Chapter 6 ~~~~~~~~~~

Micro topography, Optical and Dielectric studies

```````````````````````````````````````````````````````````` I was perpetually asking not for

mathematical equations, but for physical circumstances of

what they were trying to work out.

R. FEYNMAN.

The physical characteristics of the rare-earth doped especially Nd3+

doped phosphates, molybdates, borates, vanadates etc. are

predicted to be of mammoth implication in the field of electro-

optical devices [1 to 8].The characteristics of the solid state

materials including crystals are mainly based on micro and macro

structures. The dependence of the properties on the micro

structure is by and large very convoluted and unravelling. The

lattice structure and the associated lattice defects play a major

role in determining the properties of the crystals. Several

experimental techniques compliment one another are used for the

detection of the lattice defects. The study of the surface of the

crystal gives valuable information about its internal structure. The

subject of dislocations is an essential basis for an understanding

of many of the physical and mechanical properties of crystalline

solids. Historically speaking, the morphology or external

appearance of crystals was observed first, and from its study the

symmetry elements present in crystals were deduced. The

morphological studies of a number of phosphate crystals as well

as other crystals have been reviewed [9 to 36].

In the present chapter the surface features as well as optical and

dielectric properties of the grown crystals have been thoroughly

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investigated. Scanning Electron Microscopy and Optical

Microscopy were used to study the nature of growth patterns on

the surfaces. Dislocations have been studied by chemical etching

techniques which are a reliable and powerful tool in revealing the

lattice defects. Optical absorption measurements were done at

ultra violet visible frequency range. Dielectric properties have been

studied at microwave frequencies.

6.1 Surface Morphology by Optical Microscopy

6.1.1 Introduction

Microscopic observation of the morphology of the crystals is the

first step in crystal study and its characterization. Crystals grow or

dissolve through the surface and the surface features of a crystal

give clue to understand the mechanism and history of crystal

growth. The surface studies also provide information about the

nature and distribution of imperfection in a crystal [37, 38].

The habit of a crystal is determined by the slowest growing faces

having the lowest surface energy, but it is apparent that a crystal

habit is governed by kinetics rather than equilibrium

considerations. Morphology of the crystals depends on the growth

rates of the different crystallographic faces.

The defects on the surface of the materials have a characteristic

role on the growth and morphology of the crystals. The surface by

itself is actually a lattice defect as it is abrupt termination of the

periodic lattice. The basic problem is inherent to the surface of

solid materials. It is due to the fact that the surface atoms are

chemically unsaturated. Therefore it has an inherent tendency to

react physically and or chemically with its surroundings and this

may lead to contamination or corrosion. Hence it is expected that

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the study of the surface in detail will throw light on the

characteristics of the bulk material [39, 40].

The use of optical lenses to enlarge the image of the object allows a

wealth of information to be obtained. From the single lens

magnifying glass through to more complex optical microscopes,

visual examination enables materials and surface treatments to be

identified and characterised. The unprepared surfaces of objects

can show details of colour, surface pattern and texture, tool

marks, joins repairs, wear, surface coatings, manufacture,

corrosion attack and inscriptions [41, 42].

The grown crystals were examined under a Leitz Metallux-3 optical

microscope. A camera is attached to the vertical photo-port of the

microscope to photograph the image. Magnifications of 50, 100,

200 and1000 are possible with the adjustable objectives.

6.1.2 Calcium hydrogen phosphate crystals

The optical microscopic photograph of calcium hydrogen

phosphate crystals are shown in Figs. 6.1.2a to 6.1.2c. Parallel

lines or furrows called striations are seen here. Striations are thick

growth layers formed on the surface due to periodic incorporation

of impurities or variation of microscopic growth rate [43 to 45].

With the high concentration of reactants, thickness increases and

in low concentration, very thin layers appear to be plane, flat

surfaces [46, 47]. A typical platelet crystal is shown in Fig 6.1.2c.

6.1.3 Neodymium doped calcium hydrogen phosphate crystals

The optical microscopic photograph of neodymium doped calcium

hydrogen phosphate crystals are shown in Figs. 6.1.3a to 6.1.3c.

Fig 6.1.3a depicts a typical crystal. Microscopically examination

showed the detailed morphology of these crystals. Major faces are

plane with micro growth features. On some crystals thin platelets

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were found to grow which has got the same morphology as the

parent crystal. It is strange that these crystals are found to orient

along the longer dimension of the parent crystal.

Fig 6.1.2a CHP crystal with Fig 6.1.2b CHP crystal with striations striations × 100 × 100

Fig 6.1.2c A typical platelet Fig 6.1.3a A typical platelet

CHP crystal × 100 Nd:CHP crystal × 100

Fig 6.1.3bNd: CHP crystals Fig 6.1.3c A typical acicular

with striations × 100 crystal × 100

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This shows that the mechanism of this growth is related to the

main crystal. Sometimes further growth is observed on the

microcrystal. Some crystals show plane surfaces without any

growth features.

Microscopically observations in high magnification showed the

growth mechanism of some of another type of crystals. These

crystals are initially grown in a preferable direction in the form of

needles. Further growth takes place by spreading of thick layers

over these needles. In the process of growth, branches are

developed in an angle of 300. A typical growth pattern at this stage

is shown in Fig 6.1.3c. At this stage micro branches are also

developed in between these main branches. In the next stage these

branches are found to join together and in final stage these

branches are completely disappear forming visible faces.

Further growth on this faces show nucleation of new layers and

spreading it from the centre towards the edges of the crystal. This

growth fronts are thick and mottled in nature. This is because of

the abundant supply of nutrient at this stage.

Most of the faces shows natural etch patterns which is evident in

Fig 6.1.3a. It shows that while the crystals grow, dissolution is

also taking place. Mottled nature of the growth front may also be

due to dissolution process.

6.1.4 Barium hydrogen phosphate crystals

Figs 6.1.4a and 6.1.4b are the optical microscopic photograph

depicting the various forms of barium hydrogen phosphate

crystals grown. The most typical forms are cubic, hexagonal,

octahedron and pyramidal. It is also interesting to note that the

surface contains terraces, steps, kinks, adatoms and advacancies.

Fig 6.1.4b shows four crystals grow from a common centre.

