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MATERIALS CHARACTERIZATION. SECTION I X - Ray Diffraction. X-ray diffraction is used for the complete determination of molecular structure of crystals. Every lattice plane in a crystal behaves like diffraction grating, on the exposure of X-rays.
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SECTION I X - Ray Diffraction • X-ray diffraction is used for the complete determination of molecular structure of crystals. • Every lattice plane in a crystal behaves like diffraction grating, on the exposure of X-rays. • The position of the spectral lines when diffracted depends on the distance between successive lines; similarly the nature of the X-ray diffracted by a crystal is determined by the spacing between successive planes.
Diffraction of beam of x-rays from the layers of atoms in a crystal
X - Ray Diffraction • If a beam of monochromatic X-rays is incident on a crystal at an angle , some of the rays will be diffracted by the layers of atoms in the crystal. • The path length FCD is larger than FCD by ACB which is equal to 2AC, and since AC = dsin, the path difference is 2dsin. • This difference in path length must be an integral number (n) of wavelengths () for maximum diffraction of X-rays with destructive interference. Thus n = 2dsin (1) which is the Bragg’s equation. • With the help of the Bragg’s equation it is possible to determine the spacing d between successive lattice planes, if is known and is measured.
X - Ray Diffraction • The intensities of the reflections depends on the scattering power of the atoms within the plane and on the mean amplitude of the waves scattered by the particular atoms occupying that plane, which is called the atomic scattering factor (f). • The value of f depends both on the glancing angle and on the wavelength () of the X-rays, and is a function of sin/. • f decreases with the increase in sin/, and for small glancing angles f is almost the same as the atomic number of the element. • The atomic scattering factor (f) for any atom is thus given by, • (2) • It is evident from the equation that knowing the probability, f may be calculated for different values of sin/ for any atom.
X - Ray Diffraction Experimental Methods 1. Laue Photographic Method: • In this method, a tiny crystal is placed in the path of a narrow beam of X-rays from a tungsten filament and the diffracted beam is allowed to fall on a photographic plate. • On developing the photographic plate a characteristic pattern, called Laue pattern of spots is observed. • From the positions of the spots and the distance of the photographic plate from the crystals, is calculated and the d between the planes is estimated. Laue photographic method
2.The Rotating Crystal Method: • In this method a beam of X-rays is allowed to penetrate the crystal at right angles; the crystal being rotating round an axis parallel to one of the crystal axes. • During the rotation of the crystal various planes come successively into positions for diffraction to occur and corresponding spots are observed on a photographic plate. • In Fig. A and B represent points on two successive lattice planes. • For a diffraction maxima to occur the path difference (BR) =(n). • Horizontal lines are observed for all lattice planes having the same spacing (AB) in the direction parallel to the axis of rotation. Such lines are called layer lines. • If λ is given and the distance from the crystal to the photographic plate and the vertical distance between the layer lines are determined, and hence the spacing of the planes AB can be calculated. • The row lines, observed on the photograph is used to deduce lattice spacing's and the size of the unit cell. Rotating crystal method & X-ray rotation photograph
3. Oscillating Crystal Method: • In this method, the crystal is oscillated through an angle of 10o to 20o. • Thus, the number of reflecting positions exposed to the incident X-rays is limited. • The number of spots observed on the photographic film is less which facilitates the interpretation of the results.
4. The powder method: • A narrow beam of monochromatic X-rays fall on the finely powdered specimen to be examined, and the diffracted rays are passed on to a strip of film which almost completely surrounds the specimen. • The random orientation of crystals produces diffraction rings. • This method is commonly used for identification purposes by comparing the data with the standard files available. • For a cubic crystal the identification of lines in the powder photograph is simple compared to other types. Powder photograph method
X - Ray Diffraction-Applications • XRD is a nondestructive technique • To identify crystalline phases and orientation • To determine structural properties: Lattice parameters (10-4Å), strain, grain size, phase composition. • To measure thickness of thin films and multi-layers • To determine atomic arrangement
SECTION IINeutron diffraction • Neutron diffraction is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material. • A sample to be examined is placed in a beam of thermal or cold neutrons to obtain a diffraction pattern that provides information of the structure of the material. • Due to their different scattering properties, neutrons and X-rays provide complementary information. • Neutron diffraction methods is based on the nature of matter. • According to de Broglie equation, • Braggs law will hold good for neutrons diffraction or scattering, just as for X-rays thus, n = 2d sin • Combining equations we get,
The most probable velocity corresponds to a neutron energy of KBT where KBis the Boltzmann constant. An equivalent formula is • Where Ecv is the neutron energy in electron volt (eV). • At room temperature, T = 293o K, the most probable velocity of the Maxwell distribution is v = 2.19 × 106 cm/sec. This corresponds to so energy kBT = 0.0253 eV and a wavelength = 1.80 × 10-4 cm which is suitable for obtaining diffraction phenomenon in crystals. • According to their energy, neutrons are classified as slow neutrons (zero to 100 eV), cold neutrons (below 0.01 eV), thermal (0.25 eV at 20oC), resonance neutrons (100 eV), intermediate neutrons (1000 eV) high energy neutrons (0.5 – 10.0 meV) and ultra high energy neutrons (1 – 5 BeV). • Thermal neutrons have wavelengths in the regions of 1Å and are suitable for crystal diffraction.
