Chapter-II Analytical Techniques -...

Chapter-II

Analytical Techniques

Chapter-II Analytical Techniques

Nowadays, scientists and engineers have an impressive array of powerful and ele-gant tools for acquiring quantitative and qualitative information about the compositionand structure of matter. There are varieties of nano - particles synthesized, which arehaving numerous applications in science and technology. Characterization is necessaryto establish understanding and control of nano-particles synthesis and their applicationsand it is done by using a variety of different analytical techniques [1]. Some of the an-alytical techniques used by the present author are X-ray diffraction techniques, Trans-mission Electron Microscopy (TEM), Energy Dispersive Analysis of X-rays (EDAX),Thermo-gravimetric Analysis (TGA), Fourier Transform Infrared spectroscopy (FT-IR)and dielectric studies.

The present chapter gives a brief review of these techniques used to characterizepure and metal ion doped calcium pyrophosphate nano-particles.

2.1 Synthesis of Nano-particles

Pure and metal ion doped calcium pyrophosphate dihydrate (CPPD) nano- parti-cles in the present investigation have been synthesized by surfactant mediated approach.This particular technique is discussed in detail in the following chapters.

2.2 X-ray Diffraction by Powder Method

X-rays were discovered by Wilhelm Conrad Roentgen, the first Nobel laureate inphysics, in 1895 [2]. In 1912, Max von Laue, a German physicist and a Nobel laureate,discovered that crystalline substances act as three dimensional diffraction gratings forX-ray wavelengths. After Laue’s pioneering research, the field developed rapidly, mostnotably by the contribution from a pair of father and son physicists, namely, WilliamHenry Bragg and William Lawrence Bragg, respectively. In 1912- 1913, W. L. Braggdeveloped a well known Bragg’s law, which connects the observed scattering with re-flections from evenly spaced planes within the crystal [3, 4]. The use of X-ray tech-niques for qualitative and quantitative analysis of materials is now completing morethan its century. Following these discoveries two major fields of materials analysis havebeen developed. One of them is the method of powder XRD, which was devised inde-pendently in 1916 by Peter Joseph William Debye, a Nobel laureate, and P. Scherrer [5]in Germany and in 1917 by A. W. Hull [6, 7] in United States. In the late 1930s, thepowder XRD technique was recognized as a powerful technique for phase identificationand chemical analysis. There was then a dramatic increase of interest in powder meth-ods during the 1970s, following the introduction by Rietveld in 1967 of his powerfulRietveld method for refining crystal structures from X-ray and neutron powder diffrac-tion data [8, 9]. While the broad definition of X-ray techniques cover many techniquesbased on the scatter, emission and absorption properties of X-radiation (X-ray).

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The powder method derives its name from the fact that the specimen is typicallyin the form of a microcrystalline powder. Since single crystals are not always avail-able, this method is more suitable for structural determination of various substances.Any material which is made up of an ordered array of atoms gives a particular diffrac-tion pattern. The powder XRD, which is also known as Debye - Scherrer method isa non-destructive technique widely used for the characterization of a variety of crys-talline materials. Powder XRD has become an important tool for rapid identification ofpolymorphs and formed compounds in pharmaceutical industry. Powder XRD openstremendous possibilities for characterization of materials and stimulates an interdisci-plinary dialogue and collaboration among physicists, mineralogists, crystallographers,chemists, pharmacists and material scientists. Generally, the method is applied to datacollected under ambient conditions, but in situ diffraction as a function of an exter-nal constraint, such as temperature, pressure, stress, electric field, atmosphere, etc, isimportant for the interpretation of solid state transformations and materials behaviors.Various types of micro and nano crystalline materials can be characterized by powder-XRD, including organic and inorganic materials, drugs, minerals, zeolites, catalysts,metals and ceramics. The physical states of the materials can be loose powders, thinfilms, poly-crystalline and bulk materials. By properly using this technique one canyield a great deal of structural information about the material under investigation. Formost applications, the amount of information which is possible to extract depends onthe nature of the sample microstructure (crystallinity, structure imperfections, crystal-lite size and texture) the complexity of the crystal structure (number of atoms in theasymmetric unit cell and unit cell volume), the quality of the experimental data (instru-ment performances and counting statistics) [10].

The fundamental law, which governs the X-ray diffraction phenomenon, is theBragg’s Law and the equation is as follows;

∆s =nλ = 2d sin θ (2.1)

or

d =nλ

2 sin θ(2.2)

When X-ray is incident on the crystalline powdered sample it gets diffracted accord-ing to the above mentioned equation in form of cones, which is exhibited in figure-2.1.Basically, this powder method involves the diffraction of monochromatic X-ray by apowdered specimen.