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6.1.5 Neodymium doped barium hydrogen phosphate crystals

The harvested crystals were of different morphologies at different

regions of the growth apparatus. The crystals formed were

clustered, twinned and with multiple faces and striations. Typical

patterns are shown in Figs.6.1.5a to 6.1.5d.The region very near to

the gel interface, where rate of diffusion is more; crystals formed

were clustered, flower like patterns as shown in Fig 6.1.5b. At the

middle of the gel region less clustered, multifaceted and inter

grown twinned crystals were formed as shown in Fig 6.1.5.a. It can

be seen that the faces of the crystal are smooth, devoid of any

growth features. Sometimes it was observed that facets were

developed on the well formed octahedral faces of some crystals. Fig

6.1.5d shows a typical case. This may be due to the independent

nucleation of a separate crystal on the major face while the parent

crystal grows at a higher rate.

Growth striations in crystals appear as continuous lines running

perpendicular to the direction of growth. They are formed due to

periodic incorporation of impurities or non-stoichiometric material,

caused by variations in microscopic growth rate or diffusion layer

thickness [43,44,45].

Crystal twinning occurs when two separate crystals share some of

the same crystal lattice points in a symmetrical manner. The

result is an intergrowth of two separate crystals in a variety of

specific configurations. A twin boundary or composition surface

separates the two crystals. Crystallographers classify twinned

crystals by a number of twin laws. These twin laws are specific to

the crystal system. The type of twinning can be a diagnostic tool in

mineral identification [48].

Simple twinned crystals may be contact twins or penetration

twins. Contact twins share a single composition surface often

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appearing as mirror images across the boundary. Quartz, gypsum,

and spinel often exhibit contact twinning. In penetration twins the

individual crystals have the appearance of passing through each

other in a symmetrical manner. Orthoclase, staurolite, pyrite, and

fluorite often show penetration twinning.

If several twin crystal parts are aligned by the same twin law they

are referred to as multiple or repeated twins. If these multiple

twins are aligned in parallel they are called polysynthetic twins.

When the multiple twins are not parallel they are cyclic twins.

Albite, calcite, and pyrite often show polysynthetic twinning.

Closely spaced polysynthetic twinning is often observed as

striations or fine parallel lines on the crystal face. Rutile,

aragonite, cerussite, and chrysoberyl often exhibit cyclic twinning,

typically in a radiating pattern.

There are three modes of formation of twinned crystals. Growth

twins are the result of an interruption or change in the lattice

during formation or growth due to a possible deformation from a

larger substituting ion. Transformation twins are the result of a

change in crystal system during cooling as one form becomes

unstable and the crystal structure must re-organize or transform

into another more stable form. Deformation or gliding twins are

the result of stress on the crystal after the crystal has formed.

Deformation twinning is a common result of regional

metamorphism. Crystals that grow adjacent to each other may be

aligned to resemble twinning. This parallel growth simply reduces

system energy and is not twinning. Twin boundaries are visible as

striations within each crystallite [48].

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Fig 6.1.4a various forms of Fig 6.1.4b A typical BHP crystal

BHP crystals × 100 × 100

Fig 6.1.5a A twinned Nd:BHPcrystal Fig 6.1.5b A clustered × 100 Nd:BHPcrystal × 100

Fig 6.1.5c: A multifaceted Fig 6.1.5d Multifaceted twinned twinned Nd:BHP crystal Nd:BHP crystal × 100

× 100

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6.1.6 Strontium hydrogen phosphate crystals

In the case of strontium hydrogen phosphate, very interesting

types of crystals are found to grow unlike in other cases. Most of

them are grown in spherulites form as shown in Figs 6.1.6a to

6.1.6d. In Fig 6.1.6a symmetrical spherical aggregates can be

seen. They are of various sizes. Typical spherulites are shown in

Fig 6.1.6b. Individual crystals with shining faces can be seen on

the surface of the sphere. In another crystal, Fig 6.1.6c crystals

are found to grow from a centre. These spherulites are found to

take a form from the perfect sphere at the centre to oval shape,

having crystallites emerging outwards from the centre. The

spherulitic growth seems to have occurred through a lengthening

of the plates with accompanied plate branching [19, 20]. The

mechanism of the formation of spherulites is as follows- a single

nucleus is formed either by an impurity or of the material of the

crystal since the local concentration surrounding this nucleus is

large, rapid growth takes place resulting in formation of a number

of nuclei on the initial growth centre and crystals develop on each

centres and radiating out uniformly.

6.1.7 Neodymium doped strontium hydrogen phosphate crystals

Typical patterns of Neodymium doped strontium hydrogen

phosphate crystals are shown in Figs 6.1.7a to 6.1.7d. Spherulites

as well as single crystals can be seen in this case. A general

photograph is given in Fig 6.1.7a. Smooth surfaced spherulitic

single crystals and radiating single crystals can be seen here. Fig

6.1.7b is a typical single crystal grown in the system. They are of

rhombohedral, elongated in shape; faces are smooth and are

transparent. Fig 6.1.7c shows spherulitic growth with individual

crystal protruding from the centre. These different types of growth

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Fig 6.1.6a Spherulites of SHP Fig 6.1.6b A typical Spherulite

× 100 of SHP × 100

Fig 6.1.6c A typical spherulite Fig 6.1.6d A typical spherulite of SHP ×100 of SHP crystal × 100

can be explained due to local concentration gradient as well as

doping ions. The doped crystals are much more transparent than

the pure ones. This may be due to the elimination of vacancies or

light scattering centres from the crystal. Smooth surfaced

spherulites are formed at highly concentrated regions. In this case

deposition takes place very rapidly. In the intermediate

concentration regions, spherulites with bigger crystals are formed.

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Fig 6.1.7a typical spherulites Fig 6.1.7b A typical single

of Nd:SHP × 100 crystal of Nd:SHP × 100

Fig 6.1.7c A typical spherulite Fig 6.1.7d A typical oval of Nd:SHP ×100 crystal of Nd:SHP ×100

The spherulites were found to take a form from perfect sphere to

oval shape, having crystallites emerging outwards from the centre.

The spherulitic growth seems to have occurred through a

lengthening of the plates with accompanied plate branching,

causing it to “fill-in” the interior of the spherulites. It can be

considered as a three dimensional spherulites [49, 50].

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6.2 Surface Morphology by Scanning Electron Microscopy 6.2.1 Introduction

At the moment, the scanning electron microscope (SEM) is utilized

not only in the field of medical science and biology, but also in

varied disciplines such as materials development, metallic

materials, ceramics, and semiconductors. Electron microscopy

takes advantage of the wave nature of rapidly moving electrons.