Neutron Diffraction Versus X-ray Diffraction • Contrary to X-rays, neutron diffraction method depends on the • development of high flux reactors. • Much larger crystals are needed for diffraction in neutron • diffraction method than for X-ray diffraction. • The X-rays are scattered from electronic shell whereas • neutrons are scattered by the atomic nuclei in the crystal. • Except in special circumstances they are not affected by the • electron density. • Neutron diffraction method is better than X-ray diffraction • because with neutron diffraction, light as well as heavy atoms • can be identified.
Neutron diffraction-Instrumentation 1. Laue Photographic Method • A beam of neutrons from a nuclear reactor pass through a velocity selector to obtain a monochromatic beam of neutrons. • This is then allowed to fall on a single crystal or a thin slice of crystals and the beam of diffracted neutrons is then allowed to fall on a photographic film coated with indium in order to capture the neutrons. • The schematic diagram is indicated in Fig. The unstable nuclei emits -particles which register dark spots on the photographic film. • This is Laue pattern from the positions of the spots and distance of the photographic film from the crystal, is calculated and relative spacing between the planes is estimated.
2. Powder Method • This method employs powdered samples in which the crystals are oriented in all directions so that some of the crystals will be properly oriented for all the observable reflections. • A narrow beam of monochromatic thermal neutrons is allowed to fall on the finely powdered specimen to be examined and the diffracted beam of neutrons strike the slowly rotating BF3 counter. The counter readings, corrected for background, as a function of angle of rotation are the diffraction patterns as shown in the Fig.
Applications of Neutron Diffraction • Location of hydrogen atoms. • Investigation of magnetic substances. Thus, in case when the diffracting material is paramagnetic, ferromagnetic or ant ferromagnetic and the magnetic moments have some kind of order arrangement, neutrons will suffer a magnetic scattering. Manganese oxide (MnO) was earlier thought to be paramagnetic, but neutron diffraction studies have established that MnO is not paramagnetic but antiferromagnetic. • Used in the study of biological and medicinal processes. • In neutron diffraction the information about the sign of the two scattering amplitudes can be easily obtained but it is not possible to extract any information whether scattering length is positive or negative.
Section IIIElectron Diffraction Introduction • Electron diffraction method is also based on the wave nature of matter using the diffraction of a beam of electrons by crystals to study the internal structure of a crystal. • When a high energy electron beam strikes the material, the scattering is caused primarily by interaction with atomic nuclei, but the scattering of low energy electrons, such as an electron beam with a wave length of 1Å, is caused by the interaction with outer electrons of the atoms as well as with the nuclei. The electron beam with a wavelength of less than 1 Å is used in electron diffraction studies. Since low energy electrons can be easily absorbed by matter, samples used are usually very thin films or gases and vapours. • When electron beam is passed through a gas or vapour it produces a series of concentric rings position of maximum scattering on a photographic plate due to the diffraction by the atoms within the molecules. • The dark rings on the photographic plate represents the position of maximum scattering and the lighter portions in between corresponds to minimum electron scattering. • Due to the background scattering of the electron beam, the diffraction bands are poorly resolved. • The scattering of electron is of two types – incoherent or inelastic. The diffraction of electrons depends on spacing's between targets.
Advantage of Electron Diffraction Method • Electron source is easily available. • Higher electron beam intensities are available. Therefore, shorter exposure time produce usable patterns on films. • Electron beam length can easily be altered by adjusting the accelerating voltage. • Electron beams are sensitive to electric and magnetic fields. These fields deflect and can thereby focus electron beams, as lenses focus light. No such focusing has been developed for x-rays.