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Figure 2.1: Powder sample diffract X-ray beam in cones

Usually, “monochromatic” means the strong characteristic K component of the fil-tered radiation from an X-ray tube operated above the K excitation potential of the tar-get material.The Powder can mean either an actual, physical powder held together withsuitable binder or any specimen in polycrystalline form. Figure-2.2 gives the schematicrepresentation of powder method.

Figure 2.2: Principle of powder diffractometer

One of the most important uses of the powder method is in the identificationof an unknown material. If a set of standard diagrams of known substances, or tabularrepresentations of them, available, then it is possible to identify a pure substance withthe aid of a set of rules for finding an unknown diagram. The ASTM data cards as wellas JCPDS data files are available for large number of substances for identifications andcomparison. Statistical study of the relative orientations of the individual crystals of an

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aggregate is one of the important secondary uses of the powder method [11].Identification of phases can be done by powder technique without solving crystal

structure or assigning indices to the reflections. There are numerous computer soft-wares available for powder XRD analysis. The peak positions in XRD pattern containinformation about crystal system, space group symmetry, translational symmetry, unitcell dimension and qualitative phase identification. The information contained in peakintensities is unit cell contents, point symmetry and quantitative phase identification.

The analysis of peak shape and width (full-width at half maximum) of the Braggpeaks of the X-ray diffraction pattern provide information on the crystallite size andstrain. A perfect crystal would extend in all directions to infinity, so one can say that nocrystal is perfect due to its finite size. This deviation from perfect crystallinity leads toa broadening of the diffraction peaks. However, above a certain size (100-500 nm), thistype of broadening is negligible. Peak broadening arises from several sources: instru-mental effects, finite crystallite size (< 100-500 nm), strain (atoms deformed from idealpositions in a non-uniform manner), extended defects (terminate crystal and lead to sizebroadening). Since the peak broadening arises from a combination or convolution ofcrystallite size, microcrystalline strain and instrumental broadening effects, it is neces-sary to correct for the instrumental broadening and to sort out the strain components todetermine the average crystallite size.

There are various methods for obtaining crystallite size and strain information.Scherrer formula provides average crystallite size if strains and instrumental broad-ening are corrected. Scherrer (1918) first observed that small crystallite size could giverise to line broadening. He derived a well known equation for relating the crystallitesize to the broadening,

Crystallitesize =kλ

β cos θ(2.3)

Crystallite size is a measure of the size of a coherently diffracting domain. Due tothe presence of polycrystalline aggregates, crystallite size is generally not the same asthe particle size. Other techniques for measuring size (electron microscopy, dynamiclight scattering, X-ray or neutron scattering, atomic force microscopy etc.) measure theparticle size rather than the crystallite size.

Cystallite size refers to the size of crystal with all its defects and disorders, if everyparticle is a single crystal then particle size is also equal to crystallite size. However, aparticle could be amorphous or even polycrystalline. Hence it is possible that a particlemay consist of several grains/crystals/crystallites.

There are several well written books available on X - Ray diffraction [12], powderphotographic method [13, 14] basics of X - Ray diffraction [15], a practical approachto X- Ray diffraction [16] and review of progress of X- Ray diffraction [17]. There are

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many applications of the powder method, which are summarized in table-2.1 [10].

Table 2.1: Applications of powder XRD

Diffraction Line Parameter Applications

Peak Position

Unit-cell parameter refinementPattern indexing

Space group determination (2θ\ absentreflections)

Anisotropic thermal expansionMacro stress

Phase identification (d/I)

Intensity

Phase abundanceReaction kinetics

Crystal structure analysis(Whole pattern)Rietveld Refinement(Whole pattern)Search/match, phase identification

Preferred orientation, Texture Analysis

Width/Breadth and Shape

Instrumental resolution functionMicrostructure: line profile analysis

Microstructure(Crystallite size, size distribution, lattice

distortion)Structure mistakes, dislocations, composition

gradient)Crystallite growth kinetics

Three-dimensional microstructure (whole pattern)

Non-ambient and dynamicdiffraction

In situ diffraction under external constraintsreaction kinetics

There are numerous books available on the application of X - Ray Crystallographyto solve the structure of protein and macromolecules [19, 20]. However, the classicpaper was published by Wyckoff and Corey [21] way back in 1936.

However, there are certain limitations of powder XRD, such as limited sensitivity (aphase present in quantities lower than 5 by weight is difficult to detect), peak overlapsmay occur for high angle reflections and for non - isometric crystals the analysis of unitcell parameters and indexing pattern is difficult.

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Figure 2.3: Powder diffractometer

The present author has analyzed as synthesized and calcined nano - particle sam-ples by powder XRD analysis using PHILIPS X’PERT Modular Powder Diffractometer(MPD) system as shown in figure-2.3 in the Department of Physics, Saurashtra Univer-sity. The Cu Kα radiation was used. The crystal structures were determined by acomputer software Powder-X.