Where visible light has wavelengths from 4,000 to 7,000

Angstroms, electrons accelerated to 10,000 KeV have a wavelength

of 0.12 Angstroms. Optical microscopes have their resolution

limited by the diffraction of light to about 1000 diameters

magnification. Electron microscopes, so far, are limited to

magnifications of around 1,000,000 diameters, primarily because

of spherical and chromatic aberrations. Scanning electron

microscope resolutions are currently limited to around 25

Angstroms, though, for a variety of reasons [51, 52,53].

The scanning electron microscope generates a beam of electrons in

a vacuum. That beam is collimated by electromagnetic condenser

lenses, focused by an objective lens, and scanned across the

surface of the sample by electromagnetic deflection coils. The

primary imaging method is by collecting secondary electrons that

are released by the sample. The secondary electrons are detected

by a scintillation material that produces flashes of light from the

electrons. The light flashes are then detected and amplified by a

photomultiplier tube.

By correlating the sample scan position with the resulting signal,

an image can be formed that is strikingly similar to what would be

seen through an optical microscope. The illumination and

shadowing shows a quite natural looking surface topography.

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6.2.2 Pure and neodymium doped calcium hydrogen phosphate crystals

Crystals having a range of morphologies were observed. The

figures 6.2.2a and 6.2.2b illustrate SEM photographs of single

crystals of pure calcium hydrogen phosphate and Fig 6.2.2c and

Fig 6.2.2d that of Nd3+ doped calcium hydrogen phosphate

respectively. These crystals are grown by layer deposition. Thick

and thin layers are seen in figures. A representative thick layer is

shown in Fig 6.2.2b. Small quantities of impurity, or excess or

deficiency of native species can be accommodated in the crystal

lattice without breakdown of the growth surface. However, there is

a high probability that the incorporation will be spatially non-

uniform.

Fig 6.2.2a SEM photograph of CHP Fig 6.2.2b SEM Photograph of CHP

Fig 6.2.2c SEM photograph of Nd:CHP Fig 6.2.2d SEM photograph of Nd:CHP

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As observed by the optical microscope, no spherulitic forms are

observed. SEM photographs of a typical undoped crystal, Fig

6.2.2a, show protruding overgrowth on its smooth surface. This

might have been happened at the last stage of the developments of

crystals. The surfaces are smooth even at this magnification of

300µm. By doping with Nd3+ increased smoothness was attained

without appreciably changing the morphology. Careful examination

under the SEM shows that the surface of the doped crystals are

exceedingly plane without protruding crystallites, which is clear

from Fig 6.2.2c.As mentioned earlier doping has made the crystal

more transparent and devoid of any surface defects.

6.2.3 Pure and neodymium doped barium hydrogen phosphate crystals

SEM photographs of barium hydrogen phosphate crystals are

shown in Figs. 6.2.3a and 6.2.3b and that of neodymium doped

barium hydrogen phosphate crystals are shown in Figs. 6.2.3c

and 6.2.3d. The surface of the crystals is plane devoid of thick

growth layers except the one shown in the marked region of Fig

6.2.3a. In this case rectangular platelet is stuck on the surface

and layered structure can be visible. Examination of BHP under

higher magnification show smooth as well as striated crystals.

Striations are edges of growth layers or fine parallel lines on the

crystal face [53, 54]. Island formation can also be seen on the

surface. Fig 6.2.3b show a single platelet crystal with exceedingly

smooth surface.

In the case of Nd:BHP, the crystals are of different morphologies

at different regions of the gel growth apparatus. In most cases the

crystals formed near to the interface at greater diffusion region,

were clustered, twinned and multiple crystals [17, 23]. One such

typical pattern is shown in Fig 6.2.3c. Towards the middle of the

crystallization region clustering and multiplicity were reduced.

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Fully developed micro crystals with perfect faces can be seen in Fig

6.2.3d. Average long dimension comes to about 300μ m. By doping

with Nd3+ increased smoothness was attained without appreciably

changing the morphology.

Fig 6.2.3a SEM photograph of BHP Fig 6.2.3b SEM photograph of BHP

Fig 6.2.3c SEM photograph of Nd:BHP Fig 6.2.3d SEM photograph of Nd:BHP

6.2.4 Pure and neodymium doped strontium hydrogen

phosphate crystals SEM photographs of strontium hydrogen phosphate crystals are

shown in Figs. 6.2.4a to 6.2.4e and that of neodymium doped

strontium hydrogen phosphate crystals are shown in Figures

6.2.4f to 6.2.4h. General nature of SHP is shown in Fig 6.2.4a; it is

observed that spherulites are grown along with single crystals. The

size of the spherulites varies from 1000μ m to 3000μ m. The

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smaller spherulites are composed of very fine crystallites while

bigger ones show outwardly grown comparatively bigger crystals.

Smooth spherulites at still higher magnification show micro

crystal aggregate nature. Fig 6.2.4b shows typical spherulites in

higher magnification. Individual micro crystals can be clearly

visible. A typical example of non-spherical spherulites is shown in

Fig 6.2.4c. In this case the structure is made up of amorphous

aggregates. In Fig 6.2.4d petal like formation of the elongated

aggregate crystal is shown. An interesting observation is displayed

in Fig 6.2.4e. Here a number of spherulites are joined together

forming single agglomerate [53, 54].

Fig 6.2.4a SEM photograph of SHP Fig 6.2.4b SEM of SHP

Fig 6.2.4c SEM of SHP Fig 6.2.4d SEM of SHP

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Fig 6.2.4e SEM photograph of SHP Fig 6.2.4f SEM photograph of Nd:SHP

Fig 6.2.4g SEM photograph of Nd:SHP Fig 6.2.4h SEM photograph of Nd:SHP

In the case of Nd:SHP, spherulites similar in morphology to SHP is

also observed along with other crystals. Fig 6.2.4g shows radiating

crystals from a single centre. It is quite interesting to note the

nucleation centres of this crystal. These spherulites were found to

take a form from perfect sphere to oval shape, having crystallites

emerging outwards from the centre. The spherulitic growth seems

to have occurred through a lengthening of the plates with

accompanied plate branching, causing it to ‘fill in’ the interior of

the spherulites.

