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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