2.3 Muffle Furnace

In order to study the possible phase transition occuring at higher temperatures, thesynthesized nano-particles were calcined at 900 oC and 1250 oC in muffle furnace andyielded β and α phase of CPPD, respectively.

Figure23.pdf

Figure 2.4: Therelek furnace

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The Therelek furnace was used with graphite rod and maximum attainable temper-ature of 1500 oC. Figure-2.4 shows Therelek muffle furnace available at Department ofPhysics, Saurashtra University, Rajkot, used to calcine the nano-particles.

2.4 Electron Microscopy

Electron microscopy (Scanning Electron Microscopy, SEM and Transmission Elec-tron Microscopy, TEM) is the most powerful method to determine size and shape dis-tributions of the nano-particle assemblies. Since its invention, it has been valuable toolin the development of scientific theory and contributed greatly to biology, medicine andmaterial sciences [22]. Electron microscopes are scientific or optical instruments thatuse a beam of highly energetic electrons to examine objects on a very fine scale. Sinceits invention in the year 1931, electron microscope has been a valuable tool in biol-ogy, medicine and material science. This wide spread use of electron microscopes isbased on the fact that they permit the observation and characterization of materials on ananometer (nm) to micrometer (µm) scale.

Electron microscopes were developed due to the limitations of Optical or Light Mi-croscopes which are usually having 500X or 1000X magnification and a resolution of0.2 µm. Electron microscopes function exactly as their counterparts except that theyuse a focused beam of electrons instead of light to image the specimen and gain in-formation of its structure and composition. Electron microscope has high resolvingpower and large magnification, for example, resolution power λ = (150/ϕ)A, supposeϕ = 100kV , then λ is 0.04A. The electrons are behaving as waves as per the de -Broglie hypothesis, which is well explored in electron microscopy. The basic steps in-volved in all electron microscopes are the following:(i) A stream of electrons are formed in high vacuum (by electron guns).(ii) This stream is accelerated towards the specimen, into a thin, focused, monochro-matic beam by using metal apertures and magnetic lenses. The sample is irradiated bythe beam and interactions occur inside the irradiated sample.(iii) These interactions and effects are detected and transformed into an image.

Basically, there are two different types of electron microscopes available, viz., theScanning Electron Microscopes (SEM) and the Transmission Electron Microscopes(TEM). In the TEM, an electron beam is passed through an extremely thin section ofthe specimen, which gives two - dimensional cross - section of the specimen; whereas,in contrast with TEM, the SEM visualize the surface structure of the specimen. Severalbooks are available on electron microscopy covering SEM, TEM and X - Ray micro-analysis [23–29]. The biggest advantage of electron microscopes is that they have ahigher resolution and higher magnification (upto 2 million times). In SEM a greaterdepth of field compared to light microscopes is achieved. The higher resolution may

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also give the human eye the subjective impression of a higher depth of field. The Sam-ple preparation is often much more elaborate. It is often necessary to coat the specimenwith a very thin layer of metal (such as gold). The metal is able to reflect the electrons.The energy of the electron beam is very high and hence the sample is exposed to highradiation, and which destroys the living cells and does not allow observing functioningnormally.

2.4.1 Transmission Electron Microscopy

The first TEM (Transmission Electron Microscope) was built by Max Knoll andErnst Ruska in 1931, with this group developing the first TEM with resolving powergreater than that of light in 1933 and the first commercial TEM in 1939. Ruska won No-bel Prize in Physics in 1986 for the development of electron microscope. A schematicdiagram of TEM is shown in figure-2.5(a) and a photograph of typical set - up is shownin figure-2.5 (b).

Figure 2.5: (a)Internal setup (b) TEM set up

In figure-2.5 (a), Virtual source at the top represents the electron gun, producinga stream of monochromatic electrons. This stream is focused to a small, thin, coher-ent beam by the use of condenser lens. This condenser lens actually consists of twocondenser lenses out of which the first lens (usually controlled by the spot size knob)largely determines the spot size and the second lens (usually controlled by the intensityor brightness knob) actually changes the size of the spot on the sample from a widedispersed spot to a pinpoint beam.

The beam is restricted by the condenser aperture (usually user selectable), knockingout the high angle electrons (far from the optic axis). The beam strikes the specimen anda part of it is transmitted. This transmitted portion is focused by the objective lens intoan image optional objective and the selected area metal apertures can restrict the beam.

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The Objective aperture is enhancing the contrast by blocking out high-angle diffractedelectrons, whereas the selected area aperture is enabling the user to examine the pe-riodic diffraction of electrons by ordered arrangements of atoms in the sample. Theimage is passed down the column through the intermediate and projector lenses, beingenlarged all the way. The image strikes the phosphor screen and the light is generated,allowing the user to see the image. The darker areas of the image represent those areasof the sample that fewer electrons transmitted through (thicker or denser) medium; onthe other hand, the lighter areas of the image represent those areas of the sample thatmore electrons transmitted through (thinner or less dense) medium [28]. Apart from thefluorescent screen one can use photographic film, or a CCD camera for detection.