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6.3 Dislocation studies

6.3.1 Introduction

Studies on the microstructure and the etch patterns on habit faces

of crystals are helpful in understanding the growth mechanism

and defects of crystalline material. The morphology as well as

surface features of the crystal is more sensitive to the difference in

growth conditions. Kossel Stranski and Volmer first recognized the

importance of surface discontinuities as nucleation sites [55].

Burton, Cabrera and Frank showed how the emergence points of

dislocations with screw components at crystal surfaces acted as

continuous generators of surface ledges affording possibility of

continuous growth at much lower saturations [56].They also

suggested that surface roughness of a particular crystallographic

plane depended upon the inter atomic bonding forces between

surface atoms and their neighbours.

Since the existence of imperfections such as impurities, stacking

faults, edge and screw dislocations have profound influence on the

growth patterns; surface structure studies of crystal faces provide

information about such defects. The study of dislocation in

crystals can effectively carry out by etching technique. The micro

structure and the etching studies on the habit faces were reported

by several workers [57 to 60].

The attack of a solvent or chemical reagent on a crystal is

frequently localised in small depressions. The solvent or the

chemical reagent is called the etchant and the depressions are

called etch pits or etch figures, while the process is known as

etching. The shape of the etch figures depends upon the nature of

the solvent and the symmetry of the crystal face on which they

appear. Just as the regular geometry and external shape of the

crystal are an expression of an orderly arrangement in which the

217

units of construction are built up during growth, so also when it is

attacked by an etchant, the etch patterns produced are related to

the internal molecular structure.

Widmann-Statten, was the first who produced the characteristic

etch pattern on meteorites by the corrosion with acids in 1808,

and the first publication was due to Wollaston and detailed study

was due to Leydolt [61,62]. Daniell was the pioneer who tried to

correlate the nature of the etch figures with the molecular

structure of the crystalline solids [63]. Notable contributions were

made by the German scientists Baumhauer becke, Traube,

Tschermark, Wulff, Beckenkamp and others [64, 65]. In the first

two decades of the 20th century, Goldschmidt, Wrigdt, Kollar,

Gaubert, McNairan, Honess and many others made a goniometric

study of etch figures [66, 67 and 68].

According to Goldschmidt, both etch pits and etch hillocks are a

result of the movements developed in the solvent. The chemical

action between the corrosive and the substance upon which it is

acting gives rise to currents, some of which are directed towards

and some away from the surface which is being etched. The

interference of the ascending and the descending currents tends to

form eddies each of which is a starting point of a pit. McNairan

studied the origin and the subsequent growth of the pits and

suggested that the lines of selective pitting are also the lines of

weak cohesion, as for example, cleavage planes are corroded much

more slowly than those of the lower degree [67]. Desch performed

etching experiments on alum and showed that the explanations

offered by Goldschmidt and others, regarding the etch pits are

inadequate [69].The most obvious fact which even the simplest

etching experiments reveal that the etch pits are not evenly

distributed or scattered over the crystal surface.

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The usefulness of etching techniques lies in the formation of

visible, sharp, contrasting etch pits at dislocation sites. The

necessary condition for the formations of visible etch pits is the

proper ratio of the three dissolution rates. To make a complete

analysis of crystal defects it is often necessary to determine

experimentally those parameters such as direction of a dislocation,

the plane of the stacking fault, the thickness of the foil or the

distance the defect lies from a foil surface, since the image

contrast from a defect depends on these factors [70,71].

When a chemical reagent selectively reveals the surface

microstructure, including defects, the process is referred to as

selective etching. If the revelation of dislocations is of prime

concern, the term dislocation etching is frequently used. In

selective etching and profile etching of crystals, especially in

semiconductors, preferential and non preferential etchings are

also used [72].

Etching of a crystal for a short duration yields etch figures and

dissolution layers on its surfaces without loss of its macroscopic

appearance, but on prolonged etching the crystal acquires a

macroscopic form different from the initial one [73] . Micro- as

well as macro morphology of crystals depends on the etching

parameters, and has been a topic for investigation both

theoretically and experimentally. The effect of different

parameters, such as the nature of chemical reagents, their

concentration, etching temperature, etc. on the morphology of

etch pits are also worked out in the existing literature. The

subject of post-dislocation etching has been dealt with in a

number of reviews [74 to 76].

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6.3.2 Neodymium doped calcium hydrogen phosphate crystals

General nature of etch pits produced on (111) faces of Nd:CHP

after etching with dilute acetic acid for 10 sec is shown in Fig

6.3.2a.The density of etch pits is counted to be 15 within each

cm2. The density of the pits is very high showing that surface

defects seem to be very high. The etch pits are not evenly

distributed or scattered over the crystal surface. Possible

explanations for this irregularity in the density of etch pits have

been given by a number of investigators but these have, however,

proved inadequate. It may be realised that no satisfactory

explanation of this difference in the density of etch pits can be

given until the more fundamental problem of the origin of etch pits

is solved. The satisfactory explanation regarding the origin of the

etch pits and their development has been given on the new

concept of lattice defects, known as ‘dislocations’ [38, 71, 72].

Etch pits are triangular in nature, they are of different varieties-

point bottomed, flat bottomed, eccentric, stepped, dislocation loop,

grain boundary etc. Point bottomed etch pits are dark because of

its depth, as shown ‘a’ in Fig 6.3.2(a). Flat bottomed pits are

shallow in nature, as shown ‘b’ in Fig 6.3.2(a), which further reveal

that they are only a surface phenomena due to impurities attached

to the surface or shallow defects on the surface. Point bottomed

pits have found to be eccentric in some cases. Eccentric pits are

due to inclined nature of the defects. In some cases new pits are

found to originate in the shallow pits as shown ‘c’ in Fig

6.3.2a.This shows the displaced defect. In some other cases two

point bottomed pits can be seen inside a shallow bottomed pit as

shown‘d’ in Fig 6.3.2a. This may be an evidence of dislocation

loops in the crystal. Loops and etch patterns have been reported

by Damiano and Herman [77].That an etch pit can be formed

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where a dislocation meets a crystallographic surface has been

demonstrated by Horn and Gervers, Amelinckx and Dekeyser

[78,79]. They have shown that the etch pits develop where screw

dislocations emerge on the surface of SiC crystal. Vogel et al have

found striking evidence for the presence of small grain boundaries

in germanium and showed one to one correspondence between

etch pits and dislocations [80].