Experimental Method The instrument used for electron diffraction studies consists of • An electron gun • Lenses to focus the electron beam • Photographic screen • The instrument is also provided with related electrical power supply, vacuum pumps and controls. • A fine stream of accelerated electrons using a potential of about 50,000 volts is allowed to fall on a very thin film about 10-6 cm thickness of metal at a very low pressure of about 10-5 mm. • Since the electrons interact very strongly with the molecules of the sample and greatly affect the photographic plate, the emerging electron beam is allowed to fall on a photographic plate for a short time, e.g., 0.5 to 5 sec. • On development a series of concentric rings is observed on the photographic plate. • The plate is then held to a strong light and position of the apparent maxima and minima of scattering intensity are marked. • The accuracy in estimated bond lengths and bond angles obtained from electron diffraction studies for simple molecules is comparable to that obtained by X-ray diffraction studies. • The accuracy is usually not better than + 0.01 Å in cases of estimated bond lengths for O – H1 N – H bonds but under favourable conditions this can be good as + 0.002 Å.
Applications • The most important application involves the study of the diffraction of electrons by substances as vapours at low pressures with a view to evaluate the bond lengths and bond angles in relatively simple molecules and to determine the molecular configurations. • Electron diffraction studies on a large number of compounds, simple and complex, have been carried out which have proved to be very important to understand the structure and geometry of these compounds.
Section IVX-ray Fluorescence (XRF) Methods • XRF is a non-destructive technique used for chemical analysis of materials, elemental composition and film thickness. • An X ray source is used to irradiate the specimen and to cause the elements in the specimen to emit (or fluoresce) their characteristic X-rays. • A detection system is used to measure the peaks of the emitted X-rays for qualitative and quantitative measurements of the elements and their amounts.
X-ray Fluorescence (XRF) Methods Principle • When an element is placed in a beam of X-rays, the atoms of the element absorb X-rays, become excited and emit x-rays of characteristic wavelength. This process is called X-ray fluorescence. • Since the wavelength of the fluorescence is characteristic of the element being excited, measurement of this wavelength enables us to identify the fluorescing element. • The intensity of the fluorescence depends on how much of that element is in the X-ray beam. • For qualitative studies, the angle of diffraction is measured. • From this measurement the wavelength of fluorescence can be calculated by using the Bragg equation. • Knowing , the wavelength of fluorescence, we can identify the element from a chart of the fluorescence wavelengths of all the known elements.
X-ray Fluorescence (XRF) Methods Instrumentation 1. X-ray fluorescence system utilizing an analyzing crystal • The filtered primary x-rays from the tube hits the sample and produce the fluorescence radiation characteristic of the elements in the sample. • This radiation passes through a collimator and the relative wavelengths are separated by the diffracting crystal. • The intensity of each wavelength is determined and recorded as the synchronized detector rotates in an arc around the analyzing crystal. Schematic diagram of an X-ray fluorescence system utilizing an analyzing crystal
X-ray Fluorescence (XRF) Methods 1. X-ray fluorescence system utilizing an analyzing crystal • The problem with x-rays fluorescence is its lack of sensitivity. • The intensity of the X-ray source must be high. For the reasons the voltage to the source must be as high as 100 kV. • Selective X-ray fluorescence may be carried out by using an X-ray beam with a wavelength that excites one element but is too long to excite another. • In this system, only one element will produce fluorescence. The fluorescence intensity is measured when first one source and then a second source is used. The difference in intensity depends on how much element is present in the sample. • Background fluorescence is common to both measurements, and a correction is automatically made for this source of error.