TEMs are capable of imaging at a significantly higher resolution than optical mi-croscopes, owing to the small de - Broglie wavelength of electrons. This enables theuser of instrument to examine fine detail - even as small as a single column of atoms.TEM forms a major analysis method in a range of scientific fields, in both physicaland biological sciences. TEMs find application in cancer research, virology, materialsscience as well as semiconductor research and nano-technology. At smaller magnifica-tions TEM image contrast is due to absorption of electrons in the material, owing thethickness and composition of the material. Notwithstanding, a higher magnificationsthe complex wave interactions modulate the intensity of the image, which require ex-pert analysis of observed images. Alternate modes of use allow the TEM to observemodulations in chemical identity, crystal orientation, electronic structure and sampleinduced electron phase shift as well as the regular absorption based imaging [29]. Thenewer High Resolution TEM (HRTEM) is now available for finer details at higher res-olutions.

In the present investigation, Philips Tecnai 20 setup from SICART, Vallabh Vidyana-gar, Gujarat, was used which is having resolution upto 2 A, magnification upto 7,50,000X and accelerating voltage 200 kV.

2.5 Infrared Spectroscopy

The term, spectroscopy is generally used for the analytical techniques based on theinteraction of electromagnetic radiation with matter and variation of particular phys-ical quantity with frequency of radiation. In spectroscopy the measurements of ab-sorbance or transmittance of electromagnetic radiation, due to interaction with sampleby molecules, are carried out in a gas or vapor state or dissolved molecules/ions or soliddepending upon requirement. Spectroscopy is used for both qualitative and quantitativeinvestigations [30]. Infrared spectroscopy (IR Spectroscopy) is a type of absorptionspectroscopy that uses the infrared part of the electromagnetic spectrum (wavelength760 nm upto 500 µm). The infrared region of the electromagnetic spectrum extends

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from the red end of the visible spectrum out to the microwave region. Infrared spectralregion can be divided into three regions; near infrared, mid-infrared and far infrared.Infrared spectroscopy deals with the interaction of infrared light with matter. Infraredradiation does not trigger electronic excitation in substances but vibrational and/or ro-tational excitation. To be infrared active, a molecule must possess a dipole moment ormust generate a dipole moment by vibration. The main modes of vibrations are fallinginto basic categories of stretching and bending. A stretching vibration involves a con-tinuous change in the inter-atomic distance along the axis of bond between two atoms.However, the bending vibrations are characterized by a change in the angle between twobonds, which are of four types, scissoring, rocking, wagging and twisting. The extentof absorption of infrared photons depends mainly on the mass of the vibrating atoms.

Figure 2.6: Stretching and bending

The energy in infrared spectra is usually given in wave numbers. The use ofwave numbers offers the advantage of being directly proportional to the frequency ofthe absorbed radiation and thus the energy absorbed. The energy of an infrared photoncan be calculated using the Planck energy,

∆E =hcν (2.4)

Where, h is the Planck’s constant, ν is the wave number in cm−1 and c is the speed oflight

2.5.1 Fourier Transform Infrared (FT-IR) Spectroscopy

Multiplex types of instruments employ the mathematical tool of Fourier Transform.The apparatus of Fourier Transform Infrared (FT-IR) spectrometer is derived fromMichaelson interferometer, which is shown in figure-2.7.

The main components of the FT-IR spectrometer are:(1) Drive mechanism,(2) Beam splitters,(3) Sources and(4) Transducers or detectors.

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Figure 2.7: Schematic diagram of Michaelson interferometer

In figure-2.7, a parallel beam of radiation is directed from the source to the interfer-ometer, consisting of a beam splitter (B) and two mirrors (M1 and M2). It is well knownthat for monochromatic radiation the interference patterns are obtained. The construc-tive or destructive interference is produced depending on the relative path lengths B toM1 and B to M2. When mirror M2 moves smoothly towards or away from B, a detectorsees radiation of changing intensity. If white radiation is used, the obtained interferencepatterns can be transferred back to the original frequency distribution. This is achievedby a mathematical process known as Fourier transform, nowadays, this process is car-ried out by a computer or microprocessor of the spectrometer. Under these conditions,the detector response fluctuates at a rate, which depends upon the rate of movement ofmirror and the wavelength of radiation.

Figure 2.8: Schematic diagram of FT-IR

Figure-2.8 shows the schematic diagram of FT-IR set up. In general, any com-bination of frequencies with corresponding amplitudes will produce an interferogram

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containing all the spectral information of the original radiation. The interferogram is theFourier transform of the spectrum and the task of the computer is to apply the inverseFourier transform.