Fig 6.3.2(a) (111) face of Nd:CHP etched for 10 secs. × 100

Fig 6.3.2(b) (111) face of Nd:CHP etched for furthur10 secs. × 100

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The same crystal is etched further to reveal the nature of the

defect. Fig 6.3.2(b) shows the same area on the crystal after

further etching. It can be shown that pit ‘a’ has further developed

retaining its point bottom. After developing ’c’ shows one more flat

bottomed pit and a point bottomed pit inside it. This clearly shows

the stepped nature of dislocation. Flat bottomed pits in ‘b’ has

further developed and remains flat proving the surface defects

nature. In the case of ‘d’ double pits developed further revealing

the loop nature of the dislocation.

6.3.3 Neodymium doped barium hydrogen phosphate crystals

In order to study dislocation in (110) plane of the Nd:BHP crystal,

etching techniques have been utilized. Dislocation is a line defect,

hence it will continue in the crystal. When crystal is subjected to

dissolution in a suitable medium it will show small geometrical

depressions at the site of emergence of the dislocation on the face.

Good quality crystal of Nd:BHP with (110) face is dipped in 0.1M

concentration of HNO3 for 10 sec. and the crystal is taken out and

washed thoroughly and examined under the optical microscope.

Rectangular types of pits were originated randomly on the face,

which is shown in Fig 6.3.3(a). These pits are found to be dark

showing the relative depth. The bottom of the pits is generally

pyramidal and eccentric. Eccentricity shows the inclination of the

defect with the surface. Some pits are shallow. These shallow pits

may be due to surface defects or impurities on the surface.

Double pits are also seen as in the case of Nd:CHP. This may be

due to dislocation loops [77]. Some pits are found to be terraced in

nature. This terracing nature may be due to impurity segregation.

In order to verify the nature of dislocation another face has been

etched for the same time and medium, which is shown in Fig

6.3.3b. Different types of pits can be seen in Fig 6.3.3a. Most of

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them are point bottomed and eccentric. This face is again etched

for the same condition as before. Pits are found to develop bigger

in size. Eccentricity is found to persist. Shallow pits remain

shallow and some disappeared altogether. Second etching

produced terracing in some of the pits. Continuous growth of pits

indicate the linearity of the defect hence evidence of this

dislocation.

These crystals are found to have vicinal faces. One such face has

been etched and a typical etch pit is shown in Fig 6.3.3b. The

formation of visible dislocation etch pits depends on the nucleation

rate per unit pit at a dislocation and the rate of motion of steps

across the surface [81].

The studies of X-ray diffraction and the observed mechanical

properties of certain crystals, indicate that nearly 108

dislocation lines thread through a square centimetre of the

surface. However, the studies of crystal growth indicate a low

value of 108 to 106. This order agrees very well with the densities

of etch pits observed by Dekeyser [82]. Omar, Pandya and

Tolansky have reported that the number of etch pits per square

centimetre on the octahedral surface of diamond, etched in

potassium nitrate is of the order of 106.

The factors responsible for the preferential nucleation of

dissolution at dislocations have been discussed by Cabrera et al

[83]. He has emphasized the role of dislocation energy in the

formation of pits. He has considered the formation of pits by

evaporation. The dislocation energy which plays its role in the

nucleation of a single pit is termed as localized energy near a

dislocation. Such energy consists of core energy and a small

fraction of the total elastic energy [84, 85].

223

Fig 6.3.3(a) (110) face of Nd:BHP etched for 10 secs. ×100

Fig 6.3.3(b) (110) face of Nd:CHP etched for further 10 secs. ×100

Fig 6.3.3© (110) face of Nd:CHP etched for further 10 secs. ×100

Fig 6.3.3(d) (110) face of Nd:CHP etched for further 10 secs. ×100

6.3.4 Conclusions The general review given above indicates that under suitable

conditions etch methods are reliable, simple in operation and

powerful in revealing the lattice defects. As a summary, the etch

patterns produced on crystal faces may be effectively used for the

following purposes:

1. to decide whether a particular solid is single crystal or an

amorphous body,

2. to distinguish different faces of a crystal ,

3. to reveal the history of growth of a crystal ,

224

4. to determine the density of dislocations, their nature and

structure,

5. to determine impurity distribution in crystalline bodies.

6.4 UV-Visible Absorption Studies 6.4.1 Introduction Ultraviolet absorption spectra arise from transition of electron or

electrons within a molecule or an ion from a lower to a higher

electronic energy level and the ultraviolet emission spectra arise

from the reverse type of transition. For radiation to cause

electronic excitation, it must be in the UV region of the

electromagnetic spectrum.

When a molecule absorbs Ultraviolet radiation of frequency ν sec-1,

the electron in that molecule undergoes transition from a lower to

a higher level or molecular orbital, the energy difference is given

by, E = hν erg. The actual amount of energy required depends on

the difference in energy between the ground state E0 and excited

state E1 of the electrons. Then E1-E0 = hν.

The total energy of a molecule is the sum electronic, vibrational

and rotational energy. The magnitude of these energies decreases

in the following order: Eele, Evib and Erot [86 to 89].

As ultraviolet energy is quantised, the absorption spectrum arising

from a single electronic transition must consist of a single discrete

line. But a discrete line is not obtained because electronic

absorption is superimposed upon rotational and vibrational

sublevels. For this reason the spectra of simple molecules in the

gaseous state contain narrow absorption peaks where each peak is

representing a transition from a particular combination of

vibrational and rotational levels in the electronic ground state to a

225

corresponding combination in the excited state. This is shown in

Fig 6.4.1.

Fig 6.4.1 Energy level diagram of a diatomic molecule.

In the case of complex molecules having more than two atoms,

discrete bands coalesce to produce broad absorption bands or

band envelopes. Energy absorbed in the ultraviolet region

produces changes in the electronic energy of the molecule

resulting from transitions of valence electrons in the molecule. The

optical absorption studies of Nd3+ in various crystalline and glassy

matrices have been studied extensively [1, 3, 4, 8, 90 to 95].

6.4.2 Neodymium doped calcium hydrogen phosphate crystals

UV- visible absorption spectrum of Nd:CHP is shown in Fig 6.4.2.

The absorption peaks corresponding to various excitations of Nd3+

4F7/2

4F9/2

2H11/2

2K15/2

2K13/2

4G5/2

Ground state

Exci

ted

stat

es

4I9/2

4F5/2

226

ions from the ground state 4I9/2 are assigned [96]. The peak

position, energy and possible assignments are given in Table 6.1.

