic system, space group P21 with the unit cell

parameters a = 9.222(2) Å, b = 7.282(1) Å, c = 10.945(2) Å, β = 110.30(2)°

and V = 689.4(3) Å3. High-resolution X-ray diffractometry (HRXRD) was

carried out to evaluate the crystalline perfection of the specimen crystal.

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The low full width at half maximum (FWHM) and the low angular spread of

around 450 arc s (one eight of a degree) of the diffraction curve indicates that

the crystalline perfection is fairly good. The functional groups present in the

grown crystal were identified by FT-IR spectral analysis. The optical study

reveals high transparency of BT crystal in the entire visible region.

The optical band gap and refractive index (n) of the material were calculated

from the transmittance spectrum. The broad greenish yellow emission is

centered at 2.38 eV in PL spectrum. The thermal analyses revealed good

thermal stability of the material thus proving its suitability for NLO

applications. The work hardening coefficient ‘n’ is found to be more than 2.

Surface micrographs recorded from etching studies revealed that BT crystal

grows by two dimensional layer growth mechanisms. The SHG efficiency

was measured using Kurtz-Perry technique. BT exhibits the SHG 1.2 times

that of KDP.

The results on synthesis, growth and characterization of

2-Aminopyridinium 4-methylbenzoate dihydrate (2A4M) are elaborated. The

single crystal X-ray diffraction analysis revealed that the crystal belongs to

monoclinic system. The optical transmittance data give maximum

transparency in the range of 300-700 nm. The functional groups were

confirmed by FT-IR. The thermal behaviour of the grown crystal was studied

by TG-DTA. From the Vickers hardness studies (Hv), fracture toughness (Kc),

brittleness (Bi), yield strength (σy) and elastic stiffness constant (C11) were

calculated. The work hardening coefficient was calculated as 3. The etching

study revealed rectangular hillocks and mono layer growth mechanism. SHG

relative efficiency of 2A4M is 3.03 times that of KDP.

The synthesis and growth of Bis(tetraethylammonium)

bis(hydrogen L-tartrate) L-tartaric acid monohydrate (TELT) by solution

growth technique are presented. The structure was solved by direct methods

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using the programme SHELXS-97 (Sheldrick 2008). The refinement and all

further calculations were carried out using SHELXL-97. The single crystal

X-ray diffraction confirmed that the grown crystal belongs to monoclinic

system with space group P21, a = 7.5725 (4) Å, b = 27.7907 (13) Å,

c = 8.7620 (6) Å, β = 99.884 (5)º, V = 1816.55 (18) Å3. Fourier transform

infrared spectroscopy (FTIR) reveals the functional groups of the grown

crystal. Optical transparency of the grown crystal shows lower optical cut off

at 252 nm and optical band gap is 3.6 eV. Thermogravimetric (TG) and

differential thermal analysis (DTA) studies revealed that TELT is thermally

stable up to 192˚ C. Mechanical studies carried out on the well developed

(001) crystallographic plane using Vickers microhardness tester, revealed that

hardness increases with increasing load. Work hardening coefficient (n),

fracture toughness (Kc), brittleness index (Bi), yield strength (σy) and elastic

stiffness constant (C11) were calculated. Etching studies were carried out

using water as etchant. The observed etch patterns confirm the layer growth

mechanism. The second harmonic generation was confirmed by Kurtz-Perry

technique. The SHG efficiency of this material is low compared to standard

material.

The growth of single crystals of La4Mo7O27 by the flux growth

method using H3BO3 as the flux is presented with size 0.8×0.3×0.2 mm3. The

crystals were grown in plantium crucible using the starting materials of

La2O3, H3BO3 and MoO3 in a molar ratio of 0.16: 0.16: 0.68 under the

optimized crystal growth conditions: growth temperature 827°C, growth time

of 95 h and cooling rate of 0.5°C/h. The grown crystals were subjected to

powder X-ray diffraction (PXRD), EDX, UV-Vis, SEM, Photoluminescence,

thermal, dielectric and Second Harmonic generation (SHG) studies.

Benzil single crystal of <100> direction with 18 mm diameter and

75 mm length was successfully grown by Sankaranarayanan-Ramasamy (SR)

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method and subjected to various characterization like single crystal XRD,

Powder XRD, High-resolution X-ray diffractometry (HRXRD), Optical and

PL studies, FT-IR and laser Raman studies, Vickers microhardness, Etching,

Second Harmoinc generation (SHG) studies. Half wave voltage measurement

was made by applying high voltage to the crystal. The intensity variation on

applied voltage is plotted as well the variation is pictured from the

oscilloscope display.

The outcomes of the investigation were published in International

journals and National/ International conferences.