The Fellgett advantage is an improvement in signal to noise ratio of (M)1/2, whereM is the number of resolution elements desired in the particular spectrum. It is worthnoting that the resolving power of Fourier transform instrument is constant over theentire spectrum, whereas it varies with frequency in the conventional technique [31].The detectors employed are much more sensitive, the optical throughput is much higherwhich results in much lower noise levels, and the fast scans enable the co-addition ofseveral scans in order to reduce the random measurement noise to any desired level (re-ferred to as signal averaging). These instruments employ a He-Ne laser (Helium-Neonlaser) as an internal wavelength calibration standard (referred to as the Cones Advan-tage). The use of a Helium - Neon laser as the internal reference in many FT-IR systemsprovides an automatic calibration in an accuracy of better than 0.01 cm−1. These instru-ments are self-calibrating and never need to be calibrated by the user. Energy wastingslits are not required in the interferometer because dispersion or filtering is not needed.Instead, a circular optical aperture is commonly used in FT-IR systems. The beam areaof an instrument is usually 75 to 100 times larger than the slit width of a dispersivespectrometer. Thus, more radiation energy is made available. This constitutes a majoradvantage for many samples or sampling techniques that are energy-limited. The in-terferometer in FT-IR modulates all the frequencies. The unmodulated stray light andsample emissions (if any) are not detected. Fourier transform spectroscopy is providingsimultaneous and almost instantaneous recording of whole spectrum in the magneticresonance, microwave and infrared regions. Fourier Transform (FT) Spectroscopy isequally applicable to both emission and absorption spectroscopy.

These advantages, along with several others, make measurements made by FT-IRextremely accurate and reproducible. Thus, it is a very reliable technique for positiveidentification of functional groups of virtually any sample (solid, liquid or gas). Thesensitivity benefits enable identification of even the smallest of contaminants. In ad-dition, the sensitivity and accuracy of FT-IR detectors, along with a wide variety ofsoftware algorithms, have dramatically increased the practical use of infrared for quan-titative analysis. Thus, FT-IR technique has brought significant practical advantages toinfrared spectroscopy in qualitative and quantitative analysis.

In case of FT-IR background solvent or solid matrix must be relatively transparentin the spectral region of interest. Molecule must be active in the IR region. When ex-posed to IR radiation, a minimum of one vibrational motion must alter the net dipolemoment of the molecule in order for absorption to be observed. IR-active atmosphericcomponents (CO2, H2O) will appear in the spectrum. However, usually, a backgroundspectrum is run, and then automatically subtracted from every spectrum. FT-IR cannot

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detect atoms or mono atomic entities contain no chemical bonds. Usually, aqueous so-lutions are very difficult to analyze- water is a strong IR absorber. Infrared (IR) andFT-IR spectroscopy are covered at length by various authors in their books [1, 30–34].

Figure 2.9: Thermo Nicolet 6700 FT-IR spectrometer

The present author has used Nicolet 6700 FT-IR spectrophotometer [cf, fig.-2.9]having optical resolution of 0.04 cm−1, in the range from 400 cm−1 to 4000 cm−1 inKBr disc medium. This FT-IR set up available at Department of Physics of SaurashtraUniversity was used for the analysis.

2.6 Thermal Studies

According to International Confederation for Thermal Analysis and Calorimetry(ICTAC), thermal analysis is defined as a group of techniques in which a property of thesample is monitored against time or temperature while the temperature of the sample,in a specified atmosphere, is programmed [35]. Nearly over a dozen thermal methodscan be identified, which differ in the properties measured and temperature programs[36–38]. These methods find widespread use for both quality control and research ap-plications of various substances, such as, polymers, pharmaceuticals, crystals, clays,minerals, metals and alloys. Thermal analysis techniques involve the measurement ofvarious properties of materials subjected to dynamically changing environments underpredetermined condition of heating rate, temperature range and gaseous atmosphere orvacuum. Classifications of classical and modern thermal analysis techniques are givenelsewhere [39–41].

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2.6.1 Thermo-gravimetric Analysis

Thermo gravimetric analysis is a technique in which the mass of a substance ismeasured as a function of temperature or time while the substance is subjected to acontrolled temperature program. The curve obtained in a thermo gravimetric analy-sis is called thermogram (TG) and its first derivative is called a derivative thermogram(DTG).Modern commercial TG instrument consists of following main parts:(1) A sensitive analytical balance(2) A temperature programmable furnace(3) A purge gas system for providing suitable gas atmosphere(4) A microprocessor for instrument control, data acquisition and display