Table 6.4.1 The peak position, energy and possible spectral transitions of

Nd:CHP

Peak position (nm) Energy (cm-1) Assignments

524 19 084 4I9/2 → 2K13/2

579 17 271 4I9/2 → 4G5/2

678 14 749 4I9/2 → 4F9/2

743 13 459 4I9/2 → 4F7/2

798 12 531 4I9/2 → 4F5/2

400 500 600 700 8000.09

0.10

0.11

0.12

0.13

Abs

orba

nce

Wavelength (nm)

Fig 6.4.2 UV-Visible Absorption spectrum of Nd:CHP

The 4G5/2 transition is hypersensitive and was clearly identified

with a band at 17 271cm-1. Of the transitions to 2K13/2 and 4G7/2

227

which calculated near to the same energy, the latter was assigned

to the centre of a band at 19 084cm-1, since the former could not

account for the observed intensity.

6.4.3 Neodymium doped barium hydrogen phosphate crystals

UV- visible absorption spectrum of Nd:BHP is shown in Fig 6.4.3.

The absorption peaks corresponding to various excitations of Nd3+

ions from the ground state are assigned [96]. The peak position,

energy and possible assignments are given in Table 6.4.2.

The 4G5/2 transition is hypersensitive and was clearly identified

with a band at 17 271cm-1. Of the transitions to 2K13/2 and 4G7/2

which calculated near to the same energy, the latter was assigned

to the centre of a band at 19 084cm-1 since the former could not

account for the observed intensity.

Table 6.4.2 The peak position, energy and possible spectral transitions of

Nd:BHP

Peak position (nm) Energy (cm-1) Assignments

431 23 202 4I9/2 → 2P1/2

525 19 047 4I9/2 → 2K13/2

580 17 241 4I9/2 → 4G5/2

618 16 181 4I9/2 → 2H11/2

744 13 440 4I9/2 → 4F7/2

800 12 500 4I9/2 → 4F5/2

228

400 500 600 700 8000.09

0.10

0.11

0.12A

bsor

banc

e

Wavelength(nm)

Fig 6.4.3 UV-Visible Absorption spectrum of Nd:BHP

6.4.4 Neodymium doped strontium hydrogen phosphate crystals

UV- visible absorption spectrum of Nd:SHP is shown in Fig 6.4.4.

The absorption peaks corresponding to various excitations of Nd3+

ions from the ground state are assigned [96]. The peak position,

energy and possible assignments are given in Table 6.4.3.

The 4G5/2 transition is hypersensitive and was clearly identified

with a band at 17 271cm-1. Of the transitions to 2K13/2 and 4G7/2

which calculated near to the same energy, the latter was assigned

to the centre of a band at 19 084cm-1, since the former could not

account for the observed intensity.

229

Table 6.4.3

The peak position, energy and possible spectral transitions of Nd:SHP

Peak position (nm) Energy (cm-1) Assignments

474 21 097 4I9/2 → 2K15/2

524 19 084 4I9/2 → 2K13/2

579 17 271 4I9/2 → 4G5/2

626 15 974 4I9/2 → 2H11/2

678 14 749 4I9/2 → 4F9/2

743 13 459 4I9/2 → 4F7/2

798 12 531 4I9/2 → 4F5/2

200 300 400 500 600 700 8000.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Abs

orba

nce

Wavelength(nm)

Fig 6.4.4 UV-Visible Absorption spectrum of Nd:SHP

230

6.4.5 Conclusions

The UV-Visible absorption studies confirm the presence of Nd3+

ions in each crystal from their characteristic absorption peaks.

The absorption spectra of rare earths in the optical region arise

from the transition within the 4f configuration. Due to the

shielding habit of the 5s2, 5p6 shells perturbation by surrounding

neighbours does not takes place resulting sharp line spectra.

6.5 Microwave Dielectric studies 6.5.1 Introduction Microwaves present several interesting and unusual features not

found in other portions of the electromagnetic frequency spectrum.

These features make ‘microwaves’ uniquely suitable for several

applications. The main characteristic features of microwaves

originate from the small size of wavelengths (1cm to 10 cm) in

relation to the sizes of components or devices commonly used.

Since the wavelengths are small, the phase varies rapidly with

distance; consequently the techniques of circuit analysis and

design, of measurements and of power generation, and

amplification at these frequencies are distinct from those at lower

frequencies. The phase difference caused by the interconnection

between various components or various parts of a single

component is not negligible. Consequently, analyses based on

Kirchoff’s laws and voltage–current concepts are inadequate to

describe the circuit behaviour at microwave frequencies. It is

necessary to analyse the circuit or the component in terms of

electric and magnetic field associated with it [97].

Microwave has got several useful applications in communications,

in radar, in physical research, in medicine and in industrial

measurements [98]. An interesting feature among them is that

microwaves become a very powerful experimental tool for the study

231

of the basic properties of materials [99,100]. Molecular, atomic

and nuclear systems display various resonance phenomena when

placed in periodic electro magnetic fields. Several of these

resonance absorption lines lie in the microwave frequency range.

The resonance absorption is due to rotational transitions in the

molecules and the absorption spectra provide information on the

molecular structure and intermolecular energies.

The dielectric properties of materials have been studied by the

cavity perturbation technique at microwave frequency.

6.5.2 Principle and theory of cavity perturbation technique

The theory for cavity perturbation was first suggested by Bethe

and Schwinger [101]. The fundamental idea of cavity perturbation

is that the insertion of a small dielectric sample into a cavity

produces a small change in the geometrical configuration of the

electro magnetic fields. They showed that the real and imaginary

parts of complex permittivity are quantities measurable in terms of

the real and imaginary parts of complex frequency shift.

The method of measurement of complex permittivity was first

developed by Bimbaum and Franeu in which, a small cylindrical

sample was placed in a rectangular cavity, operating in the TE106

mode in X-band. The assumption that ‘the electric field in the

perturbing sample is equal to the electric field of the empty cavity’

was made in this calculation [102]. Chao reviewed the theory and

technique of cavity perturbation for measuring the conductivity

and dielectric constant of the materials [103].

For the measurements, small holes can be drilled in the cavity

walls and the sample can then be inserted into the sample holder.

The measurements of dielectric constant ‘’ and conductivity ‘’ are

performed by inserting a sample, appropriately shaped sample into

232

a cavity and determining the properties of the sample from the

resultant change in the resonant frequency and loaded Q-factor.