X-ray Fluorescence (XRF) Methods 2. X-ray fluorescence of a system utilizing curved crystal analyzer • The monochromator used is an analyzing crystal. • The crystal separates x-rays of different wavelengths by diffracting them at different angles. • From the Bragg equation, we can see that when varies and d is constant(in a perfect crystal), must vary. • For best sensitivity, a curved crystal as shown in Fig. is used. This refocuses the X-ray fluorescence after diffraction at the crystal. • Curved crystals have been made from such salts as sodium chloride, lithium fluoride, quartz, aluminium, and topaz. Optical system using a curved crystal analyzer to focus the fluorescence on the detector
X-ray Fluorescence (XRF) Methods 2. X-ray fluorescence of a system utilizing curved crystal analyzer • The sample holder is made of materials transparent to X-ray beams. • Polymers such as polyethylene are composed of low atomic number elements, such as carbon and hydrogen. These make excellent sample holders, because low atomic number of elements absorb very weakly. Aluminum holders are also widely used. • Elements with atomic numbers between 12 and 92 can be analyzed in air. • Elements with atomic numbers 5 (boron) through 11 (sodium) fluorescence at long wavelengths (low energy) and the fluorescence is absorbed by the air. Analysis of this group should be carried out in a vacuum or a helium atmosphere in order to reduce the loss of fluorescence intensity by air absorption.
X-ray Fluorescence (XRF) Methods 3. Pulse Height Analyzer • A proportional counter may be utilized to differentiate and measure X-ray fluorescence lines • In proportional counters the peak height is determined by the number of electron per pulse and is directly proportional to the energy, hv, of the photon. • A pulse height analyzer is an electronic circuit used to count only those pulses which lie within a predetermined wavelength (height) region. • Since no dispersion element is required they are nondispersive X-ray spectrometers. • The source is polychromatic. The detector may be either a proportional counter, a scintillation counter, or a semiconductor. • Collimation is unnecessary. Since air absorbs the longer wavelengths, a helium atmosphere is used. • Because of their simplicity, these systems are relatively inexpensive. • They are especially applicable to samples in which only a few elements are present provided the characteristic x-ray lines of these few elements are widely separated in wavelength. Schematic diagram of an X-ray fluorescence system utilizing a pulse height analyzer
X-ray Fluorescence (XRF) Methods Applications of X-ray Fluorescence • X-ray fluorescence is a method of elemental analysis. It is most useful for the analysis of metals and nonmetals with atomic number greater than 12. With special equipment (an evacuated optical system, light-gathering crystals, and highly sensitive detectors), elements of atomic number 5 through 11 can also be analyzed. • The intensity of fluorescence is independent of the chemical state of the elements. For this reason, chemical preparation prior to x-ray fluorescence measurements is frequently unnecessary. The method is nondestructive, an important feature when the sample is available in limited amounts. • The fluorescence spectra are very simple, and overlap of x-ray emission lines from different elements is unlikely; however, background emission from one element may overlap line emission from another element.
Section V Thermo gravimetric Analysis Introduction • Thermo gravimetric analysis(TGA) is a method of thermal analysis in which changes in physical and chemical properties of materials are measured as a function of increasing temperature (with constant heating rate), or as a function of time (with constant temperature and/or constant mass loss). • TGA can provide information about physical phenomena, such as second-order phase transitions, including vaporization, sublimation, absorption, adsorption, and desorption. • Likewise, TGA can provide information about chemical phenomena including chemisorptions, desolvation (especially dehydration), decomposition, and solid-gas reactions (e.g., oxidation or reduction).
Thermo gravimetric Analysis Most frequently used thermometric methods
Thermo gravimetric Analysis • Thermal methods of chemical analysis include such techniques as thermo gravimetric analysis (TGA), differential thermal analysis (DTA) and differential scanning calorimeter (DSC). • The recorded curves may be considered as thermal spectra, usually called thermograms. • TGA and DTA are valuable techniques because of no restriction on the systems being studied. • With the development of sophisticated, rugged and sensitive automatic recording thermobalances, there is an increasing tendency now to use TGA as the first stage in a multi-instrument approach for the analysis of materials such as oil shells, polymers, moon rocks and catalysts.
Thermo gravimetric Analysis Instrumentation • In thermogravimetry analysis, the determination of temperature at which a material of reproducible and recognisablestoichiometry is produced is facilitated by the so-called thermobalance. • The commonly used thermobalances in TGA are a precision balance, heating device, temperature and atmosphere control devices. A schematic modern thermo gravimetric analyzer
Thermo gravimetric Analysis 1. Weight measurement: Thermobalances. A precision torsion balance is used as thermo balance. The balance should have the following characteristics: (a) It should be simple to operate, (b) It should have an adjustable range of weight change, (c) It should be able to respond rapidly to changes in weight and (d) It should be rugged, accurate, very sensitive and mechanically stable. Almost all the thermobalances that have been used are either the null point or the deflection types of instruments. II. Heating and temperature measurement: • The main requirement is that the heating rate be smooth so that it can maintain either a linear heating programme (10o-500oC per hr). • The simplest temperature programme is a variable transformer. • Other equipments use conventional thermocouples or resistance thermometers situated as close to the furnace winding as possible. • Platinum and tungsten windings are commonly used, the nichrome windings permit a maximum temperature of 1100oC • The signal from a thermocouple in the furnace is compared electronically against a reference potential which can be programmed to correspond to a variety of heating modes and heating rates. • The usual rate of heating is 4-5oC per minute.