The null-point weighing mechanism is employed since the sample remains in thesame zone of furnace irrespective of changes in mass. The furnace is normally an elec-trical resistive heater and the temperature range for most of the furnace is from ambientto 1000-2000 oC. The rate of heat exchange between the furnace and the sample de-pends on the heating rate which influences the TG curve in a number of ways. A slowerrate gives a better resolution of the closely lying steps, while the faster heating ratemerges such steps. One of the objectives of TG is to delineate as accurately as possi-ble the various temperatures associated with the thermal behavior of a given substance,i. e., temperature of decomposition, stability range of an intermediate compound andthe temperature at which the reaction get completed. As noted earlier that the TGAinvolves change in weight with respect to temperature, the acquired data obtained as aplot of mass or loss of mass in percentage as a function of temperature is considered asa thermal spectrum, or a thermogram, or a thermal decomposition curve. These thermo-grams characterize a system in terms of temperature dependence of its thermodynamicproperties and physical-chemical kinetics. Since the TGA involves measurement of achange in weight of a system as the temperature is increased at predetermined rate,changes in weight are a result of the rupture and/or formation of various physical andchemical bonds at elevated temperatures that lead to the release of volatile products orthe formation of heavier reaction products. From such curves, parameters concerningthe thermodynamics and kinetics of the various chemical reactions can be evaluated;moreover, the reaction mechanism, the intermediate and final reaction products can beidentified. Usually, the temperature range is from ambient to 1200 oC with inert orreactive atmospheres. The derivative in TG is often used to pinpoint completion ofweight-loss steps or to increase resolution of overlapping mass-loss occurrences. Theshape of thermo-gravimetric curve of a particular compound is influenced by the heat-ing rate of the sample and the atmosphere surrounding it [1, 42, 43].

The TGA finds applications in the study of thermal degradation, decomposition,

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dehydration of different samples. The chemical reaction resulting in changes of masssuch as absorption, adsorption and desorption can also be studied.

In the present study, the thermal analysis TG of the nano-particles was carried outto determine simultaneous changes of mass and caloric reactions using PC controlledLinseis Simultaneous Thermal Analyzer (STA) PT-1600, in the atmosphere of air from35 oC to 900 oC at a heating rate of 15 oC/min. TA-WIN and WIN-STA software usedfor testing and analysis.The set up for thermal analysis is shown in figure-2.10, whichis available at Physics Department of Saurashtra University.

Figure 2.10: Linseis simultaneous thermal analyzer PT-1600

2.7 Impedance spectroscopy (IS)

The basic concept of electrical resistance is exhibiting the ability of a circuit ele-ment to resist the flow of electrical current. Ohm’s law defines resistance (R) in termsof the ratio between voltage E and current I, i. e., R = E / I. This relationship is usedto only one circuit element, the ideal resistor. The real world contains circuits gener-ally contain elements that exhibit much more complex behavior. These elements leadsto abandon the simple concept of resistance. In its place one uses impedance, a moregeneral circuit parameter. Like resistance, impedance is a measure of the ability of acircuit to resist the flow of electrical current. When ac signal is applied to a system,the impedance of the system obeys Ohm’s law, as ratio of voltage to current in the timedomain [44]. The excitation signal, expressed as a function of time, has the form

E(t) = E0 sin(ωt) (2.5)

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where, E(t) is the potential at time t, E0 is the amplitude of the signal, and ω =2πf is theradial frequency.In a linear system, the response signal is given by

I(t) = I0 sin(ωt− ψ) (2.6)

The response signal is shifted in phase (ϕ) and has different amplitude Io. An expressionanalogous to Ohm’s Law allows calculating the impedance of the system as

Z =E(t)

I(t)=

E0 sin(ωt)

I0 sin(ωt− ψ)(2.7)

The impedance is therefore expressed in terms of a magnitude (modulus) |Z| and aphase shift ψ. Impedance Z(ω)= Z

′ + Z′′ is such a vector quantity, which can be

plotted in the plane with either rectangular or polar coordinates as shown in figure-2.11.

Figure 2.11: Impedance plot

Here, the two rectangular coordinate values are:

Re(Z) = Z′= |Z| cosψ (2.8)

Im(Z) = Z′′

= |Z| sinψ (2.9)

Phase angle

ψ = tan−1(Z

′′

Z ′ ) (2.10)

Modulus = |Z| = (Z′)2 + (Z

′′)2 (2.11)

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This defines the Argand diagram or complex plane. In polar form Z can be written as

Z(ω) = |Z| exp(jψ) (2.12)

This can be converted to rectangular form by Euler relation:

exp(jψ) = cos(ψ) + j sin(ψ) (2.13)

Therefore,

Z(ω) = |Z|[cos(ψ) + j sin(ψ)] (2.14)

In impedance technique, the real and imaginary parts of impedance of the sampleare measured simultaneously as a function of frequency. The measured impedance datacan be represented in the other three forms using the inter relations as follows. Compleximpedance

Z∗ = Z′+ jZ

′′(2.15)

where, Z′ and Z′′ are the real and imaginary parts of complex impedance.Complex admittance:

Y ∗ = Y′+ jY

′′=

1

j∗(2.16)

where, Y′ and Y′′ are the real and imaginary parts of complex admittance.Complex permittivity:

ε∗ = ε′ − jε′′ =

1

jωC0Z∗ (2.17)

where, ε′ and ε′′ are the real and imaginary parts of complex permittivity.Complex modulus:

M∗ = M′+ jM

′′= jωC0Z

∗ (2.18)

where, M′ and M′′ are the real and imaginary parts of complex modulus. here, j =√−1

and C0 is the vacuum capacitance. The admittance and permittivity are parallel func-tions that can be measured at low frequencies, whereas the impedance and modulus areseries functions at high frequencies. The four quantities M, Z, Y and ε are known asimmittance functions. This detailed discussion is given by Badwal [45] and recently bythe predecessor of the present author [41].