In cavity perturbation, rectangular or cylindrical wave-guide

resonators are employed. The availability of resonator cavity

makes it possible to measure the dielectric parameters at a

number of frequencies in single band using sweep oscillators and

network analysers.

Cavity resonators are constructed from sections of brass or copper

wave-guides. If a hollow rectangular wave-guide is scaled with

conductive walls perpendicular to the direction of propagation, the

incident and reflected waves are superimposed to generate a

standing wave. The tangential electric and magnetic field

components are zero at this wall and at distances of integral half

wavelengths from it. In such a nodal plane, a second conductive

wall can be placed without disturbing the field distribution in the

waveguide, and thereby a cavity resonator is obtained. If the

resonator is excited through a coupling mechanism, the field

intensity building up within it becomes maxima when the length of

the resonator in the direction of propagation is equal to an integral

multiple of half wavelength. Because of the different field modes

possibly existing in the wave-guide, a number of resonant

frequencies can occur.

In general for a resonator of length d and guide-wavelength gλ ,

2gp

dλ

= (6.1)

where p is an integer.

For p=1 (lowest resonator mode) this equation is identical to the

resonance condition derived for the transmission line resonators

from circuit considerations [97].

233

20

0

)(1c

g

λλ

λλ

−= (6.2)

where 0λ is the wavelength in free space and cλ =2a is the cut off

wavelength for the given wave-guide. The dominant resonator

mode considered here is known as TE101 mode. Higher order

modes are also possible and are designated as TEmnp modes.

The resonant wavelength 22 )1()2(

1

c

fdp λ

λ+

= (6.3)

This expression is valid for resonators with rectangular cross

section and of circular cross section.

The performance of the wave-guide resonators is expressed in

terms of a Q factor which may be defined as, 0

L

UQWw=

where ω0 is the resonant frequency, U the energy stored in the

resonator and WL is the power loss in the resonator.

The unloaded Q-factor of the rectangular cavity resonator is given

by, [104]

( )3333

22

22 bdaddabadaabdf

Q lopc

+++

+=

μδπσ (6.4)

where c conductivity of the walls of the material of the cavity.

skin depth.

μ permeability of the medium inside the cavity.

a, b and d breadth, height and length of the cavity.

ƒ10p resonant frequency for TE10pmode.

234

The skin depth at resonance frequency, = cpf μσπ 10

1 (6.5)

Resonant frequency and Q-factor are the fundamental parameters

of a resonator. These parameters are evaluated using the above

equations.

6.5.3 Complex permittivity of materials

When a small sample is inserted in a cavity, which has the electric

field E0and magnetic field H0 in the unperturbed state, the fields in

the interior of the object are E and H. Beginning with Maxwell’s

equations, an expression for the resonant frequency shift can be

deduced. For a loss less sample, the variation of resonant

frequency is given by Harrington as [105],

−=−ωωω 0 ( )

( ) τμετμε

dHHEEdHHEE

*0

*0

*0

*0

....

+∫Δ+Δ∫

(6.6)

where and μ are the permittivity and μ permeability of the

medium in the unperturbed cavity, d is the elemental volume, Δ

and Δμ are the changes in the above quantities due to the

introduction of the sample in the cavity. Waldron gave an

expression for the shift due to a loss sample in a cavity without

affecting the generality of Maxwell’s equation as [106],

( )

( )∫

∫∫+

−+−

=ΩΩ

−

c

ss

V

Vr

Vr

dVHBED

dVHHdVEE

*00

*00

*00

*00

..

.1.)1( μμεεδ (6.7)

where Ω is the complex frequency shift, B0,H0,D0 and E0 are the

fields in the unperturbed cavity. E and H are the fields in the

interior of the sample. Vs and Vc are the volumes of the sample

and cavity respectively.

"'rrr jεεε −= (6.8)

235

"'rrr jμμμ −= (6.9)

Two approximations are made in applying equation (6.7) based on

the assumptions that the fields in the empty part of the cavity are

negligibly changed by the insertion of the sample, and that the

fields in the sample are uniform over its volume. Both these

assumptions are valid if the object is sufficiently small relative to

the resonant wavelength. The negative sign in equation (6.7)

indicates that by introducing the sample the resonant frequency is

lowered. Since the permittivity of a material is complex, the

resonant frequency should also be considered as complex.

In terms of energy, the numerator of equation (6.7) represents the

energy stored in the sample and the denominator represents the

total energy stored in the cavity. When a dielectric sample is

introduced at the position of maximum electric field as shown in

Fig 6.5.1, only the first term in the numerator of equation (6.7), is

significant, since a small change inε , at a point of zero electric

field or a small change in μ at a point of zero magnetic field does

not change the resonance frequency.

Fig 6.5.1 Electric field distribution inside a rectangular cavity

236

Thus equation (6.7) can be reduced to

∫

∫−

=ΩΩ

−

c

s

V

Vr

dVE

dVEE

20

*0

2

max.)1(εδ (6.10)

Let Q0 be the quality factor of the cavity in the unperturbed

condition and Qs the quality factor of the cavity loaded with the

object. The complex frequency shift is related to measurable

quantities by [107],

⎥⎦

⎤⎢⎣

⎡−+=

ΩΩ

−0

112 QQj

sωδωδ (6.11)

Substituting equation (6.11) into (6.10) and equating real and

imaginary parts, we get,

∫

∫−

=−

−

c

s

V

Vr

s

s

dVE

dVEE

fff

20

*0

'

0

2

max.)1(ε

(6.12)

⎥⎦

⎤⎢⎣

⎡−

0

1121

QQs

= ∫

∫

c

s

V

Vr

dVE

dVEE

20

*0

"

2

max.ε

(6.13)

It is assumed that E ≈ E0 and the value of E0 in TE10pmode is

E0 = E0 sin (mx/a) sin (px/d)

where a is the boarder dimension of the waveguide and d is the

length of the cavity.