Thermo gravimetric Analysis III. The sample cups: Generally there are four basic designs of sample cups-shallow pan, deep crucible, covered cup and retort cup. Shallow pans - When volatile products are produced during heating. Deep crucibles - Industrial scale calcinations or surface area studies. Covered cups - Self-generated atmosphere studies. Retort cups - Used in boiling point studies. IV. Atmosphere control: • Atmosphere control is extremely important in TGA because the weight change in sample is due to the gaseous products formed during sample heating or the reaction of a sample with the balance atmosphere. • The control of atmosphere can be achieved either in the sample or in the balance. • In certain kinds of kinetic studies where it is necessary to carry out the experiment in a sample generated atmosphere, the regulation is usually affected by simply covering the sample container with loose fitting lid. • Another way of maintaining the atmosphere is by flushing the whole balance with an inert gas, such as nitrogen, argon, carbon dioxide, hydrogen or helium. Because of the low thermal conductivity and very low density helium is usually preferred as an inert atmosphere for the study of pounds.
Thermo gravimetric Analysis Factors affecting TGA i) Effect of changing air buoyancy and convection: The most favored arrangement for thermo balance is to support the inert sample from below in the centre of a cylindrical, capped tube furnace. Under this condition the inert sample may show an apparent weight gain up to 10 mg. Correction has, therefore, to be applied to the recorded weight change. The causes for the apparent weight gain are: decreased air buoyancy, increased convection and the effect of heat of balance mechanism. ii) Measurement of temperature: The usual practice in TGA is to measure the temperature in the furnace near the sample; the temperatures so determined are usually higher than those determined by the more common process of measuring the temperature directly. The cause of this difference is partly due to thermal lag and partly due to the finite time required to cause a detectable change in weight. The results of various workers suggest that when thermobalances is used to study the drying of bulky precipitates, it would be well to use slow rates of heating.
Thermo gravimetric Analysis iii)Effect of atmosphere: • When a sample is dried or decomposed in thermobalances in ambient in air, the atmosphere near the sample is continuously modified due to the addition of gaseous decomposition products or the loss of the part of original gas by reaction with the sample. • Even small changes in composition of this atmosphere can affect the thermograms. It is therefore necessary to flush the thermo balance continuously with inert gas in order to maintain as constant an atmosphere as possible. iv) Effect of heat of reaction: • The heat of reaction will affect the difference between sample temperature and furnace temperature, causing the sample temperature to lag or lead the furnace temperature depending on whether the reaction is endothermic or exothermic. • When the reaction is endothermic, the effect of temperature lag is to increase the furnace temperature and the differential temperature will be additive. • But when the reaction is exothermic this effect will tend to compensate each other.
Thermo gravimetric Analysis v) Effect of heating rate: • Heating rate has been found to affect the thermo gram appreciably. • The effect of heating rate is important if the thermogram is to be used for kinetic analysis. vi) Sample characteristics • Weight of the sample: A large sample affects the T.G. curve and the curve deviates from linearity as the temperature rises. Hence, small samples are preferred. • Particle size: Particle size also affects the TG curve. Smaller particles decompose at lower temperature while larger size particles of the sample take longer time and decompose at higher temperature. • Compactness of the sample: Compact samples decompose at higher temperature than the loose samples. • Previous history of the sample: The source and method of preparation of the sample also have been found to affect TG curve. For example precipitated Mg(OH)2 decomposes at a different temperature than the naturally occurring Mg(OH)2.
Thermo gravimetric Analysis Applications of Thermo gravimetric Analysis : • Materials characterization through analysis of characteristic decomposition patterns. • Studies of degradation mechanisms and reaction kinetics. • Determination of organic content in a sample. • Determination of inorganic (e.g. ash) content in a sample. It is an especially useful technique for the study of polymeric materials, including thermoplastics, thermosets, elastomers, composites, plastic films, fibers, coatings and paints.