Impedance spectroscopy (IS) is a relatively new and powerful method of charac-

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terizing many of the electrical properties of materials and their interfaces with elec-tronically conducting electrodes. It is particularly characterized by measurements andanalysis of some or all of the four impedance related functions Z (impedance), Y (ad-mittance), M (modulus) and ε (permittivity) and the plotting of these functions in thecomplex plane[46].

2.7.1 Dielectric Studies

Every material has a unique set of electrical characteristics depending upon thetype of the materials belongs to, such as the dielectric properties, permittivity, perme-ability, resistivity, conductivity, etc. A material is classified as ”dielectric” if it hasthe ability to store energy when an external electric field is applied. In other words,materials, which are electric insulators or in which an electric field can be sustainedwith a minimum dissipation of power, are known as dielectric materials. Simply, di-electrics are insulating materials. In dielectrics all the electrons are bound to their parentmolecules and there are no free charges. Even with normal voltage or thermal energythe electrons are not released. Dielectrics are nonmetallic materials of high specificresistance and have negative temperature coefficient of resistance. The dielectric char-acteristics of the materials are important to study the lattice dynamics in the crystal. It isimportant to note that permittivity and permeability are not constant. They can changewith frequency,temperature, orientation, mixture, pressure, and molecular structure ofthe material. Many authors discussed various dielectric properties, dielectric applica-tions and dielectric theories in details [47–54]. Classical theory of dielectric constantwas given by Kachhava and Saxena [55]. Also the predecessors of the present authorhave described the dielectric properties in detail [39, 40, 56–60], therefore, it is avoidedin the present thesis.

2.7.2 Dielectric constant (k) or Relative Permittivity (εr)

Dielectric constant is defined as the ratio of the capacitance (C) of a capacitorfilled with the given material to the capacitance (Co) of an identical capacitor in a vac-uum without the dielectric material. The dielectric constant can also be defined as theratio of the permittivity of the dielectric material (ε) to the permittivity of vacuum (εo).The dielectric constant is, therefore, also known as the relative permittivity (εr) of thematerial. Sometimes it is also referred as the absolute permittivity. Dielectric constant,

k = εr = C/Co (2.19)

Since the dielectric constant is just a ratio of two similar quantities, it is dimen-sionless and is always greater than 1. It is a measure of polarization in the dielectric

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material. It denotes a large-scale property of dielectrics without specifying the electri-cal behavior on the atomic scale. In the present study dielectric constant was calculatedusing following formula,

k =εr = Cd/εoA (2.20)

Where, C is the capacitance, d is the thickness of the pellet, εo is the vacuum dielectricconstant (permittivity of free space, εo= 8.854 ×10×12 F/m) and A is the area of thepellet.

2.7.3 Complex Relative Permittivity (ε∗)

Permittivity is determined by the ability of a material to polarize in response to thefield and, thereby, reduce the total electric field inside the material. Thus, permittivityrelates to the ability of material to transmit (or permit) an electric field. The responseof normal materials to external fields generally depends on the frequency of the field.This frequency dependence reflects the fact that the polarization of material does notrespond instantaneously to an applied field. The response must always be causal whichcan be represented by a phase difference. For this reason permittivity is often treated asa complex function. The response of materials to alternating fields is characterized bya complex permittivity,

k =ε∗ = ε′ − jε′′ = |ε|e−jδ (2.21)

Where, ε′ is the real part of the relative permittivity (i. e. the dielectric constant), whichis related to the stored energy within the medium; whereas, ε′′ is the imaginary part ofthe relative permittivity, which is related to the dissipation (or loss) of energy within themedium. Equation- 2.21 expresses the complex permittivity in two ways, as real andimaginary or as magnitude and phase.

2.7.4 Dielectric Loss

The dielectric loss is a loss of energy which eventually produces a rise in tem-perature of a dielectric placed in an alternating electrical field. In other words, it is ameasure of the energy absorbed by dielectric. It is the electrical energy lost as heat inthe polarization process in applied AC electric field. The ratio of imaginary part to thereal part of the relative permittivity is known as dielectric loss or the dissipation factorD.

D =tan δ =ε′′

ε′(2.22)

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In the present study, the dissipation factor is measured along with the capacitance withinthe temperature of 30 o C to 120 o C using the LCR meter.