Integrating and rearranging, we obtain,

237

⎥⎦

⎤⎢⎣

⎡−+=

s

c

s

sr V

Vf

ff2

1 0'ε (6.14)

⎥⎦

⎤⎢⎣

⎡−⎥

⎦

⎤⎢⎣

⎡=

0

" 114 QQVV

ss

crε (6.15)

where fs is the resonant frequency.

Here ' "r r rjε ε ε= − (6.16)

rε is the relative complex permittivity of the sample. 'rε is the real

part of the complex permittivity, which is usually known as

dielectric constant and "rε is the imaginary part of the relative

complex permittivity, which is associated with the dielectric loss of

the material.

6.5.4 Conductivity of materials

For a dielectric material having non-zero conductivity,

Ampere’s law in phase form is

( )H j Eσ ωε∇× = + " '( )E j Eσ ωε ωε= + + (6.17)

The effective conductivity of the medium can be written as,

"eσ σ ωε= + (6.18)

" "02e rfσ ωε π ε ε= = , when σ is very small. (6.19)

The dielectric loss of the material will be expressed by a term loss

tangent [107] or

tanδ = "

'

σ ωεωε+ =

'

"

εε (6.20)

238

6.5.5 Experimental set up of cavity perturbation technique

Fig 6.5.2 Schematic diagram of the transmission type cavity resonator

The dielectric properties of the grown crystals were studied using a

transmission type S-band rectangular cavity resonator as shown

in Fig 6.5.2 [108]. The analysis was done on an HP 8714 ET

network analyser and an interfacing computer as shown in Fig

6.5.3.

Fig 6.5.3 Network Analyser

239

Fig 6.5.4 A typical resonant frequency spectrum

The cavity resonator was excited in the TE10p mode [109]. A typical

resonant frequency spectrum of the cavity resonator is shown in

Fig 6.5.4. Initially, the resonant frequency f0 and the

corresponding quality factor Q0 of each resonant peak of the empty

cavity are determined. Samples were finely powdered and filled in

small Teflon cups and introduced into the cavity resonator

through the non radiating slot. One of the resonant frequencies of

the loaded cavity is selected and the position of the sample is

adjusted for maximum perturbation (i.e. maximum shift of

resonant frequency towards low frequency side with maximum

amplitude for the peak).The new resonant frequency fs and 3dB

bandwidth and hence quality factor Q0 is determined. The

procedure is repeated for other resonant frequencies.

6.5.6 Dielectric constant measurements

The dielectric constant 'rε , Imaginary part "

rε , the effective

conductivity e, and loss tangent tan are determined and are

given in Table 6.5.1.The variation of conductivity, dielectric

240

constant and tan with frequency are represented graphically in

Figs.6.5.5, 6.5.6 & 6.5.7 respectively.

BHP

2400 2500 2600 2700 2800 2900 3000

BNP

2400 2500 2600 2700 2800 2900 3000

CNP

2400 2500 2600 2700 2800 2900 3000

CHP

2400 2500 2600 2700 2800 2900 3000

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

Con

duct

ivity

σe

SHP

2400 2500 2600 2700 2800 2900 3000Frequency(MHz)

SNP

Fig 6.5.5 Variation of conductivity with frequency

CHP CNP

Die

lect

ric c

onst

.

Frequency(MHz)

BHP

2400 2500 2600 2700 2800 2900 3000

BNP

2400 2500 2600 2700 2800 2900 3000

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

SHP

2.8

2.9

3.0

3.1

3.2

3.3

3.4

3.5

3.6

SNP

Fig 6.5.6 Variation of dielectric constant with frequency

241

Table 6.5.1 Dielectric constant measurements

Samples Frequency

fs (MHz)

Dielectric const. '

rε Imaginary

part "rε tan Conductivity

e

2439.405 1.81E+00 0.03118 1.72E-02 4.23E-03

2684.530 1.74E+00 0.04781 2.74E-02 7.13E-03 CHP

2970.808 1.70E+00 0.01758 1.03E-02 2.90E-03

2439.813 3.25E+00 0.06650 2.04E-02 9.01E-03

2684.572 2.73E+00 0.03603 1.32E-02 5.37E-03 Nd:CHP

2970.698 2.70E+00 0.10514 3.89E-02 1.74E-02

2439.825 2.26E+00 0.01872 8.29E-03 2.54E-03

2684.559 3.19E+00 0.04669 1.46E-02 6.96E-03 BHP

2970.696 3.57E+00 0.13634 3.82E-02 2.25E-02

2439.405 1.78E+00 0.00824 4.64E-03 1.12E-03

2684.530 1.87E+00 0.01449 7.73E-03 2.16E-03 Nd:BHP

2970.808 1.83E+00 0.02582 1.41E-02 4.26E-03

2439.818 3.61E+00 0.20678 5.73E-02 2.80E-02

2684.582 2.28E+00 0.04291 1.89E-02 6.40E-03 SHP

2970.719 3.00E+00 0.06715 2.24E-02 1.11E-02

2439.708 2.82E+00 0.06884 2.44E-02 9.33E-03

2684.593 3.27E+00 0.14240 4.36E-02 2.12E-02 Nd:SHP

2970.706 3.53E+00 0.19517 5.54E-02 3.22E-02

242

SHP

2400 2500 2600 2700 2800 2900 3000

SNP

2400 2500 2600 2700 2800 2900 3000

BNP

2400 2500 2600 2700 2800 2900 3000

CHP

2400 2500 2600 2700 2800 2900 3000

CNP

2400 2500 2600 2700 2800 2900 30000.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

tan δ

Frequency(MHz)

BHP

Fig 6.5.7 Variation of tan with frequency

6.5.7 Conclusions

The dielectric measurements were done for the samples in the

powdered form. The dielectric constant shows a progressive

decrease with increasing frequency in some cases. The

conductivity of CHP increases with frequency in the first step and

a sudden decrease in the second step and vice versa for Nd:CHP.

The conductivity increases with frequency in the case of BHP and

Nd:SHP. The initial values remain nearly the same in some cases.

The final values also remain nearly the same in some cases. The

dielectric loss also varies in the same manner as that of

conductivity. It has also been observed that CHP and SHP exhibit

considerable dielectric loss. There fore it can be used for the

preparation of microwave absorbing materials and for

electromagnetic shielding [110]. The possibility of using these

materials for developing microwave devices like attenuators,

matched loads etc. can also be considered.

243

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