2.7.5 A. C. conductivity

The values of a. c. conductivity and a. c. resistivity were calculated for thedifferent frequencies of the applied electric field using the following formulae, a. c.conductivity,

σac =2πfCDt

A(2.23)

Where, f is the frequency, C is the capacitance, D is the dissipation factor or dielectricloss or D = tan δ, t is the thickness of the pellet and A is the area of the pellet.

2.7.6 Complex Modulus

Complex modulus analysis is an alternative and important approach to exploreelectrical properties of the material and magnify other effects if present. This helpsin determining, analyzing and interpreting the dynamical aspects of electrical transportphenomena, i. e., parameters such as carrier/ion hopping rate, conductivity relaxationtime, etc. [61].The advantage of complex impedance spectroscopy study is that it canidentify the role of electrode polarization and grain boundary conduction processes.Electric modulus M′ and M′′ were calculated using equations,

M′=

ε′

ε′2 + ε′′2(2.24)

M′′

=ε′′

ε′2 + ε′′2(2.25)

Where, ε′ and ε′′ are real and imaginary part of dielectric constant, respectively.In the present investigation the dielectric study was carried out by measuring differ-

ent parameters such as capacitance and dielectric loss of the pressed pellets of samplesof known dimension from room temperature to 120 oC within the frequency range from102 Hz to 107 MHz.

Figure-2.12 shows the photograph of the set up. The powdered samples were pel-letized by using a die of 1 cm diameter and applying 2 ton pressure. The pelletswere placed in a suitably designed spring loaded sample holder. For pure and Zn iondoped CPPD nano-particles the measurement was carried out on HIOKI 3532 LCRHITESTER set up available at Physics Department, M.S. University of Baroda and forMn and Mg ion doped CPPD nano-particles it was carried out on HIOKI 3532-50 LCR

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Hitester available at Loyola college, Chennai.

Figure 2.12: HIOKI 3532 LCR HITESTER

2.8 Energy Dispersive Analysis of X-ray (EDAX)

An Energy-Dispersive X-ray Analyzer (EDX) is a common accessory which givesa very valuable capability for elemental analysis. It is sometimes referred to also asEDS or EDAX analysis. It is a technique used for identifying the elemental compo-sition of the specimen, or an area of interest thereof. EDX makes use of the X-rayspectrum emitted by a solid sample bombarded with a focused beam of electrons toobtain a localized chemical analysis. Qualitative analysis involves the identification ofthe lines in the spectrum and is fairly straight forward owing to the simplicity of X-ray spectra. Quantitative analysis (determination of the concentrations of the elementspresent) entails measuring line intensities for each element in the sample and for thesame elements in calibration standards of known composition.

The EDX analysis system works as an integrated feature of a scanning electron mi-croscope (SEM), and can not operate on its own without the later. Figure-2.13 illustratesthe interaction of an electron beam (in red) with a specimen (shaded blue). The electronbeam in an SEM has energy typically between 5,000 and 20,000 electron volts (eV).The binding energy of electrons in atoms ranges from a few eV upto many kilovolts.Many of these atomic electrons are dislodged as the incident electrons pass through thespecimen, thus ionizing atoms of the specimen. This process is illustrated schematicallyin the inset box of the figure-2.13.

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Figure 2.13: Interaction of an electron beam with a specimen

A position vacated by an ejected inner shell electron is eventually occupied by ahigher-energy electron from an outer shell. To be able to do so, however, the transfer-ring outer electron must give up some of its energy by emitting an X-ray. The amountof energy released by the transferring electron depends on which shell it is transferringfrom, as well as which shell it is transferring to. Furthermore, the atom of every elementreleases X-rays with unique amounts of energy during the transferring process. Thus,by measuring the amounts of energy present in the X-rays being released by a speci-men during electron beam bombardment, the identity of the atom from which the X-raywas emitted can be established. The output of an EDX analysis is an EDX spectrum.The EDX spectrum is just a plot of how frequently an X-ray is received for each energylevel. An EDX spectrum normally displays peaks corresponding to the energy levels for

Figure 2.14: Shell structure

which the most X-rays had been received. Each of these peaks is unique to an atom, andtherefore corresponds to a single element. The higher a peak in a spectrum, the moreconcentrated the element is in the specimen [62]. An EDX spectrum not only identifies

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the element corresponding to each of its peaks, but the type of X-ray to which it corre-sponds as well. For example, a peak corresponding to the amount of energy possessedby X-rays emitted by an electron in the L-shell going down to the K-shell is identifiedas a K-α peak. The peak corresponding to X-rays emitted by M-shell electrons goingto the K-shell is identified as a K-β peak [cf, fig.-2.14].

In the present study the EDAX was performed on FEG Nano Nova SEM 450 instru-ment at SICART, Vallabh Vidyanagar.

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